AI Code Platforms

AI Code Platforms — independent reviews, comparisons, pricing and step-by-step guides on Aizhi.

Pray.com

Pray.com is a Christian social networking service and mobile application designed to facilitate religious communities. Launched in 2016, it was founded by Steve Gatena, Michael Lynn, Ryan Beck and Matthew Potter. The platform offers features for social networking, daily prayers, sermons, biblical content, and podcasts. The COVID-19 pandemic significantly increased Pray.com's user base, with downloads surging by 955%. During this period, the platform collaborated with churches to support virtual ministry services as in-person gatherings were restricted. The Federal Election Commission issued an opinion in 2021 that allows the platform to feature members of the United States Congress. Pray.com serves as a specialized social media platform for religious groups. Congregations can establish their own groups where members and leaders can participate in discussions, livestream services, and manage donations. Additionally, users can join "prayer communities" to post and respond to prayer requests. For those who subscribe to premium services, the platform provides access to biblically-inspired meditations and bedtime stories, and Bible stories for children. Pray.com also produces Radio drama-style productions with notable actors such as Kristen Bell and Blair Underwood narrating biblical stories. == History == === Funding and development === Pray.com has secured significant funding to support its development and growth. In 2017, the platform raised $2 million in seed funding from Science Inc., Greylock Partners, and Spark Capital. This was followed by a Series A funding round in March 2018, in which the company secured an additional $14 million from TPG Growth, Science Inc., and Greylock Partners. Founder Steve Gatena has highlighted difficulties in securing funding, noting some venture capitalists' negative attitudes towards faith-based technology. === Clinical studies === There have been clinical studies on Pray.com. In one study, the app was found to be acceptable and easy to use among racial and ethnic minority groups, with participants reporting improved mental health and well-being. Greater app use was associated with better outcomes, though low and variable usage suggests the need for further research to fully understand its impact. Another study examined Pray.com's impact on mental health by assigning 192 participants to use the app freely, use its meditative prayer function, or not use it at all. Over two months, participants reported overall improvements in mental health and well-being. Although no significant differences were found between groups, greater app usage correlated with better mental health outcomes. This suggests that religiously based mobile apps may help improve mental health and well-being. Another study of pray.com had similar findings. === National Day of Prayer === Pray first hosted a National Day of Prayer event in 2020 when it streamed to nearly one million viewers on Facebook. In 2021, Pray hosted a virtual event for the National Day of Prayer in the United States. The event featured remarks from public figures including United States President Joe Biden and former Vice President Mike Pence. President Biden spoke of his faith and prayed for an end to the COVID-19 pandemic. Biden remarked: "It means the world to me to know that there are people across the country who include Jill and me in their prayers. And I hope you know that you and your families are in our prayers as well. Today I am praying for the end of this great COVID crisis." The event featured musical performances from Gary Valenciano, Brooke Ligertwood from the Christian band Hillsong Worship, Lecrae, Heather Headley and Michael Neale. Other notable speakers included Ronnie Floyd, Ed Young, Mark Driscoll, and Samuel Rodriguez. Pray.com partnered with Sirius XM, DirecTV and Facebook to stream the event across multiple platforms. Pray.com was featured as a pop-up channel on Sirius XM, channel 154, to host the prayer event and celebrate people of all faith. === Partnerships and sponsorships === In 2024, Pray.com partnered with Sting Ray Robb as the primary sponsor for his No. 41 Chevrolet in the 2024 NTT IndyCar Series. The partnership, highlighting Robb's Christian faith, aims to engage younger audiences with faith-based content. The car, featuring Pray.com's branding, was set to debut at the Firestone Grand Prix of St. Petersburg. A partnership with Palantir Technologies for use of its AI systems was also announced in 2024. === Censorship in China === The app was removed from Apple's App Store in China as part of the country's broader efforts to restrict access to religious content. The app was targeted due to China's stringent regulations on religious material, particularly content distributed through digital platforms. The removal aligns with China's ongoing campaign to control online religious expression and maintain state-approved religious activities.
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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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Marcus Hutter

Marcus Hutter (born 14 April 1967 in Munich) is a German computer scientist, professor and artificial intelligence researcher. As a senior researcher at DeepMind, he studies the mathematical foundations of artificial general intelligence. Hutter studied physics and computer science at the Technical University of Munich. In 2000, he joined Jürgen Schmidhuber's group at the Dalle Molle Institute for Artificial Intelligence Research in Manno, Switzerland. He developed a mathematical formalism of artificial general intelligence named AIXI. He has served as a professor at the College of Engineering, Computing and Cybernetics of the Australian National University in Canberra, Australia. == Research == Starting in 2000, Hutter developed and published a mathematical theory of artificial general intelligence, AIXI, based on idealised intelligent agents and reward-motivated reinforcement learning. His first book Universal Artificial Intelligence: Sequential Decisions Based on Algorithmic Probability was published in 2005 by Springer. Also in 2005, Hutter published with his doctoral student Shane Legg an intelligence test for artificial intelligence devices. In 2009, Hutter developed and published the theory of feature reinforcement learning. In 2014, Lattimore and Hutter published an asymptotically optimal extension of the AIXI agent. An accessible podcast with Lex Fridman about his theory of Universal AI appeared in 2021 and a more technical follow-up with Tim Nguyen in 2024 in the Cartesian Cafe. His new (2024) book also gives a more accessible introduction to Universal AI and progress in the 20 years since his first book, including a chapter on ASI safety, which featured as a keynote at the inaugural workshop on AI safety in Sydney. == Hutter Prize == In 2006, Hutter announced the Hutter Prize for Lossless Compression of Human Knowledge, with a total of €50,000 in prize money. In 2020, Hutter raised the prize money for the Hutter Prize to €500,000.
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Best AI Marketing Tools in 2026

