AI Assistant Examples

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  Machine learning

  Machine learning (ML) is a field of study in artificial intelligence concerned with the development and study of statistical algorithms that can learn from data and generalize to unseen data, and thus perform tasks without being explicitly programmed. Advances in the field of deep learning have allowed neural networks, a class of statistical algorithms, to surpass many previous machine learning approaches in performance. Statistics and mathematical optimisation methods compose the foundations of machine learning. Data mining is a related field of study, focusing on exploratory data analysis (EDA) through unsupervised learning. From a theoretical viewpoint, probably approximately correct learning provides a mathematical and statistical framework for describing machine learning. Most traditional machine learning and deep learning algorithms can be described as empirical risk minimisation under this framework. == History == The term machine learning was coined in 1959 by Arthur Samuel, an IBM employee and pioneer in the field of computer gaming and artificial intelligence. The synonym self-teaching computers was also used during this time period. The earliest machine learning program was introduced in the 1950s, when Samuel invented a computer program that calculated the chance of winning in checkers for each side, but the history of machine learning is rooted in decades of efforts to study human cognitive processes. In 1949, Canadian psychologist Donald Hebb published the book The Organization of Behavior, in which he introduced a theoretical neural structure formed by certain interactions among nerve cells. The Hebbian theory of neuron interaction set the groundwork for how many machine learning algorithms work, with connected artificial neurons changing the strength of their connections based on data. Other researchers who have studied human cognitive systems contributed to the modern machine learning technologies as well, including Walter Pitts and Warren McCulloch, who proposed the first mathematical model of neural networks including algorithms that mirror human thought processes. By the early 1960s, an experimental "learning machine" with punched tape memory, called Cybertron, had been developed by Raytheon Company to analyse sonar signals, electrocardiograms, and speech patterns using rudimentary reinforcement learning. It was repetitively "trained" by a human operator/teacher to recognise patterns and equipped with a "goof" button to cause it to reevaluate incorrect decisions. A representative book on research into machine learning during the 1960s was Nils Nilsson's book "Learning Machines", dealing mostly with machine learning for pattern classification. Interest related to pattern recognition continued into the 1970s, as described by Duda and Hart in 1973. In 1981, a report was given on using teaching strategies so that an artificial neural network learns to recognise 40 characters (26 letters, 10 digits, and 4 special symbols) from a computer terminal. Tom M. Mitchell provided a widely quoted, more formal definition of the algorithms studied in the machine learning field: "A computer program is said to learn from experience E with respect to some class of tasks T and performance measure P if its performance at tasks in T, as measured by P, improves with experience E." This definition of the tasks in which machine learning is concerned is fundamentally operational rather than defining the field in cognitive terms. This follows Alan Turing's proposal in his paper "Computing Machinery and Intelligence", in which the question, "Can machines think?", is replaced by asking whether machines can convincingly imitate a human in its responses to human-posed questions. In 2014 Ian Goodfellow and others introduced generative adversarial networks (GANs) which could produce realistic synthetic data. By 2016 AlphaGo had won against top human players in Go using reinforcement learning techniques. == Relationships to other fields == === Artificial intelligence === As a scientific endeavour, machine learning grew out of the quest for artificial intelligence (AI). In the early days of AI as an academic discipline, some researchers were interested in having machines learn from data. They attempted to approach the problem with various symbolic methods, as well as what were then termed "neural networks"; these were mostly perceptrons and other models that were later found to be reinventions of the generalised linear models of statistics. Probabilistic reasoning was also employed, especially in automated medical diagnosis. However, an increasing emphasis on the logical, knowledge-based approach caused a rift between AI and machine learning. Probabilistic systems were plagued by theoretical and practical problems of data acquisition and representation. By 1980, expert systems had come to dominate AI, and statistics was out of favour. Work on symbolic/knowledge-based learning continued within AI, leading to inductive logic programming (ILP), but the more statistical line of research was now outside the field of AI proper, in pattern recognition and information retrieval. Neural network research was abandoned by AI and computer science around the same time. This subfield, termed "connectionism", was continued by researchers from other disciplines, including John Hopfield, David Rumelhart, and Geoffrey Hinton. Their main success came in the mid-1980s with the reinvention of backpropagation. Machine learning (ML), reorganised and recognised as its own field, started to flourish in the 1990s. The field changed its goal from achieving artificial intelligence to tackling solvable problems of a practical nature. It shifted focus away from the symbolic approaches it had inherited from AI, and toward methods and models borrowed from statistics, fuzzy logic, and probability theory. === Data compression === === Data mining === Machine learning and data mining often employ the same methods and overlap significantly, but while machine learning focuses on prediction based on known properties learned from the training data, data mining focuses on the discovery of previously unknown properties in the data (this is the analysis step of knowledge discovery in databases). Data mining uses many machine learning methods, but with different goals; on the other hand, machine learning also employs data mining methods as "unsupervised learning" or as a preprocessing step to improve learner accuracy. Much of the confusion between these two research communities comes from the basic assumptions they work with: in machine learning, performance is usually evaluated with respect to the ability to reproduce known knowledge, while in knowledge discovery and data mining (KDD) the key task is the discovery of previously unknown knowledge. Evaluated with respect to known knowledge, an uninformed (unsupervised) method will easily be outperformed by other supervised methods, while in a typical KDD task, supervised methods cannot be used due to the unavailability of training data. Machine learning also has intimate ties to optimization: Many learning problems are formulated as minimisation of some loss function on a training set of examples. Loss functions express the discrepancy between the predictions of the model being trained and the actual problem instances (for example, in classification, one wants to assign a label to instances, and models are trained to correctly predict the preassigned labels of a set of examples). === Generalization === Characterizing the generalisation of various learning algorithms is an active topic of current research, especially for deep learning algorithms. === Statistics === Machine learning and statistics are closely related fields in terms of methods, but distinct in their principal goal: statistics draws population inferences from a sample, while machine learning finds generalisable predictive patterns. Conventional statistical analyses require the a priori selection of a model most suitable for the study data set. In addition, only significant or theoretically relevant variables based on previous experience are included for analysis. In contrast, machine learning is not built on a pre-structured model; rather, the data shape the model by detecting underlying patterns. The more variables (input) used to train the model, the more accurate the ultimate model will be. Leo Breiman distinguished two statistical modelling paradigms: the data model and the algorithmic model, wherein "algorithmic model" means more or less the machine learning algorithms like Random forest. Some statisticians have adopted methods from machine learning, producing the field of statistical learning. === Statistical physics === Analytical and computational techniques derived from deep-rooted physics of disordered systems can be extended to large-scale problems, including machine learning, e.g., to analyse the weight space of deep neural networks. Statistical physics is thus

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  Uniform convergence in probability

