AI Face Combiner

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  Speech recognition

  Speech recognition (automatic speech recognition (ASR), computer speech recognition, or speech-to-text (STT)) is a sub-field of computational linguistics concerned with methods and technologies that translate spoken language into text or other interpretable forms. Speech recognition applications include voice user interfaces, where the user speaks to a device, which "listens" and processes the audio. Common voice applications include interpreting commands for calling, call routing, home automation, and aircraft control. These applications are called direct voice input. Productivity applications include searching audio recordings, creating transcripts, and dictation. Speech recognition can be used to analyse speaker characteristics, such as identifying native language using pronunciation assessment. Voice recognition (speaker identification) refers to identifying the speaker, rather than speech contents. Recognizing the speaker can simplify the task of translating speech in systems trained on a specific person's voice. It can also be used to authenticate the speaker as part of a security process. == History == Applications for speech recognition developed over many decades, with progress accelerated due to advances in deep learning and the use of big data. These advances are reflected in an increase in academic papers, and greater system adoption. Key areas of growth include vocabulary size, more accurate recognition for unfamiliar speakers (speaker independence), and faster processing speed. === Pre-1970 === 1952 – Bell Labs researchers, Stephen Balashek, R. Biddulph, and K. H. Davis, built Audrey for single-speaker digit recognition. Their system located the formants in the power spectrum of each utterance. 1960 – Gunnar Fant developed and published the source–filter model of speech production. 1962 – IBM's 16-word "Shoebox" machine's speech recognition debuted at the 1962 World's Fair. 1966 – Linear predictive coding, a speech coding method, was proposed by Fumitada Itakura of Nagoya University and Shuzo Saito of Nippon Telegraph and Telephone. 1969 – Funding at Bell Labs came to a halt for several years after the company's head engineer, John R. Pierce, wrote an open letter criticizing speech recognition research. This defunding lasted until Pierce retired and James L. Flanagan took over. Raj Reddy was the first person to work on continuous speech recognition, as a graduate student at Stanford University in the late 1960s. Previous systems required users to pause after each word. Reddy's system issued spoken commands for playing chess. Around this time, Soviet researchers invented the dynamic time warping (DTW) algorithm and used it to create a recognizer capable of operating on a 200-word vocabulary. DTW processed speech by dividing it into short frames (e.g. 10 ms segments) and treating each frame as a unit. Speaker independence, however, remained unsolved. === 1970–1990 === 1971 – DARPA funded a five-year speech recognition research project, Speech Understanding Research, seeking a minimum vocabulary size of 1,000 words. The project considered speech understanding a key to achieving progress in speech recognition, which was later disproved. BBN, IBM, Carnegie Mellon (CMU), and Stanford Research Institute participated. 1972 – The IEEE Acoustics, Speech, and Signal Processing group held a conference in Newton, Massachusetts. 1976 – The first ICASSP was held in Philadelphia, which became a major venue for publishing on speech recognition. During the late 1960s, Leonard Baum developed the mathematics of Markov chains at the Institute for Defense Analysis. A decade later, at CMU, Raj Reddy's students James Baker and Janet M. Baker began using the hidden Markov model (HMM) for speech recognition. James Baker had learned about HMMs while at the Institute for Defense Analysis. HMMs enabled researchers to combine sources of knowledge, such as acoustics, language, and syntax, in a unified probabilistic model. By the mid-1980s, Fred Jelinek's team at IBM created a voice-activated typewriter called Tangora, which could handle a 20,000-word vocabulary. Jelinek's statistical approach placed less emphasis on emulating human brain processes in favor of statistical modelling. (Jelinek's group independently discovered the application of HMMs to speech.) This was controversial among linguists since HMMs are too simplistic to account for many features of human languages. However, the HMM proved to be a highly useful way for modelling speech and replaced dynamic time warping as the dominant speech recognition algorithm in the 1980s. 1982 – Dragon Systems, founded by James and Janet M. Baker, was one of IBM's few competitors. === Practical speech recognition === The 1980s also saw the introduction of the n-gram language model. 1987 – The back-off model enabled language models to use multiple-length n-grams, and CSELT used HMM to recognize languages (in software and hardware, e.g. RIPAC). At the end of the DARPA program in 1976, the best computer available to researchers was the PDP-10 with 4 MB of RAM. It could take up to 100 minutes to decode 30 seconds of speech. Practical products included: 1984 – the Apricot Portable was released with up to 4096 words support, of which only 64 could be held in RAM at a time. 1987 – a recognizer from Kurzweil Applied Intelligence 1990 – Dragon Dictate, a consumer product released in 1990. AT&T deployed the Voice Recognition Call Processing service in 1992 to route telephone calls without a human operator. The technology was developed by Lawrence Rabiner and others at Bell Labs. By the early 1990s, the vocabulary of the typical commercial speech recognition system had exceeded the average human vocabulary. Reddy's former student, Xuedong Huang, developed the Sphinx-II system at CMU. Sphinx-II was the first to do speaker-independent, large vocabulary, continuous speech recognition, and it won DARPA's 1992 evaluation. Handling continuous speech with a large vocabulary was a major milestone. Huang later founded the speech recognition group at Microsoft in 1993. Reddy's student Kai-Fu Lee joined Apple, where, in 1992, he helped develop the Casper speech interface prototype. Lernout & Hauspie, a Belgium-based speech recognition company, acquired other companies, including Kurzweil Applied Intelligence in 1997 and Dragon Systems in 2000. L&H was used in Windows XP. L&H was an industry leader until an accounting scandal destroyed it in 2001. L&H speech technology was bought by ScanSoft, which became Nuance in 2005. Apple licensed Nuance software for its digital assistant Siri. ==== 2000s ==== In the 2000s, DARPA sponsored two speech recognition programs: Effective Affordable Reusable Speech-to-Text (EARS) in 2002, followed by Global Autonomous Language Exploitation (GALE) in 2005. Four teams participated in EARS: IBM; a team led by BBN with LIMSI and the University of Pittsburgh; Cambridge University; and a team composed of ICSI, SRI, and the University of Washington. EARS funded the collection of the Switchboard telephone speech corpus, which contained 260 hours of recorded conversations from over 500 speakers. The GALE program focused on Arabic and Mandarin broadcast news. Google's first effort at speech recognition came in 2007 after recruiting Nuance researchers. Its first product, GOOG-411, was a telephone-based directory service. Since at least 2006, the U.S. National Security Agency has employed keyword spotting, allowing analysts to index large volumes of recorded conversations and identify speech containing "interesting" keywords. Other government research programs focused on intelligence applications, such as DARPA's EARS program and IARPA's Babel program. In the early 2000s, speech recognition was dominated by hidden Markov models combined with feed-forward artificial neural networks (ANN). Later, speech recognition was taken over by long short-term memory (LSTM), a recurrent neural network (RNN) published by Sepp Hochreiter & Jürgen Schmidhuber in 1997. LSTM RNNs avoid the vanishing gradient problem and can learn "Very Deep Learning" tasks that require memories of events that happened thousands of discrete time steps earlier, which is important for speech. Around 2007, LSTMs trained with Connectionist Temporal Classification (CTC) began to outperform. In 2015, Google reported a 49 percent error‑rate reduction in its speech recognition via CTC‑trained LSTM. Transformers, a type of neural network based solely on attention, were adopted in computer vision and language modelling, and then to speech recognition. Deep feed-forward (non-recurrent) networks for acoustic modelling were introduced in 2009 by Geoffrey Hinton and his students at the University of Toronto, and by Li Deng and colleagues at Microsoft Research. In contrast to the prioer incremental improvements, deep learning decreased error rates by 30%. Both shallow and deep forms (e.g., recurrent nets) of ANNs had been explored since the 1980s. Howev

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  Sparse identification of non-linear dynamics