Trying to pick the best AI marketing tool? An AI marketing 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 marketing 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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Vector database

A vector database, vector store or vector search engine is a database that stores and retrieves embeddings of data in vector space. Vector databases typically implement approximate nearest neighbor algorithms so users can search for records semantically similar to a given input, unlike traditional databases which primarily look up records by exact match. Use-cases for vector databases include similarity search, semantic search, multi-modal search, recommendations engines, object detection, and retrieval-augmented generation (RAG). Vector embeddings are mathematical representations of data in a high-dimensional space. In this space, each dimension corresponds to a feature of the data, with the number of dimensions ranging from a few hundred to tens of thousands, depending on the complexity of the data being represented. Each data item is represented by one vector in this space. Words, phrases, or entire documents, as well as images, audio, and other types of data, can all be vectorized. These feature vectors may be computed from the raw data using machine learning methods such as feature extraction algorithms, word embeddings or deep learning networks. The goal is that semantically similar data items receive feature vectors close to each other. Vector retrieval can be combined with metadata filtering or lexical search to support filtered and hybrid retrieval workflows. == Techniques == Common techniques for similarity search on high-dimensional vectors include: Hierarchical Navigable Small World (HNSW) graphs Locality-sensitive hashing (LSH) and sketching Product quantization (PQ) Inverted files These techniques may also be combined in vector search systems. In recent benchmarks, HNSW-based implementations have been among the best performers. Conferences such as the International Conference on Similarity Search and Applications (SISAP) and the Conference on Neural Information Processing Systems (NeurIPS) have hosted competitions on vector search in large databases. == Applications == Vector databases are used in a wide range of machine learning applications including similarity search, semantic search, multi-modal search, recommendations engines, object detection, and retrieval-augmented generation. === Retrieval-augmented generation === An especially common use-case for vector databases is in retrieval-augmented generation (RAG), a method to improve domain-specific responses of large language models. The retrieval component of a RAG can be any search system, but is most often implemented as a vector database. Text documents describing the domain of interest are collected, and for each document or document section, a feature vector (known as an "embedding") is computed, typically using a deep learning network, and stored in a vector database along with a link to the document. Given a user prompt, the feature vector of the prompt is computed, and the database is queried to retrieve the most relevant documents. These are then automatically added into the context window of the large language model, and the large language model proceeds to create a response to the prompt given this context. == Implementations ==
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Alexei A. Efros

Alexei "Alyosha" A. Efros (born 9 April 1975) is a Russian-American computer scientist and professor at University of California, Berkeley. He has contributed to the field of computer vision, and his work has been referenced in Wired, BBC News, The New York Times, and The New Yorker. == Early life and education == Efros was born in St. Petersburg in the Soviet Union. His father is Alexei L. Efros, then a physics professor at the Ioffe Physico-Technical Institute. His family emigrated to the United States when he was 14 to accommodate his father's career and the family settled in Salt Lake City in 1991. He graduated from the University of Utah in 1997, and attended University of California, Berkeley for his PhD, where he was advised by Jitendra Malik and graduated in 2003. He then spent a year as a research fellow at the University of Oxford, where he worked with Andrew Zisserman. == Career == Efros joined the faculty at Carnegie Mellon University in Pittsburgh, where he remained until 2013 when he joined the faculty of the University of California, Berkeley. He received a Guggenheim Fellowship in 2008. He received the 2016 ACM Prize in Computing.
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Structured prediction

