AI For Business Analytics

AI For Business Analytics — independent reviews, comparisons, pricing and step-by-step guides on Aizhi.

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  WikiTok

  WikiTok is a web application that shows random Wikipedia articles in an infinite scrolling format similar to TikTok. Created by New York-based civil and software engineer Isaac Gemal in February 2025, the application aims to provide an "anti-algorithmic" alternative to traditional social media platforms while combating doomscrolling. == Development == WikiTok was developed on February 3, 2025, after Gemal saw a viral tweet from developer Tyler Angert proposing "all of wikipedia on a single, scrollable page". Gemal created the initial prototype in approximately two hours, using the Claude LLM and Cursor coding editor, completing it by 2 a.m. that same night. The application was built with React 18, TypeScript, Tailwind CSS, and Vite, consisting of only a few hundred lines of code with no backend infrastructure. Gemal has made the project open-source, with the code publicly available on GitHub. == Functionality == WikiTok serves users completely random Wikipedia article snippets from Wikipedia's nearly 9.5 million entries. Each article preview includes a full-screen image from Wikipedia and a short text excerpt. Users can click "Read More" to access the full Wikipedia article, or continue scrolling to see the next random entry. The application functions as a progressive web app that can be downloaded as a hybrid between an app and a website. It works on both mobile and desktop browsers, and is designed to be responsive whether users scroll with their thumb on mobile devices or use a cursor on desktop computers. As of 2025, WikiTok supports 14 different languages for article translation. == Philosophy == Gemal has explicitly positioned WikiTok as "anti-algorithmic," resisting numerous requests to implement personalized content algorithms. In an interview with Business Insider, Gemal stated: "I have had plenty of people message me and even make issues on my GitHub asking for some insane crazy WikiTok algorithm... we're already ruled by ruthless, opaque algorithms in our everyday life; why can't we just have one little corner in the world without them?" The application aims to combat "doomscrolling" – the practice of mindlessly consuming negative news online that can cause anxiety, helplessness, and anger. Unlike traditional social media platforms, WikiTok deliberately excludes algorithms, advertisements, and user tracking.

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  Loab

  Loab ( LOBE) is a fictional character that artist and writer Steph Maj Swanson claimed to have discovered with a text-to-image AI model in April 2022. In a viral Twitter thread, Swanson described the images of Loab as an unexpectedly emergent property of the software, saying they discovered them when asking the model to produce something "as different from the prompt as possible". == History == The Sweden-based artist Steph Maj Swanson said that they first generated these images in April 2022 by using the algorithmic technique of "negative prompt weights" accessing latent space. The initial prompt - 'Brando::-1', requesting the opposite of actor Marlon Brando - generated a "skyline logo" with the cryptic lettering "DIGITA PNTICS". Attempting to generate the opposite of this image using the prompt "DIGITA PNTICS skyline logo::-1" yielded what Swanson described as "off-putting images, all of the same devastated-looking older woman with defined triangles of rosacea(?) on her cheeks". Swanson nicknamed the character "Loab", after one of the generated images resembled an album cover that included the printed word "loab". Swanson says that using the image as a prompt for further images produced increasingly violent and gory results. Swanson speculated that something about the image could be "adjacent to extremely gory and macabre imagery in the distribution of the AI's world knowledge". Swanson says that when they combined images of Loab with other pictures, the subsequent results consistently return an image including Loab, regardless of how much distortion they added to the prompts to try and remove her visage. Swanson speculated that the latent space region of the AI map that Loab is located in, in addition to being near gruesome imagery, must be isolated enough that any combinations with other images could only use Loab from her area and no related images due to its isolation. After enough crossbreeding of images and dilution attempts, Swanson was able to eventually generate images without Loab, but found that crossbreeding those diluted images would also eventually lead to a version of Loab to reappear in the resulting images. Swanson has said that "for various reasons" they declined to disclose the software used to create the images. Loab has been referred to as the "first AI-generated cryptid" and as such has gone viral. Despite hyping up the cryptid nature of the discovery in their wording, Swanson admitted that "Loab isn't really haunted, of course", but noted that the mythos that has sprung up around the AI-generated character has gone beyond their initial involvement. Swanson speculated that people sharing pictures and memes of Loab would lead future AIs to use those images as a part of their latent space maps, making her an innate part of the internet landscape, with Swanson adding "If we want to get rid of her, it's already too late." == Response == There has been discussion of whether the Loab series of images are "a legitimate quirk of AI art software, or a cleverly disguised creepypasta." Smithsonian magazine has written that "Loab sparked some lengthy ethical conversations around visual aesthetics, art and technology," and some have criticized the labeling of a woman with rosacea as a horror image, considering this to be "stigmatizing disability". Swanson responded that if the AI map is combining Loab with violent imagery, then that is a "social bias" in the data being used for the image modeling software. The Atlantic writer Stephen Marche described Loab as a "form of expression that has never existed before" whose authorship is unclear and that exists as an "emanation of the collective imagistic heritage, the unconscious visual mind". Laurens Verhagen in de Volkskrant commented that rather than showing that there are "dark horror creatures hidden deep within AI", the existence of Loab instead implies that our current "understanding of AI is limited". Mhairi Aitken at the Alan Turing Institute stated that rather than a "creepy" emergent property, output results like Loab were representative of the "limitations of AI image-generator models" and was more concerned about the urban legends that are born from such "boring" innocuous things and how easily "other people take these things seriously". Carly Cassella for ScienceAlert described Loab as a "modern day tronie" (a style of Dutch painting) that is not representative of an actual person, but just a concept or idea, similar but distinct from works like the Girl With A Pearl Earring. Wired's Joel Warner argued that Loab was only the beginning and that, with AI text generators such as ChatGPT becoming more commonplace, a "linguistic version of Loab" would emerge in that space as well and begin creating ideas through "intentional prompts" or otherwise that will be as disturbing as The 120 Days of Sodom.

