AI Bot Grammar Checker

AI Bot Grammar Checker — independent reviews, comparisons, pricing and step-by-step guides on Aizhi.

Group of Governmental Experts on Lethal Autonomous Weapons Systems

The Group of Governmental Experts on Lethal Autonomous Weapons Systems, commonly known as the GGE on LAWS, refers to a group of governmental experts established under the framework of the Convention on Certain Conventional Weapons (CCW), a United Nations arms control framework. The group examines legal, ethical, societal and moral questions that arise from the increased use of autonomous robots to carry weapons and to be programmed to engage in combat in various situations that might arise, including battles between countries, or in patrolling border areas or sensitive areas, or other similar roles. As of 18 March 2025, the Convention on Certain Conventional Weapons had 128 High Contracting Parties. In the Geneva Conventions, the term "High Contracting Parties" refers to the states that have joined the conventions and are therefore bound to uphold them. Among the countries that have joined are states with tense relations or ongoing armed conflict with one another, including Russia and Ukraine, Israel and the State of Palestine, and Pakistan and Afghanistan. == Background == In 2013, the Meeting of State Parties to the Convention on Certain Conventional Weapons agreed on a mandate on lethal autonomous weapon systems and tasked its chairperson with convening an informal Meeting of Experts to discuss issues related to emerging technologies in the area of LAWS. Those informal Meetings of Experts were then held in 2014, 2015 and 2016, and their reports fed into subsequent meetings of the High Contracting Parties. At the Fifth CCW Review Conference in 2016, the High Contracting Parties decided to establish an open-ended Group of Governmental Experts on emerging technologies in the area of LAWS, building on the earlier expert meetings. Since then, the group has been reconvened annually. In 2023, the Meeting of the High Contracting Parties to the CCW decided that the GGE on LAWS would continue its work in 2024 and 2025. The group was tasked with developing, by consensus, elements of a possible instrument, without predetermining its form, as well as other measures addressing lethal autonomous weapon systems, drawing on existing CCW protocols, earlier recommendations, state proposals, and legal, military, and technological expertise. == 2024 == In 2024, the GGE met twice, and the group was chaired by Robert in den Bosch, the Netherlands' disarmament ambassador. The 2024 Meeting of the High Contracting Parties decided that the group would meet for 10 days in 2025, in two five-day sessions, and reaffirmed its mandate to continue work by consensus on possible elements of an instrument and other measures addressing lethal autonomous weapon systems. == 2025 == At its first 2025 session, held in Geneva from 3 to 7 March 2025, the Group of Governmental Experts on Lethal Autonomous Weapon Systems discussed revisions to the chair's rolling text. The text was structured into five sections, or "boxes", though delegates held differing views on whether headings were useful or appropriate. Broadly, the discussions covered the characterization of lethal autonomous weapon systems, the application of international humanitarian law, possible prohibitions and regulations, legal review, and questions of accountability and responsibility. At its second session, held from 1 to 5 September 2025, delegations continued work on the chair's rolling text, which set out elements of a possible instrument and was organized into five thematic "boxes". == 2026 == === Developments before the 2026 session === A few weeks before the meeting, autonomous weapons drew renewed attention when the United States pressured Anthropic to revise the terms of use for its AI model Claude. Anthropic prohibited the model's use for mass domestic surveillance and for fully autonomous weapons operating without human oversight, while reports also emerged that OpenAI had reached an agreement with the U.S. Department of War for the use of its AI models, reportedly stipulating that they would not independently direct autonomous weapons where human control was required. The U.S. military nevertheless continued to use Claude during its war on Iran, and there was increasing alarm about the use of AI-assisted semi-autonomous weapons in conflicts including those in Ukraine, Sudan, Gaza, and Iran. Before the start of the sessions, Robert in den Bosch, as chair, warned that progress was urgent because technological developments were moving quickly. At the same time, although states agreed that international humanitarian law applied to LAWS, specific internationally binding standards governing such systems remained largely absent. A key divide before the session was that Russia and the United States opposed new legally binding instruments, while other states argued that new rules were necessary. According to Robert in den Bosch, the talks could lead to new rules, amendments to an existing convention, or a new treaty. === First session === From 2 to 6 March 2026, the group held its penultimate session under the group's three-year mandate. Delegations discussed the chair's rolling draft text, circulated in December 2025, on elements of a possible instrument or other measures concerning lethal autonomous weapon systems. In revised text circulated by the chair on 5 March 2026, a lethal autonomous weapon system was characterized as "a functionally integrated combination of one or more weapons and technological components, that can identify, select, and engage a target, without intervention by a human operator in the execution of these tasks". The text was divided into five boxes to structure discussion. During the session, delegates conducted a first reading of the draft text, and the chair later circulated revised language for several sections. Informal consultations were also held. According to campaign groups and participating observers, support grew during the week for moving to negotiations on the basis of the rolling text, with more than 70 states said to support that step by the end of the session, though some participants warned that attempts to bridge differences risked blurring the group's core purpose. The International Committee of the Red Cross argued that the text should not only restate existing international humanitarian law, but also clarify how those rules apply to autonomous weapons and set out additional measures tailored to the specific challenges such systems raise. Stop Killer Robots likewise emphasized the need to preserve meaningful human judgment and control over increasingly autonomous systems. During the discussions, the U.S. delegation opposed the term "human control" and reportedly proposed the alternative phrase "good faith human judgment and care". Other delegations rejected that wording as too weak, while many states continued to insist that meaningful human control over weapon systems remained essential.
Read more →
Top 10 AI Blog Writers Compared (2026)

Comparing the best AI blog writer? An AI blog writer is software that uses machine learning to help you get more done — it lowers the barrier so anyone can produce professional output. Privacy matters too: check whether your data trains the model and whether a no-log or enterprise tier is available. Whether you are a beginner or a pro, the right AI blog writer slots into your workflow and pays for itself fast. We tested the leading options and ranked them by quality, value, and ease of use.
Read more →
Human-readable medium and data

In computing, a human-readable medium or human-readable format is any encoding of data or information that can be naturally read by humans, resulting in human-readable data. It is often encoded as ASCII or Unicode text, rather than as binary data. In most contexts, the alternative to a human-readable representation is a machine-readable format or medium of data primarily designed for reading by electronic, mechanical or optical devices, or computers. For example, Universal Product Code (UPC) barcodes are very difficult to read for humans, but very effective and reliable with the proper equipment, whereas the strings of numerals that commonly accompany the label are the human-readable form of the barcode information. Since any type of data encoding can be parsed by a suitably programmed computer, the decision to use binary encoding rather than text encoding is usually made to conserve storage space. Encoding data in a binary format typically requires fewer bytes of storage and increases efficiency of access (input and output) by eliminating format parsing or conversion. With the advent of standardized, highly structured markup languages, such as Extensible Markup Language (XML), the decreasing costs of data storage, and faster and cheaper data communication networks, compromises between human-readability and machine-readability are now more common-place than they were in the past. This has led to humane markup languages and modern configuration file formats that are far easier for humans to read. In addition, these structured representations can be compressed very effectively for transmission or storage. Human-readable protocols greatly reduce the cost of debugging. Various organizations have standardized the definition of human-readable and machine-readable data and how they are applied in their respective fields of application, e.g., the Universal Postal Union. Often the term human-readable is also used to describe shorter names or strings, that are easier to comprehend or to remember than long, complex syntax notations, such as some Uniform Resource Locator strings. Occasionally "human-readable" is used to describe ways of encoding an arbitrary integer into a long series of English words. Compared to decimal or other compact binary-to-text encoding systems, English words are easier for humans to read, remember, and type in.
Read more →
Bruno Zamborlin

