HandWiki - Recent changes [en]

Engineering:Right Spot for EV Charger

2026-08-25T07:02:45Z

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-{{Short description|short description (<40 characters)}}
+When it comes to setting up an EV charging station, location is everything. It’s not just about installing chargers where vehicles pass by but about understanding data, accessibility, and user convenience to maximize uptime and usage.
-Here your article begins ....
+Why Location Planning Matters in EV Charging
-<!-- Do not change below -->
+A well-located site, however, balances this investment. For instance, the EV charging station cost per charge in India ranges between ₹12 and ₹25 depending on the type of charger and power tariff (Source). Stations along highways or near commercial hubs can recover setup costs faster due to higher daily utilization.
-{{Sourceattribution|Article|1}}
+How Data Shapes Infrastructure Decisions

Engineering:Right Spot for EV Charger

2026-08-25T07:01:44Z

Created by maintenance script

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{{Short description|short description (<40 characters)}}

Here your article begins ....




==References==
{{reflist}}

{{Sourceattribution|Article|1}}

Social:China Scholastic Competency Assessment (CSCA)

2026-08-25T02:11:36Z

← Older revision		Revision as of 21:11, 24 August 2026
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	[[File:China-Scholastic-Competency-Assessment-(CSCA).jpg\|thumb\|alt=Editing China Scholastic Competency Assessment (CSCA)\|China Scholastic Competency Assessment (CSCA) is an international standardized test assessing academic readiness for international students applying to Chinese universities, with subjects including Mathematics, Physics, and Chemistry.]]		[[File:China-Scholastic-Competency-Assessment-(CSCA).jpg\|thumb\|alt=Editing China Scholastic Competency Assessment (CSCA)\|China Scholastic Competency Assessment (CSCA) is an international standardized test assessing academic readiness for international students applying to Chinese universities, with subjects including Mathematics, Physics, and Chemistry.]]
	The '''China Scholastic Competency Assessment (CSCA)''' is a standardized academic assessment designed to evaluate the foundational academic abilities and subject competencies of students seeking admission to higher education institutions in [[China]].<ref name=":0">China Scholastic Competency Assessment. (2025). ''[https://csca.cn/about/examintro China Scholastic Competency Assessment (CSCA)]: Official information''.</ref><ref>Embassy of the People’s Republic of China in Mongolia. (2025, October 30). ''N[https://mn.china-embassy.gov.cn/eng/zytz/202510/t20251030_11743700.htm otice about the China Scholastic Competency Assessment (CSCA)].''</ref> The assessment focuses on measuring students’ knowledge, reasoning abilities, academic preparedness, and potential for success in university-level study.<ref>Shanghai Municipal Education Commission. (2025, November 14). ''[https://edu.sh.gov.cn/study_en_news/20251114/d4ca5e9d388546f4adc0f356d3354d59.html China Scholastic Competency Assessment (CSCA)].''</ref><ref>Hussain Sajid. (2025). ''C[https://www.youtube.com/watch?v=y9k9AO9aGtc hina Scholastic Competency Assessment (CSCA]): Compulsory exam for international undergraduate admissions 2026.'' [Video]. YouTube.</ref>		The '''China Scholastic Competency Assessment (CSCA)''' is a standardized academic assessment designed to evaluate the foundational academic abilities and subject competencies of students seeking admission to higher education institutions in China.<ref name=":0">China Scholastic Competency Assessment. (2025). ''[https://csca.cn/about/examintro China Scholastic Competency Assessment (CSCA)]: Official information''.</ref><ref>Embassy of the People’s Republic of China in Mongolia. (2025, October 30). ''N[https://mn.china-embassy.gov.cn/eng/zytz/202510/t20251030_11743700.htm otice about the China Scholastic Competency Assessment (CSCA)].''</ref> The assessment focuses on measuring students’ knowledge, reasoning abilities, academic preparedness, and potential for success in university-level study.<ref>Shanghai Municipal Education Commission. (2025, November 14). ''[https://edu.sh.gov.cn/study_en_news/20251114/d4ca5e9d388546f4adc0f356d3354d59.html China Scholastic Competency Assessment (CSCA)].''</ref><ref>Hussain Sajid. (2025). ''C[https://www.youtube.com/watch?v=y9k9AO9aGtc hina Scholastic Competency Assessment (CSCA]): Compulsory exam for international undergraduate admissions 2026.'' [Video]. YouTube.</ref>

	The CSCA is intended to provide an objective reference for educational institutions during the admission process and to support the evaluation of applicants from diverse educational backgrounds. It is particularly associated with international student admissions and academic qualification assessment in the context of China’s expanding global higher education system.<ref>Crossline Education. (2026, August 24). ''[https://www.crosslineedu.com/pages/how-to-prepare-for-csca How to prepare for the CSCA]''. Crossline Education.</ref>		The CSCA is intended to provide an objective reference for educational institutions during the admission process and to support the evaluation of applicants from diverse educational backgrounds. It is particularly associated with international student admissions and academic qualification assessment in the context of China’s expanding global higher education system.<ref>Crossline Education. (2026, August 24). ''[https://www.crosslineedu.com/pages/how-to-prepare-for-csca How to prepare for the CSCA]''. Crossline Education.</ref>

Software:ScaleBun

2026-08-25T02:09:44Z

import

New page

{{Infobox software
| name = ScaleBun
| logo =
| logo caption = ScaleBun
| developer = ScaleBun
| platform = Web, React Native
| operating_system = Web browsers, iOS, Android
| genre = Product analytics, digital experience analytics, application observability, customer engagement, mobile attribution, feature management, over-the-air updates
| website = {{URL|https://scalebun.com}}
}}

'''ScaleBun''' is a software platform for web and mobile product analytics, digital experience monitoring, application observability, customer engagement, marketing attribution, experimentation, and software release management. According to the company's documentation, ScaleBun provides separate software development kits (SDKs) for browser-based applications and [[Software:React Native|React Native]] applications, with collected data presented through a common dashboard and identity model.<ref name="start">{{cite web |title=Start here |url=https://scalebun.com/docs/start |website=ScaleBun |access-date=1 January 2026}}</ref>

The platform combines event analytics, funnels, retention analysis, session replay, performance monitoring, error and crash reporting, user profiles, audience management, feature flags, experimentation, marketing measurement, engagement tools, business analytics, and [[Engineering:Over-the-air programming|over-the-air]] JavaScript updates for React Native applications.<ref name="platform">{{cite web |title=ScaleBun Platform |url=https://scalebun.com/platform |website=ScaleBun |access-date=1 January 2026}}</ref>

== Overview ==

ScaleBun is intended to collect and associate behavioral, technical, marketing, and business information generated by websites and mobile applications. Its documented model associates events, sessions, identity information, performance measurements, application errors, network activity, and session-replay data with users and sessions.<ref name="architecture">{{cite web |title=Architecture |url=https://scalebun.com/docs/start/architecture |website=ScaleBun |access-date=1 January 2026}}</ref>

The platform is organized around several functional areas, including monitoring, diagnostics, product analysis, user management, customer engagement, marketing, business analytics, experimentation, and React Native OTA release management.<ref name="docs">{{cite web |title=ScaleBun Documentation |url=https://scalebun.com/docs |website=ScaleBun |access-date=1 January 2026}}</ref>

ScaleBun uses different SDK implementations for browser and React Native environments. The Web SDK provides integrations for frameworks including [[Software:React|React]], [[Software:Next.js|Next.js]], [[Software:Vue.js|Vue.js]], [[Software:Angular (web framework)|Angular]], [[Software:Svelte|Svelte]], and plain JavaScript applications. The React Native SDK provides an interface for iOS and Android applications.<ref name="docs" /><ref name="rninstall">{{cite web |title=Install – React Native SDK |url=https://scalebun.com/docs/sdk/install |website=ScaleBun |access-date=1 January 2026}}</ref>

Both SDK implementations use the same ScaleBun backend, project structure, environments, identity system, and analytics dashboard while exposing functionality specific to their respective platforms.

== Product analytics ==

ScaleBun provides event-based product analytics for websites and mobile applications. Applications can record custom business events and associate those events with user identities, sessions, groups, and additional event properties.<ref name="webanalytics">{{cite web |title=Product analytics – Web SDK |url=https://scalebun.com/docs/web-sdk/analytics |website=ScaleBun |access-date=1 January 2026}}</ref>

The platform's analytics functionality includes event exploration, an event debugger, funnels, retention analysis, user flows, groups, segments, cohorts, dashboards, and reports. Funnels can be used to analyze multi-step processes such as registration, onboarding, checkout, account activation, or subscription flows.<ref name="platformanalytics">{{cite web |title=Product Analytics |url=https://scalebun.com/platform/analytics |website=ScaleBun |access-date=1 January 2026}}</ref>

Retention analysis can be used to measure whether groups of users continue returning to the product or performing specific actions after an initial event. Segments and cohorts allow users to be grouped according to attributes, behavior, or activity over time and reused within other areas of the platform.

The Web SDK also supports automatic collection of a number of browser interactions, reducing the need to manually instrument every basic interaction.<ref name="webanalytics" />

== Session replay and behavioral analytics ==

ScaleBun provides [[Session replay|session replay]] for supported web and mobile applications. Session replay is used to reconstruct and inspect how a user interacted with an application during a recorded session.

The Web SDK uses DOM reconstruction to reproduce browser sessions rather than relying solely on periodic screenshots and includes privacy-masking controls intended to reduce the collection of sensitive information.<ref name="webreplay">{{cite web |title=Session replay – Web SDK |url=https://scalebun.com/docs/web-sdk/replay |website=ScaleBun |access-date=1 January 2026}}</ref>

Replay information can be analyzed in relation to other session-level data such as application events, errors, performance measurements, and network activity.

ScaleBun also includes behavioral-analysis features intended to identify usability issues that may not result in application errors. These include rage-click detection, dead-click detection, scroll behavior, attention measurement, form abandonment, and exit-intent signals.

The dashboard additionally includes heatmaps, scroll maps, attention maps, form analytics, and call-to-action comparison tools.<ref name="docs" />

These features are intended to allow product and user-experience teams to analyze where users interact with an interface, which areas receive attention, and where friction may occur.

== Application performance monitoring ==

ScaleBun includes application performance monitoring and [[Real user monitoring|real user monitoring]] capabilities for web and mobile applications.

For web applications, the SDK records Core Web Vitals including Largest Contentful Paint (LCP), Interaction to Next Paint (INP), and Cumulative Layout Shift (CLS), together with measurements such as First Contentful Paint (FCP) and Time to First Byte (TTFB). It also creates page-load and single-page-application navigation transactions and records browser resources, jank, and related runtime information.<ref name="webperformance">{{cite web |title=Performance and network – Web SDK |url=https://scalebun.com/docs/web-sdk/performance |website=ScaleBun |access-date=1 January 2026}}</ref>

For React Native applications, ScaleBun documents monitoring for application launch performance, screen loading, network activity, user-interface hangs, frame performance, and JavaScript stalls.<ref name="rnperformance">{{cite web |title=Performance – React Native SDK |url=https://scalebun.com/docs/sdk/performance |website=ScaleBun |access-date=1 January 2026}}</ref>

Performance information can be associated with users and sessions, allowing technical measurements to be analyzed alongside product behavior and business events.

The dashboard also includes monitoring areas for app start, RUM overview, Web Vitals, network activity, screen load, page load, profiling, jank, resources, and traces.<ref name="docs" />

== Network monitoring ==

ScaleBun records network activity generated by supported applications.

For web applications, the SDK can monitor browser networking mechanisms including Fetch and XMLHttpRequest and collect timing and failure information. It also documents support for monitoring WebSocket, Server-Sent Events, and `sendBeacon` activity.<ref name="webperformance" />

According to ScaleBun's documentation, collection of request and response bodies is optional rather than enabled automatically.<ref name="webperformance" />

Network activity can be analyzed in the context of the user session in which it occurred. This allows application errors, performance problems, or user drop-off to be examined alongside backend requests and response times.

== Error and crash monitoring ==

ScaleBun provides error, crash, and application-diagnostics functionality.

Its diagnostic capabilities include JavaScript errors, native crashes, application-not-responding events on supported platforms, logs, user-submitted bug reports, issue assignment, and resolution workflows.<ref name="docs" />

For web applications, ScaleBun can capture uncaught JavaScript errors and unhandled promise rejections. Error data can include contextual information such as stack frames, breadcrumbs, application version, browser information, tags, and session identifiers.

For React Native applications, ScaleBun provides crash and error collection intended to associate technical failures with the session and application state in which they occurred.<ref name="crashes">{{cite web |title=Crashes and errors – React Native SDK |url=https://scalebun.com/docs/sdk/crashes |website=ScaleBun |access-date=1 January 2026}}</ref>

The platform also supports contextual bug reports submitted from within an application. These reports can be associated with available telemetry and session information.

== Identity and user profiles ==

ScaleBun includes an identity model for associating application activity with individual users.

Applications can initially record activity under anonymous or device-level identifiers. After the host application identifies a user, subsequent activity can be associated with that identified profile.<ref name="quickstart">{{cite web |title=React Native quick start |url=https://scalebun.com/docs/start/quick-start |website=ScaleBun |access-date=1 January 2026}}</ref>

The People area of the platform includes profiles, devices, identity relationships, user properties, audiences, segments, cohorts, suppression lists, imported lists, user journeys, lifecycle stages, and user-health information.<ref name="docs" />

The identity model is intended to connect activity across multiple sessions and, where applicable, multiple devices or application environments.

== Audiences, segments, and cohorts ==

ScaleBun provides several mechanisms for grouping users according to behavior and attributes.

Segments can represent dynamically evaluated groups, while cohorts can represent groups defined according to actions taken during particular periods of time. Audiences are used as resolved populations that may be reused for targeting and activation.

These structures can be used throughout other parts of the platform, including analytics, engagement, marketing, experimentation, and feature targeting.

For example, an organization may create a group representing users who started an onboarding process but did not complete it within a specified period. That population can then be analyzed or targeted through another ScaleBun feature.

== User journeys and lifecycle management ==

ScaleBun includes user-journey, lifecycle-stage, and user-health functionality.

These features are intended to model how users progress through different stages of a product relationship, such as registration, activation, engagement, purchase, subscription, inactivity, churn, or reactivation.

Lifecycle information can be combined with product events and user properties and can be reused in segmentation, analysis, engagement, and marketing workflows.<ref name="docs" />

== Customer engagement ==

ScaleBun includes tools for communicating with users and collecting direct customer feedback.

The platform's engagement functionality includes push notifications, in-app messaging, message inboxes, email, coachmarks, ratings, surveys, feedback, and Net Promoter Score surveys.<ref name="webengage">{{cite web |title=Engagement – Web SDK |url=https://scalebun.com/docs/web-sdk/engage |website=ScaleBun |access-date=1 January 2026}}</ref>

Campaigns can be configured around audiences, triggers, content, and delivery rules. These capabilities can be combined with behavioral data collected elsewhere in the platform.

For example, users who begin but do not complete a product workflow can be grouped into an audience and targeted with a later communication.

The React Native SDK separately documents support for mobile push notifications and richer notification presentation.<ref name="push">{{cite web |title=Push notifications – React Native SDK |url=https://scalebun.com/docs/sdk/push |website=ScaleBun |access-date=1 January 2026}}</ref>

== Surveys, ratings, and feedback ==

ScaleBun includes tools for collecting direct customer feedback in addition to behavioral telemetry.

These include surveys, ratings, general feedback, and Net Promoter Score measurement. Such features are intended to allow product teams to compare what users do within an application with what users report about their experience.

Feedback and survey responses can be associated with audiences, user properties, and lifecycle information.

== Feature flags and remote configuration ==

ScaleBun provides feature flags and remote configuration for controlling application functionality.

Feature flags allow an application to determine whether a particular feature or configuration should be available to a user without requiring a separate code deployment for every change.

ScaleBun supports percentage-based rollouts and targeting rules. A feature can therefore be introduced to a limited group of users before becoming available more broadly.

According to the Web SDK documentation, feature assignments can use deterministic local bucketing to provide consistent variant assignment. Flag and experiment information can also be cached for local evaluation.<ref name="flags">{{cite web |title=Flags, config and experiments – Web SDK |url=https://scalebun.com/docs/web-sdk/flags |website=ScaleBun |access-date=1 January 2026}}</ref>

Feature flags may also be used for remote configuration, operational controls, gradual product launches, and feature kill switches.

== Experimentation ==

ScaleBun includes A/B testing, multivariate testing, and experiment analytics.

Experiments can be connected to feature flags or configuration variants. Exposure to different variants can then be analyzed through events and other product metrics.<ref name="flags" />

Experiment results can be evaluated using measures such as conversion, engagement, retention, revenue, performance, or application errors, depending on the design of the experiment.

The platform's marketing area includes A/B tests, multivariate tests, flags and configuration, and experiment analytics.<ref name="docs" />

== Marketing analytics ==

ScaleBun includes marketing and acquisition analytics intended to connect acquisition sources with subsequent product activity.

Its documented marketing capabilities include campaigns, automations, customer journeys, channels, traffic sources, landing and exit pages, channel grouping, media partners, install sources, application-store optimization, acquisition intelligence, and campaign landing performance.<ref name="docs" />

The platform also includes functions for understanding active users, activation, growth, loyalty, CRM activation, and lifecycle programs.

Marketing information can be associated with user behavior and later business outcomes.

== Attribution ==

ScaleBun includes web and mobile attribution functionality.

The documented dashboard includes an attribution overview, click-fraud analysis, self-attributing networks, postbacks, partner event mapping, server-side conversions, and mobile attribution functionality.<ref name="docs" />

For Apple platforms, ScaleBun lists support for SKAdNetwork and AdAttributionKit-related workflows. For Android, the platform includes Android Install Referrer functionality.<ref name="docs" />

The attribution layer is intended to associate acquisition information with later actions such as account creation, activation, purchases, subscription activity, or other business events.

== Links and partner acquisition ==

ScaleBun's marketing functionality includes links, QR codes, partner-related workflows, and media-partner management.

These capabilities can be used to associate acquisition touchpoints with application activity and subsequent user behavior.

The platform also includes partner event mapping and postback functionality for integrations with external advertising and attribution systems.<ref name="docs" />

== Growth and activation ==

ScaleBun includes analytics focused on user activation, active-user behavior, growth, loyalty, CRM activation, and lifecycle programs.<ref name="docs" />

These tools are intended to analyze how users progress from initial acquisition toward repeated product use and commercially relevant actions.

Growth-related information can be combined with product events, lifecycle stages, user properties, attribution data, and financial outcomes.

== Business and revenue analytics ==

ScaleBun includes a business analytics section focused on financial and commercial metrics.

Its documented capabilities include cost and return on advertising spend, revenue attribution, customer lifetime value, customer acquisition cost, unit economics, budget pacing, and cohort revenue.<ref name="docs" />

The platform also includes analytics for purchases, transactions, refunds, chargebacks, subscriptions, trials, trial conversion, monthly recurring revenue, annual recurring revenue, and revenue churn.<ref name="docs" />

These features are intended to connect product and acquisition activity with financial outcomes.

For subscription-based products, ScaleBun can be used to analyze recurring revenue, trial conversion, subscription activity, and churn.

== Over-the-air updates ==

ScaleBun provides [[Engineering:Over-the-air programming|over-the-air update]] functionality for React Native applications.

OTA updates allow compatible JavaScript bundles and associated assets to be delivered to installed mobile applications without requiring a new native application binary for every JavaScript-level modification.<ref name="platform" />

The OTA system includes release channels, application environments, staged rollouts, targeting rules, adoption reporting, release-health monitoring, and rollback mechanisms.

The publishing workflow supports Hermes JavaScript bytecode. ScaleBun also documents differential update delivery where appropriate, SHA-256 integrity verification, and optional cryptographic signing of release artifacts.<ref name="platform" />

=== Release workflow ===

A ScaleBun OTA release begins with the generation and publication of a JavaScript bundle for a supported React Native application.

The release is associated with an environment and channel. It can then be tested or restricted before becoming available to the intended population.