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  Possibility theory

  Possibility theory is a mathematical theory for dealing with certain types of uncertainty and is an alternative to probability theory. It uses measures of possibility and necessity between 0 and 1, ranging from impossible to possible and unnecessary to necessary, respectively. Professor Lotfi Zadeh first introduced possibility theory in 1978 as an extension of his theory of fuzzy sets and fuzzy logic. Didier Dubois and Henri Prade further contributed to its development. Earlier, in the 1950s, economist G. L. S. Shackle proposed the min/max algebra to describe degrees of potential surprise. == Formalization of possibility == For simplicity, assume that the universe of discourse Ω is a finite set. A possibility measure is a function Π {\displaystyle \Pi } from 2 Ω {\displaystyle 2^{\Omega }} to [0, 1] such that: Axiom 1: Π ( ∅ ) = 0 {\displaystyle \Pi (\varnothing )=0} Axiom 2: Π ( Ω ) = 1 {\displaystyle \Pi (\Omega )=1} Axiom 3: Π ( U ∪ V ) = max ( Π ( U ) , Π ( V ) ) {\displaystyle \Pi (U\cup V)=\max \left(\Pi (U),\Pi (V)\right)} for any disjoint subsets U {\displaystyle U} and V {\displaystyle V} . It follows that, like probability on finite probability spaces, the possibility measure is determined by its behavior on singletons: Π ( U ) = max ω ∈ U Π ( { ω } ) . {\displaystyle \Pi (U)=\max _{\omega \in U}\Pi (\{\omega \}).} Axiom 1 can be interpreted as the assumption that Ω is an exhaustive description of future states of the world, because it means that no belief weight is given to elements outside Ω. Axiom 2 could be interpreted as the assumption that the evidence from which Π {\displaystyle \Pi } was constructed is free of any contradiction. Technically, it implies that there is at least one element in Ω with possibility 1. Axiom 3 corresponds to the additivity axiom in probabilities. However, there is an important practical difference. Possibility theory is computationally more convenient because Axioms 1–3 imply that: Π ( U ∪ V ) = max ( Π ( U ) , Π ( V ) ) {\displaystyle \Pi (U\cup V)=\max \left(\Pi (U),\Pi (V)\right)} for any subsets U {\displaystyle U} and V {\displaystyle V} . Because one can know the possibility of the union from the possibility of each component, it can be said that possibility is compositional with respect to the union operator. Note however that it is not compositional with respect to the intersection operator. Generally: Π ( U ∩ V ) ≤ min ( Π ( U ) , Π ( V ) ) ≤ max ( Π ( U ) , Π ( V ) ) . {\displaystyle \Pi (U\cap V)\leq \min \left(\Pi (U),\Pi (V)\right)\leq \max \left(\Pi (U),\Pi (V)\right).} When Ω is not finite, Axiom 3 can be replaced by: For all index sets I {\displaystyle I} , if the subsets U i , i ∈ I {\displaystyle U_{i,\,i\in I}} are pairwise disjoint, Π ( ⋃ i ∈ I U i ) = sup i ∈ I Π ( U i ) . {\displaystyle \Pi \left(\bigcup _{i\in I}U_{i}\right)=\sup _{i\in I}\Pi (U_{i}).} == Necessity == Whereas probability theory uses a single number, the probability, to describe how likely an event is to occur, possibility theory uses two concepts, the possibility and the necessity of the event. For any set U {\displaystyle U} , the necessity measure is defined by N ( U ) = 1 − Π ( U ¯ ) {\displaystyle N(U)=1-\Pi ({\overline {U}})} . In the above formula, U ¯ {\displaystyle {\overline {U}}} denotes the complement of U {\displaystyle U} , that is the elements of Ω {\displaystyle \Omega } that do not belong to U {\displaystyle U} . It is straightforward to show that: N ( U ) ≤ Π ( U ) {\displaystyle N(U)\leq \Pi (U)} for any U {\displaystyle U} and that: N ( U ∩ V ) = min ( N ( U ) , N ( V ) ) {\displaystyle N(U\cap V)=\min(N(U),N(V))} . Note that contrary to probability theory, possibility is not self-dual. That is, for any event U {\displaystyle U} , we only have the inequality: Π ( U ) + Π ( U ¯ ) ≥ 1 {\displaystyle \Pi (U)+\Pi ({\overline {U}})\geq 1} However, the following duality rule holds: For any event U {\displaystyle U} , either Π ( U ) = 1 {\displaystyle \Pi (U)=1} , or N ( U ) = 0 {\displaystyle N(U)=0} Accordingly, beliefs about an event can be represented by a number and a bit. == Interpretation == There are four cases that can be interpreted as follows: N ( U ) = 1 {\displaystyle N(U)=1} means that U {\displaystyle U} is necessary. U {\displaystyle U} is certainly true. It implies that Π ( U ) = 1 {\displaystyle \Pi (U)=1} . Π ( U ) = 0 {\displaystyle \Pi (U)=0} means that U {\displaystyle U} is impossible. U {\displaystyle U} is certainly false. It implies that N ( U ) = 0 {\displaystyle N(U)=0} . Π ( U ) = 1 {\displaystyle \Pi (U)=1} means that U {\displaystyle U} is possible. I would not be surprised at all if U {\displaystyle U} occurs. It leaves N ( U ) {\displaystyle N(U)} unconstrained. N ( U ) = 0 {\displaystyle N(U)=0} means that U {\displaystyle U} is unnecessary. I would not be surprised at all if U {\displaystyle U} does not occur. It leaves Π ( U ) {\displaystyle \Pi (U)} unconstrained. The intersection of the last two cases is N ( U ) = 0 {\displaystyle N(U)=0} and Π ( U ) = 1 {\displaystyle \Pi (U)=1} meaning that I believe nothing at all about U {\displaystyle U} . Because it allows for indeterminacy like this, possibility theory relates to the graduation of a many-valued logic, such as intuitionistic logic, rather than the classical two-valued logic. Note that unlike possibility, fuzzy logic is compositional with respect to both the union and the intersection operator. The relationship with fuzzy theory can be explained with the following classic example. Fuzzy logic: When a bottle is half full, it can be said that the level of truth of the proposition "The bottle is full" is 0.5. The word "full" is seen as a fuzzy predicate describing the amount of liquid in the bottle. Possibility theory: There is one bottle, either completely full or totally empty. The proposition "the possibility level that the bottle is full is 0.5" describes a degree of belief. One way to interpret 0.5 in that proposition is to define its meaning as: I am ready to bet that it's empty as long as the odds are even (1:1) or better, and I would not bet at any rate that it's full. == Possibility theory as an imprecise probability theory == There is an extensive formal correspondence between probability and possibility theories, where the addition operator corresponds to the maximum operator. A possibility measure can be seen as a consonant plausibility measure in the Dempster–Shafer theory of evidence. The operators of possibility theory can be seen as a hyper-cautious version of the operators of the transferable belief model, a modern development of the theory of evidence. Possibility can be seen as an upper probability: any possibility distribution defines a unique credal set of admissible probability distributions by K = { P ∣ ∀ S P ( S ) ≤ Π ( S ) } . {\displaystyle K=\{\,P\mid \forall S\ P(S)\leq \Pi (S)\,\}.} This allows one to study possibility theory using the tools of imprecise probabilities. == Necessity logic == We call generalized possibility every function satisfying Axiom 1 and Axiom 3. We call generalized necessity the dual of a generalized possibility. The generalized necessities are related to a very simple and interesting fuzzy logic called necessity logic. In the deduction apparatus of necessity logic the logical axioms are the usual classical tautologies. Also, there is only a fuzzy inference rule extending the usual modus ponens. Such a rule says that if α and α → β are proved at degree λ and μ, respectively, then we can assert β at degree min{λ,μ}. It is easy to see that the theories of such a logic are the generalized necessities and that the completely consistent theories coincide with the necessities (see for example Gerla 2001).