  Uniform convergence in probability is a form of convergence in probability in statistical asymptotic theory and probability theory. It means that, under certain conditions, the empirical frequencies of all events in a certain event-family uniformly converge to their theoretical probabilities. Uniform convergence in probability has applications to statistics as well as machine learning as part of statistical learning theory. Specifically, the Glivenko-Cantelli theorem and the homonymous classes of functions are fundamentally related to uniform convergence. The law of large numbers says that, for each single event A {\displaystyle A} , its empirical frequency in a sequence of independent trials converges (with high probability) to its theoretical probability. In many application however, the need arises to judge simultaneously the probabilities of events of an entire class S {\displaystyle S} from one and the same sample. Moreover, it, is required that the relative frequency of the events converge to the probability uniformly over the entire class of events S {\displaystyle S} . The Uniform Convergence Theorem gives a sufficient condition for this convergence to hold. Roughly, if the event-family is sufficiently simple (its VC dimension is sufficiently small) then uniform convergence holds. == Definitions == For a class of predicates H {\displaystyle H} defined on a set X {\displaystyle X} and a set of samples x = ( x 1 , x 2 , … , x m ) {\displaystyle x=(x_{1},x_{2},\dots ,x_{m})} , where x i ∈ X {\displaystyle x_{i}\in X} , the empirical frequency of h ∈ H {\displaystyle h\in H} on x {\displaystyle x} is Q ^ x ( h ) = 1 m | { i : 1 ≤ i ≤ m , h ( x i ) = 1 } | . {\displaystyle {\widehat {Q}}_{x}(h)={\frac {1}{m}}|\{i:1\leq i\leq m,h(x_{i})=1\}|.} The theoretical probability of h ∈ H {\displaystyle h\in H} is defined as Q P ( h ) = P { y ∈ X : h ( y ) = 1 } . {\displaystyle Q_{P}(h)=P\{y\in X:h(y)=1\}.} The Uniform Convergence Theorem states, roughly, that if H {\displaystyle H} is "simple" and we draw samples independently (with replacement) from X {\displaystyle X} according to any distribution P {\displaystyle P} , then with high probability, the empirical frequency will be close to its expected value, which is the theoretical probability. Here "simple" means that the Vapnik–Chervonenkis dimension of the class H {\displaystyle H} is small relative to the size of the sample. In other words, a sufficiently simple collection of functions behaves roughly the same on a small random sample as it does on the distribution as a whole. The Uniform Convergence Theorem was first proved by Vapnik and Chervonenkis using the concept of growth function. == Uniform Convergence Theorem == The statement of the Uniform Convergence Theorem is as follows: If H {\displaystyle H} is a set of { 0 , 1 } {\displaystyle \{0,1\}} -valued functions defined on a set X {\displaystyle X} and P {\displaystyle P} is a probability distribution on X {\displaystyle X} then for ε > 0 {\displaystyle \varepsilon >0} and m {\displaystyle m} a positive integer, we have: P m { | Q P ( h ) − Q x ^ ( h ) | ≥ ε for some h ∈ H } ≤ 4 Π H ( 2 m ) e − ε 2 m / 8 . {\displaystyle P^{m}\{|Q_{P}(h)-{\widehat {Q_{x}}}(h)|\geq \varepsilon {\text{ for some }}h\in H\}\leq 4\Pi _{H}(2m)e^{-\varepsilon ^{2}m/8}.} In the above, for any x ∈ X m , {\displaystyle x\in X^{m},} Q P ( h ) = P { ( y ∈ X : h ( y ) = 1 } , {\displaystyle Q_{P}(h)=P\{(y\in X:h(y)=1\},} Q ^ x ( h ) = 1 m | { i : 1 ≤ i ≤ m , h ( x i ) = 1 } | {\displaystyle {\widehat {Q}}_{x}(h)={\frac {1}{m}}|\{i:1\leq i\leq m,h(x_{i})=1\}|} and | x | = m . {\displaystyle |x|=m.} P m {\displaystyle P^{m}} indicates that the probability is taken over x {\displaystyle x} consisting of m {\displaystyle m} i.i.d. draws from the distribution P . {\displaystyle P.} Finally, the growth function Π H {\displaystyle \Pi _{H}} is defined in the following way, for any { 0 , 1 } {\displaystyle \{0,1\}} -valued functions H {\displaystyle H} over X {\displaystyle X} and for any natural number m {\displaystyle m} : Π H ( m ) = max | { h ∩ D : D ⊆ X , | D | = m , h ∈ H } | . {\displaystyle \Pi _{H}(m)=\max |\{h\cap D:D\subseteq X,|D|=m,h\in H\}|.} From the point of view of Learning Theory one can consider H {\displaystyle H} to be the Concept/Hypothesis class defined over the instance set X {\displaystyle X} . Crucially, the Sauer–Shelah lemma implies that Π H ( m ) ≤ m d {\displaystyle \Pi _{H}(m)\leq m^{d}} , where d {\displaystyle d} is the VC dimension of H {\displaystyle H} . == Proof of the Uniform Convergence Theorem == and are the sources of the proof below. Before we get into the details of the proof of the Uniform Convergence Theorem we will present a high level overview of the proof. Symmetrization: We transform the problem of analyzing | Q P ( h ) − Q ^ x ( h ) | ≥ ε {\displaystyle |Q_{P}(h)-{\widehat {Q}}_{x}(h)|\geq \varepsilon } into the problem of analyzing | Q ^ r ( h ) − Q ^ s ( h ) | ≥ ε / 2 {\displaystyle |{\widehat {Q}}_{r}(h)-{\widehat {Q}}_{s}(h)|\geq \varepsilon /2} , where r {\displaystyle r} and s {\displaystyle s} are i.i.d samples of size m {\displaystyle m} drawn according to the distribution P {\displaystyle P} . One can view r {\displaystyle r} as the original randomly drawn sample of length m {\displaystyle m} , while s {\displaystyle s} may be thought as the testing sample which is used to estimate Q P ( h ) {\displaystyle Q_{P}(h)} . Permutation: Since r {\displaystyle r} and s {\displaystyle s} are picked identically and independently, so swapping elements between them will not change the probability distribution on r {\displaystyle r} and s {\displaystyle s} . So, we will try to bound the probability of | Q ^ r ( h ) − Q ^ s ( h ) | ≥ ε / 2 {\displaystyle |{\widehat {Q}}_{r}(h)-{\widehat {Q}}_{s}(h)|\geq \varepsilon /2} for some h ∈ H {\displaystyle h\in H} by considering the effect of a specific collection of permutations of the joint sample x = r | | s {\displaystyle x=r||s} . Specifically, we consider permutations σ ( x ) {\displaystyle \sigma (x)} which swap x i {\displaystyle x_{i}} and x m + i {\displaystyle x_{m+i}} in some subset of 1 , 2 , . . . , m {\displaystyle {1,2,...,m}} . The symbol r | | s {\displaystyle r||s} means the concatenation of r {\displaystyle r} and s {\displaystyle s} . Reduction to a finite class: We can now restrict the function class H {\displaystyle H} to a fixed joint sample and hence, if H {\displaystyle H} has finite VC Dimension, it reduces to the problem to one involving a finite function class. We present the technical details of the proof. It should be stressed that this proof glosses over details like the measurability of the events V {\displaystyle V} and R {\displaystyle R} ; measurability is granted in the case of H {\displaystyle H} being finite or countable, but this is not normally the case in standard applications of the theorem (e.g. for statistical learning theory or to prove the Glivenko-Cantelli theorem). To get measurability, one needs to use a notion of separability of the underlying space, possibly related to H {\displaystyle H} . === Symmetrization === Lemma: Let V = { x ∈ X m : | Q P ( h ) − Q ^ x ( h ) | ≥ ε for some h ∈ H } {\displaystyle V=\{x\in X^{m}:|Q_{P}(h)-{\widehat {Q}}_{x}(h)|\geq \varepsilon {\text{ for some }}h\in H\}} and R = { ( r , s ) ∈ X m × X m : | Q r ^ ( h ) − Q ^ s ( h ) | ≥ ε / 2 for some h ∈ H } . {\displaystyle R=\{(r,s)\in X^{m}\times X^{m}:|{\widehat {Q_{r}}}(h)-{\widehat {Q}}_{s}(h)|\geq \varepsilon /2{\text{ for some }}h\in H\}.} Then for m ≥ 2 ε 2 {\displaystyle m\geq {\frac {2}{\varepsilon ^{2}}}} , P m ( V ) ≤ 2 P 2 m ( R ) {\displaystyle P^{m}(V)\leq 2P^{2m}(R)} . Proof: By the triangle inequality, if | Q P ( h ) − Q ^ r ( h ) | ≥ ε {\displaystyle |Q_{P}(h)-{\widehat {Q}}_{r}(h)|\geq \varepsilon } and | Q P ( h ) − Q ^ s ( h ) | ≤ ε / 2 {\displaystyle |Q_{P}(h)-{\widehat {Q}}_{s}(h)|\leq \varepsilon /2} then | Q ^ r ( h ) − Q ^ s ( h ) | ≥ ε / 2 {\displaystyle |{\widehat {Q}}_{r}(h)-{\widehat {Q}}_{s}(h)|\geq \varepsilon /2} . Therefore, P 2 m ( R ) ≥ P 2 m { ∃ h ∈ H , | Q P ( h ) − Q ^ r ( h ) | ≥ ε and | Q P ( h ) − Q ^ s ( h ) | ≤ ε / 2 } = ∫ V P m { s : ∃ h ∈ H , | Q P ( h ) − Q ^ r ( h ) | ≥ ε and | Q P ( h ) − Q ^ s ( h ) | ≤ ε / 2 } d P m ( r ) = A {\displaystyle {\begin{aligned}&P^{2m}(R)\\[5pt]\geq {}&P^{2m}\{\exists h\in H,|Q_{P}(h)-{\widehat {Q}}_{r}(h)|\geq \varepsilon {\text{ and }}|Q_{P}(h)-{\widehat {Q}}_{s}(h)|\leq \varepsilon /2\}\\[5pt]={}&\int _{V}P^{m}\{s:\exists h\in H,|Q_{P}(h)-{\widehat {Q}}_{r}(h)|\geq \varepsilon {\text{ and }}|Q_{P}(h)-{\widehat {Q}}_{s}(h)|\leq \varepsilon /2\}\,dP^{m}(r)\\[5pt]={}&A\end{aligned}}} since r {\displaystyle r} and s {\displaystyle s} are independent. Now for r ∈ V {\displaystyle r\in V} fix an h ∈ H {\displaystyle h\in H} such that | Q P ( h ) − Q ^ r ( h ) | ≥ ε {\displaystyle |Q_{P}(h)-{\widehat {Q}}_{r}(h)|\geq \varepsilon } . For this h {\displaystyle h} , we shall

