AI Detector Excel File

AI Detector Excel File — independent reviews, comparisons, pricing and step-by-step guides on Aizhi.

Cloud-Based Secure File Transfer

Cloud-Based Secure File Transfer is a managed or hosted file transfer service that provides cloud storage that can be accessed via SSH File Transfer Protocol (SFTP). These services allow secure, reliable file transfers while offering the scalability, redundancy, and high availability of cloud infrastructure. == Technical overview == The evolution of file transfer protocols began with File Transfer Protocol (FTP) and SSH File Transfer Protocol (SFTP). SFTP offered enhanced security through the use of SSH (Secure Shell) encryption, which addressed many of the security concerns associated with traditional FTP. Over time, as businesses increasingly adopted cloud infrastructure, the demand for services that integrate secure file transfer with cloud storage led to the rise of Cloud-Based Secure File Transfer services. These services combine the benefits of secure, encrypted file transfer with the scalability and flexibility of cloud-based storage systems. Traditional on-premises SFTP typically involves setting up and managing physical or virtual servers to handle file transfers. In contrast, Cloud-Based Secure File Transfer utilizes managed cloud infrastructure, such as AWS EC2, Azure VMs, or Google Cloud, to automate scaling, ensure redundancy, and provide high availability. These cloud environments can be configured to automatically scale with demand, enabling businesses to handle large volumes of data transfers without the need for extensive physical hardware. == Features == Scalability and availability: Cloud-Based Secure File Transfer services are inherently scalable, with features like load balancing, multi-region deployments, and auto-scaling groups that adjust resources in response to traffic spikes. This ensures that the system can handle varying workloads and provides continuous availability, even during high-demand periods. Cost-effectiveness: By eliminating the need for physical infrastructure and reducing ongoing server maintenance costs, Cloud-Based Secure File Transfer services offer significant cost savings compared to traditional on-premises services. Cloud providers typically offer pay-as-you-go pricing models, where users only pay for the resources they use, further optimizing costs. Security and compliance: Cloud-Based Secure File Transfer products offer strong security measures, including end-to-end encryption, key management, detailed logging, and auditing. These services are often compliant with industry regulations such as HIPAA (Health Insurance Portability and Accountability Act), GDPR (General Data Protection Regulation), and SOC 2 (System and Organization Controls), ensuring that data transfers meet necessary security and privacy standards. == Cloud-Based Secure File Transfer providers == == Uses == Cloud-Based Secure File Transfer is used across various industries to securely transfer sensitive data and integrate into business workflows. In healthcare, Cloud-Based Secure File Transfer is essential for securely transferring electronic Protected Health Information (ePHI), ensuring compliance with regulations like HIPAA. In financial institutions, it is used to protect sensitive financial data during transfer, maintaining privacy and security. Data analytics also benefits from Cloud-Based Secure File Transfer, offering a secure and efficient method for transferring large datasets between systems or partners. Technically, Cloud-Based Secure File Transfer is often integrated into enterprise workflows through automated file transfers, using scripting or APIs. It also plays a key role in cloud backup and disaster recovery, ensuring that files are securely transferred and stored in cloud environments, which supports business continuity. However, businesses must address certain implementation challenges. Despite its secure design, Cloud-Based Secure File Transfer is not immune to risks such as misconfigured SSH keys, improper access control, or inadequate encryption. Regular security audits and careful configuration management are necessary to minimize the risk of data breaches. Additionally, integrating Cloud-Based Secure File Transfer with legacy systems can present challenges, such as incompatible APIs or outdated authentication methods. == Comparisons with related technologies == Cloud-Based Secure File Transfer differs from traditional SFTP primarily in its deployment and management model. Traditional SFTP services are typically hosted on-premises or on virtual servers, requiring manual configuration, ongoing infrastructure maintenance, and security management by in-house IT teams. In contrast, Cloud-Based Secure File Transfer is offered as a Software-as-a-Service (SaaS) service, reducing infrastructure overhead by eliminating the need for dedicated hardware or virtual machines. This model simplifies management through centralized web-based interfaces, automated updates, and built-in scalability. While Cloud-Based Secure File Transfer is focused on providing secure file transfers over the SFTP protocol, Managed File Transfer (MFT) platforms generally support a broader range of protocols, including FTP, FTPS, HTTP/S, and AS2. MFT services often include advanced features such as end-to-end encryption, extensive automation, compliance reporting, and integration with enterprise systems. Cloud-Based Secure File Transfer services may offer some of these features but are typically more lightweight and streamlined, targeting organizations seeking a secure and scalable alternative to traditional SFTP without the full suite of MFT capabilities. As such, Cloud-Based Secure File Transfer can be seen as a specialized subset within the broader managed file transfer ecosystem.
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Top 10 AI Content Generators Compared (2026)

