AI For Students Exam Generator

AI For Students Exam Generator — independent reviews, comparisons, pricing and step-by-step guides on Aizhi.

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  Personality computing

  Personality computing is a research field related to artificial intelligence and personality psychology that studies personality by means of computational techniques from different sources, including text, multimedia, and social networks. == Overview == Personality computing addresses three main problems involving personality: automatic personality recognition, perception, and synthesis. Automatic personality recognition is the inference of the personality type of target individuals from their digital footprint. Automatic personality perception is the inference of the personality attributed by an observer to a target individual based on some observable behavior. Automatic personality synthesis is the generation of the style or behaviour of artificial personalities in Avatars and virtual agents. Self-assessed personality tests or observer ratings are always exploited as the ground truth for testing and validating the performance of artificial intelligence algorithms for the automatic prediction of personality types. There is a wide variety of personality tests, such as the Myers Briggs Type Indicator (MBTI) or the MMPI, but the most used are tests based on the Five Factor Model such as the Revised NEO Personality Inventory. Personality computing can be considered as an extension or complement of Affective computing, where the former focuses on personality traits and the latter on affective states. A further extension of the two fields is Character Computing which combines various character states and traits including but not limited to personality and affect. == History == Personality computing began around 2005 with the pioneering research in personality recognition by Shlomo Argamon and later by François Mairesse. These works showed that personality traits could be inferred with reasonable accuracy from text, such as blogs, self-presentations, and email addresses. In 2008, the concept of "portable personality" for the distributed management of personality profiles has been developed. A few years later, research began in personality recognition and perception from multimodal and social signals, such as recorded meetings and voice calls. In the 2010s, the research focused mainly on personality recognition and perception from social media, helped by the first workshops organized by Fabio Celli. In particular personality was extracted from Facebook, Twitter and Instagram. In the same years, automatic personality synthesis helped improve the coherence of simulated behavior in virtual agents. Scientific works by Michal Kosinski demonstrated the validity of Personality Computing from different digital footprints, in particular from user preferences such as Facebook page likes, showed that machines can recognize personality better than humans and raised a warning against Cambridge Analytica and misuse of this kind of technology. == Applications == Personality computing techniques, in particular personality recognition and perception, have applications in Social media marketing, where they can help reducing the cost of advertising campaigns through psychological targeting.

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  AI Headshot Generators: Free vs Paid (2026)

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

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  Markovian discrimination

  Markovian discrimination is a class of spam filtering methods used in CRM114 and other spam filters to filter based on statistical patterns of transition probabilities between words or other lexical tokens in spam messages that would not be captured using simple bag-of-words naive Bayes spam filtering. == Markovian Discrimination vs. Bag-of-Words Discrimination == A bag-of-words model contains only a dictionary of legal words and their relative probabilities in spam and genuine messages. A Markovian model additionally includes the relative transition probabilities between words in spam and in genuine messages, where the relative transition probability is the likelihood that a given word will be written next, based on what the current word is. Put another way, a bag-of-words filter discriminates based on relative probabilities of single words alone regardless of phrase structure, while a Markovian word-based filter discriminates based on relative probabilities of either pairs of words, or, more commonly, short sequences of words. This allows the Markovian filter greater sensitivity to phrase structure. Neither naive Bayes nor Markovian filters are limited to the word level for tokenizing messages. They may also process letters, partial words, or phrases as tokens. In such cases, specific bag-of-words methods would correspond to general bag-of-tokens methods. Modelers can parameterize Markovian spam filters based on the relative probabilities of any such tokens' transitions appearing in spam or in legitimate messages. == Visible and Hidden Markov Models == There are two primary classes of Markov models, visible Markov models and hidden Markov models, which differ in whether the Markov chain generating token sequences is assumed to have its states fully determined by each generated token (the visible Markov models) or might also have additional state (the hidden Markov models). With a visible Markov model, each current token is modeled as if it contains the complete information about previous tokens of the message relevant to the probability of future tokens, whereas a hidden Markov model allows for more obscure conditional relationships. Since those more obscure conditional relationships are more typical of natural language messages including both genuine messages and spam, hidden Markov models are generally preferred over visible Markov models for spam filtering. Due to storage constraints, the most commonly employed model is a specific type of hidden Markov model known as a Markov random field, typically with a 'sliding window' or clique size ranging between four and six tokens.