Bruno Zamborlin (born 1983 in Vicenza) is an AI researcher, entrepreneur and artist based in London, working in the field of human-computer interaction. His work focuses on converting physical objects into touch-sensitive, interactive surfaces using vibration sensors and artificial intelligence. In 2013, he founded Mogees Limited a start-up to transform everyday objects into musical instruments and games using a vibration sensor and a mobile phone. With HyperSurfaces, he converts physical surfaces of any material, shape and form into data-enabled-interactive surfaces using a vibration sensor and a coin-sized chipset. As an artist, he has created art installations around the world, with his most recent work comprising a unique series of "sound furnitures" that was showcased at the Italian Pavilion of the Venice Biennale 2023. He regularly performed with UK-based electronic music duo Plaid (Warp Records). He is also honorary visiting research fellow at Goldsmiths, University of London. == Early life and education == From 2008-2011, Zamborlin worked at the IRCAM (Institute for Research and Coordination Acoustic Musical) – Centre Pompidou as a member of the Sound Music Movement Interaction team. Under the supervision of Frederic Bevilacqua, he started experimenting with the use of artificial intelligence and human movements, and contributed to the creation of Gesture Follower, a software used to analyse body movements of performers and dancers through motion sensors in order to control sound and visual media in real-time, slowing down or speeding up their reproduction based on the speed the gestures are performed. He has lived in London since 2011, where he developed a joint PhD between Goldsmiths, University of London and IRCAM - Centre Pompidou/Pierre and Marie Curie University Paris in AI, focussing on the concept of Interactive Machine Learning applied to digital musical instruments and performing arts. == Career == Zamborlin founded Mogees Limited in 2013 in London, with IRCAM being amongst the early partners. Mogees transform physical objects into musical instruments and games using a vibration sensor and a series of apps for smartphones and desktop. After a campaign on Kickstarter in 2014, Mogees was used both by common users and artists such as Rodrigo y Gabriela, Jean-Michel Jarre and Plaid. The algorithms implemented in these apps employ a special version of physical modelling sound synthesis, where the vibration produced by users when interacting with the physical object are used as exciter for a digital resonator which runs in the app. The result is a hybrid, half acoustic and half digital sound which is a function of both software and acoustic properties of the physical object the users decide to play. In 2017, Zamborlin founded HyperSurfaces together with computational artist Parag K Mital. to merge "the physical and the digital worlds". HyperSurfaces technology converts any surface made of any material, shape and size into data-enabled interactive objects, employing a vibration sensor and proprietary AI algorithms running on a coin-sized chipset. The vibrations generated by people's interactions on the surface are converted into an electric signal by a piezoelectric sensor and analysed in realtime by AI algorithms that run on the chipset. Anytime the AI recognises in the vibration signal one of the events that have been predefined by the user beforehand, a corresponding notification message is generated in realtime and sent to some application. The technology can be applied to anything ranging from button-less human-computer interaction applications for automotive and smart home to the Internet of things. Because the AI algorithms employed by HyperSurfaces run locally on a chipset, without the need to access cloud-based services, they are considered to be part of the field of edge computing. Also, because the AI can be trained beforehand to recognise the events its users are interested in, HyperSurfaces algorithms belong to the field of supervised machine learning. == Selected awards == IRISA Prix Jeune Chercheur, 13 October 2012 NeMoDe, New Economic Models in the Digital Economy, 25 October 2012 == Patents and academic publications == United States pending US10817798B2, Bruno Zamborlin & Carmine Emanuele Cella, "Method to recognize a gesture and corresponding device", published 27 April 2016, assigned to Mogees Limited GB Pending WO/2019/086862, Bruno Zamborlin; Conor Barry & Alessandro Saccoia et al., "A user interface for vehicles", published 9 May 2019, assigned to Mogees Limited GB Pending WO/2019/086863, Bruno Zamborlin; Conor Barry & Alessandro Saccoia et al., "Trigger for game events", published 9 May 2019, assigned to Mogees Limited Bevilacqua, Frédéric; Zamborlin, Bruno; Sypniewski, Anthony; Schnell, Norbert; Guédy, Fabrice; Rasamimanana, Nicolas (2010). "Continuous Realtime Gesture Following and Recognition". Gesture in Embodied Communication and Human-Computer Interaction. Lecture Notes in Computer Science. Vol. 5934. pp. 73–84. doi:10.1007/978-3-642-12553-9_7. ISBN 978-3-642-12552-2. S2CID 16251822. Retrieved 17 January 2021. Rasamimanana, Nicolas; Bevilacqua, Frédéric; Schnell, Norbert; Guédy, Fabrice; Flety, Emmanuel; Maestracci, Come; Zamborlin, Bruno (January 2010). "Modular musical objects towards embodied control of digital music". Proceedings of the fifth international conference on Tangible, embedded, and embodied interaction. Tei '11. pp. 9–12. doi:10.1145/1935701.1935704. ISBN 9781450304788. S2CID 10782645. Retrieved 17 January 2021. Bevilacqua, Frédéric; Schnell, Norbert; Rasamimanana, Nicolas; Zamborlin, Bruno; Guedy, Fabrice (2011). "Online Gesture Analysis and Control of Audio Processing". Musical Robots and Interactive Multimodal Systems. Springer Tracts in Advanced Robotics. Vol. 74. pp. 127–142. doi:10.1007/978-3-642-22291-7_8. ISBN 978-3-642-22290-0. Retrieved 17 January 2021. Zamborlin, Bruno; Bevilacqua, Frédéric; Gillies, Marco; D'Inverno, Mark (15 January 2014). "Fluid gesture interaction design: Applications of continuous recognition for the design of modern gestural interfaces". ACM Transactions on Interactive Intelligent Systems. 3 (4): 22:1–22:30. doi:10.1145/2543921. S2CID 7887245. Retrieved 17 January 2021. Leslie, Grace; Zamborlin, Bruno; Schnell, Norbert; Jodlowski, Pierre (15 June 2010). "A Collaborative, Interactive Sound Installation". Proceedings of the International Computer Music Conference. Retrieved 17 January 2021. Kimura, Mari; Rasamimanana, Nicolas; Bevilacqua, Frédéric; Zamborlin, Bruno; Schnell, Bruno; Flety, Emmanuel (2012). "Extracting Human Expression For Interactive Composition with the Augmented Violin". International Conference on New Interfaces for Musical Expression. Retrieved 17 January 2021. Ferretti, Stefano; Roccetti, Marco; Zamborlin, Bruno (13 January 2009). "On SPAWC: Discussion on a Musical Signal Parser and Well-Formed Composer". 2009 6th IEEE Consumer Communications and Networking Conference. pp. 1–5. doi:10.1109/CCNC.2009.4784966. ISBN 978-1-4244-2308-8. S2CID 14213587. Zamborlin, Bruno; Partesana, Giorgio; Liuni, Marco (15 May 2011). "(LAND)MOVES". Conference on New Interfaces for Musical Expression, NIME: 537–538. Retrieved 17 January 2021.
Read more →
Embodied cognitive science

