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  And–or tree

  An and–or tree is a graphical representation of the reduction of problems (or goals) to conjunctions and disjunctions of subproblems (or subgoals). == Example == The and–or tree: represents the search space for solving the problem P, using the goal-reduction methods: P if Q and R P if S Q if T Q if U == Definitions == Given an initial problem P0 and set of problem solving methods of the form: P if P1 and … and Pn the associated and–or tree is a set of labelled nodes such that: The root of the tree is a node labelled by P0. For every node N labelled by a problem or sub-problem P and for every method of the form P if P1 and ... and Pn, there exists a set of children nodes N1, ..., Nn of the node N, such that each node Ni is labelled by Pi. The nodes are conjoined by an arc, to distinguish them from children of N that might be associated with other methods. A node N, labelled by a problem P, is a success node if there is a method of the form P if nothing (i.e., P is a "fact"). The node is a failure node if there is no method for solving P. If all of the children of a node N, conjoined by the same arc, are success nodes, then the node N is also a success node. Otherwise the node is a failure node. == Search strategies == An and–or tree specifies only the search space for solving a problem. Different search strategies for searching the space are possible. These include searching the tree depth-first, breadth-first, or best-first using some measure of desirability of solutions. The search strategy can be sequential, searching or generating one node at a time, or parallel, searching or generating several nodes in parallel. == Relationship with logic programming == The methods used for generating and–or trees are propositional logic programs (without variables). In the case of logic programs containing variables, the solutions of conjoint sub-problems must be compatible. Subject to this complication, sequential and parallel search strategies for and–or trees provide a computational model for executing logic programs. == Relationship with two-player games == And–or trees can also be used to represent the search spaces for two-person games. The root node of such a tree represents the problem of one of the players winning the game, starting from the initial state of the game. Given a node N, labelled by the problem P of the player winning the game from a particular state of play, there exists a single set of conjoint children nodes, corresponding to all of the opponents responding moves. For each of these children nodes, there exists a set of non-conjoint children nodes, corresponding to all of the player's defending moves. For solving game trees with proof-number search family of algorithms, game trees are to be mapped to and–or trees. MAX-nodes (i.e. maximizing player to move) are represented as OR nodes, MIN-nodes map to AND nodes. The mapping is possible, when the search is done with only a binary goal, which usually is "player to move wins the game".

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  Line detection

  In image processing, line detection is an algorithm that takes a collection of n edge points and finds all the lines on which these edge points lie. The most popular line detectors are the Hough transform and convolution-based techniques. == Hough transform == The Hough transform can be used to detect lines and the output is a parametric description of the lines in an image, for example ρ = r cos(θ) + c sin(θ). If there is a line in a row and column based image space, it can be defined ρ, the distance from the origin to the line along a perpendicular to the line, and θ, the angle of the perpendicular projection from the origin to the line measured in degrees clockwise from the positive row axis. Therefore, a line in the image corresponds to a point in the Hough space. The Hough space for lines has therefore these two dimensions θ and ρ, and a line is represented by a single point corresponding to a unique set of these parameters. The Hough transform can then be implemented by choosing a set of values of ρ and θ to use. For each pixel (r, c) in the image, compute r cos(θ) + c sin(θ) for each values of θ, and place the result in the appropriate position in the (ρ, θ) array. At the end, the values of (ρ, θ) with the highest values in the array will correspond to strongest lines in the image == Convolution-based technique == In a convolution-based technique, the line detector operator consists of a convolution masks tuned to detect the presence of lines of a particular width n and a θ orientation. Here are the four convolution masks to detect horizontal, vertical, oblique (+45 degrees), and oblique (−45 degrees) lines in an image. a) Horizontal mask(R1) (b) Vertical (R3) (C) Oblique (+45 degrees)(R2) (d) Oblique (−45 degrees)(R4) In practice, masks are run over the image and the responses are combined given by the following equation: R(x, y) = max(|R1 (x, y)|, |R2 (x, y)|, |R3 (x, y)|, |R4 (x, y)|) If R(x, y) > T, then discontinuity As can be seen below, if mask is overlay on the image (horizontal line), multiply the coincident values, and sum all these results, the output will be the (convolved image). For example, (−1)(0)+(−1)(0)+(−1)(0) + (2)(1) +(2)(1)+(2)(1) + (−1)(0)+(−1)(0)+(−1)(0) = 6 pixels on the second row, second column in the (convolved image) starting from the upper left corner of the horizontal lines. page 82 == Example == These masks above are tuned for light lines against a dark background, and would give a big negative response to dark lines against a light background. == Code example == The code was used to detect only the vertical lines in an image using Matlab and the result is below. The original image is the one on the top and the result is below it. As can be seen on the picture on the right, only the vertical lines were detected

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  Control engineering

  Control engineering, also known as control systems engineering and, in some European countries, automation engineering, is an engineering discipline that deals with control systems, applying control theory to design equipment and systems with desired behaviors in control environments. The discipline of controls overlaps and is usually taught along with electrical engineering, chemical engineering and mechanical engineering at many institutions around the world. The practice uses sensors and detectors to measure the output performance of the process being controlled; these measurements are used to provide corrective feedback helping to achieve the desired performance. Systems designed to perform without requiring human input are called automatic control systems (such as cruise control for regulating the speed of a car). Multi-disciplinary in nature, control systems engineering activities focus on implementation of control systems mainly derived by mathematical modeling of a diverse range of systems. == Overview == Modern day control engineering is a relatively new field of study that gained significant attention during the 20th century with the advancement of technology. It can be broadly defined or classified as practical application of control theory. Control engineering plays an essential role in a wide range of control systems, from simple household washing machines to high-performance fighter aircraft. It seeks to understand physical systems, using mathematical modelling, in terms of inputs, outputs and various components with different behaviors; to use control system design tools to develop controllers for those systems; and to implement controllers in physical systems employing available technology. A system can be mechanical, electrical, fluid, chemical, financial or biological, and its mathematical modelling, analysis and controller design uses control theory in one or many of the time, frequency and complex-s domains, depending on the nature of the design problem. Control engineering is the engineering discipline that focuses on the modeling of a diverse range of dynamic systems (e.g. mechanical systems) and the design of controllers that will cause these systems to behave in the desired manner. Although such controllers need not be electrical, many are and hence control engineering is often viewed as a subfield of electrical engineering. Electrical circuits, digital signal processors and microcontrollers can all be used to implement control systems. Control engineering has a wide range of applications from the flight and propulsion systems of commercial airliners to the cruise control present in many modern automobiles. In most cases, control engineers utilize feedback when designing control systems. This is often accomplished using a proportional–integral–derivative controller (PID controller) system. For example, in an automobile with cruise control the vehicle's speed is continuously monitored and fed back to the system, which adjusts the motor's torque accordingly. Where there is regular feedback, control theory can be used to determine how the system responds to such feedback. In practically all such systems stability is important and control theory can help ensure stability is achieved. Although feedback is an important aspect of control engineering, control engineers may also work on the control of systems without feedback. This is known as open loop control. A classic example of open loop control is a washing machine that runs through a pre-determined cycle without the use of sensors. == History == Automatic control systems were first developed over two thousand years ago. The first feedback control device on record is thought to be the ancient Ktesibios's water clock in Alexandria, Egypt, around the third century BCE. It kept time by regulating the water level in a vessel and, therefore, the water flow from that vessel. This certainly was a successful device as water clocks of similar design were still being made in Baghdad when the Mongols captured the city in 1258 CE. A variety of automatic devices have been used over the centuries to accomplish useful tasks or simply just to entertain. The latter includes the automata, popular in Europe in the 17th and 18th centuries, featuring dancing figures that would repeat the same task over and over again; these automata are examples of open-loop control. Milestones among feedback, or "closed-loop" automatic control devices, include the temperature regulator of a furnace attributed to Drebbel, circa 1620, and the centrifugal flyball governor used for regulating the speed of steam engines by James Watt in 1788. In his 1868 paper "On Governors", James Clerk Maxwell was able to explain instabilities exhibited by the flyball governor using differential equations to describe the control system. This demonstrated the importance and usefulness of mathematical models and methods in understanding complex phenomena, and it signaled the beginning of mathematical control and systems theory. Elements of control theory had appeared earlier but not as dramatically and convincingly as in Maxwell's analysis. Control theory made significant strides over the next century. New mathematical techniques, as well as advances in electronic and computer technologies, made it possible to control significantly more complex dynamical systems than the original flyball governor could stabilize. New mathematical techniques included developments in optimal control in the 1950s and 1960s followed by progress in stochastic, robust, adaptive, nonlinear control methods in the 1970s and 1980s. Applications of control methodology have helped to make possible space travel and communication satellites, safer and more efficient aircraft, cleaner automobile engines, and cleaner and more efficient chemical processes. Before it emerged as a unique discipline, control engineering was practiced as a part of mechanical engineering and control theory was studied as a part of electrical engineering since electrical circuits can often be easily described using control theory techniques. In the first control relationships, a current output was represented by a voltage control input. However, not having adequate technology to implement electrical control systems, designers were left with the option of less efficient and slow responding mechanical systems. A very effective mechanical controller that is still widely used in some hydro plants is the governor. Later on, previous to modern power electronics, process control systems for industrial applications were devised by mechanical engineers using pneumatic and hydraulic control devices, many of which are still in use today. === Mathematical modelling === David Quinn Mayne, (1930–2024) was among the early developers of a rigorous mathematical method for analysing Model predictive control algorithms (MPC). It is currently used in tens of thousands of applications and is a core part of the advanced control technology by hundreds of process control producers. MPC's major strength is its capacity to deal with nonlinearities and hard constraints in a simple and intuitive fashion. His work underpins a class of algorithms that are probably correct, heuristically explainable, and yield control system designs which meet practically important objectives. == Control systems == == Control theory == == Education == At many universities around the world, control engineering courses are taught primarily in electrical engineering and mechanical engineering, but some courses can be instructed in mechatronics engineering, and aerospace engineering. In others, control engineering is connected to computer science, as most control techniques today are implemented through computers, often as embedded systems (as in the automotive field). The field of control within chemical engineering is often known as process control. It deals primarily with the control of variables in a chemical process in a plant. It is taught as part of the undergraduate curriculum of any chemical engineering program and employs many of the same principles in control engineering. Other engineering disciplines also overlap with control engineering as it can be applied to any system for which a suitable model can be derived. However, specialised control engineering departments do exist, for example, in Italy there are several master in Automation & Robotics that are fully specialised in Control engineering or the Department of Automatic Control and Systems Engineering at the University of Sheffield or the Department of Robotics and Control Engineering at the United States Naval Academy and the Department of Control and Automation Engineering at the Istanbul Technical University. Control engineering has diversified applications that include science, finance management, and even human behavior. Students of control engineering may start with a linear control system course dealing with the time and complex-s domain, which req