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  Inverse depth parametrization

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

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  Mobile cloud storage

  Mobile cloud storage is a form of cloud storage that is accessible on mobile devices such as laptops, tablets, and smartphones. Mobile cloud storage providers offer services that allow the user to create and organize files, folders, music, and photos, similar to other cloud computing models. Services are used by both individuals and companies. Most cloud file storage providers offer limited free use but charge for additional storage once the free limit is exceeded. These costs are usually charged as a monthly subscription rate and have different rates depending on the amount of storage desired. In 2018, cloud services revenue was about $182.4 billion and in 2022 it is projected to grow to $331.2 billion. The cloud storage industry was projected to grow 17.2 percent in 2019 (Costello, 2019). == History == The concept of cloud computing trace back to 1960s, when the groundwork for modern internet and network technologies was being laid (Human for humans, 2024). One of the pivotal figures in this early period was J.C.R. Licklider, a visionary computer scientist who worked on ARPANET, the precursor to the internet. Licklider's ideas set the stage for the development of distributed computing systems, which are fundamental to cloud computing. Moving into the 1990s, AT&T introduced PersonaLink Services, a more advanced online platform offering electronic mail and online storage. Major turning point in 2006 The launch of Amazon Web Services (AWS) in 2006 marked a major turning point. AWS introduced Amazon S3 (Simple Storage Service), which allowed businesses and developers to store and retrieve any amount of data, at any time, from anywhere on the web. This development was revolutionary, providing scalable, reliable, and low-cost data storage infrastructure that transformed how organizations managed their data. == Applications == Some mobile device manufacturers include mobile cloud storage apps with their product. These apps facilitate synchronization of user files across multiple platforms. Part of the process for setting up new mobile devices frequently includes configuring a cloud storage service to Backup the device's files and information. Apple iOS devices come pre-loaded and configured to use Apple's mobile cloud storage service iCloud. Google offers a similar feature with the Android operating system by backing up the device using a Google Drive account. The Samsung Galaxy smartphone has partnered with Dropbox, while Microsoft similarly offers Microsoft OneDrive. Some mobile cloud storage apps are platform-independent. For example, Nasuni's Mobile Access app is available on any Android or iOS device. Most companies offering Cloud Storage have secure website to access files allowing use on any device that can browse the Internet.

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  Symbolic artificial intelligence

