AI Face Combiner

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Space-based data center

Space-based data centers or orbital AI infrastructure are proposed concepts to build AI data centers in the sun-synchronous orbit or other orbits utilizing space-based solar power. Electric power has become the main bottleneck for terrestrial AI infrastructure. Space-based edge computing has historical roots in military architectures designed to bypass the latency of ground-based targeting networks. In the 1980s, the Strategic Defense Initiative's Brilliant Pebbles program first envisioned autonomous on-orbit data processing for missile defense. In 2019, the Space Development Agency (SDA) began to revive this decentralized approach through its Proliferated Warfighter Space Architecture (PWSA). This ambitious "sensor-to-shooter" infrastructure is treated as a prerequisite for the modern Golden Dome program, which would rely on space-based data processing to continuously track targets. == History == Early thinking about space-based computing infrastructure grew out of mid-20th-century visions for large orbital industrial systems, most notably proposals for space-based solar power, which were popularized in both technical literature and science writing by figures such as Isaac Asimov in the 1940s. These ideas emphasized exploiting the vacuum, continuous solar energy, and thermal characteristics of space to support power-intensive activities that would be difficult or inefficient on Earth. In the 21st century, advances in small satellites, reusable launch vehicles, and high-performance computing revived interest in space-based data centers, with governments and private companies exploring orbital or near-space platforms for edge computing, secure data handling, and low-latency processing of Earth-observation data. In September 2024, Y Combinator-backed Starcloud released a white paper detailing plans to build multiple gigawatts of AI compute in orbit. It was the first widely cited proposal to actually start building large orbital data centers. In 2025, Starcloud deployed an NVIDIA H100-class system and became the first company to train an LLM in space and run a version of Google Gemini in space. In March 2025, Lonestar deployed a data backup machine on the surface of the moon. In early January 2026, a team from the University of Pennsylvania presented a tether-based architecture for orbital data centers at the AIAA SciTech conference. The design relied on gravity gradient tension and solar-pressure-based passive attitude stabilization to minimize the mass of MW-scale orbital data centers. In January 2026, SpaceX filed plans with the Federal Communications Commission (FCC) for millions of satellites, leveraging reusable launches and Starlink integration to extend cloud and AI computing into orbit. Around the same time, Blue Origin announced the TeraWave constellation of about 5,400 satellites, designed to provide high‑throughput networking for data centers, enterprise, and government customers. Meanwhile, China announced a 200,000‑satellite constellation, focusing on state coordination, data sovereignty, and in-orbit processing for secure, time-critical applications. In February 2026, Starcloud submitted a proposal to the FCC for a constellation of up to 88,000 satellites for orbital data centers. In March, it announced intentions to be the first to mine Bitcoin in space, flying bitcoin mining ASICs on its second satellite, Starcloud-2. In May 2026, Edge Aerospace was awarded a contract by the European Space Agency under its Space Cloud program to study use cases, architectures and implementation roadmap for orbital data centers. == Feasibility == In October 2025, Nature Electronics published a study led by a research group at Nanyang Technological University on the development of carbon-neutral data centres in space. In November 2025, Google published a feasibility study on space-based data centers. The authors argued that if launch costs to low earth orbit reached US$200/kg, the launch cost for data center satellites could be cost effective relative to current energy costs for ground-based data centers. They project this may occur around 2035 if SpaceX's Starship project scales to 180 launches/year by then. == Advantages == Some sun-synchronous orbit (SSO) planes have constant sunlight in the dawn/dusk which could provide continuous solar energy. SSO is a limited resource and proper management and sharing of it is required. Solar irradiance is 36% higher in Earth orbit than on the surface No Earth weather storms or clouds, however more exposed to Solar storms. No property tax or land-use regulation. Saves space for other land use. Ample space for scalability. Won't strain the power grid. Direct access to power source without additional infrastructure. == Disadvantages == The deployment of space-based data centers raises several technical, economic, and environmental concerns. Existing launch costs are substantial and remains main cost of space infrastructure deployment Cooling is limited to heat dissipation through radiation only, which made in inefficient in comparison to convection in terrestrial data centers Space infrastructure must be designed to survive launch and to work under environment conditions of radiation, wide range of temperatures, in vacuum and in microgravity In-space assembly is on early development stage to enable deployment of mega-structures Megastructures are particularly exposed to orbital debris Solar arrays efficiency decrease 0.5% to 0.8% per year due to exposure of ultraviolet rays, space weather and orbital thermal cycles Hardware is designed for limited lifespan. Maintenance and repair in space (known as On-Orbit Servicing (OOS)) is still on early stage of practical implementation. Disposable data centre: technology obsolescence of AI data centre being a concern and difficult maintenance in space imply the single-use purpose of those space data centres. To extend lifetime, space infrastructure will require either refueling or orbit rasie by the servicer, which is going to increase its operational costs The environmental impact on Earth has its own challenges: The environmental impact of launches need to be addressed. Deployment consumes Earth resources that cannot be recovered or recycled. Computers require lots of resources, some of which are strategic. Recycling e-waste is already a challenge on Earth and extremely unlikely in space. Space debris (orbit pollution) is another sustainability challenge for space: Orbits are, like any resources, a limited physical and electromagnetic resource and available for all mankind. The accumulation of satellites on a particular orbit reduces the use of space for other purposes. A consequence of the increase of satellite in orbit is a higher risk of the runaway of space debris (see Kessler syndrome). This means some orbits could become unusable. Latency and bandwidth are constrained in space, and consumes limited electromagnetic resources. Satellite flares could inhibit ground-based and space-based observational astronomy. == Size and power generated == It would take ~1 square mile solar array in earth orbit to produce 1 gigawatt of power at 30% cell efficiency. == Companies pursuing space-based AI infrastructure == Blue Origin Cowboy Space Corporation (formerly Aetherflux) Edge Aerospace Google – Project Suncatcher Nvidia OpenAI SpaceX Starcloud
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Armin B. Cremers