  Sparse identification of nonlinear dynamics (SINDy) is a data-driven algorithm for obtaining dynamical systems from data. Given a series of snapshots of a dynamical system and its corresponding time derivatives, SINDy performs a sparsity-promoting regression (such as LASSO and sparse Bayesian inference) on a library of nonlinear candidate functions of the snapshots against the derivatives to find the governing equations. This procedure relies on the assumption that most physical systems only have a few dominant terms which dictate the dynamics, given an appropriately selected coordinate system and quality training data. It has been applied to identify the dynamics of fluids, based on proper orthogonal decomposition, as well as other complex dynamical systems, such as biological networks. == Mathematical Overview == First, consider a dynamical system of the form x ˙ = d d t x ( t ) = f ( x ( t ) ) , {\displaystyle {\dot {\textbf {x}}}={\frac {d}{dt}}{\textbf {x}}(t)={\textbf {f}}({\textbf {x}}(t)),} where x ( t ) ∈ R n {\displaystyle {\textbf {x}}(t)\in \mathbb {R} ^{n}} is a state vector (snapshot) of the system at time t {\displaystyle t} and the function f ( x ( t ) ) {\displaystyle {\textbf {f}}({\textbf {x}}(t))} defines the equations of motion and constraints of the system. The time derivative may be either prescribed or numerically approximated from the snapshots. With x {\displaystyle {\textbf {x}}} and x ˙ {\displaystyle {\dot {\textbf {x}}}} sampled at m {\displaystyle m} equidistant points in time ( t 1 , t 2 , ⋯ , t m {\displaystyle t_{1},t_{2},\cdots ,t_{m}} ), these can be arranged into matrices of the form X = [ x T ( t 1 ) x T ( t 2 ) ⋮ x T ( t m ) ] = [ x 1 ( t 1 ) x 2 ( t 1 ) ⋯ x n ( t 1 ) x 1 ( t 2 ) x 2 ( t 2 ) ⋯ x n ( t 2 ) ⋮ ⋮ ⋱ ⋮ x 1 ( t m ) x 2 ( t m ) ⋯ x n ( t m ) ] , {\displaystyle {\bf {{X}={\begin{bmatrix}\mathbf {x} ^{\mathsf {T}}(t_{1})\\\mathbf {x} ^{\mathsf {T}}(t_{2})\\\vdots \\\mathbf {x} ^{\mathsf {T}}(t_{m})\end{bmatrix}}={\begin{bmatrix}x_{1}(t_{1})&x_{2}(t_{1})&\cdots &x_{n}(t_{1})\\x_{1}(t_{2})&x_{2}(t_{2})&\cdots &x_{n}(t_{2})\\\vdots &\vdots &\ddots &\vdots \\x_{1}(t_{m})&x_{2}(t_{m})&\cdots &x_{n}(t_{m})\end{bmatrix}},}}} and similarly for X ˙ {\displaystyle {\dot {\mathbf {X} }}} . Next, a library Θ ( X ) {\displaystyle \mathbf {\Theta } (\mathbf {X} )} of nonlinear candidate functions of the columns of X {\displaystyle {\textbf {X}}} is constructed, which may be constant, polynomial, or more exotic functions (like trigonometric and rational terms, and so on): Θ ( X ) = [ | | | | | | 1 X X 2 X 3 ⋯ sin ⁡ ( X ) cos ⁡ ( X ) ⋯ | | | | | | ] {\displaystyle \ \ \ {\bf {{\Theta }({\bf {{X})={\begin{bmatrix}\vline &\vline &\vline &\vline &&\vline &\vline &\\1&{\bf {X}}&{\bf {{X}^{2}}}&{\bf {{X}^{3}}}&\cdots &\sin({\bf {{X})}}&\cos({\bf {{X})}}&\cdots \\\vline &\vline &\vline &\vline &&\vline &\vline &\end{bmatrix}}}}}}} The number of possible model structures from this library is combinatorially high. f ( x ( t ) ) {\displaystyle {\textbf {f}}({\textbf {x}}(t))} is then substituted by Θ ( X ) {\displaystyle {\bf {{\Theta }({\textbf {X}})}}} and a vector of coefficients Ξ = [ ξ 1 ξ 2 ⋯ ξ n ] {\displaystyle {\bf {{\Xi }=\left[{\bf {{\xi }_{1}{\bf {{\xi }_{2}\cdots {\bf {{\xi }_{n}}}}}}}\right]}}} determining the active terms in f ( x ( t ) ) {\displaystyle {\textbf {f}}({\textbf {x}}(t))} : X ˙ = Θ ( X ) Ξ {\displaystyle {\dot {\bf {X}}}={\bf {{\Theta }({\bf {{X}){\bf {\Xi }}}}}}} Because only a few terms are expected to be active at each point in time, an assumption is made that f ( x ( t ) ) {\displaystyle {\textbf {f}}({\textbf {x}}(t))} admits a sparse representation in Θ ( X ) {\displaystyle {\bf {{\Theta }({\textbf {X}})}}} . This then becomes an optimization problem in finding a sparse Ξ {\displaystyle {\bf {\Xi }}} which optimally embeds X ˙ {\displaystyle {\dot {\textbf {X}}}} . In other words, a parsimonious model is obtained by performing least squares regression on the system (4) with sparsity-promoting ( L 1 {\displaystyle L_{1}} ) regularization ξ k = arg ⁡ min ξ k ′ | | X ˙ k − Θ ( X ) ξ k ′ | | 2 + λ | | ξ k ′ | | 1 , {\displaystyle {\bf {{\xi }_{k}={\underset {\bf {{\xi }'_{k}}}{\arg \min }}\left|\left|{\dot {\bf {X}}}_{k}-{\bf {{\Theta }({\bf {{X}){\bf {{\xi }'_{k}}}}}}}\right|\right|_{2}+\lambda \left|\left|{\bf {{\xi }'_{k}}}\right|\right|_{1},}}} where λ {\displaystyle \lambda } is a regularization parameter. Finally, the sparse set of ξ k {\displaystyle {\bf {{\xi }_{k}}}} can be used to reconstruct the dynamical system: x ˙ k = Θ ( x ) ξ k {\displaystyle {\dot {x}}_{k}={\bf {{\Theta }({\bf {{x}){\bf {{\xi }_{k}}}}}}}}

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  Kullback–Leibler Upper Confidence Bound