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  Apps to analyse COVID-19 sounds

  Apps to analyse COVID-19 sounds are mobile software applications designed to collect respiratory sounds and aid diagnosis in response to the COVID-19 pandemic. Numerous applications are in development, with different institutions and companies taking various approaches to privacy and data collection. Current efforts are aimed at gathering data. In a later stage, it is possible that sound apps will have the capacity (and ethical approvals) to provide information back to users. In order to develop and train signal analysis approaches, large datasets are required. == History == The COVID-19 outbreak was announced as a global pandemic by the World Health Organization in March 2020 and has affected a growing number of people globally. In this context, advanced artificial intelligence techniques are being considered as tools in aiding our response to global health crisis. Other COVID-19 apps which offer solutions for user tracking have been developed. At the same time a number of approaches which tries to use respiratory sounds and artificial intelligence to understand if the disease can be diagnosed have been proposed. A few studies are available as preprints (i.e. not yet peer-reviewed) documents. == Methodologies == The potential for using speech and sound analysis by artificial intelligence to help in this scenario, by surveying which types of related or contextually significant phenomena can be automatically assessed from speech or sound has been recently overviewed. These include the automatic recognition and monitoring of breathing, dry and wet coughing or sneezing sounds, speech under cold, eating behaviour, sleepiness, or pain. Additionally, the potential use-cases of intelligent speech analysis for COVID-19 diagnosed patients has also been presented. In particular, by analysing speech recordings from these patients, an audio-only-based model to automatically categorise the health state of patients from four aspects, including the severity of illness, sleep quality, fatigue, and anxiety, is constructed. This work shows promise in estimating the severity of illness. Machine learning methods have been explored to recognize and diagnose coughs from different diseases. These included a low complexity, automated recognition and diagnostic tool for screening respiratory infections that utilizes convolutional neural networks (CNNs) to detect cough within environment audio and diagnose three potential illnesses (i.e. bronchitis, bronchiolitis and pertussis) based on their unique cough audio features. A large-scale crowdsourced dataset of respiratory sounds has been collected to aid diagnosis of COVID-19: coughs and breathing sounds are sufficient to distinguish users affected by COVID-19 versus those affected by asthma or healthy controls. Behind these studies is the ambition that automated systems to screen for respiratory diseases based on voice, raw cough or other sound data would have positive medical applications in both clinical and public health arenas. == List of apps to analyse COVID-19 sounds ==

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  Psychology in cybersecurity

  The psychology of cybersecurity (often intersecting with usable security and cyberpsychology) is an interdisciplinary field studying how human behavior, cognitive biases, and social dynamics influence information security. While traditional cybersecurity focuses on hardware and software vulnerabilities, this discipline addresses the "human factor," which is exploited in cyberattacks. Psychology in cybersecurity draws from cognitive psychology and human–computer interaction. == History and evolution == The challenge of human behavior in computing was noted as early as the 1960s with multi-user mainframes like the Compatible Time-Sharing System (CTSS). In 1966, a software error on CTSS caused the system's master password file to be displayed to every user upon login—one of the earliest documented security incidents attributable to a combination of system design and human factors. These behaviors gained broader significance in the 1990s as the Internet became widely accessible. High-profile incidents involving figures like Kevin Mitnick demonstrated how human trust could be exploited through social engineering such as pretexting over the phone. == Cognitive and behavioral factors == Much of the psychology of cybersecurity focuses on decision-making under stress or uncertainty. Researchers apply frameworks like dual process theory to explain why humans fall for phishing or business email compromise. Threat actors design malicious communications to trigger fast, emotional "System 1" thinking—using urgency, authority, or panic, which prompts users to click a link or wire funds before their analytical "System 2" can assess the situation's legitimacy. Industry research has consistently documented the effectiveness of these techniques at scale, pointing to several recurring psychological phenomena that influence daily security practices: Cognitive biases: The optimism bias leads users to believe they are unlikely to be targeted by cybercriminals, resulting in lax password practices or delayed software updates. The availability heuristic causes individuals to focus on highly publicized, sophisticated threats while ignoring common, statistically probable risks like credential reuse. Social influence: Attackers leverage established principles of persuasion, such as those categorized by Robert Cialdini. Impersonating a CEO leverages the psychological trigger of authority, while fake tech support scams use reciprocity (offering to fix a problem before asking for network credentials). == Neurological and pre-cognitive factors == Functional magnetic resonance imaging (fMRI) studies show that neural activation in visual and attentional regions decreases with repeated exposure to the same stimulus, a phenomenon termed repetition suppression. Experiments have confirmed this effect in the context of security warnings: static warning designs produce declines in user attention and adherence. Information processing research on phishing indicates that affective cues, such as artificial urgency or fear, increase cognitive load and elicit automatic heuristic processing, reducing the likelihood of analytical evaluation and facilitating compliance with malicious requests. == Security fatigue and organizational dynamics == Aggressive cybersecurity postures can sometimes lead to mental and emotional exhaustion, a phenomenon known as security fatigue. === Alert fatigue === One example is alert fatigue, which most frequently affects both end-users and security operations center analysts. Continuous exposure to browser warnings or antivirus pop-ups, particularly those that are false positives, conditions users to dismiss alerts automatically due to the volume of notifications rather than their repetitive appearance (see § Neurological and pre-cognitive factors). The scale of this problem is significant in enterprise: SOC teams in large organizations receive thousands of alerts daily, and a survey published in ACM Computer Surveys found that analysts spend over 25% of their time handling false positives, meaning that malicious indicators can be buried in the noise. === Password fatigue === Similarly, password fatigue is the feeling experienced by many people who are required to remember an excessive number of passwords as part of their daily routine, such as to log in to a computer at work. Users cope with the memory burden by making predictable, iterative changes to their passwords (such as updating "Password01!" to "Password02!"), which decreases password security.

