Nuance Communications, Inc. was an American multinational computer software technology corporation, headquartered in Burlington, Massachusetts, that markets speech recognition and artificial intelligence software. Nuance merged with its competitor in the commercial large-scale speech application business, ScanSoft, in October 2005. ScanSoft was a Xerox spin-off that was bought in 1999 by Visioneer, a hardware and software scanner company, which adopted ScanSoft as the new merged company name. The original ScanSoft had its roots in Kurzweil Computer Products. In April 2021, Microsoft announced it would buy Nuance Communications. The deal is an all-cash transaction of $19.7 billion, including company debt, or $56 per share. The acquisition was completed in March 2022. == History == The Speech Technology and Research (STAR) Laboratory at SRI International began the journey that, in 1994, resulted in a spin-off company; Corona Corporation (later renamed to Nuance Communications ). Nuance Communications (NUAN) went public on the Nasdaq Stock Market in 1995. Nuance focused on commercializing advanced speech recognition technologies. Nuance was an early spinoff of SRI's Speech Technology and Research (STAR) Laboratory, a world leader in audio processing, speech and speaker analytics and spoken language research. The technology that served as the foundation of Nuance's speech recognition solution started at the STAR Lab and helped launch Nuance more than 20 years ago. In 1995, The SRI Language Modeling Toolkit (SRILM) was developed. This provides the tools to build and apply statistical language models (LMs), primarily for use in speech recognition, statistical tagging and segmentation, and machine translation. In terms of commercialization of natural automated speech recognition, SRI's natural language speech recognition software was the first to be deployed by a major corporation. In 1996, Charles Schwab & Co., Inc., used Nuance's speech recognition technology to allow customers to receive stock quotes over the telephone. One of the key features of the ‘Schwab Discount Brokerage system’, was the ability to recognize English words even when spoken by customers with accents. In 1997, Nuance Communications developed the first large scale commercial dialog system for United Parcel Services (UPS). UPS used the voice recognition platform to handle very large numbers of inquiries about package status. The company that would later merge with Nuance Communications started life as Visioneer, incorporated in 1992. In 1999, Visioneer acquired ScanSoft, Inc. (SSFT), and the combined company became known as ScanSoft. In September 2005, ScanSoft Inc. acquired and merged with Nuance Communications (NUAN), a natural language DOD-project spinoff from SRI International. The resulting company adopted the Nuance name. During the prior decade, the two companies competed in the commercial large-scale speech application business. === Data breach === Between 2014 and 2017, Nuance exposed over 45,000 patient records. == Solutions == Customer service virtual assistants Speech recognition — for people Speech recognition — for business Speech recognition — for physicians Accessibility Power PDF Managed Print Services Transcription === ScanSoft origins === In 1974, Raymond Kurzweil founded Kurzweil Computer Products, Inc. to develop the first omni-font optical character-recognition system – a computer program capable of recognizing text written in any normal font. In 1980, Kurzweil sold his company to Xerox. The company became known as Xerox Imaging Systems (XIS), and later ScanSoft. In March 1992, a new company called Visioneer, Inc. was founded to develop scanner hardware and software products, such as a sheetfed scanner called PaperMax and the document management software PaperPort. Visioneer eventually sold its hardware division to Primax Electronics, Ltd. in January 1999. Two months later, in March, Visioneer acquired ScanSoft from Xerox to form a new public company with ScanSoft as the new company-wide name. Prior to 2001, ScanSoft focused primarily on desktop imaging software such as TextBridge, PaperPort and OmniPage. Beginning with the December 2001 acquisition of Lernout & Hauspie assets, the company moved into the speech recognition business and began to compete with Nuance. Lernout & Hauspie had acquired speech recognition company Dragon Systems in June 2001, shortly before becoming bankrupt in October. Scansoft acquired speech recognition company SpeechWorks in 2003. === Partnership with Siri and Apple Inc. === In 2013, Nuance confirmed that its natural language processing algorithms supported Apple's Siri voice assistant. === Focus on health care === In 2019, Nuance spun off its automotive division as the company Cerence, allowing it to focus on health care applications. === Acquisition by Microsoft === On April 12, 2021, Microsoft announced that it would buy Nuance Communications for $19.7 billion, or $56 a share, a 22% increase over the previous closing price. Nuance's CEO, Mark Benjamin, stayed with the company. This was Microsoft's second-biggest acquisition up to that point, after its purchase of LinkedIn for $24 billion (~$30.7 billion in 2024) in 2016. Shortly after the deal, the Competition and Markets Authority, a UK regulatory body, stated it was looking into the deal on the basis of antitrust concerns. In December 2021, it was reported that the deal would be approved by the European Union. The acquisition was completed on March 4, 2022. In May 2023, Nuance announced an unspecified number of layoffs.
