Vector quantization (VQ) is a classical quantization technique from signal processing that allows the modeling of probability density functions by the distribution of prototype vectors. Developed in the early 1980s by Robert M. Gray, it was originally used for data compression. It works by dividing a large set of points (vectors) into groups having approximately the same number of points closest to them. Each group is represented by its centroid point, as in k-means and some other clustering algorithms. In simpler terms, vector quantization chooses a set of points to represent a larger set of points. The density matching property of vector quantization is powerful, especially for identifying the density of large and high-dimensional data. Since data points are represented by the index of their closest centroid, commonly occurring data have low error, and rare data high error. This is why VQ is suitable for lossy data compression. It can also be used for lossy data correction and density estimation. Vector quantization is based on the competitive learning paradigm, so it is closely related to the self-organizing map model and to sparse coding models used in deep learning algorithms such as autoencoder. == Training == One simple training algorithm for vector quantization is: Pick a sample point at random Move the nearest quantization vector centroid towards this sample point, by a small fraction of the distance Repeat A more sophisticated algorithm reduces the bias in the density matching estimation and ensures that all points are used, by including an extra sensitivity parameter: Increase each centroid's sensitivity s i {\displaystyle s_{i}} by a small amount Pick a sample point P {\displaystyle P} at random For each quantization vector centroid c i {\displaystyle c_{i}} , let d ( P , c i ) {\displaystyle d(P,c_{i})} denote the distance of P {\displaystyle P} and c i {\displaystyle c_{i}} Find the centroid c i {\displaystyle c_{i}} for which d ( P , c i ) − s i {\displaystyle d(P,c_{i})-s_{i}} is the smallest Move c i {\displaystyle c_{i}} towards P {\displaystyle P} by a small fraction of the distance Set s i {\displaystyle s_{i}} to zero Repeat It is desirable to use a cooling schedule to produce convergence: see Simulated annealing. Another simple method is LBG, which is based on k-means. The algorithm can be iteratively updated with "live" data, rather than by picking random points from a data set, but this will introduce some bias if the data are temporally correlated over many samples. == Applications == Vector quantization is used for lossy data compression, lossy data correction, pattern recognition, density estimation and clustering. Lossy data correction, or prediction, is used to recover data missing from some dimensions. It is done by finding the nearest group with the data dimensions available, then predicting the result based on the values for the missing dimensions, assuming that they will have the same value as the group's centroid. For density estimation, the area/volume that is closer to a particular centroid than to any other is inversely proportional to the density (due to the density matching property of the algorithm). === Use in data compression === Vector quantization, also called "block quantization" or "pattern matching quantization" is often used in lossy data compression. It works by encoding values from a multidimensional vector space into a finite set of values from a discrete subspace of lower dimension. A lower-space vector requires less storage space, so the data is compressed. Due to the density matching property of vector quantization, the compressed data has errors that are inversely proportional to density. The transformation is usually done by projection or by using a codebook. In some cases, a codebook can be also used to entropy code the discrete value in the same step, by generating a prefix coded variable-length encoded value as its output. The set of discrete amplitude levels is quantized jointly rather than each sample being quantized separately. Consider a k-dimensional vector [ x 1 , x 2 , . . . , x k ] {\displaystyle [x_{1},x_{2},...,x_{k}]} of amplitude levels. It is compressed by choosing the nearest matching vector from a set of n-dimensional vectors [ y 1 , y 2 , . . . , y n ] {\displaystyle [y_{1},y_{2},...,y_{n}]} , with n < k. All possible combinations of the n-dimensional vector [ y 1 , y 2 , . . . , y n ] {\displaystyle [y_{1},y_{2},...,y_{n}]} form the vector space to which