Scale-space theory is a framework for multi-scale signal representation developed by the computer vision, image processing and signal processing communities with complementary motivations from physics and biological vision. It is a formal theory for handling image structures at different scales, by representing an image as a one-parameter family of smoothed images, the scale-space representation, parametrized by the size of the smoothing kernel used for suppressing fine-scale structures. The parameter t {\displaystyle t} in this family is referred to as the scale parameter, with the interpretation that image structures of spatial size smaller than about t {\displaystyle {\sqrt {t}}} have largely been smoothed away in the scale-space level at scale t {\displaystyle t} . The main type of scale space is the linear (Gaussian) scale space, which has wide applicability as well as the attractive property of being possible to derive from a small set of scale-space axioms. The corresponding scale-space framework encompasses a theory for Gaussian derivative operators, which can be used as a basis for expressing a large class of visual operations for computerized systems that process visual information. This framework also allows visual operations to be made scale invariant, which is necessary for dealing with the size variations that may occur in image data, because real-world objects may be of different sizes and in addition the distance between the object and the camera may be unknown and may vary depending on the circumstances. == Definition == The notion of scale space applies to signals of arbitrary numbers of variables. The most common case in the literature applies to two-dimensional images, which is what is presented here. Consider a given image f {\displaystyle f} where f ( x , y ) {\displaystyle f(x,y)} is the greyscale value of the pixel at position ( x , y ) {\displaystyle (x,y)} . The linear (Gaussian) scale-space representation of f {\displaystyle f} is a family of derived signals L ( x , y ; t ) {\displaystyle L(x,y;t)} defined by the convolution of f ( x , y ) {\displaystyle f(x,y)} with the two-dimensional Gaussian kernel g ( x , y ; t ) = 1 2 π t e − ( x 2 + y 2 ) / 2 t {\displaystyle g(x,y;t)={\frac {1}{2\pi t}}e^{-(x^{2}+y^{2})/2t}\,} such that L ( ⋅ , ⋅ ; t ) = g ( ⋅ , ⋅ ; t ) ∗ f ( ⋅ , ⋅ ) , {\displaystyle L(\cdot ,\cdot ;t)\ =g(\cdot ,\cdot ;t)f(\cdot ,\cdot ),} where the semicolon in the argument of L {\displaystyle L} implies that the convolution is performed only over the variables x , y {\displaystyle x,y} , while the scale parameter t {\displaystyle t} after the semicolon just indicates which scale level is being defined. This definition of L {\displaystyle L} works for a continuum of scales t ≥ 0 {\displaystyle t\geq 0} , but typically only a finite discrete set of levels in the scale-space representation would be actually considered. The scale parameter t = σ 2 {\displaystyle t=\sigma ^{2}} is the variance of the Gaussian filter and as a limit for t = 0 {\displaystyle t=0} the filter g {\displaystyle g} becomes an impulse function such that L ( x , y ; 0 ) = f ( x , y ) , {\displaystyle L(x,y;0)=f(x,y),} that is, the scale-space representation at scale level t = 0 {\displaystyle t=0} is the image f {\displaystyle f} itself. As t {\displaystyle t} increases, L {\displaystyle L} is the result of smoothing f {\displaystyle f} with a larger and larger filter, thereby removing more and more of the details that the image contains. Since the standard deviation of the filter is σ = t {\displaystyle \sigma ={\sqrt {t}}} , details that are significantly smaller than this value are to a large extent removed from the image at scale parameter t {\displaystyle t} , see the following figures and for graphical illustrations. === Why a Gaussian filter? === When faced with the task of generating a multi-scale representation one may ask: could any filter g of low-pass type and with a parameter t which determines its width be used to generate a scale space? The answer is no, as it is of crucial importance that the smoothing filter does not introduce new spurious structures at coarse scales that do not correspond to simplifications of corresponding structures at finer scales. In the scale-space literature, a number of different ways have been expressed to formulate this criterion in precise mathematical terms. The conclusion from several different axiomatic derivations that have been presented is that the Gaussian scale space constitutes the canonical way to generate a linear scale space, based on the essential requirement that new structures must not be created when going from a fine scale to any coarser scale. Conditions, referred to as scale-space axioms, that have been used for deriving the uniqueness of the Gaussian kernel include linearity, shift invariance, semi-group structure, non-enhancement of local extrema, scale invariance and rotational invariance. In the works, the uniqueness claimed in the arguments based on scale invariance has been criticized, and alternative self-similar scale-space kernels have been proposed. The Gaussian kernel is, however, a unique choice according to the scale-space axiomatics based on causality or non-enhancement of local extrema. === Alternative definition === Equivalently, the scale-space family can be defined as the solution of the diffusion equation (for example in terms of the heat equation), ∂ t L = 1 2 ∇ 2 L , {\displaystyle \partial _{t}L={\frac {1}{2}}\nabla ^{2}L,} with initial condition L ( x , y ; 0 ) = f ( x , y ) {\displaystyle L(x,y;0)=f(x,y)} . This formulation of the scale-space representation L means that it is possible to interpret the intensity values of the image f as a "temperature distribution" in