AI Chat Free No Limit

AI Chat Free No Limit — independent reviews, comparisons, pricing and step-by-step guides on Aizhi.

AI nationalism

AI nationalism is the idea that nations should develop and control their own artificial intelligence technologies to advance their own interests and ensure technological sovereignty. This concept is gaining traction globally, leading countries to implement new laws, form strategic alliances, and invest significantly in domestic AI capabilities. == Global trends and national strategies == In 2018, British technology investor Ian Hogarth published an influential essay titled AI Nationalism. He argued that as AI gains more power and its economic and military significance expands, governments will take measures to bolster their own domestic AI industries, and predicted that the advancement of machine learning systems would lead to what he termed "AI nationalism." He anticipated that this rise in AI would accelerate a global arms race, resulting in more closed economies, restrictions on foreign acquisitions, and limitations on the movement of talent. Hogarth predicted that AI policy would become a central focus of government agendas. He also criticized Britain’s approach to AI strategy, citing the sale of London-based DeepMind—one of the leading AI laboratories, acquired by Google for a relatively modest £400 million in 2014—as a significant misstep. AI nationalism is chiefly reflected in the escalating rhetoric of an artificial intelligence arms race, portraying AI development as a zero-sum game where the winner gains significant economic, political, and military advantages. This mindset, as highlighted in a 2017 Pentagon report, warns that sharing AI technology could erode technological supremacy and enhance rivals' capabilities. The winner-takes-all mentality of AI nationalism poses risks including unsafe AI development, increased geopolitical tension, and potential military aggression (such as cyberattacks or targeting AI professionals). Several countries, including Canada, France, and India, have formulated national strategies to advance their positions in AI. In the United States, a leading player in the global AI arena, trade policies have been enacted to restrict China's access to critical microchips, reflecting a strategic effort to maintain a technological edge. The United States’ National Security Commission on Artificial Intelligence (NSCAI) frames AI development as a critical aspect of a broader technology competition crucial for national success. It emphasizes the need to outpace China in AI to maintain strategic advantage, reflecting AI nationalism by linking geopolitical power directly to advancements in AI. France has seen notable governmental support for local AI startups, particularly those specializing in language technologies that cater to French and other non-English languages. In Saudi Arabia, Crown Prince Mohammed bin Salman is investing billions in AI research and development. The country has actively collaborated with major technology firms such as Amazon, IBM, and Microsoft to establish itself as a prominent AI hub. == Historical and cultural context == AI nationalism is seen as deeply connected to historical racism and imperialism. It is viewed not merely as a technological competition but as a contest over racial and civilizational superiority. Historically, technological achievements were often used to justify colonialism and racial hierarchies, with Western societies perceiving their advancements as evidence of superiority. In the context of AI, this historical context continues to shape views on intelligence and development. Some argue that AI nationalism reinforces the idea of fundamental civilizational divides, especially between the Western world and China. This perspective often frames China's progress in AI as a direct challenge to Western values, presenting the AI competition as a struggle over values. AI nationalism is said to draw from long-standing anti-Asian stereotypes, such as the "Yellow Peril," which portray Asian nations as threats to Western civilization. This viewpoint links Asian technological advances with dehumanization and artificiality, reflecting persistent anxieties about China's growing role in the global tech landscape. == Implications == AI nationalism is seen as a component of a broader trend towards the fragmentation of the internet, where digital services are increasingly influenced by local regulations and national interests. This shift is creating a new technological landscape in which the impact of artificial intelligence on individuals' lives can vary significantly depending on their geographic location. J. Paul Goode argues that AI nationalism may exacerbate existing societal divisions by promoting the development of systems that embed cultural biases, thereby privileging certain groups while disadvantaging others.
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Deterministic acyclic finite state automaton

In computer science, a deterministic acyclic finite state automaton (DAFSA), is a data structure that represents a set of strings, and allows for a query operation that tests whether a given string belongs to the set in time proportional to its length. Algorithms exist to construct and maintain such automata, while keeping them minimal. DAFSA is the rediscovery of a data structure called Directed Acyclic Word Graph (DAWG), although the same name had already been given to a different data structure which is related to suffix automaton. A DAFSA is a special case of a finite state recognizer that takes the form of a directed acyclic graph with a single source vertex (a vertex with no incoming edges), in which each edge of the graph is labeled by a letter or symbol, and in which each vertex has at most one outgoing edge for each possible letter or symbol. The strings represented by the DAFSA are formed by the symbols on paths in the graph from the source vertex to any sink vertex (a vertex with no outgoing edges). In fact, a deterministic finite state automaton is acyclic if and only if it recognizes a finite set of strings. == History == Blumer et al first defined terminology Directed Acyclic Word Graph (DAWG) in 1983. Appel and Jacobsen used the same naming for a different data structure in 1988. Independent of earlier work, Daciuk et al rediscovered the latter data structure in 2000 but called it DAFSA. == Comparison to tries == By allowing the same vertices to be reached by multiple paths, a DAFSA may use significantly fewer vertices than the strongly related trie data structure. Consider, for example, the four English words "tap", "taps", "top", and "tops". A trie for those four words would have 12 vertices, one for each of the strings formed as a prefix of one of these words, or for one of the words followed by the end-of-string marker. However, a DAFSA can represent these same four words using only six vertices vi for 0 ≤ i ≤ 5, and the following edges: an edge from v0 to v1 labeled "t", two edges from v1 to v2 labeled "a" and "o", an edge from v2 to v3 labeled "p", an edge v3 to v4 labeled "s", and edges from v3 and v4 to v5 labeled with the end-of-string marker. There is a tradeoff between memory and functionality, because a standard DAFSA can tell you if a word exists within it, but it cannot point you to auxiliary information about that word, whereas a trie can. The primary difference between DAFSA and trie is the elimination of suffix and infix redundancy in storing strings. The trie eliminates prefix redundancy since all common prefixes are shared between strings, such as between doctors and doctorate the doctor prefix is shared. In a DAFSA common suffixes are also shared, for words that have the same set of possible suffixes as each other. For dictionary sets of common English words, this translates into major memory usage reduction. Because the terminal nodes of a DAFSA can be reached by multiple paths, a DAFSA cannot directly store auxiliary information relating to each path, e.g. a word's frequency in the English language. However, if for each node we store the number of unique paths through that point in the structure, we can use it to retrieve the index of a word, or a word given its index. The auxiliary information can then be stored in an array.
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AI Headshot Generators: Free vs Paid (2026)