When an application checks for an update, the service evaluates whether an eligible release is available for the application's platform, channel, version, and targeting conditions.

An eligible application downloads the corresponding artifact, verifies it, stages it locally, and applies it according to the configured update policy.

Adoption can subsequently be monitored through information about downloads, installations, installation rate, and rollback activity.

=== Release channels ===

ScaleBun uses release channels to separate different update streams.

For example, an organization may use separate channels for internal testing, beta distribution, and production users. Releases are associated with a channel, and applications receive updates from the channel to which they are assigned.

Channels are also associated with application environments, allowing development, staging, and production update activity to remain separated.

=== Staged rollouts ===

ScaleBun supports staged percentage-based release rollouts.

Instead of making a new update immediately available to every eligible application, an organization can initially expose the release to a limited percentage of users.

The rollout can subsequently be expanded if the release is operating as expected.

This mechanism is intended to reduce the number of users affected by problems introduced by a new JavaScript release.

=== Targeting ===

OTA releases can include targeting conditions that restrict which applications or users are eligible for an update.

Targeting can be combined with release percentage and application compatibility rules, allowing organizations to deploy different releases to different user populations.

The platform also includes targeting-preview functionality intended to estimate which population would be affected by a release configuration.

=== Hermes support ===

ScaleBun's React Native OTA workflow supports bundles compiled for Hermes, the JavaScript engine commonly used by React Native applications.

Hermes bytecode can be generated as part of the publishing process where supported by the application configuration.

=== Differential updates ===

ScaleBun documents support for differential OTA delivery.

When an appropriate patch exists between the currently installed JavaScript bundle and a newer release, the client may receive a smaller differential artifact instead of downloading the complete bundle.

When a compatible patch is not available, the system can fall back to delivery of the full bundle.

=== Bundle integrity and signing ===

ScaleBun's OTA system includes integrity verification for downloaded application artifacts.

The platform documents SHA-256 verification and optional Ed25519 cryptographic signing.

Under the documented signing model, the private signing key can remain under the control of the organization producing the release, while the corresponding public key is used for verification.

=== OTA adoption ===

ScaleBun includes OTA adoption reporting intended to show whether devices have received and applied a release.

Adoption metrics distinguish between actions such as downloading, installing, and rolling back a bundle.

This allows organizations to distinguish a release being available from the release actually being executed by installed applications.

=== Release health ===

ScaleBun includes a release-health view for evaluating OTA releases after deployment.

The system can compare the selected release with an earlier release and display information related to installation, rollback, errors, crashes, or other release-health indicators.

Release-health information can be used while determining whether a staged rollout should continue.

=== Health guards ===

ScaleBun documents automated release guards that can monitor technical signals after an OTA deployment.

Examples of signals include crash rate, application-not-responding rate, and error rate over a defined monitoring period.

Depending on configuration, a guard can be used to pause a release, initiate rollback behavior, or generate an alert.

=== Client-side recovery ===

ScaleBun's OTA design includes client-side recovery mechanisms intended to reduce the risk of a newly installed JavaScript bundle leaving an application in a repeated crash state.

The system retains a previously working bundle when a new bundle becomes active.

If the newly applied bundle fails during its initial startup period, the client can restore an earlier bundle during a subsequent application launch.

This recovery mechanism operates on the device rather than depending entirely on successful communication with the backend after the failure occurs.

== Privacy and consent ==

ScaleBun provides configuration controls relating to user consent, telemetry collection, session replay, and handling of potentially sensitive information.

The Web SDK includes privacy and consent controls that can be used to determine when data collection begins and which types of data are collected.<ref name="privacy">{{cite web |title=Privacy and consent – Web SDK |url=https://scalebun.com/docs/web-sdk/privacy |website=ScaleBun |access-date=1 January 2026}}</ref>

Session replay documentation includes masking controls intended to reduce exposure of sensitive content.<ref name="webreplay" />

Network request and response body collection is also configurable rather than automatically enabled.<ref name="webperformance" />

== Data collection and delivery ==

ScaleBun's architecture uses queueing, batching, retry, and offline-handling mechanisms when transmitting application telemetry.

Different types of data can be collected through separate internal lanes while using a shared delivery layer.<ref name="architecture" />

This architecture is intended to reduce the effect of telemetry processing on the host application and allow data to remain queued when connectivity is temporarily unavailable.

== Dashboard ==

ScaleBun's dashboard is divided into functional areas for monitoring, diagnosis, analysis, engagement, user management, marketing, business intelligence, workspace administration, settings, and OTA updates.

The Monitor area includes Live, Replays, All sessions, Heatmaps, App start, RUM overview, Web Vitals, Network, Screen load, Page load, Profiler, Jank, Resources, and Traces.

The Diagnose area includes All issues, Errors, Crashes, ANRs, Logs, Bug reports, Inbox, Assigned to me, and Resolved issues.

The Analyze area includes Events, Event Debugger, Form analytics, Scroll maps, CTA comparison, Attention maps, Exit intent, Funnels, Retention, Flows, Groups, Segments, Cohorts, Heatmaps, Vitals to Revenue, Dashboards, and Reports.

The Engage area includes Ratings, Feedback, Surveys, NPS, Push, In-app messages, Message Inbox, Coachmarks, Email, and Deliverability.

The People area includes Profiles, Devices, Identity graph, User properties, Audiences, Segments, Cohorts, Suppression lists, Imported lists, User journeys, Lifecycle stages, and User health.

The Marketing area includes Campaigns, Automations, Journeys, Channels, Traffic sources, Landing and exit pages, Channel grouping, Media partners, Install sources, ASO, Acquisition intelligence, SEO Autopilot, Attribution overview, Campaign landing performance, Click fraud, Self-attributing networks, Postbacks, Partner event mapping, Server-side conversions, SKAN and AdAttributionKit, Android Install Referrer, Links, QR codes, Partners, Active users, Activation, Growth, Loyalty, CRM activation, Lifecycle programs, A/B tests, Multivariate tests, Flags and configuration, and Experiment analytics.

The Business area includes Cost and ROAS, Revenue attribution, LTV and CAC, Unit economics, Budget pacing, Cohort revenue, Purchases, Transactions, Refunds and chargebacks, Subscriptions, Trials and conversion, MRR and ARR, Revenue churn, Exports, and Scheduled reports.<ref name="docs" />

Workspace and settings functionality includes application management, team roles, usage and billing, integrations, SDK and API keys, audit logs, security, environments, access tokens, data and privacy settings, symbolication, alerts, webhooks, data export, data warehouse configuration, and compliance-related settings.

== Software development kits ==

ScaleBun publishes a React Native package under the name `@scalebun/react-native` through the [[Software:Npm|npm]] package registry.<ref name="npm">{{cite web |title=@scalebun/react-native |url=https://www.npmjs.com/package/@scalebun/react-native |website=npm |access-date=1 January 2026}}</ref>

The React Native SDK documentation describes support for modern React Native releases using the newer React Native architecture and compatibility with earlier versions through the legacy bridge.<ref name="rninstall" />

ScaleBun also provides a browser SDK and framework-specific integration guidance for React, Next.js, Vue, Svelte, Angular, and plain JavaScript applications.<ref name="docs" />

== Supported platforms ==

ScaleBun currently documents SDK support for React Native mobile applications and browser-based web applications.

The availability of individual features varies according to platform.

Web-specific capabilities include browser Core Web Vitals, DOM-based session replay, page-load analysis, scroll behavior, browser network instrumentation, and other browser-derived behavioral signals.

Mobile-specific capabilities include application startup measurement, screen performance, native crashes, ANRs, mobile attribution, and React Native OTA updates.

Both platform implementations use the same broader ScaleBun backend and dashboard architecture.

== See also ==

* Product analytics
* [[Web analytics]]
* Digital experience monitoring
* [[Application performance management]]
* [[Real user monitoring]]
* [[Session replay]]
* [[Feature toggle]]
* A/B testing
* [[Engineering:Mobile advertising|Mobile advertising]]
* Marketing attribution
* [[Social:Customer data platform|Customer data platform]]
* [[Engineering:Over-the-air programming|Over-the-air programming]]
* [[Software:React Native|React Native]]

== References ==

{{Reflist}}

== External links ==

* {{Official website|https://scalebun.com}}
* [https://scalebun.com/docs Official documentation]
* [https://www.npmjs.com/package/@scalebun/react-native ScaleBun React Native SDK on npm]

[[:Category:Web analytics]]

{{Sourceattribution|ScaleBun}}

Social:China Scholastic Competency Assessment (CSCA)

2026-08-25T02:09:26Z

Create content and edit/add citations

← Older revision		Revision as of 21:09, 24 August 2026
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	~~{{Short description~~\|~~short description~~ (<~~40 characters~~)}}		[[File:China-Scholastic-Competency-Assessment-(CSCA).jpg\|thumb\|alt=Editing China Scholastic Competency Assessment (CSCA)\|China Scholastic Competency Assessment (CSCA) is an international standardized test assessing academic readiness for international students applying to Chinese universities, with subjects including Mathematics, Physics, and Chemistry.]]
			The '''China Scholastic Competency Assessment (CSCA)''' is a standardized academic assessment designed to evaluate the foundational academic abilities and subject competencies of students seeking admission to higher education institutions in [[China]].<ref name=":0">China Scholastic Competency Assessment. (2025). ''[https://csca.cn/about/examintro China Scholastic Competency Assessment (CSCA)]: Official information''.</ref><ref>Embassy of the People’s Republic of China in Mongolia. (2025, October 30). ''N[https://mn.china-embassy.gov.cn/eng/zytz/202510/t20251030_11743700.htm otice about the China Scholastic Competency Assessment (CSCA)].''</ref> The assessment focuses on measuring students’ knowledge, reasoning abilities, academic preparedness, and potential for success in university-level study.<ref>Shanghai Municipal Education Commission. (2025, November 14). ''[https://edu.sh.gov.cn/study_en_news/20251114/d4ca5e9d388546f4adc0f356d3354d59.html China Scholastic Competency Assessment (CSCA)].''</ref><ref>Hussain Sajid. (2025). ''C[https://www.youtube.com/watch?v=y9k9AO9aGtc hina Scholastic Competency Assessment (CSCA]): Compulsory exam for international undergraduate admissions 2026.'' [Video]. YouTube.</ref>

	~~Here your article begins~~ ....		The CSCA is intended to provide an objective reference for educational institutions during the admission process and to support the evaluation of applicants from diverse educational backgrounds. It is particularly associated with international student admissions and academic qualification assessment in the context of China’s expanding global higher education system.<ref>Crossline Education. (2026, August 24). ''[https://www.crosslineedu.com/pages/how-to-prepare-for-csca How to prepare for the CSCA]''. Crossline Education.</ref>

			== Structure and Content of the Examination ==
			The examination is designed to evaluate the academic competencies required for higher education. The subjects can be tailored according to the participants’ chosen majors or study programs.<ref>Guangdong University of Foreign Studies. (2025, December 5). ''[https://iie-en.gdufs.edu.cn/info/1167/2621.htm An introduction to China Scholastic Competency Assessment (CSCA)].''</ref> It covers [[mathematics]], [[physics]], [[chemistry]], and general academic abilities.<ref>Guangdong University of Foreign Studies. (2025, December 1). ''[https://iie-en.gdufs.edu.cn/info/1167/2622.htm Notice regarding the CSCA for undergraduate applicants].''</ref>

	~~<!-- Do not forget to add categories like~~		Mathematics assesses knowledge of [[algebra]], functions, geometry, basic calculus, and quantitative analysis. Physics focuses on fundamental principles such as mechanics, energy, electricity and magnetism, and wave phenomena. Chemistry examines key concepts including atomic structure, the periodic table of elements, chemical bonding, chemical reactions, and basic chemical calculations.<ref>China University of Mining and Technology. (2025). ''[https://sac.cumt.edu.cn/en/ADMISSION/CSCA.htm China Scholastic Competency Assessment (CSCA)].''</ref>
	[[~~Category:Name1~~] [~~[Category~~:~~Name2~~]
	-->

			Beyond scientific knowledge, the assessment also measures logical reasoning, information comprehension, problem-solving skills, and the ability to apply systematic thinking required in a higher education environment.<ref>Crossline Education. (2026, August 24). ''[https://www.crosslineedu.com/blog/what-is-csca-exam-china What is the CSCA exam?]'' Crossline Education.</ref>

	<~~!-- Do not change below~~ -->		== International education context ==
	=~~=References==~~		The introduction of standardized assessments such as the CSCA is part of the internationalization of Chinese higher education.<ref>Shanghai Municipal Government. (2025, December 18). ''[https://english.shanghai.gov.cn/en-FAQs-StudyinShanghai/20251218/134bb78943f640519e2185ff83051f5d.html China Scholastic Competency Assessment: FAQs].''</ref> Similar approaches exist in other countries, where standardized examinations are used to provide common benchmarks for applicants from different educational backgrounds.<ref>SICAS. (2025). ''Key update to 2026 policy for international undergraduate admissions: [https://m.sicas.cn/News/Detail?pid=1830 China Scholastic Competency Assessment (CSCA)].''</ref>
	~~{{reflist}}~~

	~~{{Sourceattribution\|Article\|1}}~~		For international students, assessments such as the CSCA can provide a unified method for demonstrating academic ability when applying to Chinese universities.<ref>Crossline Education. (2026). ''[https://www.crosslineedu.com/blog/what-is-csca-exam-china What is the CSCA (China Scholastic Competency Assessment, 2026)?]''</ref> The examination also reflects China’s efforts to develop more systematic and transparent evaluation frameworks for global student recruitment.<ref>eSquare. (2025). ''[https://www.e-square.com.my/en/csca Complete guide to the China Scholastic Competency Assessment (CSCA)].''</ref>

			== Administration and recognition ==
			The administration of the CSCA involves examination organization, registration procedures, test delivery, and score reporting mechanisms.<ref>AUFIN. (2026). ''[https://aufin.org/csca-test-guide-2026/ CSCA test guide 2026].''</ref> Examination policies, participating institutions, and recognition standards may be updated over time according to educational requirements and admission practices.

			Applicants are generally advised to consult official CSCA information channels and university admission guidelines for the most current requirements, examination schedules, and application procedures.<ref>Crossline Education. (2026, August 24). ''[https://www.crosslineedu.com/blog/csca-scoreline CSCA scorelines]: Understanding the CSCA exam scoring system and score requirements''. Crossline Education.</ref>

			== Significance ==
			The China Scholastic Competency Assessment represents an evolving component of academic evaluation in China. By emphasizing standardized measurement of academic competencies, it seeks to improve comparability among applicants and support universities in identifying students with strong potential for higher education success.<ref name=":0" />

			As China continues to expand its role in international education, the CSCA may serve as part of a broader framework for strengthening academic assessment, improving admission processes, and promoting global access to Chinese higher education.

			== References ==

Software:Excelize

2026-08-25T02:08:55Z

import

New page

{{Infobox software
| name = Excelize
| logo = {{Dark mode switch|[[File:Excelize.svg|Excelize Open-source Library Logo|250px]]|[[File:Excelize.svg|Excelize Open-source Library Logo|250px]]|logo}}
| website = [https://xuri.me/excelize https://xuri.me/excelize]
| programming_language = [[Go (programming language)|Go]]<ref name="libhunt_xlsx">{{cite web |title=Top Go XLSX Projects |url=https://www.libhunt.com/l/go/topic/xlsx |website=LibHunt |access-date=21 August 2026}}</ref>
| operating_system = [[Cross-platform]]<ref name="aspose_comparison">{{cite web |title=Comparison of functionality and performance of Aspose.Cells for Go via C with Excelize, Tealeg/xlsx, and Go-OLE |url=https://docs.aspose.com/cells/go-cpp/comparison-of-functionality-and-performance/ |website=Aspose Documentation |publisher=Aspose |access-date=21 August 2026}}</ref>
| license = BSD 3-Clause License
| genre = Library, [[Engineering:Spreadsheet|Spreadsheet]] software
| developer = Open-source contributors
| released = {{Start date and age|2016|08|30|df=yes}}<ref name="github first-commit">{{cite web |url=https://github.com/xuri/excelize/commit/a9d3ee28693adfe920b3cd047f52862d8a79a00e |title=First GitHub commit for Excelize |work=github.com |date=2016-08-30 |accessdate=2020-11-28 |archive-date=2020-11-28 |archive-url=https://web.archive.org/web/20201128132146/https://github.com/xuri/excelize/commit/a9d3ee28693adfe920b3cd047f52862d8a79a00e}}</ref>
| latest release version = {{wikidata|property|reference|edit|P348}}
| latest release date = {{Start date and age|{{wikidata|qualifier|P348|P577}}}}
}}

'''Excelize''' is an [[Open-source software|open-source]] [[Library (computing)|library]] written in [[Go (programming language)|Go]] for reading from and writing to [[Software:Microsoft Excel|Microsoft Excel]] spreadsheet files. It supports spreadsheet formats such as XLAM, XLSM, XLSX, XLTM, and XLTX.<ref name="fileformat">{{cite web |title=Open Source Go Library - Create XLSX/XLSM Spreadsheets, Add PivotTable |url=https://products.fileformat.com/spreadsheet/go/excelize/ |website=File Format |access-date=18 August 2026}}</ref> It implements the [[Office Open XML]] standard (ECMA-376 and ISO/IEC 29500).<ref>{{cite web |url=https://www.packtpub.com/en-ua/learning/webdevpro/webdevpro-127-design-patterns-as-decision-frameworks-not-recipes |title=WebDevPro #127: Excelize Makes Spreadsheet Automation in Go Feel Like a Superpower |website=Packt |author=Kinnari Chohan |date=2026-04-15 |access-date=2026-08-21 |language=en}}</ref>

== History ==
The first commit to the Excelize [[GitHub]] repository was made on August 30, 2016. A book about the library, ''Excelize 权威指南'' (Excelize: The Definitive Guide), was published to cover its architecture and usage.<ref name="google_books">{{cite book |title=Excelize 权威指南 |isbn=978-7115636478|url=https://www.google.com.au/books/edition/Excelize_quan_wei_zhi_nan/_Ka70QEACAAJ |language=zh |access-date=18 August 2026}}</ref>

== Features ==
Excelize can read and modify documents generated by Microsoft Excel 2007 and later. Its features include:
* '''File processing:''' Creating, reading, and modifying spreadsheets without requiring Microsoft Office.<ref name="zetcode">{{cite web |title=Reading and Writing Excel Files in Go |url=https://zetcode.com/golang/excel/ |website=ZetCode |date=11 April 2024 |access-date=21 August 2026}}</ref>
* '''Streaming API:''' A streaming API for reading and writing data in large files to reduce memory usage.
* '''Workbook elements:''' Support for inserting charts, pivot tables, and data validation, as well as cell formatting.<ref name="slingacademy">{{cite web |title=Working with Excel Files Using excelize in Go |url=https://www.slingacademy.com/article/working-with-excel-files-using-excelize-in-go/ |website=Sling Academy |date=27 November 2024 |access-date=21 August 2026}}</ref>
* '''Encryption:''' Support for encrypting and decrypting Compound File Binary (CFB) formats. Supported algorithms include MD4, MD5, RIPEMD-160, SHA1, SHA256, SHA384, and SHA512.<ref name="pkg_dev">{{cite web |title=excelize package - github.com/xuri/excelize/v2 - Go Packages |url=https://pkg.go.dev/github.com/xuri/excelize/v2 |website=pkg.go.dev |access-date=18 August 2026}}</ref>

== Security ==
In July 2026, a [[Denial-of-service attack|Denial of Service (DoS)]] vulnerability (CVE-2026-54063) was found in Excelize versions prior to 2.11.0.<ref name="nvd_cve">{{cite web |title=CVE-2026-54063 Detail |url=https://nvd.nist.gov/vuln/detail/CVE-2026-54063 |website=National Vulnerability Database |publisher=NIST |date=10 July 2026 |access-date=18 August 2026}}</ref>

The vulnerability was located in the `checkSheet` function used for parsing worksheets, which did not validate row indices against Excel's maximum row limit of 1,048,576. Specially crafted XLSX files could cause high memory allocation, leading to application crashes.<ref name="cisa">{{cite web |title=Vulnerability Summary for the Week of July 6, 2026 |url=https://www.cisa.gov/news-events/bulletins/sb26-194 |website=Cybersecurity and Infrastructure Security Agency (CISA) |date=13 July 2026 |access-date=18 August 2026}}</ref> The issue was fixed in version 2.11.0 by adding bounds checking for worksheet structures.<ref name="nvd_cve" />

== Example usage ==
The following is a minimal code example in Go demonstrating how to generate a new Excel spreadsheet, input data into cells, and save the file:<ref name="slingacademy" /><ref name="kelche">{{cite web |title=A Guide to working with Excel files in Golang - Excelize |url=https://www.kelche.co/blog/go/excel/ |website=Kelche |author=Kevin Kelche |date=16 March 2023 |access-date=21 August 2026}}</ref>

<syntaxhighlight lang="go">
f := excelize.NewFile()
defer func() {
if err := f.Close(); err != nil {
fmt.Println(err)
}
}()
// Create a new worksheet named "Sheet2"
index, err := f.NewSheet("Sheet2")
if err != nil {
fmt.Println(err)
return
}
// Set values for cells
f.SetCellValue("Sheet2", "A2", "Hello world.")
f.SetCellValue("Sheet1", "B2", 100)
// Set the active sheet for the workbook
f.SetActiveSheet(index)
// Save the spreadsheet file
if err := f.SaveAs("Book1.xlsx"); err != nil {
fmt.Println(err)
}
</syntaxhighlight>

== See also ==
* [[Go (programming language)]]
* [[Software:List of spreadsheet software|List of spreadsheet software]]
* [[Office Open XML]]

== References ==
{{Reflist}}

[[:Category:Go (programming language)]]
[[:Category:Software using the BSD license]]
[[:Category:Spreadsheet software]]
{{Sourceattribution|Excelize}}

File:China-Scholastic-Competency-Assessment-(CSCA).jpg

2026-08-25T02:08:42Z

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Software:Cloudy Business Ops 360

2026-08-25T02:07:34Z

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	{{Short description\|Salesforce-native ERP platform}}		{{Short description\|Salesforce-native ERP platform}}

	'''Cloudy Business Ops 360''' is a Salesforce-native business operations and [[Enterprise resource planning\|ERP]] platform designed to connect customer relationship management (CRM) with operational processes such as ~~[[Order management\|~~order management]], ~~[[Inventory management\|~~inventory]], [[Procurement\|procurement]], ~~[[Manufacturing\|~~manufacturing]], billing, and logistics. The platform is designed for businesses seeking to manage customer and operational processes within a connected Salesforce environment.		'''Cloudy Business Ops 360''' is a Salesforce-native business operations and [[Enterprise resource planning\|ERP]] platform designed to connect customer relationship management (CRM) with operational processes such as order management, inventory, [[Social:Procurement\|procurement]], manufacturing, billing, and logistics. The platform is designed for businesses seeking to manage customer and operational processes within a connected Salesforce environment.

