Low-rank approximation

In mathematics, low-rank approximation refers to the process of approximating a given matrix by a matrix of lower rank. More precisely, it is a minimization problem, in which the cost function measures the fit between a given matrix (the data) and an approximating matrix (the optimization variable), subject to a constraint that the approximating matrix has reduced rank. The problem is used for mathematical modeling and data compression. The rank constraint is related to a constraint on the complexity of a model that fits the data. In applications, often there are other constraints on the approximating matrix apart from the rank constraint, e.g., non-negativity and Hankel structure. Low-rank approximation is closely related to numerous other techniques, including principal component analysis, factor analysis, total least squares, latent semantic analysis, orthogonal regression, and dynamic mode decomposition. == Definition == Given structure specification S : R n p → R m × n {\displaystyle {\mathcal {S}}:\mathbb {R} ^{n_{p}}\to \mathbb {R} ^{m\times n}} , vector of structure parameters p ∈ R n p {\displaystyle p\in \mathbb {R} ^{n_{p}}} , norm ‖ ⋅ ‖ {\displaystyle \|\cdot \|} , and desired rank r {\displaystyle r} , minimize over p ^ ‖ p − p ^ ‖ subject to rank ⁡ ( S ( p ^ ) ) ≤ r . {\displaystyle {\text{minimize}}\quad {\text{over }}{\widehat {p}}\quad \|p-{\widehat {p}}\|\quad {\text{subject to}}\quad \operatorname {rank} {\big (}{\mathcal {S}}({\widehat {p}}){\big )}\leq r.} == Applications == Linear system identification, in which case the approximating matrix is Hankel structured. Machine learning, in which case the approximating matrix is nonlinearly structured. Recommender systems, in which cases the data matrix has missing values and the approximation is categorical. Distance matrix completion, in which case there is a positive definiteness constraint. Natural language processing, in which case the approximation is nonnegative. Computer algebra, in which case the approximation is Sylvester structured. Matrix product states, in which case the approximation is usually rescaled to have fixed Frobenius norm. == Basic low-rank approximation problem == The unstructured problem with fit measured by the Frobenius norm, i.e., minimize over D ^ ‖ D − D ^ ‖ F subject to rank ⁡ ( D ^ ) ≤ r {\displaystyle {\text{minimize}}\quad {\text{over }}{\widehat {D}}\quad \|D-{\widehat {D}}\|_{\text{F}}\quad {\text{subject to}}\quad \operatorname {rank} {\big (}{\widehat {D}}{\big )}\leq r} has an analytic solution in terms of the singular value decomposition of the data matrix. The result is referred to as the matrix approximation lemma or Eckart–Young–Mirsky theorem. This problem was originally solved by Erhard Schmidt in the infinite dimensional context of integral operators (although his methods easily generalize to arbitrary compact operators on Hilbert spaces) and later rediscovered by C. Eckart and G. Young. L. Mirsky generalized the result