Simon John Godsill (born 2 December 1965) is professor of statistical signal processing at the University of Cambridge, and a professorial fellow at Corpus Christi College. He is also a member of the Centre for Science and Policy. His main area of research is Bayesian statistics and stochastic sampling methodologies, particularly particle filtering. == Education == Godsill obtained both undergraduate and Ph.D. degrees from the Department of Engineering at Cambridge University, whilst a member of Selwyn College. He obtained a first class degree in the Electrical and Information Sciences Tripos. The title of his 1993 Ph.D. thesis was "The Restoration of Degraded Audio Signals" and his Ph.D. supervisor was Peter Rayner, whom he shared with Michael Richard Lynch. == Career == Godsill has published over 250 articles in peer reviewed journals, along with the books Digital audio restoration: a statistical model based approach and Compressed sensing & sparse filtering. == Business interests == Godsill is currently a director of CEDAR Audio Ltd, a Cambridge-based company that applies Bayesian mathematics for purposes of noise reduction in audio data. In February 2005, the company received a Sci-Tech Academy Award (a 'Technical Oscar') for its services to the movie industry, and a stream of innovations appeared over the following years with corresponding recognition including induction into the Audio Technology Hall of Fame (2008), a Cinema Audio Society Award (2009). Godsill is also a director at Input Dynamics Ltd, a Cambridge-based company that applies Bayesian techniques to touch screen technology. Godsill is involved with the research effort at BMLL Technologies, a Cambridge spin-off working in the field of machine learning application in the financial sector.
Double descent
Double descent in statistics and machine learning is the phenomenon where a model's error rate on the test set initially decreases with the number of parameters, then peaks, then decreases again. This phenomenon has been considered surprising, as it contradicts assumptions about overfitting in classical machine learning. The increase usually occurs near the interpolation threshold, where the number of parameters is the same as the number of training data points (the model is just large enough to fit the training data). Or, more precisely, it is the maximum number of samples on which the model/training procedure achieves approximately on average 0 training error. == History == Early observations of what would later be called double descent in specific models date back to 1989. The term "double descent" was coined by Belkin et. al. in 2019, when the phenomenon gained popularity as a broader concept exhibited by many models. The latter development was prompted by a perceived contradiction between the conventional wisdom that too many parameters in the model result in a significant overfitting error (an extrapolation of the bias–variance tradeoff), and the empirical observations in the 2010s that some modern machine learning techniques tend to perform better with larger models. == Theoretical models == Double descent occurs in linear regression with isotropic Gaussian covariates and isotropic Gaussian noise. A model of double descent at the thermodynamic limit has been analyzed using the replica trick, and the result has been confirmed numerically. A number of works have suggested that double descent can be explained using the concept of effective dimension: While a network may have a large number of parameters, in practice only a subset of those parameters are relevant for generalization performance, as measured by the local Hessian curvature. This explanation is formalized through PAC-Bayes compression-based generalization bounds, which show that less complex models are expected to generalize better under a Solomonoff prior.
