Decorrelation is a general term for any process that is used to reduce autocorrelation within a signal, or cross-correlation within a set of signals, while preserving other aspects of the signal. A frequently used method of decorrelation is the use of a matched linear filter to reduce the autocorrelation of a signal as far as possible. Since the minimum possible autocorrelation for a given signal energy is achieved by equalising the power spectrum of the signal to be similar to that of a white noise signal, this is often referred to as signal whitening. == Process == === Signal processing === Most decorrelation algorithms are linear, but there are also non-linear decorrelation algorithms. Many data compression algorithms incorporate a decorrelation stage. For example, many transform coders first apply a fixed linear transformation that would, on average, have the effect of decorrelating a typical signal of the class to be coded, prior to any later processing. This is typically a Karhunen–Loève transform, or a simplified approximation such as the discrete cosine transform. By comparison, sub-band coders do not generally have an explicit decorrelation step, but instead exploit the already-existing reduced correlation within each of the sub-bands of the signal, due to the relative flatness of each sub-band of the power spectrum in many classes of signals. Linear predictive coders can be modelled as an attempt to decorrelate signals by subtracting the best possible linear prediction from the input signal, leaving a whitened residual signal. Decorrelation techniques can also be used for many other purposes, such as reducing crosstalk in a multi-channel signal, or in the design of echo cancellers. In image processing decorrelation techniques can be used to enhance or stretch, colour differences found in each pixel of an image. This is generally termed as 'decorrelation stretching'. === Neuroscience === In neuroscience, decorrelation is used in the analysis of the neural networks in the human visual system. The raw inputs from cone cells and rod cells under go many steps of processing before it is handled by the visual cortex. These steps generally perform decorrelation, both spatial (surround suppression in the retina) and temporal (handling of movement in the lateral geniculate nucleus). === Cryptography === In cryptography, decorrelation is used in cipher design (see Decorrelation theory) and in the design of hardware random number generators.
Iterative reconstruction
Iterative reconstruction refers to iterative algorithms used to reconstruct 2D and 3D images in certain imaging techniques. For example, in computed tomography an image must be reconstructed from projections of an object. Here, iterative reconstruction techniques are usually a better, but computationally more expensive alternative to the common filtered back projection (FBP) method, which directly calculates the image in a single reconstruction step. In recent research works, scientists have shown that extremely fast computations and massive parallelism is possible for iterative reconstruction, which makes iterative reconstruction practical for commercialization. == Basic concepts == The reconstruction of an image from the acquired data is an inverse problem. Often, it is not possible to exactly solve the inverse problem directly. In this case, a direct algorithm has to approximate the solution, which might cause visible reconstruction artifacts in the image. Iterative algorithms approach the correct solution using multiple iteration steps, which allows to obtain a better reconstruction at the cost of a higher computation time. There are a large variety of algorithms, but each starts with an assumed image, computes projections from the image, compares the original projection data and updates the image based upon the difference between the calculated and the actual projections. === Algebraic reconstruction === The Algebraic Reconstruction Technique (ART) was the first iterative reconstruction technique used for computed tomography by Hounsfield. === Iterative Sparse Asymptotic Minimum Variance === The iterative sparse asymptotic minimum variance algorithm is an iterative, parameter-free superresolution tomographic reconstruction method inspired by compressed sensing, with applications in synthetic-aperture radar, computed tomography scan, and magnetic resonance imaging (MRI). === Statistical reconstruction === There are typically five components to statistical iterative image reconstruction algorithms, e.g. An object model that expresses the unknown continuous-space function f ( r ) {\displaystyle f(r)} that is to be reconstructed in terms of a finite series with unknown coefficients that must be estimated from the data. A system model that relates the unknown object to the "ideal" measurements that would be recorded in the absence of measurement noise. Often this is a linear model of the form A x + ϵ {\displaystyle \mathbf {A} x+\epsilon } , where ϵ {\displaystyle \epsilon } represents the noise. A statistical model that describes how the noisy measurements vary around their ideal values. Often Gaussian noise or Poisson statistics are assumed. Because Poisson statistics are closer to reality, it is more widely used. A cost function that is to be minimized to estimate the image coefficient vector. Often this cost function includes some form of regularization. Sometimes the regularization is based on Markov random fields. An algorithm, usually iterative, for minimizing the cost function, including some initial estimate of the image and some stopping criterion for terminating the iterations. === Learned Iterative Reconstruction === In learned iterative reconstruction, the updating algorithm is learned from training data using techniques from machine learning such as convolutional neural networks, while still incorporating the image formation model. This typically gives faster and higher quality reconstructions and has been applied to CT and MRI reconstruction. == Advantages == The advantages of the iterative approach include improved insensitivity to noise and capability of reconstructing an optimal image in the case of incomplete data. The method has been applied in emission tomography modalities like SPECT and PET, where there is significant attenuation along ray paths and noise statistics are relatively poor. Statistical, likelihood-based approaches: Statistical, likelihood-based iterative expectation-maximization algorithms are now the preferred method of reconstruction. Such algorithms compute estimates of the likely distribution of annihilation events that led to the measured data, based on statistical principle, often providing better noise profiles and resistance to the streak artifacts common with FBP. Since the density of radioactive tracer is a function in a function space, therefore of extremely high-dimensions, methods which regularize the maximum-likelihood solution turning it towards penalized or maximum a-posteriori methods can have significant advantages for low counts. Examples such as Ulf Grenander's Sieve estimator or Bayes penalty methods, or via I.J. Good's roughness method may yield superior performance to expectation-maximization-based methods which involve a Poisson likelihood function only. As another example, it is considered superior when one does not have a large set of projections available, when the projections are not distributed uniformly in angle, or when the projections are sparse or missing at certain orientations. These scenarios may occur in intraoperative CT, in cardiac CT, or when metal artifacts require the exclusion of some portions of the projection data. In Magnetic Resonance Imaging it can be used to reconstruct images from data acquired with multiple receive coils and with sampling patterns different from the conventional Cartesian grid and allows the use of improved regularization techniques (e.g. total variation) or an extended modeling of physical processes to improve the reconstruction. For example, with iterative algorithms it is possible to reconstruct images from data acquired in a very short time as required for real-time MRI (rt-MRI). In Cryo Electron Tomography, where the limited number of projections are acquired due to the hardware limitations and to avoid the biological specimen damage, it can be used along with compressive sensing techniques or regularization functions (e.g. Huber function) to improve the reconstruction for better interpretation. Here is an example that illustrates the benefits of iterative image reconstruction for cardiac MRI.