Armin Bernd Cremers (born June 7, 1946) is a German mathematician and computer scientist. He is a professor in the computer science institute at the University of Bonn, Germany. He is most notable for his contributions to several fields of discrete mathematics including formal languages and automata theory. In more recent years he has been recognized for his work in artificial intelligence, machine learning and robotics as well as in geoinformatics and deductive databases. == Life and work == Armin B. Cremers studied mathematics and physics at the University of Karlsruhe, Germany. After his graduate diploma (1971) and PhD (1972), both in mathematics, both summa cum laude, he received his academic lectureship qualification for computer science (1974), all from the University of Karlsruhe. Following an invitation by Seymour Ginsburg, he joined the University of Southern California (USC), Los Angeles, in 1973 where he worked until 1976 as an assistant professor of electrical engineering and computer science. With Ginsburg he initiated Grammar Forms, a new formalism for grammatical families. In 1976 A. B. Cremers returned to Germany and was appointed to full professor of computer science at the University of Dortmund, where he remained until 1990, holding the chair for information systems. During the same time he continued working as a visiting research professor at USC, where together with Thomas N. Hibbard he developed the concept of Data Spaces, a comprehensive computational model, in theory and applications. At the University of Dortmund A. B. Cremers served as chairman of the computer science department and, since early 1985, as vice president for Research and Junior Scientific Staff. In this position he was liaison for the development of the Technology Center Dortmund Archived 2021-05-09 at the Wayback Machine. He was the initiator and founding director of the Center for Expert Systems Dortmund (ZEDO) and the NRW State Research Collaborative in Artificial Intelligence (KI-NRW). From 1988 to 1996 he was also a member of the supervisory board of the German National Research Center for Mathematics and Data Processing (GMD). Since 1990 A. B. Cremers has been professor and director of computer science and head of the research group in artificial intelligence at the University of Bonn. From Bonn he has contributed fundamentally to artificial intelligence and robotics (with Wolfram Burgard, Dieter Fox, Sebastian Thrun among his students), and to the development of software engineering, particularly in civil engineering, and information systems, particularly in the geosciences. The paper "The Interactive Museum Tour-Guide Robot" won the AAAI Classic Paper award of 2016. Together with Matthias Jarke A. B. Cremers established the Bonn-Aachen International Center for Information Technology (B-IT) in 2001 and led this as Founding Scientific Director from the University of Bonn side until his retirement from teaching in 2014. From 2004 to 2008 Cremers was Dean of the School of Mathematics and Natural Sciences, and from April 2009 to July 2014 University Vice President for Planning and Finance. He is member of advisory boards, e.g., as well as Chairman of the University Council of the University of Koblenz-Landau.
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Ronald J. Williams

Ronald James Williams (1945 – February 16, 2024) was an American mathematician and computer scientist who spent the majority of his career at Northeastern University. He is considered one of the pioneers of neural networks. In 1986, he co-authored the seminal paper in Nature on the backpropagation algorithm along with David Rumelhart and Geoffrey Hinton, which triggered a boom in neural network research. == Education and career == Williams was born in Southern California. He studied at California Institute of Technology as a undergraduate student and received a B.S. in mathematics there in 1966. He received his M.A. and Ph.D. in mathematics, both at University of California, San Diego (UCSD) in 1972 and 1975, respectively. His Ph.D. thesis was supervised by Donald Werner Anderson. He worked for a defense contractor for some time after graduation. From 1983 to 1986, Williams was a member of the Parallel Distributed Processing research group headed by David Rumelhart at the Institute for Cognitive Science at UCSD. In 1986, Williams accepted a professorship in computer science at Northeastern University in Boston, where he remained afterwards. In addition to the backpropagation paper, Williams made fundamental contributions to the fields of recurrent neural networks, where he, along with David Zipser, invented the teacher forcing algorithm and made important contributions to backpropagation through time. In reinforcement learning, Williams introduced the REINFORCE algorithm in 1992, which became the first policy gradient method. Besides his works on neural networks, Williams, together with Wenxu Tong and Mary Jo Ondrechen, developed Partial Order Optimum Likelihood (POOL), a machine learning method used in the prediction of active amino acids in protein structures. POOL is a maximum likelihood method with a monotonicity constraint and is a general predictor of properties that depend monotonically on the input features.
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Clement Farabet

