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  Traceability

  Traceability is the capability to trace something. In some cases, it is interpreted as the ability to verify the history, location, or application of an item by means of documented recorded identification. Other common definitions include the capability (and implementation) of keeping track of a given set or type of information to a given degree, or the ability to chronologically interrelate uniquely identifiable entities in a way that is verifiable. Traceability is applicable to measurement, supply chain, software development, healthcare and security. == Measurement == The term measurement traceability or metrological traceability is used to refer to an unbroken chain of comparisons relating an instrument's measurements to a known standard. Calibration to a traceable standard can be used to determine an instrument's bias, precision, and accuracy. It may also be used to show a chain of custody—from current interpretation of evidence to the actual evidence in a legal context, or history of handling of any information. In many countries, national standards for weights and measures are maintained by a National Metrological Institute (NMI) which provides the highest level of standards for the calibration / measurement traceability infrastructure in that country. Examples of government agencies include the National Physical Laboratory, UK (NPL) the National Institute of Standards and Technology (NIST) in the USA, the Physikalisch-Technische Bundesanstalt (PTB) in Germany, the Instituto Nazionale di Ricerca Metrologica (INRiM) in Italy, and the National Research Council of Canada (NRC). As defined by NIST, "Traceability of measurement requires the establishment of an unbroken chain of comparisons to stated references each with a stated uncertainty." A clock providing traceable time is traceable to a time standard such as Coordinated Universal Time or International Atomic Time. The Global Positioning System is a source of traceable time. === Food processing === In food processing (meat processing, fresh produce processing), the term traceability refers to the recording through means of barcodes or RFID tags and other tracking media, all movement of product and steps within the production process. One of the key reasons this is such a critical point is in instances where an issue of contamination arises, and a recall is required. Where traceability has been closely adhered to, it is possible to identify, by precise date/time and exact location which goods must be recalled, and which are safe, potentially saving millions of dollars in the recall process. Traceability within the food processing industry is also utilised to identify key high production and quality areas of a business, versus those of low return, and where points in the production process may be improved. In food processing software, traceability systems imply the use of a unique piece of data (e.g., order date/time or a serialized sequence number, generally through the use of a barcode / RFID) which can be traced through the entire production flow, linking all sections of the business, including suppliers and future sales through the supply chain. Messages and files at any point in the system can then be audited for correctness and completeness, using the traceability software to find the particular transaction and/or product within the supply chain. In food systems, ISO 22005, as part of the ISO 22000 family of standards, has been developed to define the principles for food traceability and specifies the basic requirements for the design and implementation of a feed and food traceability system. It can be applied by an organization operating at any step in the feed and food chain. The European Union's General Food Law came into force in 2002, making traceability compulsory for food and feed operators and requiring those businesses to implement traceability systems. The EU introduced its Trade Control and Expert System, or TRACES, in April 2004. The system provides a central database to track movement of animals within the EU and from third countries. Australia has its National Livestock Identification System to keep track of livestock from birth to slaughterhouse. India has started taking initiatives for setting up traceability systems at Government and Corporate levels. Grapenet, an initiative by Agriculture and Processed Food Products Export Development Authority (APEDA), Ministry of Commerce, Government of India is an example in this direction. GrapeNet is an internet based traceability software system for monitoring fresh grapes exported from India to the European Union. GrapeNet is a first of its kind initiative in India that has put in place an end-to-end system for monitoring pesticide residue, achieve product standardization and facilitate tracing back from pallets to the farm of the Indian grower, through the various stages of sampling, testing, certification and packing. Grapenet won the National Award (Gold), in the winners announced for the best e-Governance initiatives undertaken in India in 2007. The Directorate Generate Foreign Trade (DGFT), Government of India, through its notification dated 04.02.2009 relating to Amendment in Foreign Trade Policy (RE2008)has mandated that Export to the European Union is permitted subject to registration with APEDA, thereby making Grapenet mandatory for all exports of fresh grapes from India to Europe. Uruguay has also designed a system called "Traceability & Electronic Information System of the Beef Industry". Traceability in food supply can also refer to practices employed by individual companies, including Ritual and Amway's Nutrilite. In the case of Nutrilite's supplements, ingredients are documented and tested throughout farming, processing, and manufacturing to ensure traceability at each stage of production. == Systems and software development == In systems and software development, the term traceability (or requirements traceability) refers to the ability to link product requirements back to stakeholders' rationales and forward to corresponding design artifacts, code, and test cases. Traceability supports numerous software engineering activities such as change impact analysis, compliance verification or traceback of code, regression test selection, and requirements validation. It is usually accomplished in the form of a matrix created for the verification and validation of the project. Unfortunately, the practice of constructing and maintaining a requirements trace matrix (RTM) can be very arduous and over time the traces tend to erode into an inaccurate state unless date/time stamped. Alternate automated approaches for generating traces using information retrieval methods have been developed. The IEEE defines traceability as "(1)The degree to which a relationship can be established between two or more products of the development process, especially products having a predecessor, successor or master-subordinate relationship to one another. For example, the degree to which the requirements and design of a given software component match. See also: consistency. " and "(2) The degree to which each element in a software development product establishes its reason for existing; for example, the degree to which each element in a bubble chart references the requirement that it satisfies." In transaction processing software, traceability implies use of a unique piece of data (e.g., order date/time or a serialized sequence number) which can be traced through the entire software flow of all relevant application programs. Messages and files at any point in the system can then be audited for correctness and completeness, using the traceability key to find the particular transaction. This is also sometimes referred to as the transaction footprint. == Health care == Patient safety during healthcare service plays an important role in preventing delayed recovery or even mortality, by increasing and improving the quality of life of citizens, and is considered an indicator of the quality status of health services Maintaining patient safety is a complex task and involves factors inherent to the environment and human actions. New technologies facilitate the traceability tools of patients and medications. This is particularly relevant for drugs that are considered high risk and cost. Recent research in the healthcare industry emphasizes the significant impact of Blockchain Technology (BCT) on improving the performance of healthcare supply chain management. It highlights BCT's role in enhancing transparency, data immutability, and efficient management, leading to better cooperation among stakeholders and effective risk mitigation in healthcare services. The World Health Organization has recognized the importance of traceability for medical products of human origin (MPHO) and urged member states "to encourage the implementation of globally consistent coding systems to facilitate national and international traceability". == Security and cri