to arbitrary unitarily invariant norms. Let D = U Σ V ⊤ ∈ R m × n , m ≥ n {\displaystyle D=U\Sigma V^{\top }\in \mathbb {R} ^{m\times n},\quad m\geq n} be the singular value decomposition of D {\displaystyle D} , where Σ =: diag ⁡ ( σ 1 , … , σ r ) {\displaystyle \Sigma =:\operatorname {diag} (\sigma _{1},\ldots ,\sigma _{r})} , where r ≤ min { m , n } = n {\displaystyle r\leq \min\{m,n\}=n} , is the m × n {\displaystyle m\times n} rectangular diagonal matrix with r {\displaystyle r} non-zero singular values σ 1 ≥ … ≥ σ r > σ r + 1 = … = σ n = 0 {\displaystyle \sigma _{1}\geq \ldots \geq \sigma _{r}>\sigma _{r+1}=\ldots =\sigma _{n}=0} . For a given k ∈ { 1 , … , r } {\displaystyle k\in \{1,\dots ,r\}} , partition U {\displaystyle U} , Σ {\displaystyle \Sigma } , and V {\displaystyle V} as follows: U =: [ U 1 U 2 ] , Σ =: [ Σ 1 0 0 Σ 2 ] , and V =: [ V 1 V 2 ] , {\displaystyle U=:{\begin{bmatrix}U_{1}&U_{2}\end{bmatrix}},\quad \Sigma =:{\begin{bmatrix}\Sigma _{1}&0\\0&\Sigma _{2}\end{bmatrix}},\quad {\text{and}}\quad V=:{\begin{bmatrix}V_{1}&V_{2}\end{bmatrix}},} where U 1 {\displaystyle U_{1}} is m × k {\displaystyle m\times k} , Σ 1 {\displaystyle \Sigma _{1}} is k × k {\displaystyle k\times k} , and V 1 {\displaystyle V_{1}} is n × k {\displaystyle n\times k} . Then the rank k {\displaystyle k} matrix D ^ ∗ := U 1 Σ 1 V 1 ⊤ , {\displaystyle {\widehat {D}}^{}:=U_{1}\Sigma _{1}V_{1}^{\top },} obtained from the truncated singular value decomposition is such that ‖ D − D ^ ∗ ‖ F = min rank ⁡ ( D ^ ) ≤ k ‖ D − D ^ ‖ F = σ k + 1 2 + ⋯ + σ r 2 . {\displaystyle \|D-{\widehat {D}}^{}\|_{\text{F}}=\min _{\operatorname {rank} ({\widehat {D}})\leq k}\|D-{\widehat {D}}\|_{\text{F}}={\sqrt {\sigma _{k+1}^{2}+\cdots +\sigma _{r}^{2}}}.} The minimizer D ^ ∗ {\displaystyle {\widehat {D}}^{}} is unique if and only if σ k > σ k + 1 {\displaystyle \sigma _{k}>\sigma _{k+1}} . == Proof of Eckart–Young–Mirsky theorem (for spectral norm) == Let A ∈ R m × n {\displaystyle A\in \mathbb {R} ^{m\times n}} be a real (possibly rectangular) matrix with m ≤ n {\displaystyle m\leq n} . Suppose that A = U Σ V ⊤ {\displaystyle A=U\Sigma V^{\top }} is the singular value decomposition of A {\displaystyle A} . Recall that U {\displaystyle U} and V {\displaystyle V} are orthogonal matrices, and Σ {\displaystyle \Sigma } is an m × n {\displaystyle m\times n} diagonal matrix with entries ( σ 1 , σ 2 , ⋯ , σ m ) {\displaystyle (\sigma _{1},\sigma _{2},\cdots ,\sigma _{m})} such that σ 1 ≥ σ 2 ≥ ⋯ ≥ σ m ≥ 0 {\displaystyle \sigma _{1}\geq \sigma _{2}\geq \cdots \geq \sigma _{m}\geq 0} . We claim that the best rank- k {\displaystyle k} approximation to A {\displaystyle A} in the spectral norm, denoted by ‖ ⋅ ‖ 2 {\displaystyle \|\cdot \|_{2}} , is given by A k := ∑ i = 1 k σ i u i v i ⊤ {\displaystyle A_{k}:=\sum _{i=1}^{k}\sigma _{i}u_{i}v_{i}^{\top }} where u i {\displaystyle u_{i}} and v i {\displaystyle v_{i}} denote the i {\displaystyle i} th column of U {\displaystyle U} and V {\displaystyle