Clément Farabet is a computer scientist and AI expert known for his contributions to the field of deep learning. He served as a research scientist at the New York University. He serves as the Vice President of Research at Google DeepMind and previously served as the VP of AI Infrastructure at NVIDIA. His scholarly work received over 11,000 citations with an h-index of 21. == Education == In 2008, Farabet earned a master's degree in electrical engineering with honors from Institut national des sciences appliquées (INSA) de Lyon, France. In 2010, Farabet received his PhD at Université Paris-Est, co-advised by Professors Laurent Najman and Yann LeCun. His thesis focused on real-time image understanding and introduced multi-scale convolutional networks and graph-based techniques for efficient segmentations of class prediction maps. He successfully defended his thesis in 2013. == Career == In 2008, after completing his Master's degree, Farabet joined Professor Yann LeCun's laboratory at the Courant Institute of Mathematical Sciences at New York University. His Master's thesis work on reconfigurable hardware for deep neural networks resulted in a patent. He continued his collaboration with Yann LeCun, and in 2009, he began working with Yale University's e-Lab, led by Eugenio Culurciello. This collaboration eventually led to the creation of TeraDeep. He began his career as a researcher, contributing to the development of LuaTorch, one of the first AI frameworks, which later evolved into PyTorch, widely recognized and adopted globally. == Startups == Farabet co-founded MadBits, a startup with a focus on web-scale image understanding. The company was acquired by Twitter in 2014. Following this acquisition, Farabet co-founded Twitter Cortex, a team dedicated to building Twitter's deep learning platform for various applications, including recommendations, search, spam detection, and NSFW content and ads. == Publications == Farabet, Clement; Couprie, Camille; Najman, Laurent; LeCun, Yann (August 2013). "Learning Hierarchical Features for Scene Labeling". IEEE Transactions on Pattern Analysis and Machine Intelligence. 35 (8): 1915–1929. Bibcode:2013ITPAM..35.1915F. doi:10.1109/TPAMI.2012.231. PMID 23787344. S2CID 206765110. LeCun, Yann; Kavukcuoglu, Koray; Farabet, Clement (2010). "Convolutional networks and applications in vision". Proceedings of 2010 IEEE International Symposium on Circuits and Systems. pp. 253–256. doi:10.1109/ISCAS.2010.5537907. ISBN 978-1-4244-5308-5. S2CID 7625356. Collobert, Ronan; Kavukcuoglu, K.; Farabet, C. (2011). "Torch7: A Matlab-like Environment for Machine Learning". Neural Information Processing Systems. Couprie, Camille; Farabet, Clément; Najman, Laurent; LeCun, Yann (16 January 2013). "Indoor Semantic Segmentation using depth information". arXiv:1301.3572 [cs.CV]. Farabet, Clement (2011). "NeuFlow: A runtime reconfigurable dataflow processor for vision". CVPR 2011 Workshops. pp. 109–116. doi:10.1109/CVPRW.2011.5981829. ISBN 978-1-4577-0529-8. S2CID 851574. Farabet, Clement (2009). "CNP: An FPGA-based processor for Convolutional Networks". 2009 International Conference on Field Programmable Logic and Applications. pp. 32–37. doi:10.1109/FPL.2009.5272559. S2CID 5339694. Farabet, Clement (2010). "Hardware accelerated convolutional neural networks for synthetic vision systems". Proceedings of 2010 IEEE International Symposium on Circuits and Systems. pp. 257–260. doi:10.1109/ISCAS.2010.5537908. ISBN 978-1-4244-5308-5. S2CID 6542026.
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Docic

Docic is a Tunisian digital health platform available as a web and mobile application, headquartered in Tunis, Tunisia. Founded in 2022 by Sami Kallel, an orthopedic surgeon, and Sofiane Trabelsi. The service helps patients and healthcare professionals store, organize, and share medical records digitally and to connect with the doctor online. == History == Docic was founded in 2022 as a health-technology company based in Tunisia, after which the mobile application was subsequently developed and made available to users. The platform was designed to provide healthcare professionals with access to patients’ complete medical history, including updates and recent changes, aiming at supporting clinical decision-making and reducing the risk of medical errors. In January 2025, Docic was listed amongst companies that have received the Startup Act label, which is a recognition under the Tunisian legal framework made to support innovative startups.
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The Best Free AI Chatbot for Beginners

Trying to pick the best AI chatbot? An AI chatbot is software that uses machine learning to help you get more done — it scales effortlessly from a single task to thousands. The best picks balance beginner-friendly simplicity with the depth power users need, and they ship updates often. Whether you are a beginner or a pro, the right AI chatbot 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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Collocation extraction

Collocation extraction is the task of using a computer to extract collocations automatically from a corpus. The traditional method of performing collocation extraction is to find a formula based on the statistical quantities of those words to calculate a score associated to every word pairs. Proposed formulas are mutual information, t-test, z test, chi-squared test and likelihood ratio. Within the area of corpus linguistics, collocation is defined as a sequence of words or terms which co-occur more often than would be expected by chance. 'Crystal clear', 'middle management', 'nuclear family', and 'cosmetic surgery' are examples of collocated pairs of words. Some words are often found together because they make up a compound noun, for example 'riding boots' or 'motor cyclist' or ‘collocation extraction’ its very self.
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Best AI Content Generators in 2026