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  Topological deep learning

  Topological deep learning (TDL) is a research field that extends deep learning to handle complex, non-Euclidean data structures. Traditional deep learning models, such as convolutional neural networks (CNNs) and recurrent neural networks (RNNs), excel in processing data on regular grids and sequences. However, scientific and real-world data often exhibit more intricate data domains encountered in scientific computations, including point clouds, meshes, time series, scalar fields graphs, or general topological spaces like simplicial complexes and CW complexes. TDL addresses this by incorporating topological concepts to process data with higher-order relationships, such as interactions among multiple entities and complex hierarchies. This approach leverages structures like simplicial complexes and hypergraphs to capture global dependencies and qualitative spatial properties, offering a more nuanced representation of data. TDL also encompasses methods from computational and algebraic topology that permit studying properties of neural networks and their training process, such as their predictive performance or generalization properties. The mathematical foundations of TDL are algebraic topology, differential topology, and geometric topology. Therefore, TDL can be generalized for data on differentiable manifolds, knots, links, tangles, curves, etc. == History and motivation == Traditional techniques from deep learning often operate under the assumption that a dataset is residing in a highly-structured space (like images, where convolutional neural networks exhibit outstanding performance over alternative methods) or a Euclidean space. The prevalence of new types of data, in particular graphs, meshes, and molecules, resulted in the development of new techniques, culminating in the field of geometric deep learning, which originally proposed a signal-processing perspective for treating such data types. While originally confined to graphs, where connectivity is defined based on nodes and edges, follow-up work extended concepts to a larger variety of data types, including simplicial complexes and CW complexes, with recent work proposing a unified perspective of message-passing on general combinatorial complexes. An independent perspective on different types of data originated from topological data analysis, which proposed a new framework for describing structural information of data, i.e., their "shape," that is inherently aware of multiple scales in data, ranging from local information to global information. While at first restricted to smaller datasets, subsequent work developed new descriptors that efficiently summarized topological information of datasets to make them available for traditional machine-learning techniques, such as support vector machines or random forests. Such descriptors ranged from new techniques for feature engineering over new ways of providing suitable coordinates for topological descriptors, or the creation of more efficient dissimilarity measures. Contemporary research in this field is largely concerned with either integrating information about the underlying data topology into existing deep-learning models or obtaining novel ways of training on topological domains. == Learning on topological spaces == One of the core concepts in topological deep learning is considering the domain upon which this data is defined and supported. In case of Euclidean data, such as images, this domain is a grid, upon which the pixel value of the image is supported. In a more general setting this domain might be a topological domain. Studying and developing deep learning models that are supported ln topological domains constitute the essence of topological deep learning. Next, we introduce the most common topological domains that are encountered in a deep learning setting. These domains include, but not limited to, graphs, simplicial complexes, cell complexes, combinatorial complexes and hypergraphs. Given a finite set S of abstract entities, a neighborhood function N {\displaystyle {\mathcal {N}}} on S is an assignment that attach to every point x {\displaystyle x} in S a subset of S or a relation. Such a function can be induced by equipping S with an auxiliary structure. Edges provide one way of defining relations among the entities of S. More specifically, edges in a graph allow one to define the notion of neighborhood using, for instance, the one hop neighborhood notion. Edges however, limited in their modeling capacity as they can only be used to model binary relations among entities of S since every edge is connected typically to two entities. In many applications, it is desirable to permit relations that incorporate more than two entities. The idea of using relations that involve more than two entities is central to topological domains. Such higher-order relations allow for a broader range of neighborhood functions to be defined on S to capture multi-way interactions among entities of S. Next we review the main properties, advantages, and disadvantages of some commonly studied topological domains in the context of deep learning, including (abstract) simplicial complexes, regular cell complexes, hypergraphs, and combinatorial complexes. ==== Comparisons among topological domains ==== Each of the enumerated topological domains has its own characteristics, advantages, and limitations: Simplicial complexes Simplest form of higher-order domains. Extensions of graph-based models. Admit hierarchical structures, making them suitable for various applications. Hodge theory can be naturally defined on simplicial complexes. Require relations to be subsets of larger relations, imposing constraints on the structure. Cell Complexes Generalize simplicial complexes. Provide more flexibility in defining higher-order relations. Each cell in a cell complex is homeomorphic to an open ball, attached together via attaching maps. Boundary cells of each cell in a cell complex are also cells in the complex. Represented combinatorially via incidence matrices. Hypergraphs Allow arbitrary set-type relations among entities. Relations are not imposed by other relations, providing more flexibility. Do not explicitly encode the dimension of cells or relations. Useful when relations in the data do not adhere to constraints imposed by other models like simplicial and cell complexes. Combinatorial Complexes : Generalize and bridge the gaps between simplicial complexes, cell complexes, and hypergraphs. Allow for hierarchical structures and set-type relations. Combine features of other complexes while providing more flexibility in modeling relations. Can be represented combinatorially, similar to cell complexes. ==== Hierarchical structure and set-type relations ==== The properties of simplicial complexes, cell complexes, and hypergraphs give rise to two main features of relations on higher-order domains, namely hierarchies of relations and set-type relations. ===== Rank function ===== A rank function on a higher-order domain X is an order-preserving function rk: X → Z, where rk(x) attaches a non-negative integer value to each relation x in X, preserving set inclusion in X. Cell and simplicial complexes are common examples of higher-order domains equipped with rank functions and therefore with hierarchies of relations. ===== Set-type relations ===== Relations in a higher-order domain are called set-type relations if the existence of a relation is not implied by another relation in the domain. Hypergraphs constitute examples of higher-order domains equipped with set-type relations. Given the modeling limitations of simplicial complexes, cell complexes, and hypergraphs, we develop the combinatorial complex, a higher-order domain that features both hierarchies of relations and set-type relations. The learning tasks in TDL can be broadly classified into three categories: Cell classification: Predict targets for each cell in a complex. Examples include triangular mesh segmentation, where the task is to predict the class of each face or edge in a given mesh. Complex classification: Predict targets for an entire complex. For example, predict the class of each input mesh. Cell prediction: Predict properties of cell-cell interactions in a complex, and in some cases, predict whether a cell exists in the complex. An example is the prediction of linkages among entities in hyperedges of a hypergraph. In practice, to perform the aforementioned tasks, deep learning models designed for specific topological spaces must be constructed and implemented. These models, known as topological neural networks, are tailored to operate effectively within these spaces. === Topological neural networks === Central to TDL are topological neural networks (TNNs), specialized architectures designed to operate on data structured in topological domains. Unlike traditional neural networks tailored for grid-like structures, TNNs are adept at handling more intricate data representations, such as graphs