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  Fuzzy differential inclusion

  Fuzzy differential inclusion is the extension of differential inclusion to fuzzy sets introduced by Lotfi A. Zadeh. x ′ ( t ) ∈ [ f ( t , x ( t ) ) ] α {\displaystyle x'(t)\in [f(t,x(t))]^{\alpha }} with x ( 0 ) ∈ [ x 0 ] α {\displaystyle x(0)\in [x_{0}]^{\alpha }} Suppose f ( t , x ( t ) ) {\displaystyle f(t,x(t))} is a fuzzy valued continuous function on Euclidean space. Then it is the collection of all normal, upper semi-continuous, convex, compactly supported fuzzy subsets of R n {\displaystyle \mathbb {R} ^{n}} . == Second order differential == The second order differential is x ″ ( t ) ∈ [ k x ] α {\displaystyle x''(t)\in [kx]^{\alpha }} where k ∈ [ K ] α {\displaystyle k\in [K]^{\alpha }} , K {\displaystyle K} is trapezoidal fuzzy number ( − 1 , − 1 / 2 , 0 , 1 / 2 ) {\displaystyle (-1,-1/2,0,1/2)} , and x 0 {\displaystyle x_{0}} is a trianglular fuzzy number (-1,0,1). == Applications == Fuzzy differential inclusion (FDI) has applications in Cybernetics Artificial intelligence, Neural network, Medical imaging Robotics Atmospheric dispersion modeling Weather forecasting Cyclone Pattern recognition Population biology

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  Pose (computer vision)

  In the fields of computing and computer vision, pose (or spatial pose) represents the position and the orientation of an object, each usually in three dimensions. Poses are often stored internally as transformation matrices. The term “pose” is largely synonymous with the term “transform”, but a transform may often include scale, whereas pose does not. In computer vision, the pose of an object is often estimated from camera input by the process of pose estimation. This information can then be used, for example, to allow a robot to manipulate an object or to avoid moving into the object based on its perceived position and orientation in the environment. Other applications include skeletal action recognition. == Pose estimation == The specific task of determining the pose of an object in an image (or stereo images, image sequence) is referred to as pose estimation. Pose estimation problems can be solved in different ways depending on the image sensor configuration, and choice of methodology. Three classes of methodologies can be distinguished: Analytic or geometric methods: Given that the image sensor (camera) is calibrated and the mapping from 3D points in the scene and 2D points in the image is known. If also the geometry of the object is known, it means that the projected image of the object on the camera image is a well-known function of the object's pose. Once a set of control points on the object, typically corners or other feature points, has been identified, it is then possible to solve the pose transformation from a set of equations which relate the 3D coordinates of the points with their 2D image coordinates. Algorithms that determine the pose of a point cloud with respect to another point cloud are known as point set registration algorithms, if the correspondences between points are not already known. Genetic algorithm methods: If the pose of an object does not have to be computed in real-time a genetic algorithm may be used. This approach is robust especially when the images are not perfectly calibrated. In this particular case, the pose represent the genetic representation and the error between the projection of the object control points with the image is the fitness function. Learning-based methods: These methods use artificial learning-based system which learn the mapping from 2D image features to pose transformation. In short, this means that a sufficiently large set of images of the object, in different poses, must be presented to the system during a learning phase. Once the learning phase is completed, the system should be able to present an estimate of the object's pose given an image of the object. == Camera pose ==