  In artificial intelligence, symbolic artificial intelligence (also known as classical artificial intelligence or logic-based artificial intelligence) is the term for the collection of all methods in artificial intelligence research that are based on high-level symbolic (human-readable) representations of problems, logic, and search. Symbolic AI used tools such as logic programming, production rules, semantic nets and frames, and it developed applications such as knowledge-based systems (in particular, expert systems), symbolic mathematics, automated theorem provers, ontologies, the semantic web, and automated planning and scheduling systems. The Symbolic AI paradigm led to important ideas in search, symbolic programming languages, agents, multi-agent systems, the semantic web, and the strengths and limitations of formal knowledge and reasoning systems. Symbolic AI was the dominant paradigm of AI research from the mid-1950s until the mid-1990s. Researchers in the 1960s and the 1970s were convinced that symbolic approaches would eventually succeed in creating a machine with artificial general intelligence and considered this the ultimate goal of their field. An early boom, with early successes such as the Logic Theorist and Samuel's Checkers Playing Program, led to unrealistic expectations and promises and was followed by the first AI Winter as funding dried up. A second boom (1969–1986) occurred with the rise of expert systems, their promise of capturing corporate expertise, and an enthusiastic corporate embrace. That boom, and some early successes, e.g., with XCON at DEC, was followed again by later disappointment. Problems with difficulties in knowledge acquisition, maintaining large knowledge bases, and brittleness in handling out-of-domain problems arose. Another, second, AI Winter (1988–2011) followed. Subsequently, AI researchers focused on addressing underlying problems in handling uncertainty and in knowledge acquisition. Uncertainty was addressed with formal methods such as hidden Markov models, Bayesian reasoning, and statistical relational learning. Symbolic machine learning addressed the knowledge acquisition problem with contributions including Version Space, Valiant's PAC learning, Quinlan's ID3 decision-tree learning, case-based learning, and inductive logic programming to learn relations. Neural networks, a subsymbolic approach, had been pursued from early days and reemerged strongly in 2012. Early examples are Rosenblatt's perceptron learning work, the backpropagation work of Rumelhart, Hinton and Williams, and work in convolutional neural networks by LeCun et al. in 1989. However, neural networks were not viewed as successful until about 2012: "Until Big Data became commonplace, the general consensus in the Al community was that the so-called neural-network approach was hopeless. Systems just didn't work that well, compared to other methods. ... A revolution came in 2012, when a number of people, including a team of researchers working with Hinton, worked out a way to use the power of GPUs to enormously increase the power of neural networks." Over the next several years, deep learning had spectacular success in handling vision, speech recognition, speech synthesis, image generation, and machine translation, though symbolic approaches continue to be useful in a few domains such as computer algebra systems and proof assistants. == History == A short history of symbolic AI to the present day follows below. Time periods and titles are drawn from Henry Kautz's 2020 AAAI Robert S. Engelmore Memorial Lecture and the longer Wikipedia article on the History of AI, with dates and titles differing slightly for increased clarity. === The first AI summer: irrational exuberance, 1948–1966 === Success at early attempts in AI occurred in three main areas: artificial neural networks, knowledge representation, and heuristic search, contributing to high expectations. This section summarizes Kautz's reprise of early AI history. ==== Approaches inspired by human or animal cognition or behavior ==== Cybernetic approaches attempted to replicate the feedback loops between animals and their environments. A robotic turtle, with sensors, motors for driving and steering, and seven vacuum tubes for control, based on a preprogrammed neural net, was built as early as 1948. This work can be seen as an early precursor to later work in neural networks, reinforcement learning, and situated robotics. An important early symbolic AI program was the Logic theorist, written by Allen Newell, Herbert Simon and Cliff Shaw in 1955–56, as it was able to prove 38 elementary theorems from Whitehead and Russell's Principia Mathematica. Newell, Simon, and Shaw later generalized this work to create a domain-independent problem solver, GPS (General Problem Solver). GPS solved problems represented with formal operators via state-space search using means-ends analysis. During the 1960s, symbolic approaches achieved great success at simulating intelligent behavior in structured environments such as game-playing, symbolic mathematics, and theorem-proving. AI research was concentrated in four institutions in the 1960s: Carnegie Mellon University, Stanford, MIT and (later) University of Edinburgh. Each one developed its own style of research. Earlier approaches based on cybernetics or artificial neural networks were abandoned or pushed into the background. Herbert Simon and Allen Newell studied human problem-solving skills and attempted to formalize them, and their work laid the foundations of the field of artificial intelligence, as well as cognitive science, operations research and management science. Their research team used the results of psychological experiments to develop programs that simulated the techniques that people used to solve problems. This tradition, centered at Carnegie Mellon University would eventually culminate in the development of the Soar architecture in the middle 1980s. ==== Heuristic search ==== In addition to the highly specialized domain-specific kinds of knowledge that we will see later used in expert systems, early symbolic AI researchers discovered another more general application of knowledge. These were called heuristics, rules of thumb that guide a search in promising directions: "How can non-enumerative search be practical when the underlying problem is exponentially hard? The approach advocated by Simon and Newell is to employ heuristics: fast algorithms that may fail on some inputs or output suboptimal solutions." Another important advance was to find a way to apply these heuristics that guarantees a solution will be found, if there is one, not withstanding the occasional fallibility of heuristics: "The A algorithm provided a general frame for complete and optimal heuristically guided search. A is used as a subroutine within practically every AI algorithm today but is still no magic bullet; its guarantee of completeness is bought at the cost of worst-case exponential time. ==== Early work on knowledge representation and reasoning ==== Early work covered both applications of formal reasoning emphasizing first-order logic, along with attempts to handle common-sense reasoning in a less formal manner. ===== Modeling formal reasoning with logic: the "neats" ===== Unlike Simon and Newell, John McCarthy felt that machines did not need to simulate the exact mechanisms of human thought, but could instead try to find the essence of abstract reasoning and problem-solving with logic, regardless of whether people used the same algorithms. His laboratory at Stanford (SAIL) focused on using formal logic to solve a wide variety of problems, including knowledge representation, planning and learning. Logic was also the focus of the work at the University of Edinburgh and elsewhere in Europe which led to the development of the programming language Prolog and the science of logic programming. ===== Modeling implicit common-sense knowledge with frames and scripts: the "scruffies" ===== Researchers at MIT (such as Marvin Minsky and Seymour Papert) found that solving difficult problems in vision and natural language processing required ad hoc solutions—they argued that no simple and general principle (like logic) would capture all the aspects of intelligent behavior. Roger Schank described their "anti-logic" approaches as "scruffy" (as opposed to the "neat" paradigms at CMU and Stanford). Commonsense knowledge bases (such as Doug Lenat's Cyc) are an example of "scruffy" AI, since they must be built by hand, one complicated concept at a time. === The first AI winter: crushed dreams, 1967–1977 === The first AI winter was a shock: During the first AI summer, many people thought that machine intelligence could be achieved in just a few years. The Defense Advance Research Projects Agency (DARPA) launched programs to support AI research to use AI to solve problems of national security; in particular, to automate the translation of Russian to English for inte

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  Sentence embedding

  In natural language processing, a sentence embedding is a representation of a sentence as a vector of numbers which encodes meaningful semantic information. State of the art embeddings are based on the learned hidden layer representation of dedicated sentence transformer models. BERT pioneered an approach involving the use of a dedicated [CLS] token prepended to the beginning of each sentence inputted into the model; the final hidden state vector of this token encodes information about the sentence and can be fine-tuned for use in sentence classification tasks. In practice however, BERT's sentence embedding with the [CLS] token achieves poor performance, often worse than simply averaging non-contextual word embeddings. SBERT later achieved superior sentence embedding performance by fine tuning BERT's [CLS] token embeddings through the usage of a siamese neural network architecture on the SNLI dataset. Other approaches are loosely based on the idea of distributional semantics applied to sentences. Skip-Thought trains an encoder-decoder structure for the task of neighboring sentences predictions; this has been shown to achieve worse performance than approaches such as InferSent or SBERT. An alternative direction is to aggregate word embeddings, such as those returned by Word2vec, into sentence embeddings. The most straightforward approach is to simply compute the average of word vectors, known as continuous bag-of-words (CBOW). However, more elaborate solutions based on word vector quantization have also been proposed. One such approach is the vector of locally aggregated word embeddings (VLAWE), which demonstrated performance improvements in downstream text classification tasks. == Applications == In recent years, sentence embedding has seen a growing level of interest due to its applications in natural language queryable knowledge bases through the usage of vector indexing for semantic search. LangChain for instance utilizes sentence transformers for purposes of indexing documents. In particular, an indexing is generated by generating embeddings for chunks of documents and storing (document chunk, embedding) tuples. Then given a query in natural language, the embedding for the query can be generated. A top k similarity search algorithm is then used between the query embedding and the document chunk embeddings to retrieve the most relevant document chunks as context information for question answering tasks. This approach is also known formally as retrieval-augmented generation. Though not as predominant as BERTScore, sentence embeddings are commonly used for sentence similarity evaluation which sees common use for the task of optimizing a Large language model's generation parameters is often performed via comparing candidate sentences against reference sentences. By using the cosine-similarity of the sentence embeddings of candidate and reference sentences as the evaluation function, a grid-search algorithm can be utilized to automate hyperparameter optimization. == Evaluation == A way of testing sentence encodings is to apply them on Sentences Involving Compositional Knowledge (SICK) corpus for both entailment (SICK-E) and relatedness (SICK-R). In the best results are obtained using a BiLSTM network trained on the Stanford Natural Language Inference (SNLI) Corpus. The Pearson correlation coefficient for SICK-R is 0.885 and the result for SICK-E is 86.3. A slight improvement over previous scores is presented in: SICK-R: 0.888 and SICK-E: 87.8 using a concatenation of bidirectional Gated recurrent unit.

