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  • Containerization (computing)

    Containerization (computing)

    In software engineering, containerization is operating-system-level virtualization or application-level virtualization over multiple resources so that software applications can run in isolated user spaces called containers in any cloud or non-cloud environment, regardless of type or vendor. The term "container" has different meanings in different contexts, and it is important to ensure that the intended definition aligns with the audience's understanding. == Usage == Each container is basically a fully functional and portable cloud or non-cloud computing environment surrounding the application and keeping it independent of other environments running in parallel. Individually, each container simulates a different software application and runs isolated processes by bundling related configuration files, libraries and dependencies. But, collectively, multiple containers share a common operating system kernel (OS). In recent times, containerization technology has been widely adopted by cloud computing platforms like Amazon Web Services, Microsoft Azure, Google Cloud Platform, and IBM Cloud. Containerization has also been pursued by the U.S. Department of Defense as a way of more rapidly developing and fielding software updates, with first application in its F-22 air superiority fighter. == History == The concept of containerization in computing originated from early operating system–level isolation mechanisms. One of the earliest implementations was the chroot system call introduced in Version 7 Unix in 1979, which changed the apparent root directory for a process and its children, providing a basic form of filesystem isolation. In the early 2000s, more advanced forms of operating system–level virtualization were developed. FreeBSD introduced "jails" in 2000, which extended isolation by restricting processes to a subset of system resources. Around the same time, Solaris introduced "zones" (also known as Solaris Containers), providing similar capabilities with resource management and isolation features. Linux later incorporated comparable functionality through kernel features such as namespaces and control groups (cgroups), which enabled isolation of process IDs, network stacks, filesystems, and resource allocation. These features formed the foundation for Linux Containers (LXC), which provided a userspace interface for managing containers. The widespread adoption of containerization accelerated with the release of Docker in 2013, which introduced a standardized format for packaging applications and their dependencies, along with tooling for image distribution and container management. == Types of containers == OS containers Application containers == Security issues == Because of the shared OS, security threats can affect the whole containerized system. In containerized environments, security scanners generally protect the OS, but not the application containers, which adds unwanted vulnerability. == Container management, orchestration, clustering == Container orchestration or container management is mostly used in the context of application containers. Implementations providing such orchestration include Kubernetes and Docker swarm. == Container cluster management == Container clusters need to be managed. This includes functionality to create a cluster, to upgrade the software or repair it, balance the load between existing instances, scale by starting or stopping instances to adapt to the number of users, to log activities and monitor produced logs or the application itself by querying sensors. Open-source implementations of such software include OKD and Rancher. Quite a number of companies provide container cluster management as a managed service, like Alibaba, Amazon, Google, and Microsoft.

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  • Sample (graphics)

    Sample (graphics)

    In computer graphics, a sample is an intersection of a channel and a pixel. The diagram below depicts a 24-bit pixel, consisting of 3 samples for Red, Green, and Blue. In this particular diagram, the Red sample occupies 9 bits, the Green sample occupies 7 bits and the Blue sample occupies 8 bits, totaling 24 bits per pixel. Note that the samples do not have to be equal size and not all samples are mandatory in a pixel. Also, a pixel can consist of more than 3 samples (e.g. 4 samples of the RGBA color space). A sample is related to a subpixel on a physical display.

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  • Attack path management

    Attack path management

    Attack path management is a cybersecurity technique that involves the continuous discovery, mapping, and risk assessment of identity-based attack paths. Attack path management is distinct from other computer security mitigation strategies in that it does not rely on finding individual attack paths through vulnerabilities, exploits, or offensive testing. Rather, attack path management techniques analyze all attack paths present in an environment based on active identity management policies, authentication configurations, and active authenticated "sessions" between objects. == Overview == Attack path management relies on concepts such as mapping and removing attack paths, identifying attack path choke points, and remediation of attack paths. Identity-based attacks are present in most publicly disclosed breaches, whether through social engineering to gain initial access to Active Directories or lateral movement for privilege escalation. Attackers require privileges to attack an environment’s most sensitive segments. Attack path management often involves removing out-of-date privileges and privilege assignments given to overly large groups. In attack path management, attack graphs are used to represent how a network of machines’ security is vulnerable to attack. The nodes in an attack graph represent principals and other objects such as machines, accounts, and security groups. The edges in an attack graph represent the links and relationships between nodes. Some nodes are easy to penetrate due to short paths from regular users to domain admins, resulting in focal points of concentrated network traffic, which are known as attack path choke points. Attack graphs are often analyzed using algorithms and visualization. Attack path management also identifies tier 0 assets, which are considered the most vulnerable because they have direct or indirect control of an Active Directory or Microsoft Entra ID environment.