all the quantized vectors belong. Only the index of the codeword in the codebook is sent instead of the quantized values. This conserves space and achieves more compression. Twin vector quantization (VQF) is part of the MPEG-4 standard dealing with time domain weighted interleaved vector quantization. === Video codecs based on vector quantization === Bink video Cinepak Daala is transform-based but uses pyramid vector quantization on transformed coefficients Digital Video Interactive: Production-Level Video and Real-Time Video Indeo Microsoft Video 1 QuickTime: Apple Video (RPZA) and Graphics Codec (SMC) Sorenson SVQ1 and SVQ3 Smacker video VQA format, used in many games The usage of video codecs based on vector quantization has declined significantly in favor of those based on motion compensated prediction combined with transform coding, e.g. those defined in MPEG standards, as the low decoding complexity of vector quantization has become less relevant. === Audio codecs based on vector quantization === AMR-WB+ CELP CELT (now part of Opus) is transform-based but uses pyramid vector quantization on transformed coefficients Codec 2 DTS G.729 iLBC Ogg Vorbis TwinVQ === Use in pattern recognition === VQ was also used in the eighties for speech and speaker recognition. Recently it has also been used for efficient nearest neighbor search and on-line signature recognition. In pattern recognition applications, one codebook is constructed for each class (each class being a user in biometric applications) using acoustic vectors of this user. In the testing phase the quantization distortion of a testing signal is worked out with the whole set of codebooks obtained in the training phase. The codebook that provides the smallest vector quantization distortion indicates the identified user. The main advantage of VQ in pattern recognition is its low computational burden when compared with other techniques such as dynamic time warping (DTW) and hidden Markov model (HMM). The main drawback when compared to DTW and HMM is that it does not take into account the temporal evolution of the signals (speech, signature, etc.) because all the vectors are mixed up. In order to overcome this problem a multi-section codebook approach has been proposed. The multi-section approach consists of modelling the signal with several sections (for instance, one codebook for the initial part, another one for the center and a last codebook for the ending part). === Use as clustering algorithm === As VQ is seeking for centroids as density points of nearby lying samples, it can be also directly used as a prototype-based clustering method: each centroid is then associated with one prototype. By aiming to minimize the expected squared quantization error and introducing a decreasing learning gain fulfilling the Robbins-Monro conditions, multiple iterations over the whole data set with a concrete but fixed number of prototypes converges to the solution of k-means clustering algorithm in an incremental manner. === Generative adversarial networks (GAN) === VQ has been used to quantize a feature representation layer in the discriminator of generative adversarial networks. The feature quantization (FQ) technique performs implicit feature matching. It improves the GAN training, and yields an improved performance on a variety of popular GAN models: BigGAN for image generation, StyleGAN for face synthesis, and U-GAT-IT for unsupervised image-to-image translation.
Clips (software)
Clips is a discontinued mobile video editing software application created by Apple Inc. It was released onto the iOS App Store on April 6, 2017, for free. Initially, it was only available on 64-bit devices running iOS 10.3 or later; as of version 3.1.3, it requires iOS 16.0 or later. Apple describes it as an app for "making and sharing fun videos with text, effects, graphics, and more.". Its final release was on May 9, 2024 before was removed from the App Store on October 10, 2025. == Features == After launching of the app, the user sees the view of the front-facing camera. The app allows the user to create a new clip by tapping on a red record button, or use photos or videos from the device's photo library. Once a clip is recorded, it can be added to a project timeline shown at the bottom of the screen. The user can share their project on social media platforms. The user can also add filters and effects to the project. "Live Titles" (available in several styles) can also be created by dictating to the device.