Roposo
Roposo is an Indian video-sharing social media service, owned by Glance, a subsidiary of InMobi. Roposo provides a space where users can share posts related to different topics like food, comedy, music, poetry, fashion and travel. It is a platform where people express visually with homemade videos and photos. The app offers a TV-like browsing experience with user-generated content on its channels. Users can also use editing tools on the platform and upload their content. == History == Established in July 2014 under Relevant E-solutions Pvt. Ltd., Roposo is the brainchild of three IIT Delhi alumni – Mayank Bhangadia, Avinash Saxena, and Kaushal Shubhank. Under Bhangadia's leadership, the company pivoted from a fashion-based network into a short-form video platform with AI-powered moderation, and its journey was featured as a Harvard Business Publishing case study. In November 2019, Roposo was acquired by InMobi's Glance Digital Experience Pvt. Ltd.(the mobile content platform and part of the InMobi Group). When the Chinese-owned video-sharing app TikTok was banned on 30 June 2020, the app saw a huge spike in users with several TikTok users registering on Roposo. == Technology == The open platform has some features such as a TV-like browsing, different channels, a chat feature that lets buyers and sellers converse directly through the platform, and creation tools such as an option to add voice-over, music and GIF stickers for videos and photos.
Boba liberal
Boba liberal is a term mostly used within the Asian diaspora communities in the West, especially in the United States. It describes someone of East or Southeast Asian descent living in the West who has a shallow, surface-level liberal outlook. It is also occasionally used to describe conservatives who weaponize their East or Southeast Asian identity. The neologism emerged among the Asian American leftist community on Twitter who accused "boba liberals" of only holding their liberal beliefs to appear more white-adjacent by engaging in progressive social movements or viewpoints, while at the same time disregarding and trivializing issues concerning Asians. Mary Chao, writing for The North Jersey Record, said that "Asians call peers boba liberals when they aspire to liberal whiteness." An article in The Yale Herald described it as a term "used to describe the ethnocentric politics of Asian Americans, usually of East Asian descent, who exclusively advocate for issues that benefit themselves, without acknowledging problematic dimensions of their own history and working to support other people of color." The feminist magazine Fem said that "the faces of boba liberalism are Asian Americans that are part of the middle and upper economic class. As a result, boba liberals disregard the negative effects of capitalism because they profit from it. For instance, boba liberals tend to focus on advocating for Asian representation in white spaces, or discussing whether or not wearing chopsticks in one's hair is culture appropriation. These topics are popular within boba liberal circles, all while dialogue regarding inequality, globalization, and racial injustice are purposely neglected." UnHerd notes that conservative Asian Americans have used the term not to critique capitalism, but to "aim at a small but influential group of progressive Asian-American activists who are supposedly selling out other Asians, especially working-class Asians, in order to win brownie points from elite, generally white liberals." MRAsians have similarly used the term to attack Asian American feminists who supported the Black Lives Matter movement. The Asian identity of boba liberals has often been accused of being shallow and superficial. Boba liberals are accused of using surface-level stereotypical Asian traits such as liking boba tea to bolster their Asian credentials. Plan A Magazine, an Asian diaspora magazine, described the film Crazy Rich Asians and the sitcom Fresh Off the Boat as "boba liberal media", calling them the result of "a specific kind of atomized identity politics". Other media outlets have connected the Crazy Rich Asians film to boba liberalism. == Controversy == The term "boba liberal" was coined in 2019 by Vietnamese American Twitter user Redmond (@diaspora_is_red) to analyze a form of Asian American liberalism through a Marxist lens. Redmond has criticized the misappropriation of their neologism by stripping away the Marxist framework by failing to discuss "socialism, communism, the capitalist system, imperialism, and the diaspora bourgeoisie" and conflating "boba liberalism" with the flawed concept of "East Asian privilege". In 2024, Redmond criticized misuse of the term by conservatives and liberals, and said "The term boba liberalism can go away for all I care. It's corny and stale". === United States === One commentator described boba liberals as supporting policies that primarily benefit upper-income Asian-Americans, and not necessarily the Asian-American community as a whole. Therefore, while the word "liberal" is used in the term, it is not mutually exclusive to one specific ideology, as it may also extend to conservative-aligned Asians in some areas, as they would often take advantage of the "model minority" label by defending such measures.