Curious about the best AI headshot generator? An AI headshot generator is software that uses machine learning to help you get more done — it combines speed, accuracy, and an interface that just works. Hands-on testing shows real-world results vary, so a short free trial is the smartest way to decide. Whether you are a beginner or a pro, the right AI headshot generator slots into your workflow and pays for itself fast. This guide breaks down the top picks, their pros and cons, and who each one is best for.
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Janyce Wiebe

Janyce Marbury Wiebe (1959–2018) was an American computer science specializing in natural language processing and known for her work on subjectivity, sentiment analysis, opinion mining, discourse processing, and word-sense disambiguation. == Early life and education == Wiebe was born in 1959, in Albany, New York. She majored in English at the Binghamton University, graduating in 1981, and completed a Ph.D. in computer science in 1990, at the University at Buffalo. Her dissertation, Recognizing Subjective Sentences: A Computational Investigation of Narrative Text, was supervised by philosopher William J. Rapaport. == Career == After postdoctoral research at the University of Toronto, she became an assistant professor at New Mexico State University in 1992. In 2000, she moved to the University of Pittsburgh, where she became a professor of computer science and director of the Intelligent Systems Program. == Recognition == Wiebe was named a Fellow of the Association for Computational Linguistics in 2015. == Death == She died of leukemia on December 10, 2018.
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Web container

A web container (also known as a servlet container; and compare "webcontainer") is the component of a web server that interacts with Jakarta Servlets. A web container is responsible for managing the lifecycle of servlets, mapping a URL to a particular servlet and ensuring that the URL requester has the correct access-rights. A web container handles requests to servlets, Jakarta Server Pages (JSP) files, and other types of files that include server-side code. The Web container creates servlet instances, loads and unloads servlets, creates and manages request and response objects, and performs other servlet-management tasks. A web container implements the web component contract of the Jakarta EE architecture. This architecture specifies a runtime environment for additional web components, including security, concurrency, lifecycle management, transaction, deployment, and other services. == List of Servlet containers == The following is a list of notable applications which implement the Jakarta Servlet specification from Eclipse Foundation, divided depending on whether they are directly sold or not. === Open source Web containers === Apache Tomcat (formerly Jakarta Tomcat) is an open source web container available under the Apache Software License. Apache Tomcat 6 and above are operable as general application container (prior versions were web containers only) Apache Geronimo is a full Java EE 6 implementation by Apache Software Foundation. Enhydra, from Lutris Technologies. GlassFish from Eclipse Foundation (an application server, but includes a web container). Jetty, from the Eclipse Foundation. Also supports SPDY and WebSocket protocols. Open Liberty, from IBM, is a fully compliant Jakarta EE server Virgo from Eclipse Foundation provides modular, OSGi based web containers implemented using embedded Tomcat and Jetty. Virgo is available under the Eclipse Public License. WildFly (formerly JBoss Application Server) is a full Java EE implementation by Red Hat, division JBoss. === Commercial Web containers === iPlanet Web Server, from Oracle. JBoss Enterprise Application Platform from Red Hat, division JBoss is subscription-based/open-source Jakarta EE-based application server. WebLogic Application Server, from Oracle Corporation (formerly developed by BEA Systems). Orion Application Server, from IronFlare. Resin Pro, from Caucho Technology. IBM WebSphere Application Server. SAP NetWeaver.
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Transfer-based machine translation