Embodied cognitive science is an interdisciplinary field of research, the aim of which is to explain the mechanisms underlying intelligent behavior. It comprises three main methodologies: the modeling of psychological and biological systems in a holistic manner that considers the mind and body as a single entity; the formation of a common set of general principles of intelligent behavior; and the experimental use of robotic agents in controlled environments. == Contributors == Embodied cognitive science borrows heavily from embodied philosophy and the related research fields of cognitive science, psychology, neuroscience and artificial intelligence. Contributors to the field include: From the perspective of neuroscience, Gerald Edelman of the Neurosciences Institute at La Jolla, Francisco Varela of CNRS in France, and J. A. Scott Kelso of Florida Atlantic University From the perspective of psychology, Lawrence Barsalou, Michael Turvey, Vittorio Guidano and Eleanor Rosch From the perspective of linguistics, Gilles Fauconnier, George Lakoff, Mark Johnson, Leonard Talmy and Mark Turner From the perspective of language acquisition, Eric Lenneberg and Philip Rubin at Haskins Laboratories From the perspective of anthropology, Edwin Hutchins, Bradd Shore, James Wertsch and Merlin Donald. From the perspective of autonomous agent design, early work is sometimes attributed to Rodney Brooks or Valentino Braitenberg From the perspective of artificial intelligence, Understanding Intelligence by Rolf Pfeifer and Christian Scheier or How the Body Shapes the Way We Think, by Rolf Pfeifer and Josh C. Bongard From the perspective of philosophy, Andy Clark, Dan Zahavi, Shaun Gallagher, and Evan Thompson In 1950, Alan Turing proposed that a machine may need a human-like body to think and speak: It can also be maintained that it is best to provide the machine with the best sense organs that money can buy, and then teach it to understand and speak English. That process could follow the normal teaching of a child. Things would be pointed out and named, etc. Again, I do not know what the right answer is, but I think both approaches should be tried. == Traditional cognitive theory == Embodied cognitive science is an alternative theory to cognition in which it minimizes appeals to computational theory of mind in favor of greater emphasis on how an organism's body determines how and what it thinks. Traditional cognitive theory is based mainly around symbol manipulation, in which certain inputs are fed into a processing unit that produces an output. These inputs follow certain rules of syntax, from which the processing unit finds semantic meaning. Thus, an appropriate output is produced. For example, a human's sensory organs are its input devices, and the stimuli obtained from the external environment are fed into the nervous system which serves as the processing unit. From here, the nervous system is able to read the sensory information because it follows a syntactic structure, thus an output is created. This output then creates bodily motions and brings forth behavior and cognition. Of particular note is that cognition is sealed away in the brain, meaning that mental cognition is cut off from the external world and is only possible by the input of sensory information. == The embodied cognitive approach == Embodied cognitive science differs from the traditionalist approach in that it denies the input-output system. This is chiefly due to the problems presented by the Homunculus argument, which concluded that semantic meaning could not be derived from symbols without some kind of inner interpretation. If some little man in a person's head interpreted incoming symbols, then who would interpret the little man's inputs? Because of the specter of an infinite regress, the traditionalist model began to seem less plausible. Thus, embodied cognitive science aims to avoid this problem by defining cognition in three ways. === Physical attributes of the body === The first aspect of embodied cognition examines the role of the physical body, particularly how its properties affect its ability to think. This part attempts to overcome the symbol manipulation component that is a feature of the traditionalist model. Depth perception, for instance, can be better explained under the embodied approach due to the sheer complexity of the action. Depth perception requires that the brain detect the disparate retinal images obtained by the distance of the two eyes. In addition, body and head cues complicate this further. When the head is turned in a given direction, objects in the foreground will appear to move against objects in the background. From this, it is said that some kind of visual processing is occurring without the need of any kind of symbol manipulation. This is because the objects appearing to move the foreground are simply appearing to move. This observation concludes then that depth can be perceived with no intermediate symbol manipulation necessary. A more poignant example exists through examining auditory perception. Generally speaking the greater the distance between the ears, the greater the possible auditory acuity. Also relevant is the amount of density in between the ears, for the strength of the frequency wave alters as it passes through a given medium. The brain's auditory system takes these factors into account as it process information, but again without any need for a symbolic manipulation system. This is because the distance between the ears for example does not need symbols to represent it. The distance itself creates the necessary opportunity for greater auditory acuity. The amount of density between the ears is similar, in that it is the actual amount itself that simply forms the opportunity for frequency alteration. Thus under consideration of the physical properties of the body, a symbolic system is unnecessary and an unhelpful metaphor. === The body's role in the cognitive process === The second aspect draws heavily from George Lakoff's and Mark Johnson's work on concepts. They argued that humans use metaphors whenever possible to better explain their external world. Humans also have a basic stock of concepts in which other concepts can be derived from. These basic concepts include spatial orientations such as up, down, front, and back. Humans can understand what these concepts mean because they can directly experience them from their own bodies. For example, because human movement revolves around standing erect and moving the body in an up-down motion, humans innately have these concepts of up and down. Lakoff and Johnson contend this is similar with other spatial orientations such as front and back too. As mentioned earlier, these basic stocks of spatial concepts are the basis in which other concepts are constructed. Happy and sad for instance are seen now as being up or down respectively. When someone says they are feeling down, what they are really saying is that they feel sad for example. Thus the point here is that true understanding of these concepts is contingent on whether one can have an understanding of the human body. So the argument goes that if one lacked a human body, they could not possibly know what up or down could mean, or how it could relate to emotional states. [I]magine a spherical being living outside of any gravitational field, with no knowledge or imagination of any other kind of experience. What could UP possibly mean to such a being? While this does not mean that such beings would be incapable of expressing emotions in other words, it does mean that they would express emotions differently from humans. Human concepts of happiness and sadness would be different because human would have different bodies. So then an organism's body directly affects how it can think, because it uses metaphors related to its body as the basis of concepts. === Interaction of local environment === A third component of the embodied approach looks at how agents use their immediate environment in cognitive processing. Meaning, the local environment is seen as an actual extension of the body's cognitive process. The example of a personal digital assistant (PDA) is used to better imagine this. Echoing functionalism (philosophy of mind), this point claims that mental states are individuated by their role in a much larger system. So under this premise, the information on a PDA is similar to the information stored in the brain. So then if one thinks information in the brain constitutes mental states, then it must follow that information in the PDA is a cognitive state too. Consider also the role of pen and paper in a complex multiplication problem. The pen and paper are so involved in the cognitive process of solving the problem that it seems ridiculous to say they are somehow different from the process, in very much the same way the PDA is used for information like the brain. Another example examines how humans control and manipulate their environment
Read more →
Zoubin Ghahramani