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  How to Choose an AI Chatbot

  Looking for the best AI chatbot? An AI chatbot is software that uses machine learning to help you get more done — it can save you hours every week by automating repetitive work. Most options offer a generous free tier, with paid plans unlocking higher limits, faster processing, and team features. Whether you are a beginner or a pro, the right AI chatbot 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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  Database-as-IPC

  In computer programming, Database-as-IPC may be considered an anti-pattern where a disk persisted table in a database is used as the message queue store for routine inter-process communication (IPC) or subscribed data processing. If database performance is of concern, alternatives include sockets, network socket, or message queue. British computer scientist, Junade Ali, defined the Database-as-IPC Anti-Pattern as using a database to "schedule jobs or queue up tasks to be completed", noting that this anti-pattern centres around using a database for temporary messages instead of persistent data. == Controversy == The issue arises if there is a performance issue, and if additional systems (and servers) can be justified. In terms of performance, recent advancements in database systems provide more efficient mechanisms for signaling and messaging, and database systems also support memory (non-persisted) tables. There are databases with built-in notification mechanisms, such as PostgreSQL, SQL Server, and Oracle. These mechanisms and future improvements of database systems can make queuing much more efficient and avoid the need to set up a separate signaling or messaging queue system along with the server and management overhead. While MySQL doesn't have direct support for notifications, some workarounds are possible. However, they would be seen as non-standard and therefore more difficult to maintain.

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  Best AI Resume Builders in 2026

  Looking for the best AI resume builder? An AI resume builder is software that uses machine learning to help you get more done — it can save you hours every week by automating repetitive work. Most options offer a generous free tier, with paid plans unlocking higher limits, faster processing, and team features. Whether you are a beginner or a pro, the right AI resume builder 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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  Margin (machine learning)

  In machine learning, the margin of a single data point is defined to be the distance from the data point to a decision boundary. Note that there are many distances and decision boundaries that may be appropriate for certain datasets and goals. A margin classifier is a classification model that utilizes the margin of each example to learn such classification. There are theoretical justifications (based on the VC dimension) as to why maximizing the margin (under some suitable constraints) may be beneficial for machine learning and statistical inference algorithms. For a given dataset, there may be many hyperplanes that could classify it. One reasonable choice as the best hyperplane is the one that represents the largest separation, or margin, between the classes. Hence, one should choose the hyperplane such that the distance from it to the nearest data point on each side is maximized. If such a hyperplane exists, it is known as the maximum-margin hyperplane, and the linear classifier it defines is known as a maximum margin classifier (or, equivalently, the perceptron of optimal stability).

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  The Best Free AI Pair Programmer for Beginners

  Comparing the best AI pair programmer? An AI pair programmer 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 pair programmer 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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  Model-based clustering