Adobe GoLive
Adobe GoLive was a WYSIWYG HTML editor and web site management application from Adobe Systems. It replaced Adobe PageMill as Adobe's primary HTML editor and was itself discontinued in favor of Dreamweaver. The last version of GoLive that Adobe released was GoLive 9. == History == GoLive originated as the flagship product of a company named GoNet Communication, Inc. then based in Menlo Park, California, and the development company GoNet Communications GmbH in Hamburg, Germany, in 1996. Later GoNet changed its name to GoLive Systems, Inc, and the name of its product to GoLive CyberStudio. Adobe acquired GoLive in 1999 and re-branded the GoLive CyberStudio product to what became Adobe GoLive. Adobe took over the Hamburg office as an Adobe development site to continue to develop the product. At the time of the acquisition, CyberStudio was a Macintosh-only application. In the spring of 1999 Adobe released Adobe GoLive for both Macintosh and Microsoft Windows. The first versions of Dreamweaver and CyberStudio were released in a similar timeframe. However, Dreamweaver eventually became the dominant WYSIWYG HTML editor in market share. After the Adobe acquisition of Macromedia (the company that had owned Dreamweaver), GoLive was progressively re-targeted toward Adobe's traditional design market, and the product became better integrated with Adobe's existing suite of design-oriented software products and less focused on the professional web development market. The Adobe CS2 Premium suite contained GoLive CS2. With the release of Creative Suite 3, Adobe integrated Dreamweaver as a replacement for GoLive and released GoLive 9 as a standalone product. In April 2008, Adobe announced that sales and development of GoLive would cease in favor of Dreamweaver. == General description and distinctive aspects == GoLive incorporated a largely modeless workflow that relied heavily on drag-and-drop. Most user interaction was done via a contextual inspector rather than the modal workflow found in Dreamweaver. Among its features were a separate editor for tables that supported nesting, and a two-dimensional panel for applying CSS styles to elements. GoLive supported drag-and-drop of native Adobe Photoshop and Adobe Illustrator files via what the company called "Smart Objects", which then automatically guided the user through saving those files in web-supported formats. Updates to the original Photoshop or Illustrator assets were automatically tracked by GoLive. It also implemented a tool called "Components" which allowed updates to interface elements throughout a site to be updated globally by changing one single file. As a website management tool, GoLive allowed users to transfer and publish content directly from within the application, and allowed individual files to be excluded from uploading. == Features == One of the new features of GoLive version 5 was Dynamic Link, which was a method of creating dynamic, database-driven web content without the need to know a server-side language and with full WYSIWYG support in the GoLive user interface. GoLive had a powerful set of extensibility API which could be used to add additional functionality to the product. The GoLive SDK provided interfaces which allowed developers to use a combination of XML, JavaScript and C/C++ to create plugins for the product. The extensibility API allowed developers access to custom drawing and event handling using JavaScript, as well as a full JavaScript debugger and command line interpreter. This allowed intermediate-level developers using interpreted JavaScript to create sophisticated user interfaces. == Language and framework structure == Adobe GoLive is coded in the C++ programming language. It uses a custom C++ framework called SCL (Simple Class Library) which was initially built from scratch by the engineers at GoLive Systems Inc. The SCL framework was also used in the short-lived Adobe Atmosphere 3D software. == Release history == As the final version, GoLive 9 was discontinued in April 2008.
Boris FX
Boris FX is a visual effects, video editing, photography, and audio software plug-in developer based in Miami, Florida, USA. The developer is known for its flagship products, Continuum (formerly Boris Continuum Complete/BCC), Sapphire, Mocha, and Silhouette. Boris FX creates plug-in tools for feature film, broadcast television, and multimedia post-production workflows. The plug-ins are compatible with various NLEs, including Adobe After Effects and Premiere Pro, Avid Media Composer, Apple Final Cut Pro, and OFX hosts such as Autodesk Flame, Foundry Nuke, Blackmagic Design DaVinci Resolve and Fusion, and VEGAS Pro. Boris FX has incorporated artificial intelligence into its software, introducing features for noise reduction, rotoscoping, upscaling, and masking. The company has acquired technologies via mergers and acquisitions from Imagineer Systems, GenArts, Silhouette FX, Digital Film Tools, CrumplePop and Andersson Technologies to expand its visual effects, editing, photography, and audio tools. == History == Boris FX was founded in 1995 by Boris Yamnitsky. The former Media 100 engineer (a member of the original Media 100 launch team in 1993) released “Boris FX,” the first plug-in-based digital video