Ordered weighted averaging
In applied mathematics, specifically in fuzzy logic, the ordered weighted averaging (OWA) operators provide a parameterized class of mean type aggregation operators. They were introduced by Ronald R. Yager. Many notable mean operators such as the max, arithmetic average, median and min, are members of this class. They have been widely used in computational intelligence because of their ability to model linguistically expressed aggregation instructions. == Definition == An OWA operator of dimension n {\displaystyle \ n} is a mapping F : R n → R {\displaystyle F:\mathbb {R} ^{n}\rightarrow \mathbb {R} } that has an associated collection of weights W = [ w 1 , … , w n ] {\displaystyle \ W=[w_{1},\ldots ,w_{n}]} lying in the unit interval and summing to one and with F ( a 1 , … , a n ) = ∑ j = 1 n w j b j {\displaystyle F(a_{1},\ldots ,a_{n})=\sum _{j=1}^{n}w_{j}b_{j}} where b j {\displaystyle b_{j}} is the jth largest of the a i {\displaystyle a_{i}} . By choosing different W one can implement different aggregation operators. The OWA operator is a non-linear operator as a result of the process of determining the bj. == Notable OWA operators == F ( a 1 , … , a n ) = max ( a 1 , … , a n ) {\displaystyle \ F(a_{1},\ldots ,a_{n})=\max(a_{1},\ldots ,a_{n})} if w 1 = 1 {\displaystyle \ w_{1}=1} and w j = 0 {\displaystyle \ w_{j}=0} for j ≠ 1 {\displaystyle j\neq 1} F ( a 1 , … , a n ) = min ( a 1 , … , a n ) {\displaystyle \ F(a_{1},\ldots ,a_{n})=\min(a_{1},\ldots ,a_{n})} if w n = 1 {\displaystyle \ w_{n}=1} and w j = 0 {\displaystyle \ w_{j}=0} for j ≠ n {\displaystyle j\neq n} F ( a 1 , … , a n ) = a v e r a g e ( a 1 , … , a n ) {\displaystyle \ F(a_{1},\ldots ,a_{n})=\mathrm {average} (a_{1},\ldots ,a_{n})} if w j = 1 n {\displaystyle \ w_{j}={\frac {1}{n}}} for all j ∈ [ 1 , n ] {\displaystyle j\in [1,n]} == Properties == The OWA operator is a mean operator. It is bounded, monotonic, symmetric, and idempotent, as defined below. == Characterizing features == Two features have been used to characterize the OWA operators. The first is the attitudinal character, also called orness. This is defined as A − C ( W ) = 1 n − 1 ∑ j = 1 n ( n − j ) w j . {\displaystyle A-C(W)={\frac {1}{n-1}}\sum _{j=1}^{n}(n-j)w_{j}.} It is known that A − C ( W ) ∈ [ 0 , 1 ] {\displaystyle A-C(W)\in [0,1]} . In addition A − C(max) = 1, A − C(ave) = A − C(med) = 0.5 and A − C(min) = 0. Thus the A − C goes from 1 to 0 as we go from Max to Min aggregation. The attitudinal character characterizes the similarity of aggregation to OR operation(OR is defined as the Max). The second feature is the dispersion. This defined as H ( W ) = − ∑ j = 1 n w j ln ( w j ) . {\displaystyle H(W)=-\sum _{j=1}^{n}w_{j}\ln(w_{j}).} An alternative definition is E ( W ) = ∑ j = 1 n w j 2 . {\displaystyle E(W)=\sum _{j=1}^{n}w_{j}^{2}.} The dispersion characterizes how uniformly the arguments are being used. == Type-1 OWA aggregation operators == The above Yager's OWA operators are used to aggregate the crisp values. Can we aggregate fuzzy sets in the OWA mechanism? The Type-1 OWA operators have been proposed for this purpose. So the type-1 OWA operators provides us with a new technique for directly aggregating uncertain information with uncertain weights via OWA mechanism in soft decision making and data mining, where these uncertain objects are modelled by fuzzy sets. The type-1 OWA operator is defined according to the alpha-cuts of fuzzy sets as follows: Given the n linguistic weights { W i } i = 1 n {\displaystyle \left\{{W^{i}}\right\}_{i=1}^{n}} in the form of fuzzy sets defined on the domain of discourse U = [ 0 , 1 ] {\displaystyle U=[0,\;\;1]} , then for each