Comparing the best AI content generator? An AI content generator 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 content generator slots into your workflow and pays for itself fast. Below we compare features, pricing, and real output so you can choose with confidence.
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Selmer Bringsjord

Selmer Bringsjord (born November 24, 1958) is a professor of computer science and cognitive science and a former chair of the Department of Cognitive Science at Rensselaer Polytechnic Institute. He also holds an appointment in the Lally School of Management & Technology and teaches artificial Intelligence (AI), formal logic, human and machine reasoning, and philosophy of AI. == Biography == Bringsjord's education includes a B.A. in philosophy from the University of Pennsylvania and a Ph.D. in philosophy from Brown University, where he studied under Roderick Chisholm. He conducts research in AI as the director of the Rensselaer AI & Reasoning (RAIR) Laboratory. He specializes in the logico-mathematical and philosophical foundations of AI and cognitive science, and in collaboratively building AI systems on the basis of computational logic. Bringsjord believes that "the human mind will forever be superior to AI", and that "much of what many humans do for a living will be better done by indefatigable machines who require not a cent in pay". Bringsjord has stated that the "ultimate growth industry will be building smarter and smarter such machines on the one hand, and philosophizing about whether they are truly conscious and free on the other". Bringsjord has an argument for P = NP using digital physics. Other research includes developing a new computational-logic framework allowing the formalization of deliberative multi-agent "mindreading" as applied to the realm of nuclear strategy, with the goal of creating a model and simulation to enable reliable prediction. He has published an opinion piece advocating for counter-terrorism security ensured by pervasive, all-seeing sensors; automated reasoners; and autonomous, lethal robots. Bringsjord received a National Science Foundation award to research Social Robotics and the Covey Award for the advancement of philosophy of computing awarded by the International Association for Computing And Philosophy, among several others prizes. == Books authored == with Yang, Y. Mental Metalogic: A New, Unifying Theory of Human and Machine Reasoning (Mahwah, NJ: Lawrence Erlbaum).(2007) with Zenzen, M. Superminds: People Harness Hypercomputation, and More (Dordrecht, The Netherlands: Kluwer). (2003) ISBN 978-1402010958 with Ferrucci, D. Artificial Intelligence and Literary Creativity: Inside the Mind of Brutus, A Storytelling Machine (Mahwah, NJ: Lawrence Erlbaum).(2000) Abortion: A Dialogue (Indianapolis, IN: Hackett).(1997) What Robots Can and Can’t Be (Dordrecht, The Netherlands: Kluwer).(1992) Soft Wars (New York, NY: Penguin USA). A novel.(1991)
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Halbert White

Halbert Lynn White Jr. (November 19, 1950 – March 31, 2012) was the Chancellor's Associates Distinguished Professor of Economics at the University of California, San Diego, and a Fellow of the Econometric Society and the American Academy of Arts and Sciences. == Education and career == White, a native of Kansas City, Missouri, graduated salutatorian from Southwest High School in 1968. He went on to study at Princeton University, receiving his B.A. in economics in 1972. He earned his Ph.D. in economics at the Massachusetts Institute of Technology in 1976, under the supervision of Jerry A. Hausman and Robert Solow. White spent his first years as an assistant professor in the University of Rochester before moving to University of California, San Diego (UCSD) in 1979. He remained at UCSD until his untimely death from cancer. == Research == White was well known in the field of econometrics for his 1980 paper on robust standard errors (which is among the most-cited paper in economics since 1970), and for the heteroscedasticity-consistent estimator and the test for heteroskedasticity that are named after him. A 1982 paper by White contributed strongly to the development of quasi-maximum likelihood estimation. He also contributed to numerous other areas such as neural networks and medicine. In 1999, White co-founded an economic consulting firm, Bates White, which is based in Washington, D.C.
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New York Institute of Technology Computer Graphics Lab