effects (DVE) for Adobe Premiere and Media 100, in 1995. The plug-in won Best of Show at Apple Macworld in Boston, MA that same year. The Boris FX Suite includes a range of visual effects and post-production tools, such as Sapphire, Continuum, Mocha Pro, Silhouette, SynthEyes, CrumplePop, Optics, and Particle Illusion. == Media 100 == In October 2005, Yamnitsky acquired Media 100 the company that launched his plug-in career. Boris FX had a long relationship with Media 100 which bundled Boris RED software as its main titling and compositing solution. Media 100's video editing software is available as freeware for macOS. == Continuum == Continuum is a visual effect and compositing plugin suite that includes a library of over 300 effects and more than 40 transitions, including tools for image restoration, compositing, titling, particle generation, and stylized effects, along with features such as lens flares, lighting effects, and cinematic color grading presets. A key component of Continuum is its integration with the Mocha planar tracking and masking system, enabling advanced tracking and rotoscoping within the effects. The suite also includes Particle Illusion, a real-time particle generator used for creating visual effects such as explosions, smoke, and abstract motion graphics, as well as Primatte Studio, a chroma keying and compositing toolset for green screen and blue screen workflows. Continuum supports GPU acceleration and offers compatibility with HDR and 360/VR content. Regular updates introduce new effects, presets, and performance enhancements to expand its capabilities. In October 2018, Continuum relaunched Particle Illusion, a Mocha Essentials workflow with magnetic edge-snapping, and updates to Title Studio. In October 2019, Continuum introduced Corner Pin Studio with built-in Mocha tracking for quick screen replacement and inserts, 6 stylized transitions, and 4 creative effects. In October 2020, Continuum released an update that included over 80 GPU-accelerated effects such as film stocks, color grades, optical filter simulations, and a digital gobo library. The update also introduced a custom FX Editor interface, real-time particles, and more than 1,000 drag-and-drop presets. In November 2021, it added multi-frame rendering for After Effects, native Apple M1 support, fluid dynamics in Particle Illusion, and 60 color-grade presets. In October 2022, the software introduced 10 additional transitions, a revised Particle Illusion workflow, an atmospheric glow effect, and more than 250 curated presets. Continuum plugins have been used in television, streaming, and film projects, including A Black Lady Sketch Show (HBO/HBO Max), Star Trek: Discovery (CBS), Andor (Disney+), The Curse of Oak Island (History Channel), Keeping up with the Kardashians (E!), This Old House (PBS), Ms. Marvel (Disney+), MasterChef (Fox), WipeOut (TBS), The Boys (Prime Video), and The Today Show (NBC). == Mocha Pro == In December 2014, Boris FX merged with Imagineer Systems, the UK-based developer of the Academy Award-winning planar motion tracking software, Mocha Pro. Mocha Pro's features include planar tracking (motion tracking), rotoscoping, image stabilization, 3D camera tracking, and object removal. In June 2016, Mocha released (v5) which introduced Mocha Pro's tools as plug-ins for Adobe After Effects and Premiere Pro, Avid Media Composer, and OFX hosts Foundry's NUKE, Blackmagic Design Fusion, VEGAS Pro, and HitFilm. A simplified version, Mocha AE, is included with Adobe After Effects Creative Cloud and has been bundled with the software since CS4. A similar version is also available with HitFilm Pro from FXhome and VEGAS Pro. Mocha's tracking SDK is integrated into other visual effects tools, including SAM Quantel Pablo Rio, Silhouette FX, CoreMelt, and Motion VFX. Mocha Pro has been used in various film and television productions, including Birdman, Black Swan, the Harry Potter series, The Hobbit, Star Wars, The Mandalorian, Star Trek: Discovery, and The Umbrella Academy. It has also been employed in projects such as Gone Girl, The Hunger Games: Mockingjay – Part 1, Game of Thrones, and House of Cards. == Sapphire == GenArts, founded by Karl Sims in 1996, developed visual effects plug-ins that were used by studios and post-production facilities. In September 2016, Boris FX merged with former competitor, GenArts, Inc., developer of Sapphire high-end visual effects plug-ins, to expand its suite of motion graphics and VFX tools. The merger brought Sapphire alongside Boris Continuum Complete (BCC) and Mocha Pro, integrating these tools for film and television post-production. The Sapphire suite includes a library of over 270 effects and transitions, organized into categories such as lighting, stylization, distortions, textures, and transitions. Commonly used effects include glows, lens flares, film looks, and blurs. The plug-ins are designed to be GPU-accelerated, allowing for improved rendering performance and real-time previews in supported host applications. A central feature of Sapphire is the Builder tool, a node-based workspace that allows users to create custom effects and transitions by combining multiple Sapphire plug-ins. This enables a high level of creative flexibility