Zoubin Ghahramani FRS (Persian: زوبین قهرمانی; born 8 February 1970) is a British-Iranian machine learning and AI researcher, Vice President of Research at Google DeepMind and Professor of Information Engineering at the University of Cambridge. He has been a Fellow of St John's College, Cambridge since 2009. He held appointments at University College London from 1998 to 2005 and was Associate Research Professor in the Machine Learning Department at Carnegie Mellon University from 2003 to 2012. He was the Chief Scientist of Uber from 2016 until 2020. He joined Google Brain in 2020 as Senior Research Director, becoming a VP of Research in 2021, and heading Google Brain until its merger with DeepMind to form Google DeepMind. He was a founding Cambridge Liaison Director of the Alan Turing Institute and also founding Deputy Director of the Leverhulme Centre for the Future of Intelligence. Ghahramani contributed to the Royal Society's Machine Learning Report in 2017 and led the UK's Future of Compute Review, in 2023. == Education == Ghahramani was educated at the American School of Madrid in Spain and the University of Pennsylvania where he was awarded a dual degree in Cognitive Science and Computer Science in 1990. He obtained his Ph.D. in Cognitive Neuroscience from the Department of Brain and Cognitive Sciences at the Massachusetts Institute of Technology, supervised by Michael I. Jordan and Tomaso Poggio. == Research and career == Following his Ph.D., Ghahramani moved to the University of Toronto in 1995 as a Postdoctoral Fellow in the Artificial Intelligence Lab, working with Geoffrey Hinton. From 1998 to 2005, he was a member of the faculty at the Gatsby Computational Neuroscience Unit, University College London. Ghahramani has made significant contributions in the areas of Bayesian machine learning (particularly variational methods for approximate Bayesian inference), as well as graphical models and computational neuroscience. His current research focuses on nonparametric Bayesian modelling and statistical machine learning. He has also worked on artificial intelligence, information retrieval, bioinformatics and statistics which provide the mathematical foundations for handling uncertainty, making decisions, and designing learning systems. He has published over 300 papers, receiving over 100,000 citations (an h-index of 132). He co-founded Geometric Intelligence in 2014, with Gary Marcus, Doug Bemis, and Ken Stanley, which was acquired by Uber in 2016. Afterwards, he transferred to Uber's AI Labs in 2016, and later became VP of AI and Chief Scientist at Uber. In 2020 he joined Google and became VP of Research and head of Google Brain in 2021 until its merger with DeepMind in April 2023. == Awards and honors == Ghahramani was elected Fellow of the Royal Society (FRS) in 2015. His certificate of election reads: Zoubin Ghahramani is a world leader in the field of machine learning, significantly advancing the state-of-the-art in algorithms that can learn from data. He is known in particular for fundamental contributions to probabilistic modeling and Bayesian nonparametric approaches to machine learning systems, and to the development of approximate variational inference algorithms for scalable learning. He is one of the pioneers of semi-supervised learning methods, active learning algorithms, and sparse Gaussian processes. His development of novel infinite dimensional nonparametric models, such as the infinite latent feature model, has been highly influential.He was awarded the Royal Society Milner Award in 2021 in recognition of 'his fundamental contributions to probabilistic machine learning'.
Read more →
Wang-Chiew Tan

Wang-Chiew Tan is a Singaporean computer scientist specializing in data management and natural language processing. Her work in data management includes data provenance (or data lineage) and data integration. She is currently a Research Scientist at Facebook AI, and was previously the Director of Research at Megagon Labs in Mountain View, California. At Megagon Labs, Tan was the lead researcher on a study with the University of Tokyo that concluded that the company of other people is more effective than pets at making people happy. == Education and career == Tan earned her bachelor's degree in computer science (first-class) at the National University of Singapore, and completed her Ph.D. at the University of Pennsylvania. Her 2002 dissertation, Data Annotations, Provenance, and Archiving, was jointly supervised by Peter Buneman and Sanjeev Khanna. Before working at Megagon, she has been a professor of computer science at the University of California, Santa Cruz beginning in 2002, and, from 2010 to 2012, was on leave from Santa Cruz as a researcher at IBM Research - Almaden. == Recognition == Tan was named a Fellow of the Association for Computing Machinery in 2015 "for contributions to data provenance and to the foundations of information integration".
Read more →
Markov chain Monte Carlo

In statistics, Markov chain Monte Carlo (MCMC) is a class of algorithms used to draw samples from a probability distribution. Given a probability distribution, one can construct a Markov chain whose elements' distribution approximates it, i.e. the Markov chain's equilibrium distribution matches the target distribution. The more steps that are included, the more closely the distribution of the sample matches the actual desired distribution. Markov chain Monte Carlo methods are used to study probability distributions that are too complex or too high dimensional to study with analytic techniques alone. Various algorithms exist for constructing such Markov chains, including the Metropolis–Hastings algorithm. == General explanation == Markov chain Monte Carlo methods create samples from a continuous random variable, with probability density proportional to a known function. These samples can be used to evaluate an integral over that variable, as its expected value or variance. Practically, an ensemble of chains is generally developed, starting from a set of points arbitrarily chosen and sufficiently distant from each other. These chains are stochastic processes of "walkers" which move around randomly according to an algorithm that looks for places with a reasonably high contribution to the integral to move into next, assigning them higher probabilities. Random walk Monte Carlo methods are a kind of random simulation or Monte Carlo method. However, whereas the random samples of the integrand used in a conventional Monte Carlo integration are statistically independent, those used in MCMC are autocorrelated. Correlations of samples introduces the need to use the Markov chain central limit theorem when estimating the error of mean values. These algorithms create Markov chains such that they have an equilibrium distribution which is proportional to the function given. == History == The development of MCMC methods is deeply rooted in the early exploration of Monte Carlo (MC) techniques in the mid-20th century, particularly in physics. These developments were marked by the Metropolis algorithm proposed by Nicholas Metropolis, Arianna W. Rosenbluth, Marshall Rosenbluth, Augusta H. Teller, and Edward Teller in 1953, which was designed to tackle high-dimensional integration problems using early computers. Then in 1970, W. K. Hastings generalized this algorithm and inadvertently introduced the component-wise updating idea, later known as Gibbs sampling. Simultaneously, the theoretical foundations for Gibbs sampling were being developed, such as the Hammersley–Clifford theorem from Julian Besag's 1974 paper. Although the seeds of MCMC were sown earlier, including the formal naming of Gibbs sampling in image processing by Stuart Geman and Donald Geman (1984) and the data augmentation method by Martin A. Tanner and Wing Hung Wong (1987), its "revolution" in mainstream statistics largely followed demonstrations of the universality and ease of implementation of sampling methods (especially Gibbs sampling) for complex statistical (particularly Bayesian) problems, spurred by increasing computational power and software like BUGS. This transformation was accompanied by significant theoretical advancements, such as Luke Tierney's (1994) rigorous treatment of MCMC convergence, and Jun S. Liu, Wong, and Augustine Kong's (1994, 1995) analysis of Gibbs sampler structure. Subsequent developments further expanded the MCMC toolkit, including particle filters (Sequential Monte Carlo) for sequential problems, Perfect sampling aiming for exact simulation (Jim Propp and David B. Wilson, 1996), RJMCMC (Peter J. Green, 1995) for handling variable-dimension models, and deeper investigations into convergence diagnostics and the central limit theorem. Overall, the evolution of MCMC represents a paradigm shift in statistical computation, enabling the analysis of numerous previously intractable complex models and continually expanding the scope and impact of statistics. == Mathematical setting == Suppose (Xn) is a Markov Chain in the general state space X {\displaystyle {\mathcal {X}}} with specific properties. We are interested in the limiting behavior of the partial sums: S n ( h ) = 1 n ∑ i = 1 n h ( X i ) {\displaystyle S_{n}(h)={\dfrac {1}{n}}\sum _{i=1}^{n}h(X_{i})} as n goes to infinity. Particularly, we hope to establish the Law of Large Numbers and the Central Limit Theorem for MCMC. In the following, we state some definitions and theorems necessary for the important convergence results. In short, we need the existence of invariant measure and Harris recurrent to establish the Law of Large Numbers of MCMC (Ergodic Theorem). And we need aperiodicity, irreducibility and extra conditions such as reversibility to ensure the Central Limit Theorem holds in MCMC. === Irreducibility and aperiodicity === Recall that in the discrete setting, a Markov chain is said to be irreducible if it is possible to reach any state from any other state in a finite number of steps with positive probability. However, in the continuous setting, point-to-point transitions have zero probability. In this case, φ-irreducibility generalizes irreducibility by using a reference measure φ on the measurable space ( X , B ( X ) ) {\displaystyle ({\mathcal {X}},{\mathcal {B}}({\mathcal {X}}))} . Definition (φ-irreducibility) Given a measure φ {\displaystyle \varphi } defined on ( X , B ( X ) ) {\displaystyle ({\mathcal {X}},{\mathcal {B}}({\mathcal {X}}))} , the Markov chain ( X n ) {\displaystyle (X_{n})} with transition kernel K ( x , y ) {\displaystyle K(x,y)} is φ-irreducible if, for every A ∈ B ( X ) {\displaystyle A\in {\mathcal {B}}({\mathcal {X}})} with φ ( A ) > 0 {\displaystyle \varphi (A)>0} , there exists n {\displaystyle n} such that K n ( x , A ) > 0 {\displaystyle K^{n}(x,A)>0} for all x ∈ X {\displaystyle x\in {\mathcal {X}}} (Equivalently, P x ( τ A < ∞ ) > 0 {\displaystyle P_{x}(\tau _{A}<\infty )>0} , here τ A = inf { n ≥ 1 ; X n ∈ A } {\displaystyle \tau _{A}=\inf\{n\geq 1;X_{n}\in A\}} is the first n {\displaystyle n} for which the chain enters the set A {\displaystyle A} ). This is a more general definition for irreducibility of a Markov chain in non-discrete state space. In the discrete case, an irreducible Markov chain is said to be aperiodic if it has period 1. Formally, the period of a state ω ∈ X {\displaystyle \omega \in {\mathcal {X}}} is defined as: d ( ω ) := g c d { m ≥ 1 ; K m ( ω , ω ) > 0 } {\displaystyle d(\omega ):=\mathrm {gcd} \{m\geq 1\,;\,K^{m}(\omega ,\omega )>0\}} For the general (non-discrete) case, we define aperiodicity in terms of small sets: Definition (Cycle length and small sets) A φ-irreducible Markov chain ( X n ) {\displaystyle (X_{n})} has a cycle of length d if there exists a small set C {\displaystyle C} , an associated integer M {\displaystyle M} , and a probability distribution ν M {\displaystyle \nu _{M}} such that d is the greatest common divisor of: { m ≥ 1 ; ∃ δ m > 0 such that C is small for ν m ≥ δ m ν M } . {\displaystyle \{m\geq 1\,;\,\exists \,\delta _{m}>0{\text{ such that }}C{\text{ is small for }}\nu _{m}\geq \delta _{m}\nu _{M}\}.} A set C {\displaystyle C} is called small if there exists m ∈ N ∗ {\displaystyle m\in \mathbb {N} ^{}} and a nonzero measure ν m {\displaystyle \nu _{m}} such that: K m ( x , A ) ≥ ν m ( A ) , ∀ x ∈ C , ∀ A ∈ B ( X ) . {\displaystyle K^{m}(x,A)\geq \nu _{m}(A),\quad \forall x\in C,\,\forall A\in {\mathcal {B}}({\mathcal {X}}).} === Harris recurrent === Definition (Harris recurrence) A set A {\displaystyle A} is Harris recurrent if P x ( η A = ∞ ) = 1 {\displaystyle P_{x}(\eta _{A}=\infty )=1} for all x ∈ A {\displaystyle x\in A} , where η A = ∑ n = 1 ∞ I A ( X n ) {\displaystyle \eta _{A}=\sum _{n=1}^{\infty }\mathbb {I} _{A}(X_{n})} is the number of visits of the chain ( X n ) {\displaystyle (X_{n})} to the set A {\displaystyle A} . The chain ( X n ) {\displaystyle (X_{n})} is said to be Harris recurrent if there exists a measure ψ {\displaystyle \psi } such that the chain is ψ {\displaystyle \psi } -irreducible and every measurable set A {\displaystyle A} with ψ ( A ) > 0 {\displaystyle \psi (A)>0} is Harris recurrent. A useful criterion for verifying Harris recurrence is the following: Proposition If for every A ∈ B ( X ) {\displaystyle A\in {\mathcal {B}}({\mathcal {X}})} , we have P x ( τ A < ∞ ) = 1 {\displaystyle P_{x}(\tau _{A}<\infty )=1} for every x ∈ A {\displaystyle x\in A} , then P x ( η A = ∞ ) = 1 {\displaystyle P_{x}(\eta _{A}=\infty )=1} for all x ∈ X {\displaystyle x\in {\mathcal {X}}} , and the chain ( X n ) {\displaystyle (X_{n})} is Harris recurrent. This definition is only needed when the state space X {\displaystyle {\mathcal {X}}} is uncountable. In the countable case, recurrence corresponds to E x [ η x ] = ∞ {\displaystyle \mathbb {E} _{x}[\eta _{x}]=\infty } , which is equivalent to P x ( τ x < ∞ ) = 1 {\displaystyle P_{x}(\tau _{x}<\infty )=1} for all x ∈ X {\displaystyle x\i
Read more →
Microsoft Azure