  In statistics, cluster analysis is the algorithmic grouping of objects into homogeneous groups based on numerical measurements. Model-based clustering based on a statistical model for the data, usually a mixture model. This has several advantages, including a principled statistical basis for clustering, and ways to choose the number of clusters, to choose the best clustering model, to assess the uncertainty of the clustering, and to identify outliers that do not belong to any group. == Model-based clustering == Suppose that for each of n {\displaystyle n} observations we have data on d {\displaystyle d} variables, denoted by y i = ( y i , 1 , … , y i , d ) {\displaystyle y_{i}=(y_{i,1},\ldots ,y_{i,d})} for observation i {\displaystyle i} . Then model-based clustering expresses the probability density function of y i {\displaystyle y_{i}} as a finite mixture, or weighted average of G {\displaystyle G} component probability density functions: p ( y i ) = ∑ g = 1 G τ g f g ( y i ∣ θ g ) , {\displaystyle p(y_{i})=\sum _{g=1}^{G}\tau _{g}f_{g}(y_{i}\mid \theta _{g}),} where f g {\displaystyle f_{g}} is a probability density function with parameter θ g {\displaystyle \theta _{g}} , τ g {\displaystyle \tau _{g}} is the corresponding mixture probability where ∑ g = 1 G τ g = 1 {\displaystyle \sum _{g=1}^{G}\tau _{g}=1} . Then in its simplest form, model-based clustering views each component of the mixture model as a cluster, estimates the model parameters, and assigns each observation to cluster corresponding to its most likely mixture component. === Gaussian mixture model === The most common model for continuous data is that f g {\displaystyle f_{g}} is a multivariate normal distribution with mean vector μ g {\displaystyle \mu _{g}} and covariance matrix Σ g {\displaystyle \Sigma _{g}} , so that θ g = ( μ g , Σ g ) {\displaystyle \theta _{g}=(\mu _{g},\Sigma _{g})} . This defines a Gaussian mixture model. The parameters of the model, τ g {\displaystyle \tau _{g}} and θ g {\displaystyle \theta _{g}} for g = 1 , … , G {\displaystyle g=1,\ldots ,G} , are typically estimated by maximum likelihood estimation using the expectation-maximization algorithm (EM); see also EM algorithm and GMM model. Bayesian inference is also often used for inference about finite mixture models. The Bayesian approach also allows for the case where the number of components, G {\displaystyle G} , is infinite, using a Dirichlet process prior, yielding a Dirichlet process mixture model for clustering. === Choosing the number of clusters === An advantage of model-based clustering is that it provides statistically principled ways to choose the number of clusters. Each different choice of the number of groups G {\displaystyle G} corresponds to a different mixture model. Then standard statistical model selection criteria such as the Bayesian information criterion (BIC) can be used to choose G {\displaystyle G} . The integrated completed likelihood (ICL) is a different criterion designed to choose the number of clusters rather than the number of mixture components in the model; these will often be different if highly non-Gaussian clusters are present. === Parsimonious Gaussian mixture model === For data with high dimension, d {\displaystyle d} , using a full covariance matrix for each mixture component requires estimation of many parameters, which can result in a loss of precision, generalizabity and interpretability. Thus it is common to use more parsimonious component covariance matrices exploiting their geometric interpretation. Gaussian clusters are ellipsoidal, with their volume, shape and orientation determined by the covariance matrix. Consider the eigendecomposition of a matrix Σ g = λ g D g A g D g T , {\displaystyle \Sigma _{g}=\lambda _{g}D_{g}A_{g}D_{g}^{T},} where D g {\displaystyle D_{g}} is the matrix of eigenvectors of Σ g {\displaystyle \Sigma _{g}} , A g = diag { A 1 , g , … , A d , g } {\displaystyle A_{g}={\mbox{diag}}\{A_{1,g},\ldots ,A_{d,g}\}} is a diagonal matrix whose elements are proportional to the eigenvalues of Σ g {\displaystyle \Sigma _{g}} in descending order, and λ g {\displaystyle \lambda _{g}} is the associated constant of proportionality. Then λ g {\displaystyle \lambda _{g}} controls the volume of the ellipsoid, A g {\displaystyle A_{g}} its shape, and D g {\displaystyle D_{g}} its orientation. Each of the volume, shape and orientation of the clusters can be constrained to be equal (E) or allowed to vary (V); the orientation can also be spherical, with identical eigenvalues (I). This yields 14 possible clustering models, shown in this table: It can be seen that many of these models are more parsimonious, with far fewer parameters than the unconstrained model that has 90 parameters when G = 4 {\displaystyle G=4} and d = 9 {\displaystyle d=9} . Several of these models correspond to well-known heuristic clustering methods. For example, k-means clustering is equivalent to estimation of the EII clustering model using the classification EM algorithm. The Bayesian information criterion (BIC) can be used to choose the best clustering model as well as the number of clusters. It can also be used as the basis for a method to choose the variables in the clustering model, eliminating variables that are not useful for clustering. Different Gaussian model-based clustering methods have been developed with an eye to handling high-dimensional data. These include the pgmm method, which is based on the mixture of factor analyzers model, and the HDclassif method, based on the idea of subspace clustering. The mixture-of-experts framework extends model-based clustering to include covariates. == Example == We illustrate the method with a dateset consisting of three measurements (glucose, insulin, sspg) on 145 subjects for the purpose of diagnosing diabetes and the type of diabetes present. The subjects were clinically classified into three groups: normal, chemical diabetes and overt diabetes, but we use this information only for evaluating clustering methods, not for classifying subjects. The BIC plot shows the BIC values for each combination of the number of clusters, G {\displaystyle G} , and the clustering model from the Table. Each curve corresponds to a different clustering model. The BIC favors 3 groups, which corresponds to the clinical assessment. It also favors the unconstrained covariance model, VVV. This fits the data well, because the normal patients have low values of both sspg and insulin, while the distributions of the chemical and overt diabetes groups are elongated, but in different directions. Thus the volumes, shapes and orientations of the three groups are clearly different, and so the unconstrained model is appropriate, as selected by the model-based clustering method. The classification plot shows the classification of the subjects by model-based clustering. The classification was quite accurate, with a 12% error rate as defined by the clinical classification. Other well-known clustering methods performed worse with higher error rates, such as single-linkage clustering with 46%, average link clustering with 30%, complete-linkage clustering also with 30%, and k-means clustering with 28%. == Outliers in clustering == An outlier in clustering is a data point that does not belong to any of the clusters. One way of modeling outliers in model-based clustering is to include an additional mixture component that is very dispersed, with for example a uniform distribution. Another approach is to replace the multivariate normal densities by t {\displaystyle t} -distributions, with the idea that the long tails of the t {\displaystyle t} -distribution would ensure robustness to outliers. However, this is not breakdown-robust. A third approach is the "tclust" or data trimming approach which excludes observations identified as outliers when estimating the model parameters. == Non-Gaussian clusters and merging == Sometimes one or more clusters deviate strongly from the Gaussian assumption. If a Gaussian mixture is fitted to such data, a strongly non-Gaussian cluster will often be represented by several mixture components rather than a single one. In that case, cluster merging can be used to find a better clustering. A different approach is to use mixtures of complex component densities to represent non-Gaussian clusters. == Non-continuous data == === Categorical data === Clustering multivariate categorical data is most often done using the latent class model. This assumes that the data arise from a finite mixture model, where within each cluster the variables are independent. === Mixed data === These arise when variables are of different types, such as continuous, categorical or ordinal data. A latent class model for mixed data assumes local independence between the variable. The location model relaxes the local independence assumption. The clustMD approach assumes that the observed variables are manifestations of underlying continuous Gaussian latent

