AI Face Look

AI Face Look — independent reviews, comparisons, pricing and step-by-step guides on Aizhi.

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  Masking (art)

  In art, craft, and engineering, masking is the use of materials to protect areas from change, or to focus change on other areas. This can describe either the techniques and materials used to control the development of a work of art by protecting a desired area from change; or a phenomenon that (either intentionally or unintentionally) causes a sensation to be concealed from conscious attention. The term is derived from the word mask, in the sense that it hides the face from view. == In painting == Masking materials supplement a painter's dexterity and choice of applicator to control where paint is laid. Examples include the use of a stencil or masking tape to protect areas which are not to be painted. === Solid masks === Most solid masks require an adhesive to hold the mask in place while work is performed. Some, such as masking tape and frisket, come with adhesive pre-applied. Solid masks are readily available in bulk, and are used in large painting jobs. Paper products Kraft paper Butcher paper Masking tape Plastic film Frisket Polyester tape Stencils Silk screen === Liquid masks === Liquid masks are preferred where precision is needed; they prevent paint from seeping underneath, resulting in clean edges. Care must be taken to remove them without damaging the work underneath. Latex or other polymers Molten wax Gesso, typically a substrate for painting, but can also be applied to achieve masking effects == In photography == Masks used for photography are used to enhance the quality of an image. Representations of a scene—whether film, video display, or printed—do not have the dynamic contrast range available to the human eye looking directly at the same scene. Adjusting the contrast in an image helps restore some of the perceived qualities of the original scene. These adjustments are typically performed on "blown-out" highlights, and "crushed" or "muddy" shadow areas, where clipping has occurred; or on desaturated colors. Photographic masks are peculiar in that they are produced from the image they will alter, an exercise in recursion. Masks used to produce other effects are similar to those used in painting. === Controlling exposure === ==== Film ==== The basic methods of controlling exposure are dodging and burning, which respectively lighten (reduce exposure) and darken (increase exposure) areas of an image. The tools a film photographer uses range from shaped pieces of black material (such as studio foil, foam, and paper) to the photographer's hands. To create a photographic mask, a sheet of negative film is contact-exposed to the original film negative or slide positive in a particular way. Both films are then combined to produce a processed positive. The process is similar when applied using digital techniques: the inverse of the working image is reduced to an image mask; filters or other adjustments are then applied, using the mask to selectively block portions of the image. ==== Digital ==== Image editors offer at the very least a "Select All" command and a rectangular "marquee" selection tool. (The word "marquee" describes the "crawling ants" border used to highlight the active region.) Once a selection is created, further changes to the image will be confined to that area. To continue editing the rest of the image, the selection is either "deselected" or the entire image is selected. Advanced suites offer more ways to select portions of an image, as well as ways to combine these selections through. Selection masks can be switched between an editable greyscale image and a mask. They allow the user to create a mask using the suite's painting tools. === Contrast masking === When the contrast range of an image needs to be adjusted, a contrast mask is a simple solution. The processed image resembles what would be achieved when exposing through a neutral density filter, but the effects are focused highly upon the extreme regions of the image. The blocking areas of the mask coincide with the highlights of the image, and the permissive areas with the shadows, resulting in more detail appearing in each. ==== Film ==== The mask is often made from high-quality black-and-white film, such as Kodak Technical Pan, which allows for a degree of softening on the mask. Its processing time is reduced so as to not completely oppose the original negative. Both negatives are combined and registered, and collectively exposed with additional time to compensate for the presence of the mask. ==== Digital ==== Contrast masking is made simpler with digital editing. A grayscale version of the image is produced, either by desaturation or by calculating selected ratios of the image's color channels, inverted, and blurred. The mask and original image are blended together to produce the final processed image. Some image editors allow for refinement of the effect by changing the strength of the blend. Contrast masking can be considered to be the opposite of gamma correction, which adjusts the midtones of an image. Effects similar to contrast masking can be achieved by adjusting the response curves of an image. === Unsharp masking === A derivative of contrast masking is unsharp masking, an unusual term for a process intended to increase the apparent sharpness (acutance) of an image. Unsharp masking uses a blurred form of the image to increase contrast along regions of moderate contrast difference. Around edges, the blur region causes highlights to overexpose and shadows to underexpose. Taken to an extreme, the edges become overly visible and detract from the quality of the image—this is referred to as halation. Unsharp masking does not increase the actual sharpness, as it cannot recover details lost to blurring. ==== Film ==== Unsharp masking allows the photographer to sharpen areas that have become blurred in the original negative, due to long shutter speed/exposure time, or from using a wide aperture/"fast" lens. When creating the unsharp mask, extra space or diffusing material is added between the image and the mask to produce the necessary blur. ==== Digital ==== Unsharp masking has become automated in digital editing, with higher-end suites offering the process as a "tool" or "filter" in their standard sharpening kits—the actual creation of a mask is bypassed in favor of calculations that represent the mask's effect. The process depends on three factors: the radius of the blur, the strength of the effect, and the threshold degree of contrast above which the effect will be applied. (Adjusting the threshold allows the editor to apply the effect selectively upon moderately defined edges and ignore image noise.) Unsharp masking is computationally more complex than other sharpening algorithms, but results in a higher-quality remedy. Deconvolution allows for truer sharpening, but is much more complex than unsharp masking.

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  Concordance (publishing)

  A concordance is an alphabetical list of the principal words used in a book or body of work, listing every instance of each word with its immediate context. Historically, concordances have been compiled only for works of special importance, such as the Vedas, Bible, Qur'an or the works of Shakespeare, James Joyce or classical Latin and Greek authors, because of the time, difficulty, and expense involved in creating a concordance in the pre-computer era. A concordance is more than an index, with additional material such as commentary, definitions and topical cross-indexing which makes producing one a labor-intensive process even when assisted by computers. In the precomputing era, search technology was unavailable, and a concordance offered readers of long works such as the Bible something comparable to search results for every word that they would have been likely to search for. Today, the ability to combine the result of queries concerning multiple terms (such as searching for words near other words) has reduced interest in concordance publishing. In addition, mathematical techniques such as latent semantic indexing have been proposed as a means of automatically identifying linguistic information based on word context. A bilingual concordance is a concordance based on aligned parallel text. A topical concordance is a list of subjects that a book covers (usually The Bible), with the immediate context of the coverage of those subjects. Unlike a traditional concordance, the indexed word does not have to appear in the verse. The best-known topical concordance is Nave's Topical Bible. The first Bible concordance was compiled for the Vulgate Bible by Hugh of St Cher (d.1262), who employed 500 friars to assist him. In 1448, Rabbi Mordecai Nathan completed a concordance to the Hebrew Bible. It took him ten years. A concordance to the Greek New Testament was published in 1546 by Sixt Birck, and the Septuagint was done a by Conrad Kircher in 1602. The first concordance to the English Bible was published in 1550 by John Merbecke. According to Cruden, it did not employ the verse numbers devised by Robert Stephens in 1545, but "the pretty large concordance" of Mr Cotton did. Then followed Cruden's Concordance and Strong's Concordance. == Use in linguistics == Concordances are frequently used in linguistics, when studying a text. For example: comparing different usages of the same word analysing keywords analysing word frequencies finding and analysing phrases and idioms finding translations of subsentential elements, e.g. terminology, in bitexts and translation memories creating indexes and word lists (also useful for publishing) Concordancing techniques are widely used in national text corpora such as American National Corpus (ANC), British National Corpus (BNC), and Corpus of Contemporary American English (COCA) available on-line. Stand-alone applications that employ concordancing techniques are known as concordancers or more advanced corpus managers. Some of them have integrated part-of-speech taggers (POS taggers) and enable the user to create their own POS-annotated corpora to conduct various types of searches adopted in corpus linguistics. == Inversion == The reconstruction of the text of some of the Dead Sea Scrolls involved a concordance. Access to some of the scrolls was governed by a "secrecy rule" that allowed only the original International Team or their designates to view the original materials. After the death of Roland de Vaux in 1971, his successors repeatedly refused to even allow the publication of photographs to other scholars. This restriction was circumvented by Martin Abegg in 1991, who used a computer to "invert" a concordance of the missing documents made in the 1950s which had come into the hands of scholars outside of the International Team, to obtain an approximate reconstruction of the original text of 17 of the documents. This was soon followed by the release of the original text of the scrolls.