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  Project Debater

  Project Debater is an IBM artificial intelligence project, designed to participate in a full live debate with expert human debaters. It follows on from the Watson project which played Jeopardy! == Development == Project Debater was developed at IBM's lab in Haifa, Israel. The project was proposed by Noam Slonim in 2011 as the IBM Research next Grand Challenge, following Deep Blue and the victory of Watson in Jeopardy! It was exposed for the first time in a closed media event at June 18, 2018, in San Francisco, under the leadership of Ranit Aharonov and Slonim, both from the IBM Research lab in Haifa, Israel. The AI technology debated two human debaters, Noa Ovadia, who was the 2016 Israeli debate champion and Dan Zafrir. The two debated on the topics "We should subsidize space exploration" and "Should we increase the use of telemedicine." A demonstration of Project Debater also aired on the Discovery Channel in June 2018 debating the question of whether sports gambling should be legalized. == Live Debate == On February 11, 2019, Project Debater was revealed to the world in a live debate in San Francisco. Nonpartisan media group Intelligence Squared U.S. Debates hosted the debate which was moderated by journalist John Donvan. The debate took place between Project Debater and Harish Natarajan, who holds the world record in number of debate competition victories. The motion was “We should subsidize preschools.” == That's Debatable Television Show == Project Debater was featured in a television series called “That’s Debatable” presented by Intelligence Squared U.S. Debates and Bloomberg Media. For each episode of “That’s Debatable,” Project Debater provided insight into three distinct debate topics on the redistribution of wealth, modern monetary theory, and a US-China space race. More than 5,000 arguments were submitted online from around the world across the three topics, which were then analyzed and distilled into key points that were highlighted on the television show and discussed by human debaters. == Artificial Intelligence Capabilities == To develop Project Debater, the IBM Research team had to endow the system with the following AI capabilities: Data-driven speech writing and delivery: Project Debater is the first demonstration of a computer that can digest massive corpora, and given a short description of a controversial topic, write a well-structured speech, and deliver it with clarity and purpose, while even incorporating humor where appropriate. Listening comprehension: the ability to identify the key concepts and claims hidden within long continuous spoken language. Four minutes of persuasive speech: the guarantee of producing four minutes of persuasive speech. Modeling human dilemmas: modeling the world of human controversy and dilemmas in a unique knowledge representation, enabling the system to suggest principled arguments as needed. An article on the project was published in Nature in March 2021.

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  Riffusion

  Riffusion is a neural network, designed by Seth Forsgren and Hayk Martiros, that generates music using images of sound rather than audio. The resulting music has been described as "de otro mundo" (otherworldly), although unlikely to replace man-made music. The model was made available on December 15, 2022, with the code also freely available on GitHub. The first version of Riffusion was created as a fine-tuning of Stable Diffusion, an existing open-source model for generating images from text prompts, on spectrograms, resulting in a model which used text prompts to generate image files which could then be put through an inverse Fourier transform and converted into audio files. While these files were only several seconds long, the model could also use latent space between outputs to interpolate different files together (using the img2img capabilities of SD). It was one of many models derived from Stable Diffusion. In December 2022, Mubert similarly used Stable Diffusion to turn descriptive text into music loops. In January 2023, Google published a paper on their own text-to-music generator called MusicLM. Forsgren and Martiros formed a startup, also called Riffusion, and raised $4 million in venture capital funding in October 2023.

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  DARPA Prize Competitions

  Over the years, the U.S. Defense Advanced Research Projects Agency (DARPA) has conducted numerous prize competitions to spur innovation. A prize competition allows DARPA to establish an ambitious goal, opening the door to novel approaches from the public that might otherwise appear too risky for experts in a particular field to pursue. == Statutory authorities == In 1999, Congress provided prize competition authority to DARPA in the National Defense Authorization Act for Fiscal Year 2000 (P.L. 106–65), 10 U.S.C. § 4025, formerly 10 U.S.C. §2374a. DARPA also conducts prize competitions under the America COMPETES Act, 15 U.S.C. § 3719. == Recent prize competitions == DARPA Grand Challenge (2004 and 2005) was a prize competition to spur the development of autonomous vehicle technologies. The $1 million prize went unclaimed as no vehicles could complete the challenging desert route from Barstow, CA, to Primm, NV, on March 13, 2004. A year later, on October 8, 2005, the Stanford Racing Team won the $2 million prize during the second competition of the Grand Challenge in the desert Southwest near the California/Nevada state line. DARPA Urban Challenge (2007) required the competitors to build an autonomous vehicle capable of driving in traffic and performing complex maneuvers such as merging, passing, parking, and negotiating intersections. On November 3, 2007, the Carnegie Mellon Team won the $2 million prize, and its vehicle became the first autonomous vehicle that interacted with both manned and unmanned vehicle traffic in an urban environment. DARPA Network Challenge (Red Balloon Challenge) (2009) explored the roles that the Internet and social networking play in solving broad-scope, time-critical problems. On December 5, 2009, the Massachusetts Institute of Technology team won $40,000 by locating the ten moored, eight-foot, red weather balloons at ten places in the United States within seven hours. DARPA Digital Manufacturing Analysis, Correlation and Estimation Challenge (DMACE) (2010) was a three-month contest to showcase the potential of digital manufacturing of advanced materials. The University of California at Santa Barbara team won a $50,000 prize for crushing 180 digitally manufactured (DM) titanium mesh spheres with the most accurate predictive model of the components’ properties. DARPA Shredder Challenge (2011) was to identify and assess potential capabilities and vulnerabilities to sensitive information in the national security community. Participating teams must download the images of the documents shredded into more than 10,000 pieces from the Challenge website, reconstruct the documents, and solve the five puzzles. Of almost 9,000 teams, the San Francisco-based All Your Shreds Are Belong to U.S team won the $50,000 prize. DARPA UAVForge Challenge (2011-2012) aimed to build and test a user-intuitive, backpack-portable unmanned aerial vehicle (UAV) that could quietly fly in and out of critical environments to conduct sustained surveillance for up to three hours. The $100,000 prize was not claimed because none of the 140 teams met the technical matrix. DARPA Cash for Locating & Identifying Quick Response Codes (CLIQR) Quest Challenge (2012) explored the role the Internet and social media played in the timely communication, wide-area team-building, and urgent mobilization required to solve broad scope, time-critical problems. The challenge offered $40,000 to the first individual or team that could locate seven posters appearing in U.S. cities bearing the DARPA logo and a quick response code (QR) within 15 days. No team found and submitted all seven codes. DARPA Fast Adaptable Next-Generation Ground Vehicle (FANG) Challenge (2012-2013) was to use three competitions for the design of an infantry fighting vehicle, culminating in prototypes. In April 2013, DARPA awarded US$1 million to a three-man team during the first competition. DARPA decided not to proceed with the second and third competitions as originally planned and transitioned the technologies to the defense and commercial industry through the Digital Manufacturing and Design Innovation Institute (DMDII). DARPA Spectrum Challenge (2013-2014) sought to demonstrate how a software-defined radio can use a given communication channel in the presence of other users and interfering signals. Three teams emerged as the overall winners, winning a total of $150,000 in prizes. DARPA Chikungunya (CHIKV) Challenge (2014-2015) was a health-related effort to develop the most accurate predictions of CHIKV cases for all Western Hemisphere countries and territories between September 2014 and March 2015. On May 12, 2015, DARPA awarded $500,000 in prizes to the 11 winners of the competition during a scientific review DARPA Robotics Challenge (DRC) (2013-2015) aimed to develop semi-autonomous ground robots that could do "complex tasks in dangerous, degraded, human-engineered environments." A South Korean team won the first prize of $2 million, and two U.S. teams won $1 million and $500,000 as second and third winners. DARPA Cyber Grand Challenge (CGC) (2014 - 2016) was to “create automatic defensive systems capable of reasoning about flaws, formulating patches and deploying them on a network in real time.” The top three winners were awarded prizes of $2 million, $1 million, and $750,000, respectively. DARPA Spectrum Collaboration Challenge (SC2) (2016-2019) aimed to encourage the development of AI-enabled wireless networks to “ensure that the exponentially growing number of military and civilian wireless devices would have full access to the increasingly crowded electromagnetic spectrum.” A team from the University of Florida won the overall top prize of US$2 million at the final SC2 competition. DARPA Subterranean (SubT) Challenge (2017-2021) was to develop robotic technologies to map, navigate, search and exploit complex underground environments. The first-place winners of the system final competition and of the virtual final competition were awarded $2 million and $750,000, respectively, with multiple prizes awarded to the second and third-place winners. DARPA Launch Challenge (2018-2020) was a $12 million satellite launch challenge to demonstrate responsive and flexible space launch capabilities from the small launch providers and was to culminate in two separate launch competitions where the competitors must launch a satellite to low Earth orbit (LEO) within days of each other at different locations in the United States. The competition ended without a winner. DARPA Forecasting Floats in Turbulence (FFT) Challenge (2021) was to spur technologies that could predict the location of sea drifters or floats within 10 days. DARPA awarded $25,000 for first place, with prizes of $15,000 and $10,000 for second place and third place. DARPA Artificial Intelligence Cyber Challenge (AIxCC) (2023–2025) was a two-year challenge and asks competitors to design novel AI systems to secure critical software code on which Americans rely. The total prize money is $29.5 million. In March 2024, the Advanced Research Projects Agency for Health (ARPA-H) partnered with DARPA, contributing an additional $20 million to the competition's prize pool to address software vulnerabilities in medical devices, hospital IT, and biotech equipment. AIxCC collaborates with Google, Microsoft, OpenAI, Anthropic, Linux Foundation, Open Source Security Foundation, Black Hat USA, and DEF CON, all of which provide AIxCC with access to large language models. In August 2024, AIxCC held the semifinal at DEF CON in Las Vegas. DARPA and ARPA-H tested all 42 submissions by running them through various open-source coding projects with deliberately injected vulnerabilities and scored the tools based on their effectiveness in identifying and fixing security flaws. Seven teams, each winning $2 million in the semifinals, competed in the final round of the AIxCC at the August 2025 DEF CON conference. Team Atlanta won first place with a $4 million prize for its cyber reasoning systems, which identified and patched vulnerabilities across 54 million lines of code. DARPA Triage Challenge (2023 – 2026) aims to spur the development of novel physiological features for medical triage, with a total prize money of $7 million. In October 2024, Challenge Event 1 was held in Perry, Georgia, featuring to-scale replicas of disaster sites such as an airplane crash and Hurricane Katrina, and teams competed based on how closely their data aligned with the agency’s official data and how quickly and accurately their autonomous systems could identify individuals most urgently in need of medical care. DARPA concluded the second year of competitions and, in November 2025, named the top performers in systems and data categories, which will advance to the final 2026 competition. The DARPA Lift Challenge (2025-2026) is for participants to design unmanned aerial systems capable of carrying up to four times their own weight, with a minimum payload of 110 pounds. Acco