  In multi-armed bandit problems, KL-UCB (for Kullback–Leibler Upper Confidence Bound) is a UCB-type algorithm that is asymptotically optimal, in the sense that its regret matches the problem-dependent Lai-Robbins lower bound. == Multi-armed bandit problem == The Multi-armed bandit problem is a sequential game where one player has to choose at each turn between K {\displaystyle K} actions (arms). Behind every arm a {\displaystyle a} there is an unknown distribution ν a {\displaystyle \nu _{a}} that lies in a set D {\displaystyle {\mathcal {D}}} known by the player (for example, D {\displaystyle {\mathcal {D}}} can be the set of Gaussian distributions or Bernoulli distributions). At each turn t {\displaystyle t} the player chooses (pulls) an arm a t {\displaystyle a_{t}} , he then gets an observation X t {\displaystyle X_{t}} of the distribution ν a t {\displaystyle \nu _{a_{t}}} . === Regret minimization === The goal is to minimize the regret at time T {\displaystyle T} that is defined as R T := ∑ a = 1 K Δ a E [ N a ( T ) ] {\displaystyle R_{T}:=\sum _{a=1}^{K}\Delta _{a}\mathbb {E} [N_{a}(T)]} where μ a := E [ ν a ] {\displaystyle \mu _{a}:=\mathbb {E} [\nu _{a}]} is the mean of arm a {\displaystyle a} μ ∗ := max a μ a {\displaystyle \mu ^{}:=\max _{a}\mu _{a}} is the highest mean Δ a := μ ∗ − μ a {\displaystyle \Delta _{a}:=\mu ^{}-\mu _{a}} N a ( t ) {\displaystyle N_{a}(t)} is the number of pulls of arm a {\displaystyle a} up to turn t {\displaystyle t} The player has to find an algorithm that chooses at each turn t {\displaystyle t} which arm to pull based on the previous actions and observations ( a s , X s ) s < t {\displaystyle (a_{s},X_{s})_{s μ } {\displaystyle {\mathcal {K}}_{inf}(\nu ,\mu ,{\mathcal {D}}):=\inf \left\{\mathrm {KL} (\nu ,{\tilde {\nu }})\ |\ {\tilde {\nu }}\in {\mathcal {D}},\ \mathbb {E} [{\tilde {\nu }}]>\mu \right\}} K L {\displaystyle \mathrm {KL} } is the Kullback–Leibler divergence ν ^ a ( t ) {\displaystyle {\hat {\nu }}_{a}(t)} is the empirical distribution of arm a {\displaystyle a} at turn t {\displaystyle t} δ t {\displaystyle \delta _{t}} is a well-chosen sequence of positive numbers, often equal to ln ⁡ t + c ln ⁡ ln ⁡ t {\displaystyle \ln t+c\ln \ln t} with c > 0 {\displaystyle c>0} . Then we choose the arm a t {\displaystyle a_{t}} with the highest index: a t := arg ⁡ max a U a ( t ) {\displaystyle a_{t}:=\arg \max _{a}U_{a}(t)} We note that the algorithm does not require knowledge of T {\displaystyle T} . === Example === In the special case of Gaussian distribution with fixed variance σ 2 {\displaystyle \sigma ^{2}} , we have: U a ( t ) = μ ^ a ( t ) + 2 σ 2 δ t N a ( t ) {\displaystyle U_{a}(t)={\hat {\mu }}_{a}(t)+{\sqrt {\frac {2\sigma ^{2}\delta _{t}}{N_{a}(t)}}}} with μ ^ a ( t ) {\displaystyle {\hat {\mu }}_{a}(t)} being the empirical mean of arm a {\displaystyle a} at turn t {\displaystyle t} . === Pseudocode === The player gets the set D for each arm i do: n[i] ← 1; nu[i] ← None; d ← ln(K) for t from 1 to K do: select arm t observe reward r n[t] ← n[t] + 1 nu[t] ← update empirical distribution for t from K+1 to T do: for each arm i do: index[i] ← compute_index(n[i], nu[i], D, d) select arm a with highest index[a] observe reward r n[a] ← n[a] + 1 nu[a] ← update empirical distribution d ← ln(t+1) == Theoretical results == In the multi-armed bandit problem we have the Lai–Robbins asymptotic lower bound on regret. The algorithm KL-UCB matches this lower bound for one-dimensional exponential families with δ t := ln ⁡ t + 3 ln ⁡ ln ⁡ t {\displaystyle \delta _{t}:=\ln t+3\ln \ln t} and for distributions bounded in [ 0 , 1 ] {\displaystyle [0,1]} with δ t := ln ⁡ t + ln ⁡ ln ⁡ t {\displaystyle \delta _{t}:=\ln t+\ln \ln t} . === Lai–Robbins lower bound === In 1985 Lai and Robbins proved an asymptotic, problem-dependent lower bound on regret. It states that for every consistent algorithm on the set D {\displaystyle {\mathcal {D}}} — that is, an algorithm for which, for every ( ν 1 , … , ν K ) ∈ D K {\displaystyle (\nu _{1},\dots ,\nu _{K})\in {\mathcal {D}}^{K}} , the regret R T {\displaystyle R_{T}} is subpolynomial (i.e. R T = o T → + ∞ ( T α ) {\displaystyle R_{T}=o_{T\to +\infty }(T^{\alpha })} for all α > 0 {\displaystyle \alpha >0} ) — we have: R T ≥ ( ∑ a : μ a < μ ∗ Δ a K inf ( ν a , μ ∗ , D ) ) ln ⁡ T + o T → + ∞ ( ln ⁡ T ) . {\displaystyle R_{T}\geq \left(\sum _{a:\mu _{a}<\mu ^{}}{\frac {\Delta _{a}}{{\mathcal {K}}_{\inf }(\nu _{a},\mu ^{},{\mathcal {D}})}}\right)\ln T+o_{T\to +\infty }(\ln T).} This bound is asymptotic (as T → + ∞ {\displaystyle T\to +\infty } ) and gives a first-order lower bound of order ln ⁡ T {\displaystyle \ln T} with the optimal constant in front of it. === Regret bound for KL-UCB === The algorithm matches the Lai–Robbins lower bound for one-dimensional exponential-family distributions and for distributions bounded in [ 0 , 1 ] {\displaystyle [0,1]} . ==== One-dimensional exponential family ==== For D {\displaystyle {\mathcal {D}}} being the set of one-dimensional exponential families, with δ t := ln ⁡ t + 3 ln ⁡ ln ⁡ t {\displaystyle \delta _{t}:=\ln t+3\ln \ln t} we have the following upper bound on the regret of KL-UCB: R T ≤ ( ∑ a : μ a < μ ∗ Δ a K inf ( ν a , μ ∗ , D ) ) ln ⁡ T + O T ( ln ⁡ T ) . {\displaystyle R_{T}\leq \left(\sum _{a:\mu _{a}<\mu ^{}}{\frac {\Delta _{a}}{{\mathcal {K}}_{\inf }(\nu _{a},\mu ^{},{\mathcal {D}})}}\right)\ln T+O_{T}({\sqrt {\ln T}}).} ==== Bounded distributions in [0,1] ==== For D = P ( [ 0 , 1 ] ) {\displaystyle {\mathcal {D}}={\mathcal {P}}([0,1])} (the set of distributions supported on [ 0 , 1 ] {\displaystyle [0,1]} ), and for δ t := ln ⁡ t + ln ⁡ ln ⁡ t {\displaystyle \delta _{t}:=\ln t+\ln \ln t} , we have the following upper bound on the regret of KL-UCB: R T ≤ ( ∑ a : μ a < μ ∗ Δ a K inf ( ν a , μ ∗ , D ) ) ln ⁡ T + O T ( ( ln ⁡ T ) 4 / 5 ln ⁡ ln ⁡ T ) . {\displaystyle R_{T}\leq \left(\sum _{a:\mu _{a}<\mu ^{}}{\frac {\Delta _{a}}{{\mathcal {K}}_{\inf }(\nu _{a},\mu ^{},{\mathcal {D}})}}\right)\ln T+O_{T}{\big (}(\ln T)^{4/5}\ln \ln T{\big )}.} === Runtime === For D = P ( [ 0 , 1 ] ) {\displaystyle {\mathcal {D}}={\mathcal {P}}([0,1])} , the runtime needed per step and for an arm k {\displaystyle k} with n {\displaystyle n} observations is O ( n ( ln ⁡ n ) 2 ) {\displaystyle {\mathcal {O}}{\big (}n(\ln n)^{2}{\big )}} . This is higher than that of other optimal algorithms, such as NPTS with O ( n ) {\displaystyle {\mathcal {O}}(n)} . MED with O ( n ln ⁡ n ) {\displaystyle {\mathcal {O}}(n\ln n)} . and IMED with O ( n ln ⁡ n ) {\displaystyle {\mathcal {O}}(n\ln n)} . The high runtime of KL-UCB is due to a two-level optimisation: for each arm and candidate mean μ {\displaystyle \mu } , the algorithm evaluates K inf ( ν ^ a ( t ) , μ , D ) {\displaystyle {\mathcal {K}}_{\inf }({\hat {\nu }}_{a}(t),\mu ,{\mathcal {D}})} and then maximises μ {\displaystyle \mu } subject to N a ( t ) K inf ( ν ^ a ( t ) , μ , D ) ≤ δ t {\displaystyle N_{a}(t)\,{\mathcal {K}}_{\inf }({\hat {\nu }}_{a}(t),\mu ,{\mathcal {D}})\leq \delta _{t}} . For distributions bounded in [ 0 , 1 ] {\displaystyle [0,1]} the inner problem has no closed form and must be solved numerically, which increases the per-step cost.

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  Proof of authority

  Proof of authority (PoA) is a category of consensus protocols used with blockchains based on reputation and identity as a stake that delivers comparatively fast and efficient transactions (compared to proof-of-work and proof-of-stake). The most notable platforms using PoA are VeChain, Bitgert, Palm Network and Xodex. == Description == Proof-of-authority is a category of consensus protocols for networks and blockchains where transactions and blocks are built and validated by approved entities known as validators. Their permissions are often granted through a centralized authority, but they can also be granted through a council or decentralized organization. The term "proof-of-authority" was coined by Gavin Wood, co-founder of Ethereum and Parity Technologies. With PoA, validators are incentivized to maintain good behavior and honesty when validating blocks to avoid developing a negative reputation. PoA can have higher security than PoW and even PoS due to validators wanting to avoid damaging their reputation. Because PoA is permissioned, it is not fully trustless. Validators without good reputation may risk having their validator permissions removed. PoA is generally more efficient than PoW and PoS because it operates with fewer nodes and validators, thus requiring fewer duplicated resources.

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  Something Big Is Happening

  "Something Big Is Happening" is an essay by Matt Shumer, an AI entrepreneur, about the impact of artificial intelligence, published in February 2026, that has since been reportedly viewed more than 80 million times and widely discussed. Shumer noted that the technology has crossed an important threshold, where AI has become capable of creating self-improving systems. Referring to one the most recent AI models, he wrote: "It was making intelligent decisions. It had something that felt, for the first time, like judgment. Like taste." Speaking to CNBC's Power Lunch, Shumer said that his "core message" is "people in the workforce should start to use and experiment with AI tools so they can understand what’s coming". Even as the essay was widely shared and discussed, the essay also elicited criticism. Paulo Carvao, in an essay published by the Forbes Magazine stated that some of his advice is sound, but added: "It reads at times like a sales pitch. He urges readers to subscribe to the most advanced AI tools. He implies that those with access to premium models will outpace those without. He frames paid AI subscriptions as a form of insurance against obsolescence." Writing in The Guardian, Dan Milmo and Aisha Down mentioned Shumer as having a history of AI hype and stated, "He previously excited the internet by announcing the release of the world's "top open-source model", which it was not". Many workers in the technology sector criticized the article in blog posts shared on Hacker News; Edward Zitron commented that "while coding LLMs can test products, or scan/fix some bugs, this suggests they A) do this autonomously without human input, B) they do this correctly every time (or ever!)." In an article alluding to Shumer's original post, Ari Colaprete wrote "the LLM is fundamentally a writing machine, it does everything via text, and if you make it produce writing that exists purely to serve some sort of mechanical function, and you train it to succeed in that task, then it will tend to do so, even with vast intricacy."