Trying to pick the best AI content generator? An AI content generator is software that uses machine learning to help you get more done — it scales effortlessly from a single task to thousands. The best picks balance beginner-friendly simplicity with the depth power users need, and they ship updates often. Whether you are a beginner or a pro, the right AI content 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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MLOps

MLOps or ML Ops is a paradigm that aims to deploy and maintain machine learning models in production reliably and efficiently. It bridges the gap between machine learning development and production operations, ensuring that models are robust, scalable, and aligned with business goals. The word is a compound of "machine learning" and the continuous delivery practice (CI/CD) of DevOps in the software field. Machine learning models are tested and developed in isolated experimental systems. When an algorithm is ready to be launched, MLOps is practiced between data scientists, DevOps, and machine learning engineers to transition the algorithm to production systems. Similar to DevOps or DataOps approaches, MLOps seeks to increase automation and improve the quality of production models, while also focusing on business and regulatory requirements. While MLOps started as a set of best practices, it is slowly evolving into an independent approach to ML lifecycle management. MLOps applies to the entire lifecycle - from integrating with model generation (software development lifecycle, continuous integration/continuous delivery), orchestration, and deployment, to health, diagnostics, governance, and business metrics. == Definition == MLOps is a paradigm, including aspects like best practices, sets of concepts, as well as a development culture when it comes to the end-to-end conceptualization, implementation, monitoring, deployment, and scalability of machine learning products. Most of all, it is an engineering practice that leverages three contributing disciplines: machine learning, software engineering (especially DevOps), and data engineering. MLOps is aimed at productionizing machine learning systems by bridging the gap between development (Dev) and operations (Ops). Essentially, MLOps aims to facilitate the creation of machine learning products by leveraging these principles: CI/CD automation, workflow orchestration, reproducibility; versioning of data, model, and code; collaboration; continuous ML training and evaluation; ML metadata tracking and logging; continuous monitoring; and feedback loops. == History == Interest in operationalizing machine learning systems began to grow in the mid-2010s as ML projects started moving from experimentation to production use. The challenges associated with sustaining such systems were highlighted in a 2015 paper. The predicted growth in machine learning included an estimated doubling of ML pilots and implementations from 2017 to 2018, and again from 2018 to 2020. Reports show a majority (up to 88%) of corporate machine learning initiatives are struggling to move beyond test stages. However, those organizations that actually put machine learning into production saw a 3–15% profit margin increases. The MLOps market size was USD 2,191.8 Million in 2024, and is projected to be USD 16,613.4 Million in 2030. == Architecture == Machine Learning systems can be categorized in eight different categories: data collection, data processing, feature engineering, data labeling, model design, model training and optimization, endpoint deployment, and endpoint monitoring. Each step in the machine learning lifecycle is built in its own system, but requires interconnection. These are the minimum systems that enterprises need to scale machine learning within their organization. == Goals == There are a number of goals enterprises want to achieve through MLOps systems successfully implementing ML across the enterprise, including: Deployment and automation Reproducibility of models and predictions Diagnostics Governance and regulatory compliance Scalability Collaboration Business uses Monitoring and management A standard practice, such as MLOps, takes into account each of the aforementioned areas, which can help enterprises optimize workflows and avoid issues during implementation. Vendors such as Adaptive ML deliver commercial reinforcement learning operations (RLOps) and MLOps-infrastructure, targeting organizations deploying large language models in production. A common architecture of an MLOps system would include data science platforms where models are constructed and the analytical engines where computations are performed, with the MLOps tool orchestrating the movement of machine learning models, data and outcomes between the systems.
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Probabilistic automaton