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  Australian Geoscience Data Cube

  The Australian Geoscience Data Cube (AGDC) is an approach to storing, processing and analyzing large collections of Earth observation data. The technology is designed to meet challenges of national interest by being agile and flexible with vast amounts of layered grid data. The AGDC reduces processing time of traditional image analysis by calibrating, pre-computing known extents, pixel alignment and storing metadata in a cell lattice structure. The temporal-pixel aligned data can often be analysed faster across space and time dimensions than previous scene based techniques. This allows the AGDC to be flexible in tackling future challenges and improve analysis times on every-increasing data repositories of earth observation. The AGDC has also been used internationally to allow countries to maintain ecologically sustainable programs and reduce the difficulty curve of utilizing Remote Sensing data. == Background == The AGDC was originally conceived by Geoscience Australia but is now maintained in a partnership between Geoscience Australia, Commonwealth Scientific and Industrial Research Organisation (CSIRO) and National Computational Infrastructure National Facility (Australia) (NCI). This is made possible by the funding from the partnership and a number of organisations such as National Collaborative Research Infrastructure Strategy (NCRIS). == Analysis ready data, ingestion and indexing == The data processed in the cube is made analysis ready before being ingested and indexed into the AGDC. Analysis ready data is pre-processed data that has applied corrections for instrument calibration (gains and offsets), geolocation (spatial alignment) and radiometry (solar illumination, incidence angle, topography, atmospheric interference). The ingestion process manages the translation of datasets into the storage units while maintaining a database index. The data within the storage and index can be accessed via API calls often compiled within code such as Python (programming language). Example: s2a_l1c = dc.load(product='s2a_level1c_granule',x=(147.36, 147.41), y=(-35.1, -35.15), measurements=['04','03','02'], output_crs='EPSG:4326', resolution=(-0.00025,0.00025)) === Datasets currently stored === Geoscience Australia Landsat Surface Reflectance (1987 to present) Landsat Pixel Quality Landsat Fractional Cover Landsat NDVI === Datasets that have been piloted === USGS Landsat Surface Reflectance SRTM DEM Himawari 8 MODIS Sentinel-2 L1C / S2A Australian Gridded Climate Data == Open source == The AGDC code base is situated in GitHub as an open repository. The core code base moved to the Open Data Cube in early 2017 as part of an international collaboration. Whilst the code base is the Open Data Cube, individual cubes exist as their own right such as the AGDC on the National Computational Infrastructure National Facility (Australia) (NCI) using the High-Performance Computing Cluster HPCC. The core code can be installed on personal computers or public computers (using git) and has many unit tests. Documentation for the code base exists on Read the Docs. == Challenges of the AGDC == The AGDC is designed to meet nationally significant challenges such as the following. Sustainability Environment Water resource management Disaster assist Policy development Community planning Forest preservation Carbon measurement == International awards == The AGDC won the 2016 Content Platform of the Year award from Geospatial World Forum.

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  Regulation of algorithms

  Regulation of algorithms, or algorithmic regulation, is the creation of laws, rules and public sector policies for promotion and regulation of algorithms, particularly in artificial intelligence and machine learning. For the subset of AI algorithms, the term regulation of artificial intelligence is used. The regulatory and policy landscape for artificial intelligence (AI) is an emerging issue in jurisdictions globally, including in the European Union. Regulation of AI is considered necessary to both encourage AI and manage associated risks, but challenging. Another emerging topic is the regulation of blockchain algorithms (Use of the smart contracts must be regulated) and is mentioned along with regulation of AI algorithms. Many countries have enacted regulations of high frequency trades, which is shifting due to technological progress into the realm of AI algorithms. The motivation for regulation of algorithms is the apprehension of losing control over the algorithms, whose impact on human life increases. Multiple countries have already introduced regulations in case of automated credit score calculation—right to explanation is mandatory for those algorithms. For example, The IEEE has begun developing a new standard to explicitly address ethical issues and the values of potential future users. Bias, transparency, and ethics concerns have emerged with respect to the use of algorithms in diverse domains ranging from criminal justice to healthcare—many fear that artificial intelligence could replicate existing social inequalities along race, class, gender, and sexuality lines. == Regulation of artificial intelligence == === Public discussion === In 2016, Joy Buolamwini founded Algorithmic Justice League after a personal experience with biased facial detection software in order to raise awareness of the social implications of artificial intelligence through art and research. In 2017 Elon Musk advocated regulation of algorithms in the context of the existential risk from artificial general intelligence. According to NPR, the Tesla CEO was "clearly not thrilled" to be advocating for government scrutiny that could impact his own industry, but believed the risks of going completely without oversight are too high: "Normally the way regulations are set up is when a bunch of bad things happen, there's a public outcry, and after many years a regulatory agency is set up to regulate that industry. It takes forever. That, in the past, has been bad but not something which represented a fundamental risk to the existence of civilisation." In response, some politicians expressed skepticism about the wisdom of regulating a technology that is still in development. Responding both to Musk and to February 2017 proposals by European Union lawmakers to regulate AI and robotics, Intel CEO Brian Krzanich has argued that artificial intelligence is in its infancy and that it is too early to regulate the technology. Instead of trying to regulate the technology itself, some scholars suggest to rather develop common norms including requirements for the testing and transparency of algorithms, possibly in combination with some form of warranty. One suggestion has been for the development of a global governance board to regulate AI development. In 2020, the European Union published its draft strategy paper for promoting and regulating AI. Algorithmic tacit collusion is a legally dubious antitrust practise committed by means of algorithms, which the courts are not able to prosecute. This danger concerns scientists and regulators in EU, US and beyond. European Commissioner Margrethe Vestager mentioned an early example of algorithmic tacit collusion in her speech on "Algorithms and Collusion" on March 16, 2017, described as follows: "A few years ago, two companies were selling a textbook called The Making of a Fly. One of those sellers used an algorithm which essentially matched its rival’s price. That rival had an algorithm which always set a price 27% higher than the first. The result was that prices kept spiralling upwards, until finally someone noticed what was going on, and adjusted the price manually. By that time, the book was selling – or rather, not selling – for 23 million dollars a copy." In 2018, the Netherlands employed an algorithmic system SyRI (Systeem Risico Indicatie) to detect citizens perceived being high risk for committing welfare fraud, which quietly flagged thousands of people to investigators. This caused a public protest. The district court of Hague shut down SyRI referencing Article 8 of the European Convention on Human Rights (ECHR). In 2020, algorithms assigning exam grades to students in the UK sparked open protest under the banner "Fuck the algorithm." This protest was successful and the grades were taken back. In 2024, the Munich Convention on AI, Data and Human Rights was introduced as part of growing international efforts to regulate artificial intelligence through a human rights lens. Developed through a collaborative drafting process involving scholars from the Technical University of Munich, Stellenbosch University, Ulster University, and KNUST, the initiative calls for an international conversation on a binding treaty to safeguard human rights and the principles enshrined in the UN Charter in the age of AI. === Implementation === AI law and regulations can be divided into three main topics, namely governance of autonomous intelligence systems, responsibility and accountability for the systems, and privacy and safety issues. The development of public sector strategies for management and regulation of AI has been increasingly deemed necessary at the local, national, and international levels and in fields from public service management to law enforcement, the financial sector, robotics, the military, and international law. There are many concerns that there is not enough visibility and monitoring of AI in these sectors. In the United States financial sector, for example, there have been calls for the Consumer Financial Protection Bureau to more closely examine source code and algorithms when conducting audits of financial institutions' non-public data. In the United States, on January 7, 2019, following an Executive Order on 'Maintaining American Leadership in Artificial Intelligence', the White House's Office of Science and Technology Policy released a draft Guidance for Regulation of Artificial Intelligence Applications, which includes ten principles for United States agencies when deciding whether and how to regulate AI. In response, the National Institute of Standards and Technology has released a position paper, the National Security Commission on Artificial Intelligence has published an interim report, and the Defense Innovation Board has issued recommendations on the ethical use of AI. In April 2016, for the first time in more than two decades, the European Parliament adopted a set of comprehensive regulations for the collection, storage, and use of personal information, the General Data Protection Regulation (GDPR)1 (European Union, Parliament and Council 2016). The GDPR's policy on the right of citizens to receive an explanation for algorithmic decisions highlights the pressing importance of human interpretability in algorithm design. In 2016, China published a position paper questioning the adequacy of existing international law to address the eventuality of fully autonomous weapons, becoming the first permanent member of the U.N. Security Council to broach the issue, and leading to proposals for global regulation. In the United States, steering on regulating security-related AI is provided by the National Security Commission on Artificial Intelligence. In 2017, the U.K. Vehicle Technology and Aviation Bill imposes liability on the owner of an uninsured automated vehicle when driving itself and makes provisions for cases where the owner has made "unauthorized alterations" to the vehicle or failed to update its software. Further ethical issues arise when, e.g., a self-driving car swerves to avoid a pedestrian and causes a fatal accident. In 2021, the European Commission proposed the Artificial Intelligence Act. == Algorithm certification == There is a concept of algorithm certification emerging as a method of regulating algorithms. Algorithm certification involves auditing whether the algorithm used during the life cycle 1) conforms to the protocoled requirements (e.g., for correctness, completeness, consistency, and accuracy); 2) satisfies the standards, practices, and conventions; and 3) solves the right problem (e.g., correctly model physical laws), and satisfies the intended use and user needs in the operational environment. == Regulation of blockchain algorithms == Blockchain systems provide transparent and fixed records of transactions and hereby contradict the goal of the European GDPR, which is to give individuals full control of their private data. By implementing the Decree on Development of Digital Economy, Bel