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  Supper (Spotify)

  Supper is a web-based application on the Spotify digital music streaming platform. The Supper app was born from a group of friends who had backgrounds in the music and gastronomy industries. Digital music solutions company Artisan Council later executed it. The app now sits in the top 40 applications on Spotify. == About == The Supper Spotify application matches recipes for all occasions and skill levels with a playlist for both preparation and presentation, as envisioned by the chefs themselves. Supper is credited with being one of the first apps to pair music with food. Playing on the social nature of music and food culture, users can seamlessly experience both for the first time with real time music streaming. == Supper.mx == In May 2014 Supper was launched outside of the Spotify streaming platform. Though still in partnership with Spotify, supper.mx allows users to view Supper's music + food collaborations on mobile, tablet and desktop, without the need to download Spotify directly. == Curators == All of the recipes and playlists featured on the Supper app come straight from a growing network of tastemakers, including chefs, musicians and institutions around the world. Each month the recipes and playlists are updated in conjunction with current holidays, events and seasons. === Launch === Launching in October 2013 the first edition of Supper featured content from a range of eating institutions and culture makers from the US and Australia. Brooklyn Bowl (Brooklyn) Roberta's Pizza (Brooklyn) Fancy Hanks (Melbourne) The Foresters/Queenies Upstairs (Sydney) Hipstamatic Panama House (Bondi) Sweetwater Inn (Melbourne) Soul Clap (Syd record label) Yellow Birds (Melbourne) === November 2013 === Yardbird (Hong Kong) Sonoma Bakery (Sydney) Do or Dine (Brooklyn) Cameo Gallery (Brooklyn) Hypertrak (Blog) Blue Smoke (NYC) The Crepes of Wrath (Blog) Willin Low // Wild Rocket - Wild Oats - Relish === December 2013 === The Copper Mill (Sydney) Thug Kitchen Mamak (Sydney) Tutu's (Brooklyn) Chin Chin (Melbourne) Flat Iron Steak (London) Greasy Spoon (Copenhagen) === January 2014 === Mexicali Taco & Co. (LA) Church & State (LA) Salts Cure (LA) Nopa (SF) L & E Oyster (LA) 4100 bar (LA) Golden Gopher (LA) The Pie Hole (LA) State Bird Provisions (SF) === Momofuku === In February 2014 Supper teamed up with restaurant heavy weights Momofuku. The recipes featured came from their iconic New York, Toronto and Sydney restaurants. Head office also got involved with an instructional from Brand Director Sue Chan on how to paint Momofuku vibes on to any party. === SXSW === March sees the Supper team migrate to Austin, Texas for SXSW, bringing together the best eateries the city has to offer as well as the music that has influenced them. Restaurants and eateries on board in 2014 included: The Backspace Kelis Swifts Attic Uchi Jackalope Paul Qui/East Side King Thai Kun Wonderland Hole in the Wall Justine's Brasserie The Liberty === Kelis === In April 2014 Kelis presented 5 of her recipes paired with a personal playlist for Supper. Kelis shared her recipes for apple farro, jerk ribs, New York vanilla bean cheesecake and Jerk Ribs. The Kelis/Supper collaboration coincided with the release of Kelis' 2014 album titled 'Food'. === Roberta's Pizza === In May 2014 Bushwick's Roberta's Pizza was guest curator on the Supper app and website. Included in their selections were restaurants and bars from across New York including Bun-ker Vietnamese, Old Stanley's Bar, St. Anselm, Chuko, Frank's Cocktail Lounge, Junior's Cheesecake, Xi'an Famous Foods, Xe Lua, 124 Old Rabbit and Yuji Ramen.