α ∈ [ 0 , 1 ] {\displaystyle \alpha \in [0,\;1]} , an α {\displaystyle \alpha } -level type-1 OWA operator with α {\displaystyle \alpha } -level sets { W α i } i = 1 n {\displaystyle \left\{{W_{\alpha }^{i}}\right\}_{i=1}^{n}} to aggregate the α {\displaystyle \alpha } -cuts of fuzzy sets { A i } i = 1 n {\displaystyle \left\{{A^{i}}\right\}_{i=1}^{n}} is given as Φ α ( A α 1 , … , A α n ) = { ∑ i = 1 n w i a σ ( i ) ∑ i = 1 n w i | w i ∈ W α i , a i ∈ A α i , i = 1 , … , n } {\displaystyle \Phi _{\alpha }\left({A_{\alpha }^{1},\ldots ,A_{\alpha }^{n}}\right)=\left\{{{\frac {\sum \limits _{i=1}^{n}{w_{i}a_{\sigma (i)}}}{\sum \limits _{i=1}^{n}{w_{i}}}}\left|{w_{i}\in W_{\alpha }^{i},\;a_{i}}\right.\in A_{\alpha }^{i},\;i=1,\ldots ,n}\right\}} where W α i = { w | μ W i ( w ) ≥ α } , A α i = { x | μ A i ( x ) ≥ α } {\displaystyle W_{\alpha }^{i}=\{w|\mu _{W_{i}}(w)\geq \alpha \},A_{\alpha }^{i}=\{x|\mu _{A_{i}}(x)\geq \alpha \}} , and σ : { 1 , … , n } → { 1 , … , n } {\displaystyle \sigma :\{\;1,\ldots ,n\;\}\to \{\;1,\ldots ,n\;\}} is a permutation function such that a σ ( i ) ≥ a σ ( i + 1 ) , ∀ i = 1 , … , n − 1 {\displaystyle a_{\sigma (i)}\geq a_{\sigma (i+1)},\;\forall \;i=1,\ldots ,n-1} , i.e., a σ ( i ) {\displaystyle a_{\sigma (i)}} is the i {\displaystyle i} th largest element in the set { a 1 , … , a n } {\displaystyle \left\{{a_{1},\ldots ,a_{n}}\right\}} . The computation of the type-1 OWA output is implemented by computing the left end-points and right end-points of the intervals Φ α ( A α 1 , … , A α n ) {\displaystyle \Phi _{\alpha }\left({A_{\alpha }^{1},\ldots ,A_{\alpha }^{n}}\right)} : Φ α ( A α 1 , … , A α n ) − {\displaystyle \Phi _{\alpha }\left({A_{\alpha }^{1},\ldots ,A_{\alpha }^{n}}\right)_{-}} and Φ α ( A α 1 , … , A α n ) + , {\displaystyle \Phi _{\alpha }\left({A_{\alpha }^{1},\ldots ,A_{\alpha }^{n}}\right)_{+},} where A α i = [ A α − i , A α + i ] , W α i = [ W α − i , W α + i ] {\displaystyle A_{\alpha }^{i}=[A_{\alpha -}^{i},A_{\alpha +}^{i}],W_{\alpha }^{i}=[W_{\alpha -}^{i},W_{\alpha +}^{i}]} . Then membership function of resulting aggregation fuzzy set is: μ G ( x ) = ∨ α : x ∈ Φ α ( A α 1 , ⋯ , A α n ) α α {\displaystyle \mu _{G}(x)=\mathop {\vee } _{\alpha :x\in \Phi _{\alpha }\left({A_{\alpha }^{1},\cdots ,A_{\alpha }^{n}}\right)_{\alpha }}\alpha } For the left end-points, we need to solve the following programming problem: Φ α ( A α 1 , ⋯ , A α n ) − = min W α − i ≤ w i ≤ W α + i A α − i ≤ a i ≤ A α + i ∑ i = 1 n w i a σ ( i ) / ∑ i = 1 n w i {\displaystyle \Phi _{\alpha }\left({A_{\alpha }^{1},\cdots ,A_{\alpha }^{n}}\right)_{-}=\min \limits _{\begin{array}{l}W_{\alpha -}^{i}\leq w_{i}\leq W_{\alpha +}^{i}A_{\alpha -}^{i}\leq a_{i}\leq A_{\alpha +}^{i}\end{array}}\sum \limits _{i=1}^{n}{w_{i}a_{\sigma (i)}/\sum \limits _{i=1}^{n}{w_{i}}}} while for the right end-points, we need to solve the following programming problem: Φ α ( A α 1 , ⋯ , A α n ) + = max W α − i ≤ w i ≤ W α + i A α − i ≤ a i ≤ A α + i ∑ i = 1 n w i a σ ( i ) / ∑ i = 1 n w i {\displaystyle \Phi _{\alpha }\left({A_{\alpha }^{1},\cdots ,A_{\alpha }^{n}}\right)_{+}=\max \limits _{\begin{array}{l}W_{\alpha -}^{i}\leq w_{i}\leq W_{\alpha +}^{i}A_{\alpha -}^{i}\leq a_{i}\leq A_{\alpha +}^{i}\end{array}}\sum \limits _{i=1}^{n}{w_{i}a_{\sigma (i)}/\sum \limits _{i=1}^{n}{w_{i}}}} Zhou et al. presented a fast method to solve two programming problem so that the type-1 OWA aggregation operation can be performed efficiently. == OWA for committee voting == Amanatidis, Barrot, Lang, Markakis and Ries present voting rules for multi-issue voting, based on OWA and the Hamming distance. Barrot, Lang and Yokoo study the manipulability of these rules.