Transfer-based machine translation is a type of machine translation (MT). It is currently one of the most widely used methods of machine translation. In contrast to the simpler direct model of MT, transfer MT breaks translation into three steps: analysis of the source language text to determine its grammatical structure, transfer of the resulting structure to a structure suitable for generating text in the target language, and finally generation of this text. Transfer-based MT systems are thus capable of using knowledge of the source and target languages. == Design == Both transfer-based and interlingua-based machine translation have the same idea: to make a translation it is necessary to have an intermediate representation that captures the "meaning" of the original sentence in order to generate the correct translation. In interlingua-based MT this intermediate representation must be independent of the languages in question, whereas in transfer-based MT, it has some dependence on the language pair involved. The way in which transfer-based machine translation systems work varies substantially, but in general they follow the same pattern: they apply sets of linguistic rules which are defined as correspondences between the structure of the source language and that of the target language. The first stage involves analysing the input text for morphology and syntax (and sometimes semantics) to create an internal representation. The translation is generated from this representation using both bilingual dictionaries and grammatical rules. It is possible with this translation strategy to obtain fairly high quality translations, with accuracy in the region of 90% (although this is highly dependent on the language pair in question, for example the distance between the two). == Operation == In a rule-based machine translation system the original text is first analysed morphologically and syntactically in order to obtain a syntactic representation. This representation can then be refined to a more abstract level putting emphasis on the parts relevant for translation and ignoring other types of information. The transfer process then converts this final representation (still in the original language) to a representation of the same level of abstraction in the target language. These two representations are referred to as "intermediate" representations. From the target language representation, the stages are then applied in reverse. == Analysis and transformation == Various methods of analysis and transformation can be used before obtaining the final result. Along with these statistical approaches may be augmented generating hybrid systems. The methods which are chosen and the emphasis depends largely on the design of the system, however, most systems include at least the following stages: Morphological analysis. Surface forms of the input text are classified as to part-of-speech (e.g. noun, verb, etc.) and sub-category (number, gender, tense, etc.). All of the possible "analyses" for each surface form are typically made output at this stage, along with the lemma of the word. Lexical categorisation. In any given text some of the words may have more than one meaning, causing ambiguity in analysis. Lexical categorisation looks at the context of a word to try to determine the correct meaning in the context of the input. This can involve part-of-speech tagging and word sense disambiguation. Lexical transfer. This is basically dictionary translation; the source language lemma (perhaps with sense information) is looked up in a bilingual dictionary and the translation is chosen. Structural transfer. While the previous stages deal with words, this stage deals with larger constituents, for example phrases and chunks. Typical features of this stage include concordance of gender and number, and re-ordering of words or phrases. Morphological generation. From the output of the structural transfer stage, the target language surface forms are generated. == Transfer types == One of the main features of transfer-based machine translation systems is a phase that "transfers" an intermediate representation of the text in the original language to an intermediate representation of text in the target language. This can work at one of two levels of linguistic analysis, or somewhere in between. The levels are: Superficial transfer (or syntactic). This level is characterised by transferring "syntactic structures" between the source and target languages. It is suitable for languages in the same family or of the same type, for example in the Romance languages between Spanish, Catalan, French, Italian, etc. Deep transfer (or semantic). This level constructs a semantic representation that is dependent on the source language. This representation can consist of a series of structures which represent the meaning. In these transfer systems predicates are typically produced. The translation also typically requires structural transfer. This level is used to translate between more distantly related languages (e.g. Spanish-English or Spanish-Basque, etc.)
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AI Text-to-image Tools Reviews: What Actually Works in 2026

In search of the best AI text-to-image tool? An AI text-to-image tool is software that uses machine learning to help you get more done — it turns a rough idea into a polished result in seconds. When choosing one, weigh output quality, pricing, export formats, and how well it fits the tools you already use. Whether you are a beginner or a pro, the right AI text-to-image tool slots into your workflow and pays for itself fast. Below we compare features, pricing, and real output so you can choose with confidence.
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CarPlay