In mathematics and computer science, the probabilistic automaton (PA) is a generalization of the nondeterministic finite automaton; it includes the probability of a given transition into the transition function, turning it into a transition matrix. Thus, the probabilistic automaton also generalizes the concepts of a Markov chain and of a subshift of finite type. The languages recognized by probabilistic automata are called stochastic languages; these include the regular languages as a subset. The number of stochastic languages is uncountable. The concept was introduced by Michael O. Rabin in 1963; a certain special case is sometimes known as the Rabin automaton (not to be confused with the subclass of ω-automata also referred to as Rabin automata). In recent years, a variant has been formulated in terms of quantum probabilities, the quantum finite automaton. == Informal Description == For a given initial state and input character, a deterministic finite automaton (DFA) has exactly one next state, and a nondeterministic finite automaton (NFA) has a set of next states. A probabilistic automaton (PA) instead has a weighted set (or vector) of next states, where the weights must sum to 1 and therefore can be interpreted as probabilities (making it a stochastic vector). The notions states and acceptance must also be modified to reflect the introduction of these weights. The state of the machine as a given step must now also be represented by a stochastic vector of states, and a state accepted if its total probability of being in an acceptance state exceeds some cut-off. A PA is in some sense a half-way step from deterministic to non-deterministic, as it allows a set of next states but with restrictions on their weights. However, this is somewhat misleading, as the PA utilizes the notion of the real numbers to define the weights, which is absent in the definition of both DFAs and NFAs. This additional freedom enables them to decide languages that are not regular, such as the p-adic languages with irrational parameters. As such, PAs are more powerful than both DFAs and NFAs (which are famously equally powerful). == Formal Definition == The probabilistic automaton may be defined as an extension of a nondeterministic finite automaton ( Q , Σ , δ , q 0 , F ) {\displaystyle (Q,\Sigma ,\delta ,q_{0},F)} , together with two probabilities: the probability P {\displaystyle P} of a particular state transition taking place, and with the initial state q 0 {\displaystyle q_{0}} replaced by a stochastic vector giving the probability of the automaton being in a given initial state. For the ordinary non-deterministic finite automaton, one has a finite set of states Q {\displaystyle Q} a finite set of input symbols Σ {\displaystyle \Sigma } a transition function δ : Q × Σ → ℘ ( Q ) {\displaystyle \delta :Q\times \Sigma \to \wp (Q)} a set of states F {\displaystyle F} distinguished as accepting (or final) states F ⊆ Q {\displaystyle F\subseteq Q} . Here, ℘ ( Q ) {\displaystyle \wp (Q)} denotes the power set of Q {\displaystyle Q} . By use of currying, the transition function δ : Q × Σ → ℘ ( Q ) {\displaystyle \delta :Q\times \Sigma \to \wp (Q)} of a non-deterministic finite automaton can be written as a membership function δ : Q × Σ × Q → { 0 , 1 } {\displaystyle \delta :Q\times \Sigma \times Q\to \{0,1\}} so that δ ( q , a , q ′ ) = 1 {\displaystyle \delta (q,a,q^{\prime })=1} if q ′ ∈ δ ( q , a ) {\displaystyle q^{\prime }\in \delta (q,a)} and 0 {\displaystyle 0} otherwise. The curried transition function can be understood to be a matrix with matrix entries [ θ a ] q q ′ = δ ( q , a , q ′ ) {\displaystyle \left[\theta _{a}\right]_{qq^{\prime }}=\delta (q,a,q^{\prime })} The matrix θ a {\displaystyle \theta _{a}} is then a square matrix, whose entries are zero or one, indicating whether a transition q → a q ′ {\displaystyle q{\stackrel {a}{\rightarrow }}q^{\prime }} is allowed by the NFA. Such a transition matrix is always defined for a non-deterministic finite automaton. The probabilistic automaton replaces these matrices by a family of right stochastic matrices P a {\displaystyle P_{a}} , for each symbol a in the alphabet Σ {\displaystyle \Sigma } so that the probability of a transition is given by [ P a ] q q ′ {\displaystyle \left[P_{a}\right]_{qq^{\prime }}} A state change from some state to any state must occur with probability one, of course, and so one must have ∑ q ′ [ P a ] q q ′ = 1 {\displaystyle \sum _{q^{\prime }}\left[P_{a}\right]_{qq^{\prime }}=1} for all input letters a {\displaystyle a} and internal states q {\displaystyle q} . The initial state of a probabilistic automaton is given by a row vector v {\displaystyle v} , whose components are the probabilities of the individual initial states q {\displaystyle q} , that add to 1: ∑ q [ v ] q = 1 {\displaystyle \sum _{q}\left[v\right]_{q}=1} The transition matrix acts on the right, so that the state of the probabilistic automaton, after consuming the input string a b c {\displaystyle abc} , would be v P a P b P c {\displaystyle vP_{a}P_{b}P_{c}} In particular, the state of a probabilistic automaton is always a stochastic vector, since the product of any two stochastic matrices is a stochastic matrix, and the product of a stochastic vector and a stochastic matrix is again a stochastic vector. This vector is sometimes called the distribution of states, emphasizing that it is a discrete probability distribution. Formally, the definition of a probabilistic automaton does not require the mechanics of the non-deterministic automaton, which may be dispensed with. Formally, a probabilistic automaton PA is defined as the tuple ( Q , Σ , P , v , F ) {\displaystyle (Q,\Sigma ,P,v,F)} . A Rabin automaton is one for which the initial distribution v {\displaystyle v} is a coordinate vector; that is, has zero for all but one entries, and the remaining entry being one. == Stochastic languages == The set of languages recognized by probabilistic automata are called stochastic languages. They include the regular languages as a subset. Let F = Q accept ⊆ Q {\displaystyle F=Q_{\text{accept}}\subseteq Q} be the set of "accepting" or "final" states of the automaton. By abuse of notation, Q accept {\displaystyle Q_{\text{accept}}} can also be understood to be the column vector that is the membership function for Q accept {\displaystyle Q_{\text{accept}}} ; that is, it has a 1 at the places corresponding to elements in Q accept {\displaystyle Q_{\text{accept}}} , and a zero otherwise. This vector may be contracted with the internal state probability, to form a scalar. The language recognized by a specific automaton is then defined as L η = { s ∈ Σ ∗ | v P s Q accept > η } {\displaystyle L_{\eta }=\{s\in \Sigma ^{}\vert vP_{s}Q_{\text{accept}}>\eta \}} where Σ ∗ {\displaystyle \Sigma ^{}} is the set of all strings in the alphabet Σ {\displaystyle \Sigma } (so that is the Kleene star). The language depends on the value of the cut-point η {\displaystyle \eta } , normally taken to be in the range 0 ≤ η < 1 {\displaystyle 0\leq \eta <1} . A language is called η-stochastic if and only if there exists some PA that recognizes the language, for fixed η {\displaystyle \eta } . A language is called stochastic if and only if there is some 0 ≤ η < 1 {\displaystyle 0\leq \eta <1} for which L η {\displaystyle L_{\eta }} is η-stochastic. A cut-point is said to be an isolated cut-point if and only if there exists a δ > 0 {\displaystyle \delta >0} such that | v P ( s ) Q accept − η | ≥ δ {\displaystyle \vert vP(s)Q_{\text{accept}}-\eta \vert \geq \delta } for all s ∈ Σ ∗ {\displaystyle s\in \Sigma ^{}} == Properties == Every regular language is stochastic, and more strongly, every regular language is η-stochastic. A weak converse is that every 0-stochastic language is regular; however, the general converse does not hold: there are stochastic languages that are not regular. Every η-stochastic language is stochastic, for some 0 < η < 1 {\displaystyle 0<\eta <1} . Every stochastic language is representable by a Rabin automaton. If η {\displaystyle \eta } is an isolated cut-point, then L η {\displaystyle L_{\eta }} is a regular language. == p-adic languages == The p-adic languages provide an example of a stochastic language that is not regular, and also show that the number of stochastic languages is uncountable. A p-adic language is defined as the set of strings L η ( p ) = { n 1 n 2 n 3 … | 0 ≤ n k < p and 0. n 1 n 2 n 3 … > η } {\displaystyle L_{\eta }(p)=\{n_{1}n_{2}n_{3}\ldots \vert 0\leq n_{k}\eta \}} in the letters 0 , 1 , 2 , … , ( p − 1 ) {\displaystyle 0,1,2,\ldots ,(p-1)} . That is, a p-adic language is merely the set of real numbers in [0, 1], written in base-p, such that they are greater than η {\displaystyle \eta } . It is straightforward to show that all p-adic languages are stochastic. In particular, this implies that the number of stochastic languages is uncountable. A p-adic
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How to Choose an AI Humanizer