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  Conditional random field

  Conditional random fields (CRFs) are a class of statistical modeling methods often applied in pattern recognition and machine learning and used for structured prediction. Whereas a classifier predicts a label for a single sample without considering "neighbouring" samples, a CRF can take context into account. To do so, the predictions are modelled as a graphical model, which represents the presence of dependencies between the predictions. The kind of graph used depends on the application. For example, in natural language processing, "linear chain" CRFs are popular, for which each prediction is dependent only on its immediate neighbours. In image processing, the graph typically connects locations to nearby and/or similar locations to enforce that they receive similar predictions. Other examples where CRFs are used are: labeling or parsing of sequential data for natural language processing or biological sequences, part-of-speech tagging, shallow parsing, named entity recognition, gene finding, peptide critical functional region finding, and object recognition and image segmentation in computer vision. == Description == CRFs are a type of discriminative undirected probabilistic graphical model. Lafferty, McCallum and Pereira define a CRF on observations X {\displaystyle {\boldsymbol {X}}} and random variables Y {\displaystyle {\boldsymbol {Y}}} as follows: Let G = ( V , E ) {\displaystyle G=(V,E)} be a graph such that Y = ( Y v ) v ∈ V {\displaystyle {\boldsymbol {Y}}=({\boldsymbol {Y}}_{v})_{v\in V}} , so that Y {\displaystyle {\boldsymbol {Y}}} is indexed by the vertices of G {\displaystyle G} . Then ( X , Y ) {\displaystyle ({\boldsymbol {X}},{\boldsymbol {Y}})} is a conditional random field when each random variable Y v {\displaystyle {\boldsymbol {Y}}_{v}} , conditioned on X {\displaystyle {\boldsymbol {X}}} , obeys the Markov property with respect to the graph; that is, its probability is dependent only on its neighbours in G and not its past states: P ( Y v | X , { Y w : w ≠ v } ) = P ( Y v | X , { Y w : w ∼ v } ) {\displaystyle P({\boldsymbol {Y}}_{v}|{\boldsymbol {X}},\{{\boldsymbol {Y}}_{w}:w\neq v\})=P({\boldsymbol {Y}}_{v}|{\boldsymbol {X}},\{{\boldsymbol {Y}}_{w}:w\sim v\})} , where w ∼ v {\displaystyle {\mathit {w}}\sim v} means that w {\displaystyle w} and v {\displaystyle v} are neighbors in G {\displaystyle G} . What this means is that a CRF is an undirected graphical model whose nodes can be divided into exactly two disjoint sets X {\displaystyle {\boldsymbol {X}}} and Y {\displaystyle {\boldsymbol {Y}}} , the observed and output variables, respectively; the conditional distribution p ( Y | X ) {\displaystyle p({\boldsymbol {Y}}|{\boldsymbol {X}})} is then modeled. === Inference === For general graphs, the problem of exact inference in CRFs is intractable. The inference problem for a CRF is basically the same as for an MRF and the same arguments hold. However, there exist special cases for which exact inference is feasible: If the graph is a chain or a tree, message passing algorithms yield exact solutions. The algorithms used in these cases are analogous to the forward-backward and Viterbi algorithm for the case of HMMs. If the CRF only contains pair-wise potentials and the energy is submodular, combinatorial min cut/max flow algorithms yield exact solutions. If exact inference is impossible, several algorithms can be used to obtain approximate solutions. These include: Loopy belief propagation Alpha expansion Mean field inference Linear programming relaxations === Parameter learning === Learning the parameters θ {\displaystyle \theta } is usually done by maximum likelihood learning for p ( Y i | X i ; θ ) {\displaystyle p(Y_{i}|X_{i};\theta )} . If all nodes have exponential family distributions and all nodes are observed during training, this optimization is convex. It can be solved for example using gradient descent algorithms, or Quasi-Newton methods such as the L-BFGS algorithm. On the other hand, if some variables are unobserved, the inference problem has to be solved for these variables. Exact inference is intractable in general graphs, so approximations have to be used. === Examples === In sequence modeling, the graph of interest is usually a chain graph. An input sequence of observed variables X {\displaystyle X} represents a sequence of observations and Y {\displaystyle Y} represents a hidden (or unknown) state variable that needs to be inferred given the observations. The Y i {\displaystyle Y_{i}} are structured to form a chain, with an edge between each Y i − 1 {\displaystyle Y_{i-1}} and Y i {\displaystyle Y_{i}} . As well as having a simple interpretation of the Y i {\displaystyle Y_{i}} as "labels" for each element in the input sequence, this layout admits efficient algorithms for: model training, learning the conditional distributions between the Y i {\displaystyle Y_{i}} and feature functions from some corpus of training data. decoding, determining the probability of a given label sequence Y {\displaystyle Y} given X {\displaystyle X} . inference, determining the most likely label sequence Y {\displaystyle Y} given X {\displaystyle X} . The conditional dependency of each Y i {\displaystyle Y_{i}} on X {\displaystyle X} is defined through a fixed set of feature functions of the form f ( i , Y i − 1 , Y i , X ) {\displaystyle f(i,Y_{i-1},Y_{i},X)} , which can be thought of as measurements on the input sequence that partially determine the likelihood of each possible value for Y i {\displaystyle Y_{i}} . The model assigns each feature a numerical weight and combines them to determine the probability of a certain value for Y i {\displaystyle Y_{i}} . Linear-chain CRFs have many of the same applications as conceptually simpler hidden Markov models (HMMs), but relax certain assumptions about the input and output sequence distributions. An HMM can loosely be understood as a CRF with very specific feature functions that use constant probabilities to model state transitions and emissions. Conversely, a CRF can loosely be understood as a generalization of an HMM that makes the constant transition probabilities into arbitrary functions that vary across the positions in the sequence of hidden states, depending on the input sequence. Notably, in contrast to HMMs, CRFs can contain any number of feature functions, the feature functions can inspect the entire input sequence X {\displaystyle X} at any point during inference, and the range of the feature functions need not have a probabilistic interpretation. == Variants == === Higher-order CRFs and semi-Markov CRFs === CRFs can be extended into higher order models by making each Y i {\displaystyle Y_{i}} dependent on a fixed number k {\displaystyle k} of previous variables Y i − k , . . . , Y i − 1 {\displaystyle Y_{i-k},...,Y_{i-1}} . In conventional formulations of higher order CRFs, training and inference are only practical for small values of k {\displaystyle k} (such as k ≤ 5), since their computational cost increases exponentially with k {\displaystyle k} . However, another recent advance has managed to ameliorate these issues by leveraging concepts and tools from the field of Bayesian nonparametrics. Specifically, the CRF-infinity approach constitutes a CRF-type model that is capable of learning infinitely-long temporal dynamics in a scalable fashion. This is effected by introducing a novel potential function for CRFs that is based on the Sequence Memoizer (SM), a nonparametric Bayesian model for learning infinitely-long dynamics in sequential observations. To render such a model computationally tractable, CRF-infinity employs a mean-field approximation of the postulated novel potential functions (which are driven by an SM). This allows for devising efficient approximate training and inference algorithms for the model, without undermining its capability to capture and model temporal dependencies of arbitrary length. There exists another generalization of CRFs, the semi-Markov conditional random field (semi-CRF), which models variable-length segmentations of the label sequence Y {\displaystyle Y} . This provides much of the power of higher-order CRFs to model long-range dependencies of the Y i {\displaystyle Y_{i}} , at a reasonable computational cost. Finally, large-margin models for structured prediction, such as the structured Support Vector Machine can be seen as an alternative training procedure to CRFs. === Latent-dynamic conditional random field === Latent-dynamic conditional random fields (LDCRF) or discriminative probabilistic latent variable models (DPLVM) are a type of CRFs for sequence tagging tasks. They are latent variable models that are trained discriminatively. In an LDCRF, like in any sequence tagging task, given a sequence of observations x = x 1 , … , x n {\displaystyle x_{1},\dots ,x_{n}} , the main problem the model must solve is how to assign a sequence of labels y = y 1 , … , y n {\displaystyle y_{1},\dots ,y_{n}} from one finite set

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  Kleene's algorithm

  In theoretical computer science, in particular in formal language theory, Kleene's algorithm transforms a given nondeterministic finite automaton (NFA) into a regular expression. Together with other conversion algorithms, it establishes the equivalence of several description formats for regular languages. Alternative presentations of the same method include the "elimination method" attributed to Brzozowski and McCluskey, the algorithm of McNaughton and Yamada, and the use of Arden's lemma. == Algorithm description == According to Gross and Yellen (2004), the algorithm can be traced back to Kleene (1956). A presentation of the algorithm in the case of deterministic finite automata (DFAs) is given in Hopcroft and Ullman (1979). The presentation of the algorithm for NFAs below follows Gross and Yellen (2004). Given a nondeterministic finite automaton M = (Q, Σ, δ, q0, F), with Q = { q0,...,qn } its set of states, the algorithm computes the sets Rkij of all strings that take M from state qi to qj without going through any state numbered higher than k. Here, "going through a state" means entering and leaving it, so both i and j may be higher than k, but no intermediate state may. Each set Rkij is represented by a regular expression; the algorithm computes them step by step for k = -1, 0, ..., n. Since there is no state numbered higher than n, the regular expression Rn0j represents the set of all strings that take M from its start state q0 to qj. If F = { q1,...,qf } is the set of accept states, the regular expression Rn01 | ... | Rn0f represents the language accepted by M. The initial regular expressions, for k = -1, are computed as follows for i≠j: R−1ij = a1 | ... | am where qj ∈ δ(qi,a1), ..., qj ∈ δ(qi,am) and as follows for i=j: R−1ii = a1 | ... | am | ε where qi ∈ δ(qi,a1), ..., qi ∈ δ(qi,am) In other words, R−1ij mentions all letters that label a transition from i to j, and we also include ε in the case where i=j. After that, in each step the expressions Rkij are computed from the previous ones by Rkij = Rk-1ik (Rk-1kk) Rk-1kj | Rk-1ij Another way to understand the operation of the algorithm is as an "elimination method", where the states from 0 to n are successively removed: when state k is removed, the regular expression Rk-1ij, which describes the words that label a path from state i>k to state j>k, is rewritten into Rkij so as to take into account the possibility of going via the "eliminated" state k. By induction on k, it can be shown that the length of each expression Rkij is at most ⁠1/3⁠(4k+1(6s+7) - 4) symbols, where s denotes the number of characters in Σ. Therefore, the length of the regular expression representing the language accepted by M is at most ⁠1/3⁠(4n+1(6s+7)f - f - 3) symbols, where f denotes the number of final states. This exponential blowup is inevitable, because there exist families of DFAs for which any equivalent regular expression must be of exponential size. In practice, the size of the regular expression obtained by running the algorithm can be very different depending on the order in which the states are considered by the procedure, i.e., the order in which they are numbered from 0 to n. == Example == The automaton shown in the picture can be described as M = (Q, Σ, δ, q0, F) with the set of states Q = { q0, q1, q2 }, the input alphabet Σ = { a, b }, the transition function δ with δ(q0,a)=q0, δ(q0,b)=q1, δ(q1,a)=q2, δ(q1,b)=q1, δ(q2,a)=q1, and δ(q2,b)=q1, the start state q0, and set of accept states F = { q1 }. Kleene's algorithm computes the initial regular expressions as After that, the Rkij are computed from the Rk-1ij step by step for k = 0, 1, 2. Kleene algebra equalities are used to simplify the regular expressions as much as possible. Step 0 Step 1 Step 2 Since q0 is the start state and q1 is the only accept state, the regular expression R201 denotes the set of all strings accepted by the automaton.