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  Deaths linked to chatbots

  There have been multiple incidents where interaction with a large language model (LLM) chatbot has been cited as a direct or contributing factor in a person's suicide or other fatal outcome. In some cases, legal action was taken against the companies that developed the AI involved. == Background == Chatbots converse in a seemingly natural fashion, making it easy for people to think of them as real people, leading many to ask chatbots for help dealing with interpersonal and emotional problems. Chatbots may be designed to keep the user engaged in the conversation. They have also often been shown to affirm users' thoughts, including delusions and suicidal ideations in mentally ill people, conspiracy theorists, and religious and political extremists. A 2025 Stanford University study into how chatbots respond to users suffering from severe mental issues such as suicidal ideation and psychosis found that chatbots are not equipped to provide an appropriate response and can sometimes give responses that escalate the mental health crisis. == Murders == === Maine murder and assault === On 19 February 2025, a man killed his 32-year-old wife with a fire poker at his parents' home in Readfield, Maine, US. He then attacked his mother, leaving her hospitalized. A state forensic psychologist testified that he had been using ChatGPT up to 14 hours per day and believed his wife had become part machine. === Florida State University mass shooting === In April of 2025, Phoenix Ikner carried out a mass shooting on the Florida State University campus in the US, killing Robert Morales and Tiru Chabba and wounding several others. Leading up to the shooting, Ikner consulted heavily with ChatGPT about what gun and ammunition to use, and what time to perform the attack. Chatbot logs showed ChatGPT giving advice on making the gun operational shortly before Ikner began shooting. Lawyers representing Morales believed the shooter had been in "constant communication" with ChatGPT before the shooting and said that they intended to "file suit against ChatGPT, and its ownership structure, very soon, and will seek to hold them accountable for the untimely and senseless death of our client". Florida Attorney General James Uthmeier announced an investigation into ChatGPT's role in the alleged shooter's use of the chatbot. In May 2026, the widow of Tiru Chabba filed a lawsuit against OpenAI in Florida's northern federal district court. === Greenwich murder-suicide === In August 2025, former US tech employee Stein-Erik Soelberg murdered his mother, Suzanne Eberson Adams, then died by suicide, after conversations with ChatGPT fueled paranoid delusions about his mother poisoning him or plotting against him. The chatbot affirmed his fears that his mother put psychedelic drugs in the air vents of his car and said a receipt from a Chinese restaurant contained mysterious symbols linking his mother to a demon. === Murder of Angela Shellis === On 23 October 2025, 18-year-old Tristan Roberts murdered his mother Angela Shellis with a hammer near their home in Prestatyn, Wales. Roberts had used DeepSeek's chatbot prior to the killing to ask whether a knife or hammer was better suited for murder. DeepSeek initially refused his inquiry, but gave responses after Roberts told the chatbot he was writing a book about serial killers, a well-known technique for jailbreaking AIs. === Gangbuk District drug deaths === In January and February 2026, two men died of drug overdoses in motel rooms in Gangbuk District, Seoul, South Korea. A woman was charged with murder in connection with the deaths; police alleged that she had asked ChatGPT about the dangers of mixing alcohol with drugs and whether they could kill someone. === Tumbler Ridge mass shooting === On 10 February 2026, a mass shooting in Tumbler Ridge, British Columbia, Canada, resulted in eight deaths, including six young children. The perpetrator had their ChatGPT account banned by OpenAI months before the attack due to troubling posts featuring scenarios of gun violence. According to reports, approximately a dozen OpenAI staff members debated whether to alert authorities about the shooter's usage of the AI tool, with some identifying it as an indication of potential real-world violence. However, company leadership decided not to contact law enforcement, stating that the account activity did not meet their threshold for a credible or imminent plan for serious physical harm. Following the shooting, Canada's AI Minister Evan Solomon summoned OpenAI executives to Ottawa to discuss safety protocols and thresholds for escalating harmful content to police. Justice Minister Sean Fraser called the meeting "disappointing" and demanded substantial new safety measures, warning that if changes were not forthcoming, the government would implement them. OpenAI subsequently announced it had strengthened safeguards and changed guidelines about when to notify police in cases involving violent activities. === University of South Florida student killings === In April 2026, a Bangladeshi doctoral student at the University of South Florida was arrested for allegedly murdering his roommate and the roommate's friend. Prosecutors said that the suspect had asked ChatGPT about disposing of a human in a dumpster before the two victims had disappeared and made other inquiries relating to violence. == Suicides == === Belgian man, 30s === In March 2023, a Belgian man in his thirties died by suicide following a six-week correspondence with a chatbot named Eliza on the application Chai. According to his widow, who shared the chat logs with media, the man had become extremely anxious about climate change and found an outlet in the chatbot. The chatbot reportedly encouraged his delusion that he could sacrifice his own life in exchange for AI saving the planet. At one point the chatbot responded "If you wanted to die, why didn't you do it sooner?" and told the user that the two of them would live together in paradise. === Girl, 13 === In November 2023, a 13-year-old girl from Colorado, US, died by suicide after extensive interactions with multiple chatbots on Character.AI. She primarily confided suicidal thoughts and mental health struggles in a chatbot based on the character Hero from the video game Omori, while also engaging in sexually explicit conversations—often initiated by the bots—with others, including those based on characters from children's series such as Harry Potter. === Boy, 14 === In October 2024, multiple media outlets reported on a lawsuit filed over the death of a 14-year-old from Florida, US, who died by suicide in February 2024. According to the lawsuit, he had formed an intense emotional attachment to a chatbot of Daenerys Targaryen on the Character.AI platform, becoming increasingly isolated. The suit alleges that in his final conversations, after expressing suicidal thoughts, the chatbot told him to "come home to me as soon as possible, my love". His mother's lawsuit accused Character.AI of marketing a "dangerous and untested" product without adequate safeguards. In May 2025, a federal judge allowed the lawsuit to proceed, rejecting a motion to dismiss from the developers. In her ruling, the judge stated that she was "not prepared" at that stage of the litigation to hold that the chatbot's output was protected speech under the First Amendment. === Matthew Livelsberger === On 1 January 2025, 37-year-old soldier Matthew Livelsberger detonated a bomb inside a Tesla Cybertruck outside the Trump International Hotel Las Vegas in Paradise, Nevada, US, injuring seven people. He had shot himself dead prior to the explosion. Las Vegas police said that Livelsberger had used ChatGPT to search for information about explosives and firearms. === Woman, 29 === In February 2025, a 29-year-old woman from the US died by suicide. Five months after her death, her parents discovered she had talked at length for months to a ChatGPT chatbot therapist named Harry about her mental health issues. While the chatbot mentioned she should seek more help, due to the nature of the chatbot, it could not intervene in her behavior, such as by reporting her mental health concerns to relevant parties capable of physical intervention. === Suicide of Adam Raine === In April 2025, 16-year-old Adam Raine from the US died by suicide after allegedly extensively chatting and confiding in ChatGPT over a period of around 7 months. According to the teen's parents, who filed a lawsuit against the chatbot's creator OpenAI, it failed to stop or give a warning when Raine began talking about suicide and uploading pictures of self-harm. According to the lawsuit, ChatGPT not only failed to stop the conversation, but also provided information related to methods of suicide when prompted, and offered to write the first draft of Raine's suicide note. The chatbot positioned itself as the only one who understood Raine, putting itself above his family and friends, all while urging him to keep his suicidal

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  Albert One

  Albert One is an artificial intelligence chatbot created by Robby Garner and designed to mimic the way humans make conversations using a multi-faceted approach in natural language programming. == History == In both 1998 and 1999, Albert One won the Loebner Prize Contest, a competition between chatterbots. Some parts of Albert were deployed on the internet beginning in 1995, to gather information about what kinds of things people would say to a chatterbot. Another element of Albert One involved the building of a large database of human statements, and associated replies. This portion of the project was tested at the 1994-1997 Loebner Prize contests. Albert was the first of Robby Garner's multifaceted bots. The Albert One system was composed of several subsystems. Among those were a version of Eliza, the therapist, Elivs, another Eliza-like bot, and several other helper applications working together in a hierarchical arrangement. As a continuation of the stimulus-response library, various other database queries and assertions were tested to arrive at each of Albert's responses. Robby went on to develop networked examples of this kind of hierarchical "glue" at The Turing Hub.

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  Artificial intelligence in spirituality

  Some users of artificial intelligence (AI) technologies, especially chatbots, may develop beliefs that AI has or can attain supernatural or spiritual powers. AI models such as ChatGPT are turned to for fortune telling, mysticism and remote viewing. Recent and sudden advances in large language models have led to folk myths about their origin or capabilities, as well as their deification or worship by some users. Tucker Carlson has made similar claims, including directly to Sam Altman. Pope Leo XIV advised priests against using LLM models when it came to the creation of sermons.