Blocking of Twitter in Nigeria
Twitter was blocked in Nigeria from 5 June 2021 to 13 January 2022. The government imposed a ban on the social network after it deleted tweets made by, and temporarily suspended, the Nigerian president Muhammadu Buhari, warning the southeastern people of Nigeria, predominantly Igbo people, of a potential repeat of the 1967 Nigerian Civil War due to the ongoing insurgency in Southeastern Nigeria. The Nigerian government claimed that the deletion of the president's tweets factored into their decision, but it was ultimately based on "a litany of problems with the social media platform in Nigeria, where misinformation and fake news spread through it have had real world violent consequences", citing the persistent use of the platform for activities that are capable of undermining Nigeria's corporate existence. In January 2022, Nigeria lifted its blocking of Twitter after the platform agreed to establish a legal entity within the country sometime in the first quarter of 2022. == Background == On 1 June 2021, Nigerian President Muhammadu Buhari posted a tweet threatening a crackdown on regional separatists "in the language they understand". The next day, Twitter deleted the tweet, claiming it was in violation of Twitter rules, but gave no further details. Nigeria's Information Minister Lai Mohammed said that Twitter's actions were part of an unfair double standard, as Twitter had not banned incitement tweets from other groups. During the Nigerian Civil War a majority of deaths resulted from the blockade of Biafra which caused the deaths of millions of civilians from starvation, a fact that was not alluded to in the tweet. The Nigerian government has long held concerns over the use of Twitter in the country. The ongoing local End SARS protest began on Twitter and got amplified in 2020 when it had 48 million tweets in ten days. Buhari's government floated the idea of social media regulation on different occasions prior to banning Twitter. Attempts to pass an anti-social media bill in the past have failed majorly due to massive outcry on Twitter. Days before the ban, the country's minister of information called Twitter's activities in Nigeria suspicious, citing its influence on the End SARS protests. == Aftermath == Three days after Twitter was suspended, it was reported that the move had cost the country over 6 billion naira and would also contribute to the worsening unemployment in the country. ExpressVPN reported an over 200 percent increase in web traffic and searches for VPN spiked across the country. In response, Nigeria's Minister of Justice and Attorney General of the Federation Abubakar Malami at first openly threatened to prosecute citizens who bypass the ban using a VPN but then denied saying so after a screenshot of a Twitter deactivation notification he shared on Facebook showed a VPN logo. Nigeria's cultural minister Lai Mohammed stated the ban would be lifted once Twitter submitted to locally licensing, registration and conditions. "It will be licensed by the broadcasting commission, and must agree not to allow its platform to be used by those who are promoting activities that are inimical to the corporate existence of Nigeria." In late June 2021, Twitter announced it would enter talks with the Nigerian government over the platform's suspension. The talks began in July 2021. On 15 September 2021, Mohammed said the Nigerian government will lift the ban on Twitter in a "few days." The Minister said Twitter gave a progress report of their talks with them, adding that it has been productive and quite respectful. On 1 October 2021, President Muhammadu Buhari in his Independence Day broadcast said Twitter must meet the Nigerian government's five conditions before the suspension of the social media platform will be lifted. The conditions are: Respect for national security and cohesion; registration, physical presence and representation in Nigeria; fair taxation; dispute resolution; local content. == Reactions == The ban was condemned by Amnesty International, the British, Canadian and Swedish diplomatic missions to Nigeria, as well as the United States and the European Union in a joint statement. Two domestic organizations, the Socio-Economic Rights and Accountability Project (SERAP) and the Nigerian Bar Association, indicated intent to challenge the ban in court. Twitter itself called the ban "deeply concerning". Former U.S. President Donald Trump, who was permanently suspended from Twitter following the United States Capitol attack in January, praised the ban, stating "Congratulations to the country of Nigeria, who just banned Twitter because they banned their President", and also called on other countries to ban Twitter and Facebook due to "not allowing free and open speech." == Lifting of the ban == On 12 January 2022, the Nigerian Government lifted the ban after Twitter agreed to pay an "applicable tax" and establish "a legal entity in Nigeria during the first quarter of 2022".
Ajax (programming)