Web performance
Web performance refers to the speed in which web pages are downloaded and displayed on the user's web browser. Web performance optimization (WPO), or website optimization is the field of knowledge about increasing web performance. Faster website download speeds have been shown to increase visitor retention and loyalty and user satisfaction, especially for users with slow internet connections and those on mobile devices. Web performance also leads to less data travelling across the web, which in turn lowers a website's power consumption and environmental impact. Some aspects which can affect the speed of page load include browser/server cache, image optimization, and encryption (for example SSL), which can affect the time it takes for pages to render. The performance of the web page can be improved through techniques such as multi-layered cache, light weight design of presentation layer components and asynchronous communication with server side components. == History == In the first decade or so of the web's existence, web performance improvement was focused mainly on optimizing website code and pushing hardware limitations. According to the 2002 book Web Performance Tuning by Patrick Killelea, some of the early techniques used were to use simple servlets or CGI, increase server memory, and look for packet loss and retransmission. Although these principles now comprise much of the optimized foundation of internet applications, they differ from current optimization theory in that there was much less of an attempt to improve the browser display speed. Steve Souders coined the term "web performance optimization" in 2004. At that time Souders made several predictions regarding the impact that WPO as an "emerging industry" would bring to the web, such as websites being fast by default, consolidation, web standards for performance, environmental impacts of optimization, and speed as a differentiator. One major point that Souders made in 2007 is that at least 80% of the time that it takes to download and view a website is controlled by the front-end structure. This lag time can be decreased through awareness of typical browser behavior, as well as of how HTTP works. == Optimization techniques == Web performance optimization improves user experience (UX) when visiting a website and therefore is highly desired by web designers and web developers. They employ several techniques that streamline web optimization tasks to decrease web page load times. This process is known as front end optimization (FEO) or content optimization. FEO concentrates on reducing file sizes and "minimizing the number of requests needed for a given page to load." In addition to the techniques listed below, the use of a content delivery network—a group of proxy servers spread across various locations around the globe—is an efficient delivery system that chooses a server for a specific user based on network proximity. Typically the server with the quickest response time is selected. The following techniques are commonly used web optimization tasks and are widely used by web developers: Web browsers open separate Transmission Control Protocol (TCP) connections for each Hypertext Transfer Protocol (HTTP) request submitted when downloading a web page. These requests total the number of page elements required for download. However, a browser is limited to opening only a certain number of simultaneous connections to a single host. To prevent bottlenecks, the number of individual page elements are reduced using resource consolidation whereby smaller files (such as images) are bundled together into one file. This reduces HTTP requests and the number of "round trips" required to load a web page. Web pages are constructed from code files such JavaScript and Hypertext Markup Language (HTML). As web pages grow in complexity, so do their code files and subsequently their load times. File compression can reduce code files by about 40 percent, thereby improving site responsiveness. Web Caching Optimization reduces server load, bandwidth usage and latency. CDNs use dedicated web caching software to store copies of documents passing through their system. Many website platforms, such as SiteGround, IONOS, Wix, and Hostinger, rely on global CDNs and caching technologies to deliver faster page loads across different geographical regions. Subsequent requests from the cache may be fulfilled should certain conditions apply. Web caches are located on either the client side (forward position) or web-server side (reverse position) of a CDN. Web browsers are also able to store content for re-use through the HTTP cache or web cache. Requests web browsers make are typically routed to the HTTP cache to validate if a cached response may be used to fulfill a request. If such a match is made, the response is fulfilled from the cache. This can be helpful for reducing network latency and costs associated with data-transfer. The HTTP cache is configured using request and response headers. Code minification distinguishes discrepancies between codes written by web developers and how network elements interpret code. Minification removes comments and extra spaces as well as crunch variable names in order to minimize code, decreasing files sizes by as much as 60%. In addition to caching and compression, lossy compression techniques (similar to those used with audio files) remove non-essential header information and lower original image quality on many high resolution images. These changes, such as pixel complexity or color gradations, are transparent to the end-user and do not noticeably affect perception of the image. Another technique is the replacement of