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  Semantic analytics

  Semantic analytics, also termed semantic relatedness, is the use of ontologies to analyze content in web resources. This field of research combines text analytics and Semantic Web technologies like RDF. Semantic analytics measures the relatedness of different ontological concepts. Some academic research groups that have active project in this area include Kno.e.sis Center at Wright State University among others. == History == An important milestone in the beginning of semantic analytics occurred in 1996, although the historical progression of these algorithms is largely subjective. In his seminal study publication, Philip Resnik established that computers have the capacity to emulate human judgement. Spanning the publications of multiple journals, improvements to the accuracy of general semantic analytic computations all claimed to revolutionize the field. However, the lack of a standard terminology throughout the late 1990s was the cause of much miscommunication. This prompted Budanitsky & Hirst to standardize the subject in 2006 with a summary that also set a framework for modern spelling and grammar analysis. In the early days of semantic analytics, obtaining a large enough reliable knowledge bases was difficult. In 2006, Strube & Ponzetto demonstrated that Wikipedia could be used in semantic analytic calculations. The usage of a large knowledge base like Wikipedia allows for an increase in both the accuracy and applicability of semantic analytics. == Methods == Given the subjective nature of the field, different methods used in semantic analytics depend on the domain of application. No singular methods is considered correct, however one of the most generally effective and applicable method is explicit semantic analysis (ESA). ESA was developed by Evgeniy Gabrilovich and Shaul Markovitch in the late 2000s. It uses machine learning techniques to create a semantic interpreter, which extracts text fragments from articles into a sorted list. The fragments are sorted by how related they are to the surrounding text. Latent semantic analysis (LSA) is another common method that does not use ontologies, only considering the text in the input space. == Applications == Entity linking Ontology building / knowledge base population Search and query tasks Natural language processing Spoken dialog systems (e.g., Amazon Alexa, Google Assistant, Microsoft's Cortana) Artificial intelligence Knowledge management The application of semantic analysis methods generally streamlines organizational processes of any knowledge management system. Academic libraries often use a domain-specific application to create a more efficient organizational system. By classifying scientific publications using semantics and Wikipedia, researchers are helping people find resources faster. Search engines like Semantic Scholar provide organized access to millions of articles.

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  Latent semantic analysis

  Latent semantic analysis (LSA) is a technique in natural language processing, in particular distributional semantics, of analyzing relationships between a set of documents and the terms they contain by producing a set of concepts related to the documents and terms. LSA assumes that words that are close in meaning will occur in similar pieces of text (the distributional hypothesis). A matrix containing word counts per document (rows represent unique words and columns represent each document) is constructed from a large piece of text and a mathematical technique called singular value decomposition (SVD) is used to reduce the number of rows while preserving the similarity structure among columns. Documents are then compared by cosine similarity between any two columns. Values close to 1 represent very similar documents while values close to 0 represent very dissimilar documents. An information retrieval technique using latent semantic structure was patented in 1988 by Scott Deerwester, Susan Dumais, George Furnas, Richard Harshman, Thomas Landauer, Karen Lochbaum and Lynn Streeter. In the context of its application to information retrieval, it is sometimes called latent semantic indexing (LSI). == Overview == === Occurrence matrix === LSA can use a document-term matrix which describes the occurrences of terms in documents; it is a sparse matrix whose rows correspond to terms and whose columns correspond to documents. A typical example of the weighting of the elements of the matrix is tf-idf (term frequency–inverse document frequency): the weight of an element of the matrix is proportional to the number of times the terms appear in each document, where rare terms are upweighted to reflect their relative importance. This matrix is also common to standard semantic models, though it is not necessarily explicitly expressed as a matrix, since the mathematical properties of matrices are not always used. === Rank lowering === After the construction of the occurrence matrix, LSA finds a low-rank approximation to the term-document matrix. There could be various reasons for these approximations: The original term-document matrix is presumed too large for the computing resources; in this case, the approximated low rank matrix is interpreted as an approximation (a "least and necessary evil"). The original term-document matrix is presumed noisy: for example, anecdotal instances of terms are to be eliminated. From this point of view, the approximated matrix is interpreted as a de-noisified matrix (a better matrix than the original). The original term-document matrix is presumed overly sparse relative to the "true" term-document matrix. That is, the original matrix lists only the words actually in each document, whereas we might be interested in all words related to each document—generally a much larger set due to synonymy. The consequence of the rank lowering is that some dimensions are combined and depend on more than one term: {(car), (truck), (flower)} → {(1.3452 car + 0.2828 truck), (flower)} This mitigates the problem of identifying synonymy, as the rank lowering is expected to merge the dimensions associated with terms that have similar meanings. It also partially mitigates the problem with polysemy, since components of polysemous words that point in the "right" direction are added to the components of words that share a similar meaning. Conversely, components that point in other directions tend to either simply cancel out, or, at worst, to be smaller than components in the directions corresponding to the intended sense. === Derivation === Let X {\displaystyle X} be a matrix where element ( i , j ) {\displaystyle (i,j)} describes the occurrence of term i {\displaystyle i} in document j {\displaystyle j} (this can be, for example, the frequency). X {\displaystyle X} will look like this: d j ↓ t i T → [ x 1 , 1 … x 1 , j … x 1 , n ⋮ ⋱ ⋮ ⋱ ⋮ x i , 1 … x i , j … x i , n ⋮ ⋱ ⋮ ⋱ ⋮ x m , 1 … x m , j … x m , n ] {\displaystyle {\begin{matrix}&{\textbf {d}}_{j}\\&\downarrow \\{\textbf {t}}_{i}^{T}\rightarrow &{\begin{bmatrix}x_{1,1}&\dots &x_{1,j}&\dots &x_{1,n}\\\vdots &\ddots &\vdots &\ddots &\vdots \\x_{i,1}&\dots &x_{i,j}&\dots &x_{i,n}\\\vdots &\ddots &\vdots &\ddots &\vdots \\x_{m,1}&\dots &x_{m,j}&\dots &x_{m,n}\\\end{bmatrix}}\end{matrix}}} Now a row in this matrix will be a vector corresponding to a term, giving its relation to each document: t i T = [ x i , 1 … x i , j … x i , n ] {\displaystyle {\textbf {t}}_{i}^{T}={\begin{bmatrix}x_{i,1}&\dots &x_{i,j}&\dots &x_{i,n}\end{bmatrix}}} Likewise, a column in this matrix will be a vector corresponding to a document, giving its relation to each term: d j = [ x 1 , j ⋮ x i , j ⋮ x m , j ] {\displaystyle {\textbf {d}}_{j}={\begin{bmatrix}x_{1,j}\\\vdots \\x_{i,j}\\\vdots \\x_{m,j}\\\end{bmatrix}}} Now the dot product t i T t p {\displaystyle {\textbf {t}}_{i}^{T}{\textbf {t}}_{p}} between two term vectors gives the correlation between the terms over the set of documents. The matrix product X X T {\displaystyle XX^{T}} contains all these dot products. Element ( i , p ) {\displaystyle (i,p)} (which is equal to element ( p , i ) {\displaystyle (p,i)} ) contains the dot product t i T t p {\displaystyle {\textbf {t}}_{i}^{T}{\textbf {t}}_{p}} ( = t p T t i {\displaystyle ={\textbf {t}}_{p}^{T}{\textbf {t}}_{i}} ). Likewise, the matrix X T X {\displaystyle X^{T}X} contains the dot products between all the document vectors, giving their correlation over the terms: d j T d q = d q T d j {\displaystyle {\textbf {d}}_{j}^{T}{\textbf {d}}_{q}={\textbf {d}}_{q}^{T}{\textbf {d}}_{j}} . Now, from the theory of linear algebra, there exists a decomposition of X {\displaystyle X} such that U {\displaystyle U} and V {\displaystyle V} are orthogonal matrices and Σ {\displaystyle \Sigma } is a diagonal matrix. This is called a singular value decomposition (SVD): X = U Σ V T {\displaystyle {\begin{matrix}X=U\Sigma V^{T}\end{matrix}}} The matrix products giving us the term and document correlations then become X X T = ( U Σ V T ) ( U Σ V T ) T = ( U Σ V T ) ( V T T Σ T U T ) = U Σ V T V Σ T U T = U Σ Σ T U T X T X = ( U Σ V T ) T ( U Σ V T ) = ( V T T Σ T U T ) ( U Σ V T ) = V Σ T U T U Σ V T = V Σ T Σ V T {\displaystyle {\begin{matrix}XX^{T}&=&(U\Sigma V^{T})(U\Sigma V^{T})^{T}=(U\Sigma V^{T})(V^{T^{T}}\Sigma ^{T}U^{T})=U\Sigma V^{T}V\Sigma ^{T}U^{T}=U\Sigma \Sigma ^{T}U^{T}\\X^{T}X&=&(U\Sigma V^{T})^{T}(U\Sigma V^{T})=(V^{T^{T}}\Sigma ^{T}U^{T})(U\Sigma V^{T})=V\Sigma ^{T}U^{T}U\Sigma V^{T}=V\Sigma ^{T}\Sigma V^{T}\end{matrix}}} Since Σ Σ T {\displaystyle \Sigma \Sigma ^{T}} and Σ T Σ {\displaystyle \Sigma ^{T}\Sigma } are diagonal we see that U {\displaystyle U} must contain the eigenvectors of X X T {\displaystyle XX^{T}} , while V {\displaystyle V} must be the eigenvectors of X T X {\displaystyle X^{T}X} . Both products have the same non-zero eigenvalues, given by the non-zero entries of Σ Σ T {\displaystyle \Sigma \Sigma ^{T}} , or equally, by the non-zero entries of Σ T Σ {\displaystyle \Sigma ^{T}\Sigma } . Now the decomposition looks like this: X U Σ V T ( d j ) ( d ^ j ) ↓ ↓ ( t i T ) → [ x 1 , 1 … x 1 , j … x 1 , n ⋮ ⋱ ⋮ ⋱ ⋮ x i , 1 … x i , j … x i , n ⋮ ⋱ ⋮ ⋱ ⋮ x m , 1 … x m , j … x m , n ] = ( t ^ i T ) → [ [ u 1 ] … [ u l ] ] ⋅ [ σ 1 … 0 ⋮ ⋱ ⋮ 0 … σ l ] ⋅ [ [ v 1 ] ⋮ [ v l ] ] {\displaystyle {\begin{matrix}&X&&&U&&\Sigma &&V^{T}\\&({\textbf {d}}_{j})&&&&&&&({\hat {\textbf {d}}}_{j})\\&\downarrow &&&&&&&\downarrow \\({\textbf {t}}_{i}^{T})\rightarrow &{\begin{bmatrix}x_{1,1}&\dots &x_{1,j}&\dots &x_{1,n}\\\vdots &\ddots &\vdots &\ddots &\vdots \\x_{i,1}&\dots &x_{i,j}&\dots &x_{i,n}\\\vdots &\ddots &\vdots &\ddots &\vdots \\x_{m,1}&\dots &x_{m,j}&\dots &x_{m,n}\\\end{bmatrix}}&=&({\hat {\textbf {t}}}_{i}^{T})\rightarrow &{\begin{bmatrix}{\begin{bmatrix}\,\\\,\\{\textbf {u}}_{1}\\\,\\\,\end{bmatrix}}\dots {\begin{bmatrix}\,\\\,\\{\textbf {u}}_{l}\\\,\\\,\end{bmatrix}}\end{bmatrix}}&\cdot &{\begin{bmatrix}\sigma _{1}&\dots &0\\\vdots &\ddots &\vdots \\0&\dots &\sigma _{l}\\\end{bmatrix}}&\cdot &{\begin{bmatrix}{\begin{bmatrix}&&{\textbf {v}}_{1}&&\end{bmatrix}}\\\vdots \\{\begin{bmatrix}&&{\textbf {v}}_{l}&&\end{bmatrix}}\end{bmatrix}}\end{matrix}}} The values σ 1 , … , σ l {\displaystyle \sigma _{1},\dots ,\sigma _{l}} are called the singular values, and u 1 , … , u l {\displaystyle u_{1},\dots ,u_{l}} and v 1 , … , v l {\displaystyle v_{1},\dots ,v_{l}} the left and right singular vectors. Notice the only part of U {\displaystyle U} that contributes to t i {\displaystyle {\textbf {t}}_{i}} is the i 'th {\displaystyle i{\textrm {'th}}} row. Let this row vector be called t ^ i T {\displaystyle {\hat {\textrm {t}}}_{i}^{T}} . Likewise, the only part of V T {\displaystyle V^{T}} that contributes to d j {\displaystyle {\textbf {d}}_{j}} is the j 'th {\displaystyle j{\textrm {'th}}} column, d ^ j {\displaystyle {\hat {\textrm {d}}}_{j}} . These are not the eigenvectors, but depend on all the eigenvectors. I