CarPlay is an Apple standard that enables a car radio or automotive head unit to be a display and controller for an iOS device. It is available on iPhone 5 and later models running iOS 7.1 or later. More than 800 car and motorcycle models support CarPlay, according to Apple. Vehicle owners can add support by installing certain aftermarket vehicle audio products. Most CarPlay systems connect to iOS through USB, some are wireless, and wireless support can be added through aftermarket dongles. CarPlay Ultra, a more integrated version of CarPlay, was first announced on Aston Martin DBX707 in May 2025. == Software == Apple's CarPlay-enabled apps include: Phone Apple Music Apple Maps Calendar Messages Audiobooks (part of Apple Books) Podcasts Settings News Developers must obtain permission from Apple to develop CarPlay-enabled apps. Such apps fall into five categories: Audio: primarily provide audio content, such as music or podcasts. Examples: Amazon Music, Audible, Google Play Music, iHeartRadio, QQ Music, Spotify, and Overcast. Navigation: turn-by-turn guidance, including searching for points of interests and navigating to a destination. Examples: AutoNavi, Baidu Maps, Google Maps, ChargeFinder and Waze. Automaker-made apps allow a user to control vehicle-specific features such as climate controls, gas levels, or radio via CarPlay. Messaging/Voice over IP (VoIP): listen to new messages and reply using dictation in an audio-only interface. Messaging apps on CarPlay integrate with third-party Siri support (known as SiriKit), while VoIP apps integrate with the iOS calling interface using CallKit. Examples: Telegram, WhatsApp, and Zoom. Food-ordering and parking-services apps. To discourage distracted driving, Siri is used extensively, providing voice turn-by-turn navigation guidance and voice-input for text messages. Newscast-style weather and stock results are announced instead of displayed. Requests that bring up visual information may be blocked when the car is in gear, and most native CarPlay apps deliver audio content with minimal interaction. CarPlay-enabled apps installed on the device appear on the CarPlay home screen unless disabled by the user. The inclusion or exclusion and order of app appearance can be changed on a per-vehicle basis. == Hardware == Most of the CarPlay software runs on the connected iPhone. The CarPlay interface provides audio output and a visual display to the vehicle's infotainment system, while adapting to the vehicle's available control methods, including touch screens, rotary dials, physical buttons, steering-wheel controls, and hands-free microphones. Aftermarket head units may support CarPlay or Android Auto, and many support both platforms. === Wired CarPlay === In a wired CarPlay configuration, the iPhone connects to the vehicle or head unit via a USB cable. The USB connection supplies power to the iPhone and provides a stable data link for audio, video, and control input. Wired CarPlay is supported by a wide range of factory-installed infotainment systems and aftermarket head units. Some third-party devices marketed as wireless CarPlay adapters operate by emulating a wired CarPlay connection to the vehicle. These devices plug into the vehicle's USB port and present themselves as a wired CarPlay interface, while separately establishing a wireless connection to the iPhone. Such devices still require the vehicle or head unit to support standard (wired) CarPlay. === Wireless CarPlay === Wireless CarPlay allows the iPhone to connect to a compatible vehicle or head unit without a physical cable. During the initial pairing process, the iPhone exchanges network credentials with the CarPlay receiver over Bluetooth. Once paired, CarPlay data is transmitted over a two-way Wi-Fi connection between the phone and the vehicle. Wireless CarPlay support depends on both the vehicle or head unit hardware and the iPhone model, and is generally limited to newer factory systems and select aftermarket receivers. == History == === Predecessor === In 2008, one year after the release of the iPhone, Mercedes vehicles were first to sell an audio system incorporating both the iPod and iPhone, equipped with 30-pin iOS input jacks. The new 2008 Harman Kardon NTG 2.5 featured full audio streaming, syncing, charging and control integrated into the steering wheel controls, instrument panel, and head unit. Apple was working with Mercedes to develop iOS compatible audio systems into their cars first only a year after iPhone launch. With an Apple Lightning-to-30-pin adapter, iPhones/iPods remain backwards-compatible with the Harman Kardon 2.5 and later models. This is the earliest audio system specifically engineered for iPod/iPhone integration, which predated CarPlay and every other manufacturer incorporating iOS into vehicles. The concept of CarPlay was based on the iOS 4 feature called "iPod Out" which was produced through several years of joint development by Apple and the BMW Group's Technology Office USA. iPod Out enabled vehicles with the necessary infrastructure to "host" the analog video and audio from a supporting iOS device while receiving inputs, such as button presses and knob rotations, from a car's infotainment system, to drive the "hosted" user interface in the vehicle's built-in display. It was announced at WWDC 2010 and first shipped in BMW Group vehicles in early 2011. The BMW and Mini option was called "PlugIn" and paved the way for the first cross-OEM platforms, introducing the concept of requiring a car-specific interface for apps (as opposed to MirrorLink's simple and insufficient mirroring of what was shown on the smartphone's screen). === Development === CarPlay's codename was Stark. Apple's Eddy Cue announced it as iOS in the Car at WWDC 2013. In January 2014, it was reported that Apple's hardware-oriented corporate culture had led to release delays. iOS in the Car was then rebranded and launched as CarPlay with significant design changes at the Geneva Motor Show in March 2014 with Ferrari, Kia, Mercedes-Benz, and Volvo among the first car manufacturers. At WWDC 2022, Apple announced plans to release an all-new version of CarPlay, informally dubbed CarPlay 2. The new version was said to be able to control vehicle functions, access vehicle stats, and take over multiple vehicle screens. Officials said they planned to release it in late 2024 and that manufacturers that are planning to adopt the new CarPlay include: Audi, Acura, Ford, Honda, Infiniti, Jaguar, Land Rover, Lincoln, Mercedes-Benz, Nissan, Polestar, Porsche, Renault, and Volvo. In January 2025, amidst delays, Apple removed the planned released date from its website. On May 15, 2025, Apple announced that next-generation CarPlay, now called CarPlay Ultra, would be included with all new vehicles from Aston Martin. Existing vehicles will also be receiving CarPlay Ultra through a future software update. It is only available in the US and Canada. == Timeline == June 2013: Apple introduced iOS in the Car; an early version of CarPlay that was never publicly released, at WWDC 2013. June 2013: BMW officials announced their cars would not support iOS in the Car; they later changed their minds. November 2013: Siri Eyes Free mode was offered as a dealer-installed accessory in the US to some Honda Accord and Acura RDX & ILX models. In December, Honda offered additional integration, featuring new HondaLink services, on some US and Canada models of the Civic and the Fit. March 2014: Apple introduced CarPlay, which was renamed from iOS in the Car with significant design changes, at the 2014 Geneva Motor Show with automakers Ferrari, Mercedes-Benz and Volvo. September 2014: A Ferrari FF was the first car with a full version of CarPlay. November 2014: Hyundai announced the Sonata sedan would be their first model with available CarPlay by the end of the first quarter of 2015. January 2015: Volkswagen announced CarPlay support would be coming later in 2015 and would be either standard or available on the majority of their 2016 model year lineup. May 2015: General Motors announced CarPlay would be available starting with 14 different 2016 model year Chevrolet vehicles. July 2015: Honda announced CarPlay would be available in their vehicles starting with the 2016 Honda Accord. December 2015: Volvo implemented CarPlay in the 2016 Volvo XC90 as their first vehicle with CarPlay support. December 2015: Mercedes-Benz confirmed that CarPlay would be available starting with select 2016 model year vehicles. January 2016: Apple released a list detailing the car models which support CarPlay. January 2016: Ford announced CarPlay would be available on all 2017 Ford/Lincoln model year vehicles equipped with the Sync 3 infotainment system. January 2016: FCA (now a part of Stellantis) announced CarPlay would be available on their UConnect infotainment system starting with select 2016 model year vehicles. March 2016: Subaru announced the beginning of CarPlay and Android Auto support, st
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SUPS