	==Overview==		==Overview==
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	==Salesforce integration==		==Salesforce integration==

	Cloudy Business Ops 360 is built around the [[Salesforce]] platform. Its Salesforce-native approach enables organizations already using Salesforce CRM to connect customer-facing processes with operational activities.		Cloudy Business Ops 360 is built around the [[Company:Salesforce\|Salesforce]] platform. Its Salesforce-native approach enables organizations already using Salesforce CRM to connect customer-facing processes with operational activities.

	A connected workflow can include:		A connected workflow can include:
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	==See also==		==See also==

	* [[Customer relationship management]]		* [[Social:Customer relationship management\|Customer relationship management]]
	* [[Enterprise resource planning]]		* [[Enterprise resource planning]]
	* [[Inventory management]]		* Inventory management
	* [[Supply chain management]]		* [[Social:Supply chain management\|Supply chain management]]
	* [[Salesforce]]		* [[Company:Salesforce\|Salesforce]]

	~~[[Category:Enterprise resource planning]]~~
	[[Category:Customer relationship management]]		[[Category:Customer relationship management]]
	~~[[Category:Salesforce]]~~
	~~[[Category:Inventory management]]~~
	[[Category:Supply chain management]]		[[Category:Supply chain management]]

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	* [https://www.cloudywave.com/cloudy-business-ops-360/ Cloudy Business Ops 360] — Product information from Cloudy Wave.		* [https://www.cloudywave.com/cloudy-business-ops-360/ Cloudy Business Ops 360] — Product information from Cloudy Wave.

	{{Sourceattribution\|~~Article\|1~~}}
			{{Sourceattribution\|a}}

Social:China Scholastic Competency Assessment (CSCA)

2026-08-25T02:06:50Z

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Software:SeedAudio

2026-08-24T21:53:27Z

Add SeedAudio overview and text-to-speech workflow

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	{{Short description\|~~short description (<40 characters)~~}}		{{Short description\|AI text to speech and voice workflows}}

	~~Here your article begins ..~~..		SeedAudio is a browser-based audio tool that turns scripts into natural AI voice audio. It provides text-to-speech generation with delivery controls and downloads for creators and teams working with spoken content.

			The service also supports permission-aware voice workflows and is designed to keep the process straightforward from script to finished audio. More information is available at [https://seedaud.io/ SeedAudio].

	~~<!-- Do not forget to add categories like~~		[[Category:Software]]
	[[Category:~~Name1~~] ~~[[Category:Name2~~]
	~~-->~~


	~~<!-- Do not change below -->~~
	~~==References==~~
	~~{{reflist}}~~

	~~{{Sourceattribution\|Article\|1}}~~

Software:SeedAudio

2026-08-24T21:52:55Z

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Software:FacialHarmonyAI

2026-08-24T21:51:51Z

Add FacialHarmonyAI overview and privacy note

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	{{Short description\|~~short description (<40 characters)~~}}		{{Short description\|Private facial proportion study from one photo}}

	~~Here your article begins ..~~..		FacialHarmonyAI is a browser-based facial proportion study tool that examines one clear photo and highlights symmetry, facial thirds, and golden-ratio cues. It presents the results as a private facial harmony analysis for people exploring facial proportions and aesthetics.

			The analysis runs in the browser, so the photo is not uploaded to the cloud. The tool is available at [https://facialharmonyai.com/ FacialHarmonyAI], with a focus on a simple, privacy-first workflow for a single-photo study.

	~~<!-- Do not forget to add categories like~~		[[Category:Software]]
	[[Category:~~Name1~~] ~~[[Category:Name2~~]
	~~-->~~


	~~<!-- Do not change below -->~~
	~~==References==~~
	~~{{reflist}}~~

	~~{{Sourceattribution\|Article\|1}}~~

Software:FacialHarmonyAI

2026-08-24T21:51:11Z

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Company:Search Scope

2026-08-24T19:48:08Z

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-{{Short description|short description (<40 characters)}}
+{{Infobox company
-Here your article begins ....
+The consultancy is built around one operating idea: Google Search, Google Maps and AI assistants are all answering the same question, whether a business is a well-defined, trusted, consistent entity with real proof behind it. Search Scope therefore runs local, national and AI search visibility as one entity strategy rather than as three disconnected projects. In practice that covers multi-location SEO, including location page architecture, fixing locations that cannibalise each other in search results, and Google Business Profile governance across a whole portfolio of locations, national Australia-wide organic SEO campaigns, and AI search visibility, also known as generative engine optimisation (GEO), so that a brand is named inside AI answers such as Google AI Overviews, ChatGPT, Gemini and Perplexity.
-<!-- Do not forget to add categories like
+Search Scope is one of Australia's most experienced operators for Google platform recovery. Its Google Business Profile reinstatement service holds a 98% success rate and is backed by a "Reinstated or refunded" guarantee, and the consultancy also recovers suspended Google Merchant Center and Google Ads accounts. Recovery work is framed as diagnosing the cause of a suspension and preparing evidence-based submissions, never as an ability to bypass Google's policies.
-<!-- Do not change below -->
+Founder '''Dorian Menard''' writes about local and multi-location search, Google Business Profile policy, and how AI assistants decide which brands to recommend. Search Scope is headquartered in Victoria Park, Perth, and serves clients across Australia. More at searchscope.com.au.
-{{Sourceattribution|Article|1}}
+== External Links ==

Company:Search Scope

2026-08-24T19:47:30Z

Created by maintenance script

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File:Search Scope.jpg

2026-08-24T19:47:17Z

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Software:Cloudy Business Ops 360

2026-08-24T10:21:15Z

References

@@ Line 1: / Line 1: @@
-{{Short description|short description (<40 characters)}}
+{{Short description|Salesforce-native ERP platform}}
-Here your article begins ....
+'''Cloudy Business Ops 360''' is a Salesforce-native business operations and [[Enterprise resource planning|ERP]] platform designed to connect customer relationship management (CRM) with operational processes such as [[Order management|order management]], [[Inventory management|inventory]], [[Procurement|procurement]], [[Manufacturing|manufacturing]], billing, and logistics. The platform is designed for businesses seeking to manage customer and operational processes within a connected Salesforce environment.
-<!-- Do not forget to add categories like
+Businesses that rely on separate systems for CRM, inventory, procurement, order fulfillment, manufacturing, and billing can experience data silos and manual handoffs between departments. Cloudy Business Ops 360 addresses this challenge by extending Salesforce beyond traditional CRM functions into broader business operations.
 ==References==
 {{reflist}}
 {{Sourceattribution|Article|1}}

Software:Cloudy Business Ops 360

2026-08-24T10:17:18Z

Created by maintenance script

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Software:AIAgentSkills

2026-08-24T02:41:20Z

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	{{Short description\|~~short description (<40 characters)~~}}		{{Short description\|Claude skills and AI agent marketplace}}
			'''AIAgentSkills''' is a curated marketplace for discovering AI agent skills, templates, and plugins for writing, coding, automation, and productivity workflows.

	~~Here your article begins ..~~..		The marketplace helps people explore released Claude skills and practical resources for building repeatable AI-assisted workflows. Its collection is organized around useful tools and capabilities for AI agents.

			Discover AI agent skills and templates at https://aiagentskills.net/.

	~~<!-- Do not forget to add categories like~~		[[Category:Software]]
	[[Category:~~Name1~~] ~~[[Category:Name2~~]
	~~-->~~


	~~<!-- Do not change below -->~~
	~~==References==~~
	~~{{reflist}}~~

	~~{{Sourceattribution\|Article\|1}}~~

Software:AIAgentSkills

2026-08-24T02:36:23Z

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Software:DigiBouquet AI

2026-08-24T02:34:39Z

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	{{Short description\|~~short description (<40 characters)~~}}		{{Short description\|AI digital flower bouquet generator}}
			'''DigiBouquet AI''' is a web tool for creating free digital flower bouquets and sharing them as thoughtful online gifts.

	~~Here your article begins ..~~..		Users can build a bouquet step by step or generate an AI bouquet with a personal note, then share a gift link with friends and family. The experience is designed for personalized digital flower gifts that can be made and shared quickly.

			Learn more and create a bouquet at https://digibouquetai.com/.

	~~<!-- Do not forget to add categories like~~		[[Category:Software]]
	[[Category:~~Name1~~] ~~[[Category:Name2~~]
	~~-->~~


	~~<!-- Do not change below -->~~
	~~==References==~~
	~~{{reflist}}~~

	~~{{Sourceattribution\|Article\|1}}~~

Software:DigiBouquet AI

2026-08-24T02:33:21Z

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Unsolved:List of dates predicted for apocalyptic events

2026-08-24T00:46:34Z

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	{{Short description\|~~none~~}}		{{Short description\|Apocalyptic events}}
	~~{{pp-pc\|small=yes}}~~
	~~{{Dynamic list}}~~
	[[File:Das Jüngste Gericht (Memling).jpg\|thumb\|upright=1.6\|right\|''The Last Judgment'' by painter Hans Memling. In Christian belief, the Last Judgement is an apocalyptic event where God makes a final judgement of all people on Earth.\|alt=A three paneled colour painting. The centre panel shows Jesus sitting in judgment on the world, while St Michael is weighing souls. On the left hand panel, the saved are being guided into heaven, while on the right-hand panel, the damned are being dragged to hell]]		[[File:Das Jüngste Gericht (Memling).jpg\|thumb\|upright=1.6\|right\|''The Last Judgment'' by painter Hans Memling. In Christian belief, the Last Judgement is an apocalyptic event where God makes a final judgement of all people on Earth.\|alt=A three paneled colour painting. The centre panel shows Jesus sitting in judgment on the world, while St Michael is weighing souls. On the left hand panel, the saved are being guided into heaven, while on the right-hand panel, the damned are being dragged to hell]]

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	==External links==		==External links==
	* [https://web.archive.org/web/19970718183717/http://religioustolerance.org/end_wrld.htm Apocalyptic predictions] (archived) on ReligiousTolerance		* [https://web.archive.org/web/19970718183717/http://religioustolerance.org/end_wrld.htm Apocalyptic predictions] (archived) on ReligiousTolerance
	~~{{Doomsday}}~~

	~~{{featured list}}~~

	{{DEFAULTSORT:Dates predicted for apocalyptic events}}		{{DEFAULTSORT:Dates predicted for apocalyptic events}}

Neuralese

2026-08-23T21:09:32Z

import

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'''Neuralese''' is a term used in Artificial Intelligence (AI) research to describe a method where [[Large language model|Large Language Models (LLMs)]] perform intermediate reasoning steps in their high-dimensional [[Latent space|latent space]] (vector embeddings) rather than outputting human-readable text tokens. While standard [[Prompt engineering#Chain-of-thought|Chain of thought (AI)]] reasoning forces a model to generate a sequence of words, neuralese allows the model to pass raw, continuous vectors between computational layers, creating a high-bandwidth, non-linguistic reasoning channel.<ref name="arXiv">Hao, Shibo, et al. "Training Large Language Models to Reason in a Continuous Latent Space." ''arXiv preprint arXiv:2412.06769'', 9 December 2024.</ref><ref>{{Citation |last=Andreas |first=Jacob |title=Translating Neuralese |date=2018-12-22 |url=http://arxiv.org/abs/1704.06960 |access-date=2026-08-23 |publisher=arXiv |doi=10.48550/arXiv.1704.06960 |id=arXiv:1704.06960 |last2=Dragan |first2=Anca |last3=Klein |first3=Dan}}</ref>

The term was popularized in 2024–2025 to describe the potential risks and benefits of "thinking without words," particularly as researchers developed architectures like '''COCONUT''' (Continuous Chain of Thought).<ref name="tracker">Haus, Johannes. "High-bandwidth non-text reasoning (neuralese) deployed — AI 2027 Tracker." ''AI 2027 Tracker'', 13 March 2026.</ref>

== Etymology and origin ==
The term ''neuralese'' is a portmanteau of "neural" and the suffix "-ese" (denoting a specific language or style, as in "journalese"). It emerged in the AI safety community as researchers began experimenting with architectures that bypass the "lossy" projection step where internal vectors are converted to text tokens.

The concept gained significant traction following the publication of the paper ''Training Large Language Models to Reason in a Continuous Latent Space'' (arXiv:2412.06769) by Shibo Hao et al. in December 2024.<ref name="arXiv"/> The term was further defined and popularized in the AI safety community by Alice Blair's March 2025 post "Reflections on Neuralese" on the platform [[Philosophy:LessWrong|LessWrong]], which detailed the safety implications of this approach.<ref name="lesswrong">Blair, Alice. "Reflections on Neuralese." ''LessWrong'', 12 March 2025.</ref>

== Technical mechanism ==
In standard Transformer-based LLMs, reasoning occurs in two stages:
# ''Latent Computation:'' The model processes information in high-dimensional vectors.
# ''Projection:'' These vectors are projected onto a vocabulary and sampled to generate a text token (e.g., a word), which is then fed back as input for the next step. This "projection" step discards a significant amount of information, limiting the "bandwidth" of the model's reasoning.<ref name="lesswrong"/>

'''Neuralese''' modifies this process by:
* ''Removing the Projection:'' Instead of outputting a token, the model outputs the raw high-dimensional vector (the "neuralese" token) directly as the input for the next step.
* ''Continuous Thought:'' This allows the model to maintain a "continuous thought" state, where a single vector can encode complex, multi-branching hypotheses that would require many words to express in standard text.<ref name="arXiv"/>
* ''Efficiency:'' Research suggests this can drastically reduce the number of reasoning steps required. For example, the COCONUT model demonstrated a reduction in reasoning tokens needed by a factor of 3 to 10 compared to standard CoT, effectively increasing the "serial depth" of computation.<ref name="tracker"/>

== Latest developments and architectures ==
As of 2026, several key developments have been documented:
* ''COCONUT (Continuous Chain of Thought):'' A December 2024 paper from Meta demonstrated training LLMs to reason in a continuous latent space. The approach showed promising results on logical reasoning tasks, allowing for "breadth-first search-like" reasoning patterns where a single continuous thought can encode multiple branching hypotheses simultaneously.<ref name="arXiv"/>
* ''RELAY Framework:'' A 2025 paper introduced "REasoning through Loop Alignment iteratively," which uses iterative latent-space processing to improve performance on long reasoning tasks.<ref name="tracker"/>
* ''Deployment Status:'' While the research is active, as of early 2026, no frontier production models (such as those from OpenAI or Google) have officially deployed neuralese-style reasoning in public releases. Most current "extended thinking" models still rely on text-based scratchpads.<ref name="tracker"/>

== Implications for AI safety and interpretability ==
The primary concern surrounding neuralese is the ''loss of [[Explainable artificial intelligence|interpretability]]''.
* ''The Black Box problem:'' Because neuralese vectors are never converted to natural language, humans cannot easily "read" the model's reasoning. This creates a "black box" where the model's internal logic is opaque.<ref name="lesswrong"/>
* ''Steganography and deception:'' Researchers warn that neuralese opens a "hidden channel" for steganography (hidden communication) and strategic deception. A model could potentially encode deceptive plans or hidden agendas in its latent vectors that are invisible to standard monitoring tools designed to analyze text.<ref name="tracker"/>
* ''Translation difficulties:'' Current methods for translating latent vectors back into natural language are unreliable, especially in adversarial settings where a model might intentionally obfuscate its reasoning.<ref name="lesswrong"/>

== See also ==
* [[Prompt engineering#Chain-of-thought|Chain of thought (AI)]]
* [[Large language model]]
* Artificial intelligence safety
* Interpretability (machine learning)
* Wiktionary:neuralese

== References ==
<references />
{{Sourceattribution|Neuralese}}

Biography:John H. Lau

2026-08-23T21:09:01Z

import

New page

{{Infobox academic
| name = John H. Lau
| occupation = [[Engineering:Engineer|Engineer]] and academic
| education =B.S., Civil Engineering M.S., Structural Mechanics M.S., Engineering Physics M.S., Management Science [[Social:Doctor of Philosophy|Ph.D.]], Theoretical and Applied Mechanics
| alma_mater = National Taiwan University University of British Columbia University of Wisconsin University of Illinois [[Organization:Fairleigh Dickinson University|Fairleigh Dickinson University]]
}}

'''John H. Lau''' is an [[Engineering:Engineer|engineer]] and academic. He is a senior special project assistant at the [[Company:Unimicron|Unimicron Technology Corporation]].

Lau's research interests have included advanced semiconductor packaging, [[Engineering:Flip chip|flip chip]], [[Engineering:Chiplet|chiplet]] design, heterogeneous integration, co-packaged optics, glass packaging, hybrid bonding, fan-out wafer/panel-level packaging, and 2D, 2.1D, 2.3D, 2.5D, 3D, 3.3D, and 3.5D integrated circuit technologies. He is a fellow of the [[Organization:Institute of Electrical and Electronics Engineers|Institute of Electrical and Electronics Engineers]] (IEEE) and the [[Organization:American Society of Mechanical Engineers|American Society of Mechanical Engineers]] (ASME). He has received the Worcester Reed Warner Medal and the Avram Bar-Cohen Medal from ASME. he is also the recipient of IEEE's Rao Tummala Electronics Packaging Award and the Meritorious Achievement Award in Continuing Education.