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  Futuresport

  Futuresport is a 1998 American made-for-television sports film directed by Ernest Dickerson, starring Dean Cain, Vanessa Williams, and Wesley Snipes. It originally aired on ABC in October 1998, was released on VHS and DVD in March 1999 and then distributed outside of the U.S. by Minerva Pictures. == Plot == The film is set in 2025, and centers on a sport called "Futuresport" (a combination of basketball, baseball and hockey that uses hoverboards and rollerblades) created as a non-lethal way to reduce gang warfare. Tre Ramzey (Dean Cain) along with his ex-girlfriend Alex Torres (Vanessa Williams) and his old coach Obike Fixx (Wesley Snipes) must prevent an all out war between the North American Alliance and the Pan-Pacific Commonwealth (The Com). At stake is who rules over the Hawaiian Islands—which are being terrorized by Eric Sythe (JR Bourne) and his gang the Hawaiian Liberation Organization (Hilo). It takes a revolutionary sport to stop a revolution. == Cast ==

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  Tensor network

  Tensor networks or tensor network states are a class of variational wave functions used in the study of many-body quantum systems and fluids. Tensor networks extend one-dimensional matrix product states to higher dimensions while preserving some of their useful mathematical properties. The wave function is encoded as a tensor contraction of a network of individual tensors. The structure of the individual tensors can impose global symmetries on the wave function (such as antisymmetry under exchange of fermions) or restrict the wave function to specific quantum numbers, like total charge, angular momentum, or spin. It is also possible to derive strict bounds on quantities like entanglement and correlation length using the mathematical structure of the tensor network. This has made tensor networks useful in theoretical studies of quantum information in many-body systems. They have also proved useful in variational studies of ground states, excited states, and dynamics of strongly correlated many-body systems. == Diagrammatic notation == In general, a tensor network diagram (Penrose diagram) can be viewed as a graph where nodes (or vertices) represent individual tensors, while edges represent summation over an index. Free indices are depicted as edges (or legs) attached to a single vertex only. Sometimes, there is also additional meaning to a node's shape. For instance, one can use trapezoids for unitary matrices or tensors with similar behaviour. This way, flipped trapezoids would be interpreted as complex conjugates to them. == History == Foundational research on tensor networks began in 1971 with a paper by Roger Penrose. In "Applications of negative dimensional tensors" Penrose developed tensor diagram notation, describing how the diagrammatic language of tensor networks could be used in applications in physics. In 1992, Steven R. White developed the density matrix renormalization group (DMRG) for quantum lattice systems. The DMRG was the first successful tensor network and associated algorithm. In 2002, Guifré Vidal and Reinhard Werner attempted to quantify entanglement, laying the groundwork for quantum resource theories. This was also the first description of the use of tensor networks as mathematical tools for describing quantum systems. In 2004, Frank Verstraete and Ignacio Cirac developed the theory of matrix product states, projected entangled pair states, and variational renormalization group methods for quantum spin systems. In 2006, Vidal developed the multi-scale entanglement renormalization ansatz (MERA). In 2007 he developed entanglement renormalization for quantum lattice systems. In 2010, Ulrich Schollwock developed the density-matrix renormalization group for the simulation of one-dimensional strongly correlated quantum lattice systems. In 2014, Román Orús introduced tensor networks for complex quantum systems and machine learning, as well as tensor network theories of symmetries, fermions, entanglement and holography. == Connection to machine learning == Tensor networks have been adapted for supervised learning, taking advantage of similar mathematical structure in variational studies in quantum mechanics and large-scale machine learning. This crossover has spurred collaboration between researchers in artificial intelligence and quantum information science. In June 2019, Google, the Perimeter Institute for Theoretical Physics, and X (company), released TensorNetwork, an open-source library for efficient tensor calculations. The main interest in tensor networks and their study from the perspective of machine learning is to reduce the number of trainable parameters (in a layer) by approximating a high-order tensor with a network of lower-order ones. Using the so-called tensor train technique (TT), one can reduce an N-order tensor (containing exponentially many trainable parameters) to a chain of N tensors of order 2 or 3, which gives us a polynomial number of parameters.