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  Certifying algorithm

  In theoretical computer science, a certifying algorithm is an algorithm that outputs, together with a solution to the problem it solves, a proof that the solution is correct. A certifying algorithm is said to be efficient if the combined runtime of the algorithm and a proof checker is slower by at most a constant factor than the best known non-certifying algorithm for the same problem. The proof produced by a certifying algorithm should be in some sense simpler than the algorithm itself, for otherwise any algorithm could be considered certifying (with its output verified by running the same algorithm again). Sometimes this is formalized by requiring that a verification of the proof take less time than the original algorithm, while for other problems (in particular those for which the solution can be found in linear time) simplicity of the output proof is considered in a less formal sense. For instance, the validity of the output proof may be more apparent to human users than the correctness of the algorithm, or a checker for the proof may be more amenable to formal verification. Implementations of certifying algorithms that also include a checker for the proof generated by the algorithm may be considered to be more reliable than non-certifying algorithms. For, whenever the algorithm is run, one of three things happens: it produces a correct output (the desired case), it detects a bug in the algorithm or its implication (undesired, but generally preferable to continuing without detecting the bug), or both the algorithm and the checker are faulty in a way that masks the bug and prevents it from being detected (undesired, but unlikely as it depends on the existence of two independent bugs). == Examples == Many examples of problems with checkable algorithms come from graph theory. For instance, a classical algorithm for testing whether a graph is bipartite would simply output a Boolean value: true if the graph is bipartite, false otherwise. In contrast, a certifying algorithm might output a 2-coloring of the graph in the case that it is bipartite, or a cycle of odd length if it is not. Any graph is bipartite if and only if it can be 2-colored, and non-bipartite if and only if it contains an odd cycle. Both checking whether a 2-coloring is valid and checking whether a given odd-length sequence of vertices is a cycle may be performed more simply than testing bipartiteness. Analogously, it is possible to test whether a given directed graph is acyclic by a certifying algorithm that outputs either a topological order or a directed cycle. It is possible to test whether an undirected graph is a chordal graph by a certifying algorithm that outputs either an elimination ordering (an ordering of all vertices such that, for every vertex, the neighbors that are later in the ordering form a clique) or a chordless cycle. And it is possible to test whether a graph is planar by a certifying algorithm that outputs either a planar embedding or a Kuratowski subgraph. The extended Euclidean algorithm for the greatest common divisor of two integers x and y is certifying: it outputs three integers g (the divisor), a, and b, such that ax + by = g. This equation can only be true of multiples of the greatest common divisor, so testing that g is the greatest common divisor may be performed by checking that g divides both x and y and that this equation is correct.

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  Operational system

  An operational system is a term used in data warehousing to refer to a system that is used to process the day-to-day transactions of an organization. These systems are designed in a manner that processing of day-to-day transactions is performed efficiently and the integrity of the transactional data is preserved. == Synonyms == Sometimes operational systems are referred to as operational databases, transaction processing systems, or online transaction processing systems (OLTP). However, the use of the last two terms as synonyms may be confusing, because operational systems can be batch processing systems as well. Any enterprise must necessarily maintain a lot of data about its operation.

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  Controlled vocabulary

  A controlled vocabulary provides a way to organize knowledge for subsequent retrieval. Controlled vocabularies are used in subject indexing schemes, subject headings, thesauri, taxonomies and other knowledge organization systems. Controlled vocabulary schemes mandate the use of predefined, preferred terms that have been preselected by the designers of the schemes, in contrast to natural language vocabularies, which have no such restriction. == In library and information science == In library and information science, controlled vocabulary is a carefully selected list of words and phrases, which are used to tag units of information (document or work) so that they may be more easily retrieved by a search. Controlled vocabularies solve the problems of homographs, synonyms and polysemes by a bijection between concepts and preferred terms. In short, controlled vocabularies reduce unwanted ambiguity inherent in normal human languages where the same concept can be given different names and ensure consistency. For example, in the Library of Congress Subject Headings (a subject heading system that uses a controlled vocabulary), preferred terms—subject headings in this case—have to be chosen to handle choices between variant spellings of the same word (American versus British), choice among scientific and popular terms (cockroach versus Periplaneta americana), and choices between synonyms (automobile versus car), among other difficult issues. Choices of preferred terms are based on the principles of user warrant (what terms users are likely to use), literary warrant (what terms are generally used in the literature and documents), and structural warrant (terms chosen by considering the structure, scope of the controlled vocabulary). Controlled vocabularies also typically handle the problem of homographs with qualifiers. For example, the term pool has to be qualified to refer to either swimming pool or the game pool to ensure that each preferred term or heading refers to only one concept. === Types used in libraries === There are two main kinds of controlled vocabulary tools used in libraries: subject headings and thesauri. While the differences between the two are diminishing, there are still some minor differences: Historically, subject headings were designed to describe books in library catalogs by catalogers while thesauri were used by indexers to apply index terms to documents and articles. Subject headings tend to be broader in scope describing whole books, while thesauri tend to be more specialized covering very specific disciplines. Because of the card catalog system, subject headings tend to have terms that are in indirect order (though with the rise of automated systems this is being removed), while thesaurus terms are always in direct order. Subject headings tend to use more pre-coordination of terms such that the designer of the controlled vocabulary will combine various concepts together to form one preferred subject heading. (e.g., children and terrorism) while thesauri tend to use singular direct terms. Thesauri list not only equivalent terms but also narrower, broader terms and related terms among various preferred and non-preferred (but potentially synonymous) terms, while historically most subject headings did not. For example, the Library of Congress Subject Heading itself did not have much syndetic structure until 1943, and it was not until 1985 when it began to adopt the thesauri type term "Broader term" and "Narrow term". The terms are chosen and organized by trained professionals (including librarians and information scientists) who possess expertise in the subject area. Controlled vocabulary terms can accurately describe what a given document is actually about, even if the terms themselves do not occur within the document's text. Well known subject heading systems include the Library of Congress system, Medical Subject Headings (MeSH) created by the United States National Library of Medicine, and Sears. Well known thesauri include the Art and Architecture Thesaurus and the ERIC Thesaurus. When selecting terms for a controlled vocabulary, the designer has to consider the specificity of the term chosen, whether to use direct entry, inter consistency and stability of the language. Lastly the amount of pre-coordination (in which case the degree of enumeration versus synthesis becomes an issue) and post-coordination in the system is another important issue. Controlled vocabulary elements (terms/phrases) employed as tags, to aid in the content identification process of documents, or other information system entities (e.g. DBMS, Web Services) qualifies as metadata. == Indexing languages == There are three main types of indexing languages. Controlled indexing language – only approved terms can be used by the indexer to describe the document Natural language indexing language – any term from the document in question can be used to describe the document Free indexing language – any term (not only from the document) can be used to describe the document When indexing a document, the indexer also has to choose the level of indexing exhaustivity, the level of detail in which the document is described. For example, using low indexing exhaustivity, minor aspects of the work will not be described with index terms. In general the higher the indexing exhaustivity, the more terms indexed for each document. In recent years free text search as a means of access to documents has become popular. This involves using natural language indexing with an indexing exhaustively set to maximum (every word in the text is indexed). These methods have been compared in some studies, such as the 2007 article, "A Comparative Evaluation of Full-text, Concept-based, and Context-sensitive Search". === Advantages === Controlled vocabularies are often claimed to improve the accuracy of free text searching, such as to reduce irrelevant items in the retrieval list. These irrelevant items (false positives) are often caused by the inherent ambiguity of natural language. Take the English word football for example. Football is the name given to a number of different team sports. Worldwide the most popular of these team sports is association football, which also happens to be called soccer in several countries. The word football is also applied to rugby football (rugby union and rugby league), American football, Australian rules football, Gaelic football, and Canadian football. A search for football therefore will retrieve documents that are about several completely different sports. Controlled vocabulary solves this problem by tagging the documents in such a way that the ambiguities are eliminated. Compared to free text searching, the use of a controlled vocabulary can dramatically increase the performance of an information retrieval system, if performance is measured by precision (the percentage of documents in the retrieval list that are actually relevant to the search topic). In some cases controlled vocabulary can enhance recall as well, because unlike natural language schemes, once the correct preferred term is searched, there is no need to search for other terms that might be synonyms of that term. === Disadvantages === A controlled vocabulary search may lead to unsatisfactory recall, in that it will fail to retrieve some documents that are actually relevant to the search question. This is particularly problematic when the search question involves terms that are sufficiently tangential to the subject area such that the indexer might have decided to tag it using a different term (but the searcher might consider the same). Essentially, this can be avoided only by an experienced user of controlled vocabulary whose understanding of the vocabulary coincides with that of the indexer. Another possibility is that the article is just not tagged by the indexer because indexing exhaustivity is low. For example, an article might mention football as a secondary focus, and the indexer might decide not to tag it with "football" because it is not important enough compared to the main focus. But it turns out that for the searcher that article is relevant and hence recall fails. A free text search would automatically pick up that article regardless. On the other hand, free text searches have high exhaustivity (every word is searched) so although it has much lower precision, it has potential for high recall as long as the searcher overcome the problem of synonyms by entering every combination. Controlled vocabularies may become outdated rapidly in fast developing fields of knowledge, unless the preferred terms are updated regularly. Even in an ideal scenario, a controlled vocabulary is often less specific than the words of the text itself. Indexers trying to choose the appropriate index terms might misinterpret the author, while this precise problem is not a factor in a free text, as it uses the author's own words. The use of controlled vocabularies can be costly compared to free