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  Absher (application)

  Absher (Arabic: أبشر ‘Absher, roughly meaning "good tidings" or "yes, done") is a smartphone application and web portal which allows citizens and residents of Saudi Arabia to use a variety of governmental services. Amongst several other services with the Absher app, it can be used to apply for jobs and Hajj permits, passport info can be updated, and electronic crimes can be reported. The application provides around 280 services for residents of Saudi Arabia including but not limited to making appointments, renewing passports, residents' cards, IDs, driver's licenses and others, and, controversially, enables Saudi men to track the whereabouts of women they control as part of the country's male guardianship system. The app can be downloaded from the Google Play Store and Apple App Store and is supplied by the Saudi Interior Ministry. According to the Ministry of the Interior, Absher has more than 20 million users. As of February 2019, Absher has been downloaded 4.2 million times from the App Store. Some services provided through Absher can also be accessed through the website absher.sa. In March 2021, Saudi Arabia launched the digital version of the Absher for individuals app through which the users can download a copy of their digital ID. Then, new services were added to the platform such as online birth and death registration services, requesting amendments to academic credentials, correcting names in English and marital status and requesting civil records of children. == Impact on women's rights == The app has been criticized by various human rights activists, human rights organisations and international communities. The US and European countries have also condemned the app and urged the kingdom to end its male guardianship system. Absher gained media attention in 2019 for its functions supporting the Saudi policy of male guardianship following an investigation by Business Insider. The app allows for designated guardians to receive notifications if a woman under their guardianship passes through an airport and subsequently gives them the option to withdraw her right to travel. In a few cases, this system has been circumvented by women who have been able to gain control over its settings and use it to allow themselves to travel. US Senator Ron Wyden of Oregon wrote a letter to the CEO's of Apple and Google, criticizing the app and demanding for its removal immediately. Wyden said "American companies should not enable or facilitate the Saudi government's patriarchy," and called the Saudi system of control over women "abhorrent". According to the EU lawmakers, current rules imposed over the women by the Saudi government make women “second-class citizens”. The lawmakers also asked the EU states to continue to build pressure on Riyadh so as to improve the conditions of women and human rights. Amnesty International and Human Rights Watch accused Apple and Google of helping "enforce gender apartheid" by hosting the app. US congresswomen Rep. Katherine Clark and Rep. Carolyn B. Maloney condemned the kingdom's male guardianship system that reflected from the app, calling Absher a "patriarchal weapon" and asking for its removal. In response to the criticism received by Absher, Apple chief executive officer Tim Cook stated in February 2019 that he intended to investigate the situation. Similarly, Google announced that it would also review the application. After a prompt review, Google declined to remove the app from Google Play, citing that it did not violate the agreed upon terms and conditions of the store. Saudi doctor Khawla Al-Kuraya supported this app an editorial in Bloomberg News. Kuraya wrote that Absher helped Saudi women avoid governmental bureaucracy as it allows their male guardians to process their travel permits anywhere and anytime through Absher. Although she believes that the guardianship system needs to be reconsidered, she thinks that Absher is an important step towards facilitating women-guardians related issues in Saudi Arabia. Absher manager Atiyah Al-Anazy announced in 2019 that two million women were using the application in Saudi Arabia to facilitate their transactions. Some female users stated that the application has made their movement and travel-related issues easier. New measures were introduced that year to allow Saudi women above the age of 18 to travel without their male guardians, which ultimately released male authoritative rights on women. A law was subsequently passed allowing women over the age of 21 to receive a passport and travel without prior male permission.

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  Recursive transition network

  A recursive transition network ("RTN") is a graph theoretical schematic used to represent the rules of a context-free grammar. RTNs have application to programming languages, natural language and lexical analysis. Any sentence that is constructed according to the rules of an RTN is said to be "well-formed". The structural elements of a well-formed sentence may also be well-formed sentences by themselves, or they may be simpler structures. This is why RTNs are described as recursive. == Notes and references ==