Microsoft Azure, sometimes stylized Azure, and formerly Windows Azure, is the cloud computing platform developed by Microsoft. It offers management, access and development of applications and services to individuals, companies, and governments through its global infrastructure. Microsoft Azure supports many programming languages, tools, and frameworks, including Microsoft-specific and third-party software and systems. Azure was first introduced at the Professional Developers Conference (PDC) in October 2008 under the codename "Project Red Dog". It was officially launched as Windows Azure in February 2010 and later renamed to Microsoft Azure on March 25, 2014. == Services == Microsoft Azure uses large-scale virtualization at Microsoft data centers worldwide and offers more than 600 services. Microsoft Azure offers a service level agreement (SLA) that guarantees 99.9% availability for applications and data hosted on its platform, subject to specific terms and conditions outlined in the SLA documentation. === Computer services === Virtual machines, infrastructure as a service (IaaS), allowing users to launch general-purpose Microsoft Windows and Linux virtual machines, software as a service (SaaS), as well as preconfigured machine images for popular software packages. Starting in 2022, these virtual machines are now powered by Ampere Cloud-native processors. Most users run Linux on Azure, some of the many Linux distributions offered, including Microsoft's own Linux-based Azure Sphere. App services, platform as a service (PaaS) environment, letting developers easily publish and manage websites. Azure Web Sites allows developers to build sites using ASP.NET, PHP, Node.js, Java, or Python, which can be deployed using FTP, Git, Mercurial, Azure DevOps, or uploaded through the user portal. This feature was announced in preview form in June 2012 at the Meet Microsoft Azure event. Customers can create websites in PHP, ASP.NET, Node.js, or Python, or select from several open-source applications from a gallery to deploy. This comprises one aspect of the platform as a service (PaaS) offerings for the Microsoft Azure Platform. It was renamed Web Apps in April 2015. Web Jobs are applications that can be deployed to an App Service environment to implement background processing that can be invoked on a schedule, on-demand, or run continuously. The Blob, Table, and Queue services can be used to communicate between Web Apps and Web Jobs and to provide state. Azure Kubernetes Service (AKS) provides the capability to deploy production-ready Kubernetes clusters in Azure. In July 2023, watermarking support on Azure Virtual Desktop was announced as an optional feature of Screen Capture to provide additional security against data leakage. === Identity === Entra ID connect is used to synchronize on-premises directories and enable SSO (Single Sign On). Entra ID B2C allows the use of consumer identity and access management in the cloud. Entra Domain Services is used to join Azure virtual machines to a domain without domain controllers. Azure information protection can be used to protect sensitive information. Entra ID External Identities is a set of capabilities that allow organizations to collaborate with external users, including customers and partners. On July 11, 2023, Microsoft announced the renaming of Azure AD to Microsoft Entra ID. The name change took place four days later. === Mobile services === Mobile Engagement collects real-time analytics that highlight users' behavior. It also provides push notifications to mobile devices. HockeyApp can be used to develop, distribute, and beta-test mobile apps. === Storage services === Storage Services provides REST and SDK APIs for storing and accessing data on the cloud. Table Service lets programs store structured text in partitioned collections of entities that are accessed by the partition key and primary key. Azure Table Service is a NoSQL non-relational database. Blob Service allows programs to store unstructured text and binary data as object storage blobs that can be accessed by an HTTP(S) path. Blob service also provides security mechanisms to control access to data. Queue Service lets programs communicate asynchronously by message using queues. File Service allows storing and access of data on the cloud using the REST APIs or the SMB protocol. === Communication services === Azure Communication Services offers an SDK for creating web and mobile communications applications that include SMS, video calling, VOIP and PSTN calling, and web-based chat. === Data management === Azure Data Explorer provides big data analytics and data-exploration capabilities. Azure Search provides text search and a subset of OData's structured filters using REST or SDK APIs. Cosmos DB is a NoSQL database service that implements a subset of the SQL SELECT statement on JSON documents. Azure Cache for Redis is a managed implementation of Redis. StorSimple manages storage tasks between on-premises devices and cloud storage. Azure SQL Database works to create, scale, and extend applications into the cloud using Microsoft SQL Server technology. It also integrates with Active Directory, Microsoft System Center, and Hadoop. Azure Synapse Analytics is a fully managed cloud data warehouse. Azure Data Factory is a data integration service that allows creation of data-driven workflows in the cloud for orchestrating and automating data movement and data transformation. Azure Data Lake is a scalable data storage and analytic service for big data analytics workloads that require developers to run massively parallel queries. Azure HDInsight is a big data-relevant service that deploys Hortonworks Hadoop on Microsoft Azure and supports the creation of Hadoop clusters using Linux with Ubuntu. Azure Stream Analytics is a Serverless scalable event-processing engine that enables users to develop and run real-time analytics on multiple streams of data from sources such as devices, sensors, websites, social media, and other applications. === Messaging === The Microsoft Azure Service Bus allows applications running on Azure premises or off-premises devices to communicate with Azure. This helps to build scalable and reliable applications in a service-oriented architecture (SOA). The Azure service bus supports four different types of communication mechanisms: Event Hubs, which provides event and telemetry ingress to the cloud at a massive scale, with low latency and high reliability. For example, an event hub can be used to track data from cell phones such as coordinating with a GPS in real time. Queues, which allows one-directional communication. A sender application would send the message to the service bus queue and a receiver would read from the queue. Though there can be multiple readers for the queue, only one would process a single message. Topics, which provides one-directional communication using a subscriber pattern. It is similar to a queue; however, each subscriber will receive a copy of the message sent to a Topic. Optionally, the subscriber can filter out messages based on specific criteria defined by the subscriber. Relays, which provides bi-directional communication. Unlike queues and topics, a relay does not store in-flight messages in its memory; instead, it just passes them on to the destination application. === Media services === A PaaS offering that can be used for encoding, content protection, streaming, or analytics. === CDN === Azure has a worldwide content delivery network (CDN) designed to efficiently deliver audio, video, applications, images, and other static files. It improves the performance of websites by caching static files closer to users, based on their geographic location. Users can manage the network using a REST-based HTTP API. Azure has 118 point-of-presence locations across 100 cities worldwide (also known as Edge locations) as of January 2023. === Developer === Application Insights Azure DevOps === Management === With Azure Automation, users can easily automate repetitive and time-consuming tasks, often prone to cloud or enterprise setting errors. They can accomplish it using runbooks or desired state configurations for process automation. Microsoft SMA === Azure AI === Microsoft Azure Machine Learning (Azure ML) provides tools and frameworks for developers to create their own machine learning and artificial intelligence (AI) services. Azure AI Services by Microsoft comprises prebuilt APIs, SDKs, and services developers can customize. These services encompass perceptual and cognitive intelligence features such as speech recognition, speaker recognition, neural speech synthesis, face recognition, computer vision, OCR/form understanding, natural language processing, machine translation, and business decision services. Many AI characteristics in Microsoft's products and services, namely Bing, Office, Teams, Xbox, and Windows, are driven by Azure AI Services. Microsoft Foundry (formerly known as Azure AI Studio)
Read more →
Semiautomaton