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  Facial age estimation

  Facial age estimation is the use of artificial intelligence to estimate the age of a person based on their facial features. Computer vision techniques are used to analyse the facial features in the images of millions of people whose age is known and then deep learning is used to create an algorithm that tries to predict the age of an unknown person. The key use of the technology is to prevent access to age-restricted goods and services. Examples include restricting children from accessing internet pornography, checking that they meet a mandatory minimum age when registering for an account on social media, or preventing adults from accessing websites, online chat or games designed only for use by children. The technology is distinct from facial recognition systems as the software does not attempt to uniquely identify the individual. Researchers have applied neural networks for age estimation since at least 2010. == Evaluation == An ongoing study by the National Institute of Standards and Technology (NIST) entitled 'Face Analysis Technology Evaluation' seeks to establish the technical performance of prototype age estimation algorithms submitted by academic teams and software vendors including Brno University of Technology, Czech Technical University in Prague, Dermalog, IDEMIA, Incode Technologies Inc, Jumio, Nominder, Rank One Computing, Unissey and Yoti. == Public sector use == The UK government has explored using facial age estimation at the UK border as an alternative to bone X-rays and MRI scans when determining child status of asylum seekers. == Commercial use == Commercial users of facial age estimation include Instagram and OnlyFans. In January 2025, John Lewis & Partners announced that had started using the technology to check the age of people shopping for knives on its website, to comply with UK legislation to limit knife crime. In the UK, several supermarket chains have taken part in Home Office trials of the technology to automate the checking of a customer's age when buying age-restricted goods such as alcohol. UK legislation introduced in January 2025 mandates robust forms of age verification hosting adult content viewable in the UK by July 2025. Allowable methods include facial age estimation. == Criticism == Adam Schwartz, a lawyer for the Electronic Frontier Foundation, criticized the use of facial age estimation software, noting its inaccuracy especially in cases of minorities and women, as was found in NIST's 2024 report. Twenty organisations jointly under European Digital Rights called the practice a "systematic and invasive processing of young people's data" that risks discriminatory profiling.

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  Algorithmic Puzzles

  Algorithmic Puzzles is a book of puzzles based on computational thinking. It was written by computer scientists Anany and Maria Levitin, and published in 2011 by Oxford University Press. == Topics == The book begins with a "tutorial" introducing classical algorithm design techniques including backtracking, divide-and-conquer algorithms, and dynamic programming, methods for the analysis of algorithms, and their application in example puzzles. The puzzles themselves are grouped into three sets of 50 puzzles, in increasing order of difficulty. A final two chapters provide brief hints and more detailed solutions to the puzzles, with the solutions forming the majority of pages of the book. Some of the puzzles are well known classics, some are variations of known puzzles making them more algorithmic, and some are new. They include: Puzzles involving chessboards, including the eight queens puzzle, knight's tours, and the mutilated chessboard problem Balance puzzles River crossing puzzles The Tower of Hanoi Finding the missing element in a data stream The geometric median problem for Manhattan distance == Audience and reception == The puzzles in the book cover a wide range of difficulty, and in general do not require more than a high school level of mathematical background. William Gasarch notes that grouping the puzzles only by their difficulty and not by their themes is actually an advantage, as it provides readers with fewer clues about their solutions. Reviewer Narayanan Narayanan recommends the book to any puzzle aficionado, or to anyone who wants to develop their powers of algorithmic thinking. Reviewer Martin Griffiths suggests another group of readers, schoolteachers and university instructors in search of examples to illustrate the power of algorithmic thinking. Gasarch recommends the book to any computer scientist, evaluating it as "a delight".

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  Controlled vocabulary

  A controlled vocabulary provides a way to organize knowledge for subsequent retrieval. Controlled vocabularies are used in subject indexing schemes, subject headings, thesauri, taxonomies and other knowledge organization systems. Controlled vocabulary schemes mandate the use of predefined, preferred terms that have been preselected by the designers of the schemes, in contrast to natural language vocabularies, which have no such restriction. == In library and information science == In library and information science, controlled vocabulary is a carefully selected list of words and phrases, which are used to tag units of information (document or work) so that they may be more easily retrieved by a search. Controlled vocabularies solve the problems of homographs, synonyms and polysemes by a bijection between concepts and preferred terms. In short, controlled vocabularies reduce unwanted ambiguity inherent in normal human languages where the same concept can be given different names and ensure consistency. For example, in the Library of Congress Subject Headings (a subject heading system that uses a controlled vocabulary), preferred terms—subject headings in this case—have to be chosen to handle choices between variant spellings of the same word (American versus British), choice among scientific and popular terms (cockroach versus Periplaneta americana), and choices between synonyms (automobile versus car), among other difficult issues. Choices of preferred terms are based on the principles of user warrant (what terms users are likely to use), literary warrant (what terms are generally used in the literature and documents), and structural warrant (terms chosen by considering the structure, scope of the controlled vocabulary). Controlled vocabularies also typically handle the problem of homographs with qualifiers. For example, the term pool has to be qualified to refer to either swimming pool or the game pool to ensure that each preferred term or heading refers to only one concept. === Types used in libraries === There are two main kinds of controlled vocabulary tools used in libraries: subject headings and thesauri. While the differences between the two are diminishing, there are still some minor differences: Historically, subject headings were designed to describe books in library catalogs by catalogers while thesauri were used by indexers to apply index terms to documents and articles. Subject headings tend to be broader in scope describing whole books, while thesauri tend to be more specialized covering very specific disciplines. Because of the card catalog system, subject headings tend to have terms that are in indirect order (though with the rise of automated systems this is being removed), while thesaurus terms are always in direct order. Subject headings tend to use more pre-coordination of terms such that the designer of the controlled vocabulary will combine various concepts together to form one preferred subject heading. (e.g., children and terrorism) while thesauri tend to use singular direct terms. Thesauri list not only equivalent terms but also narrower, broader terms and related terms among various preferred and non-preferred (but potentially synonymous) terms, while historically most subject headings did not. For example, the Library of Congress Subject Heading itself did not have much syndetic structure until 1943, and it was not until 1985 when it began to adopt the thesauri type term "Broader term" and "Narrow term". The terms are chosen and organized by trained professionals (including librarians and information scientists) who possess expertise in the subject area. Controlled vocabulary terms can accurately describe what a given document is actually about, even if the terms themselves do not occur within the document's text. Well known subject heading systems include the Library of Congress system, Medical Subject Headings (MeSH) created by the United States National Library of Medicine, and Sears. Well known thesauri include the Art and Architecture Thesaurus and the ERIC Thesaurus. When selecting terms for a controlled vocabulary, the designer has to consider the specificity of the term chosen, whether to use direct entry, inter consistency and stability of the language. Lastly the amount of pre-coordination (in which case the degree of enumeration versus synthesis becomes an issue) and post-coordination in the system is another important issue. Controlled vocabulary elements (terms/phrases) employed as tags, to aid in the content identification process of documents, or other information system entities (e.g. DBMS, Web Services) qualifies as metadata. == Indexing languages == There are three main types of indexing languages. Controlled indexing language – only approved terms can be used by the indexer to describe the document Natural language indexing language – any term from the document in question can be used to describe the document Free indexing language – any term (not only from the document) can be used to describe the document When indexing a document, the indexer also has to choose the level of indexing exhaustivity, the level of detail in which the document is described. For example, using low indexing exhaustivity, minor aspects of the work will not be described with index terms. In general the higher the indexing exhaustivity, the more terms indexed for each document. In recent years free text search as a means of access to documents has become popular. This involves using natural language indexing with an indexing exhaustively set to maximum (every word in the text is indexed). These methods have been compared in some studies, such as the 2007 article, "A Comparative Evaluation of Full-text, Concept-based, and Context-sensitive Search". === Advantages === Controlled vocabularies are often claimed to improve the accuracy of free text searching, such as to reduce irrelevant items in the retrieval list. These irrelevant items (false positives) are often caused by the inherent ambiguity of natural language. Take the English word football for example. Football is the name given to a number of different team sports. Worldwide the most popular of these team sports is association football, which also happens to be called soccer in several countries. The word football is also applied to rugby football (rugby union and rugby league), American football, Australian rules football, Gaelic football, and Canadian football. A search for football therefore will retrieve documents that are about several completely different sports. Controlled vocabulary solves this problem by tagging the documents in such a way that the ambiguities are eliminated. Compared to free text searching, the use of a controlled vocabulary can dramatically increase the performance of an information retrieval system, if performance is measured by precision (the percentage of documents in the retrieval list that are actually relevant to the search topic). In some cases controlled vocabulary can enhance recall as well, because unlike natural language schemes, once the correct preferred term is searched, there is no need to search for other terms that might be synonyms of that term. === Disadvantages === A controlled vocabulary search may lead to unsatisfactory recall, in that it will fail to retrieve some documents that are actually relevant to the search question. This is particularly problematic when the search question involves terms that are sufficiently tangential to the subject area such that the indexer might have decided to tag it using a different term (but the searcher might consider the same). Essentially, this can be avoided only by an experienced user of controlled vocabulary whose understanding of the vocabulary coincides with that of the indexer. Another possibility is that the article is just not tagged by the indexer because indexing exhaustivity is low. For example, an article might mention football as a secondary focus, and the indexer might decide not to tag it with "football" because it is not important enough compared to the main focus. But it turns out that for the searcher that article is relevant and hence recall fails. A free text search would automatically pick up that article regardless. On the other hand, free text searches have high exhaustivity (every word is searched) so although it has much lower precision, it has potential for high recall as long as the searcher overcome the problem of synonyms by entering every combination. Controlled vocabularies may become outdated rapidly in fast developing fields of knowledge, unless the preferred terms are updated regularly. Even in an ideal scenario, a controlled vocabulary is often less specific than the words of the text itself. Indexers trying to choose the appropriate index terms might misinterpret the author, while this precise problem is not a factor in a free text, as it uses the author's own words. The use of controlled vocabularies can be costly compared to free