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  Outline of robotics

  The following outline is provided as an overview of and topical guide to robotics: Robotics is a branch of mechanical engineering, electrical engineering and computer science that deals with the design, construction, operation, and application of robots, as well as computer systems for their control, sensory feedback, and information processing. These technologies deal with automated machines that can take the place of humans in dangerous environments or manufacturing processes, or resemble humans in appearance, behaviour, and or cognition. Many of today's robots are inspired by nature contributing to the field of bio-inspired robotics. The word "robot" was introduced to the public by Czech writer Karel Čapek in his play R.U.R. (Rossum's Universal Robots), published in 1920. The term "robotics" was coined by Isaac Asimov in his 1941 science fiction short-story "Liar!" == Nature of robotics == Robotics can be described as: An applied science – scientific knowledge transferred into a physical environment. A branch of computer science – A branch of electrical engineering – A branch of mechanical engineering – Research and development – A branch of technology – == Branches of robotics == Adaptive control – control method used by a controller which must adapt to a controlled system with parameters which vary, or are initially uncertain. For example, as an aircraft flies, its mass will slowly decrease as a result of fuel consumption; a control law is needed that adapts itself to such changing conditions. Aerial robotics – development of unmanned aerial vehicles (UAVs), commonly known as drones, aircraft without a human pilot aboard. Their flight is controlled either autonomously by onboard computers or by the remote control of a pilot on the ground or in another vehicle. Android science – interdisciplinary framework for studying human interaction and cognition based on the premise that a very humanlike robot (that is, an android) can elicit human-directed social responses in human beings. Anthrobotics – science of developing and studying robots that are either entirely or in some way human-like. Artificial intelligence – the intelligence of machines and the branch of computer science that aims to create it. Artificial neural networks – a mathematical model inspired by biological neural networks. Autonomous car – an autonomous vehicle capable of fulfilling the human transportation capabilities of a traditional car Autonomous research robotics – Bayesian network – BEAM robotics – a style of robotics that primarily uses simple analogue circuits instead of a microprocessor in order to produce an unusually simple design (in comparison to traditional mobile robots) that trades flexibility for robustness and efficiency in performing the task for which it was designed. Behavior-based robotics – the branch of robotics that incorporates modular or behavior based AI (BBAI). Bio-inspired robotics – making robots that are inspired by biological systems. Biomimicry and bio-inspired design are sometimes confused. Biomimicry is copying the nature while bio-inspired design is learning from nature and making a mechanism that is simpler and more effective than the system observed in nature. Biomimetic – see Bionics. Biomorphic robotics – a sub-discipline of robotics focused upon emulating the mechanics, sensor systems, computing structures and methodologies used by animals. Bionics – also known as biomimetics, biognosis, biomimicry, or bionical creativity engineering is the application of biological methods and systems found in nature to the study and design of engineering systems and modern technology. Biorobotics – a study of how to make robots that emulate or simulate living biological organisms mechanically or even chemically. Cloud robotics – is a field of robotics that attempts to invoke cloud technologies such as cloud computing, cloud storage, and other Internet technologies centered around the benefits of converged infrastructure and shared services for robotics. Cognitive robotics – views animal cognition as a starting point for the development of robotic information processing, as opposed to more traditional Artificial Intelligence techniques. Clustering – Computational neuroscience – study of brain function in terms of the information processing properties of the structures that make up the nervous system. Robot control – a study of controlling robots Robotics conventions – Data mining Techniques – Degrees of freedom – in mechanics, the degree of freedom (DOF) of a mechanical system is the number of independent parameters that define its configuration. It is the number of parameters that determine the state of a physical system and is important to the analysis of systems of bodies in mechanical engineering, aeronautical engineering, robotics, and structural engineering. Developmental robotics – a methodology that uses metaphors from neural development and developmental psychology to develop the mind for autonomous robots Digital control – a branch of control theory that uses digital computers to act as system controllers. Digital image processing – the use of computer algorithms to perform image processing on digital images. Dimensionality reduction – the process of reducing the number of random variables under consideration, and can be divided into feature selection and feature extraction. Distributed robotics – Electronic stability control – is a computerized technology that improves the safety of a vehicle's stability by detecting and reducing loss of traction (skidding). Evolutionary computation – Evolutionary robotics – a methodology that uses evolutionary computation to develop controllers for autonomous robots Extended Kalman filter – Flexible Distribution functions – Feedback control and regulation – Human–computer interaction – a study, planning and design of the interaction between people (users) and computers Human robot interaction – a study of interactions between humans and robots Intelligent vehicle technologies – comprise electronic, electromechanical, and electromagnetic devices - usually silicon micromachined components operating in conjunction with computer controlled devices and radio transceivers to provide precision repeatability functions (such as in robotics artificial intelligence systems) emergency warning validation performance reconstruction. Computer vision – Machine vision – Kinematics – study of motion, as applied to robots. This includes both the design of linkages to perform motion, their power, control and stability; also their planning, such as choosing a sequence of movements to achieve a broader task. Laboratory robotics – the act of using robots in biology or chemistry labs Robot learning – learning to perform tasks such as obstacle avoidance, control and various other motion-related tasks Direct manipulation interface – In computer science, direct manipulation is a human–computer interaction style which involves continuous representation of objects of interest and rapid, reversible, and incremental actions and feedback. The intention is to allow a user to directly manipulate objects presented to them, using actions that correspond at least loosely to the physical world. Manifold learning – Microrobotics – a field of miniature robotics, in particular mobile robots with characteristic dimensions less than 1 mm Motion planning – (a.k.a., the "navigation problem", the "piano mover's problem") is a term used in robotics for the process of detailing a task into discrete motions. Motor control – information processing related activities carried out by the central nervous system that organize the musculoskeletal system to create coordinated movements and skilled actions. Nanorobotics – the emerging technology field creating machines or robots whose components are at or close to the scale of a nanometer (10−9 meters). Passive dynamics – refers to the dynamical behavior of actuators, robots, or organisms when not drawing energy from a supply (e.g., batteries, fuel, ATP). Programming by Demonstration – an End-user development technique for teaching a computer or a robot new behaviors by demonstrating the task to transfer directly instead of programming it through machine commands. Quantum robotics – a subfield of robotics that deals with using quantum computers to run robotics algorithms more quickly than digital computers can. Rapid prototyping – automatic construction of physical objects via additive manufacturing from virtual models in computer aided design (CAD) software, transforming them into thin, virtual, horizontal cross-sections and then producing successive layers until the items are complete. As of June 2011, used for making models, prototype parts, and production-quality parts in relatively small numbers. Reinforcement learning – an area of machine learning in computer science, concerned with how an agent ought to take actions in an environment so as to maximize some notion of cumulative reward. Robot

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  Blobotics

  Blobotics is a term describing research into chemical-based computer processors based on ions rather than electrons. Andrew Adamatzky, a computer scientist at the University of the West of England, Bristol used the term in an article in New Scientist March 28, 2005 [1]. The aim is to create 'liquid logic gates' which would be 'infinitely reconfigurable and self-healing'. The process relies on the Belousov–Zhabotinsky reaction, a repeating cycle of three separate sets of reactions. Such a processor could form the basis of a robot which, using artificial sensors, interact with its surroundings in a way which mimics living creatures. The coining of the term was featured by ABC radio in Australia [2].

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  Pixel aspect ratio

  A pixel aspect ratio (PAR) is a mathematical ratio that describes how the width of a pixel in a digital image compares to the height of that pixel. Most digital imaging systems display an image as a grid of tiny, square pixels. However, some imaging systems, especially those that must be compatible with standard-definition television motion pictures, display an image as a grid of rectangular pixels, in which the pixel width and height are different. Pixel aspect ratio describes this difference. Use of pixel aspect ratio mostly involves pictures pertaining to standard-definition television and some other exceptional cases. Most other imaging systems, including those that comply with SMPTE standards and practices, use square pixels. PAR is also known as sample aspect ratio and abbreviated SAR, though it can be confused with storage aspect ratio. == Introduction == The ratio of the width to the height of an image is known as the aspect ratio, or more precisely the display aspect ratio (DAR) – the aspect ratio of the image as displayed; for TV, DAR was traditionally 4:3 (a.k.a. fullscreen), with 16:9 (a.k.a. widescreen) now the standard for HDTV. In digital images, there is a distinction with the storage aspect ratio (SAR), which is the ratio of pixel dimensions. If an image is displayed with square pixels, then these ratios agree; if not, then non-square, "rectangular" pixels are used, and these ratios disagree. The aspect ratio of the pixels themselves is known as the pixel aspect ratio (PAR) – for square pixels this is 1:1 – and these are related by the identity: Rearranging (solving for PAR) yields: For example: A 640 × 480 VGA image has a SAR of 640/480 = 4:3, and if displayed on a 4:3 display (DAR = 4:3) has square pixels, hence a PAR of 1:1. By contrast, a 720 × 576 D-1 PAL image has a SAR of 720/576 = 5:4, but if displayed on a 4:3 display (DAR = 4:3) the PAR is 4/3 : 5/4 = 16:15 ≈ 1.066. This means that the pixels of the PAL picture must be "stretched" by this amount to fit in the 4:3 display. In analog images such as film there is no notion of pixel, nor notion of SAR or PAR, but in the digitization of analog images the resulting digital image has pixels, hence SAR (and accordingly PAR, if displayed at the same aspect ratio as the original). Non-square pixels arise often in early digital TV standards, related to digitalization of analog TV signals – whose vertical and "effective" horizontal resolutions differ and are thus best described by non-square pixels – and also in some digital video cameras and computer display modes, such as Color Graphics Adapter (CGA). Today they arise also in transcoding between resolutions with different SARs. Actual displays do not generally have non-square pixels, though digital sensors might; they are rather a mathematical abstraction used in resampling images to convert between resolutions. There are several complicating factors in understanding PAR, particularly as it pertains to digitization of analog video: First, analog video does not have pixels, but rather a raster scan, and thus has a well-defined vertical resolution (the lines of the raster), but not a well-defined horizontal resolution, since each line is an analog signal. However, by a standardized sampling rate, the effective horizontal resolution can be determined by the sampling theorem, as is done below. Second, due to overscan, some of the lines at the top and bottom of the raster are not visible, as are some of the possible image on the left and right – see Overscan: Analog to digital resolution issues. Also, the resolution may be rounded (DV NTSC uses 480 lines, rather than the 486 that are possible). Third, analog video signals are interlaced – each image (frame) is sent as two "fields", each with half the lines. Thus either the pixels are twice as tall as they would be without interlacing, or the image is deinterlaced. == Background == Video is presented as a sequential series of images called video frames. Historically, video frames were created and recorded in analog form. As digital display technology, digital broadcast technology, and digital video compression evolved separately, it resulted in video frame differences that must be addressed using pixel aspect ratio. Digital video frames are generally defined as a grid of pixels used to present each sequential image. The horizontal component is defined by pixels (or samples), and is known as a video line. The vertical component is defined by the number of lines, as in 480 lines. Standard-definition television standards and practices were developed as broadcast technologies and intended for terrestrial broadcasting, and were therefore not designed for digital video presentation. Such standards define an image as an array of well-defined horizontal "Lines", well-defined vertical "Line Duration" and a well-defined picture center. However, there is not a standard-definition television standard that properly defines image edges or explicitly demands a certain number of picture elements per line. Furthermore, analog video systems such as NTSC 480i and PAL 576i, instead of employing progressively displayed frames, employ fields or interlaced half-frames displayed in an interwoven manner to reduce flicker and double the image rate for smoother motion. === Analog-to-digital conversion === As a result of computers becoming powerful enough to serve as video editing tools, video digital-to-analog converters and analog-to-digital converters were made to overcome this incompatibility. To convert analog video lines into a series of square pixels, the industry adopted a default sampling rate at which luma values were extracted into pixels. The luma sampling rate for 480i pictures was 12+3⁄11 MHz and for 576i pictures was 14+3⁄4 MHz. The term pixel aspect ratio was first coined when ITU-R BT.601 (commonly known as Rec. 601) specified that standard-definition television pictures are made of lines of exactly 720 non-square pixels. ITU-R BT.601 did not define the exact pixel aspect ratio but did provide enough information to calculate the exact pixel aspect ratio based on industry practices: The standard luma sampling rate of precisely 13+1⁄2 MHz. Based on this information: The pixel aspect ratio for 480i would be 10:11 as: 12 3 11 ÷ 13 1 2 = 10 11 {\displaystyle 12{\tfrac {3}{11}}\div 13{\tfrac {1}{2}}={\tfrac {10}{11}}} The pixel aspect ratio for 576i would be 59:54 as: 14 3 4 ÷ 13 1 2 = 59 54 {\displaystyle 14{\tfrac {3}{4}}\div 13{\tfrac {1}{2}}={\tfrac {59}{54}}} SMPTE RP 187 further attempted to standardize the pixel aspect ratio values for 480i and 576i. It designated 177:160 for 480i or 1035:1132 for 576i. However, due to significant difference with practices in effect by industry and the computational load that they imposed upon the involved hardware, SMPTE RP 187 was simply ignored. SMPTE RP 187 information annex A.4 further suggested the use of 10:11 for 480i. As of this writing, ITU-R BT.601-6, which is the latest edition of ITU-R BT.601, still implies that the pixel aspect ratios mentioned above are correct. === Digital video processing === As stated above, ITU-R BT.601 specified that standard-definition television pictures are made of lines of 720 non-square pixels, sampled with a precisely specified sampling rate. A simple mathematical calculation reveals that a 704 pixel width would be enough to contain a 480i or 576i standard 4:3 picture: A 4:3 480-line picture, digitized with the Rec. 601-recommended sampling rate, would be 704 non-square pixels wide. x 480 × 10 11 = 4 3 ⇒ x = 480 × 11 × 4 10 × 3 = 704 {\displaystyle {\frac {x}{480}}\times {\frac {10}{11}}={\frac {4}{3}}\Rightarrow x={\frac {480\times 11\times 4}{10\times 3}}=704} A 4:3 576-line picture, digitized with the Rec. 601-recommended sampling rate, would be 702+54⁄59 non-square pixels wide. x 576 × 59 54 = 4 3 ⇒ x = 576 × 54 × 4 59 × 3 = 702 54 59 {\displaystyle {\frac {x}{576}}\times {\frac {59}{54}}={\frac {4}{3}}\Rightarrow x={\frac {576\times 54\times 4}{59\times 3}}=702{\tfrac {54}{59}}} Unfortunately, not all standard TV pictures are exactly 4:3: As mentioned earlier, in analog video, the center of a picture is well-defined but the edges of the picture are not standardized. As a result, some analog devices (mostly PAL devices but also some NTSC devices) generated motion pictures that were horizontally (slightly) wider. This also proportionately applies to anamorphic widescreen (16:9) pictures. Therefore, to maintain a safe margin of error, ITU-R BT.601 required sampling 16 more non-square pixels per line (8 more at each edge) to ensure saving all video data near the margins. This requirement, however, had implications for PAL motion pictures. PAL pixel aspect ratios for standard (4:3) and anamorphic wide screen (16:9), respectively 59:54 and 118:81, were awkward for digital image processing, especially for mixing PAL and NTSC video clips. Therefore, video editing products chose the almost equivalent value