V} , respectively. First, note that we have ‖ A − A k ‖ 2 = ‖ ∑ i = 1 n σ i u i v i ⊤ − ∑ i = 1 k σ i u i v i ⊤ ‖ 2 = ‖ ∑ i = k + 1 n σ i u i v i ⊤ ‖ 2 = σ k + 1 {\displaystyle \|A-A_{k}\|_{2}=\left\|\sum _{i=1}^{\color {red}{n}}\sigma _{i}u_{i}v_{i}^{\top }-\sum _{i=1}^{\color {red}{k}}\sigma _{i}u_{i}v_{i}^{\top }\right\|_{2}=\left\|\sum _{i=\color {red}{k+1}}^{n}\sigma _{i}u_{i}v_{i}^{\top }\right\|_{2}=\sigma _{k+1}} Therefore, we need to show that if B k = X Y ⊤ {\displaystyle B_{k}=XY^{\top }} where X {\displaystyle X} and Y {\displaystyle Y} have k {\displaystyle k} columns then ‖ A − A k ‖ 2 = σ k + 1 ≤ ‖ A − B k ‖ 2 {\displaystyle \|A-A_{k}\|_{2}=\sigma _{k+1}\leq \|A-B_{k}\|_{2}} . Since Y {\displaystyle Y} has k {\displaystyle k} columns, then there must be a nontrivial linear combination of the first k + 1 {\displaystyle k+1} columns of V {\displaystyle V} , i.e., w = γ 1 v 1 + ⋯ + γ k + 1 v k + 1 , {\displaystyle w=\gamma _{1}v_{1}+\cdots +\gamma _{k+1}v_{k+1},} such that Y ⊤ w = 0 {\displaystyle Y^{\top }w=0} . Without loss of generality, we can scale w {\displaystyle w} so that ‖ w ‖ 2 = 1 {\displaystyle \|w\|_{2}=1} or (equivalently) γ 1 2 + ⋯ + γ k + 1 2 = 1 {\displaystyle \gamma _{1}^{2}+\cdots +\gamma _{k+1}^{2}=1} . Therefore, ‖ A − B k ‖ 2 2 ≥ ‖ ( A − B k ) w ‖ 2 2 = ‖ A w ‖ 2 2 = γ 1 2 σ 1 2 + ⋯ + γ k + 1 2 σ k + 1 2 ≥ σ k + 1 2 . {\displaystyle \|A-B_{k}\|_{2}^{2}\geq \|(A-B_{k})w\|_{2}^{2}=\|Aw\|_{2}^{2}=\gamma _{1}^{2}\sigma _{1}^{2}+\cdots +\gamma _{k+1}^{2}\sigma _{k+1}^{2}\geq \sigma _{k+1}^{2}.} The result follows by taking the square root of both sides of the above inequality. == Proof of Eckart–Young–Mirsky theorem (for Frobenius norm) == Let A ∈ R m × n {\displaystyle A\in \mathbb {R} ^{m\times n}} be a real (possibly rectangular) matrix with m ≤ n {\displaystyle m\leq n} . Suppose that A = U Σ V ⊤ {\displaystyle A=U\Sigma V^{\top }} is the singular value decomposition of A {\displaystyle A} . We claim that the best rank k {\displaystyle k} approximation to A {\displaystyle A} in the Frobenius norm, denoted by ‖ ⋅ ‖ F {\displaystyle \|\cdot \|_{F}} , is given by A k = ∑ i = 1 k σ i u i v i ⊤ {\displaystyle A_{k}=\sum _{i=1}^{k}\sigma _{i}u_{i}v_{i}^{\top }} where u i {\displaystyle u_{i}} and v i {\displaystyle v_{i}} denote the i {\displaystyle i} th column of U {\displaystyle U} and V {\displaystyle V} , respectively. First, note that we have ‖ A − A k ‖ F 2 = ‖ ∑ i = k + 1 n σ i u i v i ⊤ ‖ F 2 = ∑ i = k + 1 n σ i 2 {\displaystyle \|A-A_{k}\|_{F}^{2}=\left\|\sum _{i=k+1}^{n}\sigma _{i}u_{i}v_{i}^{\top }\right\|_{F}^{2}=\sum _{i=k+1}^{n}\sigma _{i}^{2}} Therefore, we need to show that if B k = X Y ⊤ {\displaystyle B_{k}=XY^{\top }} where X {\displaystyle X} and Y {\displaystyle Y} have k {\displaystyle k} columns then ‖ A − A k ‖ F 2 = ∑ i = k + 1 n σ i 2 ≤ ‖ A − B k ‖ F 2 . {\displaystyle \|A-A_{k}\|_{F}^{2}=\sum _{i=k+1}^{n}\sigma _{i}^{2}\leq \|A-B_{k}\|_{F}^{2}.} By the triangle inequality with the spectral norm