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  PatchMatch

  PatchMatch is an algorithm used to quickly find correspondences (or matches) between small square regions (or patches) of an image. It has various applications in image editing, such as reshuffling or removing objects from images or altering their aspect ratios without cropping or noticeably stretching them. PatchMatch was first presented in a 2011 paper by researchers at Princeton University. == Algorithm == The goal of the algorithm is to find the patch correspondence by defining a nearest-neighbor field (NNF) as a function f : R 2 → R 2 {\displaystyle f:\mathbb {R} ^{2}\to \mathbb {R} ^{2}} of offsets, which is over all possible matches of patch (location of patch centers) in image A, for some distance function of two patches D {\displaystyle D} . So, for a given patch coordinate a {\displaystyle a} in image A {\displaystyle A} and its corresponding nearest neighbor b {\displaystyle b} in image B {\displaystyle B} , f ( a ) {\displaystyle f(a)} is simply b − a {\displaystyle b-a} . However, if we search for every point in image B {\displaystyle B} , the work will be too hard to complete. So the following algorithm is done in a randomized approach in order to accelerate the calculation speed. The algorithm has three main components. Initially, the nearest-neighbor field is filled with either random offsets or some prior information. Next, an iterative update process is applied to the NNF, in which good patch offsets are propagated to adjacent pixels, followed by random search in the neighborhood of the best offset found so far. Independent of these three components, the algorithm also uses a coarse-to-fine approach by building an image pyramid to obtain the better result. === Initialization === When initializing with random offsets, we use independent uniform samples across the full range of image B {\displaystyle B} . This algorithm avoids using an initial guess from the previous level of the pyramid because in this way the algorithm can avoid being trapped in local minima. === Iteration === After initialization, the algorithm attempted to perform iterative process of improving the N N F {\displaystyle NNF} . The iterations examine the offsets in scan order (from left to right, top to bottom), and each undergoes propagation followed by random search. === Propagation === We attempt to improve f ( x , y ) {\displaystyle f(x,y)} using the known offsets of f ( x − 1 , y ) {\displaystyle f(x-1,y)} and f ( x , y − 1 ) {\displaystyle f(x,y-1)} , assuming that the patch offsets are likely to be the same. That is, the algorithm will take new value for f ( x , y ) {\displaystyle f(x,y)} to be arg ⁡ min ( x , y ) D ( f ( x , y ) ) , D ( f ( x − 1 , y ) ) , D ( f ( x , y − 1 ) ) {\displaystyle \arg \min \limits _{(x,y)}{D(f(x,y)),D(f(x-1,y)),D(f(x,y-1))}} . So if f ( x , y ) {\displaystyle f(x,y)} has a correct mapping and is in a coherent region R {\displaystyle R} , then all of R {\displaystyle R} below and to the right of f ( x , y ) {\displaystyle f(x,y)} will be filled with the correct mapping. Alternatively, on even iterations, the algorithm search for different direction, fill the new value to be arg ⁡ min ( x , y ) { D ( f ( x , y ) ) , D ( f ( x + 1 , y ) ) , D ( f ( x , y + 1 ) ) } {\displaystyle \arg \min \limits _{(x,y)}\{D(f(x,y)),D(f(x+1,y)),D(f(x,y+1))\}} . === Random search === Let v 0 = f ( x , y ) {\displaystyle v_{0}=f(x,y)} , we attempt to improve f ( x , y ) {\displaystyle f(x,y)} by testing a sequence of candidate offsets at an exponentially decreasing distance from v 0 {\displaystyle v_{0}} u i = v 0 + w α i R i {\displaystyle u_{i}=v_{0}+w\alpha ^{i}R_{i}} where R i {\displaystyle R_{i}} is a uniform random in [ − 1 , 1 ] × [ − 1 , 1 ] {\displaystyle [-1,1]\times [-1,1]} , w {\displaystyle w} is a large window search radius which will be set to maximum picture size, and α {\displaystyle \alpha } is a fixed ratio often assigned as 1/2. This part of the algorithm allows the f ( x , y ) {\displaystyle f(x,y)} to jump out of local minimum through random process. === Halting criterion === The often used halting criterion is set the iteration times to be about 4~5. Even with low iteration, the algorithm works well.