The New York Institute of Technology Computer Graphics Lab is a computer lab located at the New York Institute of Technology (NYIT), founded by Alexander Schure. It was originally located at the "pink building" on the NYIT campus. It has played an important role in the history of computer graphics and animation, as founders of Pixar and Lucasfilm Limited, including Turing Award winners Edwin Catmull and Patrick Hanrahan, began their research there. It is the birthplace of entirely 3D CGI films. The lab was initially founded to produce a short high-quality feature film with the project name of The Works. The feature, which was never completed, was a 90-minute feature that was to be the first entirely computer-generated CGI movie. Production mainly focused around DEC PDP and VAX machines. Many of the original CGL team now form the elite of the CG and computer world with members going on to Silicon Graphics, Microsoft, Cisco, NVIDIA and others, including Pixar president, co-founder and Turing laureate Ed Catmull, Pixar co-founder and Microsoft graphics fellow Alvy Ray Smith, Pixar co-founder Ralph Guggenheim, Walt Disney Animation Studios chief scientist Lance Williams, Netscape and Silicon Graphics founder Jim Clark, Tableau co-founder and Turing laureate Pat Hanrahan, Microsoft graphics fellow Jim Blinn, Thad Beier, Oscar and Bafta nominee Jacques Stroweis, Andrew Glassner, and Tom Brigham. Systems programmer Bruce Perens went on to co-found the Open Source Initiative. Researchers at the New York Institute of Technology Computer Graphics Lab created the tools that made entirely 3D CGI films possible. Among NYIT CG Lab's many innovations was an eight-bit paint system to ease computer animation. NYIT CG Lab was regarded as the top computer animation research and development group in the world during the late 70s and early 80s. == The 21st century == The lab is presently located at NYIT's Long Island campus, and NYIT currently offers a Ph.D. program in Computer Science.
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Top 10 AI Paraphrasing Tools Compared (2026)

Shopping for the best AI paraphrasing tool? An AI paraphrasing tool is software that uses machine learning to help you get more done — it keeps getting smarter as the underlying models improve. Pricing, accuracy, and the size of the model behind the tool are the three factors that most affect daily usefulness. Whether you are a beginner or a pro, the right AI paraphrasing tool 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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Paul Christiano

Paul Christiano is an American researcher in the field of artificial intelligence (AI), with a specific focus on AI alignment, which is the subfield of AI safety research that aims to steer AI systems toward human interests. He serves as the Head of Safety for the Center for AI Standards and Innovation inside NIST. He formerly led the language model alignment team at OpenAI and became founder and head of the non-profit Alignment Research Center (ARC), which works on theoretical AI alignment and evaluations of machine learning models. In 2023, Christiano was named as one of the TIME 100 Most Influential People in AI (TIME100 AI). In September 2023, Christiano was appointed to the UK government's Frontier AI Taskforce advisory board. Before working at the Center for AI Standards and Innovation, he was an initial trustee on Anthropic's Long-Term Benefit Trust. == Education == Christiano attended the Harker School in San Jose, California. He competed on the U.S. team and won a silver medal at the 49th International Mathematics Olympiad (IMO) in 2008. In 2012, Christiano graduated from the Massachusetts Institute of Technology (MIT) with a degree in mathematics. At MIT, he researched data structures, quantum cryptography, and combinatorial optimization. He then went on to complete a PhD at the University of California, Berkeley. While at Berkeley, Christiano collaborated with researcher Katja Grace on AI Impacts, co-developing a preliminary methodology for comparing supercomputers to brains, using traversed edges per second (TEPS). He also experimented with putting Carl Shulman's donor lottery theory into practice, raising nearly $50,000 in a pool to be donated to a single charity. == Career == At OpenAI, Christiano co-authored the paper "Deep Reinforcement Learning from Human Preferences" (2017) and other works developing reinforcement learning from human feedback (RLHF). He is considered one of the principal architects of RLHF, which in 2017 was "considered a notable step forward in AI safety research", according to The New York Times. Other works such as "AI safety via debate" (2018) focus on the problem of scalable oversight – supervising AIs in domains where humans would have difficulty judging output quality. Christiano left OpenAI in 2021 to work on more conceptual and theoretical issues in AI alignment and subsequently founded the Alignment Research Center to focus on this area. One subject of study is the problem of eliciting latent knowledge from advanced machine learning models. ARC also develops techniques to identify and test whether an AI model is potentially dangerous. In April 2023, Christiano told The Economist that ARC was considering developing an industry standard for AI safety. As of April 2024, Christiano was listed as the head of AI safety for the US AI Safety Institute at NIST. One month earlier in March 2024, staff members and scientists at the institute threatened to resign upon being informed of Christiano's pending appointment to the role, stating that his ties to the effective altruism movement may jeopardize the AI Safety Institute's objectivity and integrity. === Views on AI risks === He is known for his views on the potential risks of advanced AI. In 2017, Wired magazine stated that Christiano and his colleagues at OpenAI weren't worried about the destruction of the human race by "evil robots", explaining that "[t]hey’re more concerned that, as AI progresses beyond human comprehension, the technology’s behavior may diverge from our intended goals." However, in a widely quoted interview with Business Insider in 2023, Christiano said that there is a “10–20% chance of AI takeover, [with] many [or] most humans dead.” He also conjectured a “50/50 chance of doom shortly after you have AI systems that are human level.” == Personal life == Christiano is married to Ajeya Cotra, a member of METR's technical staff.
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How to Choose an AI Copywriting Tool