and reusability, making it a popular tool for both editors and VFX artists. Sapphire also integrates with Mocha, Boris FX's planar tracking and masking system, allowing for advanced control of visual elements within an effect. In October 2017, Boris FX released its first new version of Sapphire since the GenArts acquisition. Sapphire (v11) now includes integrated Mocha tracking and masking tools. Sapphire is available for Adobe, Avid, the Autodesk Flame family, and OFX hosts including Blackmagic DaVinci Resolve and Fusion, and Foundry's NUKE. As part of the merger, Boris FX acquired the rights to Particle Illusion. In 2018, Boris FX reintroduced the product to the larger NLE/Compositing market. Sapphire's plug-ins transitioned from C to C++ to improve performance and support higher-resolution visual effects. This update enhanced floating-point calculations, compatibility with film editing APIs, and integration with NVIDIA's CUDA for faster rendering. The plug-ins have been used in various films, including Avatar, the Harry Potter and the Prisoner of Azkaban, Iron Man, The Lord of the Rings, The Matrix trilogy, Titanic, and X-Men. == Particle Illusion == As part of the merger with GenArts in 2016, Boris FX acquired the rights to the Particle Illusion (formerly particleIllusion) product, a storied particle system from the original developer Alan Lorence, the founder of Wondertouch. In 2018, Boris FX released a redesigned version of the product to a larger NLE/compositing market as part of Continuum (2019). The new Particle Illusion plug-in supports Adobe, Avid, and many OFX hosts. == Silhouette == In September 2019, Boris FX merged with SilhouetteFX, Academy Award-winning developer of Silhouette, a high-end digital paint, advanced rotoscoping, motion tracking, and node-based compositing application for visual effects in film post-production. The acquisition integrated Silhouette's advanced rotoscoping and paint technology, recognized by the Academy of Motion Pictures, into Boris FX's suite of products, alongside Sapphire, Continuum, and Mocha Pro. In May 2021, Boris FX released Silhouette 2021, the first version of Silhouette released by Boris FX to function both as a standalone application and as a plug-in for Adobe, Autodesk, Nuke, and other OFX hosts. Silhouette has been used in the visual effects of films such as Avatar, Avengers: Infinity War, Blade Runner 2049, Ex Machina, and Interstellar. == Optics == In June 2020, Boris FX launched Optics, its first plugin deve
Find It, Fix It
Find It, Fix It is a mobile app developed by the city of Seattle to report non-emergency issues. == History == The City of Seattle launched Find It, Fix It in 2013 for Android and iOS phones to let citizens report potholes, graffiti, and other problems they observe to the city. The app did not support Windows Phone, making it inaccessible to Microsoft employees in the city who used the company's then-supported mobile operating system. In 2015, Mayor Ed Murray led a Find It, Fix It walk with about 100 other people, including police officers, in the University District. Participants were encouraged to use the app to report problems they observed in the neighborhood. Later Find It, Fix It walks have taken place in neighborhoods including Crown Hill, First Hill, Belltown, Wallingford, and Highland Park. In 2020, Find It, Fix It added support for reporting issues with the dockless bicycle sharing systems in the city. Citing the success of Seattle’s app, the nearby city of Kent, Washington, announced that it would create a similar customer service app. == Usage == Users of Find It, Fix It can submit reports about graffiti, potholes, parking violations, broken street signs, and other issues. The app is designed to use a smartphone’s camera and GPS features to make it easier for users to file reports. The Atlantic reported in 2018 that Find It, Fix It was being used by neighborhood groups to report homeless encampments with the intention of having authorities remove them, citing examples of campaigns in Ravenna and Ballard. The executive director of Ballard Alliance, a local chamber of commerce for businesses in the neighborhood, used a private Facebook group to encourage business owners to use the app to report homeless encampments. In response to a poster campaign in the summer of 2019 with the slogan “See a tent? Report a tent”, a representative for the mayor’s office and two Seattle City Council members said that it was inappropriate to encourage use of Find It, Fix It to displace homeless people. As a backlash to these campaigns, people living far from Seattle filed hoax complaints using the app, such as by using photos of tents on display at REI stores. According to the Seattle Times, between January 1, 2020, and November 15, 2021, the city had received over 230,000 service requests, of which 77% were submitted via Find It, Fix It. The largest category of these, numbering over 55,000, concerned illegal dumping. Of complaints categorized as "parking", 3,000 had comments explicitly mentioning issues around homelessness. The ZIP code 98134, covering an industrial area south of Pioneer Square and north of Georgetown, had 5,559 service requests per 1,000 residents, by far the highest in the city.