In computational neuroscience, SUPS (for Synaptic Updates Per Second) or formerly CUPS (Connections Updates Per Second) is a measure of a neuronal network performance, useful in fields of neuroscience, cognitive science, artificial intelligence, and computer science. == Computing == For a processor or computer designed to simulate a neural network SUPS is measured as the product of simulated neurons N {\displaystyle N} and average connectivity c {\displaystyle c} (synapses) per neuron per second: S U P S = c × N {\displaystyle SUPS=c\times N} Depending on the type of simulation it is usually equal to the total number of synapses simulated. In an "asynchronous" dynamic simulation if a neuron spikes at υ {\displaystyle \upsilon } Hz, the average rate of synaptic updates provoked by the activity of that neuron is υ c N {\displaystyle \upsilon cN} . In a synchronous simulation with step Δ t {\displaystyle \Delta t} the number of synaptic updates per second would be c N Δ t {\displaystyle {\frac {cN}{\Delta t}}} . As Δ t {\displaystyle \Delta t} has to be chosen much smaller than the average interval between two successive afferent spikes, which implies Δ t < 1 υ N {\displaystyle \Delta t<{\frac {1}{\upsilon N}}} , giving an average of synaptic updates equal to υ c N 2 {\displaystyle \upsilon cN^{2}} . Therefore, spike-driven synaptic dynamics leads to a linear scaling of computational complexity O(N) per neuron, compared with the O(N2) in the "synchronous" case. == Records == Developed in the 1980s Adaptive Solutions' CNAPS-1064 Digital Parallel Processor chip is a full neural network (NNW). It was designed as a coprocessor to a host and has 64 sub-processors arranged in a 1D array and operating in a SIMD mode. Each sub-processor can emulate one or more neurons and multiple chips can be grouped together. At 25 MHz it is capable of 1.28 GMAC. After the presentation of the RN-100 (12 MHz) single neuron chip at Seattle 1991 Ricoh developed the multi-neuron chip RN-200. It had 16 neurons and 16 synapses per neuron. The chip has on-chip learning ability using a proprietary backdrop algorithm. It came in a 257-pin PGA encapsulation and drew 3.0 W at a maximum. It was capable of 3 GCPS (1 GCPS at 32 MHz). In 1991–97, Siemens developed the MA-16 chip, SYNAPSE-1 and SYNAPSE-3 Neurocomputer. The MA-16 was a fast matrix-matrix multiplier that can be combined to form systolic arrays. It could process 4 patterns of 16 elements each (16-bit), with 16 neuron values (16-bit) at a rate of 800 MMAC or 400 MCPS at 50 MHz. The SYNAPSE3-PC PCI card contained 2 MA-16 with a peak performance of 2560 MOPS (1.28 GMAC); 7160 MOPS (3.58 GMAC) when using three boards. In 2013, the K computer was used to simulate a neural network of 1.73 billion neurons with a total of 10.4 trillion synapses (1% of the human brain). The simulation ran for 40 minutes to simulate 1 s of brain activity at a normal activity level (4.4 on average). The simulation required 1 Petabyte of storage.
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Monica S. Lam

Monica Sin-Ling Lam is an American computer scientist. She is a professor in the Computer Science Department at Stanford University. == Education == Monica Lam received a B.Sc. from University of British Columbia in 1980 and a Ph.D. in computer science from Carnegie Mellon University in 1987. == Career == Lam joined the faculty of Computer Science at Stanford University in 1988. She has contributed to the research of a wide range of computer systems topics including compilers, program analysis, operating systems, security, computer architecture, and high-performance computing. More recently, she is working in natural language processing, and virtual assistants with an emphasis on privacy protection. She is the faculty director of the Open Virtual Assistant Lab, which organized the first workshop for the World Wide Voice Web. The lab developed the open-source Almond voice assistant, which is sponsored by the National Science Foundation. Almond received Popular Science's Best of What's New award in 2019. Previously, Lam led the SUIF (Stanford University Intermediate Format) Compiler project, which produced a widely used compiler infrastructure known for its locality optimizations and interprocedural parallelization. Many of the compiler techniques she developed have been adopted by industry. Her other research projects included the architecture and compiler for the CMU Warp machine, a systolic array of VLIW processors, and the Stanford DASH distributed shared memory machine. In 1998, she took a sabbatical leave from Stanford to help start Tensilica Inc., a company that specializes in configurable processor cores. In another research project, her program analysis group developed a collection of tools for improving software security and reliability. They developed the first scalable context-sensitive inclusion-based pointer analysis and a freely available tool called BDDBDDB, that allows programmers to express context-sensitive analyses simply by writing Datalog queries. Other tools developed include Griffin, static and dynamic analysis for finding security vulnerabilities in Web applications such as SQL injection, a static and dynamic program query language called QL, a static memory leak detector called Clouseau, a dynamic buffer overrun detector called CRED, and a dynamic error diagnosis tool called DIDUCE. In the Collective project, her research group and she developed the concept of a livePC: subscribers of the livePC will automatically run the latest of the published PC virtual images with each reboot. This approach allows computers to be managed scalably and securely. In 2005, the group started a company called MokaFive to transfer the technology to industry. She also directed the MobiSocial laboratory at Stanford, as part of the Programmable Open Mobile Internet 2020 initiative. Lam is also the cofounder of Omlet, which launched in 2014. Omlet is the first product from MobiSocial. Omlet is an open, decentralized social networking tool, based on an extensible chat platform. Lam chaired the ACM SIGPLAN Programming Languages Design and Implementation Conference in 2000, served on the Editorial Board of ACM Transactions on Computer Systems and numerous program committees for conferences on languages and compilers (PLDI, POPL), operating systems (SOSP), and computer architecture (ASPLOS, ISCA). == Awards and honors == National Academy of Engineering member, 2019 University of British Columbia Computer Science 50th Anniversary Research Award, 2018 Fellow of the ACM, 2007 ACM Programming Language Design and Implementation Best Paper Award in 2004 ACM SIGSOFT Distinguished Paper Award in 2002 ACM Most Influential Programming Language Design and Implementation Paper Award in 2001 NSF Young Investigator award in 1992 Two of her papers were recognized in "20 Years of PLDI--a Selection (1979-1999)" One of her papers was recognized in the "25 Years of the International Symposia on Computer Architecture", 1988. == Selected works == Compilers: Principles, Techniques and Tools (2d Ed) (2006) (the "Dragon Book") by Alfred V. Aho, Monica S. Lam, Ravi Sethi, and Jeffrey D. Ullman (ISBN 0-321-48681-1) A Systolic Array Optimizing Compiler (1989) (ISBN 0-89838-300-5) Monica Lam, Dissertation
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AI Content Generators: Free vs Paid (2026)