AI takeover
An AI takeover is a theorized future event, often depicted in fiction, in which autonomous artificial intelligence systems acquire the capability to supersede human decisions. This could occur through economic manipulation, infrastructure control, or direct intervention, leading to de facto governance. Scenarios range from gradual economic dominance, as automation supplants the human workforce, up to a sudden or aggressive global takeover by a robot uprising or other forms of rogue AI. Stories of AI takeovers have been popular throughout science fiction. Commentators argue that recent advancements in the field have heightened concern about such scenarios. In public debate, prominent figures such as Stephen Hawking have advocated research into precautionary measures to ensure future superintelligent machines remain under human control. == Types == === Automation of the economy === The traditional consensus among economists has been that technological progress does not cause long-term unemployment. However, recent innovation in the fields of robotics and artificial intelligence has raised worries that human labor will become obsolete, leaving workers in some sectors without employment. Many small and medium-sized firms may also be forced to close if they cannot afford or license the latest robotic and AI technology, and may need to focus on areas or services that cannot easily be replaced for continued viability in the face of such technology. ==== Technologies that may displace workers ==== While these technologies have replaced some traditional workers, they also create new opportunities. Industries that are most susceptible to AI-driven automation include transportation, retail, and the military. AI military technologies, for example, can reduce risk by enabling remote operation. A study in 2024 highlights AI's ability to perform routine and repetitive tasks poses significant risks of job displacement, especially in sectors like manufacturing and administrative support. Author Dave Bond argues that as AI technologies continue to develop and expand, the relationship between humans and robots will change; they will become closely integrated in several aspects of life. AI will likely displace some workers while creating opportunities for new jobs in other sectors, especially in fields where tasks are repeatable. Researchers from Stanford's Digital Economy Lab reported in 2025 that since the widespread adoption of generative AI in late 2022, early-career workers (ages 22–25) in the most AI-exposed occupations have experienced a 13 percent relative decline in employment—even after controlling for firm-level shocks—while overall employment has continued to grow robustly. The study further finds that job losses are concentrated in roles where AI automates routine tasks, whereas occupations that leverage AI to augment human work have seen stable or increasing employment. ==== Computer-integrated manufacturing ==== Computer-integrated manufacturing uses computers to control the production process. This allows individual processes to exchange information with each other and initiate actions. Although manufacturing can be faster and less error-prone through the integration of computers, the main advantage is the ability to create automated manufacturing processes. Computer-integrated manufacturing is used in automotive, aviation, space, and shipbuilding industries. ==== White-collar machines ==== The 21st century has seen a variety of skilled tasks partially taken over by machines, including translation, legal research, and journalism. Care work, entertainment, and other tasks requiring empathy, previously thought safe from automation, are increasingly performed by robots and AI systems. ==== Autonomous cars ==== An autonomous car is a vehicle that is capable of sensing its environment and navigating without human input. Many such vehicles are operational and others are being developed, with legislation rapidly expanding to allow their use. Obstacles to widespread adoption of autonomous vehicles have included concerns about the resulting loss of driving-related jobs in the road transport industry, and safety concerns. On March 18, 2018, a pedestrian was struck and killed in Tempe, Arizona by an Uber self-driving car. ==== AI-generated content ==== In the 2020s, automated content became more relevant due to technological advancements in AI models, such as ChatGPT, DALL-E, and Stable Diffusion. In most cases, AI-generated content such as imagery, literature, and music are produced through text prompts. These AI models are sometimes integrated into creative programs. AI-generated art may sample and conglomerate existing creative works, producing results that appear similar to human-made content. Low-quality AI-generated visual artwork can be informally referred to as AI slop. Some artists use a tool called Nightshade that alters images to make them detrimental to the training of text-to-image models if scraped without permission, while still looking normal to humans. AI-generated images are a potential tool for scammers and those looking to gain followers on social media, either to impersonate a famous individual or group or to monetize their audience. The New York Times has sued OpenAI, alleging copyright infringement related to the training and outputs of its AI models. === Eradication === Scientists such as Stephen Hawking are confident that superhuman artificial intelligence is physically possible, stating "there is no physical law precluding particles from being organised in ways