Structured prediction or structured output learning is an umbrella term for supervised machine learning techniques that involves predicting structured objects, rather than discrete or real values. Similar to commonly used supervised learning techniques, structured prediction models are typically trained by means of observed data in which the predicted value is compared to the ground truth, and this is used to adjust the model parameters. Due to the complexity of the model and the interrelations of predicted variables, the processes of model training and inference are often computationally infeasible, so approximate inference and learning methods are used. == Applications == An example application is the problem of translating a natural language sentence into a syntactic representation such as a parse tree. This can be seen as a structured prediction problem in which the structured output domain is the set of all possible parse trees. Structured prediction is used in a wide variety of domains including bioinformatics, natural language processing (NLP), speech recognition, and computer vision. === Example: sequence tagging === Sequence tagging is a class of problems prevalent in NLP in which input data are often sequential, for instance sentences of text. The sequence tagging problem appears in several guises, such as part-of-speech tagging (POS tagging) and named entity recognition. In POS tagging, for example, each word in a sequence must be 'tagged' with a class label representing the type of word: The main challenge of this problem is to resolve ambiguity: in the above example, the words "sentence" and "tagged" in English can also be verbs. While this problem can be solved by simply performing classification of individual tokens, this approach does not take into account the empirical fact that tags do not occur independently; instead, each tag displays a strong conditional dependence on the tag of the previous word. This fact can be exploited in a sequence model such as a hidden Markov model or conditional random field that predicts the entire tag sequence for a sentence (rather than just individual tags) via the Viterbi algorithm. == Techniques == Probabilistic graphical models form a large class of structured prediction models. In particular, Bayesian networks and random fields are popular. Other algorithms and models for structured prediction include inductive logic programming, case-based reasoning, structured SVMs, Markov logic networks, Probabilistic Soft Logic, and constrained conditional models. The main techniques are: Conditional random fields Structured support vector machines Structured k-nearest neighbours Recurrent neural networks, in particular Elman networks Transformers. === Structured perceptron === One of the easiest ways to understand algorithms for general structured prediction is the structured perceptron by Collins. This algorithm combines the perceptron algorithm for learning linear classifiers with an inference algorithm (classically the Viterbi algorithm when used on sequence data) and can be described abstractly as follows: First, define a function ϕ ( x , y ) {\displaystyle \phi (x,y)} that maps a training sample x {\displaystyle x} and a candidate prediction y {\displaystyle y} to a vector of length n {\displaystyle n} ( x {\displaystyle x} and y {\displaystyle y} may have any structure; n {\displaystyle n} is problem-dependent, but must be fixed for each model). Let G E N {\displaystyle GEN} be a function that generates candidate predictions. Then: Let w {\displaystyle w} be a weight vector of length n {\displaystyle n} For a predetermined number of iterations: For each sample x {\displaystyle x} in the training set with true output t {\displaystyle t} : Make a prediction y ^ {\displaystyle {\hat {y}}} : y ^ = a r g m a x { y ∈ G E N ( x ) } ( w T , ϕ ( x , y ) ) {\displaystyle {\hat {y}}={\operatorname {arg\,max} }\,\{y\in GEN(x)\}\,(w^{T},\phi (x,y))} Update w {\displaystyle w} (from y ^ {\displaystyle {\hat {y}}} towards t {\displaystyle t} ): w = w + c ( − ϕ ( x , y ^ ) + ϕ ( x , t ) ) {\displaystyle w=w+c(-\phi (x,{\hat {y}})+\phi (x,t))} , where c {\displaystyle c} is the learning rate. In practice, finding the argmax over G E N ( x ) {\displaystyle {GEN}({x})} is done using an algorithm such as Viterbi or a max-sum, rather than an exhaustive search through an exponentially large set of candidates. The idea of learning is similar to that for multiclass perceptrons.
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The Best Free AI Sales Assistant for Beginners

Comparing the best AI sales assistant? An AI sales assistant 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 sales assistant 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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Weak artificial intelligence

Weak artificial intelligence (weak AI) is artificial intelligence that implements a limited part of the mind, or, as narrow AI, artificial narrow intelligence (ANI), is focused on one narrow task. Weak AI is contrasted with strong AI, which can be interpreted in various ways: Artificial general intelligence (AGI): a machine with the ability to apply intelligence to any problem, rather than just one specific problem. Artificial superintelligence (ASI): a machine with a vastly superior intelligence to the average human being. Artificial consciousness: a machine that has consciousness, sentience and mind (John Searle uses "strong AI" in this sense). Narrow AI can be classified as being "limited to a single, narrowly defined task. Most modern AI systems would be classified in this category." Artificial general intelligence is conversely the opposite. == Applications and risks == Some examples of narrow AI are AlphaGo, self-driving cars, robot systems used in the medical field, and diagnostic doctors. Narrow AI systems are sometimes dangerous if unreliable. And the behavior that it follows can become inconsistent. It could be difficult for the AI to grasp complex patterns and get to a solution that works reliably in various environments. This "brittleness" can cause it to fail in unpredictable ways. Narrow AI failures can sometimes have significant consequences. It could for example cause disruptions in the electric grid, damage nuclear power plants, cause global economic problems, and misdirect autonomous vehicles. Medicines could be incorrectly sorted and distributed. Also, medical diagnoses can ultimately have serious and sometimes deadly consequences if the AI is faulty or biased. Simple AI programs have already worked their way into society, oftentimes unnoticed by the public. Autocorrection for typing, speech recognition for speech-to-text programs, and vast expansions in the data science fields are examples. Narrow AI has also been the subject of some controversy, including resulting in unfair prison sentences, discrimination against women in the workplace for hiring, resulting in death via autonomous driving, among other cases. Despite being "narrow" AI, recommender systems are efficient at predicting user reactions based on their posts, patterns, or trends. For instance, TikTok's "For You" algorithm can determine a user's interests or preferences in less than an hour. Some other social media AI systems are used to detect bots that may be involved in propaganda or other potentially malicious activities. == Weak AI versus strong AI == John Searle contests the possibility of strong AI (by which he means conscious AI). He further believes that the Turing test (created by Alan Turing and originally called the "imitation game", used to assess whether a machine can converse indistinguishably from a human) is not accurate or appropriate for testing whether an AI is "strong". Scholars such as Antonio Lieto have argued that the current research on both AI and cognitive modelling are perfectly aligned with the weak-AI hypothesis (that should not be confused with the "general" vs "narrow" AI distinction) and that the popular assumption that cognitively inspired AI systems espouse the strong AI hypothesis is ill-posed and problematic since "artificial models of brain and mind can be used to understand mental phenomena without pretending that that they are the real phenomena that they are modelling" (as, on the other hand, implied by the strong AI assumption).
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Suffix automaton