Site-specific browser

A site-specific browser (SSB) is a software application dedicated to accessing pages from a single source (site) on a computer network such as the Internet or a private intranet. SSBs typically simplify the more complex functions of a web browser by excluding the menus, toolbars and browser graphical user interface associated with functions that are external to the workings of a single site. Modern site-specific browsers range from simple browser windows without navigation controls to sophisticated desktop applications built with frameworks like Electron that bundle entire browser engines. This evolution has enabled many popular desktop applications to be built using web technologies, effectively making them advanced site-specific browsers. == History == === Early development === One of the earliest examples of an SSB was MacDICT, a Mac OS 9 application that accessed various websites to define, translate, or find synonyms for words typed into a text box. However, the first general-purpose SSB is considered to be Bubbles, which launched in late 2005 on the Windows platform. Bubbles introduced the term "Site Specific Extensions" for SSB userscripts and created the first SSB JavaScript API. In 2007, Mozilla announced Prism (originally called WebRunner), a project to integrate web applications with the desktop. That same year, Todd Ditchendorf, a former Apple Dashboard engineer, released Fluid for macOS. On 2 September 2008, Google Chrome was released with a built-in "Create application shortcut" feature, bringing SSB functionality to mainstream users. This feature allowed any website to be launched in a separate window without the browser interface. === Modern era === The landscape of site-specific browsers changed dramatically with the introduction of Electron in 2013 (originally called Atom Shell). Electron combined Chromium and Node.js into a single runtime, enabling developers to build desktop applications using web technologies. This framework has since powered applications used by hundreds of millions of users, including Visual Studio Code, Slack, Discord, and Microsoft Teams. In 2015, the concept of Progressive Web Apps (PWAs) was introduced by Google engineers Alex Russell and Frances Berriman, representing a parallel evolution in web-to-desktop technology. While PWAs share similar goals with SSBs, they follow web standards and can be installed directly from browsers. More recently, alternative frameworks like Tauri have emerged, offering significantly smaller application sizes by using the system's native web renderer instead of bundling Chromium. == Technical implementation == Site-specific browsers can be implemented through various approaches: === Browser-based SSBs === The simplest form of SSB is created through browser features that allow websites to run in separate windows without the standard browser interface. Modern Chromium-based browsers offer "Install as app" or "Create shortcut" functionality that creates a dedicated window for a specific website. These SSBs share the browser's underlying engine and resources but operate in isolated windows. === Framework-based SSBs === More sophisticated SSBs are built using application frameworks: Electron: Bundles a complete Chromium browser with Node.js, resulting in applications of 85MB or larger. Each Electron application runs its own browser instance, providing full access to system APIs but consuming significant resources. Tauri: Uses the operating system's native web rendering engine (WebView2 on Windows, WebKit on macOS, and WebKitGTK on Linux), resulting in applications typically 2.5-10MB in size. Other frameworks: Include Neutralino.js (ultra-lightweight using system browser), Wails (Go-based), and the Chromium Embedded Framework (CEF). == Comparison with Progressive Web Apps == While site-specific browsers and Progressive Web Apps (PWAs) share the goal of bringing web content to the desktop, they differ in several key aspects: == Applications == Site-specific browsers have become the foundation for many popular desktop applications: Communication and collaboration: Many modern communication tools are built as SSBs, including Slack, Discord, Microsoft Teams, and WhatsApp Desktop. These applications benefit from web-based development while providing desktop integration. Development tools: Visual Studio Code, used by 73.6% of developers according to Stack Overflow's 2024 survey, is built with Electron, as are Atom and GitHub Desktop. Productivity software: Applications like Notion, Obsidian, and various project management tools use SSB technology to provide consistent experiences across platforms. Security and Privacy: Web browsers can be modified to only have access to a single site, in order to protect the security and privacy of the user via compartmentalization == Security and performance == === Memory usage === Framework-based SSBs, particularly those using Electron, are known for high memory consumption. Studies show Electron applications typically use 120-300MB at baseline, with complex applications consuming significantly more. This is approximately 5-10 times more memory than equivalent native applications. === Security considerations === SSBs can provide security benefits through process isolation, where each application runs in its own sandboxed environment. However, bundling an entire browser engine also means each application must be updated independently to patch security vulnerabilities. Research presented at the Network and Distributed System Security (NDSS) Symposium has identified various security challenges specific to Electron applications. === Bundle sizes === The choice of framework significantly impacts application size: Electron applications: 85MB+ (includes full Chromium) Tauri applications: 2.5-10MB (uses system WebView) Browser-based SSBs: No additional download (uses existing browser) == Software == === Browser support === Most modern browsers provide some form of SSB functionality: Chromium-based browsers (Google Chrome, Microsoft Edge, Brave, Opera, Vivaldi): "Install as app" or "Create shortcut" feature Safari: "Add to Dock" feature in macOS Sonoma (2023) Firefox: Removed SSB support in December 2020 (version 85) GNOME Web: "Install Site as Web Application" feature === Standalone tools === ==== Active ==== WebCatalog (Windows, macOS, Linux) – Manages multiple SSBs with isolated storage Fluid (macOS) – Pioneering SSB creator for Mac Unite (macOS) – Creates SSBs with customization options Coherence X (macOS) – Advanced SSB creation tool Pake (cross-platform) – Open-source SSB creator Wavebox (cross-platform) – Workspace browser with SSB features ==== Discontinued ==== Mozilla Prism – Cross-platform SSB creator (discontinued 2011) Nativefier – Command-line SSB creator (discontinued 2023) Epichrome – macOS SSB creator (discontinued 2021) === Development frameworks === Electron – Most popular framework, bundles Chromium and Node.js Tauri – Rust-based framework using system WebView Chromium Embedded Framework (CEF) – C++ library for embedding Chromium Neutralino.js – Lightweight framework using system browser Wails – Go-based framework for web frontends