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  Prompt engineering

  Prompt engineering is the process of structuring natural language inputs (known as prompts) to produce specified outputs from a generative artificial intelligence (GenAI) model. Context engineering is the related area of software engineering that focuses on the management of non-prompt contexts supplied to the GenAI model, such as metadata, API tools, and tokens. It can also be defined as the practice of designing and refining input instructions given to a generative AI model to produce more accurate, relevant, or useful outputs. Effective prompt engineering involves understanding how a model interprets language, and may include techniques such as few-shot prompting, chain-of-thought prompting, and role assignment. It is increasingly considered a skill for working with large language models (LLMs) in both research and professional contexts. During the 2020s AI boom, prompt engineering became regarded as a business capability across corporations and industries. Employees with the title prompt engineer were hired to create prompts that would increase productivity and efficacy, although the individual title has since lost traction amid AI models that produce better prompts than humans and corporate training in prompting for general employees. Common prompting techniques include multi-shot, chain-of-thought, and tree-of-thought prompting, as well as the use of assigning roles to the model. Automated prompt generation methods, such as retrieval-augmented generation (RAG), provide for greater accuracy and a wider scope of functions for prompt engineers. Prompt injection is a type of cybersecurity attack that targets machine learning models through malicious prompts. == Terminology == The Oxford English Dictionary defines prompt engineering as "The action or process of formulating and refining prompts for an artificial intelligence program, algorithm, etc., in order to optimize its output or to achieve a desired outcome; the discipline or profession concerned with this." In 2023, prompt ("an instruction given to an artificial intelligence program, algorithm, etc., which determines or influences the content it generates") was the runner-up to Oxford's word of the year. === Prompt === A prompt is some natural language text that describes and prescribes the task that an artificial intelligence (AI) should perform. A prompt for a text-to-text language model can be a query, a command, or a longer statement referencing context, instructions, and conversation history. The process of prompt engineering may involve designing clear queries, refining wording, providing relevant context, specifying the style of output, and assigning a character for the AI to mimic in order to guide the model toward more accurate, useful, and consistent responses. When communicating with a text-to-image or a text-to-audio model, a typical prompt contains a description of a desired output such as "a high-quality photo of an astronaut riding a horse" or "Lo-fi slow BPM electro chill with organic samples". Prompt engineering may be applied to text-to-image models to achieve a desired subject, style, layout, lighting, and aesthetic. === Techniques === Common terms used to describe various specific prompt engineering techniques include chain-of-thought, tree-of-thought, and retrieval-augmented generation (RAG). A 2024 survey of the field identified over 50 distinct text-based prompting techniques, 40 multimodal variants, and a vocabulary of 33 terms used across prompting research, highlighting a present lack of standardised terminology for prompt engineering. Vibe coding is an AI-assisted software development method where a user prompts an LLM with a description of what they want and lets it generate or edit the code. In 2025, "vibe coding" was the Collins Dictionary word of the year. === Context engineering === Context engineering is a related process that focuses on the context elements that accompany user prompts, which include system instructions, retrieved knowledge, tool definitions, conversation summaries, and task metadata. Context engineering is performed to improve reliability, provenance and token efficiency in production LLM systems. The concept emphasises operational practices such as token budgeting, provenance tags, versioning of context artifacts, observability (logging which context was supplied), and context regression tests to ensure that changes to supplied context do not silently alter system behaviour. == Rationale == Research has found that the performance of large language models (LLMs) is highly sensitive to choices such as the ordering of examples, the quality of demonstration labels, and even small variations in phrasing. In some cases, reordering examples in a prompt produced accuracy shifts of more than 40 percent. === In-context learning === A model's ability to temporarily learn from prompts is known as in-context learning. In-context learning is an emergent ability of large language models. It is an emergent property of model scale, meaning that breaks in scaling laws occur, leading to its efficacy increasing at a different rate in larger models than in smaller models. Unlike training and fine-tuning, which produce lasting changes, in-context learning is temporary. Training models to perform in-context learning can be viewed as a form of meta-learning, or "learning to learn". === Prompting to estimate model sensitivity === Research consistently demonstrates that LLMs are highly sensitive to subtle variations in prompt formatting, structure, and linguistic properties. Some studies have shown up to 76 accuracy points across formatting changes in few-shot settings. Linguistic features significantly influence prompt effectiveness—such as morphology, syntax, and lexico-semantic changes—which meaningfully enhance task performance across a variety of tasks. Clausal syntax, for example, improves consistency and reduces uncertainty in knowledge retrieval. This sensitivity persists even with larger model sizes, additional few-shot examples, or instruction tuning. To address sensitivity of models and make them more robust, several evaluative methods have been proposed. FormatSpread facilitates systematic analysis by evaluating a range of plausible prompt formats, offering a more comprehensive performance interval. Similarly, PromptEval estimates performance distributions across diverse prompts, enabling robust metrics such as performance quantiles and accurate evaluations under constrained budgets. == Prompting techniques == === Multi-shot === A prompt may include a few examples for a model to learn from in context, an approach called few-shot learning. For example, the prompt may ask the model to complete "maison → house, chat → cat, chien →", with the expected response being dog. === Chain-of-thought === Chain-of-thought (CoT) prompting is a technique that allows large language models (LLMs) to solve a problem as a series of intermediate steps before giving a final answer. In 2022, Google Brain reported that chain-of-thought prompting improves reasoning ability by inducing the model to answer a multi-step problem with steps of reasoning that mimic a train of thought. Chain-of-thought techniques were developed to help LLMs handle multi-step reasoning tasks, such as arithmetic or commonsense reasoning questions. When applied to PaLM, a 540 billion parameter language model, according to Google, CoT prompting significantly aided the model, allowing it to perform comparably with task-specific fine-tuned models on several tasks, achieving state-of-the-art results at the time on the GSM8K mathematical reasoning benchmark. It is possible to fine-tune models on CoT reasoning datasets to enhance this capability further and stimulate better interpretability. As originally proposed by Google, each CoT prompt is accompanied by a set of input/output examples—called exemplars—to demonstrate the desired model output, making it a few-shot prompting technique. However, according to a later paper from researchers at Google and the University of Tokyo, simply appending the words "Let's think step-by-step" was also effective, which allowed for CoT to be employed as a zero-shot technique. ==== Self-consistency ==== Self-consistency performs several chain-of-thought rollouts, then selects the most commonly reached conclusion out of all the rollouts. === Tree-of-thought === Tree-of-thought prompting generalizes chain-of-thought by generating multiple lines of reasoning in parallel, with the ability to backtrack or explore other paths. It can use tree search algorithms like breadth-first, depth-first, or beam. === Text-to-image prompting === In 2022, text-to-image models like DALL-E 2, Stable Diffusion, and Midjourney were released to the public. These models take text prompts as input and use them to generate images. Early text-to-image models typically do not understand negation, grammar and sentence structure in the same way as large language models, and may thus requi