In mathematics and theoretical computer science, a semiautomaton is a deterministic finite automaton having inputs but no output. It consists of a set Q of states, a set Σ called the input alphabet, and a function T: Q × Σ → Q called the transition function. Associated with any semiautomaton is a monoid called the characteristic monoid, input monoid, transition monoid or transition system of the semiautomaton, which acts on the set of states Q. This may be viewed either as an action of the free monoid of strings in the input alphabet Σ, or as the induced transformation semigroup of Q. In older books like Clifford and Preston (1967) semigroup actions are called "operands". In category theory, semiautomata essentially are functors. == Transformation semigroups and monoid acts == A transformation semigroup or transformation monoid is a pair ( M , Q ) {\displaystyle (M,Q)} consisting of a set Q (often called the "set of states") and a semigroup or monoid M of functions, or "transformations", mapping Q to itself. They are functions in the sense that every element m of M is a map m : Q → Q {\displaystyle m\colon Q\to Q} . If s and t are two functions of the transformation semigroup, their semigroup product is defined as their function composition ( s t ) ( q ) = ( s ∘ t ) ( q ) = s ( t ( q ) ) {\displaystyle (st)(q)=(s\circ t)(q)=s(t(q))} . Some authors regard "semigroup" and "monoid" as synonyms. Here a semigroup need not have an identity element; a monoid is a semigroup with an identity element (also called "unit"). Since the notion of functions acting on a set always includes the notion of an identity function, which when applied to the set does nothing, a transformation semigroup can be made into a monoid by adding the identity function. === M-acts === Let M be a monoid and Q be a non-empty set. If there exists a multiplicative operation μ : Q × M → Q {\displaystyle \mu \colon Q\times M\to Q} ( q , m ) ↦ q m = μ ( q , m ) {\displaystyle (q,m)\mapsto qm=\mu (q,m)} which satisfies the properties q 1 = q {\displaystyle q1=q} for 1 the unit of the monoid, and q ( s t ) = ( q s ) t {\displaystyle q(st)=(qs)t} for all q ∈ Q {\displaystyle q\in Q} and s , t ∈ M {\displaystyle s,t\in M} , then the triple ( Q , M , μ ) {\displaystyle (Q,M,\mu )} is called a right M-act or simply a right act. In long-hand, μ {\displaystyle \mu } is the right multiplication of elements of Q by elements of M. The right act is often written as Q M {\displaystyle Q_{M}} . A left act is defined similarly, with μ : M × Q → Q {\displaystyle \mu \colon M\times Q\to Q} ( m , q ) ↦ m q = μ ( m , q ) {\displaystyle (m,q)\mapsto mq=\mu (m,q)} and is often denoted as M Q {\displaystyle \,_{M}Q} . An M-act is closely related to a transformation monoid. However the elements of M need not be functions per se, they are just elements of some monoid. Therefore, one must demand that the action of μ {\displaystyle \mu } be consistent with multiplication in the monoid (i.e. μ ( q , s t ) = μ ( μ ( q , s ) , t ) {\displaystyle \mu (q,st)=\mu (\mu (q,s),t)} ), as, in general, this might not hold for some arbitrary μ {\displaystyle \mu } , in the way that it does for function composition. Once one makes this demand, it is completely safe to drop all parenthesis, as the monoid product and the action of the monoid on the set are completely associative. In particular, this allows elements of the monoid to be represented as strings of letters, in the computer-science sense of the word "string". This abstraction then allows one to talk about string operations in general, and eventually leads to the concept of formal languages as being composed of strings of letters. Another difference between an M-act and a transformation monoid is that for an M-act Q, two distinct elements of the monoid may determine the same transformation of Q. If we demand that this does not happen, then an M-act is essentially the same as a transformation monoid. === M-homomorphism === For two M-acts Q M {\displaystyle Q_{M}} and B M {\displaystyle B_{M}} sharing the same monoid M {\displaystyle M} , an M-homomorphism f : Q M → B M {\displaystyle f\colon Q_{M}\to B_{M}} is a map f : Q → B {\displaystyle f\colon Q\to B} such that f ( q m ) = f ( q ) m {\displaystyle f(qm)=f(q)m} for all q ∈ Q M {\displaystyle q\in Q_{M}} and m ∈ M {\displaystyle m\in M} . The set of all M-homomorphisms is commonly written as H o m ( Q M , B M ) {\displaystyle \mathrm {Hom} (Q_{M},B_{M})} or H o m M ( Q , B ) {\displaystyle \mathrm {Hom} _{M}(Q,B)} . The M-acts and M-homomorphisms together form a category called M-Act. == Semiautomata == A semiautomaton is a triple ( Q , Σ , T ) {\displaystyle (Q,\Sigma ,T)} where Σ {\displaystyle \Sigma } is a non-empty set, called the input alphabet, Q is a non-empty set, called the set of states, and T is the transition function T : Q × Σ → Q . {\displaystyle T\colon Q\times \Sigma \to Q.} When the set of states Q is a finite set—it need not be—, a semiautomaton may be thought of as a deterministic finite automaton ( Q , Σ , T , q 0 , A ) {\displaystyle (Q,\Sigma ,T,q_{0},A)} , but without the initial state q 0 {\displaystyle q_{0}} or set of accept states A. Alternately, it is a finite-state machine that has no output, and only an input. Any semiautomaton induces an act of a monoid in the following way. Let Σ ∗ {\displaystyle \Sigma ^{}} be the free monoid generated by the alphabet Σ {\displaystyle \Sigma } (so that the superscript is understood to be the Kleene star); it is the set of all finite-length strings composed of the letters in Σ {\displaystyle \Sigma } . For every word w in Σ ∗ {\displaystyle \Sigma ^{}} , let T w : Q → Q {\displaystyle T_{w}\colon Q\to Q} be the function, defined recursively, as follows, for all q in Q: If w = ε {\displaystyle w=\varepsilon } , then T ε ( q ) = q {\displaystyle T_{\varepsilon }(q)=q} , so that the empty word ε {\displaystyle \varepsilon } does not change the state. If w = σ {\displaystyle w=\sigma } is a letter in Σ {\displaystyle \Sigma } , then T σ ( q ) = T ( q , σ ) {\displaystyle T_{\sigma }(q)=T(q,\sigma )} . If w = σ v {\displaystyle w=\sigma v} for σ ∈ Σ {\displaystyle \sigma \in \Sigma } and v ∈ Σ ∗ {\displaystyle v\in \Sigma ^{}} , then T w ( q ) = T v ( T σ ( q ) ) {\displaystyle T_{w}(q)=T_{v}(T_{\sigma }(q))} . Let M ( Q , Σ , T ) {\displaystyle M(Q,\Sigma ,T)} be the set M ( Q , Σ , T ) = { T w | w ∈ Σ ∗ } . {\displaystyle M(Q,\Sigma ,T)=\{T_{w}\vert w\in \Sigma ^{}\}.} The set M ( Q , Σ , T ) {\displaystyle M(Q,\Sigma ,T)} is closed under function composition; that is, for all v , w ∈ Σ ∗ {\displaystyle v,w\in \Sigma ^{}} , one has T w ∘ T v = T v w {\displaystyle T_{w}\circ T_{v}=T_{vw}} . It also contains T ε {\displaystyle T_{\varepsilon }} , which is the identity function on Q. Since function composition is associative, the set M ( Q , Σ , T ) {\displaystyle M(Q,\Sigma ,T)} is a monoid: it is called the input monoid, characteristic monoid, characteristic semigroup or transition monoid of the semiautomaton ( Q , Σ , T ) {\displaystyle (Q,\Sigma ,T)} . == Properties == If the set of states Q is finite, then the transition functions are commonly represented as state transition tables. The structure of all possible transitions driven by strings in the free monoid has a graphical depiction as a de Bruijn graph. The set of states Q need not be finite, or even countable. As an example, semiautomata underpin the concept of quantum finite automata. There, the set of states Q are given by the complex projective space C P n {\displaystyle \mathbb {C} P^{n}} , and individual states are referred to as n-state qubits. State transitions are given by unitary n×n matrices. The input alphabet Σ {\displaystyle \Sigma } remains finite, and other typical concerns of automata theory remain in play. Thus, the quantum semiautomaton may be simply defined as the triple ( C P n , Σ , { U σ 1 , U σ 2 , … , U σ p } ) {\displaystyle (\mathbb {C} P^{n},\Sigma ,\{U_{\sigma _{1}},U_{\sigma _{2}},\dotsc ,U_{\sigma _{p}}\})} when the alphabet Σ {\displaystyle \Sigma } has p letters, so that there is one unitary matrix U σ {\displaystyle U_{\sigma }} for each letter σ ∈ Σ {\displaystyle \sigma \in \Sigma } . Stated in this way, the quantum semiautomaton has many geometrical generalizations. Thus, for example, one may take a Riemannian symmetric space in place of C P n {\displaystyle \mathbb {C} P^{n}} , and selections from its group of isometries as transition functions. The syntactic monoid of a regular language is isomorphic to the transition monoid of the minimal automaton accepting the language. == Literature == A. H. Clifford and G. B. Preston, The Algebraic Theory of Semigroups. American Mathematical Society, volume 2 (1967), ISBN 978-0-8218-0272-4. F. Gecseg and I. Peak, Algebraic Theory of Automata (1972), Akademiai Kiado, Budapest. W. M. L. Holcombe, Algebraic Automata Theory (1982), Cambridge University Press J. M. Howie, Automata and Languages, (1991), Cla
Read more →
Pietro Perona