raster graphics with resolution-independent vector graphics. Vector substitution is best suited for simple geometric images. Lazy loading of images and video reduces initial page load time, initial page weight, and system resource usage, all of which have positive impacts on website performance. It is used to defer initialization of an object right until the point at which it is needed. The browser loads the images in a page or post when they are needed such as when the user scrolls down the page and not all images at once, which is the default behavior, and naturally, takes more time. == HTTP/1.x and HTTP/2 == Since web browsers use multiple TCP connections for parallel user requests, congestion and browser monopolization of network resources may occur. Because HTTP/1 requests come with associated overhead, web performance is impacted by limited bandwidth and increased usage. Compared to HTTP/1, HTTP/2 is binary instead of textual is fully multiplexed instead of ordered and blocked can therefore use one connection for parallelism uses header compression to reduce overhead allows servers to "push" responses proactively into client caches Instead of a website's hosting server, CDNs are used in tandem with HTTP/2 in order to better serve the end-user with web resources such as images, JavaScript files and Cascading Style Sheet (CSS) files since a CDN's location is usually in closer proximity to the end-user. == Metrics == In recent years, several metrics have been introduced that help developers measure various aspects of the performance of their websites. In 2019, Google introduced metrics such as Time to First Byte (TTFB), First Contentful Paint (FCP), First Paint (FP), First Input Delay (FID), Cumulative Layout Shift (CLS) and Largest Contentful Paint (LCP) allow for website owner to gain insights into issues that might hurt the performance of their websites making it seem sluggish or slow to the user. Other metrics including Request Count (number of requests required to load a page), DOMContentLoaded (time when HTML document is completely loaded and parsed excluding CSS style sheets, images, etc.), Above The Fold Time (content that is visible without scrolling), Round Trip Time, number of Render Blocking Resources (such as scripts, stylesheets), Onload Time, Connection Time, Total Page Size help provide an accurate picture of latencies and slowdowns occurring at the networking level which might slow down a site. Modules to measure metrics such as TTFB, FCP, LCP, FP etc are provided with major frontend JavaScript libraries such as React, NuxtJS and Vue. Google publishes a library, the core-web-vitals library that allows for easy measurement of these metrics in frontend applications. In addition to this, Google also provides the Lighthouse, a Chrome dev-tools component and PageSpeed Insight a site that allows developers to measure and compare the performance of their website with Google's recommended minimums and maximums. In addition to this, tools such as the Network Monitor by Mozilla Firefox help provide insight into network-level slowdowns that might occur during transmission of data.
UCSD Pascal
UCSD Pascal is a Pascal programming language system that runs on the UCSD p-System, a portable, highly machine-independent operating system. UCSD Pascal was first released in 1977. It was developed at the University of California, San Diego (UCSD). == The p-System == In 1977, the University of California, San Diego (UCSD) Institute for Information Systems developed UCSD Pascal to provide students with a common environment that could run on any of the then available microcomputers as well as campus DEC PDP-11 minicomputers. The operating system became known as UCSD p-System. There were three operating systems that IBM offered for its original IBM PC: the UCSD p-System, CP/M-86, and IBM PC DOS. Vendor SofTech Microsystems emphasized p-System's application portability, with virtual machines for 20 CPUs as of the IBM PC's release. It predicted that users would be able to use applications they purchased on future computers running p-System; advertisements called it "the Universal Operating System". PC Magazine denounced UCSD p-System on the IBM PC, stating in a review of Context MBA, written in the language, that it "simply does not produce good code". The p-System did not sell very well for the IBM PC, because of a lack of applications and because it was more expensive than the other choices. Previously, IBM had offered the UCSD p-System as an option for IBM Displaywriter, an 8086-based dedicated word processing machine. (The Displaywriter's native operating system had been developed completely internally and was not opened for end-user programming.) Notable extensions to standard Pascal include separately compilable Units and a String type. Some intrinsics were provided to accelerate string processing (e.g. scanning in an array for a particular search pattern); other language extensions were provided to allow the UCSD p-System to be self-compiling and self-hosted. UCSD Pascal was based on a p-code machine architecture. Its contribution to these early virtual machines was to extend p-code away from its roots as a compiler intermediate language into a full execution environment. The UCSD Pascal p-Machine was optimized for the new small microcomputers with addressing restricted to 16-bit (only 64 KB of memory). James Gosling cites UCSD Pascal as a key influence (along with the Smalltalk virtual machine) on the design of the Java virtual machine. UCSD p-System achieved machine independence by defining a virtual machine, called the p-Machine (or pseudo-machine, which many users began to call the "Pascal-machine" like