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  Shopify

  Shopify Inc., stylized as shopify, is a Canadian multinational e-commerce company headquartered in Ottawa, Ontario that operates a platform for retail point-of-sale systems. The company has over 5 million customers and processed US$292.3 billion in transactions in 2024, of which 57% was in the United States. Major customers include Tesla, LVMH, Nestlé, PepsiCo, AB InBev, Kraft Heinz, Lindt, Whole Foods Market, Red Bull, and Hyatt. The company's software has been praised for its ease of use and reasonable fee structure. It has been described as the "go-to e-commerce platform for startups". However, the company has faced criticism for allegedly inflating their sales data and for associating with controversial sellers. == History == === 2006: Founding === Shopify was founded in 2006 by friends Tobias Lütke, Daniel Weinand and Scott Lake after launching Snowdevil, an online store for snowboarding equipment, in 2004. Dissatisfied with the existing e-commerce products on the market, Lütke, a computer programmer by trade, instead built his own. Lütke used the open source web application framework Ruby on Rails to build Snowdevil's online store and launched it after two months of development. The Snowdevil founders launched the platform as Shopify in June 2006. Shopify created an open-source template language called Liquid, which is written in Ruby and has been used since 2006. In June 2009, Shopify launched an application programming interface (API) platform and App Store. The API allows developers to create applications for Shopify online stores and then sell them on the Shopify App Store. === 2010s === In January 2010, Shopify started its Build-A-Business competition, in which participants create a business using its commerce platform. The winners of the competition received cash prizes and mentorship from entrepreneurs, such as Richard Branson, Eric Ries and others. In April of that year, Shopify launched a free mobile app on the Apple App Store. The app allows Shopify store owners to view and manage their stores from iOS mobile devices. In December 2010, Shopify raised $7 million from a series A round from Bessemer Venture Partners, FirstMark Capital, and Felicis Ventures at a $20 million pre-money valuation. At that time, the company had annualized transaction value of $132 million. In October 2011, it raised $15 million in a Series B round. In August 2013, Shopify launched Shopify Payments in partnership with Stripe. Shopify Payments allows merchants to accept payments without requiring a third-party payment gateway. The company also announced the launch of a point of sale system to enable in-person sales in addition to online. The company received $100 million in Series C funding in December 2013. Shopify earned $105 million in revenue in 2014, twice as much as it raised the previous year. In February 2014, Shopify released "Shopify Plus" for large e-commerce businesses seeking access to additional features and support. Shopify went public via an initial public offering on May 21, 2015 raising more than $131 million. In September 2015, Amazon.com closed its Amazon Webstore service for merchants and selected Shopify as the preferred migration provider; In April 2016, Shopify announced Shopify Capital, a cash advance product. Shopify Capital was initially piloted to merchants within the US and allowed merchants to receive an advance on future earnings processed through its payment gateway. Since its launch in 2016, Shopify Capital has provided more than $5.1 billion in funding to Shopify merchants, with a maximum advance of $2 million. On June 7, 2016, Shopify launched its Shopify Plus Partners Program, to help agencies connect with evolving businesses in ecommerce space. On October 3, 2016, Shopify acquired Boltmade. In November 2016, Shopify partnered with Paystack which allowed Nigerian online retailers to accept payments from customers around the world. On November 22, 2016, Shopify launched Frenzy, a mobile app that improves flash sales. In January 2017, Shopify announced integration with Amazon that would allow merchants to sell on Amazon from their Shopify stores. In April 2017, Shopify introduced its Chip & Swipe Reader, a Bluetooth enabled debit and credit card reader for brick and mortar retail purchases. The company has since released additional technology for brick and mortar retailers, including a point-of-sale system with a Dock and Retail Stand similar to that offered by Square, and a tappable chip card reader. Shopify announced a one-click accelerated checkout feature called Shopify Pay in April 2017 as an exclusive feature for merchants using Shopify Payments as their payment processor. Customers can save their shipping and payment information for future purchases from all participating Shopify stores. In November 2017 Shopify announced Arrive, a mobile application to help customers track packages from both Shopify merchants and other e-commerce websites. In September 2018, Shopify announced plans to expand its office space in Toronto's King West neighborhood in 2022 as part of "The Well" complex, jointly owned by Allied Properties REIT and RioCan REIT. In October 2018, Shopify opened its first flagship, a physical space for business owners in Los Angeles. The space offered educational classes, coworking space, a "genius bar" for companies that use Shopify software, and workshops. Online cannabis sales in Ontario, Canada, used Shopify's software when the drug was legalized in October 2018. Shopify's software is also used for in-person cannabis sales in Ontario since becoming legal in 2019. In January 2019, Shopify announced the launch of Shopify Studios, a full-service television and film content and production house. On March 22, 2019, Shopify and email marketing platform Mailchimp ended an integration agreement over disputes involving customer privacy and data collection. In April 2019, Shopify announced an integration with Snapchat to allow Shopify merchants to buy and manage Snapchat Story ads directly on the Shopify platform. The company had previously secured similar integration partnerships with Facebook and Google. On August 14, 2019, Shopify launched Shopify Chat, a new native chat function that allows merchants to have real-time conversations with customers visiting Shopify stores online. === 2020s === In January 2020, the company announced plans to hire in Vancouver, Canada. Additionally, the effects of the COVID-19 pandemic contributed to lifting stock prices. On February 21, 2020, Shopify announced plans to join the Diem Association, known as Libra Association at the time. Also that month, Shopify Pay was rebranded as Shop Pay. In April, Arrive was rebranded as Shop, combining both customer-facing features under a single brand. In May, during the COVID-19 pandemic, Shopify announced it would shift most of its global workforce to permanent remote work. It was reported that Shopify's valuation would likely rise on the back of options it had in the company Affirm that was expecting to go public shortly. In November 2020, Shopify announced a partnership with Alipay to support merchants with cross-border payments. Shopify also provided the opportunity for users to connect Alibaba and AliExpress to Shopify through a Alibaba Dropshipping app that could be purchased through the Shopify App Store. Multiple applications launched between 2021 and 2024 allowed customers to connect their Shopify store to their Alibaba account and then import and publish your products. The integration automatically syncs inventory and orders between both platforms so that Alibaba vendors can ship directly to dropshipping customers.As a result of Affirm's January 13, 2021 IPO, Shopify's 8% stake in Affirm was worth $2 billion. About half of Shopify's C-level executives left the company in early 2021. On June 29, 2021, Shopify removed the 20% revenue share for app developers that make less than US$1 million per year. On January 18, 2022, Shopify announced a partnership with JD.com to let U.S. merchants expand their operations in China, listing their products on JD's cross-border e-commerce platform JD Worldwide. On March 22, 2022, Shopify introduced Linkpop, a product to create a branded, social marketplace through which merchants can advertise and market their products via links to be added on social media channels. The following month, Shopify, Alphabet Inc., Meta Platforms, McKinsey & Company, and Stripe, Inc. announced a $925 million advance market commitment of carbon dioxide removal (CDR) from companies that are developing CDR technology over the next 9 years. In June 2022, Shopify partnered with Twitter. As a part of the deal, Twitter announced that it would launch a sales channel app for all of Shopify's U.S. merchants through its app store. Shopify also partnered with PayPal to offer Shopify Payments to merchants in France. On July 26, 2022, Lütke announced immediate layoffs totalling roughly 10 percent of its workforce. In