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  Synthetic data

  Synthetic data are artificially generated data not produced by real-world events. Typically created using algorithms, synthetic data can be deployed to validate mathematical models and to train machine learning models. Data generated by a computer simulation can be seen as synthetic data. This encompasses most applications of physical modeling, such as music synthesizers or flight simulators. The output of such systems approximates the real thing, but is fully algorithmically generated. Synthetic data is used in a variety of fields as a filter for information that would otherwise compromise the confidentiality of particular aspects of the data. In many sensitive applications, datasets theoretically exist but cannot be released to the general public; synthetic data sidesteps the privacy issues that arise from using real consumer information without permission or compensation. == Usefulness == Synthetic data is generated to meet specific needs or certain conditions that may not be found in the original, real data. One of the hurdles in applying up-to-date machine learning approaches for complex scientific tasks is the scarcity of labeled data, a gap effectively bridged by the use of synthetic data, which closely replicates real experimental data. This can be useful when designing many systems, from simulations based on theoretical value, to database processors, etc. This helps detect and solve unexpected issues such as information processing limitations. Synthetic data are often generated to represent the authentic data and allows a baseline to be set. Another benefit of synthetic data is to protect the privacy and confidentiality of authentic data, while still allowing for use in testing systems. Computer security experts claim generated synthetic data "... enables us to create realistic behavior profiles for users and attackers. The data is used to train the fraud detection system itself, thus creating the necessary adaptation of the system to a specific environment." In defense and military contexts, synthetic data is seen as a potentially valuable tool to develop and improve complex AI systems, particularly in contexts where high-quality real-world data is scarce. At the same time, synthetic data together with the testing approach can give the ability to model real-world scenarios. == History == Scientific modelling of physical systems has a long history that runs concurrent with the history of physics. For example, research into synthesis of audio and voice can be traced back to the 1930s and before, driven forward by the developments of the telephone and audio recording technologies. Digitization gave rise to software synthesizers from the 1970s onwards. In the context of privacy-preserving statistical analysis, in 1993, the idea of original fully synthetic data was created by Donald Rubin. Rubin originally designed this to synthesize the Decennial Census long form responses for the short form households. He then released samples that did not include any actual long form records - in this he preserved anonymity of the household. Later that year, the idea of original partially synthetic data was created by Little. Little used this idea to synthesize the sensitive values on the public use file. A 1993 work fitted a statistical model to 60,000 MNIST digits, then it was used to generate over 1 million examples. Those were used to train a LeNet-4 to reach state of the art performance. In 1994, Stephen Fienberg introduced 'critical refinement', in which a parametric posterior predictive distribution (instead of a Bayes bootstrap) is used to do the sampling. Later, other important contributors to the development of synthetic data generation were Trivellore Raghunathan, Jerry Reiter, Donald Rubin, John M. Abowd, and Jim Woodcock. Collectively they came up with a solution for how to treat partially synthetic data with missing data. Similarly, they developed the technique of Sequential Regression Multivariate Imputation. == Calculations == Researchers test the framework on synthetic data, which is "the only source of ground truth on which they can objectively assess the performance of their algorithms". Synthetic data can be generated through the use of random lines, having different orientations and starting positions. Datasets can get fairly complicated. A more complicated dataset can be generated by using a synthesizer build. To create a synthesizer build, first use the original data to create a model or equation that fits the data the best. This model or equation will be called a synthesizer build. This build can be used to generate more data. Constructing a synthesizer build involves constructing a statistical model. In a linear regression line example, the original data can be plotted, and a best fit linear line can be created from the data. This line is a synthesizer created from the original data. The next step will be generating more synthetic data from the synthesizer build or from this linear line equation. In this way, the new data can be used for studies and research, and it protects the confidentiality of the original data. David Jensen from the Knowledge Discovery Laboratory explains how to generate synthetic data: "Researchers frequently need to explore the effects of certain data characteristics on their data model." To help construct datasets exhibiting specific properties, such as auto-correlation or degree disparity, proximity can generate synthetic data having one of several types of graph structure: random graphs that are generated by some random process; lattice graphs having a ring structure; lattice graphs having a grid structure, etc. In all cases, the data generation process follows the same process: Generate the empty graph structure. Generate attribute values based on user-supplied prior probabilities. Since the attribute values of one object may depend on the attribute values of related objects, the attribute generation process assigns values collectively. == Applications == === Fraud detection and confidentiality systems === Testing and training fraud detection and confidentiality systems are devised using synthetic data. Specific algorithms and generators are designed to create realistic data, which then assists in teaching a system how to react to certain situations or criteria. For example, intrusion detection software is tested using synthetic data. This data is a representation of the authentic data and may include intrusion instances that are not found in the authentic data. The synthetic data allows the software to recognize these situations and react accordingly. If synthetic data was not used, the software would only be trained to react to the situations provided by the authentic data and it may not recognize another type of intrusion. === Scientific research === Researchers doing clinical trials or any other research may generate synthetic data to aid in creating a baseline for future studies and testing. Real data can contain information that researchers may not want released, so synthetic data is sometimes used to protect the privacy and confidentiality of a dataset. Using synthetic data reduces confidentiality and privacy issues since it holds no personal information and cannot be traced back to any individual. Beyond privacy protection, synthetic data is also being explored for methodological innovation in drug development. For instance, synthetic data may be used to construct synthetic control arms as an alternative to conventional external control arms based on real-world data (RWD) or randomized controlled trials (RCTs). Collectively, regulatory agencies such as the FDA and EMA appear to be at various stages of recognizing and integrating AI-generated synthetic data into their methodologies. While there is growing consensus on the potential of such data to support model development and the broader lifecycle of medicinal products, to date no drug or medical device has been approved using solely or predominantly synthetic data—particularly not as a comparator arm generated entirely via data-driven algorithms. The quality and statistical handling of synthetic data are expected to become more prominent in future regulatory discussions, particularly in contexts such as predictive modeling (e.g., digital twins), where innovative approaches have already been referenced. === Machine learning === Synthetic data is increasingly being used for machine learning applications: a model is trained on a synthetically generated dataset with the intention of transfer learning to real data. Efforts have been made to enable more data science experiments via the construction of general-purpose synthetic data generators, such as the Synthetic Data Vault. In general, synthetic data has several natural advantages: once the synthetic environment is ready, it is fast and cheap to produce as much data as needed; synthetic data can have perfectly accurate labels, including labeling that may be very expensive or impo

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  A Logical Calculus of the Ideas Immanent in Nervous Activity