Trying to pick the best AI copywriting tool? An AI copywriting tool 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 copywriting tool slots into your workflow and pays for itself fast. Read on for hands-on impressions, pricing tiers, and the standout features that matter.
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LRE Map

The LRE Map (Language Resources and Evaluation) is a freely accessible large database on resources dedicated to Natural language processing. The original feature of LRE Map is that the records are collected during the submission of different major Natural language processing conferences. The records are then cleaned and gathered into a global database called "LRE Map". The LRE Map is intended to be an instrument for collecting information about language resources and to become, at the same time, a community for users, a place to share and discover resources, discuss opinions, provide feedback, discover new trends, etc. It is an instrument for discovering, searching and documenting language resources, here intended in a broad sense, as both data and tools. The large amount of information contained in the Map can be analyzed in many different ways. For instance, the LRE Map can provide information about the most frequent type of resource, the most represented language, the applications for which resources are used or are being developed, the proportion of new resources vs. already existing ones, or the way in which resources are distributed to the community. == Context == Several institutions worldwide maintain catalogues of language resources (ELRA, LDC, NICT Universal Catalogue, ACL Data and Code Repository, OLAC, LT World, etc.) However, it has been estimated that only 10% of existing resources are known, either through distribution catalogues or via direct publicity by providers (web sites and the like). The rest remains hidden, the only occasions where it briefly emerges being when a resource is presented in the context of a research paper or report at some conference. Even in this case, nevertheless, it might be that a resource remains in the background simply because the focus of the research is not on the resource per se. == History == The LRE Map originated under the name "LREC Map" during the preparation of LREC 2010 conference. More specifically, the idea was discussed within the FlaReNet project, and in collaboration with ELRA and the Institute of Computational Linguistics of CNR in Pisa, the Map was put in place at LREC 2010. The LREC organizers asked the authors to provide some basic information about all the resources (in a broad sense, i.e. including tools, standards and evaluation packages), either used or created, described in their papers. All these descriptors were then gathered in a global matrix called the LREC Map. The same methodology and requirements from the authors has been then applied and extended to other conferences, namely COLING-2010, EMNLP-2010, RANLP-2011, LREC 2012, LREC 2014 and LREC 2016. After this generalization to other conferences, the LREC Map has been renamed as the LRE Map. == Size and content == The size of the database increases over time. The data collected amount to 4776 entries. Each resource is described according to the following attributes: Resource type, e.g. lexicon, annotation tool, tagger/parser. Resource production status, e.g. newly created finished, existing-updated. Resource availability, e.g. freely available, from data center. Resource modality, e.g. speech, written, sign language. Resource use, e.g. named entity recognition, language identification, machine translation. Resource language, e.g. English, 23 European Union languages, official languages of India. == Uses == The LRE map is a very important tool to chart the NLP field. Compared to other studied based on subjective scorings, the LRE map is made of real facts. The map has a great potential for many uses, in addition to being an information gathering tool: It is a great instrument for monitoring the evolution of the field (useful for funders), if applied in different contexts and times. It can be seen as a huge joint effort, the beginning of an even larger cooperative action not just among few leaders but among all the researchers. It is also an "educational" means towards the broad acknowledgment of the need of meta-research activities with the active involvement of many. It is also instrumental in introducing the new notion of "citation of resources" that could provide an award and a means of scholarly recognition for researchers engaged in resource creation. It is used to help the organization of the conferences of the field like LREC. == Derived matrices == The data were then cleaned and sorted by Joseph Mariani (CNRS-LIMSI IMMI) and Gil Francopoulo (CNRS-LIMSI IMMI + Tagmatica) in order to compute the various matrices of the final FLaReNet reports. One of them, the matrix for written data at LREC 2010 is as follows: English is the most studied language. Secondly, come French and German languages and then Italian and Spanish. == Future == The LRE Map has been extended to Language Resources and Evaluation Journal and other conferences.
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Indic OCR