Shopping for the best AI content generator? An AI content generator is software that uses machine learning to help you get more done — it keeps getting smarter as the underlying models improve. Pricing, accuracy, and the size of the model behind the tool are the three factors that most affect daily usefulness. Whether you are a beginner or a pro, the right AI content generator slots into your workflow and pays for itself fast. We tested the leading options and ranked them by quality, value, and ease of use.
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Cobham's theorem

Cobham's theorem is a theorem in combinatorics on words that has important connections with number theory, notably transcendental numbers, and automata theory. Informally, the theorem gives the condition for the members of a set S of natural numbers written in bases b1 and base b2 to be recognised by finite automata. Specifically, consider bases b1 and b2 such that they are not powers of the same integer. Cobham's theorem states that S written in bases b1 and b2 is recognised by finite automata if and only if S differs by a finite set from a finite union of arithmetic progressions. The theorem was proved by Alan Cobham in 1969 and has since given rise to many extensions and generalisations. == Definitions == Let n > 0 {\displaystyle n>0} be an integer. The representation of a natural number n {\textstyle n} in base b {\textstyle b} is the sequence of digits n 0 n 1 ⋯ n h {\displaystyle n_{0}n_{1}\cdots n_{h}} such that n = n 0 + n 1 b + ⋯ + n h b h {\displaystyle n=n_{0}+n_{1}b+\cdots +n_{h}b^{h}} where 0 ≤ n 0 , n 1 , … , n h < b {\displaystyle 0\leq n_{0},n_{1},\ldots ,n_{h} 0 {\displaystyle n_{h}>0} . The word n 0 n 1 ⋯ n h {\displaystyle n_{0}n_{1}\cdots n_{h}} is often denoted ⟨ n ⟩ b {\displaystyle \langle n\rangle _{b}} , or more simply, n b {\displaystyle n_{b}} . A set of natural numbers S is recognisable in base b {\textstyle b} or more simply b {\textstyle b} -recognisable or b {\textstyle b} -automatic if the set { n b ∣ n ∈ S } {\displaystyle \{n_{b}\mid n\in S\}} of the representations of its elements in base b {\displaystyle b} is a language recognisable by a finite automaton on the alphabet { 0 , 1 , … , b − 1 } {\displaystyle \{0,1,\ldots ,b-1\}} . Two positive integers k {\displaystyle k} and ℓ {\displaystyle \ell } are multiplicatively independent if there are no non-negative integers p {\displaystyle p} and q {\displaystyle q} such that k p = ℓ q {\displaystyle k^{p}=\ell ^{q}} . For example, 2 and 3 are multiplicatively independent, but 8 and 16 are not since 8 4 = 16 3 {\displaystyle 8^{4}=16^{3}} . Two integers are multiplicatively dependent if and only if they are powers of a same third integer. == Problem statements == === Original problem statement === More equivalent statements of the theorem have been given. The original version by Cobham is the following: Another way to state the theorem is by using automatic sequences. Cobham himself calls them "uniform tag sequences." The following form is found in Allouche and Shallit's book:We can show that the characteristic sequence of a set of natural numbers S recognisable by finite automata in base k is a k-automatic sequence and that conversely, for all k-automatic sequences u {\displaystyle u} and all integers 0 ≤ i < k {\displaystyle 0\leq i 1 {\displaystyle \alpha >1} is the dominant eigenvalue of the matrix of morphism f {\displaystyle f} , namely, the matrix M ( f ) = ( m x , y ) x ∈ B , y ∈ A {\displaystyle M(f)=(m_{x,y})_{x\in B,y\in A}} , where m x , y {\displaystyle m_{x,y}} is the number of occurrences of the letter x {\displaystyle x} in the word f ( y ) {\displaystyle f(y)} . A set S of natural numbers is α {\displaystyle \alpha } -recognisable if its characteristic sequence s {\displaystyle s} is α {\displaystyle \alpha } -substitutive. A last definition: a Perron number is an algebraic number z > 1 {\displaystyle z>1} such that all its conjugates belong to the disc { z ′ ∈ C , | z ′ | < z } {\displaystyle \{z'\in \mathbb {C} ,|z'| Read more →
Anaconda (Python distribution)