Pietro Perona (born 3 September 1961) is an Italian-American educator and computer scientist. He is the Allan E. Puckett Professor of Electrical Engineering and Computation and Neural Systems at the California Institute of Technology and director of the National Science Foundation Engineering Research Center in Neuromorphic Systems Engineering. He is known for his research in computer vision and is the director of the Caltech Computational Vision Group. == Academic biography == Perona obtained his D.Eng. in electrical engineering cum laude from the University of Padua in 1985 and completed his Ph.D. at the University of California, Berkeley in 1990. His dissertation was titled Finding Texture and Brightness Boundaries in Images, and his adviser was Jitendra Malik. In 1990, Perona was a postdoctoral fellow at the International Computer Science Institute at Berkeley. From 1990 to 1991, he was a postdoctoral fellow at the Massachusetts Institute of Technology in the Laboratory for Information and Decision Systems. He has been on the faculty of the California Institute of Technology since 1991, and he was named Allan E. Puckett Professor in 2008. == Research == Perona’s research focuses on the computational aspects of vision and learning. He developed the anisotropic diffusion equation, a partial differential equation that reduces noise in images while enhancing region boundaries. He is currently interested in visual recognition and in visual analysis of behavior. Perona and Serge Belongie lead the Visipedia project, which facilitates research on visual knowledge representation, visual search, and human-in-the-loop machine learning systems. Perona pioneered the study of visual categorization (including the publication of the Caltech 101 dataset) for which he was awarded the Longuet-Higgins Prize in 2013. He is also the recipient of the 2010 Koenderink Prize for Fundamental Contributions in Computer Vision, the 2003 Conference on Computer Vision and Pattern Recognition best paper award, and a 1996 NSF Presidential Young Investigator Award. == Media coverage == Perona has been quoted or had his research featured in various national media outlets, including the New York Times, Science Friday, The New Yorker, and the Los Angeles Times. In 2003, Perona and Stephen Nowlin organized the NEURO art exhibition, which brought together contemporary artists and scientists to explore neuromorphic engineering.
Read more →
Best AI Paragraph Rewriters in 2026