the OS—although UCSD documentation always used "pseudo-machine") with its own instruction set called p-code (or pseudo-code). Urs Ammann, a student of Niklaus Wirth, originally presented a p-code in his PhD thesis, from which the UCSD implementation was derived, the Zurich Pascal-P implementation. The UCSD implementation changed the Zurich implementation to be "byte oriented". The UCSD p-code was optimized for execution of the Pascal programming language. Each hardware platform then only needed a p-code interpreter program written for it to port the entire p-System and all the tools to run on it. Later versions also included additional languages that compiled to the p-code base. For example, Apple Computer offered a Fortran Compiler (written by Silicon Valley Software, Sunnyvale California) producing p-code that ran on the Apple version of the p-system. Later, TeleSoft (also located in San Diego) offered an early Ada development environment that used p-code and was therefore able to run on a number of hardware platforms including the Motorola 68000, the System/370, and the Pascal MicroEngine. UCSD p-System shares some concepts with the later Java platform. Both use a virtual machine to hide operating system and hardware differences, and both use programs written to that virtual machine to provide cross-platform support. Likewise both systems allow the virtual machine to be used either as the complete operating system of the target computer or to run in a "box" under another operating system. The UCSD Pascal compiler was distributed as part of a portable operating system, the p-System. == History == UCSD p-System began around 1974 as the idea of UCSD's Kenneth Bowles, who believed that the number of new computing platforms coming out at the time would make it difficult for new programming languages to gain acceptance. He based UCSD Pascal on the Pascal-P2 release of the portable compiler from Zurich. He was particularly interested in Pascal as a language to teach programming. UCSD introduced two features that were important improvements on the original Pascal: variable length strings, and "units" of independently compiled code (an idea included into the then-evolving Ada (programming language)). Niklaus Wirth credits the p-System, and UCSD Pascal in particular, with popularizing Pascal. It was not until the release of Turbo Pascal that UCSD's version started to slip from first place among Pascal users. The Pascal dialect of UCSD Pascal came from the subset of Pascal implemented in Pascal-P2, which was not designed to be a full implementation of the language, but rather "the minimum subset that would self-compile", to fit its function as a bootstrap kit for Pascal compilers. UCSD added strings from BASIC, and several other implementation dependent features. Although UCSD Pascal later obtained many of the other features of the full Pascal language, the Pascal-P2 subset persisted in other dialects, notably Borland Pascal, which copied much of the UCSD dialect. == Versions == There were four versions of UCSD p-code engine, each with several revisions of the p-System and UCSD Pascal. A revision of the p-code engine (i.e., the p-Machine) meant a change to the p-code language, and therefore compiled code is not portable between different p-Machine versions. Each revision was represented with a leading Roman Numeral, while operating system revisions were enumerated as the "dot" number following the p-code Roman Numeral. For example, II.3 represented the third revision of the p-System running on the second revision of the p-Machine. === Version I === Original version, never officially distributed outside of the University of California, San Diego. However, the Pascal sources for both Versions I.3 and I.5 were freely exchanged between interested users. Specifically, the patch revision I.5a was known to be one of the most stable. === Version II === Widely distributed, available on many early microcomputers. Numerous versions included Apple II ultimately Apple Pascal, DEC PDP-11, Intel 8080, Zilog Z80, and MOS 6502 based machines, Motorola 68000 and the IBM PC (Version II on the PC was restricted to one 64K code segment and one 64K stack/heap data segment; Version IV removed the code segment limit but cost a lot more). Project members from this era include Dr Kenneth L Bowles, Mark Allen, Richard Gleaves, Richard Kaufmann, Pete Lawrence, Joel McCormack, Mark Overgaard, Keith Shillington, Roger Sumner, and John Van Zandt. === Version III === Custom version written for Western Digital to run on their Pascal MicroEngine microcomputer. Included support for parallel processes for the first time. === Version IV === Commercial version, developed and sold by SofTech. Based on Version II; did not include changes from Version III. Did not sell well due to combination of their pricing structure, performance problems due to p-code interpreter, and competition with native operating systems (on top of which it often ran). After SofTech dropped the product, it was picked up by Pecan Systems, a relatively small company formed of p-System users and fans. Sales revived somewhat, due mostly to Pecan's reasonable pricing structure, but the p-System and UCSD Pascal gradually lost the market to native operating systems and compilers. Available for the TI-99/4A equipped with p-code card, Commodore CBM 8096, Sage II/IV, HP 9000, and BBC Micro with 6502 second processor. == Further use == The Corvus Systems computer used UCSD Pascal for all its user software. The "innovative concept" of the Constellation OS was to run Pascal (interpretively or compiled) and include all common software in the manual, so users could modify as needed.