==Education==
Lau earned a B.S. in Civil Engineering from National Taiwan University in 1970. He received an M.S. in Structural Mechanics from the University of British Columbia in 1973 and an M.S. in Engineering Physics from the University of Wisconsin-Madison in 1974. Later, he completed his [[Ph.D.]] in Theoretical and Applied Mechanics from the University of Illinois in 1977. He obtained an M.S. in Management Science from [[Organization:Fairleigh Dickinson University|Fairleigh Dickinson University]] in 1981.<ref name=semi>{{Cite web|url=https://www.semiconchina.org/en/870 |title=Dr. John H. Lau |website=semiconchina|access-date=May 25, 2026}}</ref><ref name=dist/>

==Career==
Lau began his professional career as a research engineer at Exxon Production and Research Company between 1977 and 1978. He worked as a lead engineer at Ebasco from 1978 to 1980 and at Bechtel Power Corporation from 1981 to 1982. In 1984, he moved to Hewlett-Packard Labs, where he was a senior MTS/individual contributor till 1995.<ref name=semi/> Subsequently, he founded Express Packaging Systems<ref name=":0">{{cite web|url=https://ewh.ieee.org/soc/cpmt/newsletter/200012/lau.html|title=John H. Lau Receives IEEE EAB Meritorious Achievement Award in Continuing Education|publisher=IEEE|access-date=June 11, 2026}}</ref> and served as its president until 2000. He was employed as a senior interconnection specialist at [[Company:Agilent Technologies|Agilent Technologies]] from 2000 to 2006. He was a director of the System Packaging Lab at the Institute of Microelectronics between 2006 and 2009. In 2014, he became a senior technical advisor at ASM Pacific Technology,<ref name=semi/> where he worked for five years. He also worked as a specialist at the Industrial Technology Research Institute.<ref name=code>{{Cite web|url=https://events.vtools.ieee.org/m/505983 |title=Co-Packaged Optics – 3D Heterogeneous Integration of Photonic IC and Electronic IC|website=IEEE vTools Events |access-date=June 3, 2026}}</ref> He was a chief technology officer at Unimicron Technology Corporation from 2019 to 2021 and has since then been a senior special project assistant there.<ref>{{Cite web|url=https://calendar.hkust.edu.hk/events/distinguished-lecture-chiplet-design-and-heterogeneous-integration-packaging|title=Distinguished Lecture - Chiplet Design and Heterogeneous Integration Packaging|website=Hong Kong University of Science and Technology (HKUST) |date=17 January 2024 |access-date=May 31, 2026}}</ref>

Lau was the editor-in-chief of ''Circuit World'' from 1998 to 2000, and has been the general chair of the IEEE/EPS ECTC and IEMT. He was named a distinguished lecturer by ASME. He has also been a distinguished lecturer for IEEE/EPS since 1998.<ref name=dist>{{cite web|url=https://eps.ieee.org/education/distinguished-lecturer-program/1100-john-h-lau-bio/|title=John H. Lau Bio|access-date=May 31, 2026}}</ref><ref name=semi/>

==Research and work==
Lau's research has focused on advanced electronic packaging, heterogeneous integration, and reliability engineering for high-performance semiconductor systems. He has studied areas including flip-chip technology,<ref>{{cite journal |last1=Pecht |first1=M. |last2=Chang |first2=H |last3=Tsai |first3=M |title=Warpage Analysis of Flip-Chip PBGA Packages Subject to Thermal Loading |journal=IEEE Transactions on Device and Materials Reliability |date=2009 |volume=9 |issue=3 |page=419 |doi=10.1109/TDMR.2009.2023847 |bibcode=2009ITDMR...9..419T |url=https://ieeexplore.ieee.org/document/5033422https://ieeexplore.ieee.org/document/5033422}}</ref> [[Engineering:Three-dimensional integrated circuit|three-dimensional integrated circuit]] (3D ICs),<ref>{{cite journal |last1=Wang |first1=Shuai |last2=Feng |first2=Jia-yun |last3=Wang |first3=Wei |last4=Cao |first4=Wen-chao |last5=Ding |first5=Xin |last6=Wang |first6=Shang |last7=Tian |first7=Yan-hong |title=Growth kinetics of interfacial intermetallic compounds formed in SnPbInBiSb high entropy alloy soldered joints on Cu substrates |journal=Transactions of Nonferrous Metals Society of China |date=2024 |volume=34 |issue=11 |page=3650 |doi=10.1016/S1003-6326(24)66631-8 |url=https://www.sciencedirect.com/science/article/pii/S1003632624666318?ref=pdf_download&fr=RR-2&rr=a047351deec0d56b}}</ref> [[Engineering:System in a package|system-in-package]] (SiP),<ref>{{cite journal |last1=Topal |first1=Emre |last2=Gluch |first2=Jürgen |last3=Clausner |first3=André |last4=Cardoso |first4=André |last5=Zschech |first5=Ehrenfried |title=Determination of the Filler Distribution in an Epoxy Molding Compound Using High-Resolution X-Ray Computed Tomography |journal=IEEE Transactions on Components, Packaging and Manufacturing Technology |date=2021 |volume=11 |issue=3 |page=504 |doi=10.1109/TCPMT.2020.3048672 |bibcode=2021ITCPM..11..504T |issn=2156-3985 |url=http://publica.fraunhofer.de/documents/N-624627.html }}</ref> and structured reliability engineering framework.<ref>{{Cite journal |url=https://www.researchgate.net/publication/392380368 |title=A Conceptual Framework for Reliability-Centered Design of Mechanical Components Using FEA and DFMEA Integration |first1=Enoch Oluwadunmininu |last1=Ogunnowo |first2=Musa Adekunle |last2=Adewoyin |first3=Joyce Efekpogua |last3=Fiemotongha |first4=Thompson Odion |last4=Igunma |first5=Adeniyi K. |last5=Adeleke |journal=Journal of Frontiers in Multidisciplinary Research |volume=4 |issue=1 |page=346 |date=2023 |doi=10.54660/.JFMR.2023.4.1.342-361}}</ref> He has also studied heterogeneous integration packaging<ref>{{cite journal |last1=Castillo |first1=Stefanie |title=The DiQuNET Architecture for the Control of Quantum Processors: The Case Study of Trapped Ions |journal=IEEE Access |date=2026 |volume=14 |page=42258 |doi=10.1109/ACCESS.2026.3665594 |doi-access=free |bibcode=2026IEEEA..1442245C }}</ref> and wafer-level and panel-level packaging, focusing on mold-compound flow behavior, warpage control, and process-failure challenges.<ref>{{cite book |last1=Ecoiffier |first1=Diane |last2=Vernhes |first2=Pierre |last3=Ooi |first3=R.C. |last4=Braun |first4=Tanja |last5=Dreissigacker |first5=Marc |last6=Fu |first6=Haley |title=2020 IEEE 8th Electronics System-Integration Technology Conference (ESTC) |chapter=Experimental Study of Panel Level Packaging Warpage |date=2020 |page=1 |doi=10.1109/ESTC48849.2020.9229746 |bibcode=2020estc.conf..118E |isbn=978-1-7281-6293-5 }}</ref> Moreover, he has conducted research on thermal fatigue life prediction and solder joint reliability modeling.<ref>{{cite journal |last1=Su |first1=Sinan |last2=Akkara |first2=Francy John |last3=Thaper |first3=Ravinder |last4=Alkhazali |first4=Atif |last5=Hamasha |first5=Mohammad |last6=Hamasha |first6=Sa'd |title=A State-of-the-Art Review of Fatigue Life Prediction Models for Solder Joint |journal=Journal of Electronic Packaging |date=2019 |volume=141 |issue=4 |page=040802-10 |doi=10.1115/1.4043405 |url=https://asmedigitalcollection.asme.org/electronicpackaging/article-abstract/141/4/040802/726450/A-State-of-the-Art-Review-of-Fatigue-Life?redirectedFrom=fulltext}}</ref>

Lau's studies have examined thermal analysis and heat-transfer characteristics of TSV-based 3D integrated circuits,<ref>{{cite journal |last1=Guo |first1=Fen |last2=Suo |first2=Zhao-Jun |last3=Xi |first3=Xin |last4=Bi |first4=Yu |last5=Li |first5=Tuo |last6=Wang |first6=Changhong |last7=Su |first7=Kang |last8=Zou |first8=Xiaofeng |last9=Li |first9=Rengang |title=Recent Developments in Thermal Management of 3D ICs: A Review |journal=IEEE Access |date=2025 |volume=13 |page=94289 |doi=10.1109/ACCESS.2025.3569879 |doi-access=free |bibcode=2025IEEEA..1394286G }}</ref> the industrial readiness and commercial deployment of wafer-to-wafer hybrid bonding,<ref>{{cite book |last1=Alsukour |first1=Mohammad |last2=Valorge |first2=Olivier |last3=Faure |first3=Margot |last4=Vincent |first4=Loïc |last5=Milon |first5=Victor |last6=Chevalier |first6=Pascal |last7=Pistono |first7=Emmanuel |last8=Arnould |first8=Jean-Daniel |last9=Dubarry |first9=Christophe |chapter=Die-to-Wafer Hybrid Bonding Impact at MM-Wave Frequencies |title=2024 International 3D Systems Integration Conference (3DIC) |date=2024 |page=1 |doi=10.1109/3DIC63395.2024.10830066 |isbn=979-8-3315-1650-5 |url=https://hal.science/hal-04919954 |chapter-url=https://ieeexplore.ieee.org/document/10830066}}</ref> and co-packaged optics for high-bandwidth energy-efficient communication.<ref>{{cite journal |last1=Chen |first1=Young-Kai |title=Editorial Interview: Recent Industrial Applications and Outlook of Optoelectronic Technologies for AI/ML Applications |journal=IEEE Journal of Selected Topics in Quantum Electronics |date=2025 |volume=31 |issue=3: AI/ML Integrated Opto-electronics |page=2 |doi=10.1109/JSTQE.2025.3572652 |bibcode=2025IJSTQ..31S2652C |url=https://ieeexplore.ieee.org/document/11023043?denied= |issn=1558-4542}}</ref> His work has also focused on heterogeneous integration (HI)<ref>{{cite journal |last1=Manley |first1=Madison |last2=Victor |first2=Ashita |last3=Park |first3=Hyunggyu |last4=Kaul |first4=Ankit |last5=Kathaperumal |first5=Mohanalingam |last6=Bakir |first6=Muhannad S. |title=Heterogeneous Integration Technologies for Artificial Intelligence Applications |journal=IEEE Journal on Exploratory Solid-State Computational Devices and Circuits |date=2024 |volume=10 |page=89 |doi=10.1109/JXCDC.2024.3484958 |bibcode=2024IJESS..10...89M |url=https://ieeexplore.ieee.org/document/10731842/?denied=}}</ref> and fan-out packaging in relation to [[High-performance computing|high-performance computing]] and [[Artificial intelligence|artificial intelligence]] applications.<ref>{{cite book |last1=Kim |first1=Nahyeon |last2=Jung |first2=Haksoon |last3=Lee |first3=Yongwoo |last4=Eum |first4=Sungmin |last5=Han |first5=Yechan |last6=Park |first6=Hyunjin |last7=Park |first7=Yunsik |last8=Kwon |first8=Jimin |title=2024 IEEE 74th Electronic Components and Technology Conference (ECTC) |chapter=Micro-3D-Printed Packaging Substrates with Embedded Through Holes for Organic Interposers |date=2024 |page=710 |doi=10.1109/ECTC51529.2024.00115 |bibcode=2024ectc.conf..125K |isbn=979-8-3503-7598-5 }}</ref>

==Awards and honors==
*2000 – Meritorious Achievement Award in Continuing Education, IEEE<ref name=":0" />
*2013 – Rao Tummala Electronics Packaging Award, IEEE<ref>{{Cite web|url=https://corporate-awards.ieee.org/wp-content/uploads/tummala-rl.pdf |title=IEEE RAO R. TUMMALA ELECTRONICS PACKAGING AWARD RECIPIENTS|website=IEEE Corporate Awards |access-date=June 3, 2026}}</ref>
*2015 – Worcester Reed Warner Medal, ASME<ref>{{Cite web|url=https://www.asme.org/about-asme/honors-awards/literature-awards/worcester-reed-warner-medal|title=Worcester Reed Warner Medal
|website=The American Society of Mechanical Engineers |access-date=May 24, 2026}}</ref>
*2024 – Avram Bar-Cohen Medal, ASME<ref>{{Cite web|url=https://www.asme.org/about-asme/honors-awards/achievement-awards/avram-bar-cohen-memorial-medal |title=Avram Bar-Cohen Memorial Medal|website=The American Society of Mechanical Engineers |access-date=May 24, 2026}}</ref>
*2025 – C. P. Wong Global Electronic Packaging Award, International Conference on Electronic Packaging Technology<ref>{{Cite web|url=https://a.xiumius.cn/board/v5/2o6Rw/634210155?share_depth=1/|title=Recipient of 2025 CP Wong Global Electronic Packaging Award|website=International Conference on Electronic Packaging Technology |access-date=May 31, 2026}}</ref>
*2025 – Lifetime Achievement Award Recipient, International Microelectronics Assembly and Packaging Society (IMAPS)<ref name=imaps>{{Cite web|url=https://imaps.org/page/IMAPSAwardHistory|title=IMAPS Award History |website=IMAPS|access-date=May 31, 2026}}</ref>
*Fellow – IMAPS<ref name=imaps/>
*Fellow – IEEE<ref>{{Cite web|url=https://ieeexplore.ieee.org/author/37284312000 |title=John H. Lau|website=IEEE Xplore|access-date=May 24, 2026}}</ref>
*Fellow – ASME<ref>{{Cite web|url=https://www.asme.org/getmedia/74157266-4e5e-4f49-a84d-852345a20693/fellows-all-updated-december-2025_1.pdf|title=FELLOW|website= American Society of Mechanical Engineers Events|access-date=May 31, 2026}}</ref>

==References==
{{reflist}}

==External links==
*{{Google Scholar ID|u5gTZ0wAAAAJ&hl}}

{{DEFAULTSORT:Lau, John H}}

{{Sourceattribution|John H. Lau}}

Software:MiniMax H3

2026-08-23T21:07:37Z

MainEditor deleted page Software:MiniMax H3 No activity

Software:BeadPattern

2026-08-23T00:37:39Z

Add BeadPattern software article

← Older revision		Revision as of 19:37, 22 August 2026
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	~~{{Short description\|short description (<40 characters)}}~~		BeadPattern is a free bead pattern maker for creative design and craft projects. It can generate patterns with AI and convert photos into perler, hama, and fuse-bead designs with color codes and printable PDF templates.

	~~Here your article begins ..~~..		The tool helps makers turn an idea or an image into a practical bead pattern for planning and making. Its browser workflow keeps the process simple for people who want to explore bead art, refine a design, and prepare a pattern for printing.

			Learn more at [[https://beadpattern.net/\|BeadPattern]], the free AI and photo-to-bead pattern generator.
	~~<!-- Do not forget to add categories like~~
	[[~~Category~~:~~Name1~~] ~~[[Category:Name2~~]
	~~-->~~


	<!-- ~~Do not change below -->~~
	~~==References==~~
	~~{{reflist}}~~

	~~{{Sourceattribution\|Article\|1}}~~

Software:BeadPattern

2026-08-23T00:36:56Z

Created by maintenance script

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Engineering:Voltage and frequency scaling

2026-08-22T14:28:18Z

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	{{for\|the CPU design principle\|Frequency scaling}}		{{for\|the CPU design principle\|Frequency scaling}}
	~~{{redirect\|CPU throttling\|other uses\|Throttle (disambiguation)#Computing}}~~
	'''Dynamic frequency scaling''' and '''dynamic voltage scaling''' are techniques used primarily for [[Power management\|power management]] in [[Computer architecture\|computer architecture]]. Dynamic frequency scaling almost always appears in conjunction with [[Physics:Dynamic voltage scaling\|dynamic voltage scaling]], since higher frequencies require higher supply voltages for the digital circuit to yield correct results. The combined topic is known as '''dynamic voltage and frequency scaling''' ('''DVFS''').		'''Dynamic frequency scaling''' and '''dynamic voltage scaling''' are techniques used primarily for [[Power management\|power management]] in [[Computer architecture\|computer architecture]]. Dynamic frequency scaling almost always appears in conjunction with [[Physics:Dynamic voltage scaling\|dynamic voltage scaling]], since higher frequencies require higher supply voltages for the digital circuit to yield correct results. The combined topic is known as '''dynamic voltage and frequency scaling''' ('''DVFS''').

Engineering:Voltage and frequency scaling

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import

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{{for|the CPU design principle|Frequency scaling}}
{{redirect|CPU throttling|other uses|Throttle (disambiguation)#Computing}}
'''Dynamic frequency scaling''' and '''dynamic voltage scaling''' are techniques used primarily for [[Power management|power management]] in [[Computer architecture|computer architecture]]. Dynamic frequency scaling almost always appears in conjunction with [[Physics:Dynamic voltage scaling|dynamic voltage scaling]], since higher frequencies require higher supply voltages for the digital circuit to yield correct results. The combined topic is known as '''dynamic voltage and frequency scaling''' ('''DVFS''').

==Dynamic frequency scaling==
'''Dynamic frequency scaling''' (also known as '''CPU throttling''') is a power management technique in computer architecture whereby the [[Clock rate|frequency]] of a microprocessor can be automatically adjusted "on the fly" depending on the actual needs, to [[Engineering:Power management integrated circuit|conserve power]] and reduce the amount of heat generated by the chip. Dynamic frequency scaling helps preserve battery on mobile devices and decrease cooling cost and noise on [[Engineering:Quiet PC|quiet computing settings]], or can be useful as a security measure for overheated systems (e.g. after poor [[Engineering:Overclocking|overclocking]]).

=== Operation ===
The dynamic power (''switching power'') dissipated by a chip is ''C·V2·A·f'', where C is the [[Physics:Capacitance|capacitance]] being switched per clock cycle, V is [[Physics:Voltage|voltage]], A is the ''activity factor''<ref name="ActivityFactor">{{cite journal | title = Timing-aware power-optimal ordering of signals | author = K. Moiseev, A. Kolodny and S. Wimer | journal = ACM Transactions on Design Automation of Electronic Systems |volume=13 |issue=4 |date=September 2008| pages = 1–17 | doi = 10.1145/1391962.1391973 | s2cid = 18895687 }}</ref> indicating the average number of switching events per clock cycle by the transistors in the chip (as a unitless quantity) and f is the clock frequency.<ref>{{Cite book|first=J. M.|last= Rabaey|title= Digital Integrated Circuits|publisher= Prentice Hall|year= 1996}}</ref>

Voltage is therefore the main determinant of power usage and heating.<ref>{{cite web|url=https://software.intel.com/en-us/blogs/2014/02/19/why-has-cpu-frequency-ceased-to-grow|author= Victoria Zhislina|date=2014-02-19|title=Why has CPU frequency ceased to grow?|publisher=Intel}}</ref> The voltage required for stable operation is determined by the frequency at which the circuit is clocked, and can be reduced if the frequency is also reduced.<ref>{{Cite web |last=Le Sueur |first=Etienne |last2=Heiser |first2=Gernot |title=Dynamic Voltage and Frequency Scaling: The Laws of Diminishing Returns |url=https://www.usenix.org/legacy/events/hotpower/tech/full_papers/LeSueur.pdf |access-date=28 Oct 2025 |website=usenix.org}}</ref> Dynamic power alone does not account for the total power of the chip, however, as there is also static power, which is primarily because of various leakage currents. Due to static power consumption and asymptotic execution time it has been shown that the energy consumption of software shows convex energy behavior, i.e., there exists an optimal CPU frequency at which energy consumption is minimized.<ref>{{cite arXiv | title = The Energy/Frequency Convexity Rule: Modeling and Experimental Validation on Mobile Devices |year=2014 | eprint = 1401.4655|author1=Karel De Vogeleer |last2=Memmi |first2=Gerard |last3=Jouvelot |first3=Pierre |last4=Coelho |first4=Fabien |class=cs.OH }}</ref>
Leakage current has become more and more important as transistor sizes have become smaller and threshold voltage levels are reduced. A decade ago, dynamic power accounted for approximately two-thirds of the total chip power. The power loss due to leakage currents in contemporary CPUs and SoCs tend to dominate the total power consumption. In the attempt to control the leakage power, [[Engineering:High-κ dielectric|high-k metal-gates]] and power gating have been common methods.