  "A Logical Calculus of the Ideas Immanent in Nervous Activity" is a 1943 paper written by Warren Sturgis McCulloch and Walter Pitts, published in the journal The Bulletin of Mathematical Biophysics. The paper proposed a mathematical model of the nervous system as a network of simple logical elements, later known as artificial neurons, or McCulloch–Pitts neurons. These neurons receive inputs, perform a weighted sum, and fire an output signal based on a threshold function. By connecting these units in various configurations, McCulloch and Pitts demonstrated that their model could perform all logical functions. It is a seminal work in cognitive science, computational neuroscience, computer science, and artificial intelligence. It was a foundational result in automata theory. John von Neumann cited it as a significant result. == Mathematics == The artificial neuron used in the original paper is slightly different from the modern version. They considered neural networks that operate in discrete steps of time t = 0 , 1 , … {\displaystyle t=0,1,\dots } . The neural network contains a number of neurons. Let the state of a neuron i {\displaystyle i} at time t {\displaystyle t} be N i ( t ) {\displaystyle N_{i}(t)} . The state of a neuron can either be 0 or 1, standing for "not firing" and "firing". Each neuron also has a firing threshold θ {\displaystyle \theta } , such that it fires if the total input exceeds the threshold. Each neuron can connect to any other neuron (including itself) with positive synapses (excitatory) or negative synapses (inhibitory). That is, each neuron can connect to another neuron with a weight w {\displaystyle w} taking an integer value. A peripheral afferent is a neuron with no incoming synapses. We can regard each neural network as a directed graph, with the nodes being the neurons, and the directed edges being the synapses. A neural network has a circle or a circuit if there exists a directed circle in the graph. Let w i j ( t ) {\displaystyle w_{ij}(t)} be the connection weight from neuron j {\displaystyle j} to neuron i {\displaystyle i} at time t {\displaystyle t} , then its next state is N i ( t + 1 ) = H ( ∑ j = 1 n w i j ( t ) N j ( t ) − θ i ( t ) ) , {\displaystyle N_{i}(t+1)=H\left(\sum _{j=1}^{n}w_{ij}(t)N_{j}(t)-\theta _{i}(t)\right),} where H {\displaystyle H} is the Heaviside step function (outputting 1 if the input is greater than or equal to 0, and 0 otherwise). === Symbolic logic === The paper used, as a logical language for describing neural networks, "Language II" from The Logical Syntax of Language by Rudolf Carnap with some notations taken from Principia Mathematica by Alfred North Whitehead and Bertrand Russell. Language II covers substantial parts of classical mathematics, including real analysis and portions of set theory. To describe a neural network with peripheral afferents N 1 , N 2 , … , N p {\displaystyle N_{1},N_{2},\dots ,N_{p}} and non-peripheral afferents N p + 1 , N p + 2 , … , N n {\displaystyle N_{p+1},N_{p+2},\dots ,N_{n}} they considered logical predicate of form P r ( N 1 , N 2 , … , N p , t ) {\displaystyle Pr(N_{1},N_{2},\dots ,N_{p},t)} where P r {\displaystyle Pr} is a first-order logic predicate function (a function that outputs a boolean), N 1 , … , N p {\displaystyle N_{1},\dots ,N_{p}} are predicates that take t {\displaystyle t} as an argument, and t {\displaystyle t} is the only free variable in the predicate. Intuitively speaking, N 1 , … , N p {\displaystyle N_{1},\dots ,N_{p}} specifies the binary input patterns going into the neural network over all time, and P r ( N 1 , N 2 , … , N n , t ) {\displaystyle Pr(N_{1},N_{2},\dots ,N_{n},t)} is a function that takes some binary input patterns, and constructs an output binary pattern P r ( N 1 , N 2 , … , N n , 0 ) , P r ( N 1 , N 2 , … , N n , 1 ) , … {\displaystyle Pr(N_{1},N_{2},\dots ,N_{n},0),Pr(N_{1},N_{2},\dots ,N_{n},1),\dots } . A logical sentence P r ( N 1 , N 2 , … , N n , t ) {\displaystyle Pr(N_{1},N_{2},\dots ,N_{n},t)} is realized by a neural network iff there exists a time-delay T ≥ 0 {\displaystyle T\geq 0} , a neuron i {\displaystyle i} in the network, and an initial state for the non-peripheral neurons N p + 1 ( 0 ) , … , N n ( 0 ) {\displaystyle N_{p+1}(0),\dots ,N_{n}(0)} , such that for any time t {\displaystyle t} , the truth-value of the logical sentence is equal to the state of the neuron i {\displaystyle i} at time t + T {\displaystyle t+T} . That is, ∀ t = 0 , 1 , 2 , … , P r ( N 1 , N 2 , … , N p , t ) = N i ( t + T ) {\displaystyle \forall t=0,1,2,\dots ,\quad Pr(N_{1},N_{2},\dots ,N_{p},t)=N_{i}(t+T)} === Equivalence === In the paper, they considered some alternative definitions of artificial neural networks, and have shown them to be equivalent, that is, neural networks under one definition realizes precisely the same logical sentences as neural networks under another definition. They considered three forms of inhibition: relative inhibition, absolute inhibition, and extinction. The definition above is relative inhibition. By "absolute inhibition" they meant that if any negative synapse fires, then the neuron will not fire. By "extinction" they meant that if at time t {\displaystyle t} , any inhibitory synapse fires on a neuron i {\displaystyle i} , then θ i ( t + j ) = θ i ( 0 ) + b j {\displaystyle \theta _{i}(t+j)=\theta _{i}(0)+b_{j}} for j = 1 , 2 , 3 , … {\displaystyle j=1,2,3,\dots } , until the next time an inhibitory synapse fires on i {\displaystyle i} . It is required that b j = 0 {\displaystyle b_{j}=0} for all large j {\displaystyle j} . Theorem 4 and 5 state that these are equivalent. They considered three forms of excitation: spatial summation, temporal summation, and facilitation. The definition above is spatial summation (which they pictured as having multiple synapses placed close together, so that the effect of their firing sums up). By "temporal summation" they meant that the total incoming signal is ∑ τ = 0 T ∑ j = 1 n w i j ( t ) N j ( t − τ ) {\displaystyle \sum _{\tau =0}^{T}\sum _{j=1}^{n}w_{ij}(t)N_{j}(t-\tau )} for some T ≥ 1 {\displaystyle T\geq 1} . By "facilitation" they meant the same as extinction, except that b j ≤ 0 {\displaystyle b_{j}\leq 0} . Theorem 6 states that these are equivalent. They considered neural networks that do not change, and those that change by Hebbian learning. That is, they assume that at t = 0 {\displaystyle t=0} , some excitatory synaptic connections are not active. If at any t {\displaystyle t} , both N i ( t ) = 1 , N j ( t ) = 1 {\displaystyle N_{i}(t)=1,N_{j}(t)=1} , then any latent excitatory synapse between i , j {\displaystyle i,j} becomes active. Theorem 7 states that these are equivalent. === Logical expressivity === They considered "temporal propositional expressions" (TPE), which are propositional formulas with one free variable t {\displaystyle t} . For example, N 1 ( t ) ∨ N 2 ( t ) ∧ ¬ N 3 ( t ) {\displaystyle N_{1}(t)\vee N_{2}(t)\wedge \neg N_{3}(t)} is such an expression. Theorem 1 and 2 together showed that neural nets without circles are equivalent to TPE. For neural nets with loops, they noted that "realizable P r {\displaystyle Pr} may involve reference to past events of an indefinite degree of remoteness". These then encodes for sentences like "There was some x such that x was a ψ" or ( ∃ x ) ( ψ x ) {\displaystyle (\exists x)(\psi x)} . Theorems 8 to 10 showed that neural nets with loops can encode all first-order logic with equality and conversely, any looped neural networks is equivalent to a sentence in first-order logic with equality, thus showing that they are equivalent in logical expressiveness. As a remark, they noted that a neural network, if furnished with a tape, scanners, and write-heads, is equivalent to a Turing machine, and conversely, every Turing machine is equivalent to some such neural network. Thus, these neural networks are equivalent to Turing computability and Church's lambda-definability. == Context == === Previous work === The paper built upon several previous strands of work. In the symbolic logic side, it built on the previous work by Carnap, Whitehead, and Russell. This was contributed by Walter Pitts, who had a strong proficiency with symbolic logic. Pitts provided mathematical and logical rigor to McCulloch’s vague ideas on psychons (atoms of psychological events) and circular causality. In the neuroscience side, it built on previous work by the mathematical biology research group centered around Nicolas Rashevsky, of which McCulloch was a member. The paper was published in the Bulletin of Mathematical Biophysics, which was founded by Rashevsky in 1939. During the late 1930s, Rashevsky's research group was producing papers that had difficulty publishing in other journals at the time, so Rashevsky decided to found a new journal exclusively devoted to mathematical biophysics. Also in the Rashevsky's group was Alston Scott Householder, who in 1941 published an abstract model

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  Semantic translation

  Semantic translation is the process of using semantic information to aid in the translation of data in one representation or data model to another representation or data model. Semantic translation takes advantage of semantics that associate meaning with individual data elements in one dictionary to create an equivalent meaning in a second system. An example of semantic translation is the conversion of XML data from one data model to a second data model using formal ontologies for each system such as the Web Ontology Language (OWL). This is frequently required by intelligent agents that wish to perform searches on remote computer systems that use different data models to store their data elements. The process of allowing a single user to search multiple systems with a single search request is also known as federated search. Semantic translation should be differentiated from data mapping tools that do simple one-to-one translation of data from one system to another without actually associating meaning with each data element. Semantic translation requires that data elements in the source and destination systems have "semantic mappings" to a central registry or registries of data elements. The simplest mapping is of course where there is equivalence. There are three types of Semantic equivalence: Class Equivalence - indicating that class or "concepts" are equivalent. For example: "Person" is the same as "Individual" Property Equivalence - indicating that two properties are equivalent. For example: "PersonGivenName" is the same as "FirstName" Instance Equivalence - indicating that two individual instances of objects are equivalent. For example: "Dan Smith" is the same person as "Daniel Smith" Semantic translation is very difficult if the terms in a particular data model do not have direct one-to-one mappings to data elements in a foreign data model. In that situation, an alternative approach must be used to find mappings from the original data to the foreign data elements. This problem can be alleviated by centralized metadata registries that use the ISO-11179 standards such as the National Information Exchange Model (NIEM).