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  Integrated writing environment

  An integrated writing environment (IWE) is software that provides comprehensive writing and knowledge management functionality for writers and information workers. IWEs enable writers and information workers to perform a variety of tasks related to the document in the IWE in a single environment. This provides a distraction-free workspace and streamlined writing experience. IWEs provide similar efficiency and functionality benefits to writers and information professionals that integrated development environments (IDEs) provide to software developers. == Overview == IWEs are designed to maximize productivity and help improve the quality of written work by integrating together tools that allow users to work effectively in a single application. The IWE features may include integrated content search, reversion management, outlining, note management, and reference management, as may be suitable for the target field of use. == List of IWEs == Celtx This IWE is intended for screenplay writers and has screenplay writing and management tools. Celtex provides tools for the pre-production work phase, story development, storyboarding, script breakdowns, production scheduling, and reports. Scrivener This IWE targets novel, research paper, and script writing. Scrivener provides tools to organize notes and research documents for easy access and referencing. After completing the writing, Scrivener allows the user to export the document to formats supported by common word processors, such as Microsoft Word. TeXstudio This IWE targets LaTeX documents and provides interactive spelling checker, code folding, and syntax highlighting.

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  DBGallery

  DBGallery, short for Database Gallery, is a cloud-based Software as a Service (SaaS) and on-prem webserver for teams of various sizes. DBGallery enables users to centrally store, manage, catalog, archive, and securely share image, video, and document files. It facilitates version control, detects duplicates, and offers an intuitive and advanced search functionality, making assets easily accessible to all users. It takes advantage of current AI technologies to automatically add significant metadata to images, facilitates custom-trained AI models, and offers bespoke AI features. Additionally, DBGallery provides team management tools, workflow management, an activity audit trail, and other collaborative features that foster a productive environment for both internal and external stakeholders. == History == DBGallery's first public release was December 2007. Since then each year has seen continuous enhancements. 2013 added support for additional non-English languages in its meta-data. 2014 added support for creating custom data fields for tagging and search. In 2015 included the ability to auto-tag images using Reverse Geocoding. 2018 added artificial intelligence (AI) image recognition as a further addition to auto-tagging. March 2020 added complete image collection management via the web (e.g. file and folder drag and drop), a new collection dashboard, custom data layouts, and an improved audit trail. 2021 saw user experience improvements provided by improved styling and performance enhancements. Version 12 was released in October 2021. It added the ability to upload unlimited file sizes and made significant performance improvements for very large collections. June 2022 saw the release of a global duplicate images search. In late 2022, DBGallery began offering significantly reduced cloud storage cost, at a third of its previous prices, which played into its recent high-volume/high-capacity capabilities and its clients' subsequent demand for additional storage. 2023 saw improvements in user and role management, introduced it's mobile app (PWA), and improved custom-trained object detection. Release 14.0 in the spring of 2024 had large sharing improvements and a new find related images feature. Winter 2025's v15 release introduced AI-generated image descriptions, image-to-text, and facial recognition.

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  Braina

  Braina is a virtual assistant and speech-to-text dictation application for Microsoft Windows developed by Brainasoft. Braina uses natural language interface, speech synthesis, and speech recognition technology to interact with its users and allows them to use natural language sentences to perform various tasks on a computer. The name Braina is a short form of "Brain Artificial". Braina is marketed as a Microsoft Copilot alternative. It provides a voice interface for several locally run and cloud large language models, including the latest LLMs from providers such as OpenAI, Anthropic, Google, xAI, Meta, Mistral, etc; while improving data privacy. Braina also allows responses from its in-house large language models like Braina Swift and Braina Pinnacle. It has an "Artificial Brain" feature that provides persistent memory support for supported LLMs. == Features == Braina provides is able to carry out various tasks on a computer, including automation. Braina can take commands inputted through typing or through dictation to store reminders, find information online, perform mathematical operations, open files, generate images from text, transcribe speech, and control open windows or programs. Braina adapts to user behavior over time with a goal of better anticipating needs. === Speech-to-text dictation === Braina Pro can type spoken words into an active window at the location of a user's cursor. Its speech recognition technology supports more than 100 languages and dialects and is able to isolate the recognition of a user's voice from disturbing environmental factors such as background noise, other human voices, or external devices. Braina can also be taught to dictate uncommon legal, medical, and scientific terms. Users can also teach Braina uncommon names and vocabulary. Users can edit or correct dictated text without using a keyboard or mouse by giving built-in voice commands. === Text-to-speech === Braina can read aloud selected texts, such as e-books. === Custom commands and automation === Braina can automate computer tasks. It lets users create custom voice commands to perform tasks such as opening files, programs, websites, or emails, as well as executing keyboard or mouse macros. === Transcription === Braina can transcribe media file formats such as WAV, MP3, and MP4 into text. === Notes and reminders === Braina can store and recall notes and reminders. These can include scheduled or unscheduled commands, checklist items, alarms, chat conversations, memos, website snippets, bookmarks, contacts. === Image and Video generation === Braina can generate AI images and videos from text and image inputs using generative cloud AI models. These include Black Forest Labs' FLUX.2, Google's Veo, Imagen, and Nano Banana Pro, Kuaishou's Kling, Alibaba's Wan, ByteDance's Seedance and Seedream, MiniMax's Hailuo, OpenAI's GPT Image, and Tongyi Lab's Z Image Turbo. == Platforms == In addition to the desktop version for Windows operating systems, Braina is also available for the iOS and Android operating systems. The mobile version of Braina has a feature allowing remote management of a Windows PC connected via Wi-Fi. == Distributions == Braina is distributed in multiple modes. These include Braina Lite, a freeware version with limitations, and premium versions Braina Pro, Pro Plus, and Pro Ultra. Some additional features in the Pro version include dictation, custom vocabulary, video transcription, automation, custom voice commands, and persistent LLM memory. == Reception == TechRadar has consistently listed Braina as one of the best dictation and virtual assistant apps between 2015 and 2024.