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  Video editing software

  Video editing software or a video editor is software used for performing the post-production video editing of digital video sequences on a non-linear editing system (NLE). It has replaced traditional flatbed celluloid film editing tools and analog video tape editing machines. Video editing software serves a lot of purposes, such as filmmaking, audio commentary, and general editing of video content. In NLE software, the user manipulates sections of video, images, and audio on a sequence. These clips can be trimmed, cut, and manipulated in many different ways. When editing is finished, the user exports the sequence as a video file. == Components == === Timeline === NLE software is typically based on a timeline interface where sections moving image video recordings, known as clips, are laid out in sequence and played back. The NLE offers a range of tools for trimming, splicing, cutting, and arranging clips across the timeline. Another kind of clip is a text clip, used to add text to a video, such as title screens or movie credits. Audio clips can additionally be mixed together, such as mixing a soundtrack with multiple sound effects. Typically, the timeline is divided into multiple rows on the y-axis for different clips playing simultaneously, whereas the x-axis represents the run time of the video. Effects such as transitions can be performed on each clip, such as a crossfade effect going from one scene to another. === Exporting === Since video editors represent a project with a file format specific to the program, one needs to export the video file in order to publish it. Once a project is complete, the editor can then export to movies in a variety of formats in a context that may range from broadcast tape formats to compressed video files for web publishing (such as on an online video platform or personal website), optical media, or saved to mobile devices. To facilitate editing, source video typically has a higher resolution than the desired output. Therefore, higher resolution video needs to be downscaled during exporting, or after exporting in a process known as transsizing. === Visual effects === As digital video editing advanced, visual effects became possible, and is part of the standard toolkit, usually found in prosumer and professional grade software. A common ability is to do compositing techniques such as chroma keying or luma keying, among others, which allow different objects to look as if they are in the same scene. A different kind of visual effects is motion capture. Software such as Blender can perform motion capture to make animated objects follow an actor's movements. === Additional features === Most professional video editors are able to do color grading, which is to manipulate visual attributes of a video such as contrast to enhance output, and improve emotional impact. Some video editors such as iMovie include stock footage available for use. == Hardware requirements == As video editing puts great demands on storage and graphics performance, especially at high resolutions such as 4K, and for videos with many visual effects, powerful hardware is often required. It is not uncommon for a computer built for video editing to have a lot of drive capacity, and a powerful graphics processing unit, which optimally has hardware accelerated video encoding. Having sufficient disk space is important since videos can take up large amounts of storage, depending on the resolution and compression format used. Each minute of a Full HD (1080p) video at 30 fps takes up 60MB of space. When visual effects are used, a server farm can be employed to speed up the rendering process. == Examples == Video editing software can be divided into consumer grade, which focuses on ease-of-use, along with professional grade software, which focuses on feature availability, and advanced editing techniques. The typical use case for the former is to edit personal videos on the go, when more advanced editing is not required. === Consumer grade === Photos (Apple) Google Photos YouTube Create === Prosumer grade === ==== Proprietary software ==== iMovie CyberLink PowerDirector === Professional grade === ==== Proprietary software ==== Final Cut Pro Adobe Premiere Pro DaVinci Resolve Vegas Pro Lightworks Camtasia Media Composer ==== Free and open source software ==== Avidemux Blender Cinelerra Flowblade Kdenlive OpenShot Shotcut While most video editing software has been separate from the operating systems, some operating systems have had a video editor installed by default, such as Windows Movie Maker in Windows XP, or as a component of the default photo viewer, such as the Photos app on iOS. Some social media platforms, such as TikTok and Instagram may include a rudimentary video editor to trim clips.

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  Augment (app)

  Augment is an augmented reality SaaS platform that allows users to visualize their products in 3D in real environment and in real-time through tablets or smartphones. The software can be used for retail, e-commerce, architecture, and other purposes. Augment created a mobile app of the same name, used to visualize 3D models in augmented reality and a web application called Augment Manager for 3D content management. The company is based in Paris, France, and was founded in October 2011 by Jean-François Chianetta, Cyril Champier, and Mickaël Jordan. In March 2016, Augment announced €3 million in its series-A round from Salesforce Ventures, which bringing the total funding since launch to $4.7 million. Augment lets businesses and 3D professionals visualize projects in their actual size and environment, on iPhone, iPad, and Android, using the power of augmented reality. Users can print the Augment tracker or create their own tracker to place the 3D models in space and at scale in real time. Common uses of the technology include product presentations, interactive print campaigns and e-Commerce product visualization. Augment has just released its augmented reality SDK solutions for retail and augmented commerce. The SDK solutions, available for both native mobile app and web integrations, allow companies to embed augmented reality product visualization in their existing eCommerce platforms. == Technology == Augment uses the following 3D technologies: Vuforia Augmented Reality SDK OpenGL == Customer cases == Companies such as Coca-Cola, Siemens, Nokia, Nestle, and Boeing are using Augment's solutions. == History == Augment was first created by Jean-François Chianetta in October 2011. Chianetta later teamed up with Cyril Champier and Mickaël Jordan for further development. The co-founding team was among the 12 startups of Season 3 of French accelerator Le Camping. The team raised one million euros (US$1,300,000) in April 2013 and moved its office to Paris. In March 2016, Augment raised US$3M Series A funding from Salesforce and other investors. In 2013, Augment's first service, Boost Business Catalog, was made available to help businesses catalogue and display their product models. Customers can rotate the images in 3D and view augmented content before deciding what to buy. == Awards == "Best Innovation" at Ecommerce Mag Trophy 2013