that perform even more advanced computations than the arrangements of particles in human brains". According to Nick Bostrom, a superintelligent machine would not necessarily be motivated by the same emotional desire to collect power that often drives human beings but might rather treat power as a means toward attaining its ultimate goals; taking over the world would both increase its access to resources and help to prevent other agents from stopping the machine's plans. As a simplified example, a paperclip maximizer designed solely to create as many paperclips as possible would want to take over the world so that it can use all of the world's resources to create as many paperclips as possible, and, additionally, prevent humans from shutting it down or using those resources on things other than paperclips. There are debates on how realistic AI takeover scenarios are. According to a 2026 research paper, many of the arguments about existential risks are based on speculative assumptions about how intelligent AI systems could become, how they would behave and what goals they might develop over time. A 2023 Reuters/Ipsos survey showed that 61% of American adults feared AI could pose a threat to civilization. Philosopher Niels Wilde refutes the common thread that artificial intelligence inherently presents a looming threat to humanity, stating that these fears stem from perceived intelligence and lack of transparency in AI systems that more closely reflects the human aspects of it rather than those of a machine. AI alignment research studies how to design AI systems so that they follow intended objectives. == Debate == Physicist Stephen Hawking, Microsoft founder Bill Gates, and SpaceX founder Elon Musk have expressed concerns about the possibility that AI could develop to the point that humans could not control it, with Hawking theorizing that this could "spell the end of the human race". Stephen Hawking said in 2014 that "Success in creating AI would be the biggest event in human history. Unfortunately, it might also be the last, unless we learn how to avoid the risks." Hawking believed that in the coming decades, AI could offer "incalculable benefits and risks" such as "technology outsmarting financial markets, out-inventing human researchers, out-manipulating human leaders, and developing weapons we cannot even understand." In January 2015, Nick Bostrom joined Stephen Hawking, Max Tegmark, Elon Musk, Lord Martin Rees, Jaan Tallinn, and numerous AI researchers in signing the Future of Life Institute's open letter speaking to the potential risks and benefits associated with artificial intelligence. The signatories "believe that research on how to make AI systems robust and beneficial is both important and timely, and that there are concrete research directions that can be pursued today." Some focus has been placed on the development of trustworthy AI. Three statements have been posed as to why AI is not inherently trustworthy: 1. An entity X is trustworthy only if X has the right motivations, goodwill and/or adheres to moral obligations towards the trustor; 2. AI systems lack motivations, goodwill, and moral obligations; 3. Therefore, AI systems cannot be trustworthy. There are additional considerations within this framework of trustworthy AI that go further into the fields of explainable artificial intelligence and respect for human privacy. Zanotti and colleagues
Thompson sampling
Thompson sampling, named after William R. Thompson, is a heuristic for choosing actions that address the exploration–exploitation dilemma in the multi-armed bandit problem. It consists of choosing the action that maximizes the expected reward with respect to a randomly drawn belief. == Description == Consider a set of contexts X {\displaystyle {\mathcal {X}}} , a set of actions A {\displaystyle {\mathcal {A}}} , and rewards in R {\displaystyle \mathbb {R} } . The aim of the player is to play actions under the various contexts, such as to maximize the cumulative rewards. Specifically, in each round, the player obtains a context x ∈ X {\displaystyle x\in {\mathcal {X}}} , plays an action a ∈ A {\displaystyle a\in {\mathcal {A}}} and receives a reward r ∈ R {\displaystyle r\in \mathbb {R} } following a distribution that depends on the context and the issued action. The elements of Thompson sampling are as follows: a likelihood function P ( r | θ , a , x ) {\displaystyle P(r|\theta ,a,x)} ; a set Θ {\displaystyle \Theta } of parameters θ {\displaystyle \theta } of the distribution of r {\displaystyle r} ; a prior distribution P ( θ ) {\displaystyle P(\theta )} on these parameters; past observations triplets D = { ( x ; a ; r ) } {\displaystyle {\mathcal {D}}=\{(x;a;r)\}} ; a posterior distribution P ( θ | D ) ∝ P ( D | θ ) P ( θ ) {\displaystyle P(\theta |{\mathcal {D}})\propto P({\mathcal {D}}|\theta )P(\theta )} , where P ( D | θ ) {\displaystyle P({\mathcal {D}}|\theta )} is the likelihood function. Thompson sampling consists of playing the action a ∗ ∈ A {\displaystyle a^{\ast }\in {\mathcal {A}}} according to the probability that it maximizes the expected reward; action a ∗ {\displaystyle a^{\ast }} is chosen with probability ∫ I [ E ( r | a ∗ , x , θ ) = max a ′ E ( r | a ′ , x , θ ) ] P ( θ | D ) d θ , {\displaystyle \int \mathbb {I} \left[\mathbb {E} (r|a^{\ast },x,\theta )=\max _{a'}\mathbb {E} (r|a',x,\theta )\right]P(\theta |{\mathcal {D}})d\theta ,} where I {\displaystyle \mathbb {I} } is the indicator function. In practice, the rule is implemented by sampling. In each round, parameters θ ∗ {\displaystyle \theta ^{\ast }} are sampled from the posterior P ( θ | D ) {\displaystyle P(\theta |{\mathcal {D}})} , and an action a ∗ {\displaystyle a^{\ast }} chosen that maximizes E [ r | θ ∗ , a ∗ , x ] {\displaystyle \mathbb {E} [r|\theta ^{\ast },a^{\ast },x]} , i.e. the expected reward given the sampled parameters, the action, and the current context. Conceptually, this means that the player instantiates their beliefs randomly in each round according to the posterior distribution, and then acts optimally according to them. In most practical applications, it is computationally onerous to maintain and sample from a posterior distribution over models. As such, Thompson sampling is often used in conjunction with approximate sampling techniques. == History == Thompson sampling was originally described by Thompson in 1933. It was subsequently rediscovered numerous times independently in the context of multi-armed bandit problems. A first proof of convergence for the bandit case has been shown in 1997. The first application to Markov decision processes was in 2000. A related approach (see Bayesian control rule) was published in 2010. In 2010 it was also shown that Thompson sampling is instantaneously self-correcting. Asymptotic convergence results for contextual bandits were published in 2011. Thompson Sampling has been widely used in many online learning problems including A/B testing in website design and online advertising, and accelerated learning in decentralized decision making. A Double Thompson Sampling (D-TS) algorithm has been proposed for dueling bandits, a variant of traditional MAB, where feedback comes in the form of pairwise comparison. == Relationship to other approaches == === Probability matching === Probability matching is a decision strategy in which predictions of class membership are proportional to the class base rates. Thus, if in the training set positive examples are observed 60% of the time, and negative examples are observed 40% of the time, the observer using a probability-matching strategy will predict (for unlabeled examples) a class label of "positive" on 60% of instances, and a class label of "negative" on 40% of instances. === Bayesian control rule === A generalization of Thompson sampling to arbitrary dynamical environments and causal structures, known as Bayesian control rule, has been shown to be the optimal solution to the adaptive coding problem with actions and observations. In this formulation, an agent is conceptualized as a mixture over a set of behaviours. As the agent interacts with its environment, it learns the causal properties and adopts the behaviour that minimizes the relative entropy to the behaviour with the best prediction of the environment's behaviour. If these behaviours have been chosen according to the maximum expected utility principle, then the asymptotic behaviour of the Bayesian control rule matches the asymptotic behaviour of the perfectly rational agent. The setup is as follows. Let a 1 , a 2 , … , a T {\displaystyle a_{1},a_{2},\ldots ,a_{T}} be the actions issued by an agent up to time T {\displaystyle T} , and let o 1 , o 2 , … , o T {\displaystyle o_{1},o_{2},\ldots ,o_{T}} be the observations gathered by the agent up to time T {\displaystyle T} . Then, the agent issues the action a T + 1 {\displaystyle a_{T+1}} with probability: P ( a T + 1 | a ^ 1 : T , o 1 : T ) , {\displaystyle P(a_{T+1}|{\hat {a}}_{1:T},o_{1:T}),} where the "hat"-notation a ^ t {\displaystyle {\hat {a}}_{t}} denotes the fact that a t {\displaystyle a_{t}} is a causal intervention (see Causality), and not an ordinary observation. If the agent holds beliefs θ ∈ Θ {\displaystyle \theta \in \Theta } over its behaviors, then the Bayesian control rule becomes P ( a T + 1 | a ^ 1 : T , o 1 : T ) = ∫ Θ P ( a T + 1 | θ , a ^ 1 : T , o 1 : T ) P ( θ | a ^ 1 : T , o 1 : T ) d θ {\displaystyle P(a_{T+1}|{\hat {a}}_{1:T},o_{1:T})=\int _{\Theta }P(a_{T+1}|\theta ,{\hat {a}}_{1:T},o_{1:T})P(\theta |{\hat {a}}_{1:T},o_{1:T})\,d\theta } , where P ( θ | a ^ 1 : T , o 1 : T ) {\displaystyle P(\theta |{\hat {a}}_{1:T},o_{1:T})} is the posterior distribution over the parameter θ {\displaystyle \theta } given actions a 1 : T {\displaystyle a_{1:T}} and observations o 1 : T {\displaystyle o_{1:T}} . In practice, the Bayesian control amounts to sampling, at each time step, a parameter θ ∗ {\displaystyle \theta ^{\ast }} from the posterior distribution P ( θ | a ^ 1 : T , o 1 : T ) {\displaystyle P(\theta |{\hat {a}}_{1:T},o_{1:T})} , where the posterior distribution is computed using Bayes' rule by only considering the (causal) likelihoods of the observations o 1 , o 2 , … , o T {\displaystyle o_{1},o_{2},\ldots ,o_{T}} and ignoring the (causal) likelihoods of the actions a 1 , a 2 , … , a T {\displaystyle a_{1},a_{2},\ldots ,a_{T}} , and then by sampling the action a T + 1 ∗ {\displaystyle a_{T+1}^{\ast }} from the action distribution P ( a T + 1 | θ ∗ , a ^ 1 : T , o 1 : T ) {\displaystyle P(a_{T+1}|\theta ^{\ast },{\hat {a}}_{1:T},o_{1:T})} . === Upper-confidence-bound (UCB) algorithms === Thompson sampling and upper-confidence bound algorithms share a fundamental property that underlies many of their theoretical guarantees. Roughly speaking, both algorithms allocate exploratory effort to actions that might be optimal and are in this sense "optimistic". Leveraging this property, one can translate regret bounds established for UCB algorithms to Bayesian regret bounds for Thompson sampling or unify regret analysis across both these algorithms and many classes of problems.