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  Algorithm IMED

  In multi-armed bandit problems, IMED (for Indexed Minimum Empirical Divergence) is an algorithm developed in 2015 by Junya Honda and Akimichi Takemura. It is the first algorithm proved to be asymptotically optimal respect to the problem-dependant Lai–Robbins lower bound for distributions in ( − ∞ , 1 ] {\displaystyle (-\infty ,1]} . == Multi-armed bandit problem == The Multi-armed bandit problem is a sequential game where one player has to choose at each turn between K {\displaystyle K} actions (arms). Behind every arm a {\displaystyle a} there is an unknown distribution ν a {\displaystyle \nu _{a}} that lies in a set D {\displaystyle {\mathcal {D}}} known by the player (for example, D {\displaystyle {\mathcal {D}}} can be the set of Gaussian distributions or Bernoulli distributions). At each turn t {\displaystyle t} the player chooses (pulls) an arm a t {\displaystyle a_{t}} , he then gets an observation X t {\displaystyle X_{t}} of the distribution ν a t {\displaystyle \nu _{a_{t}}} . === Regret minimization === The goal is to minimize the regret at time T {\displaystyle T} that is defined as R T := ∑ a = 1 K Δ a E [ N a ( T ) ] {\displaystyle R_{T}:=\sum _{a=1}^{K}\Delta _{a}\mathbb {E} [N_{a}(T)]} where μ a := E [ ν a ] {\displaystyle \mu _{a}:=\mathbb {E} [\nu _{a}]} is the mean of arm a {\displaystyle a} μ ∗ := max a μ a {\displaystyle \mu ^{}:=\max _{a}\mu _{a}} is the highest mean Δ a := μ ∗ − μ a {\displaystyle \Delta _{a}:=\mu ^{}-\mu _{a}} N a ( t ) {\displaystyle N_{a}(t)} is the number of pulls of arm a {\displaystyle a} up to turn t {\displaystyle t} The player has to find an algorithm that chooses at each turn t {\displaystyle t} which arm to pull based on the previous actions and observations ( a s , X s ) s < t {\displaystyle (a_{s},X_{s})_{s μ } {\displaystyle {\mathcal {K}}_{inf}(\nu ,\mu ,{\mathcal {D}}):=\inf \left\{\mathrm {KL} (\nu ,{\tilde {\nu }})\ |\ {\tilde {\nu }}\in {\mathcal {P}}([-\infty ,1]),\ \mathbb {E} [{\tilde {\nu }}]>\mu \right\}} K L {\displaystyle \mathrm {KL} } is the Kullback–Leibler divergence P ( [ − ∞ , 1 ] ) {\displaystyle {\mathcal {P}}([-\infty ,1])} is the set of distribution in [ − ∞ , 1 ] {\displaystyle [-\infty ,1]} ν ^ a ( t ) {\displaystyle {\hat {\nu }}_{a}(t)} is the empirical distribution of arm a {\displaystyle a} at turn t {\displaystyle t} μ ^ ∗ ( t ) {\displaystyle {\hat {\mu }}^{}(t)} is the highest empirical mean of turn t {\displaystyle t} Remark : For arms a {\displaystyle a} that verify μ ^ a ( t ) = μ ^ ∗ ( t ) {\displaystyle {\hat {\mu }}_{a}(t)={\hat {\mu }}^{}(t)} we have K i n f ( ν ^ a ( t ) , μ ^ ∗ ( t ) ) = 0 {\displaystyle K_{inf}({\hat {\nu }}_{a}(t),{\hat {\mu }}^{}(t))=0} . Then there index is equal to ln ⁡ ( N a ( t ) ) {\displaystyle \ln(N_{a}(t))} === Pseudocode === for each arm i do: n[i] ← 1; nu[i] ← None; mu[i] ← None for t from 1 to K do: select arm t observe reward r n[t] ← n[t] + 1 nu[t] ← update empirical distribution mu[t] ← update empirical mean for t from K+1 to T do: mu ← highest mu for each arm i do: scoreK[i] ← n[i] K_inf(nu[i],mu) scoreN[i] ← ln(n[i]) index[i] ← scoreK[i] + scoreN[i] select arm a with smallest index[a] observe reward r n[a] ← n[a] + 1 nu[a] ← update empirical distribution mu[a] ← update empirical mean == Theoretical results == In the multi-armed bandit problem we have the asymptotic Lai–Robbins lower bound asymptotic lower bound on regret. The algorithm IMED is the first algorithm that matches this lower bound for distribution in ( − ∞ , 1 ] {\displaystyle (-\infty ,1]} in the first order. If the distribution are also bounded then it also match the second order. It is the first algorithm that match the second under of this lower bound. === Lai–Robbins lower bound === In 1985 Lai and Robbins proved an asymptotic, problem-dependent lower bound on regret. In 2018, Aurelien Garivier, Pierre Menard and Gilles Stoltz proved a refined lower bound that gives the second order It states that for every consistent algorithm on the set P ( [ − ∞ , 1 ] ) {\displaystyle {\mathcal {P}}([-\infty ,1])} — that is, an algorithm for which, for every ( ν 1 , … , ν K ) ∈ P ( [ − ∞ , 1 ] ) K {\displaystyle (\nu _{1},\dots ,\nu _{K})\in {\mathcal {P}}([-\infty ,1])^{K}} , the regret R T {\displaystyle R_{T}} is subpolynomial (i.e. R T = o T → + ∞ ( T α ) {\displaystyle R_{T}=o_{T\to +\infty }(T^{\alpha })} for all α > 0 {\displaystyle \alpha >0} ) — we have: R T ≥ ( ∑ a : μ a < μ ∗ Δ a K inf ( ν a , μ ∗ ) ) ln ⁡ T − Ω T → + ∞ ( ln ⁡ ln ⁡ T ) . {\displaystyle R_{T}\geq \left(\sum _{a:\mu _{a}<\mu ^{}}{\frac {\Delta _{a}}{{\mathcal {K}}_{\inf }(\nu _{a},\mu ^{})}}\right)\ln T-\Omega _{T\to +\infty }(\ln \ln T).} This bound is asymptotic (as T → + ∞ {\displaystyle T\to +\infty } ) and gives a first-order lower bound of order ln ⁡ T {\displaystyle \ln T} with the optimal constant in front of it and the second order in − Ω ( ln ⁡ ln ⁡ T ) {\displaystyle -\Omega (\ln \ln T)} . === Regret bound for IMED === If the distribution of every arm a {\displaystyle a} is ( − ∞ , 1 ] {\displaystyle (-\infty ,1]} ( i.e. ν a ∈ P ( [ − ∞ , 1 ] ) ) {\displaystyle \nu _{a}\in {\mathcal {P}}([-\infty ,1]))} then the regret of the algorithm IMED verify R T ≤ ( ∑ a : μ a < μ ∗ Δ a K inf ( ν a , μ ∗ ) ) ln ⁡ T + O ( 1 ) {\displaystyle R_{T}\leq \left(\sum _{a:\mu _{a}<\mu ^{}}{\frac {\Delta _{a}}{{\mathcal {K}}_{\inf }(\nu _{a},\mu ^{})}}\right)\ln T+O(1)} If all the distribution ν a {\displaystyle \nu _{a}} are bounded then it exists a constant C > 0 {\displaystyle C>0} such that for T {\displaystyle T} large enough the regret of IMED is upper bounded by R T ≤ ( ∑ a : μ a < μ ∗ Δ a K inf ( ν a , μ ∗ ) ) ln ⁡ T − C ln ⁡ ln ⁡ T {\displaystyle R_{T}\leq \left(\sum _{a:\mu _{a}<\mu ^{}}{\frac {\Delta _{a}}{{\mathcal {K}}_{\inf }(\nu _{a},\mu ^{})}}\right)\ln T-C\ln \ln T} == Computation time == The algorithm only requiere to compute the K i n f {\displaystyle K_{inf}} for suboptimal arms who are pulled O ( ln ⁡ T ) {\displaystyle O(\ln T)} times, which make it a lot faster than KL-UCB. A faster version of IMED was developed in 2023 to make it even faster, using a Taylor development of the K i n f {\displaystyle K_{inf}} in the first order .