Latent semantic analysis
Latent semantic analysis (LSA) is a technique in natural language processing, in particular distributional semantics, of analyzing relationships between a set of documents and the terms they contain by producing a set of concepts related to the documents and terms. LSA assumes that words that are close in meaning will occur in similar pieces of text (the distributional hypothesis). A matrix containing word counts per document (rows represent unique words and columns represent each document) is constructed from a large piece of text and a mathematical technique called singular value decomposition (SVD) is used to reduce the number of rows while preserving the similarity structure among columns. Documents are then compared by cosine similarity between any two columns. Values close to 1 represent very similar documents while values close to 0 represent very dissimilar documents. An information retrieval technique using latent semantic structure was patented in 1988 by Scott Deerwester, Susan Dumais, George Furnas, Richard Harshman, Thomas Landauer, Karen Lochbaum and Lynn Streeter. In the context of its application to information retrieval, it is sometimes called latent semantic indexing (LSI). == Overview == === Occurrence matrix === LSA can use a document-term matrix which describes the occurrences of terms in documents; it is a sparse matrix whose rows correspond to terms and whose columns correspond to documents. A typical example of the weighting of the elements of the matrix is tf-idf (term frequency–inverse document frequency): the weight of an element of the matrix is proportional to the number of times the terms appear in each document, where rare terms are upweighted to reflect their relative importance. This matrix is also common to standard semantic models, though it is not necessarily explicitly expressed as a matrix, since the mathematical properties of matrices are not always used. === Rank lowering === After the construction of the occurrence matrix, LSA finds a low-rank approximation to the term-document matrix. There could be various reasons for these approximations: The original term-document matrix is presumed too large for the computing resources; in this case, the approximated low rank matrix is interpreted as an approximation (a "least and necessary evil"). The original term-document matrix is presumed noisy: for example, anecdotal instances of terms are to be eliminated. From this point of view, the approximated matrix is interpreted as a de-noisified matrix (a better matrix than the original). The original term-document matrix is presumed overly sparse relative to the "true" term-document matrix. That is, the original matrix lists only the words actually in each document, whereas we might be interested in all words related to each document—generally a much larger set due to synonymy. The consequence of the rank lowering is that some dimensions are combined and depend on more than one term: {(car), (truck), (flower)} → {(1.3452 car + 0.2828 truck), (flower)} This mitigates the problem of identifying synonymy, as the rank lowering is expected to merge the dimensions associated with terms that have similar meanings. It also partially mitigates the problem with polysemy, since components of polysemous words that point in the "right" direction are added to the components of words that share a similar meaning. Conversely, components that point in other directions tend to either simply cancel out, or, at worst, to be smaller than components in the directions corresponding to the intended sense. === Derivation === Let X {\displaystyle X} be a matrix where element ( i , j ) {\displaystyle (i,j)} describes the occurrence of term i {\displaystyle i} in document j {\displaystyle j} (this can be, for example, the frequency). X {\displaystyle X} will look like this: d j ↓ t i T → [ x 1 , 1 … x 1 , j … x 1 , n ⋮ ⋱ ⋮ ⋱ ⋮ x i , 1 … x i , j … x i , n ⋮ ⋱ ⋮ ⋱ ⋮ x m , 1 … x m , j … x m , n ] {\displaystyle {\begin{matrix}&{\textbf {d}}_{j}\\&\downarrow \\{\textbf {t}}_{i}^{T}\rightarrow &{\begin{bmatrix}x_{1,1}&\dots &x_{1,j}&\dots &x_{1,n}\\\vdots &\ddots &\vdots &\ddots &\vdots \\x_{i,1}&\dots &x_{i,j}&\dots &x_{i,n}\\\vdots &\ddots &\vdots &\ddots &\vdots \\x_{m,1}&\dots &x_{m,j}&\dots &x_{m,n}\\\end{bmatrix}}\end{matrix}}} Now a row