In computer science, a suffix automaton is an efficient data structure for representing the substring index of a given string which allows the storage, processing, and retrieval of compressed information about all its substrings. The suffix automaton of a string S {\displaystyle S} is the smallest directed acyclic graph with a dedicated initial vertex and a set of "final" vertices, such that paths from the initial vertex to final vertices represent the suffixes of the string. In terms of automata theory, a suffix automaton is the minimal partial deterministic finite automaton that recognizes the set of suffixes of a given string S = s 1 s 2 … s n {\displaystyle S=s_{1}s_{2}\dots s_{n}} . The state graph of a suffix automaton is called a directed acyclic word graph (DAWG), a term that is also sometimes used for any deterministic acyclic finite state automaton. Suffix automata were introduced in 1983 by a group of scientists from the University of Denver and the University of Colorado Boulder. They suggested a linear time online algorithm for its construction and showed that the suffix automaton of a string S {\displaystyle S} having length at least two characters has at most 2 | S | − 1 {\textstyle 2|S|-1} states and at most 3 | S | − 4 {\textstyle 3|S|-4} transitions. Further works have shown a close connection between suffix automata and suffix trees, and have outlined several generalizations of suffix automata, such as compacted suffix automaton obtained by compression of nodes with a single outgoing arc. Suffix automata provide efficient solutions to problems such as substring search and computation of the largest common substring of two and more strings. == History == The concept of suffix automaton was introduced in 1983 by a group of scientists from University of Denver and University of Colorado Boulder consisting of Anselm Blumer, Janet Blumer, Andrzej Ehrenfeucht, David Haussler and Ross McConnell, although similar concepts had earlier been studied alongside suffix trees in the works of Peter Weiner, Vaughan Pratt and Anatol Slissenko. In their initial work, Blumer et al. showed a suffix automaton built for the string S {\displaystyle S} of length greater than 1 {\displaystyle 1} has at most 2 | S | − 1 {\displaystyle 2|S|-1} states and at most 3 | S | − 4 {\displaystyle 3|S|-4} transitions, and suggested a linear algorithm for automaton construction. In 1983, Mu-Tian Chen and Joel Seiferas independently showed that Weiner's 1973 suffix-tree construction algorithm while building a suffix tree of the string S {\displaystyle S} constructs a suffix automaton of the reversed string S R {\textstyle S^{R}} as an auxiliary structure. In 1987, Blumer et al. applied the compressing technique used in suffix trees to a suffix automaton and invented the compacted suffix automaton, which is also called the compacted directed acyclic word graph (CDAWG). In 1997, Maxime Crochemore and Renaud Vérin developed a linear algorithm for direct CDAWG construction. In 2001, Shunsuke Inenaga et al. developed an algorithm for construction of CDAWG for a set of words given by a trie. == Definitions == Usually when speaking about suffix automata and related concepts, some notions from formal language theory and automata theory are used, in particular: "Alphabet" is a finite set Σ {\displaystyle \Sigma } that is used to construct words. Its elements are called "characters"; "Word" is a finite sequence of characters ω = ω 1 ω 2 … ω n {\displaystyle \omega =\omega _{1}\omega _{2}\dots \omega _{n}} . "Length" of the word ω {\displaystyle \omega } is denoted as | ω | = n {\displaystyle |\omega |=n} ; "Formal language" is a set of words over given alphabet; "Language of all words" is denoted as Σ ∗ {\displaystyle \Sigma ^{}} (where the "" character stands for Kleene star), "empty word" (the word of zero length) is denoted by the character ε {\displaystyle \varepsilon } ; "Concatenation of words" α = α 1 α 2 … α n {\displaystyle \alpha =\alpha _{1}\alpha _{2}\dots \alpha _{n}} and β = β 1 β 2 … β m {\displaystyle \beta =\beta _{1}\beta _{2}\dots \beta _{m}} is denoted as α ⋅ β {\displaystyle \alpha \cdot \beta } or α β {\displaystyle \alpha \beta } and corresponds to the word obtained by writing β {\displaystyle \beta } to the right of α {\displaystyle \alpha } , that is, α β = α 1 α 2 … α n β 1 β 2 … β m {\displaystyle \alpha \beta =\alpha _{1}\alpha _{2}\dots \alpha _{n}\beta _{1}\beta _{2}\dots \beta _{m}} ; "Concatenation of languages" A {\displaystyle A} and B {\displaystyle B} is denoted as A ⋅ B {\displaystyle A\cdot B} or A B {\displaystyle AB} and corresponds to the set of pairwise concatenations A B = { α β : α ∈ A , β ∈ B } {\displaystyle AB=\{\alpha \beta :\alpha \in A,\beta \in B\}} ; If the word ω ∈ Σ ∗ {\displaystyle \omega \in \Sigma ^{}} may be represented as ω = α γ β {\displaystyle \omega =\alpha \gamma \beta } , where α , β , γ ∈ Σ ∗ {\displaystyle \alpha ,\beta ,\gamma \in \Sigma ^{}} , then words α {\displaystyle \alpha } , β {\displaystyle \beta } and γ {\displaystyle \gamma } are called "prefix", "suffix" and "subword" (substring) of the word ω {\displaystyle \omega } correspondingly; If T = T 1 … T n {\displaystyle T=T_{1}\dots T_{n}} and T l T l + 1 … T r = S {\displaystyle T_{l}T_{l+1}\dots T_{r}=S} (with 1 ≤ l ≤ r ≤ n {\displaystyle 1\leq l\leq r\leq n} ) then S {\displaystyle S} is said to "occur" in T {\displaystyle T} as a subword. Here l {\displaystyle l} and r {\displaystyle r} are called left and right positions of occurrence of S {\displaystyle S} in T {\displaystyle T} correspondingly. == Automaton structure == Formally, deterministic finite automaton is determined by 5-tuple A = ( Σ , Q , q 0 , F , δ ) {\displaystyle {\mathcal {A}}=(\Sigma ,Q,q_{0},F,\delta )} , where: Σ {\displaystyle \Sigma } is an "alphabet" that is used to construct words, Q {\displaystyle Q} is a set of automaton "states", q 0 ∈ Q {\displaystyle q_{0}\in Q} is an "initial" state of automaton, F ⊂ Q {\displaystyle F\subset Q} is a set of "final" states of automaton, δ : Q × Σ ↦ Q {\displaystyle \delta :Q\times \Sigma \mapsto Q} is a partial "transition" function of automaton, such that δ ( q , σ ) {\displaystyle \delta (q,\sigma )} for q ∈ Q {\displaystyle q\in Q} and σ ∈ Σ {\displaystyle \sigma \in \Sigma } is either undefined or defines a transition from q {\displaystyle q} over character σ {\displaystyle \sigma } . Most commonly, deterministic finite automaton is represented as a directed graph ("diagram") such that: Set of graph vertices corresponds to the state of states Q {\displaystyle Q} , Graph has a specific marked vertex corresponding to initial state q 0 {\displaystyle q_{0}} , Graph has several marked vertices corresponding to the set of final states F {\displaystyle F} , Set of graph arcs corresponds to the set of transitions δ {\displaystyle \delta } , Specifically, every transition δ ( q 1 , σ ) = q 2 {\textstyle \delta (q_{1},\sigma )=q_{2}} is represented by an arc from q 1 {\displaystyle q_{1}} to q 2 {\displaystyle q_{2}} marked with the character σ {\displaystyle \sigma } . This transition also may be denoted as q 1 σ ⟶ q 2 {\textstyle q_{1}{\begin{smallmatrix}{\sigma }\\[-5pt]{\longrightarrow }\end{smallmatrix}}q_{2}} . In terms of its diagram, the automaton recognizes the word ω = ω 1 ω 2 … ω m {\displaystyle \omega =\omega _{1}\omega _{2}\dots \omega _{m}} only if there is a path from the initial vertex q 0 {\displaystyle q_{0}} to some final vertex q ∈ F {\displaystyle q\in F} such that concatenation of characters on this path forms ω {\displaystyle \omega } . The set of words recognized by an automaton forms a language that is set to be recognized by the automaton. In these terms, the language recognized by a suffix automaton of S {\displaystyle S} is the language of its (possibly empty) suffixes. === Automaton states === "Right context" of the word ω {\displaystyle \omega } with respect to language L {\displaystyle L} is a set [ ω ] R = { α : ω α ∈ L } {\displaystyle [\omega ]_{R}=\{\alpha :\omega \alpha \in L\}} that is a set of words α {\displaystyle \alpha } such that their concatenation with ω {\displaystyle \omega } forms a word from L {\displaystyle L} . Right contexts induce a natural equivalence relation [ α ] R = [ β ] R {\displaystyle [\alpha ]_{R}=[\beta ]_{R}} on the set of all words. If language L {\displaystyle L} is recognized by some deterministic finite automaton, there exists unique up to isomorphism automaton that recognizes the same language and has the minimum possible number of states. Such an automaton is called a minimal automaton for the given language L {\displaystyle L} . Myhill–Nerode theorem allows it to define it explicitly in terms of right contexts: In these terms, a "suffix automaton" is the minimal deterministic finite automaton recognizing the language of suffixes of the word S = s 1 s 2 … s n {\displaystyle S=s_{1}s_{2}\dots s_{n}} . The right context of the word ω {\displaystyle \omeg
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F-score