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  Information history

  Information history may refer to the history of each of the categories listed below (or to combinations of them). It should be recognized that the understanding of, for example, libraries as information systems only goes back to about 1950. The application of the term information for earlier systems or societies is a retronym. == Academic discipline == Information history is an emerging discipline related to, but broader than, library history. An important introduction and review was made by Alistair Black (2006). A prolific scholar in this field is also Toni Weller, for example, Weller (2007, 2008, 2010a and 2010b). As part of her work Toni Weller has argued that there are important links between the modern information age and its historical precedents. A description from Russia is Volodin (2000). Alistair Black (2006, p. 445) wrote: "This chapter explores issues of discipline definition and legitimacy by segmenting information history into its various components: The history of print and written culture, including relatively long-established areas such as the histories of libraries and librarianship, book history, publishing history, and the history of reading. The history of more recent information disciplines and practice, that is to say, the history of information management, information systems, and information science. The history of contiguous areas, such as the history of the information society and information infrastructure, necessarily enveloping communication history (including telecommunications history) and the history of information policy. The history of information as social history, with emphasis on the importance of informal information networks." "Bodies influential in the field include the American Library Association’s Round Table on Library History, the Library History Section of the International Federation of Library Associations and Institutions (IFLA), and, in the U.K., the Library and Information History Group of the Chartered Institute of Library and Information Professionals (CILIP). Each of these bodies has been busy in recent years, running conferences and seminars, and initiating scholarly projects. Active library history groups function in many other countries, including Germany (The Wolfenbuttel Round Table on Library History, the History of the Book and the History of Media, located at the Herzog August Bibliothek), Denmark (The Danish Society for Library History, located at the Royal School of Library and Information Science), Finland (The Library History Research Group, University of Tamepere), and Norway (The Norwegian Society for Book and Library History). Sweden has no official group dedicated to the subject, but interest is generated by the existence of a museum of librarianship in Bods, established by the Library Museum Society and directed by Magnus Torstensson. Activity in Argentina, where, as in Europe and the U.S., a "new library history" has developed, is described by Parada (2004)." (Black (2006, p. 447). === Journals === Information & Culture (previously Libraries & the Cultural Record, Libraries & Culture) Library & Information History (until 2008: Library History; until 1967: Library Association. Library History Group. Newsletter) == Information technology (IT) == The term IT is ambiguous although mostly synonym with computer technology. Haigh (2011, pp. 432-433) wrote "In fact, the great majority of references to information technology have always been concerned with computers, although the exact meaning has shifted over time (Kline, 2006). The phrase received its first prominent usage in a Harvard Business Review article (Haigh, 2001b; Leavitt & Whisler, 1958) intended to promote a technocratic vision for the future of business management. Its initial definition was at the conjunction of computers, operations research methods, and simulation techniques. Having failed initially to gain much traction (unlike related terms of a similar vintage such as information systems, information processing, and information science) it was revived in policy and economic circles in the 1970s with a new meaning. Information technology now described the expected convergence of the computing, media, and telecommunications industries (and their technologies), understood within the broader context of a wave of enthusiasm for the computer revolution, post-industrial society, information society (Webster, 1995), and other fashionable expressions of the belief that new electronic technologies were bringing a profound rupture with the past. As it spread broadly during the 1980s, IT increasingly lost its association with communications (and, alas, any vestigial connection to the idea of anybody actually being informed of anything) to become a new and more pretentious way of saying "computer". The final step in this process is the recent surge in references to "information and communication technologies" or ICTs, a coinage that makes sense only if one assumes that a technology can inform without communicating". Some people use the term information technology about technologies used before the development of the computer. This is however to use the term as a retronym. =

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  Residual neural network

  A residual neural network (also referred to as a residual network or ResNet) is a deep learning architecture in which the layers learn residual functions with reference to the layer inputs. It was developed in 2015 for image recognition, and won the ImageNet Large Scale Visual Recognition Challenge (ILSVRC) of that year. As a point of terminology, "residual connection" refers to the specific architectural motif of x ↦ f ( x ) + x {\displaystyle x\mapsto f(x)+x} , where f {\displaystyle f} is an arbitrary neural network module. The motif had been used previously (see §History for details). However, the publication of ResNet made it widely popular for feedforward networks, appearing in neural networks that are seemingly unrelated to ResNet. The residual connection stabilizes the training and convergence of deep neural networks with hundreds of layers, and is a common motif in deep neural networks, such as transformer models (e.g., BERT, and GPT models such as ChatGPT), the AlphaGo Zero system, the AlphaStar system, and the AlphaFold system. == Mathematics == === Residual connection === In a multilayer neural network model, consider a (non-residual) subnetwork with a certain number of stacked layers (e.g., 2 or 3). Let H ( x ; α ) {\displaystyle H(x;\alpha )} denote the subnetwork. Suppose H ∗ {\displaystyle H^{}} is the desired optimal output of this subnetwork. Residual learning simply adds x {\displaystyle x} directly to the output, such that the optimal learned output now becomes be H ∗ − x {\displaystyle H^{}-x} , which is interpreted as a "residual" with respect to x {\displaystyle x} . The operation of "adding x {\displaystyle x} " is implemented via a "skip connection" that performs an identity mapping to connect the input of the subnetwork with its output. This connection is referred to as a "residual connection" in later work. Let F ( x ; α ) = H ( x ; a ) + x {\displaystyle F(x;\alpha )=H(x;a)+x} . The function F {\displaystyle F} is often represented by matrix multiplication interlaced with activation functions and normalization operations (e.g., batch normalization or layer normalization). As a whole, one of these subnetworks is referred to as a "residual block". A deep residual network is constructed by simply stacking these blocks. Long short-term memory (LSTM) has a memory mechanism that serves as a residual connection. In an LSTM without a forget gate, an input x t {\displaystyle x_{t}} is processed by a function F {\displaystyle F} and added to a memory cell c t {\displaystyle c_{t}} , resulting in c t + 1 = c t + F ( x t ) {\displaystyle c_{t+1}=c_{t}+F(x_{t})} . An LSTM with a forget gate essentially functions as a highway network. To stabilize the variance of the layers' inputs, it is recommended to replace the residual connections x + f ( x ) {\displaystyle x+f(x)} with x / L + f ( x ) {\displaystyle x/L+f(x)} , where L {\displaystyle L} is the total number of residual layers. === Projection connection === If the function F {\displaystyle F} is of type F : R n → R m {\displaystyle F:\mathbb {R} ^{n}\to \mathbb {R} ^{m}} where n ≠ m {\displaystyle n\neq m} , then F ( x ) + x {\displaystyle F(x)+x} is undefined. To handle this special case, a projection connection is used: y = F ( x ) + P ( x ) {\displaystyle y=F(x)+P(x)} where P {\displaystyle P} is typically a linear projection, defined by P ( x ) = M x {\displaystyle P(x)=Mx} where M {\displaystyle M} is a m × n {\displaystyle m\times n} matrix. The matrix is trained via backpropagation, as is any other parameter of the model. === Signal propagation === The introduction of identity mappings facilitates signal propagation in both forward and backward paths. ==== Forward propagation ==== If the output of the ℓ {\displaystyle \ell } -th residual block is the input to the ( ℓ + 1 ) {\displaystyle (\ell +1)} -th residual block (assuming no activation function between blocks), then the ( ℓ + 1 ) {\displaystyle (\ell +1)} -th input is: x ℓ + 1 = F ( x ℓ ) + x ℓ {\displaystyle x_{\ell +1}=F(x_{\ell })+x_{\ell }} Applying this formulation recursively, e.g.: x ℓ + 2 = F ( x ℓ + 1 ) + x ℓ + 1 = F ( x ℓ + 1 ) + F ( x ℓ ) + x ℓ {\displaystyle {\begin{aligned}x_{\ell +2}&=F(x_{\ell +1})+x_{\ell +1}\\&=F(x_{\ell +1})+F(x_{\ell })+x_{\ell }\end{aligned}}} yields the general relationship: x L = x ℓ + ∑ i = ℓ L − 1 F ( x i ) {\displaystyle x_{L}=x_{\ell }+\sum _{i=\ell }^{L-1}F(x_{i})} where L {\textstyle L} is the index of a residual block and ℓ {\textstyle \ell } is the index of some earlier block. This formulation suggests that there is always a signal that is directly sent from a shallower block ℓ {\textstyle \ell } to a deeper block L {\textstyle L} . ==== Backward propagation ==== The residual learning formulation provides the added benefit of mitigating the vanishing gradient problem to some extent. However, it is crucial to acknowledge that the vanishing gradient issue is not the root cause of the degradation problem, which is tackled through the use of normalization. To observe the effect of residual blocks on backpropagation, consider the partial derivative of a loss function E {\displaystyle {\mathcal {E}}} with respect to some residual block input x ℓ {\displaystyle x_{\ell }} . Using the equation above from forward propagation for a later residual block L > ℓ {\displaystyle L>\ell } : ∂ E ∂ x ℓ = ∂ E ∂ x L ∂ x L ∂ x ℓ = ∂ E ∂ x L ( 1 + ∂ ∂ x ℓ ∑ i = ℓ L − 1 F ( x i ) ) = ∂ E ∂ x L + ∂ E ∂ x L ∂ ∂ x ℓ ∑ i = ℓ L − 1 F ( x i ) {\displaystyle {\begin{aligned}{\frac {\partial {\mathcal {E}}}{\partial x_{\ell }}}&={\frac {\partial {\mathcal {E}}}{\partial x_{L}}}{\frac {\partial x_{L}}{\partial x_{\ell }}}\\&={\frac {\partial {\mathcal {E}}}{\partial x_{L}}}\left(1+{\frac {\partial }{\partial x_{\ell }}}\sum _{i=\ell }^{L-1}F(x_{i})\right)\\&={\frac {\partial {\mathcal {E}}}{\partial x_{L}}}+{\frac {\partial {\mathcal {E}}}{\partial x_{L}}}{\frac {\partial }{\partial x_{\ell }}}\sum _{i=\ell }^{L-1}F(x_{i})\end{aligned}}} This formulation suggests that the gradient computation of a shallower layer, ∂ E ∂ x ℓ {\textstyle {\frac {\partial {\mathcal {E}}}{\partial x_{\ell }}}} , always has a later term ∂ E ∂ x L {\textstyle {\frac {\partial {\mathcal {E}}}{\partial x_{L}}}} that is directly added. Even if the gradients of the F ( x i ) {\displaystyle F(x_{i})} terms are small, the total gradient ∂ E ∂ x ℓ {\textstyle {\frac {\partial {\mathcal {E}}}{\partial x_{\ell }}}} resists vanishing due to the added term ∂ E ∂ x L {\textstyle {\frac {\partial {\mathcal {E}}}{\partial x_{L}}}} . == Variants of residual blocks == === Basic block === A basic block is the simplest building block studied in the original ResNet. This block consists of two sequential 3x3 convolutional layers and a residual connection. The input and output dimensions of both layers are equal. === Bottleneck block === A bottleneck block consists of three sequential convolutional layers and a residual connection. The first layer in this block is a 1×1 convolution for dimension reduction (e.g., to 1/2 of the input dimension); the second layer performs a 3×3 convolution; the last layer is another 1×1 convolution for dimension restoration. The models of ResNet-50, ResNet-101, and ResNet-152 are all based on bottleneck blocks. === Pre-activation block === The pre-activation residual block applies activation functions before applying the residual function F {\displaystyle F} . Formally, the computation of a pre-activation residual block can be written as: x ℓ + 1 = F ( ϕ ( x ℓ ) ) + x ℓ {\displaystyle x_{\ell +1}=F(\phi (x_{\ell }))+x_{\ell }} where ϕ {\displaystyle \phi } can be any activation (e.g. ReLU) or normalization (e.g. LayerNorm) operation. This design reduces the number of non-identity mappings between residual blocks, and allows an identity mapping directly from the input to the output. This design was used to train models with 200 to over 1000 layers, and was found to consistently outperform variants where the residual path is not an identity function. The pre-activation ResNet with 200 layers took 3 weeks to train for ImageNet on 8 GPUs in 2016. Since GPT-2, transformer blocks have been mostly implemented as pre-activation blocks. This is often referred to as "pre-normalization" in the literature of transformer models. == Applications == Originally, ResNet was designed for computer vision. All transformer architectures include residual connections. Indeed, very deep transformers cannot be trained without them. The original ResNet paper made no claim on being inspired by biological systems. However, later research has related ResNet to biologically-plausible algorithms. A study published in Science in 2023 disclosed the complete connectome of an insect brain (specifically that of a fruit fly larva). This study discovered "multilayer shortcuts" that resemble the skip connections in artificial neural networks, including ResNets. == History == === Previous work === Residual connections were noticed in neu