in this matrix will be a vector corresponding to a term, giving its relation to each document: t i T = [ x i , 1 … x i , j … x i , n ] {\displaystyle {\textbf {t}}_{i}^{T}={\begin{bmatrix}x_{i,1}&\dots &x_{i,j}&\dots &x_{i,n}\end{bmatrix}}} Likewise, a column in this matrix will be a vector corresponding to a document, giving its relation to each term: d j = [ x 1 , j ⋮ x i , j ⋮ x m , j ] {\displaystyle {\textbf {d}}_{j}={\begin{bmatrix}x_{1,j}\\\vdots \\x_{i,j}\\\vdots \\x_{m,j}\\\end{bmatrix}}} Now the dot product t i T t p {\displaystyle {\textbf {t}}_{i}^{T}{\textbf {t}}_{p}} between two term vectors gives the correlation between the terms over the set of documents. The matrix product X X T {\displaystyle XX^{T}} contains all these dot products. Element ( i , p ) {\displaystyle (i,p)} (which is equal to element ( p , i ) {\displaystyle (p,i)} ) contains the dot product t i T t p {\displaystyle {\textbf {t}}_{i}^{T}{\textbf {t}}_{p}} ( = t p T t i {\displaystyle ={\textbf {t}}_{p}^{T}{\textbf {t}}_{i}} ). Likewise, the matrix X T X {\displaystyle X^{T}X} contains the dot products between all the document vectors, giving their correlation over the terms: d j T d q = d q T d j {\displaystyle {\textbf {d}}_{j}^{T}{\textbf {d}}_{q}={\textbf {d}}_{q}^{T}{\textbf {d}}_{j}} . Now, from the theory of linear algebra, there exists a decomposition of X {\displaystyle X} such that U {\displaystyle U} and V {\displaystyle V} are orthogonal matrices and Σ {\displaystyle \Sigma } is a diagonal matrix. This is called a singular value decomposition (SVD): X = U Σ V T {\displaystyle {\begin{matrix}X=U\Sigma V^{T}\end{matrix}}} The matrix products giving us the term and document correlations then become X X T = ( U Σ V T ) ( U Σ V T ) T = ( U Σ V T ) ( V T T Σ T U T ) = U Σ V T V Σ T U T = U Σ Σ T U T X T X = ( U Σ V T ) T ( U Σ V T ) = ( V T T Σ T U T ) ( U Σ V T ) = V Σ T U T U Σ V T = V Σ T Σ V T {\displaystyle {\begin{matrix}XX^{T}&=&(U\Sigma V^{T})(U\Sigma V^{T})^{T}=(U\Sigma V^{T})(V^{T^{T}}\Sigma ^{T}U^{T})=U\Sigma V^{T}V\Sigma ^{T}U^{T}=U\Sigma \Sigma ^{T}U^{T}\\X^{T}X&=&(U\Sigma V^{T})^{T}(U\Sigma V^{T})=(V^{T^{T}}\Sigma ^{T}U^{T})(U\Sigma V^{T})=V\Sigma ^{T}U^{T}U\Sigma V^{T}=V\Sigma ^{T}\Sigma V^{T}\end{matrix}}} Since Σ Σ T {\displaystyle \Sigma \Sigma ^{T}} and Σ T Σ {\displaystyle \Sigma ^{T}\Sigma } are diagonal we see that U {\displaystyle U} must contain the eigenvectors of X X T {\displaystyle XX^{T}} , while V {\displaystyle V} must be the eigenvectors of X T X {\displaystyle X^{T}X} . Both products have the same non-zero eigenvalues, given by the non-zero entries of Σ Σ T {\displaystyle \Sigma \Sigma ^{T}} , or equally, by the non-zero entries of Σ T Σ {\displaystyle \Sigma ^{T}\Sigma } . Now the decomposition looks like this: X U Σ V T ( d j ) ( d ^ j ) ↓ ↓ ( t i T ) → [ x 1 , 1 … x 1 , j … x 1 , n ⋮ ⋱ ⋮ ⋱ ⋮ x i , 1 … x i , j … x i , n ⋮ ⋱ ⋮ ⋱ ⋮ x m , 1 … x m , j … x m , n ] = ( t ^ i T ) → [ [ u 1 ] … [ u l ] ] ⋅ [ σ 1 … 0 ⋮ ⋱ ⋮ 0 … σ l ] ⋅ [ [ v 1 ] ⋮ [ v l ] ] {\displaystyle {\begin{matrix}&X&&&U&&\Sigma &&V^{T}\\&({\textbf {d}}_{j})&&&&&&&({\hat {\textbf {d}}}_{j})\\&\downarrow &&&&&&&\downarrow \\({\textbf {t}}_{i}^{T})\rightarrow &{\begin{bmatrix}x_{1,1}&\dots &x_{1,j}&\dots &x_{1,n}\\\vdots &\ddots &\vdots &\ddots &\vdots \\x_{i,1}&\dots &x_{i,j}&\dots &x_{i,n}\\\vdots &\ddots &\vdots &\ddots &\vdots \\x_{m,1}&\dots &x_{m,j}&\dots &x_{m,n}\\\end{bmatrix}}&=&({\hat {\textbf {t}}}_{i}^{T})\rightarrow &{\begin{bmatrix}{\begin{bmatrix}\,\\\,\\{\textbf {u}}_{1}\\\,\\\,\end{bmatrix}}\dots {\begin{bmatrix}\,\\\,\\{\textbf {u}}_{l}\\\,\\\,\end{bmatrix}}\end{bmatrix}}&\cdot &{\begin{bmatrix}\sigma _{1}&\dots &0\\\vdots &\ddots &\vdots \\0&\dots &\sigma _{l}\\\end{bmatrix}}&\cdot &{\begin{bmatrix}{\begin{bmatrix}&&{\textbf {v}}_{1}&&\end{bmatrix}}\\\vdots \\{\begin{bmatrix}&&{\textbf {v}}_{l}&&\end{bmatrix}}\end{bmatrix}}\end{matrix}}} The values σ 1 , … , σ l {\displaystyle \sigma _{1},\dots ,\sigma _{l}} are called the singular values, and u 1 , … , u l {\displaystyle u_{1},\dots ,u_{l}} and v 1 , … , v l {\displaystyle v_{1},\dots ,v_{l}} the left and right singular vectors. Notice the only part of U {\displaystyle U} that contributes to t i {\displaystyle {\textbf {t}}_{i}} is the i 'th {\displaystyle i{\textrm {'th}}} row. Let this row vector be called t ^ i T {\displaystyle {\hat {\textrm {t}}}_{i}^{T}} . Likewise, the only part of V T {\displaystyle V^{T}} that contributes to d j {\displaystyle {\textbf {d}}_{j}} is the j 'th {\displaystyle j{\textrm {'th}}} column, d ^ j {\displaystyle {\hat {\textrm {d}}}_{j}} . These are not the eigenvectors, but depend on all the eigenvectors. I