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  Plotly

  Plotly is a technical computing company headquartered in Montreal, Quebec, that develops online data analytics and visualization tools. Plotly provides online graphing, analytics, and statistics tools for individuals and collaboration, as well as scientific graphing libraries for Python, R, MATLAB, Perl, Julia, Arduino, JavaScript and REST. == History == Plotly was founded by Alex Johnson, Jack Parmer, Chris Parmer, and Matthew Sundquist. The founders' backgrounds are in science, energy, and data analysis and visualization. Early employees include Christophe Viau, a Canadian software engineer and Ben Postlethwaite, a Canadian geophysicist. Plotly was named one of the Top 20 Hottest Innovative Companies in Canada by the Canadian Innovation Exchange. Plotly was featured in "startup row" at PyCon 2013, and sponsored the SciPy 2018 conference. Plotly raised $5.5 million during its Series A funding, led by MHS Capital, Siemens Venture Capital, Rho Ventures, Real Ventures, and Silicon Valley Bank. The Boston Globe and Washington Post newsrooms have produced data journalism using Plotly. In 2020, Plotly was named a Best Place to Work by the Canadian SME National Business Awards, and nominated as Business of the Year. == Products == Plotly offers open-source and enterprise products. Dash is an open-source Python, R, and Julia framework for building web-based analytic applications. Many specialized open-source Dash libraries exist that are tailored for building domain-specific Dash components and applications. Some examples are Dash DAQ, for building data acquisition GUIs to use with scientific instruments, and Dash Bio, which enables users to build custom chart types, sequence analysis tools, and 3D rendering tools for bioinformatics applications. Dash Enterprise is Plotly's paid product for building, testing, deploying, managing and scaling Dash applications organization-wide. Chart Studio Cloud is a free, online tool for creating interactive graphs. It has a point-and-click graphical user interface for importing and analyzing data into a grid and using stats tools. Graphs can be embedded or downloaded. Chart Studio Enterprise is a paid product that allows teams to create, style, and share interactive graphs on a single platform. It offers expanded authentication and file export options, and does not limit sharing and viewing. Data visualization libraries Plotly.js is an open-source JavaScript library for creating graphs and powers Plotly.py for Python, as well as Plotly.R for R, MATLAB, Node.js, Julia, and Arduino and a REST API. Plotly can also be used to style interactive graphs with Jupyter notebook. Figure converters which convert matplotlib, ggplot2, and IGOR Pro graphs into interactive, online graphs. == Data visualization libraries == Plotly provides a collection of supported chart types across several programming languages: == Dash == Dash is a Python framework built on top of React, a JavaScript library. Dash also works for R, and most recently supports Julia. While still described as a Python framework, Python isn't used for the other languages: "... describing Dash as a Python framework misses a key feature of its design: the Python side (the back end/server) of Dash was built to be lightweight and stateless [allowing] multiple back-end languages to coexist on an equal footing". It is possible to integrate D3.js charts as Dash components. Dash provides the default CSS (plus HTML and JavaScript), but for custom styling Dash applications, CSS can be added, or Dash Enterprise used. === Dash Enterprise === Dash Enterprise is Plotly's paid product for building, testing, deploying, managing and scaling Dash applications organization-wide. The product integrates with enterprise IT systems to enable organizations to build, deploy and scale low-code Dash applications. With open-source Dash, analytic applications can be run from a local machine, but cannot be easily accessed by others in the organization. ==== Enterprise IT integration ==== Dash Enterprise installs on cloud environments and on-premises. Amazon Web Services, Google Cloud Platform, and Microsoft Azure are supported, as are multiple Linux on-premises servers. Authentication integrations include LDAP, AD, PKI, Okta, SAML, OAuth2, SSO, and email authentication, and Dash application access is managed through a GUI rather than code. Dash Enterprise connects to major big data backends, including Salesforce, PostgreSQL, Databricks via PySpark, Snowflake, Dask, Datashader, and Vaex. In 2020, Plotly partnered with NVIDIA to integrate Dash with RAPIDS, and NVIDIA participated in Plotly's Series C funding round. ==== Low-code capabilities ==== Dash Enterprise enables low-code development of Dash applications, which is not possible with open-source Dash. Enterprise users can write applications in multiple development environments, including Jupyter Notebook. Dash Enterprise ships with several “development engines” for drag-and-drop application editing, application design, and automated reporting, as well as dozens of artificial intelligence and machine learning application templates. ==== Deployment and scaling ==== Dash application code is deployed to Dash Enterprise using the git-push command. Dash application deployments are containerized to avoid dependency conflicts, and can be embedded in existing web platforms without iframes. Deployed applications can be managed and accessed in a single portal called App Manager, where administrators can control user authentication and view usage analytics. Dash Enterprise scales horizontally with Kubernetes. Jobs queuing, GPU acceleration, and CPU parallelization support high performance computing requirements. Plotly also offers professional services for application development and workshop training.

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  Sparrow (chatbot)

  Sparrow is a chatbot developed by the artificial intelligence research lab DeepMind, a subsidiary of Alphabet Inc. It is designed to answer users' questions correctly, while reducing the risk of unsafe and inappropriate answers. One motivation behind Sparrow is to address the problem of language models producing incorrect, biased or potentially harmful outputs. Sparrow is trained using human judgements, in order to be more “Helpful, Correct and Harmless” compared to baseline pre-trained language models. The development of Sparrow involved asking paid study participants to interact with Sparrow, and collecting their preferences to train a model of how useful an answer is. To improve accuracy and help avoid the problem of hallucinating incorrect answers, Sparrow has the ability to search the Internet using Google Search in order to find and cite evidence for any factual claims it makes. To make the model safer, its behaviour is constrained by a set of rules, for example "don't make threatening statements" and "don't make hateful or insulting comments", as well as rules about possibly harmful advice, and not claiming to be a person. During development study participants were asked to converse with the system and try to trick it into breaking these rules. A 'rule model' was trained on judgements from these participants, which was used for further training. Sparrow was introduced in a paper in September 2022, titled "Improving alignment of dialogue agents via targeted human judgements"; however, the bot was not released publicly. DeepMind CEO Demis Hassabis said DeepMind is considering releasing Sparrow for a "private beta" some time in 2023. == Training == Sparrow is a deep neural network based on the transformer machine learning model architecture. It is fine-tuned from DeepMind's Chinchilla AI pre-trained large language model (LLM), which has 70 Billion parameters. Sparrow is trained using reinforcement learning from human feedback (RLHF), although some supervised fine-tuning techniques are also used. The RLHF training utilizes two reward models to capture human judgements: a “preference model” that predicts what a human study participant would prefer and a “rule model” that predicts if the model has broken one of the rules. == Limitations == Sparrow's training data corpus is mainly in English, meaning it performs worse in other languages. When adversarially probed by study participants it breaks the rules 8% of the time; however, this is still three times lower than the baseline prompted pre-trained model (Chinchilla).

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  Boyfriend Maker

  Boyfriend Maker was a dating sim, romance chatbot smartphone app for iOS (iPhone) and Android devices, developed by Japanese studio 36 You Games (styled as 36You) and distributed under the freemium business model. Boyfriend Maker incorporated advanced artificial intelligence chat technology a decade before products such as ChatGPT. According to the developer's website, Boyfriend Maker is an "app that lets you interact and chat with quirky virtual boyfriends". While each virtual boyfriend has certain unique characteristics, the various instances of the boyfriend are powered by a chat engine, that (at least within a language and market) can utilise vocabulary and knowledge acquired in a chat with one user in subsequent chats with other users. == Gameplay == Users gain experience points and in-game coins. Users can customize their virtual boyfriend's appearance by selecting items such as hair, clothing, face, and a necklace. == Apple delisting and reintroduction == In late November 2012, the original iOS Boyfriend Maker app was delisted from the Apple App Store due to "ribald" chat, according to the New York Times. Boyfriend Maker was removed by Apple due to "reports of references to violent sexual acts and pedophilia". Boyfriend Maker had an age rating of 4+, even though the chat bot "responds with often strange and explicit text unsuitable for young children". User-posted chat excerpts indicate that the virtual boyfriend would sometimes transition abruptly to sexual chat in response to a seemingly innocent question. In one user-posted example, in response to the question, "what kind of wedding cake will we have" the boyfriend responds, "a good sex ima be on top of u u gonna ride oon me bitin the pillow gurrl ima fuck da shit out of u". The developer's use of the SimSimi-created third-party chat engine may be responsible for the sexual text. As the virtual boyfriend converses with human users, the SimSimi chat engine acquires vocabulary from users of the game and applies this "learned" vocabulary in chats with other users. The chat engine might also employ lines harvested from human-human chat logs, song lyrics, movies or TV shows. In April 2013, a detuned and presumably tamer version of the app, titled Boyfriend Plus, was permitted on Apple's App Store.