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  Leiden algorithm

  The Leiden algorithm is a community detection algorithm developed by Traag et al at Leiden University. It was developed as a modification of the Louvain method. Like the Louvain method, the Leiden algorithm attempts to optimize modularity in extracting communities from networks; however, it addresses key issues present in the Louvain method, namely poorly connected communities and the resolution limit of modularity. == Improvement over Louvain method == Broadly, the Leiden algorithm uses the same two primary phases as the Louvain algorithm: a local node moving step (though, the method by which nodes are considered in Leiden is more efficient) and a graph aggregation step. However, to address the issues with poorly-connected communities and the merging of smaller communities into larger communities (the resolution limit of modularity), the Leiden algorithm employs an intermediate refinement phase in which communities may be split to guarantee that all communities are well-connected. Consider, for example, the following graph: Three communities are present in this graph (each color represents a community). Additionally, the center "bridge" node (represented with an extra circle) is a member of the community represented by blue nodes. Now consider the result of a node-moving step which merges the communities denoted by red and green nodes into a single community (as the two communities are highly connected): Notably, the center "bridge" node is now a member of the larger red community after node moving occurs (due to the greedy nature of the local node moving algorithm). In the Louvain method, such a merging would be followed immediately by the graph aggregation phase. However, this causes a disconnection between two different sections of the community represented by blue nodes. In the Leiden algorithm, the graph is instead refined: The Leiden algorithm's refinement step ensures that the center "bridge" node is kept in the blue community to ensure that it remains intact and connected, despite the potential improvement in modularity from adding the center "bridge" node to the red community. == Graph components == Before defining the Leiden algorithm, it will be helpful to define some of the components of a graph. === Vertices and edges === A graph is composed of vertices (nodes) and edges. Each edge is connected to two vertices, and each vertex may be connected to zero or more edges. Edges are typically represented by straight lines, while nodes are represented by circles or points. In set notation, let V {\displaystyle V} be the set of vertices, and E {\displaystyle E} be the set of edges: V := { v 1 , v 2 , … , v n } E := { e i j , e i k , … , e k l } {\displaystyle {\begin{aligned}V&:=\{v_{1},v_{2},\dots ,v_{n}\}\\E&:=\{e_{ij},e_{ik},\dots ,e_{kl}\}\end{aligned}}} where e i j {\displaystyle e_{ij}} is the directed edge from vertex v i {\displaystyle v_{i}} to vertex v j {\displaystyle v_{j}} . We can also write this as an ordered pair: e i j := ( v i , v j ) {\displaystyle {\begin{aligned}e_{ij}&:=(v_{i},v_{j})\end{aligned}}} === Community === A community is a unique set of nodes: C i ⊆ V C i ⋂ C j = ∅ ∀ i ≠ j {\displaystyle {\begin{aligned}C_{i}&\subseteq V\\C_{i}&\bigcap C_{j}=\emptyset ~\forall ~i\neq j\end{aligned}}} and the union of all communities must be the total set of vertices: V = ⋃ i = 1 C i {\displaystyle {\begin{aligned}V&=\bigcup _{i=1}C_{i}\end{aligned}}} === Partition === A partition is the set of all communities: P = { C 1 , C 2 , … , C n } {\displaystyle {\begin{aligned}{\mathcal {P}}&=\{C_{1},C_{2},\dots ,C_{n}\}\end{aligned}}} == Partition quality == How communities are partitioned is an integral part on the Leiden algorithm. How partitions are decided can depend on how their quality is measured. Additionally, many of these metrics contain parameters of their own that can change the outcome of their communities. === Modularity === Modularity is a highly used quality metric for assessing how well a set of communities partition a graph. The equation for this metric is defined for an adjacency matrix, A, as: Q = 1 2 m ∑ i j ( A i j − k i k j 2 m ) δ ( c i , c j ) {\displaystyle Q={\frac {1}{2m}}\sum _{ij}(A_{ij}-{\frac {k_{i}k_{j}}{2m}})\delta (c_{i},c_{j})} where: A i j {\displaystyle A_{ij}} represents the edge weight between nodes i {\displaystyle i} and j {\displaystyle j} ; see Adjacency matrix; k i {\displaystyle k_{i}} and k j {\displaystyle k_{j}} are the sum of the weights of the edges attached to nodes i {\displaystyle i} and j {\displaystyle j} , respectively; m {\displaystyle m} is the sum of all of the edge weights in the graph; c i {\displaystyle c_{i}} and c j {\displaystyle c_{j}} are the communities to which the nodes i {\displaystyle i} and j {\displaystyle j} belong; and δ {\displaystyle \delta } is Kronecker delta function: δ ( c i , c j ) = { 1 if c i and c j are the same community 0 otherwise {\displaystyle {\begin{aligned}\delta (c_{i},c_{j})&={\begin{cases}1&{\text{if }}c_{i}{\text{ and }}c_{j}{\text{ are the same community}}\\0&{\text{otherwise}}\end{cases}}\end{aligned}}} === Reichardt Bornholdt Potts Model (RB) === One of the most well used metrics for the Leiden algorithm is the Reichardt Bornholdt Potts Model (RB). This model is used by default in most mainstream Leiden algorithm libraries under the name RBConfigurationVertexPartition. This model introduces a resolution parameter γ {\displaystyle \gamma } and is highly similar to the equation for modularity. This model is defined by the following quality function for an adjacency matrix, A, as: Q = ∑ i j ( A i j − γ k i k j 2 m ) δ ( c i , c j ) {\displaystyle Q=\sum _{ij}(A_{ij}-\gamma {\frac {k_{i}k_{j}}{2m}})\delta (c_{i},c_{j})} where: γ {\displaystyle \gamma } represents a linear resolution parameter === Constant Potts Model (CPM) === Another metric similar to RB is the Constant Potts Model (CPM). This metric also relies on a resolution parameter γ {\displaystyle \gamma } The quality function is defined as: H = − ∑ i j ( A i j w i j − γ ) δ ( c i , c j ) {\displaystyle H=-\sum _{ij}(A_{ij}w_{ij}-\gamma )\delta (c_{i},c_{j})} === Understanding Potts Model resolution parameters/Resolution limit === Typically Potts models such as RB or CPM include a resolution parameter in their calculation. Potts models are introduced as a response to the resolution limit problem that is present in modularity maximization based community detection. The resolution limit problem is that, for some graphs, maximizing modularity may cause substructures of a graph to merge and become a single community and thus smaller structures are lost. These resolution parameters allow modularity adjacent methods to be modified to suit the requirements of the user applying the Leiden algorithm to account for small substructures at a certain granularity. The figure on the right illustrates why resolution can be a helpful parameter when using modularity based quality metrics. In the first graph, modularity only captures the large scale structures of the graph; however, in the second example, a more granular quality metric could potentially detect all substructures in a graph. == Algorithm == The Leiden algorithm starts with a graph of disorganized nodes (a) and sorts it by partitioning them to maximize modularity (the difference in quality between the generated partition and a hypothetical randomized partition of communities). The method it uses is similar to the Louvain algorithm, except that after moving each node it also considers that node's neighbors that are not already in the community it was placed in. This process results in our first partition (b), also referred to as P {\displaystyle {\mathcal {P}}} . Then the algorithm refines this partition by first placing each node into its own individual community and then moving them from one community to another to maximize modularity. It does this iteratively until each node has been visited and moved, and each community has been refined - this creates partition (c), which is the initial partition of P refined {\displaystyle {\mathcal {P}}_{\text{refined}}} . Then an aggregate network (d) is created by turning each community into a node. P refined {\displaystyle {\mathcal {P}}_{\text{refined}}} is used as the basis for the aggregate network while P {\displaystyle {\mathcal {P}}} is used to create its initial partition. Because we use the original partition P {\displaystyle {\mathcal {P}}} in this step, we must retain it so that it can be used in future iterations. These steps together form the first iteration of the algorithm. In subsequent iterations, the nodes of the aggregate network (which each represent a community) are once again placed into their own individual communities and then sorted according to modularity to form a new P refined {\displaystyle {\mathcal {P}}_{\text{refined}}} , forming (e) in the above graphic. In the case depicted by the graph, the nodes were already sorted optimally, so no change too