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  Spherical basis

  In pure and applied mathematics, particularly quantum mechanics and computer graphics and their applications, a spherical basis is the basis used to express spherical tensors. The spherical basis closely relates to the description of angular momentum in quantum mechanics and spherical harmonic functions. While spherical polar coordinates are one orthogonal coordinate system for expressing vectors and tensors using polar and azimuthal angles and radial distance, the spherical basis are constructed from the standard basis and use complex numbers. == In three dimensions == A vector A in 3D Euclidean space R3 can be expressed in the familiar Cartesian coordinate system in the standard basis ex, ey, ez, and coordinates Ax, Ay, Az: or any other coordinate system with associated basis set of vectors. From this extend the scalars to allow multiplication by complex numbers, so that we are now working in C 3 {\displaystyle \mathbb {C} ^{3}} rather than R 3 {\displaystyle \mathbb {R} ^{3}} . === Basis definition === In the spherical bases denoted e+, e−, e0, and associated coordinates with respect to this basis, denoted A+, A−, A0, the vector A is: where the spherical basis vectors can be defined in terms of the Cartesian basis using complex-valued coefficients in the xy plane: in which i {\displaystyle i} denotes the imaginary unit, and one normal to the plane in the z direction: e 0 = e z {\displaystyle \mathbf {e} _{0}=\mathbf {e} _{z}} The inverse relations are: === Commutator definition === While giving a basis in a 3-dimensional space is a valid definition for a spherical tensor, it only covers the case for when the rank k {\displaystyle k} is 1. For higher ranks, one may use either the commutator, or rotation definition of a spherical tensor. The commutator definition is given below, any operator T q ( k ) {\displaystyle T_{q}^{(k)}} that satisfies the following relations is a spherical tensor: [ J ± , T q ( k ) ] = ℏ ( k ∓ q ) ( k ± q + 1 ) T q ± 1 ( k ) {\displaystyle [J_{\pm },T_{q}^{(k)}]=\hbar {\sqrt {(k\mp q)(k\pm q+1)}}T_{q\pm 1}^{(k)}} [ J z , T q ( k ) ] = ℏ q T q ( k ) {\displaystyle [J_{z},T_{q}^{(k)}]=\hbar qT_{q}^{(k)}} === Rotation definition === Analogously to how the spherical harmonics transform under a rotation, a general spherical tensor transforms as follows, when the states transform under the unitary Wigner D-matrix D ( R ) {\displaystyle {\mathcal {D}}(R)} , where R is a (3×3 rotation) group element in SO(3). That is, these matrices represent the rotation group elements. With the help of its Lie algebra, one can show these two definitions are equivalent. D ( R ) T q ( k ) D † ( R ) = ∑ q ′ = − k k T q ′ ( k ) D q ′ q ( k ) {\displaystyle {\mathcal {D}}(R)T_{q}^{(k)}{\mathcal {D}}^{\dagger }(R)=\sum _{q'=-k}^{k}T_{q'}^{(k)}{\mathcal {D}}_{q'q}^{(k)}} === Coordinate vectors === For the spherical basis, the coordinates are complex-valued numbers A+, A0, A−, and can be found by substitution of (3B) into (1), or directly calculated from the inner product ⟨, ⟩ (5): A 0 = ⟨ e 0 , A ⟩ = ⟨ e z , A ⟩ = A z {\displaystyle A_{0}=\left\langle \mathbf {e} _{0},\mathbf {A} \right\rangle =\left\langle \mathbf {e} _{z},\mathbf {A} \right\rangle =A_{z}} with inverse relations: In general, for two vectors with complex coefficients in the same real-valued orthonormal basis ei, with the property ei·ej = δij, the inner product is: where · is the usual dot product and the complex conjugate must be used to keep the magnitude (or "norm") of the vector positive definite. == Properties (three dimensions) == === Orthonormality === The spherical basis is an orthonormal basis, since the inner product ⟨, ⟩ (5) of every pair vanishes meaning the basis vectors are all mutually orthogonal: ⟨ e + , e − ⟩ = ⟨ e − , e 0 ⟩ = ⟨ e 0 , e + ⟩ = 0 {\displaystyle \left\langle \mathbf {e} _{+},\mathbf {e} _{-}\right\rangle =\left\langle \mathbf {e} _{-},\mathbf {e} _{0}\right\rangle =\left\langle \mathbf {e} _{0},\mathbf {e} _{+}\right\rangle =0} and each basis vector is a unit vector: ⟨ e + , e + ⟩ = ⟨ e − , e − ⟩ = ⟨ e 0 , e 0 ⟩ = 1 {\displaystyle \left\langle \mathbf {e} _{+},\mathbf {e} _{+}\right\rangle =\left\langle \mathbf {e} _{-},\mathbf {e} _{-}\right\rangle =\left\langle \mathbf {e} _{0},\mathbf {e} _{0}\right\rangle =1} hence the need for the normalizing factors of 1 / 2 {\displaystyle 1/\!{\sqrt {2}}} . === Change of basis matrix === The defining relations (3A) can be summarized by a transformation matrix U: ( e + e − e 0 ) = U ( e x e y e z ) , U = ( − 1 2 − i 2 0 + 1 2 − i 2 0 0 0 1 ) , {\displaystyle {\begin{pmatrix}\mathbf {e} _{+}\\\mathbf {e} _{-}\\\mathbf {e} _{0}\end{pmatrix}}=\mathbf {U} {\begin{pmatrix}\mathbf {e} _{x}\\\mathbf {e} _{y}\\\mathbf {e} _{z}\end{pmatrix}}\,,\quad \mathbf {U} ={\begin{pmatrix}-{\frac {1}{\sqrt {2}}}&-{\frac {i}{\sqrt {2}}}&0\\+{\frac {1}{\sqrt {2}}}&-{\frac {i}{\sqrt {2}}}&0\\0&0&1\end{pmatrix}}\,,} with inverse: ( e x e y e z ) = U − 1 ( e + e − e 0 ) , U − 1 = ( − 1 2 + 1 2 0 + i 2 + i 2 0 0 0 1 ) . {\displaystyle {\begin{pmatrix}\mathbf {e} _{x}\\\mathbf {e} _{y}\\\mathbf {e} _{z}\end{pmatrix}}=\mathbf {U} ^{-1}{\begin{pmatrix}\mathbf {e} _{+}\\\mathbf {e} _{-}\\\mathbf {e} _{0}\end{pmatrix}}\,,\quad \mathbf {U} ^{-1}={\begin{pmatrix}-{\frac {1}{\sqrt {2}}}&+{\frac {1}{\sqrt {2}}}&0\\+{\frac {i}{\sqrt {2}}}&+{\frac {i}{\sqrt {2}}}&0\\0&0&1\end{pmatrix}}\,.} It can be seen that U is a unitary matrix, in other words its Hermitian conjugate U† (complex conjugate and matrix transpose) is also the inverse matrix U−1. For the coordinates: ( A + A − A 0 ) = U ∗ ( A x A y A z ) , U ∗ = ( − 1 2 + i 2 0 + 1 2 + i 2 0 0 0 1 ) , {\displaystyle {\begin{pmatrix}A_{+}\\A_{-}\\A_{0}\end{pmatrix}}=\mathbf {U} ^{\mathrm {} }{\begin{pmatrix}A_{x}\\A_{y}\\A_{z}\end{pmatrix}}\,,\quad \mathbf {U} ^{\mathrm {} }={\begin{pmatrix}-{\frac {1}{\sqrt {2}}}&+{\frac {i}{\sqrt {2}}}&0\\+{\frac {1}{\sqrt {2}}}&+{\frac {i}{\sqrt {2}}}&0\\0&0&1\end{pmatrix}}\,,} and inverse: ( A x A y A z ) = ( U ∗ ) − 1 ( A + A − A 0 ) , ( U ∗ ) − 1 = ( − 1 2 + 1 2 0 − i 2 − i 2 0 0 0 1 ) . {\displaystyle {\begin{pmatrix}A_{x}\\A_{y}\\A_{z}\end{pmatrix}}=(\mathbf {U} ^{\mathrm {} })^{-1}{\begin{pmatrix}A_{+}\\A_{-}\\A_{0}\end{pmatrix}}\,,\quad (\mathbf {U} ^{\mathrm {} })^{-1}={\begin{pmatrix}-{\frac {1}{\sqrt {2}}}&+{\frac {1}{\sqrt {2}}}&0\\-{\frac {i}{\sqrt {2}}}&-{\frac {i}{\sqrt {2}}}&0\\0&0&1\end{pmatrix}}\,.} === Cross products === Taking cross products of the spherical basis vectors, we find an obvious relation: e q × e q = 0 {\displaystyle \mathbf {e} _{q}\times \mathbf {e} _{q}={\boldsymbol {0}}} where q is a placeholder for +, −, 0, and two less obvious relations: e ± × e ∓ = ± i e 0 {\displaystyle \mathbf {e} _{\pm }\times \mathbf {e} _{\mp }=\pm i\mathbf {e} _{0}} e ± × e 0 = ± i e ± {\displaystyle \mathbf {e} _{\pm }\times \mathbf {e} _{0}=\pm i\mathbf {e} _{\pm }} === Inner product in the spherical basis === The inner product between two vectors A and B in the spherical basis follows from the above definition of the inner product: ⟨ A , B ⟩ = A + B + ⋆ + A − B − ⋆ + A 0 B 0 ⋆ {\displaystyle \left\langle \mathbf {A} ,\mathbf {B} \right\rangle =A_{+}B_{+}^{\star }+A_{-}B_{-}^{\star }+A_{0}B_{0}^{\star }}

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  Statistical learning theory