CodePen

CodePen is an online community for testing and showcasing user-created HTML, CSS and JavaScript code snippets. It functions as an online code editor and open-source learning environment, where developers can create code snippets, called "pens," and test them. It was founded in 2012 by full-stack developers Alex Vazquez and Tim Sabat and front-end designer Chris Coyier. Its employees work remotely, rarely all meeting together in person. CodePen is a large community for web designers and developers to showcase their coding skills, with an estimated 330,000 registered users and 14.16 million monthly visitors.

Vintage computer

A vintage computer is an older computer system that is largely regarded as obsolete. The personal computer has been around since around 1971, and in that time technological advancement means existing models get replaced every few years. Nevertheless, these otherwise useless computers have spawned a sub-culture of vintage computer collectors who often spend large sums for the rarest examples, not only to display but functionally restore. This involves active software development and adaptation to modern uses. This often includes homebrew developers and hackers who add on, update and create hybrid composites from new and old computers for uses they were otherwise never intended. Ethernet interfaces have been designed for many vintage 8-bit machines to allow limited connectivity to the Internet, where users can access discussion groups, bulletin boards, and software databases. Most of this hobby centers on computers made after 1960, though some collectors also specialize in older computers. The Vintage Computer Festival, an event held by the Vintage Computer Federation for the exhibition and celebration of vintage computers, has been held annually since 1997 and has expanded internationally. == By platform == === MITS Inc. === Micro Instrumentation and Telemetry Systems (MITS) produced the Altair 8800 in 1975. According to Harry Garland, the Altair 8800 was the product that catalyzed the microcomputer revolution of the 1970s. === IMSAI === The IMSAI 8080 is a clone of the Altair 8800. It was introduced in 1975, first as a kit, and later as an assembled system. The list price was $591 (equivalent to $3,584 in 2025) for a kit, and $931 (equivalent to $5,570 in 2025) assembled. === Processor Technology === Processor Technology produced the Sol-20. This was one of the first machines to have a case that included a keyboard; a design feature copied by many of later "home computers". === SWTPC === Southwest Technical Products Corporation (SWTPC) produced the 8-bit SWTPC 6800 and later the 16-bit SWTPC 6809 kits that employed the Motorola 68xx series microprocessors. === Apple Inc. === The earliest Apple Inc. personal computers, using the MOS Technology 6502 processors, are among some of the most collectible. They are relatively easy to maintain in an operational state thanks to Apple's use of readily available off-the-shelf parts. Apple I (1976): The Apple-1 was Apple's first product and has brought some of the highest prices ever paid for a microcomputer at auction. Apple II (1977): The Apple II series of computers are some of the easiest to adapt, thanks to the original expansion architecture designed for them. New peripheral cards are still being designed by an avid thriving community, thanks to the longevity of this platform, manufactured from 1977 through 1993. Numerous websites exist to support not only legacy users but new adopters who weren't even born when the Apple II was discontinued by Apple. Macintosh (1984): The original Macintosh used a 32-bit Motorola 68000 processor running at 7.8336 MHz and came with 128 KB of RAM. The list price was $2495 (equivalent to $7,732 in 2025).Perhaps because of its friendly design and first commercially successful graphical user interface as well as its enduring Finder application that persists on the most current Macs, the Macintosh is one of the most collected and used vintage computers. With dozens of websites around the world, old Macintosh hardware and software are input into daily use. The Macintosh had a strong presence in many early computer labs, creating a nostalgia factor for former students who