Indic OCR refers to the process of converting text images written in Indic scripts into e-text using Optical character recognition (OCR) techniques. Broadly, it can also refer to the OCR systems of Brahmic scripts for languages of South Asia and Southeast Asia, not just the scripts of the Indian subcontinent, which are all written in an abugida-based writing system. OCR for Latin characters is still not 100% accurate but a relatively high degree of accuracy in conversion has been able to be achieved. Such accuracy has not yet been able to be achieved for Indic scripts using OCR. This is due in part to the writing systems of Indic languages as well as a lack of standard representation, encoding, and support among operating systems and keyboards. The Centre for Development of Advanced Computing (C-DAC) and Technology Development for Indian Languages, the premier R&D organisation of the Ministry of Electronics and Information Technology (also known as MeitY) of India have carried out many projects relating to OCR. Their projects include OCR for Malayalam, Odia, Punjabi, Telugu and Devanagari script. == Properties of Indian writing systems == There are 22 officially recognised languages in India. Of these, Hindi, Bengali and Punjabi are the most widely spoken Indo-Aryan languages and are also the fourth, seventh and tenth most widely spoken languages in the world respectively. Two or more languages can be written with same script. For example, Devanagari is used to write Hindi, Marathi, Rajasthani, Sanskrit, Bhojpuri and others, while Eastern Nagari is used to write Bengali, Assamese, Manipuri and others. Apart from basic characters as consonants and vowels, most Indic languages combine 2 or more basic characters to form compound characters. The shape of a compound character is more complex than the constituent basic characters. Some Indo-Aryan languages (including Hindi and Punjabi) have a horizontal line over the characters, while other languages (including Gujarati) and Dravidian languages (Malayalam, Kannada, Tamil, and Telugu) do not. These are some of the main challenges for creating a single OCR for all Indic languages. Indic OCR also generally includes support for recently invented scripts in India like Ol Chiki, Warang Citi, Mundari Bani, etc. which are mainly created for writing Munda languages of Austroasiatic family. The concept of upper/lower case is absent in Indic scripts. Apart from Urdu, Sindhi, Kashmiri and Thaana, all other Indic languages are written from left to right. == Examples == SanskritOCR - OCR software for Sanskrit, Hindi and other Indo-Aryan languages based on the Devanagari script. Sanskrit OCR is developed by a Sanskrit scholar from Germany - Dr. Oliver Hellwig of Department for Languages and Cultures of Southern Asia, Freie Universität Berlin. The official website is in German. The interface of earlier versions of the software was also in German, but later versions have an English interface too. E-aksharayan - Optical character recognition engine for Indian languages Chitrankan - This technology was developed by ISI, Kolkata, and transferred to C-DAC. It processes printed Hindi text from a scanner or from an image. Indic OCR models for Tesseract (software) == OCR in use == OCR has been used for Wikisource and other projects.
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Markov chain