Cloud computing
Cloud computing is defined by the International Organization for Standardization (ISO) as "a paradigm for enabling network access to a scalable and elastic pool of shareable physical or virtual resources with self-service provisioning and administration on demand". It is commonly referred to as "the cloud". == Characteristics == In 2011, the National Institute of Standards and Technology (NIST) identified five "essential characteristics" for cloud systems. Below are the exact definitions according to NIST: On-demand self-service: "A consumer can unilaterally provision computing capabilities, such as server time and network storage, as needed automatically without requiring human interaction with each service provider." Broad network access: "Capabilities are available over the network and accessed through standard mechanisms that promote use by heterogeneous thin or thick client platforms (e.g., mobile phones, tablets, laptops, and workstations)." Resource pooling: " The provider's computing resources are pooled to serve multiple consumers using a multi-tenant model, with different physical and virtual resources dynamically assigned and reassigned according to consumer demand." Rapid elasticity: "Capabilities can be elastically provisioned and released, in some cases automatically, to scale rapidly outward and inward commensurate with demand. To the consumer, the capabilities available for provisioning often appear unlimited and can be appropriated in any quantity at any time." Measured service: "Cloud systems automatically control and optimize resource use by leveraging a metering capability at some level of abstraction appropriate to the type of service (e.g., storage, processing, bandwidth, and active user accounts). Resource usage can be monitored, controlled, and reported, providing transparency for both the provider and consumer of the utilized service. By 2023, the International Organization for Standardization (ISO) had expanded and refined the list. == History == The history of cloud computing extends to the 1960s, with the initial concepts of time-sharing becoming popularized via remote job entry (RJE). The "data center" model, where users submitted jobs to operators to run on mainframes, was predominantly used during this era. This period saw broad experimentation with making large-scale computing power more accessible through time-sharing, while optimizing infrastructure, platforms, and applications to improve efficiency for end users. The "cloud" metaphor for virtualized services dates to 1994, when it was used by General Magic for the universe of "places" that mobile agents in the Telescript environment could "go". The metaphor is credited to David Hoffman, a General Magic communications specialist, based on its long-standing use in networking and telecom. The expression cloud computing became more widely known in 1996 when Compaq Computer Corporation drew up a business plan for future computing and the Internet. The company's ambition was to supercharge sales with "cloud computing-enabled applications". The business plan foresaw that online consumer file storage would likely be commercially successful. As a result, Compaq decided to sell server hardware to internet service providers. In the 2000s, the application of cloud computing began to take shape with the establishment of Amazon Web Services (AWS) in 2002, which allowed developers to build applications independently. In 2006 Amazon Simple Storage Service, known as Amazon S3, and the Amazon Elastic Compute Cloud (EC2) were released. In 2008 NASA's development of the first open-source software for deploying private and hybrid clouds. The following decade saw the launch of various cloud services. In 2010, Microsoft launched Microsoft Azure, and Rackspace Hosting and NASA initiated an open-source cloud-software project, OpenStack. IBM introduced the IBM SmartCloud framework in 2011, and Oracle announced the Oracle Cloud in 2012. In December 2019, Amazon launched AWS Outposts, a service that extends AWS infrastructure, services, APIs, and tools to customer data centers, co-location spaces, or on-premises facilities. == Value proposition == Cloud computing can shorten time to market by offering pre-configured tools, scalable resources, and managed services, allowing users to focus on core business value rather than maintaining infrastructure. Cloud platforms can enable organizations and individuals to reduce upfront capital expenditures on physical infrastructure by shifting to an operational expenditure model, where costs scale with usage. Cloud platforms also offer managed services and tools, such as artificial intelligence, data analytics, and machine learning, which might otherwise require significant in-house expertise and infrastructure investment. While cloud computing can offer cost advantages through effective resource optimization, organizations often face challenges such as unused resources, inefficient configurations, and hidden costs without proper oversight and governance. Many cloud platforms provide cost management tools, such as AWS Cost Explorer and Azure Cost Management, and frameworks like FinOps have emerged to standardize financial operations in the cloud. Cloud computing also facilitates collaboration, remote work, and global service delivery by enabling secure access to data and applications from any location with an internet connection. Cloud providers offer various redundancy options for core services, such as managed storage and managed databases, though redundancy configurations often vary by service tier. Advanced redundancy strategies, such as cross-region replication or failover systems, typically require explicit configuration and may incur additional costs or licensing fees. Cloud environments operate under a shared responsibility model, where providers are typically responsible for infrastructure security, physical hardware, and software updates, while customers are accountable for data encryption, identity and access management (IAM), and application-level security. These responsibilities vary