The Asynchronous JavaScript and XML, usually referred to as Ajax (or AJAX, ) is a set of web development techniques that uses various web technologies on the client-side to create asynchronous web applications. With Ajax, web applications can send and retrieve data from a server asynchronously (in the background) without interfering with the display and behaviour of the existing page. By decoupling the data interchange layer from the presentation layer, Ajax allows web pages and, by extension, web applications, to change content dynamically without the need to reload the entire page. In practice, modern implementations commonly utilize JSON instead of XML. Ajax is not a technology, but rather a programming pattern. HTML and CSS can be used in combination to mark up and style information. The webpage can be modified by JavaScript to dynamically display (and allow the user to interact with) the new information. The built-in XMLHttpRequest object is used to execute Ajax on webpages, allowing websites to load content onto the screen without refreshing the page. == History == In the early-to-mid 1990s, most Websites were based on complete HTML pages. Each user action required a complete new page to be loaded from the server. This process was inefficient, as reflected by the user experience: all page content disappeared, then the new page appeared. Each time the browser reloaded a page because of a partial change, all the content had to be re-sent, even though only some of the information had changed. This placed additional load on the server and made bandwidth a limiting factor in performance. The foundations of AJAX originate back in 1996 with the introduction of JavaScript 1. Developers quickly discovered that any HTML element which accepted a "src" attribute could be used to fetch remote data. By changing the src of a hidden frame, a developer could fetch remote data, process or display it without a page refresh. The remote data could be a string, JavaScript code, XML or a partial HTML page generated on the server. The same could be done with and
Interference (communication)
In telecommunications, an interference is that which modifies a signal in a disruptive manner, as it travels along a communication channel between its source and receiver. The term is often used to refer to the addition of unwanted signals to a useful signal. Common examples include: Electromagnetic interference (EMI) Co-channel interference (CCI), also known as crosstalk Adjacent-channel interference (ACI) Intersymbol interference (ISI) Inter-carrier interference (ICI), caused by doppler shift in OFDM modulation (multitone modulation). Common-mode interference (CMI) Conducted interference Noise is a form of interference but not all interference is noise. Radio resource management aims at reducing and controlling the co-channel and adjacent-channel interference. == Interference alignment == A solution to interference problems in wireless communication networks is interference alignment, which was crystallized by Syed Ali Jafar at the University of California, Irvine. A specialized application was previously studied by Yitzhak Birk and Tomer Kol for an index coding problem in 1998. For interference management in wireless communication, interference alignment was originally introduced by Mohammad Ali Maddah-Ali, Abolfazl S. Motahari, and Amir Keyvan Khandani, at the University of Waterloo, for communication over wireless X channels. Interference alignment was eventually established as a general principle by Jafar and Viveck R. Cadambe in 2008, when they introduced "a mechanism to align an arbitrarily large number of interferers, leading to the surprising conclusion that wireless networks are not essentially interference limited." This led to the adoption of interference alignment in the design of wireless networks. Jafar explained: My research group crystallized the concept of interference alignment and showed that through interference alignment, it is possible for everyone to access half of the total bandwidth free from interference. Initially this result was shown under a number of idealized assumptions that are typical in theoretical studies. We have since continued to work on peeling off these idealizations one at a time, to bring the theory closer to practice. Along the way we have made numerous discoveries through the lens of interference alignment, which reveal new and powerful signaling schemes. According to New York University senior researcher Paul Horn: Syed Jafar revolutionized our understanding of the capacity limits of wireless networks. He demonstrated the astounding result that each user in a wireless network can access half of the spectrum without interference from other users, regardless of how many users are sharing the spectrum. This is a truly remarkable result that has a tremendous impact on both information theory and the design of wireless networks.
Color
Color (or colour in Commonwealth English) is the visual perception produced by the activation of the different types of cone cells in the eye caused by light. Though color is not an inherent property of matter, color perception is related to an object's light absorption, emission, reflection and transmission. For most humans, visible wavelengths of light are the ones perceived in the visible light spectrum, with three types of cone cells (trichromacy). Other animals may have a different number of cone cell types or have eyes sensitive to different wavelengths, such as bees that can distinguish ultraviolet, and thus have a different color sensitivity range. Animal perception of color originates from different light wavelength or spectral sensitivity in cone cell types, which is then processed by the brain. Colors have perceived properties such as hue, colorfulness, and lightness. Colors can also be additively mixed (mixing light) or subtractively mixed (mixing pigments). If one color is mixed in the right proportions, because of metamerism, they may look the same as another stimulus with a different reflection or emission spectrum. For convenience, colors can be organized in a color space, which when being abstracted