In statistical analysis of binary classification and information retrieval systems, the F-score or F-measure is a measure of predictive performance. It is calculated from the precision and recall of the test, where the precision is the number of true positive results divided by the number of all samples predicted to be positive, including those not identified correctly, and the recall is the number of true positive results divided by the number of all samples that should have been identified as positive. Precision is also known as positive predictive value, and recall is also known as sensitivity in diagnostic binary classification. The F1 score is the harmonic mean of the precision and recall. It thus symmetrically represents both precision and recall in one metric. The more generic F β {\displaystyle F_{\beta }} score applies additional weights, valuing one of precision or recall more than the other. The highest possible value of an F-score is 1.0, indicating perfect precision and recall, and the lowest possible value is 0, if the precision or the recall is zero. == Etymology == The name F-measure is believed to be named after a different F function in Van Rijsbergen's book, when introduced to the Fourth Message Understanding Conference (MUC-4, 1992). == Definition == The traditional F-measure or balanced F-score (F1 score) is the harmonic mean of precision and recall: F 1 = 2 r e c a l l − 1 + p r e c i s i o n − 1 = 2 p r e c i s i o n ⋅ r e c a l l p r e c i s i o n + r e c a l l = 2 T P 2 T P + F P + F N {\displaystyle F_{1}={\frac {2}{\mathrm {recall} ^{-1}+\mathrm {precision} ^{-1}}}=2{\frac {\mathrm {precision} \cdot \mathrm {recall} }{\mathrm {precision} +\mathrm {recall} }}={\frac {2\mathrm {TP} }{2\mathrm {TP} +\mathrm {FP} +\mathrm {FN} }}} With precision = TP / (TP + FP) and recall = TP / (TP + FN), it follows that the numerator of F1 is the sum of their numerators and the denominator of F1 is the sum of their denominators. If FP=FN F 1 = 2 T P 2 T P + 2 F P = T P T P + F P {\displaystyle F_{1}={\frac {2\mathrm {TP} }{2\mathrm {TP} +2\mathrm {FP} }}={\frac {\mathrm {TP} }{\mathrm {TP} +\mathrm {FP} }}} or F 1 = 2 T P 2 T P + 2 F N = T P T P + F N {\displaystyle F_{1}={\frac {2\mathrm {TP} }{2\mathrm {TP} +2\mathrm {FN} }}={\frac {\mathrm {TP} }{\mathrm {TP} +\mathrm {FN} }}} So, F1 = precision = recall If TP=FP=FN F 1 = 2 T P 2 T P + 2 F P = 2 T P 4 T P = 1 2 = 0.5 {\displaystyle F_{1}={\frac {2\mathrm {TP} }{2\mathrm {TP} +2\mathrm {FP} }}={\frac {2\mathrm {TP} }{4\mathrm {TP} }}={\frac {1}{2}}=0.5} or F 1 = 2 T P 2 T P + 2 F N = 2 T P 4 T P = 1 2 = 0.5 {\displaystyle F_{1}={\frac {2\mathrm {TP} }{2\mathrm {TP} +2\mathrm {FN} }}={\frac {2\mathrm {TP} }{4\mathrm {TP} }}={\frac {1}{2}}=0.5} To see it as a harmonic mean, note that F 1 − 1 = 1 2 ( r e c a l l − 1 + p r e c i s i o n − 1 ) {\displaystyle F_{1}^{-1}={\frac {1}{2}}(\mathrm {recall} ^{-1}+\mathrm {precision} ^{-1})} . === Fβ score === A more general F score, F β {\displaystyle F_{\beta }} , that uses a positive real factor β {\displaystyle \beta } , where β {\displaystyle \beta } is chosen such that recall is considered β {\displaystyle \beta } times as important as precision, is: F β = β 2 + 1 ( β 2 ⋅ r e c a l l − 1 ) + p r e c i s i o n − 1 = ( 1 + β 2 ) ⋅ p r e c i s i o n ⋅ r e c a l l ( β 2 ⋅ p r e c i s i o n ) + r e c a l l {\displaystyle F_{\beta }={\frac {\beta ^{2}+1}{(\beta ^{2}\cdot \mathrm {recall} ^{-1})+\mathrm {precision} ^{-1}}}={\frac {(1+\beta ^{2})\cdot \mathrm {precision} \cdot \mathrm {recall} }{(\beta ^{2}\cdot \mathrm {precision} )+\mathrm {recall} }}} To see that as a weighted harmonic mean, note that F β − 1 = 1 β + β − 1 ( β ⋅ r e c a l l − 1 + β − 1 ⋅ p r e c i s i o n − 1 ) {\displaystyle F_{\beta }^{-1}={\frac {1}{\beta +\beta ^{-1}}}(\beta \cdot \mathrm {recall} ^{-1}+\beta ^{-1}\cdot \mathrm {precision} ^{-1})} . In terms of Type I and type II errors this becomes: F β = ( 1 + β 2 ) ⋅ T P ( 1 + β 2 ) ⋅ T P + β 2 ⋅ F N + F P = ( 1 + β 2 ) ⋅ T P ( T P + F N ) ⋅ β 2 + ( T P + F P ) {\displaystyle F_{\beta }={\frac {(1+\beta ^{2})\cdot \mathrm {TP} }{(1+\beta ^{2})\cdot \mathrm {TP} +\beta ^{2}\cdot \mathrm {FN} +\mathrm {FP} }}\,={\frac {(1+\beta ^{2})\cdot \mathrm {TP} }{(\mathrm {TP} +\mathrm {FN} )\cdot \beta ^{2}+(\mathrm {TP} +\mathrm {FP} )}}\,} Two commonly used values for β {\displaystyle \beta } are 2, which weighs recall higher than precision, and 1/2, which weighs recall lower than precision. The F-measure was derived so that F β {\displaystyle F_{\beta }} "measures the effectiveness of retrieval with respect to a user who attaches β {\displaystyle \beta } times as much importance to recall as precision". It is based on Van Rijsbergen's effectiveness measure E = 1 − ( α p + 1 − α r ) − 1 {\displaystyle E=1-\left({\frac {\alpha }{p}}+{\frac {1-\alpha }{r}}\right)^{-1}} Their relationship is: F β = 1 − E {\displaystyle F_{\beta }=1-E} where α = 1 1 + β 2 {\displaystyle \alpha ={\frac {1}{1+\beta ^{2}}}} == Diagnostic testing == This is related to the field of binary classification where recall is often termed "sensitivity". == Dependence of the F-score on class imbalance == Precision-recall curve, and thus the F β {\displaystyle F_{\beta }} score, explicitly depends on the ratio r {\displaystyle r} of positive to negative test cases. This means that comparison of the F-score across different problems with differing class ratios is problematic. One way to address this issue (see e.g., Siblini et al., 2020) is to use a standard class ratio r 0 {\displaystyle r_{0}} when making such comparisons. == Applications == The F-score is often used in the field of information retrieval for measuring search, document classification, and query classification performance. It is particularly relevant in applications which are primarily concerned with the positive class and where the positive class is rare relative to the negative class. Earlier works focused primarily on the F1 score, but with the proliferation of large scale search engines, performance goals changed to place more emphasis on either precision or recall and so F β {\displaystyle F_{\beta }} is seen in wide application. The F-score is also used in machine learning. However, the F-measures do not take true negatives into account, hence measures such as the Matthews correlation coefficient, Informedness or Cohen's kappa may be preferred to assess the performance of a binary classifier. The F-score has been widely used in the natural language processing literature, such as in the evaluation of named entity recognition and word segmentation. == Properties == The F1 score is the Dice coefficient of the set of retrieved items and the set of relevant items. The F1-score of a classifier which always predicts the positive class converges to 1 as the probability of the positive class increases. The F1-score of a classifier which always predicts the positive class is equal to 2 proportion_of_positive_class / ( 1 + proportion_of_positive_class ), since the recall is 1, and the precision is equal to the proportion of the positive class. If the scoring model is uninformative (cannot distinguish between the positive and negative class) then the optimal threshold is 0 so that the positive class is always predicted. F1 score is concave in the true positive rate. == Criticism == David Hand and others criticize the widespread use of the F1 score since it gives equal importance to precision and recall. In practice, different types of mis-classifications incur different costs. In other words, the relative importance of precision and recall is an aspect of the problem. According to Davide Chicco and Giuseppe Jurman, the F1 score is less truthful and informative than the Matthews correlation coefficient (MCC) in binary evaluation classification. David M W Powers has pointed out that F1 ignores the True Negatives and thus is misleading for unbalanced classes, while kappa and correlation measures are symmetric and assess both directions of predictability - the classifier predicting the true class and the true class predicting the classifier prediction, proposing separate multiclass measures Informedness and Markedness for the two directions, noting that their geometric mean is correlation. Another source of critique of F1 is its lack of symmetry. It means it may change its value when dataset labeling is changed - the "positive" samples are named "negative" and vice versa. This criticism is met by the P4 metric definition, which is sometimes indicated as a symmetrical extension of F1. Finally, Ferrer and Dyrland et al. argue that the expected cost (or its counterpart, the expected utility) is the only principled metric for evaluation of classification decisions, having various advantages over the F-score and the MCC. Both works show that the F-score can result in wrong conclusions about the absolute and relative quality of systems. == Difference from Fowlkes–Mallows index == While the F-measur
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Comparing the best AI writing assistant? An AI writing assistant 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 writing assistant 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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JAUS Tool Set