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  Algorithm

  In mathematics and computer science, an algorithm ( ) is a finite sequence of mathematically rigorous instructions, typically used to solve a class of specific problems or to perform a computation. Algorithms are used as specifications for performing calculations and data processing. More advanced algorithms can use conditionals to divert the code execution through various routes (referred to as automated decision-making) and deduce valid inferences (referred to as automated reasoning). In contrast, a heuristic is an approach to solving problems without well-defined correct or optimal results. For example, although social media recommender systems are commonly called "algorithms", they actually rely on heuristics as there is no truly "correct" recommendation. As an effective method, an algorithm can be expressed within a finite amount of space and time and in a well-defined formal language for calculating a function. Starting from an initial state and input, a computation occurs at each step, eventually producing output and terminating. The transition between states can be non-deterministic; randomized algorithms incorporate random input. == Etymology == Around 825 AD, Persian scientist and polymath Muḥammad ibn Mūsā al-Khwārizmī wrote kitāb al-ḥisāb al-hindī ("Book of Indian computation") and kitab al-jam' wa'l-tafriq al-ḥisāb al-hindī ("Addition and subtraction in Indian arithmetic"). In the early 12th century, Latin translations of these texts involving the Hindu–Arabic numeral system and arithmetic appeared, for example Liber Alghoarismi de practica arismetrice, attributed to John of Seville, and Liber Algoritmi de numero Indorum, attributed to Adelard of Bath. Here, alghoarismi or algoritmi is the Latinization of Al-Khwarizmi's name; the text starts with the phrase Dixit Algoritmi, or "Thus spoke Al-Khwarizmi". The word algorism in English came to mean the use of place-value notation in calculations; it occurs in the Ancrene Wisse from circa 1225. By the time Geoffrey Chaucer wrote The Canterbury Tales in the late 14th century, he used a variant of the same word in describing augrym stones, stones used for place-value calculation. In the 15th century, under the influence of the Greek word ἀριθμός (arithmos, "number"; cf. "arithmetic"), the Latin word was altered to algorithmus. By 1596, this form of the word was used in English, as algorithm, by Thomas Hood. == Definition == One informal definition is "a set of rules that precisely defines a sequence of operations", which would include all computer programs, and any bureaucratic procedure or cook-book recipe. In general, a program is an algorithm only if it stops eventually. Formally, algorithm is an explicit set of instructions to produce an output, that can be followed by a computer or a human performing specific operations on symbols.. == History == === Ancient algorithms === Step-by-step procedures for solving mathematical problems have been recorded since antiquity. This includes in Babylonian mathematics (around 2500 BC), Egyptian mathematics (around 1550 BC), Indian mathematics (around 800 BC and later), the Ifa Oracle (around 500 BC), Greek mathematics (around 240 BC), Chinese mathematics (around 200 BC and later), and Arabic mathematics (around 800 AD). The earliest evidence of algorithms is found in ancient Mesopotamian mathematics. A Sumerian clay tablet found in Shuruppak near Baghdad and dated to c. 2500 BC describes the earliest division algorithm. During the Hammurabi dynasty c. 1800 – c. 1600 BC, Babylonian clay tablets described algorithms for computing formulas. Algorithms were also used in Babylonian astronomy. Babylonian clay tablets describe and employ algorithmic procedures to compute the time and place of significant astronomical events. Algorithms for arithmetic are also found in ancient Egyptian mathematics, dating back to the Rhind Mathematical Papyrus c. 1550 BC. Algorithms were later used in ancient Hellenistic mathematics. Two examples are the Sieve of Eratosthenes, which was described in the Introduction to Arithmetic by Nicomachus, and the Euclidean algorithm, which was first described in Euclid's Elements (c. 300 BC).Examples of ancient Indian mathematics included the Shulba Sutras, the Kerala School, and the Brāhmasphuṭasiddhānta. In the 9th century, Muḥammad ibn Mūsā al-Khwārizmī revolutionized the field by establishing the algorithm as a systematic, finite sequence of logical steps to solve mathematical problems. In his influential work, The Compendious Book on Calculation by Completion and Balancing, he moved beyond specific numerical solutions to introduce general procedures for algebraic reduction and balancing. This transformed mathematics into a 'mechanical' process of well-defined rules—a fundamental shift that laid the groundwork for modern algorithmic theory. The Latin translation of his arithmetic treatise, titled Algoritmi de numero Indorum, led to the term algorithm being derived from the Latinization of his name, Algoritmi, specifically to describe this new rule-based approach to mathematics. The first cryptographic algorithm for deciphering encrypted code was developed by Al-Kindi, a 9th-century Arab mathematician, in A Manuscript On Deciphering Cryptographic Messages. He gave the first description of cryptanalysis by frequency analysis, the earliest codebreaking algorithm. === Computers === ==== Weight-driven clocks ==== Weight-driven clocks were a key European invention in Middle Ages, specifically the verge escapement mechanism producing the tick of mechanical clocks. Accurate automatic machines led to mechanical automata in the 13th century and computational machines—the difference and analytical engines of Charles Babbage and Ada Lovelace in the mid-19th century. Lovelace designed the first algorithm intended for a computer, Babbage's analytical engine, the first real Turing-complete computer, more than the mechanical calculators of the time. Although the full implementation of Babbage's second device was only built decades after her lifetime, Lovelace has been called "history's first programmer". ==== Electromechanical relay ==== The Jacquard loom, a precursor to punch cards, and telephone switching machines led to the development of the first computers. By the mid-19th century, the telegraph, was in use throughout the world. By the late 19th century, ticker tape (c. 1870s) and punch cards (c. 1890) were developed. Then came the teleprinter (c. 1910) with its punched-paper use of Baudot code on tape. Telephone-switching networks of electromechanical relays were invented in 1835. These led to the invention of the digital adding device by George Stibitz in 1937. While working in Bell Laboratories, he observed the "burdensome" use of mechanical calculators with gears, prompting him to experiment create an experimental digital adder at home. === Formalization === In 1928, a partial formalization of the modern concept of algorithms began with attempts to solve David Hilbert's Entscheidungsproblem (decision problem). Later formalizations were framed as attempts to define "effective calculability" or "effective method". Those formalizations included the Gödel–Herbrand–Kleene recursive functions of 1930, 1934 and 1935, Alonzo Church's lambda calculus of 1936, Emil Post's Formulation 1 of 1936, and Alan Turing's Turing machines of 1936–37 and 1939. === Modern Algorithms === For decades, it was assumed that algorithm evolution progresses from heuristics to formal algorithms. A Symbolic integration provides a classic illustration. In 1961, James Slagle’s program SAINT used heuristics to solve 52 of 54 freshman calculus exercises from an MIT textbook (≈96%). In 1967, Larry Moses’s SIN refined the heuristics and achieved 100% success, though it remained heuristic. Finally, in 1969, Robert Risch introduced the Risch Algorithm with formal guarantees. This trajectory defined the traditional path: heuristics evolving until a definitive, guaranteed algorithm emerged. However, the rise of transformer-based AI has inverted this sequence — classical algorithms are now being displaced by heuristics once again. Algorithms have evolved and improved in many ways as time goes on. Common uses of algorithms today include social media apps like Instagram and YouTube. Algorithms are used as a way to analyze what people like and push more of those things to the people who interact with them. Quantum computing uses quantum algorithm procedures to solve problems faster. More recently, in 2024, NIST updated their post-quantum encryption standards, which includes new encryption algorithms to enhance defenses against attacks using quantum computing. == Representations == Algorithms can be expressed in many kinds of notation, including natural languages, pseudocode, flowcharts, drakon-charts, programming languages or control tables. Natural language expressions of algorithms tend to be verbose and ambiguous and are rarely used for complex or technical algor

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  Webometrics Ranking of Business Schools

  The Webometrics Ranking of Business Schools, also known as Ranking Web of Business Schools, is a ranking system for the world's business schools based on a composite indicator that takes into account both the volume of the Web content (number of web pages and files) and the visibility and impact of these web publications according to the number of external inlinks (site citations) they received. The ranking is published by the Cybermetrics Lab, a research group of the Spanish National Research Council (CSIC) located in Madrid. This ranking was discontinued in 2013 and is no longer updated. This discontinued ranking is, however, often cited (as of 2017-06-16) by Google as its main ranking reference. Examples are: "Spain business school ranking " = "Zurich business school ranking" etc. The Webometrics Ranking of World Universities is a similar ranking of universities.

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  Zolostays

  Zolostays is a real-tech co-living focused startup that provides ready-to-move rooms/beds. It was founded in 2015 by Nikhil Sikri, Akhil Sikri and Sneha Choudhry. == Overview == During the pandemic, Zolo provided 75 of rent-free accommodation to those who lost their jobs. Zolo uses bulk inventory in usually residential township and ties up with real estate companies to make the rooms/beds available. Zolostays has both revenue sharing and leased model. == History == Zolostays was founded in 2015 to solve the problem of students and young professionals who would move to temporarily go to other cities to study and work and look for affordable housing. In 2020, it was operating in 10 Indian cities. It has four round of funding, with total $98 million.