In probability theory and statistics, a Markov chain or Markov process is a stochastic process describing a sequence of possible events in which the probability of each event depends only on the state attained in the previous event. Informally, this may be thought of as, "What happens next depends only on the state of affairs now." A countably infinite sequence, in which the chain moves state at discrete time steps, gives a discrete-time Markov chain (DTMC). A continuous-time process is called a continuous-time Markov chain (CTMC). Markov processes are named in honor of the Russian mathematician Andrey Markov. Markov chains have many applications as statistical models of real-world processes. They provide the basis for general stochastic simulation methods known as Markov chain Monte Carlo, which are used for simulating sampling from complex probability distributions, and have found application in areas including Bayesian statistics, biology, chemistry, economics, finance, information theory, physics, signal processing, and speech processing. The adjectives Markovian and Markov are used to describe something that is related to a Markov process. == Principles == === Definition === A Markov process is a stochastic process that satisfies the Markov property (sometimes characterized as "memorylessness"). In simpler terms, it is a process for which predictions can be made regarding future outcomes based solely on its present state and—most importantly—such predictions are just as good as the ones that could be made knowing the process's full history. In other words, conditional on the present state of the system, its future and past states are independent. A Markov chain is a type of Markov process that has either a discrete state space or a discrete index set (often representing time), but the precise definition of a Markov chain varies. For example, it is common to define a Markov chain as a Markov process in either discrete or continuous time with a countable state space (thus regardless of the nature of time), but it is also common to define a Markov chain as having discrete time in either countable or continuous state space (thus regardless of the state space). === Types of Markov chains === The system's state space and time parameter index need to be specified. The following table gives an overview of the different instances of Markov processes for different levels of state space generality for both discrete and continuous time: Note that there is no definitive agreement in the literature on the use of some of the terms that signify special cases of Markov processes. Usually the term "Markov chain" is reserved for a process with a discrete set of times, that is, a discrete-time Markov chain (DTMC), but a few authors use the term "Markov process" to refer to a continuous-time Markov chain (CTMC) without explicit mention. In addition, there are other extensions of Markov processes that are referred to as such but do not necessarily fall within any of these four categories (see Markov model). Moreover, the time index need not necessarily be real-valued; like with the state space, there are conceivable processes that move through index sets with other mathematical constructs. Notice that the general state space continuous-time Markov chain is general to such a degree that it has no designated term. While the time parameter is usually discrete, the state space of a Markov chain does not have any generally agreed-on restrictions: the term may refer to a process on an arbitrary state space. However, many applications of Markov chains employ finite or countably infinite state spaces, which have a more straightforward statistical analysis. Besides time-index and state-space parameters, there are many other variations, extensions and generalizations (see Variations). For simplicity, most of this article concentrates on the discrete-time, discrete state-space case, unless mentioned otherwise. === Transitions === The changes of state of the system are called transitions. The probabilities associated with various state changes are called transition probabilities. The process is characterized by a state space, a transition matrix describing the probabilities of particular transitions, and an initial state (or initial distribution) across the state space. By convention, we assume all possible states and transitions have been included in the definition of the process, so there is always a next state, and the process does not terminate. A discrete-time random process involves a system which is in a certain state at each step, with the state changing randomly between steps. The steps are often thought of as moments in time, but they can equally well refer to physical distance or any other discrete measurement. Formally, the steps are the integers or natural numbers, and the random process is a mapping of these to states. The Markov property states that the conditional probability distribution for the system at the next step (and in fact at all future steps) depends only on the current state of the system, and not additionally on the state of the system at previous steps. Since the system changes randomly, it is generally impossible to predict with certainty the state of a Markov chain at a given point in the future. However, the statistical properties of the system's future can be predicted. In many applications, it is these statistical properties that are important. == History == Andrey Markov studied Markov processes in the early 20th century, publishing his first paper on the topic in 1906. Markov processes in continuous time were discovered long before his work in the early 20th century in the form of the Poisson process. Markov was interested in studying an extension of independent random sequences, motivated by a disagreement with Pavel Nekrasov who claimed independence was necessary for the weak law of large numbers to hold. In his first paper on Markov chains, published in 1906, Markov showed that under certain conditions the average outcomes of the Markov chain would converge to a fixed vector of values, so proving a weak law of large numbers without the independence assumption, which had been commonly regarded as a requirement for such mathematical laws to hold. Markov later used Markov chains to study the distribution of vowels in Eugene Onegin, written by Alexander Pushkin, and proved a central limit theorem for such chains. In 1912 Henri Poincaré studied Markov chains on finite groups with an aim to study card shuffling. Other early uses of Markov chains include a diffusion model, introduced by Paul and Tatyana Ehrenfest in 1907, and a branching process, introduced by Francis Galton and Henry William Watson in 1873, preceding the work of Markov. After the work of Galton and Watson, it was later revealed that their branching process had been independently discovered and studied around three decades earlier by Irénée-Jules Bienaymé. Starting in 1928, Maurice Fréchet became interested in Markov chains, eventually resulting in him publishing in 1938 a detailed study on Markov chains. Andrey Kolmogorov developed in a 1931 paper a large part of the early theory of continuous-time Markov processes. Kolmogorov was partly inspired by Louis Bachelier's 1900 work on fluctuations in the stock market as well as Norbert Wiener's work on Einstein's model of Brownian movement. He introduced and studied a particular set of Markov processes known as diffusion processes, where he derived a set of differential equations describing the processes. Independent of Kolmogorov's work, Sydney Chapman derived in a 1928 paper an equation, now called the Chapman–Kolmogorov equation, in a less mathematically rigorous way than Kolmogorov, while studying Brownian movement. The differential equations are now called the Kolmogorov equations or the Kolmogorov–Chapman equations. Other mathematicians who contributed significantly to the foundations of Markov processes include William Feller, starting in 1930s, and then later Eugene Dynkin, starting in the 1950s. == Examples == Mark V. Shaney is a third-order Markov chain program, and a Markov text generator. It ingests the sample text (the Tao Te Ching, or the posts of a Usenet group) and creates a massive list of every sequence of three successive words (triplet) which occurs in the text. It then chooses two words at random, and looks for a word which follows those two in one of the triplets in its massive list. If there is more than one, it picks at random (identical triplets count separately, so a sequence which occurs twice is twice as likely to be picked as one which only occurs once). It then adds that word to the generated text. Then, in the same way, it picks a triplet that starts with the second and third words in the generated text, and that gives a fourth word. It adds the fourth word, then repeats with the third and fourth words, and so on. Random walks based on integers and the gambler's ruin problem are ex
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Arthur Zimek