the image plane and that the process that generates the scale-space representation as a function of t corresponds to heat diffusion in the image plane over time t (assuming the thermal conductivity of the material equal to the arbitrarily chosen constant 1/2). Although this connection may appear superficial for a reader not familiar with differential equations, it is indeed the case that the main scale-space formulation in terms of non-enhancement of local extrema is expressed in terms of a sign condition on partial derivatives in the 2+1-D volume generated by the scale space, thus within the framework of partial differential equations. Furthermore, a detailed analysis of the discrete case shows that the diffusion equation provides a unifying link between continuous and discrete scale spaces, which also generalizes to nonlinear scale spaces, for example, using anisotropic diffusion. Hence, one may say that the primary way to generate a scale space is by the diffusion equation, and that the Gaussian kernel arises as the Green's function of this specific partial differential equation. == Motivations == The motivation for generating a scale-space representation of a given data set originates from the basic observation that real-world objects are composed of different structures at different scales. This implies that real-world objects, in contrast to idealized mathematical entities such as points or lines, may appear in different ways depending on the scale of observation. For example, the concept of a "tree" is appropriate at the scale of meters, while concepts such as leaves and molecules are more appropriate at finer scales. For a computer vision system analysing an unknown scene, there is no way to know a priori what scales are appropriate for describing the interesting structures in the image data. Hence, the only reasonable approach is to consider descriptions at multiple scales in order to be able to capture the unknown scale variations that may occur. Taken to the limit, a scale-space representation considers representations at all scales. Another motivation to the scale-space concept originates from the process of performing a physical measurement on real-world data. In order to extract any information from a measurement process, one has to apply operators of non-infinitesimal size to the data. In many branches of computer science and applied mathematics, the size of the measurement operator is disregarded in the theoretical modelling of a problem. The scale-space theory on the other hand explicitly incorporates the need for a non-infinitesimal size of the image operators as an integral part of any measurement as well as any other operation that depends on a real-world measurement. There is a close link between scale-space theory and biological vision. Many scale-space operations show a high degree of similarity with receptive field profiles recorded from the mammalian retina and the first stages in the visual cortex. In these respects, the scale-space framework can be seen as a theoretically well-founded paradigm for early vision, which in addition has been thoroughly tested by algorithms and experiments. == Gaussian derivatives == At any scale in scale space, we c
Software diagnosis
Software diagnosis (also: software diagnostics) refers to concepts, techniques, and tools that allow for obtaining findings, conclusions, and evaluations about software systems and their implementation, composition, behaviour, and evolution. It serves as means to monitor, steer, observe and optimize software development, software maintenance, and software re-engineering in the sense of a business intelligence approach specific to software systems. It is generally based on the automatic extraction, analysis, and visualization of corresponding information sources of the software system. It can also be manually done and not automatic. == Applications == Software diagnosis supports all branches of software engineering, in particular project management, quality management, risk management as well as implementation and test. Its main strength is to support all stakeholders of software projects (in particular during software maintenance and for software re-engineering tasks) and to provide effective communication means for software development projects. For example, software diagnosis facilitates "bridging an essential information gap between management and development, improve awareness, and serve as early risk detection instrument". Software diagnosis includes assessment methods for "perfective maintenance" that, for example, apply "visual analysis techniques to combine multiple indicators for low maintainability, including code complexity and entanglement with other parts of the system, and recent changes applied to the code". == Characteristics == In contrast to manifold approaches and techniques in software engineering, software diagnosis does not depend on programming languages, modeling techniques, software development processes or the specific techniques used in the various stages of the software development process. Instead, software diagnosis aims at analyzing and evaluating the software system in its as-is state and based on system-generated information to bypass any subjective or potentially outdated information sources (e.g., initial software models). For it, software diagnosis combines and relates sources of information that are typically not directly linked. Examples: Source-code metrics are related with software developer activity to gain insight into developer-specific effects on software code quality. System structure and run-time execution traces are correlated to facilitate program comprehension through dynamic analysis in software maintenance tasks. == Principles == The core principle of software diagnosis is to automatically extract information from all available information sources of a given software projects such as source code base, project repository, code metrics, execution traces, test results, etc. To combine information, software-specific data mining, analysis, and visualization techniques are applied. Its strength results, among various reasons, from integrating decoupled information spaces in the scope of a typical software project, for example development and developer activities (recorded by the repository) and code and quality metrics (derived by analyzing source code) or key performance indicators (KPIs). == Examples == Examples of software diagnosis tools include software maps and software metrics. == Critics == Software diagnosis—in contrast to many approaches in software engineering—does not assume that developer capabilities, development methods, programming or modeling languages are right or wrong (or better or worse compared to each other): Software diagnosis aims at giving insight into a given software system and its status regardless of the methods, languages, or models used to create and maintain the system. === Related subjects === Cost estimation in software engineering Programming productivity Rapid application development Software design Software development Software documentation Software map Software release life cycle Systems design Systems Development Life Cycle
Stewart Nelson
Stewart Nelson is an American mathematician and programmer from The Bronx who co-founded Systems Concepts. == Biography == From a young age, Nelson was tinkering with electronics, aided and abetted by his father who was a physicist that had become an engineer. Stewart attended Poughkeepsie High School, graduating in the spring of 1963. From his first few days of High School, Stewart displayed his talents for hacking the international telephone trunk lines, along with an uncanny skill for picking combination locks, although this was always done as innocent entertainment. He simply loved the challenge of seeing how quickly he could accomplish this feat. His quirky sense of humor was always visible, as was his disdain for any rule that got in the way of his gaining knowledge. Stewart was an inspiration to the school's Tech-elec Club, as well as a ringleader in the founding of the school's pirate radio station. Nelson enrolled at MIT in 1963 and quickly became known for hooking up the AI Lab's PDP-1 (and later the PDP-6) to the telephone network, making him one of the first phreakers. Nelson later accomplished other feats like hard-wiring additional instructions into the PDP-1. Nelson was hired by Ed Fredkin's Information International Inc. at the urging of Marvin Minsky to work on PDP-7 programs at the MIT Computer Science and Artificial Intelligence Laboratory. Nelson was known as a brilliant software programmer. He was influential in LISP, the assembly instructions for the Digital Equipment Corporation PDP, and a number of other systems. The group of young hackers was known for working on systems after hours. One night, Nelson and others decided to rewire MIT's PDP-1 as a prank. Later, Margaret Hamilton tried to use the DEC-supplied DECAL assembler on the machine and it crashed repeatedly.
Aidan Gomez
Aidan Gomez is a British-Canadian computer scientist working in the field of artificial intelligence, with a focus on natural language processing. He is the co-founder and CEO of the technology company Cohere. == Early life and education == Gomez grew up in Brighton, Ontario. He graduated from the University of Toronto with a bachelor's degree in computer science and mathematics. He was pursuing a PhD in computer science from the University of Oxford. He paused his studies to launch Cohere. He was granted the PhD in 2024. == Career == In 2017, as a 20 year-old intern at Google Brain, Gomez was one of eight authors of the research paper "Attention Is All You Need", which is credited with changing the AI industry and helping lead to the creation of ChatGPT. The paper proposed a novel deep learning architecture called the transformer, that enables machine learning models to analyze large amounts of data for patterns, and then use those patterns to make predictions while leveraging GPU parallelization. It has been commonly adopted for training large language models and in the development of generative AI. In the same year, Gomez founded FOR.ai, a program to help researchers learn machine learning techniques in a collaborative format. An outgrowth of this project was Cohere For AI (now Cohere Labs), which released Aya, an open-source multilingual LLM. As a PhD student, Gomez worked as a machine learning researcher at Google Brain. At that time, he co-authored the paper "One Model to Learn Them All" about multi-task learning by a single neural network. In 2019, Gomez left Google Brain to launch Cohere, an enterprise-focused company that helps businesses implement AI into chatbots, search engines, and other products. As of Sept 2025, Cohere has raised about US$1.6 billion at valuation north of $7 billion, as Gomez leads the company as its CEO. Gomez was named to the 2023 Time 100/AI list of the most influential people in the field of artificial intelligence. He and his fellow Cohere founders Ivan Zhang and Nick Frosst were named number 1 on 2023 Maclean's AI Trailblazers Power List. In April 2025, Gomez was elected to the board of Rivian. == Views on AI == Gomez has stated that warnings regarding the existential risk from artificial intelligence are overblown, and that real risks involve the automated spread of misinformation on social media. He said that the United States would win the AI arms race over China.