In search of the best AI humanizer? An AI humanizer 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 humanizer 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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Krzysztof Wołk

Krzysztof Wołk (born 16 August 1986) is a Polish IT researcher who specializes in artificial intelligence, machine learning, mobile applications, linguistic engineering, multimedia, NLP and graphic applications. His research works have been cited in more than 70 international research journals, books and research papers. He is member of scientific committee at the Health and Social Care Information Systems and Technologies (HCist), an international conference which brings in new ideas, new technologies, academic scientists, healthcare IT professionals, managers and solution providers from all over the world. His research in statistical machine learning has been recognized as one of the most cited researches in the world. He is the member of Scientific Committee-Reviewers at Research Conference in Technical Disciplines (RCITD), based in Slovakia, which brings together the academic scientists and researchers from all around the world. == Biography == He obtained the doctorate degree in 2016 from the Polish-Japanese Academy of Information and Technology in Warsaw, Poland. He is currently working as researcher and assistant professor at the Polish-Japanese Computer Science Academy (PJATK) in Warsaw, Poland. == Achievements == He has published three books: Biblia Windows Server 2012, Administrator's Guide, Mac OS X Server 10.8, and MAC OS X Server 10.6 and 10.7 Practical Guide has been cited by many researchers in the scholarly books, research journals and articles. His research work on the Polish-English statistical machine translation has been featured in the book New Research in Multimedia and Internet System. Similarly, his works regarding the machine translation system have been featured in the books New Perspective in Information System and Technologies Volume 1, Multimedia and Network Information System, and Recent Advances in Information Systems and Technologies, Volume 1.
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Graph cut optimization