  Statistical learning theory is a framework for machine learning drawing from the fields of statistics and functional analysis. Statistical learning theory deals with the statistical inference problem of finding a predictive function based on data. Statistical learning theory has led to successful applications in fields such as computer vision, speech recognition, and bioinformatics. == Introduction == The goals of learning are understanding and prediction. Learning falls into many categories, including supervised learning, unsupervised learning, online learning, and reinforcement learning. From the perspective of statistical learning theory, supervised learning is best understood. Supervised learning involves learning from a training set of data. Every point in the training is an input–output pair, where the input maps to an output. The learning problem consists of inferring the function that maps between the input and the output, such that the learned function can be used to predict the output from future input. Depending on the type of output, supervised learning problems are either problems of regression or problems of classification. If the output takes a continuous range of values, it is a regression problem. Using Ohm's law as an example, a regression could be performed with voltage as input and current as an output. The regression would find the functional relationship between voltage and current to be R {\displaystyle R} , such that V = I R {\displaystyle V=IR} Classification problems are those for which the output will be an element from a discrete set of labels. Classification is very common for machine learning applications. In facial recognition, for instance, a picture of a person's face would be the input, and the output label would be that person's name. The input would be represented by a large multidimensional vector whose elements represent pixels in the picture. After learning a function based on the training set data, that function is validated on a test set of data, data that did not appear in the training set. == Formal description == Take X {\displaystyle X} to be the vector space of all possible inputs, and Y {\displaystyle Y} to be the vector space of all possible outputs. Statistical learning theory takes the perspective that there is some unknown probability distribution over the product space Z = X × Y {\displaystyle Z=X\times Y} , i.e. there exists some unknown p ( z ) = p ( x , y ) {\displaystyle p(z)=p(\mathbf {x} ,y)} . The training set is made up of n {\displaystyle n} samples from this probability distribution, and is notated S = { ( x 1 , y 1 ) , … , ( x n , y n ) } = { z 1 , … , z n } {\displaystyle S=\{(\mathbf {x} _{1},y_{1}),\dots ,(\mathbf {x} _{n},y_{n})\}=\{\mathbf {z} _{1},\dots ,\mathbf {z} _{n}\}} Every x i {\displaystyle \mathbf {x} _{i}} is an input vector from the training data, and y i {\displaystyle y_{i}} is the output that corresponds to it. In this formalism, the inference problem consists of finding a function f : X → Y {\displaystyle f:X\to Y} such that f ( x ) ∼ y {\displaystyle f(\mathbf {x} )\sim y} . Let H {\displaystyle {\mathcal {H}}} be a space of functions f : X → Y {\displaystyle f:X\to Y} called the hypothesis space. The hypothesis space is the space of functions the algorithm will search through. Let V ( f ( x ) , y ) {\displaystyle V(f(\mathbf {x} ),y)} be the loss function, a metric for the difference between the predicted value f ( x ) {\displaystyle f(\mathbf {x} )} and the actual value y {\displaystyle y} . The expected risk is defined to be I [ f ] = ∫ X × Y V ( f ( x ) , y ) p ( x , y ) d x d y {\displaystyle I[f]=\int _{X\times Y}V(f(\mathbf {x} ),y)\,p(\mathbf {x} ,y)\,d\mathbf {x} \,dy} The target function, the best possible function f {\displaystyle f} that can be chosen, is given by the f {\displaystyle f} that satisfies f = argmin h ∈ H ⁡ I [ h ] {\displaystyle f=\mathop {\operatorname {argmin} } _{h\in {\mathcal {H}}}I[h]} Because the probability distribution p ( x , y ) {\displaystyle p(\mathbf {x} ,y)} is unknown, a proxy measure for the expected risk must be used. This measure is based on the training set, a sample from this unknown probability distribution. It is called the empirical risk I S [ f ] = 1 n ∑ i = 1 n V ( f ( x i ) , y i ) {\displaystyle I_{S}[f]={\frac {1}{n}}\sum _{i=1}^{n}V(f(\mathbf {x} _{i}),y_{i})} A learning algorithm that chooses the function f S {\displaystyle f_{S}} that minimizes the empirical risk is called empirical risk minimization. == Loss functions == The choice of loss function is a determining factor on the function f S {\displaystyle f_{S}} that will be chosen by the learning algorithm. The loss function also affects the convergence rate for an algorithm. It is important for the loss function to be convex. Different loss functions are used depending on whether the problem is one of regression or one of classification. === Regression === The most common loss function for regression is the square loss function (also known as the L2-norm). This familiar loss function is used in Ordinary Least Squares regression. The form is: V ( f ( x ) , y ) = ( y − f ( x ) ) 2 {\displaystyle V(f(\mathbf {x} ),y)=(y-f(\mathbf {x} ))^{2}} The absolute value loss (also known as the L1-norm) is also sometimes used: V ( f ( x ) , y ) = | y − f ( x ) | {\displaystyle V(f(\mathbf {x} ),y)=|y-f(\mathbf {x} )|} === Classification === In some sense the 0-1 indicator function is the most natural loss function for classification. It takes the value 0 if the predicted output is the same as the actual output, and it takes the value 1 if the predicted output is different from the actual output. For binary classification with Y = { − 1 , 1 } {\displaystyle Y=\{-1,1\}} , this is: V ( f ( x ) , y ) = θ ( − y f ( x ) ) {\displaystyle V(f(\mathbf {x} ),y)=\theta (-yf(\mathbf {x} ))} where θ {\displaystyle \theta } is the Heaviside step function. == Regularization == In machine learning problems, a major problem that arises is that of overfitting. Because learning is a prediction problem, the goal is not to find a function that most closely fits the (previously observed) data, but to find one that will most accurately predict output from future input. Empirical risk minimization runs this risk of overfitting: finding a function that matches the data exactly but does not predict future output well. Overfitting is symptomatic of unstable solutions; a small perturbation in the training set data would cause a large variation in the learned function. It can be shown that if the stability for the solution can be guaranteed, generalization and consistency are guaranteed as well. Regularization can solve the overfitting problem and give the problem stability. Regularization can be accomplished by restricting the hypothesis space H {\displaystyle {\mathcal {H}}} . A common example would be restricting H {\displaystyle {\mathcal {H}}} to linear functions: this can be seen as a reduction to the standard problem of linear regression. H {\displaystyle {\mathcal {H}}} could also be restricted to polynomial of degree p {\displaystyle p} , exponentials, or bounded functions on L1. Restriction of the hypothesis space avoids overfitting because the form of the potential functions are limited, and so does not allow for the choice of a function that gives empirical risk arbitrarily close to zero. One example of regularization is Tikhonov regularization. This consists of minimizing 1 n ∑ i = 1 n V ( f ( x i ) , y i ) + γ ‖ f ‖ H 2 {\displaystyle {\frac {1}{n}}\sum _{i=1}^{n}V(f(\mathbf {x} _{i}),y_{i})+\gamma \left\|f\right\|_{\mathcal {H}}^{2}} where γ {\displaystyle \gamma } is a fixed and positive parameter, the regularization parameter. Tikhonov regularization ensures existence, uniqueness, and stability of the solution. == Bounding empirical risk == Consider a binary classifier f : X → { 0 , 1 } {\displaystyle f:{\mathcal {X}}\to \{0,1\}} . We can apply Hoeffding's inequality to bound the probability that the empirical risk deviates from the true risk to be a Sub-Gaussian distribution. P ( | R ^ ( f ) − R ( f ) | ≥ ϵ ) ≤ 2 e − 2 n ϵ 2 {\displaystyle \mathbb {P} (|{\hat {R}}(f)-R(f)|\geq \epsilon )\leq 2e^{-2n\epsilon ^{2}}} But generally, when we do empirical risk minimization, we are not given a classifier; we must choose it. Therefore, a more useful result is to bound the probability of the supremum of the difference over the whole class. P ( sup f ∈ F | R ^ ( f ) − R ( f ) | ≥ ϵ ) ≤ 2 S ( F , n ) e − n ϵ 2 / 8 ≈ n d e − n ϵ 2 / 8 {\displaystyle \mathbb {P} {\bigg (}\sup _{f\in {\mathcal {F}}}|{\hat {R}}(f)-R(f)|\geq \epsilon {\bigg )}\leq 2S({\mathcal {F}},n)e^{-n\epsilon ^{2}/8}\approx n^{d}e^{-n\epsilon ^{2}/8}} where S ( F , n ) {\displaystyle S({\mathcal {F}},n)} is the shattering number and n {\displaystyle n} is the number of samples in your dataset. The exponential term comes from Hoeffding but there is an extra cost of taking the supremum over the whole cla

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  Aarogya Setu

  Aarogya Setu (lit. 'The bridge to health') is an Indian COVID-19 "contact tracing, syndromic mapping and self-assessment" digital service, primarily a mobile app, developed by the National Informatics Centre under the Ministry of Electronics and Information Technology (MeitY). The app reached more than 100 million installs in 40 days. On 26 May, amid growing privacy and security concerns, the source code of the app was made public. == Full view == The stated purpose of this app is to spread awareness of COVID-19 and to connect essential COVID-19-related health services to the people of India. This app augments the initiatives of the Department of Health to contain COVID-19 and shares best practices and advisories. It is a tracking app which uses the smartphone's GPS and Bluetooth features to track COVID-19 cases. The app is available for Android and iOS mobile operating systems. With Bluetooth, it tries to determine the risk if one has been near (within six feet of) a COVID-19-infected person, by scanning through a database of known cases across India. Using location information, it determines whether the location one is in belongs to one of the infected areas based on the data available. This app is an updated version of an earlier app called Corona Kavach (now discontinued) which was released earlier by the Government of India. == Features and tools == Aarogya Setu has four sections: User Status (tells the risk of getting COVID-19 for the user) Self Assess (helps the users identify COVID-19 symptoms and their risk profile) COVID-19 Updates (gives updates on local and national COVID-19 cases) E-pass integration (if applied for E-pass, it will be available) See Recent Contacts option (allows the users to assess the risk level of their Bluetooth contacts) It tells how many COVID-19 positive cases are likely in a radius of 500 m, 1 km, 2 km, 5 km and 10 km from the user. The app is built on a platform that can provide an application programming interface (API) so that other computer programs, mobile applications, and web services can make use of the features and data available in Aarogya Setu. == Response == Aarogya Setu crossed five million downloads within three days of its launch, making it one of the most popular government apps in India. It became the world's fastest-growing mobile app, beating Pokémon Go, with more than 50 million installs 13 days after launching in India on 2 April 2020. It reached 100 million installs by 13 May 2020, that is in 40 days since its launch. In an order on 29 April 2020 the central government made it mandatory for all employees to download the app and use it – "Before starting for office, they must review their status on Aarogya Setu and commute only when the app shows safe or low risk". The Union Home Ministry also said that the application is mandatory for all living in the COVID-19 containment zone. The government gave the announcement along with the nationwide lockdown extension by two weeks from the 4 May with certain relaxations. On 21 May 2020, the Airport Authority of India issued a Standard Operating Procedure (SOP) stating that all departing passengers must compulsorily be registered with the Aarogya Setu app. It added that the app would not be mandatory for children below 14 years. However, the next day, Civil Aviation Minister Hardeep Singh Puri clarified that the app would not be mandatory for any passengers. On 26 May 2020, the Aarogya Setu app code was made open to developers across the globe to help other countries manage contact tracing in their fight against COVID-19 pandemic. In March 2021, Co-WIN portal was integrated with the app. This allowed users to schedule an appointment through the app for COVID-19 vaccine by registering their phone number and providing relevant documents. == Effectiveness == NITI Aayog CEO revealed that "the app has been able to identify more than 3,000 hotspots in 3–17 days ahead of time." However, users and experts in India and around the world say the app raises huge data security concerns. The app collects name, number, gender, travel history, and uses a phone's Bluetooth and location data to let users know if they have been near a person with COVID-19 by scanning a database of known cases of infection, and also share it with the government simultaneously. This is the major area of concern as the app's constant access to a phone's Bluetooth imposes a form of security threat. But it stood to clarify itself that the informations received are not going to be made public. Amidst all these, the app hits a record of about one-hundred million downloads. == Reception == Rahul Gandhi, leader of the Congress party, termed the Aarogya Setu application a "sophisticated surveillance system" after the government announced that downloading the app would be mandatory for both government and private employees. Following this, others raised the same concerns about the Aarogya Setu app. The Ministry of Electronics and Information Technology (MeitY) responded to these concerns by asserting that Gandhi's claims were false, and that the app was being appreciated internationally. On 5 May, French ethical hacker Robert Baptiste, who goes by the name Elliot Alderson on Twitter, claimed that there were security issues with the app. The Indian government, as well as the app developers, responded to this claim by thanking the hacker for his attention, but dismissed his concerns. The developers of the app stated that the fetching of location data is a documented feature of the app, rather than a flaw, since the app is designed to track the distribution of the virus-infected population. They also asserted that no personal information of any user has been proven to be at risk. On 6 May, Robert Baptiste tweeted that security vulnerabilities in Aarogya Setu allowed hackers to "know who is infected, unwell, [or] made a self assessment in the area of his choice". He also gave details of how many people were unwell and infected at the Prime Minister's Office, the Indian Parliament and the Home Office. The Economic Times pointed out that a clause in the app's Terms and Conditions stated that the user "agrees and acknowledges that the Government of India will not be liable for ... any unauthorised access to your information or modification thereof". In response, several software developers called for the source code to be made public. On 12 May, former Supreme Court Judge Justice B.N. Srikrishna termed the government's push mandating the use of Aarogya Setu app "utterly illegal". He said so far it is not backed by any law and questioned "under what law, government is mandating it on anyone". MIT Technology Review gave 2 out of 5 stars to Aarogya Setu app after analyzing the COVID contact tracing apps launched in 25 countries. The app got stars only for the policy which suggests that data collected is deleted after a period of time and that the data collection, as far as user inputs go, is minimal. It also highlighted that India is the only democracy making its app mandatory for millions of people. The rating was further downgraded from 2 to 1 for collecting more information than the app needs to function. Following this, the MeitY made the source code of the Android app public on GitHub on 26 May, which will be followed by iOS and API documentation. Further, the Government has also launched a "bug bounty program". This was done to "promote transparency and ensure security and integrity of the app". However, experts stated that the server-side code had not yet been publicly released, which meant that public opinion on security and privacy was yet to be completely assuaged. Following this, ZDNet noted that the source code seemed to confirm the government's claim that user location data, if collected, would be anonymised and would be deleted after 45 days, or 60 days for high-risk individuals.