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  Corpus language

  A corpus language is a language that has no living speakers but for which numerous records produced by its native speakers survive. Examples of corpus languages are Ancient Greek, Latin, the Egyptian language, Old English, Old Norse, Elamite, and Sanskrit. Some corpus languages, such as Ancient Greek and Latin, left very large corpora and therefore can be fully reconstructed, even though some details of pronunciation may be unclear. Such languages can be used even today, as is the case with Sanskrit and Latin. Other languages have such limited corpora that some important words—e.g., some pronouns—are lacking in the corpora. Examples of these are Ugaritic and Gothic. Languages attested only by a few words, often names, and a few phrases, are called Trümmersprache (literally "rubble languages") in German linguistics. These can be reconstructed only in a very limited way, and often their genetic relationship to other languages remains unclear. Examples are Dalmatian, Etruscan, also known as Rasenna, Dadanitic, a Semitic language that may be close to classical Arabic, Lombardic, Burgundian, Vandalic, and Oscan, Umbrian, and Faliscan, all Italic languages that were related to Latin. Corpus languages are studied using the methods of corpus linguistics, but corpus linguistics can also be used (and is commonly used) for the study of the writings and other records of living languages. Not all extinct languages are corpus languages, since there are many extinct languages in which few or no writings or other records survive, as is the case in the vast majority of languages that have ever existed.

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  AI Paraphrasing Tools: Free vs Paid (2026)