recall their first computing experiences. === RCA === The COSMAC Elf in 1976 was an inexpensive (about $100) single-board computer that was easily built by hobbyists. Many people who could not afford an Altair could afford an ELF, which was based on the RCA 1802 chip. Because the chips are still available from other sources, modern recreations of the ELF are fairly common and there are several fan websites. === IBM === The IBM 1130 (1965) was a desk-sized small computer. It was the often the first computer used by many college students, still has a following of interested users. Most of the remaining 1130 systems in 2023 are in museums, but an emulator is available for users who don't have access to a physical 1130. The 5100 also has an avid collector and fan base. The PC series (5150 PC, 5155 Portable PC, 5160 PC/XT, 5170 PC/AT) has become very popular in recent years, with the earliest models (PC) being considered the most collectible. === Acorn BBC & Archimedes === The Acorn BBC Micro was a very popular British computer in the 1980s with home and educational users and enjoyed near-universal usage in British schools into the mid-1990s. It was possible to use 100K 5+1⁄4-inch disks, and it had many expansion ports. The Archimedes series – the de facto successor to the BBC Micro – has also enjoyed a following in recent years, thanks to its status as the first computer to be based around ARM's RISC microprocessor. === Tandy/Radio Shack === The Tandy/RadioShack Model 100 is still widely collected and used as one of the earliest examples of a truly portable computer. Other Tandy offerings, such as the TRS-80 line, are also very popular, and early systems, like the Model I, in good condition can command premium prices on the vintage computer market. === Sinclair === The Sinclair ZX81 and ZX Spectrum series were the most popular British home computers of the early 1980s, with a wide choice of emulators available for both platforms. The Spectrum in particular enjoys a cult following due to its popularity as a games platform, with new games titles still being developed even today. Original "rubber key" Spectrums fetch the highest prices on the second-hand market, with the later Amstrad-built models attracting less of a following. The earlier ZX81 is not as popular in original hardware form due to its monochrome display and limited abilities next to the Spectrum, but still unassembled ZX81 kits still appear on eBay occasionally. === MSX === Although nearly nonexistent in the United States, the MSX architecture has strong communities of fans and hobbyists worldwide, particularly in Japan (where the standard was conceived and developed), South Korea (the only country that had an MSX-based game console, Zemmix), Netherlands, Spain, Brazil, Argentina, Russia, Chile, the Middle East, and others. New hardware and software are being actively developed to this day as well. One of the latest fundamental (from hardware and software perspectives) revivals of the MSX is the GR8BIT. === Robotron === The Robotron Z1013 was an East German home computer produced by VEB Robotron. It had a U880 processor, 16 KB RAM, and a membrane keyboard. The KC 85 series of computers was a modular 8-bit computer system used in East German schools. === Commodore === VIC-20 Commodore 64 Commodore PET Amiga === Xerox === The Xerox Alto, designed and manufactured by Xerox PARC and released in 1973, was the first personal computer equipped with a graphic user interface. In 1979, Steve Jobs of Apple Inc. arranged for his engineers to visit Xerox in order to see the Alto. The design concepts of the Alto soon appeared in the Apple Lisa and Macintosh systems. The Xerox Star, also known as the 8010/40, was made available in 1981. It followed on the Alto. Like the Alto, this machine was expensive and was only intended for corporate office usage. Therefore, being out of the price range of the average user, this product had little market penetration. === Silicon Graphics === The SGI Indy, built in 1993 for Silicon Graphics has a history of usage in the development of the Nintendo 64 as well as various CGI projects throughout the 1990s and early 2000s. The Indy and other machines in the SGI lineup have remained cult classics.