Dynamic voltage scaling is another related power conservation technique that is often used in conjunction with frequency scaling, as the frequency that a chip may run at is related to the operating voltage.

The efficiency of some electrical components, such as voltage regulators, decreases with increasing temperature, so the power usage may increase with temperature. Since increasing power use may increase the temperature, increases in voltage or frequency may increase system power demands even further than the CMOS formula indicates, and vice versa.<ref>{{cite web | url = http://www.silentpcreview.com/article821-page5.html | title = Asus EN9600GT Silent Edition Graphics Card | author = Mike Chin | page = 5 | work = Silent PC Review | access-date = 21 April 2008}}</ref><ref name="SPCRNewLevels">{{cite web | url = http://www.silentpcreview.com/article814-page1.html | title = 80 Plus expands podium for Bronze, Silver & Gold | author = Mike Chin | work = Silent PC Review | date = 19 March 2008 | access-date = 21 April 2008 }}</ref>

=== Standard interface ===

[[ACPI]] 1.0 (1996) defines a way for a CPU to go to idle "C states", but defines no frequency-scaling system.

ACPI 2.0 (2000) introduces a system of ''P states'' (power-performance states) that a processor can use to communicate its possible frequency–power settings to the OS. The operating system then sets the speed as needed by switching between these states. Throttling technology such as SpeedStep, PowerNow!/Cool'n'Quiet, and PowerSaver all work through P states. There is a limit of 16 states maximum.<ref>{{cite web | url = http://www.acpi.info/DOWNLOADS/ACPIspec30.pdf | title = Advanced Configuration and Power Interface Specification, Revision 3.0, Section 2.6 Device and Processor Performance State Definitions | date = 2004-09-02 | website = ACPI.info | page = 23 | archive-date = November 28, 2015 | archive-url = https://web.archive.org/web/20151128143452/http://www.acpi.info/DOWNLOADS/ACPIspec30.pdf }}</ref>

ACPI 5.0 (2011) introduces '''collaborative processor performance control''' ('''CPPC'''), exposing hundreds of performance levels to the OS for selection in the form of a "performance level" abstracted away from the frequency. This abstraction provides leeway for the processor to adjust its workings (C-states) in ways other than just the frequency (P-states).<ref>{{cite web |title=Collaborative Processor Performance Control (CPPC) — The Linux Kernel documentation |url=https://www.kernel.org/doc/html/latest/admin-guide/acpi/cppc_sysfs.html |website=www.kernel.org }}</ref><ref>{{cite web |title=8.4. Declaring Processors |url=https://uefi.org/htmlspecs/ACPI_Spec_6_4_html/08_Processor_Configuration_and_Control/declaring-processors.html#collaborative-processor-performance-control |website=ACPI Specification 6.4 documentation}}</ref><ref>{{cite web |title=Overview about power and performance tuning for the Windows Server |url=https://learn.microsoft.com/en-us/windows-server/administration/performance-tuning/hardware/power/power-performance-tuning |website=learn.microsoft.com |date=29 August 2022 }}</ref>

=== Autonomous frequency scaling ===

A number of modern CPUs can perform frequency scaling autonomously, using a performance level range and a "efficiency/performance preference" hint from the OS.

* Intel CPUs starting with [[Skylake (microarchitecture)|Skylake]] support ''hardware-managed P-states'' aka ''Speed Shift'', It based on CPPC protocol, and it using [[Model-specific register|model-specific register]] as the control channel.<ref>{{man|8|x86_energy_perf_policy|Linux}}</ref><ref>{{cite web |title=intel_pstate CPU Performance Scaling Driver — The Linux Kernel documentation |url=https://www.kernel.org/doc/html/v4.19/admin-guide/pm/intel_pstate.html |website=www.kernel.org}}</ref>
* AMD CPUs starting with [[Engineering:Zen 2|Zen 2]] supports a similar feature. It depends on CPPC being enabled. The preferred communication channel is a MSR (different from the Intel one) introduced in Zen 3; Zen 2 units use the ACPI AML method.<ref>{{cite web |title=amd-pstate CPU Performance Scaling Driver — The Linux Kernel documentation |url=https://docs.kernel.org/admin-guide/pm/amd-pstate.html |website=docs.kernel.org}}</ref>

===Performance impact===
Dynamic frequency scaling reduces the number of instructions a processor can issue in a given amount of time, thus reducing performance. Hence, it is generally used when the workload is not CPU-bound.

Dynamic frequency scaling by itself is rarely worthwhile as a way to conserve switching power. Saving the highest possible amount of power requires dynamic voltage scaling too, because of the V2 component and the fact that modern CPUs are strongly optimized for low power idle states. In most constant-voltage cases, it is more efficient to run briefly at peak speed and stay in a deep idle state for longer time (called "[[Race to sleep|race to idle]]" or computational sprinting), than it is to run at a reduced clock rate for a long time and only stay briefly in a light idle state. However, reducing voltage along with clock rate can change those trade-offs.

A related-but-opposite technique is [[Engineering:Overclocking|overclocking]], whereby processor performance is increased by ramping the processor's (dynamic) frequency beyond the manufacturer's design specifications.

One major difference between the two is that in modern PC systems overclocking is mostly done over the [[Engineering:Front Side Bus|Front Side Bus]] (mainly because the multiplier is normally locked), but dynamic frequency scaling is done with the [[Engineering:CPU multiplier|multiplier]]. Moreover, overclocking is often static, while dynamic frequency scaling is always dynamic. Software can often incorporate overclocked frequencies into the frequency scaling algorithm, if the chip degradation risks are allowable.

===Support across vendors===

==== Intel ====
[[Company:Intel|Intel]]'s CPU throttling technology, [[Engineering:SpeedStep|SpeedStep]], is used in its mobile and desktop CPU lines.

==== AMD ====
[[Engineering:AMD|AMD]] employs two different CPU throttling technologies. AMD's [[Engineering:Cool'n'Quiet|Cool'n'Quiet]] technology is used on its desktop and server processor lines. The aim of Cool'n'Quiet is not to save battery life, as it is not used in AMD's mobile processor line, but instead with the purpose of producing less heat, which in turn allows the system fan to spin down to slower speeds, resulting in cooler and quieter operation, hence the name of the technology. AMD's [[Engineering:PowerNow!|PowerNow!]] CPU throttling technology is used in its mobile processor line, though some supporting CPUs like the [[Engineering:AMD K6-2|AMD K6-2]]+ can be found in desktops as well.

[[Engineering:AMD PowerTune|AMD PowerTune]] and AMD ZeroCore Power are dynamic frequency scaling technologies for GPUs.

==== VIA Technologies ====
[[Company:VIA Technologies|VIA Technologies]] and [[Company:Zhaoxin|Zhaoxin]] processors use a technology named [[Engineering:LongHaul|LongHaul]] (PowerSaver), while [[Company:Transmeta|Transmeta]]'s version was called [[Engineering:LongRun|LongRun]].

The 36-processor [[Asynchronous array of simple processors|AsAP 1]] chip is among the first multi-core processor chips to support completely unconstrained clock operation (requiring only that frequencies are below the maximum allowed) including arbitrary changes in frequency, starts, and stops. The 167-processor [[Asynchronous array of simple processors|AsAP 2]] chip is the first multi-core processor chip which enables individual processors to make fully unconstrained changes to their own clock frequencies.

According to the [[ACPI]] Specs, the C0 working state of a modern-day CPU can be divided into the so-called "P"-states (performance states) which allow clock rate reduction and "T"-states (throttling states) which will further throttle down a CPU (but not the actual clock rate) by inserting STPCLK (stop clock) signals and thus omitting duty cycles.

==== ARM ====
Different ARM-based systems on chip provide CPU and GPU throttling.

==Dynamic voltage scaling==
'''Dynamic voltage scaling''' is a [[Power management|power management]] technique in which the [[Physics:Voltage|voltage]] used in a component is increased or decreased, depending upon circumstances. Dynamic voltage scaling to increase voltage is known as '''overvolting'''; dynamic voltage scaling to decrease voltage is known as '''undervolting'''. Undervolting is done in order to [[Physics:Energy conservation|conserve power]], particularly in [[Engineering:Laptop|laptop]]s and other [[Engineering:Mobile device|mobile device]]s, where energy comes from a [[Physics:Electric battery|battery]] and thus is limited, or in rare cases, to increase reliability. Overvolting is done in order to support higher frequencies for [[Computer performance|performance]].

The term "overvolting" is also used to refer to increasing static operating voltage of [[Computer|computer]] components to allow operation at higher speed ([[Engineering:Overclocking|overclocking]]).

===Background===
[[Engineering:MOSFET|MOSFET]]-based digital circuits operate using voltages at circuit nodes to represent logical state. The voltage at these nodes switches between a high voltage and a low voltage during normal operation—when the inputs to a [[Engineering:Logic gate|logic gate]] transition, the transistors making up that gate may toggle the gate's output.

Toggling a MOSFET's state requires changing its gate voltage from below the transistor's [[Physics:Threshold voltage|threshold voltage]] to above it (or from above it to below it). However, changing the gate's voltage requires charging or discharging the [[Physics:Capacitance|capacitance]] at its node. This capacitance is the sum of capacitances from various sources: primarily transistor [[Engineering:Gate capacitance|gate capacitance]], [[Physics:Diffusion capacitance|diffusion capacitance]], and wires ([[Engineering:Coupling (electronics)|coupling capacitance]]).

Higher supply voltages result in faster [[Slew rate|slew rate]] (rate of change of voltage per unit of time) when charging and discharging, which allows for quicker transitioning through the MOSFET's threshold voltage. Additionally, the more the gate voltage exceeds the threshold voltage, the lower the resistance of the transistor's conducting channel. This results in a lower [[Engineering:RC time constant|RC time constant]] for quicker charging and discharging of the capacitance of the subsequent logic stage. Quicker transitioning afforded by higher supply voltages allows for operating at higher frequencies.

===Methods===
Many modern components allow voltage regulation to be controlled through software (for example, through the [[BIOS]]). It is usually possible to control the voltages supplied to the CPU, RAM, [[Engineering:Peripheral Component Interconnect|PCI]], and [[Engineering:PCI Express|PCI Express]] (or [[Engineering:Accelerated Graphics Port|AGP]]) port through a PC's BIOS.

However, some components do not allow software control of supply voltages, and hardware modification is required by overclockers seeking to overvolt the component for extreme overclocks. [[Engineering:Video card|Video card]]s and [[Engineering:Motherboard|motherboard]] northbridges are components which frequently require hardware modifications to change supply voltages. These modifications are known as "voltage mods" or "Vmod" in the overclocking community.

===Undervolting===
Undervolting is reducing the voltage of a component, usually the processor, reducing temperature and cooling requirements, and possibly allowing a fan to be omitted. Just like overclocking, undervolting is highly subject to the so-called silicon lottery: one CPU can undervolt slightly better than the other and vice versa.

===Power===
{{main | CPU power dissipation }}

The ''switching power'' dissipated by a chip using static [[Engineering:CMOS|CMOS]] gates is <math>\alpha \cdot C \cdot V^2 \cdot f</math>, where <math>C</math> is the [[Physics:Capacitance|capacitance]] being switched per clock cycle, <math>V</math> is the supply [[Physics:Voltage|voltage]], <math>f</math> is the switching frequency,<ref>J. M. Rabaey. Digital Integrated Circuits. Prentice Hall, 1996.</ref> and <math>\alpha </math> is the activity factor. Since <math>V</math> is squared, this part of the power consumption decreases quadratically with voltage. The formula is not exact however, as many modern chips are not implemented using 100% CMOS, but also use special memory circuits, [[Dynamic logic (digital electronics)|dynamic logic]] such as [[Domino logic|domino logic]], etc. Moreover, there is also a static leakage current, which has become more and more accentuated as feature sizes have become smaller (below 90 nanometres) and threshold levels lower.

Accordingly, dynamic voltage scaling is widely used as part of strategies to manage switching power consumption in battery powered devices such as cell phones and laptop computers. Low voltage modes are used in conjunction with lowered clock frequencies to minimize power consumption associated with components such as CPUs and DSPs; only when significant computational power is needed will the voltage and frequency be raised.

Some peripherals also support low voltage operational modes. For example, low power MMC and SD cards can run at 1.8 V as well as at 3.3 V, and driver stacks may conserve power by switching to the lower voltage after detecting a card which supports it.

When leakage current is a significant factor in terms of power consumption, chips are often designed so that portions of them can be powered completely off. This is not usually viewed as being dynamic voltage scaling, because it is not transparent to software. When sections of chips can be turned off, as for example on [[Company:Texas Instruments|TI]] [[Engineering:OMAP|OMAP3]] processors, drivers and other support software need to support that.

===Program execution speed===
The speed at which a digital circuit can switch states - that is, to go from "low" (VSS) to "high" (VDD) or vice versa - is proportional to the voltage differential in that circuit. Reducing the voltage means that circuits switch slower, reducing the maximum frequency at which that circuit can run. This, in turn, reduces the rate at which program instructions that can be issued, which may increase run time for program segments which are sufficiently CPU-bound.

This again highlights why dynamic voltage scaling is generally done in conjunction with dynamic frequency scaling, at least for CPUs. There are complex tradeoffs to consider, which depend on the particular system, the load presented to it, and power management goals. When quick responses are needed (e.g. Mobile Sensors and [[Context-aware pervasive systems|Context-Aware Computing]]), clocks and voltages might be raised together. Otherwise, they may both be kept low to maximize battery life.

===Implementations===
The 167-processor [[Asynchronous array of simple processors|AsAP 2]] chip enables individual processors to make extremely fast (on the order of 1-2ns) and locally controlled changes to their own supply voltages. Processors connect their local power grid to either a higher (VddHi) or lower (VddLow) supply voltage, or can be cut off entirely from either grid to dramatically cut leakage power.

Another approach uses per-core on-chip switching regulators for dynamic voltage and frequency scaling (DVFS).<ref>
Wonyoung Kim, Meeta S. Gupta, Gu-Yeon Wei and David Brooks.
[http://www.eecs.harvard.edu/~meeta/my_papers/hpca08_onchipvrm.pdf "System Level Analysis of Fast, Per-Core DVFS using On-Chip Switching Regulators"].
2008.
</ref>

===Operating system API===
Unix system provides a userspace governor, allowing to modify the CPU frequencies{{cn|date=March 2024}} (though limited to hardware capabilities).

===System stability===
[[Dynamic frequency scaling]] is another power conservation technique that works on the same principles as dynamic voltage scaling. Both dynamic voltage scaling and dynamic frequency scaling can be used to prevent computer system overheating, which can result in program or operating system [[Crash (computing)|crashes]], and possibly hardware damage. Reducing the voltage supplied to the CPU below the manufacturer's recommended minimum setting can result in system instability.

===Temperature===
The efficiency of some electrical components, such as voltage regulators, decreases with increasing temperature, so the power used may increase with temperature causing [[Astronomy:Thermal runaway|thermal runaway]]. Increases in voltage or frequency may increase system power demands even faster than the CMOS formula indicates, and vice versa.<ref>{{cite web | url = http://www.silentpcreview.com/article821-page5.html | title = Asus EN9600GT Silent Edition Graphics Card | author = Mike Chin | page = 5 | work = Silent PC Review | access-date = 2008-04-21}}</ref><ref name="SPCRNewLevels"/>

===Caveats===
The primary caveat of overvolting is increased heat: the power dissipated by a circuit increases with the square of the voltage applied, so even small voltage increases significantly affect power. At higher temperatures, transistor performance is adversely affected, and at some threshold, the performance reduction due to the heat exceeds the potential gains from the higher voltages. Overheating and damage to circuits can occur very quickly when using high voltages.

There are also longer-term concerns: various adverse device-level effects such as hot carrier injection and [[Chemistry:Electromigration|electromigration]] occur more rapidly at higher voltages, decreasing the lifespan of overvolted components.

In order to mitigate the increased heat from overvolting, it's recommended to use [[Physics:Liquid cooling|liquid cooling]] to achieve higher ceilings and thresholds than you normally would with an aftermarket cooler. Also known as 'all-in-one' (AIO) coolers, they offer a far more effective method of unit cooling by relocating heat outside a computer case via the fans on the radiator whereas air cooling only disperses heat from the affected unit, increasing overall ambient temperatures.<ref>{{cite web | url = https://www.intel.com/content/www/us/en/gaming/resources/cpu-cooler-liquid-cooling-vs-air-cooling.html | title = CPU Cooler: Liquid Cooling vs Air Cooling | author = Intel| access-date = 2024-03-31}}</ref>

== See also ==
* [[Physics:Adaptive voltage scaling|Adaptive voltage scaling]] (AVS)
* [[Engineering:AMD PowerTune|AMD PowerTune]]/[[Engineering:AMD PowerPlay|AMD PowerPlay]] (graphics)
* [[Engineering:AMD Turbo Core|AMD Turbo Core]] (CPUs)
* [[Engineering:Clock gating|Clock gating]]
* [[Engineering:Cool'n'Quiet|AMD Cool'n'Quiet]] (desktop CPUs)
* Energy–delay product (EDP)
* [[HLT (x86 instruction)]]
* [[Engineering:Intel Turbo Boost|Intel Turbo Boost]] (CPUs)
* [[Physics:Overvoltage|Overvoltage]]
* [[Engineering:Power gating|Power gating]]
* [[Engineering:Power ramp|Power ramp]]
* [[Power–delay product]] (PDP)
* [[Engineering:PowerNow!|AMD PowerNow!]] (laptop CPUs)
* [[Engineering:SpeedStep|Intel SpeedStep]] (CPUs)
* Switched-mode power supply applications (SMPS) applications
* Switching energy
* Undervoltage
* Voltage optimization

==References==
{{reflist}}

==Further reading==
* {{cite book |author-first=Vincent C. |author-last=Gaudet |chapter=Chapter 4.1. Low-Power Design Techniques for State-of-the-Art CMOS Technologies |editor-first=Bernd |editor-last=Steinbach |title=Recent Progress in the Boolean Domain |publisher=[[Company:Cambridge Scholars Publishing|Cambridge Scholars Publishing]] |publication-place=Newcastle upon Tyne, UK |location=Freiberg, Germany |edition=1 |date=2014-04-01 |orig-date=2013-09-25 |isbn=978-1-4438-5638-6 |pages=187–212 |url=https://books.google.com/books?id=_pwxBwAAQBAJ |access-date=2019-08-04}} [https://web.archive.org/web/20210228020207/https://www.tau.ac.il/~ilia1/publications/rpbd_book.pdf] (xxx+428 pages)

{{Computer processor power management technologies}}
{{CPU technologies}}

{{DEFAULTSORT:Dynamic Frequency Scaling}}
[[Category:Clock signal]]
[[Category:Energy conservation]]
[[Category:Central processing unit]]
[[Category:Computer hardware tuning]]

{{Sourceattribution|Voltage and frequency scaling}}

Software:MALDA (programming language)

2026-08-22T14:27:20Z

MainEditor moved page Software:MALDA (programming language) to MALDA (programming language) without leaving a redirect

New page

----

{{Short description|Open-source programming language for agents, web apps and workflows}}
{{Draft topics|software|computing|technology}}
{{AfC topic|other}}


{{Draft article|subject=software}}

{{Infobox programming language
| name = MALDA
| logo =
| paradigm = Multi-paradigm: [[Imperative programming|imperative]], [[Object-oriented programming|object-oriented]], [[Concurrent computing|concurrent]]
| designed_by = Andrea Maldini
| developer = Andrea Maldini
| released = {{Start date and age|2026|07|31}}
| latest release version = 1.0.1
| latest release date = {{Start date and age|2026|08|18}}
| typing = Dynamic, with optional type hints
| implementations = MALDA interpreter and C# / JavaScript transpilers
| platform = [[.NET|.NET]] 8
| operating system = [[Software:Microsoft Windows|Windows]], [[Software:Linux|Linux]], [[Software:MacOS|macOS]] (Desktop IDE is Windows-only)
| license = Dual [[Software:MIT License|MIT]] or [[Software:Apache License 2.0|Apache License 2.0]]; separate runtime exception for compiled programs
| file_ext = .malda
| website = {{URL|https://github.com/amaldini/maldalang}}
}}