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  Construction robots

  Construction robots are a subset of industrial robots used for building and infrastructure construction on site, or in the production of materials and components offsite. A 2021 survey said 55% of construction companies in the United States, Europe, and China used robots in some form. This figure, however, reflects reported use across the construction value chain rather than widespread deployment of robots on active construction sites. Real-world adoption remains limited, with many robotic systems confined to pilot projects, controlled environments, or specific task applications rather than continuous on-site construction use. One of the main challenges in deploying robots on construction sites is the unstructured and variable nature of the environment, which differs fundamentally from controlled factory settings where industrial robots have traditionally operated. Some robots currently deployed on job sites assist with physically demanding or repetitive tasks: excavating, lifting heavy materials, surveying, laying out markers, tying rebar, and installing drywall. More advanced systems are being developed for exterior finishing, steel placement, masonry, and reinforced concrete work. In practice, rather than autonomous systems performing core building tasks, the most widely adopted robot applications on construction sites involve technologies such as aerial drones (or, less frequently, robot 'dogs' - for example, Boston Dynamics' Spot - or humanoid robots) used for surveying, inspection, and progress monitoring (the robots typically carry video and/or 360-degree cameras, LiDar scanners or other data capture devices, with data analysed using artificial intelligence and machine learning). Some emerging systems are designed as multifunctional construction robots, integrating multiple tools and capabilities within a single robotic platform to perform different stages of the construction process. These systems aim to improve operational flexibility and increase automation in complex construction environments. Experimental projects using robotic construction technologies and additive manufacturing have been demonstrated in several countries as part of broader efforts to industrialize the construction sector and improve productivity through automation and digitalization. == Features == Construction robots are generally required to meet the following criteria: Mobility: the ability to navigate around a construction site, including uneven terrain and confined spaces. Adaptability: the ability to handle components of variable size, weight, and shape. Environmental awareness: the ability to sense and respond to changing on-site conditions. Interactivity: the ability to operate alongside human workers and other equipment. Multitasking: the ability to perform several different operations within a single deployment. == Capabilities == Construction robots have been developed and tested for a range of on-site tasks, including: Progress monitoring — robots equipped with cameras and sensors can track construction progress and identify deviations from plans. Inspection — robots are used to investigate infrastructure at dangerous or inaccessible locations, reducing risk to human workers and eliminating human error. Wall construction — robotic systems can lay bricks and blocks with greater speed and consistency than manual labour. Earthmoving and material handling — autonomous excavators and haul trucks use GPS, lidar, and motion sensors to perform digging, trenching, and loading tasks with minimal human input. Grading and dozing — autonomous bulldozers use GPS, gyroscopes, and laser sensors to control blade angle and depth, improving surface finish accuracy and reducing material overuse. 3D printing — additive manufacturing systems can construct walls and structural elements directly from digital models. == Notable construction-related activities undertaken by robots == The distribution of robotic applications in construction varies across the project lifecycle. Most applications are concentrated in structural construction tasks such as masonry, concrete work, and assembly, while other phases, including planning, maintenance, and demolition, remain less represented. === Automated building systems === The Nisseki Yokohama Building (also known as Rail City Yokohama), a 30-storey office building in Yokohama, Japan, was constructed between 1994 and 1997 using the SMART system (Shimizu Manufacturing system by Advanced Robotics Technology), developed by Shimizu Corporation and a consortium of seven other Japanese companies. The system used automated horizontal hoists and vertical lifts to position steel beams, columns, precast concrete floor slabs, and prefabricated facade panels, with welding robots connecting structural elements under laser-guided precision. Each component was tracked by barcode to monitor progress and coordinate just-in-time delivery of materials. Obayashi Corporation developed the Advanced Building Construction System (ABCS), a similar automated platform used in several high-rise projects in Japan in the 1990s, including the NEC Head Office in Kanagawa (1997–2000). === Progress monitoring, inspection === Boston Dynamics' Spot was used in February 2024 to inspect sections of the M5 motorway in England for National Highways. A £15,000 humanoid robot (a G1 model from Chinese manufacturer Unitree) was deployed to capture 360-degree imagery and progress reports to support health and safety monitoring and reporting for UK contractor Tilbury Douglas in April 2026. In the US, Virginia Tech's ARCADE research lab is developing MARIO (Multi-Agent Robotic system for Inspection On-site), a heterogenous robotic system deploying multiple robots capable of different locomotion to perform remote real-time construction progress monitoring in complex construction sites. === Earthmoving === === Concrete works === Obayashi Corporation developed and deployed a robotic system for placing concrete layers in dam construction in Japan. A concrete floor finishing robot was deployed by Kajima and Tokimec in Japan. The MARK series were designed in 1984 to automate the levelling and trowelling of concrete slabs on construction sites, providing consistent finishing accuracy, improved efficiency, and reduced dependence on skilled labour === Masonry === SAM100 (Semi-Automated Mason), developed by Construction Robotics, is one of the first commercially available bricklaying robots for on-site masonry construction. In 2018, it was used in the construction of the University Arts Building at the University of Nevada, Reno — a $35.5 million facility — where it laid over 60,000 of the 100,000 bricks required, reducing the brick veneer installation time by approximately 50%. Hadrian X, developed by the Australian company Fastbrick Robotics, is a fully autonomous mobile bricklaying robot. In November 2022, it completed its first commercial project — five four-bedroom houses in Wellard, Western Australia. In February 2025, PulteGroup, one of the largest homebuilders in the United States, piloted Hadrian X on a site in Florida, constructing an entire house in a single day. === 3D printing === In May 2025, a residential building in Arinaga, Gran Canaria, Spain, was completed using 3D printing construction technology, as part of broader efforts to demonstrate robotic and additive manufacturing methods in the housing sector. In 2026, a three-storey apartment block in France was constructed using concrete 3D printing technology, three months faster than conventional building methods. Finland's Hyperion Robotics has opened a UK factory and used 3D printing with concrete to produce foundations for pipelines and for electricity substation bases, reducing time-consuming and weather-dependent onsite construction processes. == Social impact == The adoption of construction robots varies significantly by region and is shaped by labour market conditions, cultural attitudes, and regulatory frameworks. In Japan, construction robots have been embraced as a response to an ageing workforce and chronic labour shortages, and are generally viewed positively by the industry. In the United States, adoption has historically been slower, partly due to resistance from labour unions concerned about job displacement. Research suggests that the impact of automation on workers is uneven: while robots can create a productivity effect that benefits some workers, displacement effects are most pronounced among younger, less-educated workers in manufacturing-heavy regions. More than 60% of construction firms now report difficulty finding skilled operators, which has increased openness to automation as a practical solution to workforce shortages rather than a replacement for workers. In the UK, during onsite deployment of a humanoid robot for monitoring purposes, there were concerns that staff might think they were being watched ("It's not there to spy on people.... So, we insist that everyone is blurred out. N

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