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

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  Samer Hassan

  Samer Hassan is a computer scientist, social scientist, activist and researcher, focused on the study of the collaborative economy, online communities and decentralized technologies. He is an associate professor at Universidad Complutense de Madrid (Spain) and Faculty Associate at the Berkman Klein Center for Internet & Society at Harvard University. He is the recipient of an ERC Grant of 1.5M€ with the P2P Models project, to research blockchain-based decentralized autonomous organizations for the collaborative economy. == Education and career == Hassan is a Spanish/Lebanese scholar with an interdisciplinary background, which combines computer sciences with social sciences and activism. He received a degree in Computer Science and MSc in Artificial Intelligence from the Universidad Complutense de Madrid (UCM) in Spain. He also studied three years of Political Science at the distance learning university UNED. He then pursued a PhD in Social Simulation at the department of Software Engineering and Artificial Intelligence of UCM, supervised by the computer scientist Juan Pavón and the sociologist Millán Arroyo-Menéndez. He has been researching in several institutions, funded by several scholarships and awards, most notably Harvard's Real Colegio Complutense, and the Spanish postdoctoral grants Juan de la Cierva and José Castillejo. Thus, he was a visiting researcher at the Centre for Research in Social Simulation, in the Department of Sociology at the University of Surrey in the UK, working under the supervision of Nigel Gilbert (2007-2008), and a lecturer at the American University of Science and Technology in Lebanon (2010–11). He was selected as Fellow at the Berkman Klein Center for Internet & Society at Harvard University (2015-2017) and is presently a Faculty Associate at the same structure. Starting in 2024, he joined, as affiliate faculty, the Institute for Digital Cooperative Economy (The New School), part of the Platform Cooperativism Consortium. == Activism and social engagement == As an activist, Hassan has been engaged in both offline (La Tabacalera de Lavapiés, Medialab-Prado) and online (Ourproject.org, Barrapunto, Wikipedia) initiatives. He was accredited as a grassroots facilitator by the Altekio Cooperative. He co-founded the Comunes Nonprofit in 2009 and the Move Commons webtool project in 2010. He has co-organized practitioner-oriented workshops on platform co-ops and free/open source decentralized tools for communities, and has presented his work in non-academic conferences of Mozilla, the Internet Archive, and others. As a privacy advocate, he co-created a course on cyber-ethics which has been teaching since 2013 (as of 2021). He was co-founder of the Sci-Fdi Spanish science-fiction magazine. His gender is non-binary and uses he/they pronouns. == Work == Hassan's interdisciplinary research spans multiple fields, including online communities, online governance, online collaboration, decentralized technologies, blockchain-based decentralized autonomous organizations, free/libre/open source software, Commons-based peer production, agent-based social simulation, social movements and cyberethics. He has published more than 60 works in these fields. Hassan's PhD thesis focused on the methodological challenges for building data-driven social simulation models. The main model built simulated the transition from modern values to postmodern values in Spain. His methodological work also explored the combination of different artificial intelligence technologies, i.e. software agents with fuzzy logic, data mining, natural language processing, and microsimulation. In his postdoctoral period, he focused on experimenting with multiple software systems to facilitate the collaborative economy, e.g. semantic-web labelling for commons-based initiatives, distribution of value in peer production communities, agent-supported online assemblies, decentralized real-time collaborative software, decentralized blockchain based reputation, or blockchain-enabled commons governance. Hassan was Principal Investigator of the UCM partner in the EU-funded P2Pvalue project on building decentralized web-tools for collaborative communities. As such, he