Competition in artificial intelligence
Competition in artificial intelligence refers to the rivalry among companies, research institutions, and governments to develop and deploy the most capable artificial intelligence (AI) systems. The competition spans multiple domains, including large language models (LLMs), autonomous vehicles, robotics, computer vision systems, natural language processing (NLP), and AI-optimized hardware. == Background == Competition in AI is driven by potential economic, strategic, and scientific advantages. Breakthroughs in AI can enhance productivity, enable new products and services, and provide geopolitical leverage. The field has experienced rapid progress since the mid-2010s, particularly in machine learning and artificial neural networks, leading to intense rivalry among leading actors. == Corporate competition == Major technology companies are among the most visible competitors in AI. In the United States, firms such as OpenAI, Google DeepMind, Meta Platforms, Microsoft, Anthropic, and Nvidia compete in building advanced LLMs, generative AI platforms, and AI-optimized graphics processing units (GPUs). In China, companies such as Baidu, Alibaba Group, Tencent, and startups such DeepSeek have become leaders in AI deployment, often with state backing. The "[war for talent]" in AI research has become a defining feature of corporate competition. Leading firms often recruit top AI researchers from rivals, sometimes offering multi-million-dollar compensation packages. == National competition == Governments see leadership in AI as a strategic priority. The United States has funded AI research for military, economic, and societal applications, while China has set a target to lead the world in AI by 2030 through its "New Generation Artificial Intelligence Development Plan". Other nations, including the UK, India, Israel, Russia, South Korea, and members of the European Union, have launched national AI strategies. In February 2026 Anthropic said Chinese companies - DeepSeek, Moonshot AI, and MiniMax - were conducting "distillation attacks" in an attempt to copy their model's capabilities, and warned that business wars were closely tied to geopolitical ones: "foreign labs that illicitly distill American models can remove safeguards, feeding model capabilities into their own military, intelligence, and surveillance systems." == Sectors of competition == === Large language models and chatbots competition === Competition to produce the most capable generative text models, with benchmarks such as MMLU and ARC used to evaluate performance has been on scale since the emergence of AI. These systems leverage deep learning, especially transformer architectures, to understand and generate human-like language. Companies and research groups globally compete to develop chatbots that are more capable, reliable, and context-aware. Among the most well-known chatbots is ChatGPT, developed by OpenAI. Since its public release in 2022, ChatGPT has rapidly gained widespread attention for its ability to engage in coherent and versatile conversations, assist with creative writing, and solve complex problems. In response, technology firms introduced competing chatbots aiming to challenge or surpass ChatGPT's capabilities. Notably, DeepSeek, a Chinese AI company, launched an advanced chatbot integrated with their R1 language model, emphasizing strong natural language understanding and multilingual support. Similarly, Grok, developed by xAI (company), integrates conversational AI into vehicles and digital assistants, combining natural language processing with real-time data for personalized user interaction. These chatbots not only compete in language tasks but also demonstrate strategic reasoning capabilities by playing complex games such as chess and Go. This form of competition is reminiscent of historic AI milestones set by programs such as Deep Blue and AlphaGo. The OpenAI’s ChatGPT has been tested in playing chess at various levels, while DeepSeek’s chatbot showcased its prowess in online chess tournaments in early 2024, winning several matches against human and AI opponents. Grok, leveraging Tesla's vast data infrastructure, has demonstrated real-time strategic decision-making in simulation environments that include chess-like games. The competition pushes rapid innovation, with firms racing to improve chatbot conversational depth, reduce biases, increase factual accuracy, and integrate multimodal inputs like images and videos. At the same time, the competition raises questions about AI safety, ethical use, and the societal impacts of increasingly human-like chatbots. === Autonomous vehicles === Companies such as Waymo, Tesla, and Baidu are racing to deploy safe and reliable self-driving car technology. === AI chips === Rivalry between Nvidia, AMD, Intel, and Huawei in designing processors optimized for AI workloads. === Military applications === Development of AI-enabled drones, surveillance systems, and decision-support tools, with associated ethical debates. == Events == In 2023, OpenAI released GPT-4, prompting competitors such as Google DeepMind to accelerate the release of their own models, including Gemini. In 2024, Chinese AI company DeepSeek launched the R1 model, leading OpenAI to release an open-source system, GPT-OSS, as a strategic countermeasure. In 2022, Tesla and Waymo both expanded autonomous taxi services in U.S. cities, competing for regulatory approval and public trust. The U.S. Department of Defense's Project Maven and China's AI-enabled surveillance programs have been cited as examples of military AI rivalry. In 2025, Microsoft hired several senior engineers from Google DeepMind, highlighting the ongoing "talent poaching" competition in the AI sector. == Risks and concerns == Critics warn that unrestrained competition in AI can undermine safety, ethics, and governance. Concerns include the proliferation of biased or unsafe models, escalation in autonomous weapons, and reduced cooperation on safety standards.