depending on the cloud service model—Infrastructure as a Service (IaaS), Platform as a Service (PaaS), or Software as a Service (SaaS)—with customers typically having more control and responsibility in IaaS environments and progressively less in PaaS and SaaS models, often trading control for convenience and managed services. == Adoption and suitability == The decision to adopt cloud computing or maintain on-premises infrastructure depends on factors such as scalability, cost structure, latency requirements, regulatory constraints, and infrastructure customization. Organizations with variable or unpredictable workloads, limited capital for upfront investments, or a focus on rapid scalability benefit from cloud adoption. Startups, SaaS companies, and e-commerce platforms often prefer the pay-as-you-go operational expenditure (OpEx) model of cloud infrastructure. Additionally, companies prioritizing global accessibility, remote workforce enablement, disaster recovery, and leveraging advanced services such as AI/ML and analytics are well-suited for the cloud. In recent years, some cloud providers have started offering specialized services for high-performance computing and low-latency applications, addressing some use cases previously exclusive to on-premises setups. On the other hand, organizations with strict regulatory requirements, highly predictable workloads, or reliance on deeply integrated legacy systems may find cloud infrastructure less suitable. Businesses in industries like defense, government, or those handling highly sensitive data often favor on-premises setups for greater control and data sovereignty. Additionally, companies with ultra-low latency requirements, such as high-frequency trading (HFT) firms, rely on custom hardware (e.g., FPGAs) and physical proximity to exchanges, which most cloud providers cannot fully replicate despite recent advancements. Similarly, tech giants like Google, Meta, and Amazon build their own data centers due to economies of scale, predictable workloads, and the ability to customize hardware and network infrastructure for optimal efficiency. However, these companies also use cloud services selectively for certain workloads and applications where it aligns with their operational needs. In practice, many organizations are increasingly adopting hybrid cloud architectures, combining on-premises infrastructure with cloud services. This approach allows businesses to balance scalability, cost-effectiveness, and control, offering the benefits of both deployment models while mitigating their respective limitations. == Challenges and limitations == One of the primary challenges of cloud computing, compared with traditional on-premises systems, is maintaining data security and privacy. Cloud users entrust their sensitive data to third-party providers, who may not have adequate measures to protect it from unau
KitKat (cat)
KitKat was a bodega cat from the Mission District of San Francisco who was killed by a Waymo car on October 27, 2025. Locals built altars and the death has raised comments about the safety of self-driving cars. == Life == Mike Zeidan, the owner of Randa's Market, adopted KitKat as a stray to help keep rodents out of his store. KitKat lived in Randa's Market for six years and was well-loved by the neighborhood, including an appearance on a shop cats map that went viral in 2022 as a "particularly friendly cat". After KitKat arrived at the bodega, customers were said to come more often, and regularly brought the cat food and gifts. == Death == At around 11:40 pm on October 27, 2025, witnesses saw KitKat sitting in front of a stopped Waymo car for seven seconds. He walked under the car as the car pulled out, and the right rear tire ran over the back half of his body. A bartender who was taking a cigarette break used a sandwich board sign as a stretcher and took KitKat to an emergency animal clinic. An hour later, KitKat was pronounced dead. Waymo confirmed that the cat was killed by one of its vehicles on October 30. Surveillance footage of the incident was released in December. From Waymo's report to the National Highway Traffic Safety Administration (NHTSA): The Waymo AV was stopped next to the curb for a passenger pickup facing east on 16th Street. As the passengers were boarding the Waymo AV, a cat approached the Waymo AV from the southern sidewalk of 16th Street and sat in the roadway partially under the front right corner of the Waymo AV. A pedestrian approached the Waymo AV from the east on the southern sidewalk of 16th Street and began crouching near the front of the Waymo AV, stepping partially into the roadway, appearing to reach for the cat. As they did so, the cat moved farther from the sidewalk under the Waymo AV and the pedestrian stepped back onto the sidewalk. The Waymo AV then departed the pickup location and the rear right tire made contact with the cat. At the time of impact, the Waymo AV's Level 4 ADS was engaged in autonomous mode. Waymo later received notice that the cat did not survive. The passengers in the Waymo AV did not have seatbelts fastened at the time, having just boarded the Waymo AV. Prior to KitKat's death, the NHTSA had logged 14 collisions between Waymo cars and animals, of which 5 were confirmed fatalities. == Aftermath == After KitKat's death, an altar was created outside Randa's Market. People left flowers, candles, cat food, written notes, and Kit Kat candy bars in the cat's honor. A city worker took down the memorial for fire safety reasons, but neighbors built it again. Local supervisor Jackie Fielder held a rally called "Justice for KitKat" in support of a non-binding San Francisco resolution to shift decision-making about the operation of self-driving cars from the state to individual counties. Critics say that the resolution is performative because it is non-binding, that local control would make autonomous vehicle operation impractical, and that Waymo is still far less dangerous to animals than human drivers. Elon Musk commented that "many pets will be saved by autonomy". There are multiple meme coins inspired by KitKat.