led the team that created SwellRT, a federated backend-as-a-service focused to ease development of apps featuring real-time collaboration. Intellectual Property of this project was transferred to the Apache Software Foundation in 2017. As part of this research line, Hassan's team also develop two SwellRT-based apps, "Teem" for management of social collectives and Jetpad, a federated real time editor. He presented the innovations concerning these software at Harvard's Berkman Klein Center and Harvard's Center for Research on Computation and Society. Other research lines offered outcomes beyond publications. "Wikichron", coled by Javier Arroyo, is a web tool to visualize MediaWiki community metrics, currently in production and available for third-parties. "Decentralized Science", led by Hassan's PhD student Ámbar Tenorio-Fornés, is a framework to facilitate decentralized infrastructure and open peer review in the scientific publication process, which has been selected by the European Commission to receive funding as a spin-off social enterprise. His research on blockchain and crowdfunding models awarded him with a commission from Triple Canopy. His team pushed forward a mapping of the ecosystem of blockchain for social good, led by the Joint Research Centre and published by the European Commission. As part of his ERC project P2P Models, Hassan and his team –including Silvia Semenzin– are investigating whether blockchain technology and Decentralized Autonomous Organizations could contribute to improving the governance of commons-oriented communities, both online and offline. Their work has been showcased for tackling the impact of blockchain on governance, proposing alternatives to the current sharing economy, emerging forms of techno-social systems like NFTs or prediction markets, or giving relevance to gender issues in the field. Hassan was invited to present the project achievements in Harvard Kennedy School, MIT Media Lab, Harvard's Data Privacy Lab, Harvard's Center for Research on Computation and Society, and Harvard's SEAS EconCS. British MP and Opposition Leader Ed Miliband showcased his research and its potential impact on policy. The project made public its way of organizing and its core values. In particular, it has shown a commitment to diversity as a core value in hiring, or choosing case studies. == Selected works == Arroyo, Javier; Davó, David; Martínez-Vicente, Elena; Faqir-Rhazoui, Youssef; Hassan, Samer (8 November 2022). "DAO-Analyzer: Exploring Activity and Participation in Blockchain Organizations" (PDF). Companion Publication of the 2022 Conference on Computer Supported Cooperative Work and Social Computing. CSCW'22 Companion. New York, NY, USA: Association for Computing Machinery. pp. 193–196. doi:10.1145/3500868.3559707. ISBN 978-1-4503-9190-0. Rozas, David; Tenorio-Fornés, Antonio; Díaz-Molina, Silvia; Hassan, Samer (2021). "When Ostrom Meets Blockchain: Exploring the Potentials of Blockchain for Commons Governance". SAGE Open. 11 (1): 215824402110025. doi:10.1177/21582440211002526. ISSN 2158-2440. Faqir-Rhazoui, Youssef; Ariza-Garzón, Miller-Janny; Arroyo, Javier; Hassan, Samer (8 May 2021). "Effect of the Gas Price Surges on User Activity in the DAOs of the Ethereum Blockchain" (PDF). Extended Abstracts of the 2021 CHI Conference on Human Factors in Computing Systems. CHI EA '21. New York, NY, USA: Association for Computing Machinery. pp. 1–7. doi:10.1145/3411763.3451755. ISBN 978-1-4503-8095-9. Hassan, Samer; Filippi, Primavera De (20 April 2021). "Decentralized Autonomous Organization". Internet Policy Review. 10 (2). doi:10.14763/2021.2.1556. hdl:10419/235960. ISSN 2197-6775. Joint Research Centre (European Commission); Hassan, Samer; Hakami, Anna; Brekke, Jaya Klara; De Filippi, Primavera; Lopéz Morales, Genoveva; Pólvora, Alexandre; Orgaz Alonso, Christian; Bodó, Balázs (2020). Scanning the European ecosystem of distributed ledger technologies for social and public good: what, why, where, how, and ways to move forward. LU: Publications Office of the European Union. doi:10.2760/300796. ISBN 978-92-76-21578-3. Filippi, Primavera De; Hassan, Samer (14 November 2016). "Blockchain technology as a regulatory technology: From code is law to law is code". First Monday. arXiv:1801.02507. doi:10.5210/fm.v21i12.7113. ISSN 1396-0466.