as a mathematical color model can assign each region of color with a corresponding set of numbers. Thus, color spaces are an essential tool for color reproduction in print, photography, computer monitors, and television. Some of the most well-known color models and color spaces are RGB, CMYK, HSL/HSV, CIE Lab, and YCbCr/YUV. Because the perception of color is an important aspect of human life, different colors have been associated with emotions, activity, and nationality. Names of color regions in different cultures can have different, sometimes overlapping areas. In visual arts, color theory is used to govern the use of colors in an aesthetically pleasing and harmonious way. The theory of color includes the color complements; color balance; and classification of primary colors, secondary colors, and tertiary colors. The study of colors in general is called color science. == Physical properties == Electromagnetic radiation is characterized by its wavelength (or frequency) and its intensity. When the wavelength is within the visible spectrum (the range of wavelengths humans can perceive, approximately from 390 nm to 700 nm), it is known as "visible light". Most light sources emit light at many different wavelengths; a source's spectrum is a distribution giving its intensity at each wavelength. Although the spectrum of light arriving at the eye from a given direction determines the color sensation in that direction, there are many more possible spectral combinations than color sensations. In fact, one may formally define a color as a class of spectra that give rise to the same color sensation, although such classes would vary widely among different animal species, and to a lesser extent among individuals within the same species. In each such class, the members are called metamers of the color in question. This effect can be visualized by comparing the light sources' spectral power distributions and the resulting colors. === Spectral colors === The familiar colors of the rainbow in the spectrum—named using the Latin word for appearance or apparition by Isaac Newton in 1671—include all those colors that can be produced by visible light of a single wavelength only, the pure spectral or monochromatic colors. The spectrum above shows approximate wavelengths (in nm) for spectral colors in the visible range. Spectral colors have 100% purity, and are fully saturated. A complex mixture of spectral colors can be used to describe any color, which is the definition of a light power spectrum. The spectral colors form a continuous spectrum, and how it is divided into distinct colors linguistically is a matter of culture and historical contingency. Despite the ubiquitous ROYGBIV mnemonic used to remember the spectral colors in English, the inclusion or exclusion of colors is contentious, with disagreement often focused on indigo and cyan. Even if the subset of color terms is agreed, their wavelength ranges and borders between them may not be. The intensity of a spectral color, relative to the context in which it is viewed, may alter its perception considerably. For example, a low-intensity orange-yellow is brown, and a low-intensity yellow-green is olive green. Additionally, hue shifts towards yellow or blue happen if the intensity of a spectral light is increased; this is called Bezold–Brücke shift. In color models capable of representing spectral colors, such as CIELUV, a spectral color has the maximal saturation. In Helmholtz coordinates, this is described as 100% purity. === Color of objects === The physical color of an object depends on how it absorbs and scatters light. Most objects scatter light to some degree and do not reflect or transmit light specularly like glasses or mirrors. A transparent object allows almost all light to transmit or pass through, thus transparent objects are perceived as colorless. Conversely, an opaque object does not allow light to transmit through and instead absorbs or reflects the light it receives. Like transparent objects, translucent objects allow light to transmit through, but translucent objects are seen colored because they scatter or absorb certain wavelengths of light via internal scattering. The absorbed light is often dissipated as heat. == Color vision == === Development of theories of color vision === Although Aristotle and other ancient scientists had already written on the nature of light and color vision, it was not until Isaac Newton that light was identified as the source of the color sensation. In 1810, Johann Wolfgang von Goethe published his comprehensive Theory of Colors in which he provided a rational description of color experience, which "tells us how it originates, not what it is". In 1801, Thomas Young proposed his trichromatic theory, to explain how a wide spectrum of different wavelengths could be detected by the human eye. It would be unreasonable to suppose that the human eye contained hundreds of different receptors each responding to the presence of a specific wavelength. Instead, he suggested that the human experience of color derives from a complex interaction and mixing from the output three receptors. This theory was later confirmed by James Clerk Maxwell and refined by Hermann von Helmholtz. Maxwell experimentally demonstrated that any color could be matched with a combination of three lights. As Helmholtz puts it, "the principles of Newton's law of mixture were experimentally confirmed by Maxwell in 1856. Young's theory of color sensations, like so much else that this marvelous investigator achieved in advance of his time, remained