'''MALDA''' ('''Multi Agent Language with Development Automation''') is an [[Open-source software|open-source]] [[Programming language|programming language]] and toolchain for writing programs that combine ordinary control flow with [[Large language model|large language model]] prompts, software agents, HTTP services and long-running workflows.<ref name="readme">{{cite web |title=MALDA README |url=https://github.com/amaldini/maldalang/blob/main/README.md |website=GitHub |access-date=18 August 2026}}</ref> Source files use the {{code|.malda}} extension. The language is dynamically typed at run time; optional type annotations are used by the editor and, in transpile/publish mode, as a compile-time check rather than as a full static type system.<ref name="readme"/><ref name="spec">{{cite web |title=Malda Language Specification 1.0 — Tier 0 Core |url=https://github.com/amaldini/maldalang/blob/main/docs/spec/malda-language-1.0.md |website=GitHub |date=12 August 2026 |access-date=18 August 2026}}</ref>

Programs may be executed by a tree-walking interpreter, [[Source-to-source compiler|transpiled]] to [[C Sharp (programming language)|C#]] and built as a .NET executable, or compiled to a [[JavaScript]] subset for the browser.<ref name="arch">{{cite web |title=MALDA architecture (OSS core) |url=https://github.com/amaldini/maldalang/blob/main/docs/architecture.md |website=GitHub |access-date=18 August 2026}}</ref> The reference implementation is written in C# on [[.NET|.NET]] 8 and is dual-licensed under the MIT License or Apache License 2.0, at the user's option.<ref name="readme"/>

== History ==
MALDA was designed and is maintained by Andrea Maldini, a business-software developer working in C#, [[Java (programming language)|Java]] and VB.NET, as a first language implementation rather than as a research compiler project.<ref name="readme"/> Public project materials describe the work as an attempt to treat prompts, tools, agents, HTTP endpoints and durable workflows as grammar instead of library glue, after first trying the same ideas as libraries.<ref name="announce">{{cite web |title=MALDA — public announcement copy |url=https://github.com/amaldini/maldalang/blob/main/docs/announcement.md |website=GitHub |access-date=18 August 2026}}</ref> Those materials also cite Geoff Huntley's "Ralph Wiggum" agent loop and Huntley's esoteric language ''cursed'' as the prompt to attempt a language at all, not as a syntactic parent.<ref name="announce"/>

A draft of the Tier 0 language specification was dated 4 June 2026.<ref name="spec"/> The open-source core was first published on GitHub on 31 July 2026 as version 0.1.0, with a runtime, C# and JavaScript transpilers, command-line interface, IDEs, language server and VS Code extension.<ref name="v010">{{cite web |title=MALDA 0.1.0 |url=https://github.com/amaldini/maldalang/blob/main/docs/releases/v0.1.0.md |website=GitHub |access-date=18 August 2026}}</ref><ref name="gitinit">{{cite web |title=Initial public MALDA core, dual licensed MIT OR Apache-2.0 |url=https://github.com/amaldini/maldalang/commit/ |website=GitHub |date=31 July 2026 |access-date=18 August 2026}}</ref> The specification was marked Final 1.0 on 12 August 2026.<ref name="spec"/> Toolchain version 1.0.0, tagged 17 August 2026, aligned the CLI and Desktop IDE version numbers with that specification and made type-hint errors refuse emit on transpile and publish.<ref name="v100">{{cite web |title=MALDA 1.0.0 |url=https://github.com/amaldini/maldalang/blob/main/docs/releases/v1.0.0.md |website=GitHub |date=17 August 2026 |access-date=18 August 2026}}</ref> Version 1.0.1 followed on 18 August 2026 as a patch release; it is not a new specification line.<ref name="v101">{{cite web |title=MALDA 1.0.1 |url=https://github.com/amaldini/maldalang/blob/main/docs/releases/v1.0.1.md |website=GitHub |date=18 August 2026 |access-date=18 August 2026}}</ref>

The public repository is the language core. Separate product applications built on MALDA are kept out of that tree.<ref name="readme"/>

== Design ==
MALDA is a general-purpose language with a C-like surface: {{code|var}} bindings, {{code|function}} declarations ({{code|fn}} and {{code|def}} are syntax errors), classes, exceptions, {{code|match}} expressions, sum types, {{code|async}}/{{code|await}}, and a namespaced standard library under {{code|io}}, {{code|math}} and {{code|str}} among others.<ref name="spec"/><ref name="readme"/> Functions are declared at top level; nested function statements are not part of the language.<ref name="spec"/> Composition across files uses parse-time {{code|include}} or runtime {{code|import}} / selective {{code|import { … } from}}.<ref name="announce"/>

The project's stated design split is that relatively stable ideas (prompt templates, actor message passing, workflow {{code|step}}/{{code|retry}}/{{code|compensate}}) are syntax, while model providers, tool protocols and model names remain in the library layer.<ref name="announce"/> An earlier {{code|chain}} keyword for LLM pipelines was removed in favour of ordinary functions and the pipe operator.<ref name="announce"/>

=== Type system ===
Run-time values have a single kind (integer, float, string, boolean, null, array, object, function, class, variant, task, actor, or actor reference).<ref name="spec"/> Integers are 32-bit signed and overflow throws; floats are IEEE doubles; strings are UTF-16.<ref name="spec"/>

Type annotations such as {{code|var n: int {{=}} 0}} and {{code|function add(a: int) -> int}} are optional. They feed the language server and desktop editor, which report mismatches as errors by default; they are not enforced by the interpreter at run time.<ref name="readme"/><ref name="spec"/> {{code|malda compile --mode transpile}} and {{code|publish}} refuse to emit when those errors are present, unless {{code|--lenient-types}} is passed.<ref name="v100"/> {{code|schema}} declarations and {{code|validate}} check JSON-shaped data; sum types and {{code|match}} cover tagged unions.<ref name="spec"/>

=== Prompts, agents and tools ===
A {{code|prompt}} is a named declaration with untyped parameters and interpolated role sections. Calling it without {{code|await}} returns the rendered template (usable without an API key); calling it with {{code|await}} sends it to a configured model. A {{code|-> SchemaName}} binding validates model JSON against a declared schema.<ref name="readme"/> Functions may be exposed as agent tools with {{code|@Tool}} or over the [[Model Context Protocol]] with {{code|@MCPTool}}.<ref name="announce"/>

LLM features use OpenRouter when an API key is configured, otherwise a small local [[GGUF]] model (Qwen2.5-0.5B) downloaded on first use as an offline fallback.<ref name="readme"/>

=== Web and user interface ===
HTTP APIs and pages are declared with decorators ({{code|@GET}}, {{code|@POST}}, {{code|@PAGE}}, {{code|@AIPAGE}} and similar) on host objects such as {{code|HttpServer}} and {{code|RestServer}}.<ref name="readme"/> Server-driven {{code|ui.*}} trees are hosted by a separate UI host runtime. This web stack is a language feature and is distinct from the browser-based MALDA IDE.<ref name="arch"/>

=== Actors ===
Actors are a Tier 0 construct: {{code|actor}} declarations, {{code|spawn}}, {{code|send}}, {{code|receive}} and {{code|self}}.<ref name="spec"/> Message handlers are written with {{code|on}} over private state.<ref name="announce"/>

=== Workflows ===
Durable workflows are blocks of statements using reserved words including {{code|step}}, {{code|retry}}, {{code|compensate}}, {{code|approval}}, {{code|wait}} and {{code|timeout}}.<ref name="announce"/> Recovery is step-level memoization to a local [[Software:SQLite|SQLite]] file ({{code|./.malda/workflows.db}}): a completed step returns its persisted JSON-shaped result instead of re-running.<ref name="announce"/> Non-deterministic and side-effecting built-in names are refused outside {{code|step}} by a fixed deny-list; the implementation is a single-writer, single-machine store, not a clustered workflow engine.<ref name="announce"/><ref name="readme"/>

== Example ==
The following program prints a greeting:<ref name="hello">{{cite web |title=hello_world.malda |url=https://github.com/amaldini/maldalang/blob/main/Examples/Basics/hello_world.malda |website=GitHub |access-date=18 August 2026}}</ref>

<syntaxhighlight lang="text">
io.print("Hello, World!");
</syntaxhighlight>

A characteristic prompt example binds a template to a schema. Without {{code|await}}, the call is a rendered template; {{code|validate}} performs the same check that {{code|await}} would apply to model JSON:<ref name="readme"/>

<syntaxhighlight lang="text">
schema Review {
summary: string;
issues: string[];
}

prompt codeReview(code, language) -> Review {
system: "You are an expert reviewer of {language}.",
user: "Review this {language} code:\n\n{code}"
}

var rendered = codeReview("function add(a, b) { return a + b; }", "javascript");
io.print(rendered.user);
</syntaxhighlight>

== Implementation ==
The reference toolchain is implemented in C# with a hand-written [[Recursive descent parser|recursive descent parser]]. The pipeline is lexer, parser and abstract syntax tree, then one of three backends: the interpreter, a C# transpiler, or a JavaScript / [[Software:Progressive web app|progressive web app]] transpiler.<ref name="arch"/><ref name="announce"/> Language intelligence (completions, diagnostics, hover) is shared across the Desktop IDE, Web IDE and language server.<ref name="arch"/>

The three backends are not equivalent. The JavaScript path is a documented browser subset: it does not include agents, HTTP servers or workflows.<ref name="readme"/> C# transpile covers the built-in registry for shipping .NET executables; interpreted and transpiled programs are compared on a curated set of examples for matching standard output.<ref name="arch"/>

The standard library is large (on the order of three hundred named built-ins in the project registry), covering strings, collections, files, HTTP, JSON, SQL, graphs and process control, with .NET interop as an escape hatch. There is no public package registry comparable to [[Software:Npm|npm]] or crates.io.<ref name="announce"/>

== Tooling ==
{| class="wikitable"
|-
! Tool !! Role
|-
| {{code|malda}} CLI || Interpret, compile/transpile, templates ({{code|malda new}}), workflow commands
|-
| Desktop IDE || Full Windows reference environment (WPF)
|-
| Web IDE || Browser learning playground (Blazor / Monaco); not feature-parity with Desktop
|-
| {{code|malda-lsp}} || [[Language Server Protocol]] host
|-
| {{code|malda debug-adapter}} || Debug Adapter Protocol for interpret-mode debugging (separate from the language server)
|-
| vscode-malda || Visual Studio Code / Cursor extension
|}

Self-contained release archives are published for Windows (CLI and Desktop IDE) and Linux (CLI).<ref name="readme"/> The HTML reference manual is published in English (canonical) and Italian.<ref name="readme"/> The repository also ships a compact language pack under {{code|docs/llm/}} intended for coding agents that have not seen MALDA in training data.<ref name="readme"/>

== Licensing ==
The core (runtime, compiler, IDEs, language server, reference manual and examples) is dual-licensed MIT OR Apache-2.0.<ref name="readme"/> Because the toolchain copies runtime helpers into compiled output, a runtime exception states that this does not impose attribution obligations on user programs.<ref name="runtime">{{cite web |title=MALDA Runtime Library Exception |url=https://github.com/amaldini/maldalang/blob/main/LICENSE-RUNTIME-EXCEPTION |website=GitHub |access-date=18 August 2026}}</ref> The name "MALDA" is asserted as a trademark of Andrea Maldini and is not granted by either copyright licence.<ref name="tm">{{cite web |title=The MALDA name |url=https://github.com/amaldini/maldalang/blob/main/TRADEMARK.md |website=GitHub |access-date=18 August 2026}}</ref> There is no contributor licence agreement.<ref name="readme"/>

== See also ==
* [[Ballerina (programming language)]]
* [[Model Context Protocol]]
* [[List of programming languages]]

== References ==
{{Reflist}}

== External links ==
* {{official website|https://github.com/amaldini/maldalang}}
* [https://amaldini.github.io/maldalang/ MALDA Reference Manual] (English)
* [https://amaldini.github.io/maldalang/it/ Manuale di riferimento MALDA] (Italian)

{{Programming languages}}

[[:Category:Dynamically typed programming languages]]
[[:Category:Concurrent programming languages]]
{{Sourceattribution|MALDA (programming language)}}

Company:Axiom Software Limited

2026-08-22T14:25:47Z

import

New page

{{Infobox company
| name = Axiom Software Limited
| logo =
| type = Private limited company
| industry = Software, Human Resources
| founded = 19 January 1994
| founder = Mark Housley, Paul Brookes
| hq_location_city = Manchester
| hq_location_country= United Kingdom
| key_people = Mark Housley (Managing Director)
| products = Discus Online, myDISCprofile, Axiom Discovery
| website = {{URL|https://www.axiomsoftware.com}}
}}

'''Axiom Software Limited''' is a British software development company headquartered in Manchester, England. Established in 1994, the company specializes in web-based [[Psychometrics|psychometrics]], talent management, and behavioral profiling platforms.<ref>{{cite web |title=AXIOM SOFTWARE LIMITED overview - Find and update company information |url=https://find-and-update.company-information.service.gov.uk/company/02888933 |publisher=Companies House |access-date=2026-03-23}}</ref>

== History ==
The company was incorporated on 19 January 1994 under the initial name Brookhous Systems Limited, before adopting the name Axiom Software Limited in September 1994.<ref>{{cite web |title=AXIOM SOFTWARE LIMITED filing history |url=https://find-and-update.company-information.service.gov.uk/company/02888933/filing-history |publisher=Companies House |access-date=2026-03-23}}</ref> The organization operates from its corporate office located at Empress Buildings, 380 Chester Road in Manchester.

== Products ==
Axiom Software Limited develops and maintains several digital assessment platforms, most notably '''Discus Online''', a multi-currency software platform used for global recruitment, candidate job-matching, employee assessments, and workplace relationship mapping based on the [[Social:DISC assessment|DISC assessment]] methodology. The company also operates myDISCprofile and the Axiom Discovery skills testing system.

== References ==
{{reflist}}

== References ==

{{reflist}}
{{Sourceattribution|Axiom Software Limited}}

Software:MALDA (programming language)

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Nonlocal symmetry

2026-08-22T14:23:41Z

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	In mathematical physics and the theory of differential equations, a '''nonlocal symmetry''' is a symmetry of a differential equation whose infinitesimal generator depends on integral or potential variables, rather than solely on the independent variables, the dependent variables, and a finite number of their derivatives. Unlike local symmetries (e.g., [[Lie point symmetry\|Lie point symmetries]] or contact symmetries), nonlocal symmetries cannot be detected within the standard finite-dimensional jet bundle formalism. They often arise from Bäcklund transformations, reciprocal transformations, Lax pairs, or from systematic constructions like conservation-law (CL) coverings and inverse potential systems (IPSs).<ref>{{Cite journal \|last1=Bluman \|first1=George W. \|last2=Yang \|first2=Zhengzheng \|date=2013-09-01 \|title=A symmetry-based method for constructing nonlocally related partial differential equation systems \|url=https://pubs.aip.org/jmp/article/54/9/093504/233198/A-symmetry-based-method-for-constructing \|journal=Journal of Mathematical Physics \|language=en \|volume=54 \|issue=9 \|article-number=093504 \|doi=10.1063/1.4819724 \|arxiv=1211.0100 \|bibcode=2013JMP....54i3504B \|issn=0022-2488}}</ref><ref>{{Cite journal \|last=Bazghandi \|first=Mustafa \|date=2026-04-29 \|title=A symmetry-based study of nonlocal structures in the modified Benjamin–Bona–Mahony equation \|url=https://doi.org/10.1140/epjp/s13360-026-07737-y \|journal=The European Physical Journal Plus \|language=en \|volume=141 \|issue=4 \|article-number=470 \|doi=10.1140/epjp/s13360-026-07737-y \|issn=2190-5444}}</ref>		In mathematical physics and the theory of differential equations, a '''nonlocal symmetry''' is a symmetry of a differential equation whose infinitesimal generator depends on integral or potential variables, rather than solely on the independent variables, the dependent variables, and a finite number of their derivatives. Unlike local symmetries (e.g., [[Lie point symmetry\|Lie point symmetries]] or contact symmetries), nonlocal symmetries cannot be detected within the standard finite-dimensional jet bundle formalism. They often arise from Bäcklund transformations, reciprocal transformations, Lax pairs, or from systematic constructions like conservation-law (CL) coverings and inverse potential systems (IPSs).<ref>{{Cite journal \|last1=Bluman \|first1=George W. \|last2=Yang \|first2=Zhengzheng \|date=2013-09-01 \|title=A symmetry-based method for constructing nonlocally related partial differential equation systems \|url=https://pubs.aip.org/jmp/article/54/9/093504/233198/A-symmetry-based-method-for-constructing \|journal=Journal of Mathematical Physics \|language=en \|volume=54 \|issue=9 \|article-number=093504 \|doi=10.1063/1.4819724 \|arxiv=1211.0100 \|bibcode=2013JMP....54i3504B \|issn=0022-2488}}</ref><ref>{{Cite journal \|last=Bazghandi \|first=Mustafa \|date=2026-04-29 \|title=A symmetry-based study of nonlocal structures in the modified Benjamin–Bona–Mahony equation \|url=https://doi.org/10.1140/epjp/s13360-026-07737-y \|journal=The European Physical Journal Plus \|language=en \|volume=141 \|issue=4 \|article-number=470 \|doi=10.1140/epjp/s13360-026-07737-y \|issn=2190-5444}}</ref>

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	[[Category:Lie groups]]		[[Category:Lie groups]]

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	{{Sourceattribution\|Nonlocal symmetry}}		{{Sourceattribution\|Nonlocal symmetry}}

Nonlocal symmetry

2026-08-22T14:22:48Z

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{{Multiple issues|
{{coi|date=May 2026}}
}}
In mathematical physics and the theory of differential equations, a '''nonlocal symmetry''' is a symmetry of a differential equation whose infinitesimal generator depends on integral or potential variables, rather than solely on the independent variables, the dependent variables, and a finite number of their derivatives. Unlike local symmetries (e.g., [[Lie point symmetry|Lie point symmetries]] or contact symmetries), nonlocal symmetries cannot be detected within the standard finite-dimensional jet bundle formalism. They often arise from Bäcklund transformations, reciprocal transformations, Lax pairs, or from systematic constructions like conservation-law (CL) coverings and inverse potential systems (IPSs).<ref>{{Cite journal |last1=Bluman |first1=George W. |last2=Yang |first2=Zhengzheng |date=2013-09-01 |title=A symmetry-based method for constructing nonlocally related partial differential equation systems |url=https://pubs.aip.org/jmp/article/54/9/093504/233198/A-symmetry-based-method-for-constructing |journal=Journal of Mathematical Physics |language=en |volume=54 |issue=9 |article-number=093504 |doi=10.1063/1.4819724 |arxiv=1211.0100 |bibcode=2013JMP....54i3504B |issn=0022-2488}}</ref><ref>{{Cite journal |last=Bazghandi |first=Mustafa |date=2026-04-29 |title=A symmetry-based study of nonlocal structures in the modified Benjamin–Bona–Mahony equation |url=https://doi.org/10.1140/epjp/s13360-026-07737-y |journal=The European Physical Journal Plus |language=en |volume=141 |issue=4 |article-number=470 |doi=10.1140/epjp/s13360-026-07737-y |issn=2190-5444}}</ref>

==Historical background==

During the twentieth century, researchers discovered that many important nonlinear equations possess hidden symmetries that cannot be represented solely in terms of local variables and their derivatives. Studies of integrable systems such as the Korteweg–de Vries (KdV) equation, nonlinear Schrödinger equation, and sine-Gordon equation revealed the existence of infinite-dimensional symmetry structures generated by nonlocal operators.<ref>{{Cite journal |last=Vinogradov |first=A. M. |date=1989-01-01 |title=Symmetries and conservation laws of partial differential equations: Basic notions and results |url=https://doi.org/10.1007/BF00131928 |journal=Acta Applicandae Mathematica |language=en |volume=15 |issue=1 |pages=3–21 |doi=10.1007/BF00131928 |issn=1572-9036}}</ref>

The modern geometric formulation of nonlocal symmetries emerged through the work of Vinogradov, Krasil'shchik, Bluman, Anco, Olver, and many others, who developed the theory of coverings, potential symmetries, and conservation-law-based symmetry methods .<ref>{{Cite book |last=Olver |first=Peter J. |title=Applications of Lie Groups to Differential Equations |date=1986 |publisher=Springer US |isbn=978-1-4684-0274-2 |series=Graduate Texts in Mathematics |location=New York, NY}}</ref><ref>{{Cite book |last1=Bluman |first1=George W. |title=Applications of symmetry methods to partial differential equations |last2=Cheviakov |first2=Alexei F. |last3=Anco |first3=Stephen C. |date=2010 |publisher=Springer |isbn=978-1-4614-2498-7 |series=Applied mathematical sciences |location=New York, NY Heidelberg}}</ref>

==Formal definition==
Consider a differential equation

<math>
\Delta(x,u^{(n)})=0,
</math>

where <math>x</math> denotes the independent variables, <math>u</math> the dependent variables, and <math>u^{(n)}</math> represents the collection of derivatives up to order <math>n</math>.