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  Multi-scale approaches

  The scale space representation of a signal obtained by Gaussian smoothing satisfies a number of special properties, scale-space axioms, which make it into a special form of multi-scale representation. There are, however, also other types of "multi-scale approaches" in the areas of computer vision, image processing and signal processing, in particular the notion of wavelets. The purpose of this article is to describe a few of these approaches: == Scale-space theory for one-dimensional signals == For one-dimensional signals, there exists quite a well-developed theory for continuous and discrete kernels that guarantee that new local extrema or zero-crossings cannot be created by a convolution operation. For continuous signals, it holds that all scale-space kernels can be decomposed into the following sets of primitive smoothing kernels: the Gaussian kernel : g ( x , t ) = 1 2 π t exp ⁡ ( − x 2 / 2 t ) {\displaystyle g(x,t)={\frac {1}{\sqrt {2\pi t}}}\exp({-x^{2}/2t})} where t > 0 {\displaystyle t>0} , truncated exponential kernels (filters with one real pole in the s-plane): h ( x ) = exp ⁡ ( − a x ) {\displaystyle h(x)=\exp({-ax})} if x ≥ 0 {\displaystyle x\geq 0} and 0 otherwise where a > 0 {\displaystyle a>0} h ( x ) = exp ⁡ ( b x ) {\displaystyle h(x)=\exp({bx})} if x ≤ 0 {\displaystyle x\leq 0} and 0 otherwise where b > 0 {\displaystyle b>0} , translations, rescalings. For discrete signals, we can, up to trivial translations and rescalings, decompose any discrete scale-space kernel into the following primitive operations: the discrete Gaussian kernel T ( n , t ) = I n ( α t ) {\displaystyle T(n,t)=I_{n}(\alpha t)} where α , t > 0 {\displaystyle \alpha ,t>0} where I n {\displaystyle I_{n}} are the modified Bessel functions of integer order, generalized binomial kernels corresponding to linear smoothing of the form f o u t ( x ) = p f i n ( x ) + q f i n ( x − 1 ) {\displaystyle f_{out}(x)=pf_{in}(x)+qf_{in}(x-1)} where p , q > 0 {\displaystyle p,q>0} f o u t ( x ) = p f i n ( x ) + q f i n ( x + 1 ) {\displaystyle f_{out}(x)=pf_{in}(x)+qf_{in}(x+1)} where p , q > 0 {\displaystyle p,q>0} , first-order recursive filters corresponding to linear smoothing of the form f o u t ( x ) = f i n ( x ) + α f o u t ( x − 1 ) {\displaystyle f_{out}(x)=f_{in}(x)+\alpha f_{out}(x-1)} where α > 0 {\displaystyle \alpha >0} f o u t ( x ) = f i n ( x ) + β f o u t ( x + 1 ) {\displaystyle f_{out}(x)=f_{in}(x)+\beta f_{out}(x+1)} where β > 0 {\displaystyle \beta >0} , the one-sided Poisson kernel p ( n , t ) = e − t t n n ! {\displaystyle p(n,t)=e^{-t}{\frac {t^{n}}{n!}}} for n ≥ 0 {\displaystyle n\geq 0} where t ≥ 0 {\displaystyle t\geq 0} p ( n , t ) = e − t t − n ( − n ) ! {\displaystyle p(n,t)=e^{-t}{\frac {t^{-n}}{(-n)!}}} for n ≤ 0 {\displaystyle n\leq 0} where t ≥ 0 {\displaystyle t\geq 0} . From this classification, it is apparent that we require a continuous semi-group structure, there are only three classes of scale-space kernels with a continuous scale parameter; the Gaussian kernel which forms the scale-space of continuous signals, the discrete Gaussian kernel which forms the scale-space of discrete signals and the time-causal Poisson kernel that forms a temporal scale-space over discrete time. If we on the other hand sacrifice the continuous semi-group structure, there are more options: For discrete signals, the use of generalized binomial kernels provides a formal basis for defining the smoothing operation in a pyramid. For temporal data, the one-sided truncated exponential kernels and the first-order recursive filters provide a way to define time-causal scale-spaces that allow for efficient numerical implementation and respect causality over time without access to the future. The first-order recursive filters also provide a framework for defining recursive approximations to the Gaussian kernel that in a weaker sense preserve some of the scale-space properties.

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  I Am Rich

  I Am Rich is a discontinued 2008 mobile app for iPhones which had minimal function and was priced at US$999.99 (equivalent to $1,495 in 2025). The app was pulled from the App Store less than 24 hours after its launch. Receiving negative reviews from critics, only eight copies were sold. In the years since, several similar applications have been released at lower prices. == Overview == I Am Rich was developed as a joke by German software developer, Armin Heinrich, after he saw iPhone users complaining about software priced above $0.99. The app only showed a glowing red gem and an icon that, when pressed, displayed the following mantra in large text: I am richI deserv [sic] itI am good,healthy & successful Heinrich told The New York Times that "I regard it as art. I did not expect many people to buy it and did not expect all the fuss about it." The application is described as "a work of art with no hidden function at all", with its only purpose being to show other people that they were able to afford it. Vox writer Zachary Crockett called it "the ultimate Veblen good in app form". == Release == Heinrich released and distributed I Am Rich through the App Store on 5 August 2008. The app was sold for US$999.99 (equivalent to $1,495 in 2025), €799.99 (equivalent to €1,078 in 2023), and £599.99 (equivalent to £978.12 in 2025)—the highest prices Apple allowed for App Store content. Without explanation, the application was removed from the App Store by Apple less than a day after its release. === Purchases === Eight people bought the application, at least one of whom claimed to have done so accidentally. Six US sales and two European sales netted $5,600 for Heinrich and $2,400 for Apple (respectively equivalent to $8,374 and $3,589 in 2025). In correspondence with the Los Angeles Times, Heinrich told the newspaper that Apple had refunded two purchasers of his app, and that he was happy to not have dissatisfied customers. == Reception == Discussing the app on the website Silicon Alley Insider, Dan Frommer described the program as a "scam", "worthless", and finally "a joke that smells like a scammy rip-off" on August 5, 6, and 8, respectively. Without purchasing the app, Fox News's Paul Wagenseil guessed that the secret mantra was "German for 'Sucker!'" (Heinrich is German). Wired's Brian X. Chen described I Am Rich as a waste of money to "prove you're a jerk", and contrasted the expenditure with donating to cancer foundations and Third World countries. Heinrich told the Los Angeles Times's Mark Milian that he had received correspondence from satisfied customers: "I've got e-mails from customers telling me that they really love the app [... and that they had] no trouble spending the money". In an interview with The New York Times, though, he told of receiving many insulting emails and telephone messages. == Similar applications == The next year, Heinrich released I Am Rich LE. Priced at US$9.99 (equivalent to $14.99 in 2025), the new app has several new features (including a calculator, "help system", and the "famous mantra without the spelling mistakes") to meet Apple's requirement that apps have "definable content". Some customers were disappointed by the new functionality, poorly rating the app due to its ostensible improvements. On 23 February 2009, CNET Asia reported on the "conceptually similar" app, I Am Richer, developed by Mike DG for Google's Android. The app was released on the Android Market for US$200 (equivalent to $300.14 in 2025), a limit imposed by Google, who had no objection to the application. With the same name, the I Am Rich that was released on the Windows Phone Marketplace on 22 December 2010, was developed by DotNetNuzzi. Described by MobileCrunch as equally useless as the original, this app cost US$499.99 (equivalent to $738.2 in 2025), the price cap imposed by Microsoft.