Anaconda is an open source data science and artificial intelligence distribution platform for the Python programming language. Developed by Anaconda, Inc., an American company founded in 2012, the platform is used to develop and manage data science and AI projects. In 2024, Anaconda Inc. has about 300 employees and 45 million users. == History == Co-founded in Austin, Texas in 2012 as Continuum Analytics by Peter Wang and Travis Oliphant, Anaconda Inc. operates from the United States and Europe. Anaconda Inc. developed Conda, a cross-platform, language-agnostic binary package manager. It also launched PyData community workshops and the Jupyter Cloud Notebook service (Wakari.io). In 2013, it received funding from DARPA. In 2015, the company had two million users including 200 of the Fortune 500 companies and raised $24 million in a Series A funding round led by General Catalyst and BuildGroup. Anaconda secured an additional $30 million in funding in 2021. Continuum Analytics rebranded as Anaconda in 2017. That year, it announced the release of Anaconda Enterprise 5, an integration with Microsoft Azure, and had over 13 million users by year's end. In 2022, it released Anaconda Business; new integrations with Snowflake and others; and the open-source PyScript. It also acquired PythonAnywhere, while Anaconda's user base exceeded 30 million in 2022. In 2023, Anaconda released Python in Excel, a new integration with Microsoft Excel, and launched PyScript.com. The company made a series of investments in AI during 2024. That February, Anaconda partnered with IBM to import its repository of Python packages into Watsonx, IBM's generative AI platform. The same year, Anaconda joined IBM's AI Alliance and released an integration with Teradata and Lenovo. In 2024, Anaconda's user base reached 45 million users and Barry Libert was named company CEO, after serving on Anaconda's board of directors. He was succeeded as CEO in October 2025 by David DeSanto, who also became a company director. In May 2025, the company introduced the first unified AI platform for Open Source, Anaconda AI Platform, a central control for AI workflows that enables customization in Python-based enterprise AI development. That July, after reaching over $150 million in a Series C funding round, Anaconda was evaluated at about $1.5 billion. == Overview == Anaconda distribution comes with over 300 packages automatically installed, and over 7,500 additional open-source packages can be installed from the Anaconda repository as well as the Conda package and virtual environment manager. It also includes a GUI, Anaconda Navigator, as a graphical alternative to the command-line interface (CLI). Conda was developed to address dependency conflicts native to the pip package manager, which would automatically install any dependent Python packages without checking for conflicts with previously installed packages (until its version 20.3, which later implemented consistent dependency resolution). The Conda package manager's historical differentiation analyzed and resolved these installation conflicts. Anaconda is a distribution of the Python programming language (and previously also R) for scientific computing (data science, machine learning applications, large-scale data processing, predictive analytics, etc.), that aims to simplify package management and deployment. Anaconda distribution includes data-science packages suitable for Windows, Linux, and macOS. Other company products include Anaconda Free, and subscription-based Starter, Business and Enterprise. Anaconda's business tier offers Package Security Manager. Package versions in Anaconda are managed by the package management system Conda, which was spun out as a separate open-source package as useful both independently and for applications other than Python. There is also a small, bootstrap version of Anaconda called Miniconda, which includes only Conda, Python, the packages they depend on, and a small number of other packages. Open source packages can be individually installed from the Anaconda repository, Anaconda Cloud (anaconda.org), or the user's own private repository or mirror, using the conda install command. Anaconda, Inc. compiles and builds the packages available in the Anaconda repository itself, and provides binaries for Windows 32/64 bit, Linux 64 bit and MacOS 64-bit (Intel, Apple Silicon). Anything available on PyPI may be installed into a Conda environment using pip, and Conda will keep track of what it has installed and what pip has installed. Custom packages can be made using the conda build command, and can be shared with others by uploading them to Anaconda Cloud, PyPI or other repositories. The default installation of Anaconda2 includes Python 2.7 and Anaconda3 includes Python 3.7. However, it is possible to create new environments that include any version of Python packaged with Conda. === Anaconda Navigator === Anaconda Navigator is a desktop graphical user interface (GUI) included in Anaconda distribution that allows users to launch applications and manage Conda packages, environments and channels without using command-line commands. Navigator can search for packages on Anaconda Cloud or in a local Anaconda Repository, install them in an environment, run the packages and update them. It is available for Windows, macOS and Linux. The following applications are available by default in Navigator: JupyterLab Jupyter Notebook QtConsole Spyder Glue Orange RStudio Visual Studio Code === Conda === Conda is an open source, cross-platform, language-agnostic package manager and environment management system that installs, runs, and updates packages and their dependencies. It was created for Python programs, but it can package and distribute software for any language, including multi-language projects. The Conda package and environment manager is included in all versions of Anaconda, Miniconda, and Anaconda Repository. == Anaconda.org == Anaconda Cloud is a package management service by Anaconda where users can find, access, store and share public and private notebooks, environments, and Conda and PyPI packages. Cloud hosts useful Python packages, notebooks and environments for a wide variety of applications. Users do not need to log in or to have a Cloud account, to search for public packages, download and install them. Users can build new Conda packages using Conda-build and then use the Anaconda Client CLI to upload packages to Anaconda.org. Notebooks users can be aided with writing and debugging code with Anaconda's AI Assistant.
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Dan Klein

Daniel Klein (born c. 1976) is an American computer scientist and professor of computer science at the University of California, Berkeley. His research focuses on natural language processing and artificial intelligence. He was educated at Mt. Lebanon High School in Mt. Lebanon Township, Pennsylvania and earned a B.A. in mathematics, computer science, and linguistics from Cornell University (1998), a MSt in linguistics by Oxford University (1999) and a Ph.D. from Stanford University (2004), under Christopher D. Manning. He attended Oxford on a Marshall Scholarship. In addition to the Marshall scholarship, he has been awarded the ACM's Grace Murray Hopper Award, the Sloan Research Fellowship, the NSF CAREER Award, and the Microsoft New Faculty Fellowship.
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Markov chain central limit theorem