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  Proof assistant

  In computer science and mathematical logic, a proof assistant or interactive theorem prover is a software tool to assist with the development of formal proofs by human–machine collaboration. This involves some sort of interactive proof editor, or other interface, with which a human can guide the search for proofs, the details of which are stored in, and some steps provided by, a computer. A recent effort within this field is making these tools use artificial intelligence to automate the formalization of ordinary mathematics. == Automated proof checking == Automated proof checking is the process of using software for checking proofs for correctness. It is one of the most developed fields in automated reasoning. Automated proof checking differs from automated theorem proving in that automated proof checking simply mechanically checks the formal workings of an existing proof, instead of trying to develop new proofs or theorems itself. Because of this, the task of automated proof verification is much simpler than that of automated theorem proving, allowing automated proof checking software to be much simpler than automated theorem proving software. Because of this small size, some automated proof checking systems can have less than a thousand lines of core code, and are thus themselves amenable to both hand-checking and automated software verification. The Mizar system, HOL Light, and Metamath are examples of automated proof checking systems. Automated proof checking can be done either as a batch operation, or interactively, as part of an interactive theorem proving system. == History == Automath, which was developed by Nicolaas Govert de Bruijn starting in 1967, is often considered the first proof checker and the first system to utilize the Curry–Howard correspondence between programs and proofs. Automath was used by L.S. van Benthem Jutting in 1977 to formalize Landau's Foundations of Analysis, which was the first formalization of the real numbers. In 1973, Robert Boyer and J Moore published Proving Theorems about LISP Functions which aimed to verify programs, not mathematics. Their theorem prover is now known as ACL2. In the 1970s, Edinburgh LCF introduced the idea of using a functional programming language as the metalanguage for a theorem prover, and led to the HOL family of proof assistants. The 1990s saw the rise of Rocq, (then known as Coq), which has been used for many large-scale formalization projects. Since the late 2010s, Lean, a proof assistant strongly influenced by Rocq, has become another popular choice, especially for formalizing mathematics. == System comparison == ACL2 – a programming language, a first-order logical theory, and a theorem prover (with both interactive and automatic modes) in the Boyer–Moore tradition. HOL theorem provers – A family of tools ultimately derived from the LCF theorem prover. In these systems, the logical core is a library of their programming language. Theorems represent new elements of the language and can only be introduced via "strategies" which guarantee logical correctness. Strategy composition gives users the ability to produce significant proofs with relatively few interactions with the system. Members of the family include: HOL4 – The "primary descendant", still under active development. Support for both Moscow ML and Poly/ML. Has a BSD-style license. HOL Light – A thriving "minimalist fork". OCaml based. ProofPower – Went proprietary, then returned to open source. Based on Standard ML. IMPS, An Interactive Mathematical Proof System. Isabelle is an interactive theorem prover where other systems can be encoded. Isabelle/HOL is its most popular instance, whose foundation is close to that of the HOL prover. Other instances include Isabelle/ZF and Isabelle/FOL. The main code-base is BSD-licensed, but the Isabelle distribution bundles many add-on tools with different licenses. Jape – Java based. Lean is both an interactive theorem prover and a functional, dependently-typed programming language. It is based on the calculus of inductive constructions with non-cumulative universes. Since version 4 (released in 2023), it is self-hosting. It can be used to formalise mathematics (and has a large, coherent library for formal mathematics), but also for software and hardware verification. LEGO Matita – A light system based on the calculus of inductive constructions. MINLOG – A proof assistant based on first-order minimal logic. Mizar – A proof assistant based on first-order logic, in a natural deduction style, and Tarski–Grothendieck set theory. PhoX – A proof assistant based on higher-order logic which is eXtensible. Prototype Verification System (PVS) – a proof language and system based on higher-order logic. Rocq (formerly named Coq) – A popular interactive theorem prover based on the calculus of inductive constructions. Theorem Proving System (TPS) and ETPS – Interactive theorem provers also based on simply typed lambda calculus, but based on an independent formulation of the logical theory and independent implementation. == User interfaces == A commonly used front-end for proof assistants was the Emacs-based Proof General, developed at the University of Edinburgh. Nowadays, many provers include their own editor. Rocq includes RocqIDE, which is based on OCaml/Gtk. Isabelle includes Isabelle/jEdit, which is based on jEdit and the Isabelle/Scala infrastructure for document-oriented proof processing. More recently, Visual Studio Code extensions have been developed for Rocq, Isabelle by Makarius Wenzel, and for Lean 4 by the leanprover developers. == Formalization extent == Freek Wiedijk has been keeping a ranking of proof assistants by the amount of formalized theorems out of a list of 100 well-known theorems. As of September 2025, only six systems have formalized proofs of more than 70% of the theorems, namely Isabelle, HOL Light, Lean, Rocq, Metamath and Mizar. == Notable formalized proofs == The following is a list of notable proofs that have been formalized within proof assistants.