Comet (browser)
Comet is an AI-powered web browser based on Chromium. It was released by Perplexity AI for Microsoft Windows and macOS on July 9, 2025, for Android on November 20, 2025, and for iOS on March 18, 2026. Initial access to the browser was limited to users subscribed to Perplexity's most expensive tier, with broader availability expected over time. The browser was released for free download in October 2025. == Features == Comet is integrated with Perplexity's AI-assisted search engine. The browser features an assistant which enables users to perform a variety of tasks such as generating article summaries, sending emails, or buying products. == Security concerns == Researchers at LayerX Security identified a malicious attack vector which they call CometJacking. The exploit could possibly exfiltrate a user's personal sensitive data to a remote server controlled by the attacker. LayerX attempted to responsibly disclose their findings to Comet's developer Perplexity AI in August 2025. Perplexity responded that they saw no security impact and marked the disclosure as not applicable.
Co–Star
Co–Star is an American astrological social networking service founded in 2017, and headquartered in New York City. Users enter the date, time and place they were born to generate an astrological chart and daily horoscopes, which can be compared with those of other users. == History == The concept for Co-Star began in 2015 when Banu Guler created an astrological chart as a gift. The idea later developed into a mobile application with collaborators Anna Kopp and Ben Weitzman. The app publicly launched in 2017. The app includes astrological readings, charts, and daily push notifications that have been noted for their unconventional tone. In early 2018, the company raised a $750,000 pre-seed round from Female Founders Fund. In 2019, Co–Star raised a $5.2 million seed round from Maveron, Aspect, and 14W. In January 2020, Co–Star for Android was launched to a 120,000-person waitlist—two years after their iOS version. In April 2021, the company announced a $15 million Series A, led by Spark Capital. As of that date, Co–Star reported more than 20 million downloads and increased adoption among young women in the United States. == Features == Co–Star employs artificial intelligence to analyze publicly accessible NASA JPL data and find patterns in a user's transits. Co–Star's algorithm maps human-written snippets of text to planetary movements to display personalized content for each user. That content has been called “slightly robotic,” “wildly beautiful,” “truly insane," “brutally honest,” and compared to “a free therapy session.” In July 2023, Co–Star released an in-app service called The Void that allows users to ask open-ended questions and receive answers informed by Co–Star's astrological database.
Tag (metadata)
In information systems, a tag is a keyword or term assigned to a piece of information (such as an Internet bookmark, multimedia, database record, or computer file). This kind of metadata helps describe an item and allows it to be found again by browsing or searching. Tags are generally chosen informally and personally by the item's creator or by its viewer, depending on the system, although they may also be chosen from a controlled vocabulary. Tagging was popularized by websites associated with Web 2.0 and is an important feature of many Web 2.0 services. It is now also part of other database systems, desktop applications, and operating systems. == Overview == People use tags to aid classification, mark ownership, note boundaries, and indicate online identity. Tags may take the form of words, images, or other identifying marks. An analogous example of tags in the physical world is museum object tagging. People were using textual keywords to classify information and objects long before computers. Computer based search algorithms made the use of such keywords a rapid way of exploring records. Tagging gained popularity due to the growth of social bookmarking, image sharing, and social networking websites. These sites allow users to create and manage labels (or "tags") that categorize content using simple keywords. Websites that include tags often display collections of tags as tag clouds, as do some desktop applications. On websites that aggregate the tags of all users, an individual user's tags can be useful both to them and to the larger community of the website's users. Tagging systems have sometimes been classified into two kinds: top-down and bottom-up. Top-down taxonomies are created by an authorized group of designers (sometimes in the form of a controlled vocabulary), whereas bottom-up taxonomies (called folksonomies) are created by all users. This definition of "top down" and "bottom up" should not be confused with the distinction between a single hierarchical tree structure (in which there is one correct way to classify each item) versus multiple non-hierarchical sets (in which there are multiple ways to classify an item); the structure of both top-down and bottom-up taxonomies may be either hierarchical, non-hierarchical, or a combination of both. Some researchers and applications have experimented with combining hierarchical and non-hierarchical tagging to aid in information retrieval. Others are combining top-down and bottom-up tagging, including in some large library catalogs (OPACs) such as WorldCat. When tags or other taxonomies have further properties (or semantics) such as relationships and attributes, they constitute an ontology. In folder system a file cannot exist in two or more folders so tag system has been thought more convenient. But transitioning to tag system requires awareness of difference between properties of two systems. In folder system the information of classification is put outside of the file and we can change folder at once. In tag system the information of classification is put inside