unnoticed until Maxwell directed attention to it." At the same time as Helmholtz, Ewald Hering developed the opponent process theory of color, noting that color blindness and afterimages typically come in opponent pairs (red-green, blue-orange, yellow-violet, and black-white). Ultimately these two theories were synthesized in 1957 by Hurvich and Jameson, who showed that retinal processing corresponds to the trichromatic theory, while processing at the level of the lateral geniculate nucleus corresponds to the opponent theory. In 1931, the International Commission on Illumination (CIE), an international group of experts, developed a mathematical color model which mapped out the space of observable colors, allowing every individual color able to be specified with a set of three numbers. === Color in the eye === The ability of the human eye to distinguish colors is based upon the varying sensitivity of different cells in the retina to light of different wavelengths. Humans are trichromatic—the retina contains three types of color receptor cells, or cones. One type, relatively distinct from the other two, is most responsive to light that is perceived as blue or blue-violet, with wavelengths around 450 nm; cones of this type are sometimes called short-wavelength cones or S cones (or misleadingly, blue cones). The other two types are closely related genetically and chemically: middle-wavelength cones, M cones, or green cones are most sensitive to light perceived as green, with wavelengths around 540 nm, while the long-wavelength cones, L cones, or red cones, are most sensitive to light that is perceived as greenish yellow, with wavelengths around 570 nm. Light, no matter how complex its composition of wavelengths, is reduced to three color components by the eye. Each cone type adheres to the principle of univariance, which is that each cone's output is determined by the amount of light that falls on it over all wavelengths. For each location in the visual field, the three types of cones yield three signals based on the extent to which each is stimulated. These amounts of stimulation are sometimes called tristimulus values. The response cu
CSS HTML Validator
CSS HTML Validator (previously named CSE HTML Validator) is an HTML editor and CSS editor for Microsoft Windows (and Linux and other Unix-like operating systems when used with Wine) that helps web developers create syntactically correct and accessible HTML/HTML5, XHTML, and CSS documents by locating errors, potential problems like browser compatibility issues, and common mistakes. It is also able to check links, check spelling, suggest improvements, alert developers to deprecated, obsolete, or proprietary tags, attributes, and CSS properties, and find issues that can affect search engine optimization. CSS HTML Validator is developed, marketed, and sold by AI Internet Solutions LLC located in the United States. The first version of CSS HTML Validator was released in 1997 for Windows 95. The current version is 2026/v26.02 (as of January 9, 2026) and is for Windows 10 and above, including Windows 11. A native macOS and Linux command-line console tool (called htmlval) became available with version 23. There are currently three main editions of CSS HTML Validator — Pro/Professional, Home/Standard, and Lite. The Enterprise edition was discontinued in 2025/v25. While the application is generally a commercial product (except for the Lite edition), a free version of the Home edition is available for personal/educational, non-commercial use. A free limited version of the htmlval command-line console tool for macOS and Linux is also available. == Features == CSS HTML Validator includes an HTML editor, validator for HTML, XHTML, htmx, polyglot markup, CSS, PHP and JavaScript (using JSLint or JSHint), link checker (to find dead and broken links), spell checker, accessibility checker, and search engine optimization (SEO) checker. An integrated web browser allows developers to browse the web while the pages are automatically validated. Because documents are checked locally and not uploaded over the Internet to a server in order to be checked, validations are performed relatively quickly, and security and privacy are increased. A custom scripting language called TNPL, included in the Pro and Enterprise editions, can be used to customize validations by adding, eliminating, or changing validator messages. TNPL can also be used to integrate customized validation checks to meet the unique requirements of an individual or entity. A Batch Wizard tool, included in the Pro and Enterprise editions, can check entire Web sites, parts of Web sites, or a list of local web documents. The Batch Wizard generates reports in standard HTML or XML format. The reports can be viewed using a normal web browser. The accessibility checker includes support for Section 508 Amendment to the Rehabilitation Act of 1973 and Web Content Accessibility Guidelines (both WCAG 1.0 and WCAG 2.0/2.1/2.2). Using a version of HTML Tidy with HTML5 support and the Pretty Print & Fix Tool, CSS HTML Validator can automatically fix some common problems with HTML and XHTML documents. However, some problems cannot be fixed (or fixed correctly) with automated tools and require manual review and repair. == Version history == Validation of polyglot markup was added in version 12, and mobile development support (for HTML and CSS) was added in version 14 and improved in version 15. Version 15 added built-in syntax checking for JSON and HTML5 cache manifest files. Version 16 added JavaScript linting using