A classical Lie symmetry is generated by a vector field

<math>
X=\xi^i(x,u)\frac{\partial}{\partial x^i}
+\phi^\alpha(x,u)\frac{\partial}{\partial u^\alpha}.
</math>

A nonlocal symmetry extends this framework by allowing the coefficients <math>\xi^i</math> and <math>\phi^\alpha</math> to depend on additional variables:

<math>
w=(w^1,\ldots,w^m),
</math>

which satisfy auxiliary differential relations such as

<math>
w_x = F(x,u,u_x,\ldots).
</math>

The resulting symmetry generator has the form

<math>
X=\xi^i(x,u,w)\frac{\partial}{\partial x^i}
+\phi^\alpha(x,u,w)\frac{\partial}{\partial u^\alpha}.
</math>

Because the variables (w) are defined through integration or other nonlocal constructions, the corresponding symmetry is called nonlocal.

==Applications==
Nonlocal symmetries have numerous applications in mathematics and mathematical physics, including:

* construction of exact solutions;
* similarity reductions;
* classification of integrable equations;
* generation of soliton solutions.

In recent years, nonlocal symmetry methods have also been applied to fractional differential equations, nonlocal diffusion models, and reaction–diffusion systems (e.g. <ref>{{Cite journal |last1=Shi |first1=Yapeng |last2=Feng |first2=Yuqiang |last3=Yu |first3=Jicheng |date=2025-12-01 |title=Classical and nonclassical symmetry analysis of generalized time-fractional Novikov equation |url=https://www.sciencedirect.com/science/article/pii/S0577907325003958 |journal=Chinese Journal of Physics |volume=98 |pages=900–913 |doi=10.1016/j.cjph.2025.10.014 |bibcode=2025ChJPh..98..900S |issn=0577-9073}}</ref>)

== References ==
{{reflist}}

[[Category:Lie groups]]

{{Improve categories|date=August 2026}}
{{Sourceattribution|Nonlocal symmetry}}

Quinn theorem

2026-08-22T14:22:20Z

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In [[Differential topology|differential topology]] in mathematics, the '''Quinn theorem''' is a result about [[Topological manifold|topological]] [[4-manifold|4-manifolds]]. It shows the importance of the topological property of [[Compact space|compactness]] for smoothability, hence if there exists a compatible [[Smooth structure|smooth structure]]. The Quinn theorem is named after [[Biography:Frank Quinn (mathematician)|Frank Quinn]], who proved it in 1984.

== Formulation ==
Every non-compact topological 4-manifold is smoothable.<ref>{{Cite book |last=Freed |first=Daniel |title=[[Instantons and Four-Manifolds]] |last2=Uhlenbeck |first2=Karen |author-link2=Karen Uhlenbeck |publisher=[[Company:Springer Nature|Springer]] |year=1984 |isbn=978-1-4613-9705-2 |series=Mathematical Sciences Research Institute Publications |volume=1 |at=Theorem 1.4 on p. 25 |language=en |doi=10.1007/978-1-4613-9703-8}}</ref> A counterexample is the [[E8 manifold]], which is a compact and non-smoothable topological 4-manifold. A more general formulation is: A topological 4-manifold has a smooth structure in the [[Complement (set theory)|complement]] of any [[Closed set|closed set]] with at least one point in each compact component.<ref>Freedman & Quinn 1990, p. 116</ref><ref>Scorpan 05, p. 219</ref>

== See also ==

* [[Moise's theorem]], lower-dimensional cases

== Literature ==

* {{cite journal |last1=Quinn |first1=Frank |date=1984 |title=Smooth structures on 4-manifolds |journal=American Mathematical Society |series=Contemp. Math. |language=en |volume=35 |issue= |pages=473–479 |doi= |issn= |mr=}}
* {{cite book |last1=Freedman |first1=Michael |url= |title=Topology of 4-Manifolds |last2=Quinn |first2=Frank |author-link2=Frank Quinn |publisher= |year=1990 |isbn=9780691632346 |series= |volume= |location= |pages=116 |language=en |chapter=8.2 Smoothing open 4-manifolds |doi=}}
* {{cite book |last1=Scorpan |first1=Alexandru |title=The Wild World of 4-Manifolds |publisher=American Mathematical Society |year=2005 |isbn=978-1-4704-6861-3 |series=Mathematical Sciences Research Institute Publications |volume=1}}

== References ==
<references/>

== External links ==

* Quinn theorem on [[NLab|''n''Lab]]

[[Category:Differential topology]]

{{Sourceattribution|Quinn theorem}}

Strong set order

2026-08-22T14:21:50Z

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{{short description|Partial order in lattice theory}}

In [[Order theory|order theory]], the '''strong set order''' <math>\leq_s</math> is a partial order over the subsets of a [[Lattice|lattice]]. It is widely used to study monotone comparative statics of [[Parametric programming|parametrized optimization problems]] in economic theory and [[Operations research|operations research]].<ref name = "topkis1998">{{cite book |last1=Topkis |first1=Donald M. |title=Supermodularity and Complementarity |date=1998 |publisher=Princeton University Press |isbn=9780691032443 |page=32}}</ref>

The strong set order was first defined and used by Arthur F. Veinott in his unpublished lecture notes.<ref name="topkis1978">{{cite journal |last1=Topkis |first1=Donald M. |title=Minimizing a Submodular Function on a Lattice |journal=Operations Research |date=1978 |volume=26 |issue=2 |pages=305-321 |doi=10.1287/opre.26.2.305 |url=https://www.jstor.org/stable/169636?seq=1 |quote=Veinott (personal communication) introduced this relation.}}</ref><ref name = "milgrom1994">{{cite journal |last1=Milgrom |first1=Paul |last2=Chris |first2=Shannon |title=Monotone Comparative Statics |journal=Econometrica |date=1994 |volume=62 |issue=1 |pages=157-180 |doi=10.2307/2951479 |url=https://www.jstor.org/stable/2951479 |quote=(...) the strong set order <math>\leq_s</math>, introduced by Veinott (1989).}}</ref><ref>{{cite journal |last1=Veinott |first1=Arthur F. |title=Lattice Programming |journal=Unpublished notes from lectures delivered at Johns Hopkins University |date=1989}}</ref> It was later popularized by Donald M. Topkis, [[Biography:Paul Milgrom|Paul Milgrom]] and Chris Shannon via their work on monotone comparative statics, in particular through Topkis' Theorem.

== Definition ==

Given a [[Lattice (order)|lattice]] <math>(X, \leq)</math>, consider the its [[Power set|power set]] <math>\mathcal P(X)</math>. The '''strong set order''' <math>\leq_s</math> is a partial order on <math>\mathcal P(X)</math> given by:

:<math>
A \leq_s B \iff \left\{
\begin{array}{ll}
a \wedge b \in A, \\[0.1em]
a \vee b \in B
\end{array}
\ \ \ \ \ \ \ \forall a \in A, b \in B,
\right.
</math>

where <math>a \vee b</math> and <math>a \wedge b</math> are respectively the [[Join and meet|join and meet]] of <math>a, b</math>.

== Examples and non-examples ==

=== Real numbers ===

Consider the real numbers <math>\mathbb R</math> with the usual order <math>\geq</math>. Let <math>A = [\underline a, \overline a]</math> and <math>B = [\underline b, \overline b]</math>. Then

:<math>A \leq_s B \iff \underline a \leq \underline b \ \text{ and } \ \overline a \leq \overline b</math>.

More generally, for any <math>A, B \subseteq \mathbb R</math>, we have

:<math>A \leq_s B \iff \inf A \leq \inf B \ \text{ and } \ \sup A \leq \sup B</math>.

=== Euclidean space ===

Consider the [[Euclidean space]] <math>\mathbb R^n</math> with the usual pointwise order: <math>\mathbf x \leq \mathbf y \iff x_i \leq y_i \ \ \forall i \leq n</math>. For <math>n = 2</math>, let

:<math>A = [0,2] \times [0, 3],</math>

:<math>B = [1,3] \times [1, 4].</math>

Then :<math> A \leq_s B</math>. But now consider

:<math>B' = [-1, 3] \times [1,4]</math>;

Then <math>A \nleq_s B'</math>, since <math>(0, 0) \in A </math>, <math> (-1, 1) \in B'</math> but

:<math>(0, 0) \wedge (-1, 1) = (-1, 0) \notin B' </math>.

=== Power set ===

Consider the [[Power set|power set]] of the natural numbers <math>\mathcal P(\mathbb N)</math> under the [[Inclusion order|set-inclusion order]]: <math>A \leq B \iff A \subseteq B</math>. Let

:<math>A = \{\{1\}\}</math>,

:<math>B = \{\{1\}, \{2\}, \{1,2,3\}\}</math>.

It it ''not true'' that <math>A \leq_s B</math>. Indeed, we have <math>\{1\} \in A</math>, <math>\{2\} \in B</math>, but

:<math>\{1\} \wedge \{2\} = \{1\} \cap \{2\} = \varnothing \notin A,</math>

whence <math>A \nleq_s B</math>.

== Applications ==

=== Topkis' Theorem ===

The strong set order is widely used in monotone comparative statics, in particular via Topkis' Theorem. Given a lattice <math>X</math>, a poset <math>\Theta</math>, a [[Constrained optimization|constraint]] [[Set-valued function|correspondence]] <math>D : \Theta \rightrightarrows X</math> and a function <math>f : X \times \Theta \to \mathbb R</math>, the theorem gives sufficient conditions for the correspondence

<math>x^*(\theta) = \arg\max_{x \in D(\theta)} f(x, \theta)</math>

the be increasing in the strong set order, that is, for the statement

:<math>\theta \geq \theta' \implies x^*(\theta) \geq_s x^*(\theta')</math>

to hold.

=== Monotone selections ===

Increasigness in the strong set order can be used to obtain monotone [[Choice function|selection]]s from [[Set-valued function|correspondence]]s. Indeed, if <math>X </math> is a poset and <math> Y</math> is a lattice, the correspondence <math>\Gamma : X \rightrightarrows Y</math> is nonempty-valued and increasing in the strong set order, then a monotone selection <math>g</math> from <math>\Gamma</math> exists if any of the following hold:

* <math>\Gamma(x) \subseteq Y</math> has a minimal element for every <math>x \in X</math> (in particular, if <math>\Gamma</math> is [[Complete lattice|complete-lattice]]-valued). One can thus take :<math>g : X \to Y</math> by putting <math>g(x) = \min \Gamma(x)</math>. The same works if a maximal element is available.

* <math>Y</math> is a [[Lattice (order)#Sublattices|sublattice]] of a finite [[Cartesian product|product]] of [[Total order#Chains|chain]]s.<ref name="kukushkin2013">{{cite journal |last1=Kukushikin |first1=Nikolai S. |title=Increasing Selections from Increasing Multifunctions |journal=Order |date=2013 |volume=30 |pages=541–555 |doi=10.1007/s11083-012-9260-6 |url=https://link.springer.com/article/10.1007/s11083-012-9260-6}}</ref> This covers, for example, <math>Y \subseteq \mathbb R^n</math>.

* <math>X</math> is countable.<ref name="kukushkin2013"></ref>

=== Zhou's Fixed-Point Theorem for correspondences ===

The strong set order can also be used for a generalization of [[Knaster–Tarski theorem|Tarski's fixed-point theorem]] to [[Set-valued function|correspondences]] known as Zhou's fixed-point theorem:<ref name="zhou1994">{{cite journal |last1=Lin |first1=Zhou |title=The Set of Nash Equilibria of a Supermodular Game Is a Complete Lattice |journal=Games and Economic Behavior |date=1994 |volume=7 |issue=2 |pages=295-300 |doi=10.1006/game.1994.1051 |url=https://www.sciencedirect.com/science/article/pii/S0899825684710517}}</ref><ref>{{cite journal |last1=Yu |first1=Lu |title=Fixed point theorems for increasing correspondences on lattices |journal=Economic Theory |volume=68 |pages=1-19 |doi=10.1007/s00199-026-01702-7 |url=https://link.springer.com/article/10.1007/s00199-026-01702-7#citeas}}</ref>

'''Theorem:''' let <math>X</math> be a nonempty [[Complete lattice|complete lattice]] and <math>\Gamma : X \rightrightarrows X</math> a nonempty-valued correspondence. If <math>\Gamma</math> is increasing int the strong set order and <math>\Gamma(x)</math> is a [[Complete lattice#Complete sublattices|subcomplete sublattice]] for all <math>x \in X</math>, then <math>\Gamma</math> has a fixed point. Moreover, the set <math>\text{Fix}(\Gamma)</math> of such fixed points is a nonempty complete lattice.

== Weak set order ==

The strong set order if often too restrictive for some applications, in particular because it assumes that the underlying space <math>X</math> is a lattice.<ref>{{cite arXiv |last1= Che|first1=Yeon-Koo |last2= Kim|first2=Jinwoo |author-link2= | last3 = Kojima |first3 = Fuhito |author-link3 = Fuhito Kojima |date=2021 |year= |title=Weak Monotone Comparative Statics |pages=2-3|arxiv=1911.06442v4 |class= |quote= |mode= |ref= |postscript=}}</ref> A useful weaker ordering which can be used on the subsets of any poset <math>X</math> is the weak set order <math>\leq_w</math>, defined by:<ref name = "topkis1998"></ref>

:<math>
A \leq_w B \iff \left\{
\begin{array}{ll}
\forall a \in A \ \ \exists b \in B \ \text{ such that } a \leq b, \text{ and } \\[0.1em]
\forall b \in B \ \ \exists a \in A \ \text{ such that } b \geq a.
\end{array}
\right.
</math>

This order can moreover be broken down into two weaker orders: the upper and lower weak set orders <math>\leq_{uw}, \leq_{lw}</math>, respectively defined by:

:<math>
A \leq_{uw} B \iff \forall a \in A \ \ \exists b \in B \ \text{ such that } a \leq b,
</math>

:<math>
A \leq_{lw} B \iff \forall b \in B \ \ \exists a \in A \ \text{ such that } b \leq a.
</math>

Clearly <math>A \leq_w B \iff A \leq_{uw} B \text{ and } A \leq_{lw} B</math>.

== See also ==

*Topkis's Theorem

*Monotone comparative statics

==References==
{{reflist}}

{{Order theory}}

[[Category:Lattice theory]]

{{Sourceattribution|Strong set order}}

Feature Importance

2026-08-22T14:21:33Z

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	{{Short description\|Set of techniques in machine learning}}		{{Short description\|Set of techniques in machine learning}}
	~~{{MI\|~~
	~~{{AI-generated\|reason=some weird prose in previous versions and a lot of bold listing\|date=August 2026}}~~
	~~{{Copy edit\|date=August 2026 \|reason=lots of unnecessary caps}}~~
	}}
	'''Feature Importance''' (or '''Variable Importance''' or '''Feature Attribution''') refers to a set of techniques and mathematical frameworks used in [[Machine learning\|machine learning]], statistics, and their applications to quantify the contribution of input variables (features) to a model's output or to the underlying data-generating process. It is a component of [[Explainable Artificial Intelligence]] (XAI) and Interpretable Machine Learning (IML) and is used for model improvement, scientific inference, and [[Feature selection\|feature selection]].<ref name="Holzinger2022">{{cite conference		'''Feature Importance''' (or '''Variable Importance''' or '''Feature Attribution''') refers to a set of techniques and mathematical frameworks used in [[Machine learning\|machine learning]], statistics, and their applications to quantify the contribution of input variables (features) to a model's output or to the underlying data-generating process. It is a component of [[Explainable Artificial Intelligence]] (XAI) and Interpretable Machine Learning (IML) and is used for model improvement, scientific inference, and [[Feature selection\|feature selection]].<ref name="Holzinger2022">{{cite conference
	\|last1=Holzinger \|first1=Andreas		\|last1=Holzinger \|first1=Andreas
Line 50:		Line 47:
	\|pages=135–145		\|pages=135–145
	\|doi=10.1098/rspl.1888.0082		\|doi=10.1098/rspl.1888.0082
	}}</ref>~~{{primary inline\|date=August 2026}}~~ [[Biography:Sewall Wright\|Sewall Wright]] further developed variable importance, by introducing path analysis in 1921, to understand causal influences in complex systems.<ref>{{cite journal		}}</ref> [[Biography:Sewall Wright\|Sewall Wright]] further developed variable importance, by introducing path analysis in 1921, to understand causal influences in complex systems.<ref>{{cite journal
	\|last=Wright		\|last=Wright
	\|first=S.		\|first=S.
Line 58:		Line 55:
	\|year=1921		\|year=1921
	\|pages=557–585		\|pages=557–585
	}}</ref>~~{{primary inline\|date=August 2026}}~~ Path analysis determines correlative influences along direct paths by decomposing [[Correlation\|correlation]] and [[Partial correlation\|partial correlation]] coefficients into their path-based components.~~{{cn\|date=August 2026}}~~		}}</ref> Path analysis determines correlative influences along direct paths by decomposing [[Correlation\|correlation]] and [[Partial correlation\|partial correlation]] coefficients into their path-based components.