Graph cut optimization is a combinatorial optimization method applicable to a family of functions of discrete variables, named after the concept of cut in the theory of flow networks. Thanks to the max-flow min-cut theorem, determining the minimum cut over a graph representing a flow network is equivalent to computing the maximum flow over the network. Given a pseudo-Boolean function f {\displaystyle f} , if it is possible to construct a flow network with positive weights such that each cut C {\displaystyle C} of the network can be mapped to an assignment of variables x {\displaystyle \mathbf {x} } to f {\displaystyle f} (and vice versa), and the cost of C {\displaystyle C} equals f ( x ) {\displaystyle f(\mathbf {x} )} (up to an additive constant) then it is possible to find the global optimum of f {\displaystyle f} in polynomial time by computing a minimum cut of the graph. The mapping between cuts and variable assignments is done by representing each variable with one node in the graph and, given a cut, each variable will have a value of 0 if the corresponding node belongs to the component connected to the source, or 1 if it belong to the component connected to the sink. Not all pseudo-Boolean functions can be represented by a flow network, and in the general case the global optimization problem is NP-hard. There exist sufficient conditions to characterise families of functions that can be optimised through graph cuts, such as submodular quadratic functions. Graph cut optimization can be extended to functions of discrete variables with a finite number of values, that can be approached with iterative algorithms with strong optimality properties, computing one graph cut at each iteration. Graph cut optimization is an important tool for inference over graphical models such as Markov random fields or conditional random fields, and it has applications in computer vision problems such as image segmentation, denoising, registration and stereo matching. == Representability == A pseudo-Boolean function f : { 0 , 1 } n → R {\displaystyle f:\{0,1\}^{n}\to \mathbb {R} } is said to be representable if there exists a graph G = ( V , E ) {\displaystyle G=(V,E)} with non-negative weights and with source and sink nodes s {\displaystyle s} and t {\displaystyle t} respectively, and there exists a set of nodes V 0 = { v 1 , … , v n } ⊂ V − { s , t } {\displaystyle V_{0}=\{v_{1},\dots ,v_{n}\}\subset V-\{s,t\}} such that, for each tuple of values ( x 1 , … , x n ) ∈ { 0 , 1 } n {\displaystyle (x_{1},\dots ,x_{n})\in \{0,1\}^{n}} assigned to the variables, f ( x 1 , … , x n ) {\displaystyle f(x_{1},\dots ,x_{n})} equals (up to a constant) the value of the flow determined by a minimum cut C = ( S , T ) {\displaystyle C=(S,T)} of the graph G {\displaystyle G} such that v i ∈ S {\displaystyle v_{i}\in S} if x i = 0 {\displaystyle x_{i}=0} and v i ∈ T {\displaystyle v_{i}\in T} if x i = 1 {\displaystyle x_{i}=1} . It is possible to classify pseudo-Boolean functions according to their order, determined by the maximum number of variables contributing to each single term. All first order functions, where each term depends upon at most one variable, are always representable. Quadratic functions f ( x ) = w 0 + ∑ i w i ( x i ) + ∑ i < j w i j ( x i , x j ) . {\displaystyle f(\mathbf {x} )=w_{0}+\sum _{i}w_{i}(x_{i})+\sum _{i 0 {\displaystyle p>0} then w i j k ( x i , x j , x k ) = w i j k ( 0 , 0 , 0 ) + p 1 ( x i − 1 ) + p 2 ( x j − 1 ) + p 3 ( x k − 1 ) + p 23 ( x j − 1 ) x k + p 31 x i ( x k − 1 ) + p 12 ( x i − 1 ) x j − p x i x j x k {\displaystyle w_{ijk}(x_{i},x_{j},x_{k})=w_{ijk}(0,0,0)+p_{1}(x_{i}-1)+p_{2}(x_{j}-1)+p_{3}(x_{k}-1)+p_{23}(x_{j}-1)x_{k}+p_{31}x_{i}(x_{k}-1)+p_{12}(x_{i}-1)x_{j}-px_{i}x_{j}x_{k}} with p 1 = w i j k ( 1 , 0 , 1 ) − w i j k ( 0 , 0 , 1 ) p 2 = w i j k ( 1 , 1 , 0 ) − w i j k ( 1 , 0 , 1 ) p 3 = w i j k ( 0 , 1 , 1 ) − w i j k ( 0 , 1 , 0 ) p 23 = w i j k ( 0 , 0 , 1 ) + w i j k ( 0 , 1 , 0 ) − w i j k ( 0 , 0 , 0 ) − w i j k ( 0 , 1 , 1 ) p 31 = w i j k ( 0 , 0 , 1 ) + w i j k ( 1 , 0 , 0 ) − w i j k ( 0 , 0 , 0 ) − w i j k ( 1 , 0 , 1 ) p 12 = w i j k ( 0 , 1 , 0 ) + w i j k ( 1 , 0 , 0 ) − w i j k ( 0 , 0 , 0 ) − w i j k ( 1 , 1 , 0 ) . {\displaystyle {\begin{aligned}p_{1}&=w_{ijk}(1,0,1)-w_{ijk}(0,0,1)\\p_{2}&=w_{ijk}(1,1,0)-w_{ijk}(1,0,1)\\p_{3}&=w_{ijk}(0,1,1)-w_{ijk}(0,1,0)\\p_{23}&=w_{ijk}(0,0,1)+w_{ijk}(0,1,0)-w_{ijk}(0,0,0)-w_{ijk}(0,1,1)\\p_{31}&=w_{ijk}(0,0,1)+w_{ijk}(1,0,0)-w_{ijk}(0,0,0)-w_{ijk}(1,0,1)\\p_{12}&=w_{ijk}(0,1,0)+w_{ijk}(1,0,0)-w_{ijk}(0,0,0)-w_{ijk}(1,1
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Yasuo Matsuyama