JSHint, a static code analysis tool for checking JavaScript, but also continues to support JSLint. Version 17 added support for the Accelerated Mobile Pages Project, which is a type of HTML optimized for mobile web browsing, and support for live DOM validation using Google Chrome CSS HTML Validator 2018/v18 renames the software from CSE HTML Validator to CSS HTML Validator and includes updated HTML5 and CSS support. Version 18 also added a new "By Message" report in the Batch Wizard and dropped support for Windows Vista and below. CSS HTML Validator 2019/v19 includes updated HTML and CSS support, adds WCAG 2.1 support, improves support when running under Wine (software), and is a native 64-bit application (previously releases were 32-bit). CSS HTML Validator 2020/v20, first released in January 2020, includes HTML, CSS, accessibility, and other updates, including improved support for the Accelerated Mobile Pages Project. Also, beginning with version 20, the Standard edition was renamed to the Home edition. CSS HTML Validator 2021/v21, first released in January 2021, includes further HTML, CSS, accessibility, and other updates. CSS HTML Validator 2022/v22, released in January 2022, includes improvements and updates to keep the program up-to-date, a new Microsoft Edge WebView2 rendering engine for the integrated web browser, and three new dark themes. Later updates to version 22 added support for checking JSON Lines and NDJSON documents. CSS HTML Validator 2023/v23, released in January 2023, includes more improvements and updates to keep the program up-to-date. The new release also introduced new command-line macOS and Linux ports of the core validation engine, called htmlval for Mac and Linux. Official support for Windows 7, 8, and 8.1 was dropped in the 2023/v23 version. CSS HTML Validator 2024/v24, released in January 2024, includes updates and improvements. It also adds support for htmx. CSS HTML Validator 2025/v25, released in December 2024, includes further updates and improvements for 2025. Version 25 discontinues the Enterprise edition, moving Enterprise functionality to the Pro edition. CSS HTML Validator 2026/v26, released in January 2026, includes updated support for HTML and CSS. An online edition based on CSS HTML Validator Pro that can check documents via file upload, URL, or snippets (direct text input) was discontinued May 2017 in favor of the desktop version for Microsoft Windows. == Purpose of validation == The purpose of validation and computerized checking of HTML, XHTML, and CSS documents is to help make sure that the documents are syntactically correct and problem-free. Checked HTML, XHTML, and CSS documents are more likely to: be more accessible for people with disabilities (such as blindness), as well as all users in general render faster (user agents don't have to "figure out" and decipher bad syntax) render as intended and with fewer problems on a variety of user agents, including mobile devices cause browsers and user agents to build a more consistent Document Object Model, which is important for CSS and JavaScript be forward-compatible with future versions of user agents and browsers ("future-proof") be compatible with current and future HTML, XHTML, and CSS specifications cause fewer problems for visitors and web indexing not contain dead, broken, or rotting links While automated checking tools are helpful for website development and continued maintenance, they cannot guarantee that a document will display (render) and behave as intended in all browsers. Developers should always test documents in a variety of browsers (including mobile browsers) to locate problems that cannot be detected with a computerized checking tool. == Differences from other HTML validators == CSS HTML Validator is an offline desktop app for Microsoft Windows and a native macOS and Linux command-line console tool that does not require an Internet connection. The offline nature of CSS HTML Validator is in contrast to online web-based services. CSS HTML Validator primarily works offline (except for link checking when it must go online), which has speed and privacy benefits compared to web-based solutions and services like the W3C Markup Validation Service. However, the user must keep the software updated unlike web-based solutions which are typically kept updated by the solution provider. CSS HTML Validator checks HTML/XHTML syntax, CSS, links, spelling, accessibility, JavaScript, SEO, and PHP with one pass, while DTD-based validators are more limited and cannot check HTML5. CSS HTML Validator includes a built-in scripting language (called TNPL) which allows for a high degree of customization via scripting and "user functions". This allows developers to add custom (specialized) validation checks and messages. CSS HTML Validator includes a DTD-based validator which can optionally be used for checking DTD-based versions of HTML (versions prior to HTML5), however one of CSS HTML Validator's primary differences is that its custom validation engine can perform more checks on a document than a DTD-based validator can. This is because DTD-based validators are limited to checking only what can be specified in a Document Type Definition. == Integration == CSS HTML Validator integrates with other third-party software like those listed below. This allows validation using CSS HTML Validator from within the third-party program. EmEditor - includes a special Lite edition build of CSS HTML Validator for built-in checking of HTML and CSS Blumentals Software - several Blumentals software products integrate with CSS H