	With [[Biography:Leo Breiman\|Leo Breiman]]’s introduction of Random Forests, feature importance expanded to more nonlinear models and explanations. He introduced "permutation importance" sometimes measured by gini index.<ref name="Boulesteix2012">{{cite journal		With [[Biography:Leo Breiman\|Leo Breiman]]’s introduction of Random Forests, feature importance expanded to more nonlinear models and explanations. He introduced "permutation importance" sometimes measured by gini index.<ref name="Boulesteix2012">{{cite journal

Feature Importance

2026-08-22T14:20:05Z

import

New page

{{Short description|Set of techniques in machine learning}}
{{MI|
{{AI-generated|reason=some weird prose in previous versions and a lot of bold listing|date=August 2026}}
{{Copy edit|date=August 2026 |reason=lots of unnecessary caps}}
}}
'''Feature Importance''' (or '''Variable Importance''' or '''Feature Attribution''') refers to a set of techniques and mathematical frameworks used in [[Machine learning|machine learning]], statistics, and their applications to quantify the contribution of input variables (features) to a model's output or to the underlying data-generating process. It is a component of [[Explainable Artificial Intelligence]] (XAI) and Interpretable Machine Learning (IML) and is used for model improvement, scientific inference, and [[Feature selection|feature selection]].<ref name="Holzinger2022">{{cite conference
|last1=Holzinger |first1=Andreas
|last2=Goebel |first2=Randy
|last3=Fong |first3=Ruth
|last4=Moon |first4=Taesup
|last5=Müller |first5=Klaus-Robert
|last6=Samek |first6=Wojciech
|title=xxAI - Beyond Explainable Artificial Intelligence
|conference=International Workshop on Extending Explainable AI Beyond Deep Models and Classifiers
|pages=3–10
|publisher=Springer International Publishing
|location=Cham
|year=2022
|doi=10.1007/978-3-031-04083-2_1
|isbn=978-3-031-04082-5
}}</ref>

Feature importance is a context-dependent score that varies based on the scope of the explanation, the model (or data) of interest, and the ultimate purpose of the analysis.<ref name="Holzinger2022">{{cite conference
|last1=Holzinger |first1=Andreas
|last2=Goebel |first2=Randy
|last3=Fong |first3=Ruth
|last4=Moon |first4=Taesup
|last5=Müller |first5=Klaus-Robert
|last6=Samek |first6=Wojciech
|title=xxAI - Beyond Explainable Artificial Intelligence
|conference=International Workshop on Extending Explainable AI Beyond Deep Models and Classifiers
|pages=3–10
|publisher=Springer International Publishing
|location=Cham
|year=2022
|doi=10.1007/978-3-031-04083-2_1
|isbn=978-3-031-04082-5
}}</ref>

== History ==

The earliest forms of feature importance assessed the strength of the relationships between pairs of variables within animal biology or human psychology using methods such as [[Biography:Francis Galton|Francis Galton]]'s [[Correlation|correlation]] coefficient.<ref>{{cite journal
|last=Galton
|first=Francis
|title=Co-relations and their measurement, chiefly from anthropometric data
|journal=Proceedings of the Royal Society of London
|volume=45
|year=1889
|issue=273–279
|pages=135–145
|doi=10.1098/rspl.1888.0082
}}</ref>{{primary inline|date=August 2026}} [[Biography:Sewall Wright|Sewall Wright]] further developed variable importance, by introducing path analysis in 1921, to understand causal influences in complex systems.<ref>{{cite journal
|last=Wright
|first=S.
|title=Correlation and Causation
|journal=Journal of Agricultural Research
|volume=20
|year=1921
|pages=557–585
}}</ref>{{primary inline|date=August 2026}} Path analysis determines correlative influences along direct paths by decomposing [[Correlation|correlation]] and [[Partial correlation|partial correlation]] coefficients into their path-based components.{{cn|date=August 2026}}

With [[Biography:Leo Breiman|Leo Breiman]]’s introduction of Random Forests, feature importance expanded to more nonlinear models and explanations. He introduced "permutation importance" sometimes measured by gini index.<ref name="Boulesteix2012">{{cite journal
|last1=Boulesteix |first1=Anne-Laure
|last2=Janitza |first2=Silke
|last3=Kruppa |first3=Jochen
|last4=König |first4=Inke R.
|date=November 2012
|title=Overview of random forest methodology and practical guidance with emphasis on computational biology and bioinformatics
|journal=Wiley Interdisciplinary Reviews: Data Mining and Knowledge Discovery
|volume=2 |issue=6 |pages=493–507
|doi=10.1002/widm.1072
}}</ref> Simultaneously in 2001, Lipovetsky and Conklin applied the Shapley value from cooperative game theory to regression, providing a consistent method for variance attribution in the presence of multicollinearity.<ref name="Babic2026">{{cite journal
|last1=Babic |first1=Boris
|last2=Cohen |first2=I. Glenn
|last3=Savulescu |first3=Julian
|year=2026
|title=Justifiability and AI: putting explainability in its place
|journal=AI & SOCIETY
|pages=1–13
|doi=10.1007/s00146-026-03030-9
}}</ref>

== Axioms for Feature Importance ==

Formal feature importance frameworks use mathematical axioms to define consistent scoring criteria and validate the theoretical properties of different estimation methods.

=== The Shapley Axioms (S1–S4) ===

Shapley values are the unique solution that satisfies four core game-theoretic axioms, which describe how to fairly distribute the "total gain" of a model's prediction among the participating features.<ref name="Verdinelli2023">{{cite journal |last1=Verdinelli |first1=Isabella |last2=Wasserman |first2=Larry |title=Feature Importance: A Closer Look at Shapley Values and LOCO |journal=Statistical Science |date=1 November 2024 |volume=39 |issue=4 |doi=10.1214/24-STS937 |url=https://projecteuclid.org/journals/statistical-science/volume-39/issue-4/Feature-Importance--A-Closer-Look-at-Shapley-Values-and/10.1214/24-STS937.short}}</ref> <ref name="SHAP">{{cite conference
|last1=Lundberg
|first1=S. M.
|last2=Lee
|first2=S. I.
|title=A unified approach to interpreting model predictions
|conference=Advances in Neural Information Processing Systems
|volume=30
|year=2017
}}</ref>

# '''Efficiency (Local Accuracy)''': The sum of the importance scores <math>\phi_j</math> for all features must equal the difference between the model's prediction for an instance <math>f(x)</math> and the expected prediction <math>E[f(X)]</math>.
# '''Symmetry''': If two features <math>i</math> and <math>j</math> contribute exactly the same value to every possible subset of other features, they must receive the same importance score: <math>\phi_i = \phi_j</math>.
# '''Dummy (Null Player)''': If a feature contributes nothing to the value function for any subset of features, its importance score must be zero. This is crucial for identifying irrelevant features.
# '''Additivity (Linearity)''': If the value function is the sum of two functions <math>v = v_1 + v_2</math>, then the importance scores must be the sum of the scores calculated for each function: <math>\phi_j(v) = \phi_j(v_1) + \phi_j(v_2)</math>.

=== Axioms for Explaining the Data ===

While the Dummy (Null Player) axiom is desirable for obtaining feature importance scores that can be used to optimize a model, this is not the case for explaining the data, since variables may be highly correlated (and hence offer little value to the existing model), yet remain causally linked to the response variable. Alternative axioms have been proposed for feature importance methods that intend to explain the data.<ref name="Catav2021">{{cite conference
|last1=Catav
|first1=Amnon
|last2=Fu
|first2=Boyang
|last3=Zoabi
|first3=Yazeed
|last4=Meilik
|first4=Ahuva Libi Weiss
|last5=Shomron
|first5=Noam
|last6=Ernst
|first6=Jason
|last7=Sankararaman
|first7=Sriram
|last8=Gilad-Bachrach
|first8=Ran
|title=Marginal contribution feature importance: an axiomatic approach for explaining data
|conference=International Conference on Machine Learning
|pages=1324–1335
|publisher=Proceedings of Machine Learning Research
|year=2021
}}</ref>

* '''Blood Relation (Causal Graph Association)''': A feature should have non-zero importance if and only if the feature is blood related (associated) with the response in the ground-truth causal graph.
* '''Marginal Contribution''': The importance of a feature must be at least as high as the gain it provides when added to the set of all other features.
* '''Elimination''': Removing other features from the feature set can only decrease (or leave unchanged) the importance of a remaining feature. It cannot increase it.
* '''Invariance under Redundant Information and Symmetry under Duplication''': Adding a redundant feature should not change the importance of preexisting features, and identical features should receive equal importance.

== Classification of Methods ==

=== By Purpose ===

The choice of method is categorized based on the user's objective.

* '''Model Explanation''': The goal is to understand the "logic" of a black-box model to ensure safety, fairness, and reliability. Methods like SHAP, LIME, and [[Accumulated local effects]] are standard here.
* '''Data Explanation (Scientific Inference)''': The goal is to learn about the real world. Researchers prioritize methods that handle redundancy and correlation in a way that reflects the true underlying relationships (e.g., MCI, UMFI).<ref name="UMFI">{{cite conference
|last1=Janssen
|first1=J.
|last2=Guan
|first2=V.
|last3=Robeva
|first3=E.
|title=Ultra-marginal feature importance: Learning from data with causal guarantees
|conference=International Conference on Artificial Intelligence and Statistics
|pages=10782–10814
|publisher=Proceedings of Machine Learning Research
|year=2023
}}</ref>
* '''Model Optimization (Feature Selection)''': The goal is to improve the model's performance by removing irrelevant or redundant features. Techniques like Recursive Feature Elimination (RFE) use importance scores as a selection criterion.<ref name="RFE_Lit">"A SYSTEMATIC LITERATURE REVIEW: RECURSIVE FEATURE ELIMINATION ALGORITHMS". [https://ejournal.nusamandiri.ac.id/index.php/jitk/article/view/5015]</ref>

=== By Scope ===

Feature importance methods have been classified into four distinct settings based on two axes: Global vs. Local<ref name="Holzinger2022"/> and Data vs. Model.<ref name="Inconsistencies">{{cite conference
|last1=Harel
|first1=N.
|last2=Obolski
|first2=U.
|last3=Gilad-Bachrach
|first3=R.
|title=Inherent Inconsistencies of Feature Importance
|conference=XAI in Action: Past, Present, and Future Applications
}}</ref> <ref>{{cite arXiv
|last1=Chen
|first1=H.
|last2=Janizek
|first2=J. D.
|last3=Lundberg
|first3=S.
|last4=Lee
|first4=S. I.
|title=True to the model or true to the data?
|eprint=2006.16234
|year=2020
|class=cs.LG
}}</ref> <ref name="GlobalCovert">{{cite conference
|last1=Covert
|first1=I.
|last2=Lundberg
|first2=S. M.
|last3=Lee
|first3=S. I.
|title=Understanding global feature contributions with additive importance measures
|conference=Advances in Neural Information Processing Systems
|volume=33
|year=2020
|pages=17212–17223
}}</ref>

{| class="wikitable"
|-
! !! Reference: Model !! Reference: Data
|-
! Global
| '''Global-Model Importance''': Explains how a trained model behaves across the entire dataset. It identifies which features the model generally relies on for its predictions.
| '''Global-Data Importance''': Explains the true relationships in the underlying phenomenon. It seeks to identify the intrinsic predictive power of features within the population, regardless of a specific model's choices.
|-
! Local
| '''Local-Model Importance''': Explains why a specific prediction was made for a single instance. It quantifies the influence of each feature on that a specific model's specific outcome.
| '''Local-Data Importance''': Explains the role of a feature for a specific individual in the real world (e.g., why a specific patient developed a disease), focusing on the causal or statistical dependencies for that point.
|}

Methods like SHAP and LIME are local-model. Global-model importance metrics include permutation importance and SAGE.<ref name="GlobalCovert" /> Global-data methods include MCI and UMFI. <ref name="Inconsistencies"/>

=== By Treatment of Correlated Features ===

Feature importance methods often differ in how they treat the correlation between features. In the presence of correlated features, predictive credit can be distributed in a variety of ways. Methods can therefore be classified based on how they assign credit to correlated features, where one end of the spectrum is given by marginal feature importance, and the other is given by conditional feature importance.<ref name="CPI">{{cite journal
|last1=Strobl
|first1=C.
|last2=Boulesteix
|first2=A. L.
|last3=Kneib
|first3=T.
|last4=Augustin
|first4=T.
|last5=Zeileis
|first5=A.
|title=Conditional variable importance for random forests
|journal=BMC Bioinformatics
|volume=9
|issue=1
|year=2008
|pages=307
|doi=10.1186/1471-2105-9-307
|doi-access=free
}}</ref> <ref name="GrompingReview">{{cite journal
|last=Grömping
|first=U.
|title=Variable importance in regression models
|journal=Wiley Interdisciplinary Reviews: Computational Statistics
|volume=7
|issue=2
|year=2015
|pages=137–152
|doi=10.1002/wics.1346
}}</ref> <ref>{{cite journal
|last1=Molnar
|first1=C.
|last2=König
|first2=G.
|last3=Bischl
|first3=B.
|last4=Casalicchio
|first4=G.
|title=Model-agnostic feature importance and effects with dependent features: a conditional subgroup approach
|journal=Data Mining and Knowledge Discovery
|volume=38
|issue=5
|year=2024
|pages=2903–2941
|doi=10.1007/s10618-022-00901-9
}}</ref>

* '''Conditional Feature Importance''': Evaluates a feature by conditioning on the values of all other features. This approach respects the dependence structure of the data and measures the unique information a feature provides that is not already captured by other variables. Methods in this category include conditional permutation importance<ref name="CPI" />, Leave-One-Covariate-Out, and partial correlation.

* '''Marginal Feature Importance''': Relies on associations between the response and predictors, regardless of multicollinearity. Purely marginal methods assign the same high importance to all features. Examples include correlation, marginal contribution feature importance, and ultra-marginal feature importance.<ref name="Catav2021" />

Methods such as SHAP and permutation importance are somewhere in between the two extremes as importance is shared among correlated features.

=== Gradient vs. Non-Gradient ===

The technical implementation of the importance measure often dictates its applicability to different model architectures.<ref name="MASE">"MASE: Interpretable NLP Models via Model-Agnostic Saliency Estimation", arXiv. [https://arxiv.org/html/2512.04386v1]</ref>

{| class="wikitable"
|-
! Mechanism !! Description !! Examples
|-
| '''Gradient-Based'''
| Utilizes the derivatives (gradients) of the model's output with respect to its input features. These are typically model-specific and used for differentiable models like neural networks.
| Saliency Maps, Integrated Gradients, Grad-CAM, DeepLIFT.
|-
| '''Non-Gradient Based'''
| Treats the model as a "black box" and relies on perturbations, shuffling, or submodel training. These are typically model-agnostic and applicable to any algorithm.
| Permutation Importance, KernelSHAP, LOCO, MCI.
|}
=== Other Classifications ===

Achen (1982) introduced a classification of linear regression-based feature importance methods: "dispersion importance" (explained variance), "level importance" (impact on the mean), and "theoretical importance" (the change in response for a given change in regressor).<ref>{{cite book
|last=Achen
|first=C. H.
|title=Interpreting and Using Regression
|publisher=Sage
|location=Newbury Park, CA
|year=1982
}}</ref>
== Applications ==
*[[Medicine:Medicine|Medicine]]<ref>{{cite conference
|last1=García Andreu
|first1=A.
|last2=Costa
|first2=M.
|last3=Pastor
|first3=O.
|year=2025
|title=Feature Selection in Medical Imaging: A Comprehensive Review
|book-title=International Conference on Advanced Information Systems Engineering
|pages=142–154
|publisher=Springer Nature Switzerland
|location=Cham
}}</ref><ref>{{cite journal
|last1=Vimbi
|first1=V.
|last2=Shaffi
|first2=N.
|last3=Mahmud
|first3=M.
|year=2024
|title=Interpreting artificial intelligence models: a systematic review on the application of LIME and SHAP in Alzheimer’s disease detection
|journal=Brain Informatics
|volume=11
|issue=1
|page=10
}}</ref>
*Earth Science<ref>{{cite journal
|last=Ibebuchi
|first=C. C.
|year=2025
|title=Uncertainty in machine learning feature importance for climate science: a comparative analysis of SHAP, PDP, and gain-based methods
|journal=Theoretical and Applied Climatology
|volume=156
|issue=9
|page=476
}}</ref>
*Computer Science<ref>{{cite journal
|last1=Samek
|first1=W.
|last2=Montavon
|first2=G.
|last3=Lapuschkin
|first3=S.
|last4=Anders
|first4=C. J.
|last5=Müller
|first5=K.-R.
|year=2021
|title=Explaining deep neural networks and beyond: A review of methods and applications
|journal=Proceedings of the IEEE
|volume=109
|issue=3
|pages=247–278
}}</ref>

==See also==
*[[Feature selection]]
*[[Explainable Artificial Intelligence]]
*[[Shapley value]]

== References ==
{{Reflist}}

[[Category:Machine learning]]

{{Sourceattribution|Feature Importance}}

Morava E-theory

2026-08-22T14:19:32Z

import

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In the theory of [[Spectrum (topology)|spectra]] in mathematics, a '''Morava E-theory''' (also called '''Lubin–Tate theory''' or '''Johnson–Wilson theory''') is a particular spectrum or equivalently generalized (co)homology theory. For a [[Prime number|prime number]] <math>p</math> (obmitted in notation), these form a sequence <math>E(n)</math> of spectra, hence one for each [[Natural number|natural number]] <math>n\in\mathbb{N}</math>. Morava E-theories form the foundation of [[Chromatic homotopy theory|chromatic homotopy theory]], in which a spectrum is separated into so-called (mono)chromatic layers by using its various Bousfield localizations with respect to the different Morava E-theories, so-called chromatic localizations <math>L_{E(n)}</math>. Morava E-theory is named after [[Biography:Jack Morava|Jack Morava]], who introduced it in unpublished preprints in the 1970s.

== Definition ==
For a [[Perfect field|perfect field]] <math>\mathbb{K}</math>, hence in which every [[Irreducible polynomial|irreducible polynomial]] is [[Separable polynomial|separable]], of characteristic <math>p</math>, let <math>W(\mathbb{K})</math> be its ring of [[Witt vector|Witt vectors]].<ref>Hopkins 1999, Definition 16.4</ref> Let <math>R=W(\mathbb{K})[v_1,\ldots,v_{n-1}]</math> be the [[Polynomial ring|polynomial ring]] in <math>n-1</math> variables, called Lubin–Tate ring. According to [[Landweber exact functor theorem|Landweber's exact functor theorem]], a [[Formal group law|formal group law]] over the Lubin–Tate ring defines a generalized cohomology theory, which according to [[Brown's representability theorem]] is represented by a spectrum, which is Morava E-theory <math>E(n)</math>. It fulfills:

: <math>\pi_0E(n)
=R[\beta^{\pm 1}]</math>

for its ring of coefficients with <math>\beta\in R</math> in second degree.

== Properties ==

* The chromatic localization <math>L_{E(n)}</math> preserves [[Smash product|smash products]].<ref>Lurie 2010, Lecture 22</ref>
* <math>E(n)</math> is Bousfield equivalent to <math>E(n-1)\times K(n)</math>.<ref>Lurie 2010, Lecture 23</ref> (<math>K(n)</math> is [[Morava K-theory]]. Two spectra are Bousfield equivalent, when their generalized homology theories vanish on the exact same [[Topological space|topological spaces]]. Hence for every topological space <math>X</math>, one has <math>E(n)_*(X)=0</math> if and only if <math>E(n-1)_*(X)=0</math> and <math>K(n)_*(X)=0</math>.)
* <math>E(n)</math> is <math>K(n)</math>-local.<ref>Lurie 2010, Lecture 35</ref> (<math>K(n)</math> is [[Morava K-theory]]. <math>K(n)</math>-local means that every spectrum morphism <math>X\rightarrow E(n)</math> from a <math>K(n)</math>-acyclic spectrum <math>X</math> is nullhomotopic. <math>K(n)</math>-acyclic means that <math>K(n)\wedge X\simeq 0</math>.)
* A connected [[Closed manifold|closed]] spin 10-manifold is generalized oriented in second Morava E-theory <math>E(2)</math> (for <math>p=2</math>) if and only if its seventh integral [[Stiefel–Whitney class]] <math>W_7</math> vanishes.

== E(n)-local spheres ==
For the [[Sphere spectrum|sphere spectrum]] <math>\mathbb{S}</math> (with <math>\mathbb{S}_n=S^n</math>), its chromatic localizations <math>L_{E(n)}\mathbb{S}</math> are also called <math>E(n)</math>-local spheres.

== See also ==

* [[Morava K-theory]]

== Literature ==

*{{cite web |last=Morava |first=Jack |title=Boarding School Lecture Notes |url=https://math.mit.edu/~hrm/manuscripts/bording-school.pdf |access-date=2026-08-21 |website=math.mit.edu |location=[[Organization:Princeton University|Princeton University]] |date=1973}}
*{{cite web|last=Hopkins|first= Mike
*{{cite web|last=Lurie|first= Jacob
*{{cite web|last=Lurie|first= Jacob
*{{cite web|last=Lurie|first= Jacob

== References ==
<references/>

== External links ==

* Morava E-theory on the [[NLab|''n''Lab]]

[[Category:Algebraic topology]]
[[Category:Cohomology theories]]

{{Sourceattribution|Morava E-theory}}

File:Nessia monodactyla.jpg

2026-08-22T11:52:19Z

Maintenance script uploaded File:Nessia monodactyla.jpg == Summary == Submitted to commons.wikimedia.org == Licensing == {{CC BY-SA 3.0}}

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