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  Iteration

  Iteration means repeating a process to generate a (possibly unbounded) sequence of outcomes. Each repetition of the process is a single iteration, and the outcome of each iteration is the starting point of the next iteration. In mathematics and computer science, iteration (along with the related technique of recursion) is a standard element of algorithms. == Mathematics == In mathematics, iteration may refer to the process of iterating a function, i.e. applying a function repeatedly, using the output from one iteration as the input to the next. Iteration of apparently simple functions can produce complex behaviors and difficult problems – for examples, see the Collatz conjecture and juggler sequences. Another use of iteration in mathematics is in iterative methods which are used to produce approximate numerical solutions to certain mathematical problems. Newton's method is an example of an iterative method. Manual calculation of a number's square root is a common use and a well-known example. == Computing == In computing, iteration is a technique that marks out of a block of statements within a computer program for a defined number of repetitions. That block of statements is said to be iterated. A computer programmer might also refer to that block of statements as an iteration. === Implementations === Loops constitute the most common language constructs for performing iterations. The following pseudocode "iterates" three times the line of code between begin & end through a for loop, and uses the values of i as increments. It is permissible, and often necessary, to use values from other parts of the program outside the bracketed block of statements, to perform the desired function. Iterators constitute alternative language constructs to loops, which ensure consistent iterations over specific data structures. They can eventually save time and effort in later coding attempts. In particular, an iterator allows one to repeat the same kind of operation at each node of such a data structure, often in some pre-defined order. Iteratees are purely functional language constructs, which accept or reject data during the iterations. === Relation with recursion === Recursions and iterations have different algorithmic definitions, even though they can generate identical results. The primary difference is that recursion can be a solution without prior knowledge as to how many times the action must repeat, while a successful iteration requires that foreknowledge. Some types of programming languages, known as functional programming languages, are designed such that they do not set up a block of statements for explicit repetition, as with the for loop. Instead, those programming languages exclusively use recursion. Rather than call out a block of code to repeate a pre-defined number of times, the executing code block instead "divides" the work into a number of separate pieces, after which the code block executes itself on each individual piece. Each piece of work is divided repeatedly until the "amount" of work is as small as possible, at which point the algorithm does that work very quickly. The algorithm then "reverses" and reassembles the pieces into a complete whole. The classic example of recursion is in list-sorting algorithms, such as merge sort. The merge sort recursive algorithm first repeatedly divides the list into consecutive pairs. Each pair is then ordered, then each consecutive pair of pairs, and so forth until the elements of the list are in the desired order. The code below is an example of a recursive algorithm in the Scheme programming language that outputs the same result as the pseudocode under the previous heading. == Education == In some schools of pedagogy, iterations are used to describe the process of teaching or guiding students to repeat experiments, assessments, or projects, until more accurate results are found, or the student has mastered the technical skill. This idea is found in the old adage, "Practice makes perfect." In particular, "iterative" is defined as the "process of learning and development that involves cyclical inquiry, enabling multiple opportunities for people to revisit ideas and critically reflect on their implication." Unlike computing and math, educational iterations are not predetermined; instead, the task is repeated until success according to some external criteria (often a test) is achieved.

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  Personal, Inc.

  Personal (also referred to as Personal.com or Personal, Inc.) was a consumer personal data service and identity management system for individuals to aggregate, manage and reuse their own data. It merged with digi.me in August 2017, a business in Europe that has the same business model. The combined company is called digi.me. One of its product lines, a collaborative data management and information security solution for the workplace called TeamData, was spun off as a new company as a result of the merger. == History == Personal was founded in 2009 in Washington, DC by the management team that built The Map Network, a location data and mapping platform that was acquired by Nokia/NAVTEQ in 2006. Personal was the first online consumer-facing company to be named an Ambassador for Privacy by Design for its technical, business and legal commitments to providing users with control over the data they store in Personal's service. Called a “life management platform” by The Economist and a “personal encrypted cloud service” by TIME for its user-centric approach to data, the company has been associated with both the Infomediary model originated in 1999 by John Hagel III and Mark Singer, as well as the vendor relationship management (VRM) model developed by Doc Searls. Personal raised $30m in funding to develop its platform and products from such leading investors as Steve Case's Revolution Ventures, Grotech Ventures, Allen & Company, Ted Leonsis, Neil Ashe, Jonathan Miller, Bill Miller of Legg Mason, Esther Dyson of EDventures, and Eric C. Anderson. The company received recognition for its user agreement, called the Owner Data Agreement, which acted like a reverse license agreement when data was shared between registered parties and emphasized that data ownership resides with the user. Doc Searls wrote in The Intention Economy: When Customers Take Charge that the Owner Data Agreement “had no precedent and modeled a new legal position, both for vendors and for intermediaries.” Personal was early to embrace “small data,” which it defines as “big data for the benefit of individuals.” The term “small data” may have been originally coined by Jeremie Miller of Sing.ly, who mentioned it in a talk at the Web 2.0 Summit in November 2011 and is cited in The Intention Economy. In 2011, Personal was a part of the first group of companies to join the Personal Data Ecosystem Consortium's Startup Circle. A Small Data Meetup group has also formed in New York City, bringing together technology, legal and business experts to exchange ideas about user-centric and user-driven models for internet products and services. Personal has been included in case studies by Ctrl-Shift and Forrester regarding Personal Data Stores and Personal Identity Management. In 2011, Personal received the Innovator Spotlight Award at Privacy Identity Innovation Conference (pii2011) and participated in the Technology Showcase at pii2012. In 2012, TechHive named Personal as one of the top five apps or web services of SXSW. Personal won the 2013 Campus Technology Innovators Award with Lone Star College in July 2013. Personal was included in a list of Executive Travel Magazine's favorite travel apps for 2013 in its May/June issue. In 2013, Personal was also included as part of NYU GovLab's Open Data 500 and was named by J. Walter Thompson as one of 100 things to watch for in 2014. In 2015, the National Law Journal named Company Chief Policy Officer and General Counsel, Joshua P. Galper, as one of their 50 "Cybersecurity & Privacy Trailblazers." == Products and services == === Overview === The Personal Platform was a privacy- and security-by-design platform for individuals to manage and reuse their own data and information. The Fill It app was a 1-click form-filling solution for web and mobile logins, checkouts and forms, and the Data Vault app served as the main cloud-based repository for a user's data. Personal helped individuals take control and benefit from their information while knowing that the information in their Data Vault remained legally theirs and could not be used without their permission. === Data Vault with Cloud Sync === Personal spent two years building the Personal Platform before launching its Data Vault product in beta in November 2011. Following Privacy by Design principles, Personal only enabled users to see or share the sensitive data and all the files they stored in their Data Vault. Such information was encrypted, and could only be decrypted with a user's password. Only users could choose and know their passwords to their vault because Personal did not store user passwords – and therefore could not reset them without deleting a user's sensitive data and all files stored in their vault. All Personal apps and services were linked to a user's private Data Vault. The Data Vault featured automatic synchronization of data and files added on any device logged into Personal. It also featured a “Secure Share” function that created a live, private network, allowing registered users to share access to data and files through an exchange of encrypted keys without the risk of transmitting the data or files through non-secure, direct means. It also allowed users to immediately update data across their own network and revoke access to it when they choose. Fast Company called the Data Vault “a tool that will simplify our lives.” Personal launched its Android app on November 30, 2011. The iOS Data Vault app was released on May 7, 2012. Personal officially launched its application programming interface (APIs) on October 2, 2012 at the Mashery Business of APIs Conference. A review by CNET highlighted the challenges of getting people to trust such a new service with their sensitive data and spending the time required entering enough data to make it useful. === Fill It App and Form Index === When the Data Vault was launched in November 2011, Mashable posed the question: “Never Fill Out a Form Again?” The World Economic Forum in its February 2013 report highlighted the possibility of saving 10 billion hours globally “and improv[ing] the delivery of public and private sector services” through automated form-filling tools, specifically citing Personal's Fill It app. In January 2013, Personal launched Fill It in beta as a web bookmarklet for automatic form-filling. On June 11, 2014, Personal released Fill It as a web extension and announced that it was publishing an index of over 140,000 1-click online forms at www.fillit.com. The company also announced that a mobile version of the product will launch later in the year. According to a story in Tech Cocktail about the launch, Personal's “web extension and mobile app are able to support over 1,200 different types of reusable data, even enabling them to unlock more confidential information so they can complete longer forms, including patient registrations, job applications, event registrations, school admissions, insurance and bank applications, and government forms.” In November 2014, a mobile version of Fill It was launched that could autofill mobile forms using APIs. Personal's form portal ultimately indexed more than 500,000 forms with three components, which, together, allowed data to be captured and reused across any of the forms: (1) a form graph, which mapped individual form fields to the Personal ontology; (2) a semantic layer, which determined how data was required on a form (e.g. one field vs. three fields for a U.S. telephone number); and (3) a correlations graph, which helped individuals match their specific data to a form without looking at the data value (e.g. knowing which phone number is a mobile phone number, which address is a billing address, or that a person uses their middle name as a first name on most forms). === Monetizing personal data === With the initial public offering of Facebook in May 2012, there was media interest in the question of the monetary value of personal data and whether tools and services might emerge to help consumers monetize their own data. Personal was frequently cited as a company that could potentially offer such a service. Articles and pieces focusing on this subject have appeared in The New York Times, AdWeek, the MIT Technology Review, and on CNN and National Public Radio. Company Co-founder and CEO Shane Green was quoted as saying that “the average American consumer would soon be able to realize over $1,000 per year” by granting limited, anonymous access to their data to marketers, but that figure was never supported by Green or the company. === Launch of TeamData === In May 2016, Personal shifted its product focus to TeamData, which focuses on the problem of securing and collaboratively managing data in the workplace. It is now a separate business.

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