Arthur Zimek is a professor in data mining, data science and machine learning at the University of Southern Denmark in Odense, Denmark. He graduated from LMU Munich in Germany, where he worked with Prof. Hans-Peter Kriegel. His dissertation on "Correlation Clustering" was awarded the "SIGKDD Doctoral Dissertation Award 2009 Runner-up" by the Association for Computing Machinery. He is well known for his work on outlier detection, density-based clustering, correlation clustering, and the curse of dimensionality. He is one of the founders and core developers of the open-source ELKI data mining framework.
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Inverse depth parametrization

In computer vision, the inverse depth parametrization is a parametrization used in methods for 3D reconstruction from multiple images such as simultaneous localization and mapping (SLAM). Given a point p {\displaystyle \mathbf {p} } in 3D space observed by a monocular pinhole camera from multiple views, the inverse depth parametrization of the point's position is a 6D vector that encodes the optical centre of the camera c 0 {\displaystyle \mathbf {c} _{0}} when in first observed the point, and the position of the point along the ray passing through p {\displaystyle \mathbf {p} } and c 0 {\displaystyle \mathbf {c} _{0}} . Inverse depth parametrization generally improves numerical stability and allows to represent points with zero parallax. Moreover, the error associated to the observation of the point's position can be modelled with a Gaussian distribution when expressed in inverse depth. This is an important property required to apply methods, such as Kalman filters, that assume normality of the measurement error distribution. The major drawback is the larger memory consumption, since the dimensionality of the point's representation is doubled. == Definition == Given 3D point p = ( x , y , z ) {\displaystyle \mathbf {p} =(x,y,z)} with world coordinates in a reference frame ( e 1 , e 2 , e 3 ) {\displaystyle (e_{1},e_{2},e_{3})} , observed from different views, the inverse depth parametrization y {\displaystyle \mathbf {y} } of p {\displaystyle \mathbf {p} } is given by: y = ( x 0 , y 0 , z 0 , θ , ϕ , ρ ) {\displaystyle \mathbf {y} =(x_{0},y_{0},z_{0},\theta ,\phi ,\rho )} where the first five components encode the camera pose in the first observation of the point, being c 0 = ( x 0 , y 0 , z 0 ) {\displaystyle \mathbf {c_{0}} =(x_{0},y_{0},z_{0})} the optical centre, ϕ {\displaystyle \phi } the azimuth, θ {\displaystyle \theta } the elevation angle, and ρ = 1 ‖ p − c 0 ‖ {\displaystyle \rho ={\frac {1}{\left\Vert \mathbf {p} -\mathbf {c} _{0}\right\Vert }}} the inverse depth of p {\displaystyle p} at the first observation.
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Top 10 AI Content Generators Compared (2026)

Comparing the best AI content generator? An AI content generator 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 content generator slots into your workflow and pays for itself fast. Below we compare features, pricing, and real output so you can choose with confidence.
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Janyce Wiebe

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