The JAUS Tool Set (JTS) is a software engineering tool for the design of software services used in a distributed computing environment. JTS provides a graphical user interface (GUI) and supporting tools for the rapid design, documentation, and implementation of service interfaces that adhere to the Society of Automotive Engineers' standard AS5684A, the JAUS Service Interface Design Language (JSIDL). JTS is designed to support the modeling, analysis, implementation, and testing of the protocol for an entire distributed system. == Overview == The JAUS Tool Set (JTS) is a set of open source software specification and development tools accompanied by an open source software framework to develop Joint Architecture for Unmanned Systems (JAUS) designs and compliant interface implementations for simulations and control of robotic components per SAE-AS4 standards. JTS consists of the components: GUI based Service Editor: The Service Editor (referred to as the GUI in this document) provides a user friendly interface with which a system designer can specify and analyze formal specifications of Components and Services defined using the JAUS Service Interface Definition Language (JSIDL). Validator: A syntactic and semantic validator provides on-the-fly validation of specifications entered (or imported) by the user with respect to JSIDL syntax and semantics is integrated into the GUI. Specification Repository: A repository (or database) that is integrated into the GUI that allows for the storage of and encourages the reuse of existing formal specifications. C++ Code Generator: The Code Generator automatically generates C++ code that has a 1:1 mapping to the formal specifications. The generated code includes all aspects of the service, including the implementations of marshallers and unmarshallers for messages, and implementations of finite-state machines for protocol behavior that are effectively decoupled from application behavior. Document Generator: The Document Generator automatically generates documentation for sets of Service Definitions. Documents may be generated in several formats. Software Framework: The software framework implements the transport layer specification AS5669A, and provides the interfaces necessary to integrate the auto-generated C++ code with the transport layer implementation. Present transport options include UDP and TCP in wired or wireless networks, as well as serial connections. The transport layer itself is modular, and allows end-users to add additional support as needed. Wireshark Plugin: The Wireshark plugin implements a plugin to the popular network protocol analyzer called Wireshark. This plugin allows for the live capture and offline analysis of JAUS message-based communication at runtime. A built-in repository facilitates easy reuse of service interfaces and implementations traffic across the wire. The JAUS Tool Set can be downloaded from www.jaustoolset.org User documentation and community forum are also available at the site. == Release history == Following a successful Beta test, Version 1.0 of the JAUS Tool Set was released in July 2010. The initial offering focused on core areas of User Interface, HTML document generation, C++ code generation, and the software framework. The Version 1.1 update was released in October 2010. In addition to bug fixes and UI improvements, this version offered several important upgrades including enhancement to the Validator, Wireshark plug-in, and generated code. The JTS 2.0 release is scheduled for the second quarter of 2011 and further refines the Tool Set functionality: Protocol Validation: Currently, JTS provides validation for message creation, to ensure users cannot create invalid messages specifications. That capability does not currently exist for protocol definitions, but is being added. This will help ensure that users create all necessary elements of a service definition, and reduce user error. C# and Java Code Generation: Currently, JTS generates cross-platform C++ code. However, other languages including Java and C# are seeing a dramatic increase in their use in distributed systems, particularly in the development of graphical clients to embedded services. MS Word Document Generation: HTML and JSIDL output is supported, but native Office-Open-XML (OOXML) based MS Word generation has advantages in terms of output presentation, and ease of use for integration with other documents. Therefore, we plan to integrate MS Word service document generation. In addition, the development team has several additional goals that are not-yet-scheduled for a particular release window: Protocol Verification: This involves converting the JSIDL definition of a service into a PROMELA model, for validation by the SPIN model checking tool. Using PROMELA to model client and server interfaces will allow developers to formally validate JAUS services. End User Experience: We plan to conduct formal User Interface testing. This involves defining a set of tasks and use cases, asking users with various levels of JAUS experience to accomplish those tasks, and measuring performance and collecting feedback, to look for areas where the overall user experience can be improved. Improved Service Re-Use: JSIDL allows for inheritance of protocol descriptions, much like object-oriented programming languages allow child classes to re-use and extend behaviors defined by the parent class. At present, the generated code 'flattens' these state machines into a series of nested states which gives the correct interface behavior, but only if each single leaf (child) service is generated within its own component. This limits service re-use and can lead to a copy-and-paste of the same implementation across multiple components. The team is evaluating other inheritance solutions that would allow for multiple leaf (child) services to share access to a common parent, but at present the approach is sufficient to address the requirements of the JAUS Core Service Set. == Domains and application == The JAUS Tool Set is based on the JAUS Service Interface Definition Language (JSIDL), which was originally developed for application within the unmanned systems, or robotics, communities. As such, JTS has quickly gained acceptance as a tool for generation of services and interfaces compliant with the SAE AS-4 "JAUS" publications. Although usage statistics are not available, the Tool Set has been downloaded by representatives of US Army, Navy, Marines, and numerous defense contractors. It was also used in a commercial product called the JAUS Expansion Module sold by DeVivo AST, Inc. Since the JSIDL schema is independent of the data being exchanged, however, the Tool Set can be used for the design and implementation of a Service Oriented Architecture for any distributed systems environment that uses binary encoded message exchange. JSIDL is built on a two-layered architecture that separates the application layer and the transport layer, effectively decoupling the data being exchanges from the details of how that data moves from component to component. Furthermore, since the schema itself is widely generic, it's possible to define messages for any number of domains including but not limited to industrial control systems, remote monitoring and diagnostics, and web-based applications. == Licensing == JTS is released under the open source BSD license. The JSIDL Standard is available from the SAE. The Jr Middleware on which the Software Framework (Transport Layer) is based is open source under LGPL. Other packages distributed with JTS may have different licenses. == Sponsors == Development of the JAUS Tool Set was sponsored by several United States Department of Defense organizations: Office of Under Secretary of Defense for Acquisition, Technology & Logistics / Unmanned Warfare. Navy Program Executive Officer Littoral and Mine Navy Program Executive Officer Unmanned Aviation and Strike Weapons Office of Naval Research Air Force Research Lab
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Geoffrey J. Gordon

Geoffrey J. Gordon is a professor at the Machine Learning Department at Carnegie Mellon University in Pittsburgh and director of research at the Microsoft Montréal lab. He is known for his research in statistical relational learning (a subdiscipline of artificial intelligence and machine learning) and on anytime dynamic variants of the A search algorithm. His research interests include multi-agent planning, reinforcement learning, decision-theoretic planning, statistical models of difficult data (e.g. maps, video, text), computational learning theory, and game theory. Gordon received a B.A. in computer science from Cornell University in 1991, and a PhD at Carnegie Mellon in 1999.
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Is an AI Voice Assistant Worth It in 2026?

Trying to pick the best AI voice assistant? An AI voice assistant 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 voice assistant 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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