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  Server.com

  Server.com is a domain name that was owned by software as a service (SaaS) company Server Corporation. They offered a suite of services from 1996 until 2007. It was the first SaaS site to offer a variety of services and the first to use the term WebApp to describe its services. It was selected as an Incredibly Useful Site by Yahoo! Internet Life magazine. net magazine listed Server.com among the 100 most influential websites of all time. Server.com launched in 1996 offering the first online personal information manager. In 1997, they rolled out the first threaded message board service; the first web based mailing list manager; one of the first online calendar services; and one of the first online form builders. In 2000, Server.com partnered with NBCi and became server.snap.com until 2001. In 2001, Server.com was serving 100 million monthly pageviews. Media Life declared it one of the 20 biggest ad domains on the Web. In 2002, Server.com developed one of the first web-based RSS aggregators. In 2007, all services were moved to YourWebApps.com. The domain name Server.com was sold in 2009 for $770,000.

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  AI Image Generators Reviews: What Actually Works in 2026

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

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  Powerset construction

  In the theory of computation and automata theory, the powerset construction or subset construction is a standard method for converting a nondeterministic finite automaton (NFA) into a deterministic finite automaton (DFA) that recognizes the same formal language. It is important in theory because it establishes that NFAs, despite their additional flexibility, are unable to recognize any language that cannot be recognized by some DFA. It is also important in practice for converting easier-to-construct NFAs into more efficiently executable DFAs. However, if the NFA has n states, the resulting DFA may have up to 2n states, an exponentially larger number, which sometimes makes the construction impractical for large NFAs. The construction, sometimes called the Rabin–Scott powerset construction (or subset construction) to distinguish it from similar constructions for other types of automata, was first published by Michael O. Rabin and Dana Scott in 1959. == Intuition == To simulate the operation of a DFA on a given input string, one needs to keep track of a single state at any time: the state that the automaton will reach after seeing a prefix of the input. In contrast, to simulate an NFA, one needs to keep track of a set of states: all of the states that the automaton could reach after seeing the same prefix of the input, according to the nondeterministic choices made by the automaton. If, after a certain prefix of the input, a set S of states can be reached, then after the next input symbol x the set of reachable states is a deterministic function of S and x. Therefore, the sets of reachable NFA states play the same role in the NFA simulation as single DFA states play in the DFA simulation, and in fact the sets of NFA states appearing in this simulation may be re-interpreted as being states of a DFA. == Construction == The powerset construction applies most directly to an NFA that does not allow state transformations without consuming input symbols (aka: "ε-moves"). Such an automaton may be defined as a 5-tuple (Q, Σ, T, q0, F), in which Q is the set of states, Σ is the set of input symbols, T is the transition function (mapping a state and an input symbol to a set of states), q0 is the initial state, and F is the set of accepting states. The corresponding DFA has states corresponding to subsets of Q. The initial state of the DFA is {q0}, the (one-element) set of initial states. The transition function of the DFA maps a state S (representing a subset of Q) and an input symbol x to the set T(S,x) = ∪{T(q,x) | q ∈ S}, the set of all states that can be reached by an x-transition from a state in S. A state S of the DFA is an accepting state if and only if at least one member of S is an accepting state of the NFA. In the simplest version of the powerset construction, the set of all states of the DFA is the powerset of Q, the set of all possible subsets of Q. However, many states of the resulting DFA may be useless as they may be unreachable from the initial state. An alternative version of the construction creates only the states that are actually reachable. === NFA with ε-moves === For an NFA with ε-moves (also called an ε-NFA), the construction must be modified to deal with these by computing the ε-closure of states: the set of all states reachable from some given state using only ε-moves. Van Noord recognizes three possible ways of incorporating this closure computation in the powerset construction: Compute the ε-closure of the entire automaton as a preprocessing step, producing an equivalent NFA without ε-moves, then apply the regular powerset construction. This version, also discussed by Hopcroft and Ullman, is straightforward to implement, but impractical for automata with large numbers of ε-moves, as commonly arise in natural language processing application. During the powerset computation, compute the ε-closure { q ′ | q → ε ∗ q ′ } {\displaystyle \{q'~|~q\to _{\varepsilon }^{}q'\}} of each state q that is considered by the algorithm (and cache the result). During the powerset computation, compute the ε-closure { q ′ | ∃ q ∈ Q ′ , q → ε ∗ q ′ } {\displaystyle \{q'~|~\exists q\in Q',q\to _{\varepsilon }^{}q'\}} of each subset of states Q' that is considered by the algorithm, and add its elements to Q'. === Multiple initial states === If NFAs are defined to allow for multiple initial states, the initial state of the corresponding DFA is the set of all initial states of the NFA, or (if the NFA also has ε-moves) the set of all states reachable from initial states by ε-moves. == Example == The NFA below has four states; state 1 is initial, and states 3 and 4 are accepting. Its alphabet consists of the two symbols 0 and 1, and it has ε-moves. The initial state of the DFA constructed from this NFA is the set of all NFA states that are reachable from state 1 by ε-moves; that is, it is the set {1,2,3}. A transition from {1,2,3} by input symbol 0 must follow either the arrow from state 1 to state 2, or the arrow from state 3 to state 4. Additionally, neither state 2 nor state 4 have outgoing ε-moves. Therefore, T({1,2,3},0) = {2,4}, and by the same reasoning the full DFA constructed from the NFA is as shown below. As can be seen in this example, there are five states reachable from the start state of the DFA; the remaining 11 sets in the powerset of the set of NFA states are not reachable. == Complexity == Because the DFA states consist of sets of NFA states, an n-state NFA may be converted to a DFA with at most 2n states. For every n, there exist n-state NFAs such that every subset of states is reachable from the initial subset, so that the converted DFA has exactly 2n states, giving Θ(2n) worst-case time complexity. A simple example requiring nearly this many states is the language of strings over the alphabet {0,1} in which there are at least n characters, the nth from last of which is 1. It can be represented by an (n + 1)-state NFA, but it requires 2n DFA states, one for each n-character suffix of the input; cf. picture for n=4. == Applications == Brzozowski's algorithm for DFA minimization uses the powerset construction, twice. It converts the input DFA into an NFA for the reverse language, by reversing all its arrows and exchanging the roles of initial and accepting states, converts the NFA back into a DFA using the powerset construction, and then repeats its process. Its worst-case complexity is exponential, unlike some other known DFA minimization algorithms, but in many examples it performs more quickly than its worst-case complexity would suggest. Safra's construction, which converts a non-deterministic Büchi automaton with n states into a deterministic Muller automaton or into a deterministic Rabin automaton with 2O(n log n) states, uses the powerset construction as part of its machinery.

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