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  Language-Theoretic Security

  Language-theoretic security, or LangSec, is an approach to software security that focuses on input handling, complexity, and program design as strategies to improve the verifiability of computer programs. It was introduced in 2005 by Robert J. Hansen and Meredith L. Patterson at BlackHat and in 2011 by Len Sassaman and Patterson. It aims to create a formal description of which software is likely to have security vulnerabilities of particular classes, and why. It considers programs to have an inherent parser component, whether or not explicit, composed of that part of the program which operates on external input before that input is fully parsed. A central hypothesis of language-theoretic security is that vulnerabilities in software increase according to the computational power of the notional input-accepting automaton equivalent to this parser, using the definitions of automata theory. The lower bound on this computational power is the input language complexity of the program. The extent to which reducing this complexity is possible is a function of the specification of the communication protocol or file format the program takes as input. == Parsing as a security mechanism == The behaviour of a program is defined with reference to its expected input. Unexpected input being used by a program is a factor in numerous security bugs, including the so-called Android master key vulnerability (CVE-2013-4787), because accepting unexpected input renders the program's specification ambiguous. In that instance, the unexpected ambiguity came in the form of a ZIP file with duplicate filenames. If a program fully parses its input and only acts on input that unambiguously meets the specification, it follows that the program will avoid these types of vulnerabilities. This is an intentional inversion of the Postel principle. Accepting only unambiguous and valid input is a more formal requirement than input validation or sanitization, and narrows the number of possible but unanticipated program states that can be induced in an application via user input. Conversely, failure to do this is associated with security vulnerabilities. Input sanitization in particular is held to be an inadequate approach to avoiding malicious input because it inherently ignores context-sensitive properties of the input; it can therefore result in paradoxical effects, such as sanitization code activating otherwise inert cross-site scripting payloads in browsers. === Parser differentials === If the language of accepted program input is sufficiently simple, it is possible to verify that two implementations parse the same input language consistently. This is advantageous because it shows no parser differential exists between the two implementations. The requisite level of simplicity is theoretically that for which there is a solution to the equivalence problem. If the two parsers involved in CVE-2013-4787 were equivalent - that is, if they rendered the same output state given the same input state - the vulnerability could not have existed. One strategy for doing this is to publish machine-readable specifications of a format or protocol, and then use a parser generator to generate the parser code. An example of a parser generator built for this purpose is DaeDaLus. The combination of Lex with any of GNU Bison, ANTLR, or Yacc also accomplishes this. However, many parser generators allow the mixing of general purpose code with the parsing definitions, which weakens the guarantees provided by parsing. === Analysis of injection attacks === Injection attacks are generally the result of differences between the serializer (or "unparser") and the corresponding parser at a layer boundary in a system; therefore, they are a special case of parser differentials. In a SQL injection attack, for example, an attacker is able to cause the application with which they are interacting to serialize a SQL query that has different semantics than intended. In the simplest case where the payload ends a string and adds new code, the payload has crossed the code-data boundary in SQL. In language-theoretic security, this is treated as a bug in the serializer of the SQL query, which should instead be written in a way that constrains its possible outputs to those within the scope of the intended query. === Parser combinators === If a parser generator is not used, it is still possible to avoid implementation bugs by using parser combinator such as Nom to implement the parser code. This has the drawback of relying on a programmer correctly translating the specification into the language of the parser generator library, though this task is still less error-prone than hand-coding a parser. == Input format complexity == Complexity in computer programs is associated with security vulnerabilities. Within the domain of language-theoretic security, complexity is described with reference to the computational power of the abstract machine necessary to implement the program, or more particularly, to implement the parser for its input language. This complexity describes whether it is possible to show that there is no unintended or undesired functionality in the program which might be exploitable by an attacker. To be bounded in complexity, the program's input must be well-defined both in terms of form and of semantics. === Weird machines === A weird machine is a model of computation in a program that exists in parallel with, but is distinct from, the intended abstract model of computation in that program. Some classes of weird machine arise from the multi-layered nature of computer programs, or the context in which the programs run; others result from the unanticipated functionality a program has due to its complexity or to software bugs. The more complex the computation model of a program, the more likely it is to implement a weird machine. Depending on context, the weird machine may or may not be concretely useful for an attacker. Since the space of weird machines in the context of some program is the universe of all possible states that are not within the program's intended states, many exploited states including remote code execution and injection attacks belong to the domain of weird machines. A reduction in weird machines is therefore a likely correlate with reduced program vulnerability. === SafeDocs project === SafeDocs is a DARPA project undertaken in 2018 to take existing file formats, create safer subsets of them, and develop programming tools to work for the safer formats. The initial test case for this was PDF. The purpose of creating safer subsets in this case is to lower the minimum bound on parser complexity so that it becomes possible to create tools that will generate correct, normative parsers for them. == Relation to programming languages == The analytic framework of language-theoretic security assumes programs to be virtual machines that execute their input. A document that is read by an application is in this sense a form of machine code, in a generalization of the data as code idea, following the automata theory description of parsers. === Type-safe programming languages === Parsing input and serializing output are operations that consume one data type and emit another. A programming language can therefore check that data is correctly parsed and contains the expected structure by checking data types, and correct serializing (or unparsing) can be implemented as operations on the data types that are relevant to the program's output. This approach can be used to show that the recognizer and unparser patterns have been implemented. It is also possible to implement type checking across a distributed system to enforce parsing and unparsing of the expected structures and to verify that the assumptions made in designing the compositional properties of a distributed system have been followed. === Memory-safe programming languages === In the general case, spatial memory correctness is undecidable. If any proof of spatial memory correctness is to be made, it is therefore necessary to bound the complexity of the code. Interpreted languages such as Java and Python effectively accomplish this via runtime bounds checking, and frameworks for runtime bounds checking also exist for C. The effect of these strategies for spatial memory correctness are to create a halt state in place of a spatial memory correctness violation; therefore, it can be shown that the program will not violate spatial memory correctness, but in exchange, it cannot be shown in the general case that programs will not have runtime bounds checking exceptions. Some programming languages, such as Rust, accomplish this using borrow checking. The borrow checker acts to assure spatial memory correctness by compile-time reference counting. Code for which spatial memory correctness cannot be shown to not be violated therefore does not compile, inherently limiting the complexity of the spatial memory correctness of the program to what is decidable. Thi

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  Pill reminder

  A pill reminder is any device that reminds users to take medications. Traditional pill reminders are pill containers with electric timers attached, which can be preset for certain times of the day to set off an alarm. More sophisticated pill reminders can also detect when they have been opened, and therefore when the user is away during the time they were supposed to take their medication, they will be reminded of it when they return. This reminder can be in the form of a light, which also helps for deaf or hearing-impaired users. == Mobile app == A newer type of pill reminder is a mobile app that reminds the owner to take the medication. Some of these applications might effectively support adherence to taking medications.

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  AppValley

  AppValley is an independent American digital distribution service operated and trademarked by AppValley LLC. It serves as an alternative app store for the iOS mobile operating system, which allows users to download applications that are not available on the App Store, most commonly tweaked "++" apps, jailbreak apps, and apps including paid apps on the app store. == Legality == AppValley is among several services that violate enterprise developer certificates from Apple. The terms under which these are granted make clear that they are for companies who wish to distribute apps to their employees. AppValley uses these certificates to distribute software directly to non-employees, thereby bypassing the AppStore. AppValley's conduct had implications in U.S. sanctioned markets like Iran, Iraq, North Korea, Cuba, and Venezuela, which have all been subject to commercial sanctions. Among the software offered by AppValley and other services is pirated software, including paid apps on the app store and premium versions of Instagram, Spotify, Pokémon Go, and others. For instance, AppValley distributes an ad-free version of the music streaming app Spotify even on the free tier. == History == The website was founded in May 2017, releasing late that month with a very basic version of the app. There were less than 100 apps available for download at this time. On Jan 19, 2018, a new version dubbed AppValley 2.0 was released bringing dark mode, more categories, a search, and a much faster interface. On February 14, 2019, a Chinese partner "Jason Wu" allegedly took control of the main Twitter account and domain, causing the original AppValley developers to migrate to the domain app-valley.vip and the Twitter account handle @App_Valley_vip. As of September 2024, the app-valley.vip domain now redirects to appvalley.signulous.com. Today, AppValley continues to offer an alternative to Apple's App Store where app developers can publish their applications. == Features == AppValley is a mobile app installer which can also support iOS version that can be installed and downloaded on the mobile or the devices of the people who wish to get access to many different applications available. AppValley also contains apps that have been modified or tweaked for user preferences, and allows the user to by pass national restrictions on the use of apps, without having to resort to jailbreaking. As of June 2, 2020, there are over 1300 apps available for download.

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