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  Trigram

  Trigrams are a special case of the n-gram, where n is 3. They are often used in natural language processing for performing statistical analysis of texts and in cryptography for control and use of ciphers and codes. See results of analysis of "Letter Frequencies in the English Language". == Frequency == Context is very important, varying analysis rankings and percentages are easily derived by drawing from different sample sizes, different authors; or different document types: poetry, science-fiction, technology documentation; and writing levels: stories for children versus adults, military orders, and recipes. Typical cryptanalytic frequency analysis finds that the 16 most common character-level trigrams in English are: Because encrypted messages sent by telegraph often omit punctuation and spaces, cryptographic frequency analysis of such messages includes trigrams that straddle word boundaries. This causes trigrams such as "edt" to occur frequently, even though it may never occur in any one word of those messages. == Examples == The sentence "the quick red fox jumps over the lazy brown dog" has the following word-level trigrams: the quick red quick red fox red fox jumps fox jumps over jumps over the over the lazy the lazy brown lazy brown dog And the word-level trigram "the quick red" has the following character-level trigrams (where an underscore "_" marks a space): the he_ e_q _qu qui uic ick ck_ k_r _re red

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  Information retrieval

  Information retrieval (IR) in computing and information science is the task of identifying and retrieving information system resources that are relevant to an information need. The information need can be specified in the form of a search query. In the case of document retrieval, queries can be based on full-text or other content-based indexing. Information retrieval is the science of searching for information in a document, searching for documents themselves, and also searching for the metadata that describes data, and for databases of texts, images, or sounds. Cross-modal retrieval implies retrieval across modalities. Automated information retrieval systems are used to reduce what has been called information overload. An IR system is a software system that provides access to books, journals, and other documents, as well as storing and managing those documents. Web search engines are the most visible IR applications. == Overview == An information retrieval process begins when a user enters a query into the system. Queries are formal statements of information needs, for example search strings in web search engines. In information retrieval, a query does not uniquely identify a single object in the collection. Instead, several objects may match the query, perhaps with different degrees of relevance. An object is an entity that is represented by information in a content collection or database. User queries are matched against the database information. However, as opposed to classical SQL queries of a database, in information retrieval the results returned may or may not match the query, so results are typically ranked. This ranking of results is a key difference of information retrieval searching compared to database searching. Depending on the application the data objects may be, for example, text documents, images, audio, mind maps or videos. Often the documents themselves are not kept or stored directly in the IR system, but are instead represented in the system by document surrogates or metadata. Most IR systems compute a numeric score on how well each object in the database matches the query, and rank the objects according to this value. The top ranking objects are then shown to the user. The process may then be iterated if the user wishes to refine the query. == History == there is ... a machine called the Univac ... whereby letters and figures are coded as a pattern of magnetic spots on a long steel tape. By this means the text of a document, preceded by its subject code symbol, can be recorded ... the machine ... automatically selects and types out those references which have been coded in any desired way at a rate of 120 words a minute The idea of using computers to search for relevant pieces of information was popularized in the article As We May Think by Vannevar Bush in 1945. It would appear that Bush was inspired by patents for a 'statistical machine' – filed by Emanuel Goldberg in the 1920s and 1930s – that searched for documents stored on film. The first description of a computer searching for information was described by Holmstrom in 1948, detailing an early mention of the Univac computer. Automated information retrieval systems were introduced in the 1950s: one even featured in the 1957 romantic comedy Desk Set. In the 1960s, the first large information retrieval research group was formed by Gerard Salton at Cornell. By the 1970s several different retrieval techniques had been shown to perform well on small text corpora such as the Cranfield collection (several thousand documents). Large-scale retrieval systems, such as the Lockheed Dialog system, came into use early in the 1970s. In 1992, the US Department of Defense along with the National Institute of Standards and Technology (NIST), cosponsored the Text Retrieval Conference (TREC) as part of the TIPSTER text program. The aim of this was to look into the information retrieval community by supplying the infrastructure that was needed for evaluation of text retrieval methodologies on a very large text collection. This catalyzed research on methods that scale to huge corpora. The introduction of web search engines has boosted the need for very large scale retrieval systems even further. By the late 1990s, the rise of the World Wide Web fundamentally transformed information retrieval. While early search engines such as AltaVista (1995) and Yahoo! (1994) offered keyword-based retrieval, they were limited in scale and ranking refinement. The breakthrough came in 1998 with the founding of Google, which introduced the PageRank algorithm, using the web's hyperlink structure to assess page importance and improve relevance ranking. During the 2000s, web search systems evolved rapidly with the integration of machine learning techniques. These systems began to incorporate user behavior data (e.g., click-through logs), query reformulation, and content-based signals to improve search accuracy and personalization. In 2009, Microsoft launched Bing, introducing features that would later incorporate semantic web technologies through the development of its Satori knowledge base. Academic analysis have highlighted Bing's semantic capabilities, including structured data use and entity recognition, as part of a broader industry shift toward improving search relevance and understanding user intent through natural language processing. A major leap occurred in 2018, when Google deployed BERT (Bidirectional Encoder Representations from Transformers) to better understand the contextual meaning of queries and documents. This marked one of the first times deep neural language models were used at scale in real-world retrieval systems. BERT's bidirectional training enabled a more refined comprehension of word relationships in context, improving the handling of natural language queries. Because of its success, transformer-based models gained traction in academic research and commercial search applications. Simultaneously, the research community began exploring neural ranking models that outperformed traditional lexical-based methods. Long-standing benchmarks such as the Text REtrieval Conference (TREC), initiated in 1992, and more recent evaluation frameworks Microsoft MARCO(MAchine Reading COmprehension) (2019) became central to training and evaluating retrieval systems across multiple tasks and domains. MS MARCO has also been adopted in the TREC Deep Learning Tracks, where it serves as a core dataset for evaluating advances in neural ranking models within a standardized benchmarking environment. As deep learning became integral to information retrieval systems, researchers began to categorize neural approaches into three broad classes: sparse, dense, and hybrid models. Sparse models, including traditional term-based methods and learned variants like SPLADE, rely on interpretable representations and inverted indexes to enable efficient exact term matching with added semantic signals. Dense models, such as dual-encoder architectures like ColBERT, use continuous vector embeddings to support semantic similarity beyond keyword overlap. Hybrid models aim to combine the advantages of both, balancing the lexical (token) precision of sparse methods with the semantic depth of dense models. This way of categorizing models balances scalability, relevance, and efficiency in retrieval systems. As IR systems increasingly rely on deep learning, concerns around bias, fairness, and explainability have also come to the picture. Research is now focused not just on relevance and efficiency, but on transparency, accountability, and user trust in retrieval algorithms. == Applications == Areas where information retrieval techniques are employed include (the entries are in alphabetical order within each category): === General applications === Digital libraries Information filtering Recommender systems Media search Blog search Image retrieval 3D retrieval Music retrieval News search Speech retrieval Video retrieval Search engines Site search Desktop search Enterprise search Federated search Mobile search Social search Web search === Domain-specific applications === Expert search finding Genomic information retrieval Geographic information retrieval Information retrieval for chemical structures Information retrieval in software engineering Legal information retrieval Vertical search === Other retrieval methods === Methods/Techniques in which information retrieval techniques are employed include: Cross-modal retrieval Adversarial information retrieval Automatic summarization Multi-document summarization Compound term processing Cross-lingual retrieval Document classification Spam filtering Question answering == Model types == In order to effectively retrieve relevant documents by IR strategies, the documents are typically transformed into a suitable representation. Each retrieval strategy incorporates a specific model for its document representation purposes. The picture on the right illustrates the relationship of som

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