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  Database index

  A database index is a data structure that improves the speed of data retrieval operations on a database table at the cost of additional writes and storage space to maintain the index data structure. Indexes are used to quickly locate data without having to search every row in a database table every time said table is accessed. Indexes can be created using one or more columns of a database table, providing the basis for both rapid random lookups and efficient access of ordered records. An index is a copy of selected columns of data, from a table, that is designed to enable very efficient search. An index normally includes a "key" or direct link to the original row of data from which it was copied, to allow the complete row to be retrieved efficiently. Some databases extend the power of indexing by letting developers create indexes on column values that have been transformed by functions or expressions. For example, an index could be created on upper(last_name), which would only store the upper-case versions of the last_name field in the index. Another option sometimes supported is the use of partial index, where index entries are created only for those records that satisfy some conditional expression. A further aspect of flexibility is to permit indexing on user-defined functions, as well as expressions formed from an assortment of built-in functions. == Usage == === Support for fast lookup === Most database software includes indexing technology that enables sub-linear time lookup to improve performance, as linear search is inefficient for large databases. Suppose a database contains N data items and one must be retrieved based on the value of one of the fields. A simple implementation retrieves and examines each item according to the test. If there is only one matching item, this can stop when it finds that single item, but if there are multiple matches, it must test everything. This means that the number of operations in the average case is O(N) or linear time. Since databases may contain many objects, and since lookup is a common operation, it is often desirable to improve performance. An index is any data structure that improves the performance of lookup. There are many different data structures used for this purpose. There are complex design trade-offs involving lookup performance, index size, and index-update performance. Many index designs exhibit logarithmic (O(log(N))) lookup performance and in some applications it is possible to achieve flat (O(1)) performance. === Policing the database constraints === Indexes are used to police database constraints, such as UNIQUE, EXCLUSION, PRIMARY KEY and FOREIGN KEY. An index may be declared as UNIQUE, which creates an implicit constraint on the underlying table. Database systems usually implicitly create an index on a set of columns declared PRIMARY KEY, and some are capable of using an already-existing index to police this constraint. Many database systems require that both referencing and referenced sets of columns in a FOREIGN KEY constraint are indexed, thus improving performance of inserts, updates and deletes to the tables participating in the constraint. Some database systems support an EXCLUSION constraint that ensures that, for a newly inserted or updated record, a certain predicate holds for no other record. This can be used to implement a UNIQUE constraint (with equality predicate) or more complex constraints, like ensuring that no overlapping time ranges or no intersecting geometry objects would be stored in the table. An index supporting fast searching for records satisfying the predicate is required to police such a constraint. == Index architecture and indexing methods == === Non-clustered === The data is present in arbitrary order, but the logical ordering is specified by the index. The data rows may be spread throughout the table regardless of the value of the indexed column or expression. The non-clustered index tree contains the index keys in sorted order, with the leaf level of the index containing the pointer to the record (page and the row number in the data page in page-organized engines; row offset in file-organized engines). In a non-clustered index, The physical order of the rows is not the same as the index order. The indexed columns are typically non-primary key columns used in JOIN, WHERE, and ORDER BY clauses. There can be more than one non-clustered index on a database table. === Clustered === Clustering alters the data block into a certain distinct order to match the index, resulting in the row data being stored in order. Therefore, only one clustered index can be created on a given database table. Clustered indexes can greatly increase overall speed of retrieval, but usually only where the data is accessed sequentially in the same or reverse order of the clustered index, or when a range of items is selected. Since the physical records are in this sort order on disk, the next row item in the sequence is immediately before or after the last one, and so fewer data block reads are required. The primary feature of a clustered index is therefore the ordering of the physical data rows in accordance with the index blocks that point to them. Some databases separate the data and index blocks into separate files, others put two completely different data blocks within the same physical file(s). === Cluster === When multiple databases and multiple tables are joined, it is called a cluster (not to be confused with clustered index described previously). The records for the tables sharing the value of a cluster key shall be stored together in the same or nearby data blocks. This may improve the joins of these tables on the cluster key, since the matching records are stored together and less I/O is required to locate them. The cluster configuration defines the data layout in the tables that are parts of the cluster. A cluster can be keyed with a B-tree index or a hash table. The data block where the table record is stored is defined by the value of the cluster key. == Column order == The order that the index definition defines the columns in is important. It is possible to retrieve a set of row identifiers using only the first indexed column. However, it is not possible or efficient (on most databases) to retrieve the set of row identifiers using only the second or greater indexed column. For example, in a phone book organized by city first, then by last name, and then by first name, in a particular city, one can easily extract the list of all phone numbers. However, it would be very tedious to find all the phone numbers for a particular last name. One would have to look within each city's section for the entries with that last name. Some databases can do this, others just won't use the index. In the phone book example with a composite index created on the columns (city, last_name, first_name), if we search by giving exact values for all the three fields, search time is minimal—but if we provide the values for city and first_name only, the search uses only the city field to retrieve all matched records. Then a sequential lookup checks the matching with first_name. So, to improve the performance, one must ensure that the index is created on the order of search columns. == Applications and limitations == Indexes are useful for many applications but come with some limitations. Consider the following SQL statement: SELECT first_name FROM people WHERE last_name = 'Smith';. To process this statement without an index the database software must look at the last_name column on every row in the table (this is known as a full table scan). With an index the database simply follows the index data structure (typically a B-tree) until the Smith entry has been found; this is much less computationally expensive than a full table scan. Consider this SQL statement: SELECT email_address FROM customers WHERE email_address LIKE '%@wikipedia.org';. This query would yield an email address for every customer whose email address ends with "@wikipedia.org", but even if the email_address column has been indexed the database must perform a full index scan. This is because the index is built with the assumption that words go from left to right. With a wildcard at the beginning of the search-term, the database software is unable to use the underlying index data structure (in other words, the WHERE-clause is not sargable). This problem can be solved through the addition of another index created on reverse(email_address) and a SQL query like this: SELECT email_address FROM customers WHERE reverse(email_address) LIKE reverse('%@wikipedia.org');. This puts the wild-card at the right-most part of the query (now gro.aidepikiw@%), which the index on reverse(email_address) can satisfy. When the wildcard characters are used on both sides of the search word as %wikipedia.org%, the index available on this field is not used. Rather only a sequential search is performed, which takes ⁠ O ( N ) {\displaystyle

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  CADE ATP System Competition

  The CADE ATP System Competition (CASC) is an annual competition of fully automated theorem provers for classical logic. == Competition == CASC is associated with the Conference on Automated Deduction and the International Joint Conference on Automated Reasoning organized by the Association for Automated Reasoning. It has inspired similar competition in related fields, in particular the successful SMT-COMP competition for satisfiability modulo theories, the SAT Competition for propositional reasoners, and the modal logic reasoning competition. The first CASC, CASC-13, was held as part of the 13th Conference on Automated Deduction at Rutgers University, New Brunswick, NJ, in 1996. Among the systems competing were Otter and SETHEO.

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  The Machine That Won the War (short story)

  "The Machine That Won the War" is a science fiction short story by American writer Isaac Asimov. The story first appeared in the October 1961 issue of The Magazine of Fantasy & Science Fiction, and was reprinted in the collections Nightfall and Other Stories (1969) and Robot Dreams (1986). It was also printed in a contemporary edition of Reader's Digest, illustrated. It is one of a loosely connected series of such stories concerning a fictional supercomputer called Multivac. == Plot summary == Three influential leaders of the human race meet in the aftermath of a successful war against the Denebians. Discussing how the vast and powerful Multivac computer was a decisive factor in the war, each of the men admits that in fact, he falsified his part of the decision process because he felt that the situation was too complex to follow normal procedures. John Henderson, Multivac's Chief Programmer, admits that he altered the data being fed to Multivac, since the populace could not be trusted to report accurate information in the current situation. Max Jablonski then admits that he altered the data that Multivac produced, since he knew that Multivac was not in good working order due to manpower and spare parts shortage. Finally, Lamar Swift, executive director of the Solar Federation, reveals that he had not trusted the reports produced by Multivac, and had made the final decisions purely on the toss of a coin.

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