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  Wearable computer

  A wearable computer, also known as a body-borne computer or wearable, is a computing device worn on the body. The definition of 'wearable computer' may be narrow or broad, extending to smartphones or even ordinary wristwatches. Wearables may be for general use, in which case they are just a particularly small example of mobile computing. Alternatively, they may be for specialized purposes such as fitness trackers. They may incorporate special sensors such as accelerometers, heart rate monitors, or on the more advanced side, electrocardiogram (ECG) and blood oxygen saturation (SpO2) monitors. Under the definition of wearable computers, we also include novel user interfaces such as Google Glass, an optical head-mounted display controlled by gestures. It may be that specialized wearables will evolve into general all-in-one devices, as happened with the convergence of PDAs and mobile phones into smartphones. Wearables are typically worn on the wrist (e.g. fitness trackers), hung from the neck (like a necklace), strapped to the arm or leg (electronic tagging), or on the head (as glasses or a helmet), though some have been located elsewhere (e.g. on a finger or in a shoe). Devices carried in a pocket or bag – such as smartphones and before them, pocket calculators and PDAs, may or may not be regarded as 'worn'. Wearable computers have various technical issues common to other mobile computing, such as batteries, heat dissipation, software architectures, wireless and personal area networks, and data management. Many wearable computers are active all the time, e.g. processing or recording data continuously. == Applications == Wearable computers are not only limited to computers such as fitness trackers that are worn on wrists; they also include wearables such as heart pacemakers and other prosthetics. They are used most often in research that focuses on behavioral modeling, health monitoring systems, IT and media development, where the person wearing the computer actually moves or is otherwise engaged with his or her surroundings. Wearable computers have been used for the following: general-purpose computing (e.g. smartphones and smartwatches) sensory integration, e.g. to help people see better or understand the world better (whether in task-specific applications like camera-based welding helmets or for everyday use like Google Glass) behavioral modeling health care monitoring systems service management electronic textiles and fashion design, e.g. Microsoft's 2011 prototype "The Printing Dress". Wearable computing is the subject of active research, especially the form-factor and location on the body, with areas of study including user interface design, augmented reality, and pattern recognition. The use of wearables for specific applications, for compensating disabilities or supporting elderly people steadily increases. == Operating systems == The dominant operating systems for wearable computing are: FreeRTOS is a real-time operating system kernel for embedded devices; most of the Smartbands that are currently available in the market are based on FreeRTOS, which include Huawei, Honor, Lenovo, realme, TCL and Xiaomi smartbands. LiteOS is a lightweight open source real-time operating system that is part of Huawei's "1+8+N" Internet of Things solution. Tizen OS from Samsung (there was an announcement in May 2021 that Wear OS and Tizen OS will merge and will be called simply Wear.) watchOS watchOS is a proprietary mobile operating system developed by Apple Inc. to run on the Apple Watch. Wear OS Wear OS (previously known as Android Wear) is a smartwatch operating system developed by Google Inc. == History == Due to the varied definitions of wearable and computer, the first wearable computer could be as early as the first abacus on a necklace, a 16th-century abacus ring, a wristwatch and 'finger-watch' owned by Queen Elizabeth I of England, or the covert timing devices hidden in shoes to cheat at roulette by Thorp and Shannon in the 1960s and 1970s. However, a general-purpose computer is not merely a time-keeping or calculating device, but rather a user-programmable item for arbitrary complex algorithms, interfacing, and data management. By this definition, the wearable computer was invented by Steve Mann, in the late 1970s: Steve Mann, a professor at the University of Toronto, was hailed as the father of the wearable computer and the ISSCC's first virtual panelist, by moderator Woodward Yang of Harvard University (Cambridge Mass.). The development of wearable items has taken several steps of miniaturization from discrete electronics over hybrid designs to fully integrated designs, where just one processor chip, a battery, and some interface conditioning items make the whole unit. === 1500s === Queen Elizabeth I of England received a watch from Robert Dudley in 1571, as a New Year's present; it may have been worn on the forearm rather than the wrist. She also possessed a 'finger-watch' set in a ring, with an alarm that prodded her finger. === 1600s === The Qing dynasty saw the introduction of a fully functional abacus on a ring, which could be used while it was being worn. === 1960s === In 1961, mathematicians Edward O. Thorp and Claude Shannon built some computerized timing devices to help them win a game of roulette. One such timer was concealed in a shoe and another in a pack of cigarettes. Various versions of this apparatus were built in the 1960s and 1970s. Thorp refers to himself as the inventor of the first "wearable computer". In other variations, the system was a concealed cigarette-pack-sized analog computer designed to predict the motion of roulette wheels. A data-taker would use microswitches hidden in his shoes to indicate the speed of the roulette wheel, and the computer would indicate an octant of the roulette wheel to bet on by sending musical tones via radio to a miniature speaker hidden in a collaborator's ear canal. The system was successfully tested in Las Vegas in June 1961, but hardware issues with the speaker wires prevented it from being used beyond test runs. This was not a wearable computer because it could not be re-purposed during use; rather it was an example of task-specific hardware. This work was kept secret until it was first mentioned in Thorp's book Beat the Dealer (revised ed.) in 1966 and later published in detail in 1969. === 1970s === Pocket calculators became mass-market devices in 1970, starting in Japan. Programmable calculators followed in the late 1970s, being somewhat more general-purpose computers. The HP-01 algebraic calculator watch by Hewlett-Packard was released in 1977. A camera-to-tactile vest for the blind, launched by C.C. Collins in 1977, converted images into a 1024-point, ten-inch square tactile grid on a vest. === 1980s === The 1980s saw the rise of more general-purpose wearable computers. In 1981, Steve Mann designed and built a backpack-mounted 6502-based wearable multimedia computer with text, graphics, and multimedia capability, as well as video capability (cameras and other photographic systems). Mann went on to be an early and active researcher in the wearables field, especially known for his 1994 creation of the Wearable Wireless Webcam, the first example of lifelogging. Seiko Epson released the RC-20 Wrist Computer in 1984. It was an early smartwatch, powered by a computer on a chip. In 1989, Reflection Technology marketed the Private Eye head-mounted display, which scans a vertical array of LEDs across the visual field using a vibrating mirror. This display gave rise to several hobbyist and research wearables, including Gerald "Chip" Maguire's IBM/Columbia University Student Electronic Notebook, Doug Platt's Hip-PC, and Carnegie Mellon University's VuMan 1 in 1991. The Student Electronic Notebook consisted of the Private Eye, Toshiba diskless AIX notebook computers (prototypes), a stylus based input system and a virtual keyboard. It used direct-sequence spread spectrum radio links to provide all the usual TCP/IP based services, including NFS mounted file systems and X11, which all ran in the Andrew Project environment. The Hip-PC included an Agenda palmtop used as a chording keyboard attached to the belt and a 1.44 megabyte floppy drive. Later versions incorporated additional equipment from Park Engineering. The system debuted at "The Lap and Palmtop Expo" on 16 April 1991. VuMan 1 was developed as part of a Summer-term course at Carnegie Mellon's Engineering Design Research Center, and was intended for viewing house blueprints. Input was through a three-button unit worn on the belt, and output was through Reflection Tech's Private Eye. The CPU was an 8 MHz 80188 processor with 0.5 MB ROM. === 1990s === In the 1990s PDAs became widely used, and in 1999 were combined with mobile phones in Japan to produce the first mass-market smartphone. In 1993, the Private Eye was used in Thad Starner's wearable, based on Doug Platt's system and built from a kit from Park Enterprises, a Pri

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