In search of the best AI paragraph rewriter? An AI paragraph rewriter 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 paragraph rewriter slots into your workflow and pays for itself fast. We tested the leading options and ranked them by quality, value, and ease of use.
Read more →
Natural language processing

Natural language processing (NLP) is the processing of natural language information by a computer. NLP is a subfield of computer science and is closely associated with artificial intelligence. NLP is also related to information retrieval, knowledge representation, computational linguistics, and linguistics more broadly. Major processing tasks in an NLP system include: speech recognition, text classification, natural language understanding, and natural language generation. == History == Natural language processing has its roots in the 1950s. Already in 1950, Alan Turing published an article titled "Computing Machinery and Intelligence," which proposed what is now called the Turing test as a criterion of intelligence, though at the time that was not articulated as a problem separate from artificial intelligence. The proposed test includes a task that involves the automated interpretation and generation of natural language. === Symbolic NLP (1950s – early 1990s) === The premise of symbolic NLP is often illustrated using John Searle's Chinese room thought experiment: Given a collection of rules (e.g., a Chinese phrasebook, with questions and matching answers), the computer emulates natural language understanding (or other NLP tasks) by applying those rules to the data it confronts. 1950s: The Georgetown experiment in 1954 involved fully automatic translation of more than sixty Russian sentences into English. The authors claimed that within three or five years, machine translation would be a solved problem. However, real progress was much slower, and after the ALPAC report in 1966, which found that ten years of research had failed to fulfill the expectations, funding for machine translation was dramatically reduced. Little further research in machine translation was conducted in America (though some research continued elsewhere, such as Japan and Europe) until the late 1980s when the first statistical machine translation systems were developed. 1960s: Some notably successful natural language processing systems developed in the 1960s were SHRDLU, a natural language system working in restricted "blocks worlds" with restricted vocabularies, and ELIZA, a simulation of Rogerian psychotherapy, written by Joseph Weizenbaum between 1964 and 1966. Despite using minimal information about human thought or emotion, ELIZA was able to produce interactions that appeared human-like. When the "patient" exceeded the very small knowledge base, ELIZA might provide a generic response, for example, responding to "My head hurts" with "Why do you say your head hurts?". Ross Quillian's successful work on natural language was demonstrated with a vocabulary of only twenty words, because that was all that would fit in a computer memory at the time. 1970s: During the 1970s, many programmers began to write "conceptual ontologies", which structured real-world information into computer-understandable data. Examples are MARGIE (Schank, 1975), SAM (Cullingford, 1978), PAM (Wilensky, 1978), TaleSpin (Meehan, 1976), QUALM (Lehnert, 1977), Politics (Carbonell, 1979), and Plot Units (Lehnert 1981). During this time, the first chatterbots were written (e.g., PARRY). 1980s: The 1980s and early 1990s mark the heyday of symbolic methods in NLP. Focus areas of the time included research on rule-based parsing (e.g., the development of HPSG as a computational operationalization of generative grammar), morphology (e.g., two-level morphology), semantics (e.g., Lesk algorithm), reference (e.g., within Centering Theory) and other areas of natural language understanding (e.g., in the Rhetorical Structure Theory). Other lines of research were continued, e.g., the development of chatterbots with Racter and Jabberwacky. An important development (that eventually led to the statistical turn in the 1990s) was the rising importance of quantitative evaluation in this period. === Statistical NLP (1990s–present) === Up until the 1980s, most natural language processing systems were based on complex sets of hand-written rules. Starting in the late 1980s, however, there was a revolution in natural language processing with the introduction of machine learning algorithms for language processing. This shift was influenced by increasing computational power (see Moore's law) and a decline in the dominance of Chomskyan linguistic theories (e.g. transformational grammar), whose theoretical underpinnings discouraged the sort of corpus linguistics that underlies the machine-learning approach to language processing. 1990s: Many of the notable early successes in statistical methods in NLP occurred in the field of machine translation, due especially to work at IBM Research, such as IBM alignment models. These systems were able to take advantage of existing multilingual textual corpora that had been produced by the Parliament of Canada and the European Union as a result of laws calling for the translation of all governmental proceedings into all official languages of the corresponding systems of government. However, many systems relied on corpora that were specifically developed for the tasks they were designed to perform. This reliance has been a major limitation to their broader effectiveness and continues to affect similar systems. Consequently, significant research has focused on methods for learning effectively from limited amounts of data. 2000s: With the growth of the web, increasing amounts of raw (unannotated) language data have become available since the mid-1990s. Research has thus increasingly focused on unsupervised and semi-supervised learning algorithms. Such algorithms can learn from data that has not been hand-annotated with the desired answers or using a combination of annotated and non-annotated data. Generally, this task is much more difficult than supervised learning, and typically produces less accurate results for a given amount of input data. However, large quantities of non-annotated data are available (including, among other things, the entire content of the World Wide Web), which can often make up for the worse efficiency if the algorithm used has a low enough time complexity to be practical. 2003: word n-gram model, at the time the best statistical algorithm, is outperformed by a multi-layer perceptron (with a single hidden layer and context length of several words, trained on up to 14 million words, by Bengio et al.) 2010: Tomáš Mikolov (then a PhD student at Brno University of Technology) with co-authors applied a simple recurrent neural network with a single hidden layer to language modeling, and in the following years he went on to develop Word2vec. In the 2010s, representation learning and deep neural network-style (featuring many hidden layers) machine learning methods became widespread in natural language processing. This shift gained momentum due to results showing that such techniques can achieve state-of-the-art results in many natural language tasks, e.g., in language modeling and parsing. This is increasingly important in medicine and healthcare, where NLP helps analyze notes and text in electronic health records that would otherwise be inaccessible for study when seeking to improve care or protect patient privacy. == Approaches: Symbolic, statistical, neural networks == Symbolic approach, i.e., the hand-coding of a set of rules for manipulating symbols, coupled with a dictionary lookup, was historically the first approach used both by AI in general and by NLP in particular: such as by writing grammars or devising heuristic rules for stemming. Machine learning approaches, which include both statistical and neural networks, on the other hand, have many advantages over the symbolic approach: both statistical and neural network methods tend to focus more on the most common cases extracted from a corpus of texts, whereas the rule-based approach needs to provide rules for both rare and common cases equally. language models, produced by either statistical or neural networks methods, are more robust to both unfamiliar (e.g. containing words or structures that have not been seen before) and erroneous input (e.g. with misspelled words or words accidentally omitted) in comparison to the rule-based systems, which are also more costly to produce. the larger such a (probabilistic) language model is, the more accurate it becomes, in contrast to rule-based systems that can gain accuracy only by increasing the amount and complexity of the rules leading to intractability problems. Rule-based systems are commonly used: when the amount of training data is insufficient to successfully apply machine learning methods, e.g., for the machine translation of low-resource languages such as provided by the Apertium system, for preprocessing in NLP pipelines, e.g., tokenization, or for post-processing and transforming the output of NLP pipelines, e.g., for knowledge extraction from syntactic parses. === Statistical approach === In the late 1980s and mid-1990s, the statistical approach ended a peri
Read more →
AI Customer-support Bots: Free vs Paid (2026)

Curious about the best AI customer-support bot? An AI customer-support bot 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 customer-support bot 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.
Read more →
Top 10 AI Image Generators Compared (2026)

Curious about the best AI image generator? An AI image 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 image generator slots into your workflow and pays for itself fast. Read on for hands-on impressions, pricing tiers, and the standout features that matter.
Read more →