Yasuo Matsuyama (born March 23, 1947) is a Japanese researcher in machine learning and human-aware information processing. Matsuyama is a Professor Emeritus and an Honorary Researcher of the Research Institute of Science and Engineering of Waseda University. == Early life and education == Matsuyama received his bachelor’s, master’s and doctoral degrees in electrical engineering from Waseda University in 1969, 1971, and 1974 respectively. The dissertation title for the Doctor of Engineering is Studies on Stochastic Modeling of Neurons. There, he contributed to the spiking neurons with stochastic pulse-frequency modulation. Advisors were Jun’ichi Takagi, Kageo, Akizuki, and Katsuhiko Shirai. Upon the completion of the doctoral work at Waseda University, he was dispatched to the United States as a Japan-U.S. exchange fellow by the joint program of the Japan Society for the Promotion of Science, Fulbright Program, and the Institute of International Education. Through this exchange program, he completed his Ph.D. program at Stanford University in 1978. The dissertation title is Process Distortion Measures and Signal Processing. There, he contributed to the theory of probabilistic distortion measures and its applications to speech encoding with spectral clustering or vector quantization. His advisor was Robert. M. Gray. == Career == From 1977 to 1078, Matsuyama was a research assistant at the Information Systems Laboratory of Stanford University Archived 2018-03-16 at the Wayback Machine. From 1979 to 1996, he was a faculty of Ibaraki University, Japan (the final position was a professor and chairperson of the Information and System Sciences Major). Since 1996, he was a Professor of Waseda University, Department of Computer Science and Engineering. From 2011 to 2013, he was the director of the Media Network Center of Waseda University. At the 2011 Tōhoku earthquake and tsunami of March 11, 2011, he was in charge of the safety inquiry of 65,000 students, staffs and faculties. Since 2017, Matsuyama is a Professor Emeritus and an Honorary Researcher of the Research Institute of Science and Engineering of Waseda University. Since 2018, he serves as an acting president of the Waseda Electrical Engineering Society. == Work == Matsuyama’s works on machine learning and human-aware information processing have dual foundations. Studies on the competitive learning (vector quantization) for his Ph.D. at Stanford University brought about his succeeding works on machine learning contributions. Studies on stochastic spiking neurons for his Dr. Engineering at Waseda University set off applications of biological signals to the machine learning. Thus, his works can be grouped reflecting these dual foundations. Statistical machine learning algorithms: The use of the alpha-logarithmic likelihood ratio in learning cycles generated the alpha-EM algorithm (alpha-Expectation maximization algorithm). Because the alpha-logarithm includes the usual logarithm, the alpha-EM algorithm contains the EM-algorithm (more precisely, the log-EM algorithm). The merit of the speedup by the alpha-EM over the log-EM is due to the ability to utilize the past information. Such a usage of the messages from the past brought about the alpha-HMM estimation algorithm (alpha-hidden Markov model estimation algorithm) that is a generalized and faster version of the hidden Markov model estimation algorithm (HMM estimation algorithm). Competitive learning on empirical data: Starting from the speech compression studies at Stanford, Matsuyama developed generalized competitive learning algorithms; the harmonic competition and the multiple descent cost competition. The former realizes the multiple-object optimization. The latter admits deformable centroids. Both algorithms generalize the batch-mode vector quantization (simply called, vector quantization) and the successive-mode vector quantization (or, called learning vector quantization). A hierarchy from the alpha-EM to the vector quantization: Matsuyama contributed to generate and identify the hierarchy of the above algorithms. Alpha-EM ⊃ log-EM ⊃ basic competitive learning (vector quantization, VQ; or clustering). On the class of the vector quantization and competitive learning, he contributed to generate and identify the hierarchy of VQs. VQ ⇔ {batch mode VQ, and learning VQ} ⊂ {harmonic competition} ⊂ {multiple descent cost competition}. Applications to Human-aware information processing: The dual foundations of his led to the applications to huma-aware information processing. Retrieval systems for similar images and videos. Bipedal humanoid operations via invasive and noninvasive brain signals as well as gestures. Continuous authentication of uses by brain signals. Self-organization and emotional feature injection based on the competitive learning. Decomposition of DNA sequences by the independent component analysis (US Patent: US 8,244,474 B2). Data compression of speech signals by the competitive learning. The above theories and applications work as contributions to IoCT (Internet of Collaborative Things) and IoXT (http://www.asc-events.org/ASC17/Workshop.php Archived 2018-02-06 at the Wayback Machine). == Awards and honors == 2016: e-Teaching Award of Waseda University 2015: Best Textbook Award by the Japanese Society of Information Processing 2014: Fellow of the Japanese Society of Information Processing 2013: IEEE Life Fellow 2008: Y. Dote Memorial Best Paper Award of CSTST 2008 from ACM and IEEE 2006: LSI Intellectual Property Design Award from the LSI IP Committee 2004: Best Paper Award for Application Oriented Research from Asia Pacific Neural Network Assembly 2002: Fellow Award from the Institute of Electronics, Information and Communication Engineers. 2001: Telecommunication System Major Award of the Telecommunications Advancement Foundation 2001: Outstanding Paper Award of IEEE Transactions on Neural Networks Archived 2013-01-17 at the Wayback Machine 1998: Fellow Award from IEEE for contributions to learning algorithms with competition. 1992: Best Paper Award from the Institute of Electronics, Information and Communication Engineers 1989: Telecommunication System Promotion Award of the Telecommunications Advancement Foundation
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Best AI Chatbots in 2026

Curious about the best AI chatbot? An AI chatbot 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 chatbot 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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