the file so changing its tag means changing the file and it needs to be saved again and takes time. Metadata tags as described in this article should not be confused with the use of the word "tag" in some software to refer to an automatically generated cross-reference; examples of the latter are tags tables in Emacs and smart tags in Microsoft Office. == History == The use of keywords as part of an identification and classification system long predates computers. Paper data storage devices, notably edge-notched cards, that permitted classification and sorting by multiple criteria were already in use prior to the twentieth century, and faceted classification has been used by libraries since the 1930s. In the late 1970s and early 1980s, Emacs, the text editor for Unix systems, offered a companion software program called Tags that could automatically build a table of cross-references called a tags table that Emacs could use to jump between a function call and that function's definition. This use of the word "tag" did not refer to metadata tags, but was an early use of the word "tag" in software to refer to a word index. Online databases and early websites deployed keyword tags as a way for publishers to help users find content. In the early days of the World Wide Web, the keywords meta element was used by web designers to tell web search engines what the web page was about, but these keywords were only visible in a web page's source code and were not modifiable by users. In 1997, the collaborative portal "A Description of the Equator and Some ØtherLands" produced by documenta X, Germany, used the folksonomic term Tag for its co-authors and guest authors on its Upload page. In "The Equator" the term Tag for user-input was described as an abstract literal or keyword to aid the user. However, users defined singular Tags, and did not share Tags at that point. In 2003, the social bookmarking website Delicious provided a way for its users to add "tags" to their bookmarks (as a way to help find them later); Delicious also provided browseable aggregated views of the bookmarks of all users featuring a particular tag. Within a couple of years, the photo sharing website Flickr allowed its users to add their own text tags to each of their pictures, constructing flexible and easy metadata that made the pictures highly searchable. The success of Flickr and the influence of Delicious popularized the concept, and other social software websites—such as YouTube, Technorati, and Last.fm—also implemented tagging. In 2005, the Atom web syndication standard provided a "category" element for inserting subject categories into web feeds, and in 2007 Tim Bray proposed a "tag" URN. == Examples == === Within a blog === Many systems (and other web content management systems) allow authors to add free-form tags to a post, along with (or instead of) placing the post into a predetermined category. For example, a post may display that it has been tagged with baseball and tickets. Each of those tags is usually a web link leading to an index page listing all of the posts associated with that tag. The blog may have a sidebar listing all the tags in use on that blog, with each tag leading to an index page. To reclassify a post, an author edits its list of tags. All connections between posts are automatically tracked and updated by the blog software; there is no need to relocate the page within a complex hierarchy of categories. === Within application software === Some desktop applications and web applications feature their own tagging systems, such as email tagging in Gmail and Mozilla Thunderbird, bookmark tagging in Firefox, audio tagging in iTunes or Winamp, and photo tagging in various applications. Some of these applications display collections of tags as tag clouds. === Assigned to computer files === There are various systems for applying tags to the files in a computer's file system. In Apple's Mac System 7, released in 1991, users could assign one of seven editable colored labels (with editable names such as "Essential", "Hot", and "In Progress") to each file and folder. In later iterations of the Mac operating system ever since OS X 10.9 was released in 2013, users could assign multiple arbitrary tags as extended file attributes to any file or folder, and before that time the open-source OpenMeta standard provided similar tagging functionality for Mac OS X. Several semantic file systems that implement tags are available for the Linux kernel, including Tagsistant. Microsoft Windows allows users to set tags only on Microsoft Office documents and some kinds of picture files. Cross-platform file tagging standards include Extensible Metadata Platform (XMP), an ISO standard for embedding metadata into popular image, video and document file formats, such as JPEG and PDF, without breaking their readability by applications that do not support XMP. XMP largely supersedes the earlier IPTC Information Interchange Model. Exif is a standard that specifies the image and audio file formats used by digital cameras, including some metadata tags. TagSpaces is an open-source cross-platform application for tagging files; it inserts tags into the filename. === For an event === An official tag is a keyword adopted by events and conferences for participants to use in their web publications, such as blog entries, photos of the event, and presentation slides. Search engines can then index them to make relevant materials related to the event searchable in a uniform way. In this case, the tag is part of a controlled vocabulary. === In research === A researcher may work with a large collection of items (e.g. press quotes, a bibliography, images) in digital form. If he/she wishes to associate each with a small number of themes (e.g. to chapters of a book, or to sub-themes of the overall subject), then a group of tags for these themes can be attached to each of the items in