Shape factor (image analysis and microscopy)
Shape factors are dimensionless quantities used in image analysis and microscopy that numerically describe the shape of a particle, independent of its size. Shape factors are calculated from measured dimensions, such as diameter, chord lengths, area, perimeter, centroid, moments, etc. The dimensions of the particles are usually measured from two-dimensional cross-sections or projections, as in a microscope field, but shape factors also apply to three-dimensional objects. The particles could be the grains in a metallurgical or ceramic microstructure, or the microorganisms in a culture, for example. The dimensionless quantities often represent the degree of deviation from an ideal shape, such as a circle, sphere or equilateral polyhedron. Shape factors are often normalized, that is, the value ranges from zero to one. A shape factor equal to one usually represents an ideal case or maximum symmetry, such as a circle, sphere, square or cube. == Aspect ratio == The most common shape factor is the aspect ratio, a function of the largest diameter and the smallest diameter orthogonal to it: A R = d min d max {\displaystyle A_{R}={\frac {d_{\min }}{d_{\max }}}} The normalized aspect ratio varies from approaching zero for a very elongated particle, such as a grain in a cold-worked metal, to near unity for an equiaxed grain. The reciprocal of the right side of the above equation is also used, such that the AR varies from one to approaching infinity. == Circularity == Another very common shape factor is the circularity (or isoperimetric quotient), a function of the perimeter P and the area A: f circ = 4 π A P 2 {\displaystyle f_{\text{circ}}={\frac {4\pi A}{P^{2}}}} The circularity of a circle is 1, and much less than one for a starfish footprint. The reciprocal of the circularity equation is also used, such that fcirc varies from one for a circle to infinity. == Elongation shape factor == The less-common elongation shape factor is defined as the square root of the ratio of the two second moments in of the particle around its principal axes. f elong = i 2 i 1 {\displaystyle f_{\text{elong}}={\sqrt {\frac {i_{2}}{i_{1}}}}} == Compactness shape factor == The compactness shape factor is a function of the polar second moment in of a particle and a circle of equal area A. f comp = A 2 2 π i 1 2 + i 2 2 {\displaystyle f_{\text{comp}}={\frac {A^{2}}{2\pi {\sqrt {{i_{1}}^{2}+{i_{2}}^{2}}}}}} The fcomp of a circle is one, and much less than one for the cross-section of an I-beam. == Waviness shape factor == The waviness shape factor of the perimeter is a function of the convex portion Pcvx of the perimeter to the total. f wav = P cvx P {\displaystyle f_{\text{wav}}={\frac {P_{\text{cvx}}}{P}}} Some properties of metals and ceramics, such as fracture toughness, have been linked to grain shapes. == An application of shape factors == Greenland, the largest island in the world, has an area of 2,166,086 km2; a coastline (perimeter) of 39,330 km; a north–south length of 2670 km; and an east–west length of 1290 km. The aspect ratio of Greenland is A R = 1290 2670 = 0.483 {\displaystyle A_{R}={\frac {1290}{2670}}=0.483} The circularity of Greenland is f circ = 4 π ( 2166086 ) 39330 2 = 0.0176. {\displaystyle f_{\text{circ}}={\frac {4\pi (2166086)}{39330^{2}}}=0.0176.} The aspect ratio is agreeable with an eyeball-estimate on a globe. Such an estimate on a typical flat map, using the Mercator projection, would be less accurate due to the distorted scale at high latitudes. The circularity is deceptively low, due to the fjords that give Greenland a very jagged coastline (see the coastline paradox). A low value of circularity does not necessarily indicate a lack of symmetry, and shape factors are not limited to microscopic objects.