Directed-energy weapon wildfire conspiracy theories
The directed-energy weapon wildfire conspiracy theories are claims circulating on social media and in fringe commentary that 2020s wildfires in places such as California, Hawaii and Texas were started or steered by directed-energy weapons or other lasers or directed-energy systems rather than by the documented ignition sources identified by investigators. Fact-checking organisations and newsrooms have repeatedly shown that widely shared images and clips said to depict “beams from the sky” are unrelated, miscaptioned or fabricated, and that official inquiries point to causes such as damaged or re-energised power lines, vegetation and extreme wind conditions. Coverage of the January 2025 Los Angeles fires described a resurgence of familiar hoaxes while local and federal agencies coordinated public rebuttals. == Background == Rumours linking directed-energy weapons to wildfire outbreaks appeared during earlier disaster seasons, then re-emerged at scale during the 2018 Camp Fire and again with the 2023 Maui wildfires and the 2025 Los Angeles fires. Journalists documented how large disasters reliably attract miscaptioned imagery and speculative narratives that portray official explanations as cover stories, while researchers and emergency managers noted that such claims tend to flourish during the information vacuum that accompanies fast-moving events. == Narratives and debunks == Recurring claims include assertions that videos show lasers igniting neighbourhoods, that “green” or “blue” items or roofs were spared because lasers cannot burn those colours, that trees remaining upright indicate precision targeting of houses, and that beams recorded over Hawaii or Texas came from secret platforms. Investigations show that a purported laser-strike video was actually an explosion at a Russian gas station recorded years earlier, that a photograph said to capture an “attack” was an Ohio gas flare from 2018, and that a separate video of green lights over Hawaii was captured months before the Maui fires by an astronomical camera and is unrelated. Fact-checks addressing colour myths have further explained that images of intact blue roofs were either misinterpreted or in at least one widely shared instance artificially generated, and that laser interaction with materials is not governed by such simplistic rules. == Investigations and identified causes == Authorities who examined specific incidents have published findings that contradict DEW narratives. A multi-agency investigation into the Maui disaster concluded that downed and later re-energised lines ignited an initial morning fire that re-kindled under extreme winds in the afternoon, with reports detailing the timeline and infrastructure context; summaries by national outlets echoed those conclusions. Investigators of the February 2024 Smokehouse Creek Fire in the Texas Panhandle reported that power lines ignited both the state’s largest wildfire and another major blaze, and the regional utility acknowledged its facilities appeared to have been involved; subsequent media coverage outlined the findings and regulatory follow-up. For the 2018 Camp Fire in Northern California, public reports from Butte County and subsequent proceedings identified PG&E transmission equipment as the source of ignition, with documentation of maintenance issues on the Caribou–Palermo line preceding the event. == Platform and agency responses == As major fires burned in and around Los Angeles in January 2025, officials from city agencies and national partners pursued a coordinated strategy to counter falsehoods by issuing timely updates, flagging fake imagery and directing residents to verified resources. Reporters described how federal emergency managers and local departments used social channels and briefings to rebut specific rumours, including claims about lasers and targeted ignition, and to clarify that early imagery often misleads during fast-moving disasters.