In the mathematical theory of random processes, the Markov chain central limit theorem has a conclusion somewhat similar in form to that of the classic central limit theorem (CLT) of probability theory, but the quantity in the role taken by the variance in the classic CLT has a more complicated definition. See also the general form of Bienaymé's identity. == Statement == Suppose that: the sequence X 1 , X 2 , X 3 , … {\textstyle X_{1},X_{2},X_{3},\ldots } of random elements of some set is a Markov chain that has a stationary probability distribution; and the initial distribution of the process, i.e. the distribution of X 1 {\textstyle X_{1}} , is the stationary distribution, so that X 1 , X 2 , X 3 , … {\textstyle X_{1},X_{2},X_{3},\ldots } are identically distributed. In the classic central limit theorem these random variables would be assumed to be independent, but here we have only the weaker assumption that the process has the Markov property; and g {\textstyle g} is some (measurable) real-valued function for which var ⁡ ( g ( X 1 ) ) < + ∞ . {\textstyle \operatorname {var} (g(X_{1}))<+\infty .} Now let μ = E ⁡ ( g ( X 1 ) ) , μ ^ n = 1 n ∑ k = 1 n g ( X k ) σ 2 := lim n → ∞ var ⁡ ( n μ ^ n ) = lim n → ∞ n var ⁡ ( μ ^ n ) = var ⁡ ( g ( X 1 ) ) + 2 ∑ k = 1 ∞ cov ⁡ ( g ( X 1 ) , g ( X 1 + k ) ) . {\displaystyle {\begin{aligned}\mu &=\operatorname {E} (g(X_{1})),\\{\widehat {\mu }}_{n}&={\frac {1}{n}}\sum _{k=1}^{n}g(X_{k})\\\sigma ^{2}&:=\lim _{n\to \infty }\operatorname {var} ({\sqrt {n}}{\widehat {\mu }}_{n})=\lim _{n\to \infty }n\operatorname {var} ({\widehat {\mu }}_{n})=\operatorname {var} (g(X_{1}))+2\sum _{k=1}^{\infty }\operatorname {cov} (g(X_{1}),g(X_{1+k})).\end{aligned}}} Then as n → ∞ , {\textstyle n\to \infty ,} we have n ( μ ^ n − μ ) → D Normal ( 0 , σ 2 ) , {\displaystyle {\sqrt {n}}({\hat {\mu }}_{n}-\mu )\ {\xrightarrow {\mathcal {D}}}\ {\text{Normal}}(0,\sigma ^{2}),} where the decorated arrow indicates convergence in distribution. == Monte Carlo Setting == The Markov chain central limit theorem can be guaranteed for functionals of general state space Markov chains under certain conditions. In particular, this can be done with a focus on Monte Carlo settings. An example of the application in a MCMC (Markov Chain Monte Carlo) setting is the following: Consider a simple hard spheres model on a grid. Suppose X = { 1 , … , n 1 } × { 1 , … , n 2 } ⊆ Z 2 {\displaystyle X=\{1,\ldots ,n_{1}\}\times \{1,\ldots ,n_{2}\}\subseteq Z^{2}} . A proper configuration on X {\displaystyle X} consists of coloring each point either black or white in such a way that no two adjacent points are white. Let χ {\displaystyle \chi } denote the set of all proper configurations on X {\displaystyle X} , N χ ( n 1 , n 2 ) {\displaystyle N_{\chi }(n_{1},n_{2})} be the total number of proper configurations and π be the uniform distribution on χ {\displaystyle \chi } so that each proper configuration is equally likely. Suppose our goal is to calculate the typical number of white points in a proper configuration; that is, if W ( x ) {\displaystyle W(x)} is the number of white points in x ∈ χ {\displaystyle x\in \chi } then we want the value of E π W = ∑ x ∈ χ W ( x ) N χ ( n 1 , n 2 ) {\displaystyle E_{\pi }W=\sum _{x\in \chi }{\frac {W(x)}{N_{\chi }{\bigl (}n_{1},n_{2}{\bigr )}}}} If n 1 {\displaystyle n_{1}} and n 2 {\displaystyle n_{2}} are even moderately large then we will have to resort to an approximation to E π W {\displaystyle E_{\pi }W} . Consider the following Markov chain on χ {\displaystyle \chi } . Fix p ∈ ( 0 , 1 ) {\displaystyle p\in (0,1)} and set X 1 = x 1 {\displaystyle X_{1}=x_{1}} where x 1 ∈ χ {\displaystyle x_{1}\in \chi } is an arbitrary proper configuration. Randomly choose a point ( x , y ) ∈ X {\displaystyle (x,y)\in X} and independently draw U ∼ U n i f o r m ( 0 , 1 ) {\displaystyle U\sim \mathrm {Uniform} (0,1)} . If u ≤ p {\displaystyle u\leq p} and all of the adjacent points are black then color ( x , y ) {\displaystyle (x,y)} white leaving all other points alone. Otherwise, color ( x , y ) {\displaystyle (x,y)} black and leave all other points alone. Call the resulting configuration X 1 {\displaystyle X_{1}} . Continuing in this fashion yields a Harris ergodic Markov chain { X 1 , X 2 , X 3 , … } {\displaystyle \{X_{1},X_{2},X_{3},\ldots \}} having π {\displaystyle \pi } as its invariant distribution. It is now a simple matter to estimate E π W {\displaystyle E_{\pi }W} with w n ¯ = ∑ i = 1 n W ( X i ) / n {\displaystyle {\overline {w_{n}}}=\sum _{i=1}^{n}W(X_{i})/n} . Also, since χ {\displaystyle \chi } is finite (albeit potentially large) it is well known that X {\displaystyle X} will converge exponentially fast to π {\displaystyle \pi } which implies that a CLT holds for w n ¯ {\displaystyle {\overline {w_{n}}}} . == Implications == Not taking into account the additional terms in the variance which stem from correlations (e.g. serial correlations in markov chain monte carlo simulations) can result in the problem of pseudoreplication when computing e.g. the confidence intervals for the sample mean.
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