Vintage computer

National Cyber Security Policy 2013

National Cyber Security Policy is a policy framework by Department of Electronics and Information Technology (DeitY) It aims at protecting the public and private infrastructure from cyber attacks. The policy also intends to safeguard "information, such as personal information (of web users), financial and banking information and sovereign data". This was particularly relevant in the wake of US National Security Agency (NSA) leaks that suggested the US government agencies are spying on Indian users, who have no legal or technical safeguards against it. Ministry of Communications and Information Technology (India) defines Cyberspace as a complex environment consisting of interactions between people, software services supported by worldwide distribution of information and communication technology. == Reason for Cyber Security policies == India had no Cyber security policy before 2013. In 2013, The Hindu newspaper, citing documents leaked by NSA whistle-blower Edward Snowden, has alleged that much of the NSA surveillance was focused on India's domestic politics and its strategic and commercial interests. This sparked a furore among people. Under pressure, the government unveiled a National Cyber Security Policy 2013 on 2 July 2013. == Vision == To build a secure and resilient cyberspace for citizens, business, and government and also to protect anyone from intervening in user's privacy.It mentioned a five year target of training five lakh cyber security personnel by 2018. == Mission == To protect information and information infrastructure in cyberspace, build capabilities to prevent and respond to cyber threat, reduce vulnerabilities and minimize damage from cyber incidents through a combination of institutional structures, people, processes, technology, and cooperation. == Objective == Ministry of Communications and Information Technology (India) define objectives as follows: To create a secure cyber ecosystem in the country, generate adequate trust and confidence in IT system and transactions in cyberspace and thereby enhance adoption of IT in all sectors of the economy. To create an assurance framework for the design of security policies and promotion and enabling actions for compliance to global security standards and best practices by way of conformity assessment (Product, process, technology & people). To strengthen the Regulatory Framework for ensuring a SECURE CYBERSPACE ECOSYSTEM. To enhance and create National and Sectoral level 24x7 mechanism for obtaining strategic information regarding threats to ICT infrastructure, creating scenarios for response, resolution and crisis management through effective predictive, preventive, protective response and recovery actions. -To improve visibility of integrity of ICT products and services by establishing infrastructure for testing & validation of security of such product. To create workforce for 500,000 professionals skilled in next 5 years through capacity building skill development and training. To provide fiscal benefit to businesses for adoption of standard security practices and processes. To enable Protection of information while in process, handling, storage & transit so as to safeguard privacy of citizen's data and reducing economic losses due to cyber crime or data theft. To enable effective prevention, investigation and prosecution of cybercrime and enhancement of law enforcement capabilities through appropriate legislative intervention. == Strategies == Creating a secured Ecosystem. Creating an assurance framework. Encouraging Open Standards. Strengthening The regulatory Framework. Creating a mechanism for Security Threats Early Warning, Vulnerability management, and response to security threats. Securing E-Governance services. Protection and resilience of Critical Information Infrastructure. Promotion of Research and Development in cyber security. Reducing supply chain risks Human Resource Development (fostering education and training programs both in formal and informal sectors to Support the Nation's cyber security needs and build capacity. Creating cyber security awareness. Developing effective Public-Private partnerships. To develop bilateral and multilateral relationships in the area of cyber security with another country. (Information sharing and cooperation) a Prioritized approach for implementation.

Computer aided transceiver

Computer aided transceiver (CAT) is a non-generic serial protocol used by radio amateurs for (remotely) controlling a transceiver radio receiver equipment using a computer. Conventional transmitters are manually controlled and used to transmit voice using buttons, dials, etc. However, advances in electronics have come to market devices that can be controlled by a computer and allow digital modes such as packet radio and also the use of satellite tracking, because it can continuously change the device's frequency according to the Doppler effect. This is done by connecting a Radio receiver and a PC using a CAT interface and a CAT Program Additionally, CAT interfaces can also be used to position tracking antennas, in controllers. As a satellite moves overhead. A CAT interface is a piece of hardware that connects the PC and radio that provides a connection to allows the radio and the PC to communicate with each other. The CAT interface provides the signals to and fro via correct voltage levels and in the case of a Universal Serial Bus (USB) CAT interface it requires a "protocol" for communication but communication itself is down to the radio and the software on the PC. Software that may be called a CAT program allows a radio to be controlled through the PC. Changes made on the radio through user interactions on the CAT Program are (generally) shown on the PC's screen. The functionality of CAT equipment (software & interface) depends on the radio and what features the software writers included in the CAT software. Modern radio systems do have more CAT functionality If you run a logging program that supports CAT, then that software may take advantage of the CAT system by retrieving information from the radio to help fill in log details, such as the frequency that the contact was made. CAT is also useful on many radios where there are many sub-menus in the radios menu system, and many of the sub-menu items can be easily changed via the PC. On many HF radios, the CAT system is also used to program the memories on the radio, but you would need to use appropriate programming software. A CAT interface does not receive or transmit any DATA mode, that is the purpose of a DATA interface. Although, both may be used at the same time with the correct CAT Equipment. DATA modes, and getting audio to and from the PC is the function of a DATA interface. A completely different thing but it is easier and more useful when CAT and DATA are used at the same time. Wouldn't it be nice to have an interface that could operate Frequency-shift keying (FSK), Audio FSK (AFSK), (real) Morse Code (CW), with a CAT interface and its own sound card..... (eg. The DigiMaster Pro3).

Site-specific browser

CodePen

Vintage computer

Vintage computer

National Cyber Security Policy 2013

Computer aided transceiver

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