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  • Psychology in cybersecurity

    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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  • Parkerian Hexad

    Parkerian Hexad

    The Parkerian Hexad is a set of six elements of information security proposed by Donn B. Parker in 1998. The Parkerian Hexad adds three additional attributes to the three classic security attributes of the CIA triad (confidentiality, integrity, availability). The Parkerian Hexad attributes are the following: Confidentiality Possession or Control Integrity Authenticity Availability Utility These attributes of information are atomic in that they are not broken down into further constituents; they are non-overlapping in that they refer to unique aspects of information. Any information security breach can be described as affecting one or more of these fundamental attributes of information. == Attributes from the CIA triad == === Confidentiality === Confidentiality refers to the "quality or state of being private or secret; known only to a limited few", or "the property that information is not made available or disclosed to unauthorized individuals, entities, or processes". For example: If an enterprise's strategic plans are leaked to competitors then this is a breach of confidentiality; If unauthorized persons gain access to an individual's financial records then that individual's confidentiality is breached. === Integrity === Integrity refers to being correct or consistent with the intended state of information. Any unauthorized modification of data, whether deliberate or accidental, is a breach of data integrity. For example: Data stored on disk are expected to be stable. If the data is changed at random by problems with a disk controller then this is a breach of integrity; Data generated by a medical device is transmitted and stored in the healthcare center but neither altered nor tampered with; Application programs are supposed to record information correctly. If the application introduces deviations from the intended values then this is a breach of integrity. "From Donn Parker: My definition of information integrity comes from the dictionaries. Integrity means that the information is whole, sound, and unimpaired (not necessarily correct). It means nothing is missing from the information it is complete and in intended good order". === Availability === Availability means having timely access to information. For example: A disk crash or denial-of-service attacks both cause a breach of availability. Any delay in response of a system that exceeds the expected service levels for that system can be described as a breach of availability. GPS jamming can lead to loss of Availability of the GPS system. == Parker's added attributes == === Authenticity === Authenticity is the "quality of being authentic or of established authority for truth and correctness". Parker defines it thus: "is the information genuine and accurate? Does it conform to reality and have validity?" and "authoritative, valid, true, real, genuine, or worthy of acceptance or belief by reason of conformity to fact and reality". === Possession or control === Possession or control refers to the loss of data by the authorized user (even if the ʺthiefʺ cannot access the data). From a control systems perspective, it is any loss of control (the ability to change settings and functions) or loss of view (the ability to monitor the system’s operation and its response to controls). Suppose a thief were to steal a sealed envelope containing a bank debit card and its personal identification number. Even if the thief did not open that envelope, it's reasonable for the victim to be concerned that the thief could do so at any time. That situation illustrates a loss of control or possession of information but does not involve the breach of confidentiality. === Utility === Utility refers to the data's usefulness. For example: Suppose someone encrypted data on disk to prevent unauthorized access or undetected modifications–and then lost the decryption key: that would be a breach of utility. The data would be confidential, controlled, integral, authentic, and available–they just wouldn't be useful in that form. The conversion of salary data from one currency into an inappropriate currency would be a breach of utility, as would the storage of data in a format inappropriate for a specific computer architecture; e.g., EBCDIC instead of ASCII or 9-track magnetic tape instead of DVD-ROM. A tabular representation of data substituted for a graph could be described as a breach of utility if the substitution made it more difficult to interpret the data. Utility is often confused with availability because breaches such as those described in these examples may also require time to work around the change in data format or presentation. However, the concept of usefulness is distinct from that of availability.

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  • Jordan Antiquities Database and Information System

    Jordan Antiquities Database and Information System

    The Jordan Antiquities Database and Information System (JADIS) was a computer database of antiquities in Jordan, the first of its kind in the Arab world. It was established by the Department of Antiquities in 1990, in cooperation with the American Center for Oriental Research in Amman and sponsored by the United States Agency for International Development. JADIS was in use until 2002, when it was superseded by a new system, MEGA-J. Over 10,841 antiquities were registered in the database. An introduction and printed summary of the database was published by the Department of Antiquities in 1994, edited by Gaetano Palumbo.

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  • Computer Law & Security Review

    Computer Law & Security Review

    The Computer Law & Security Review is an international peer-reviewed journal published by Elsevier. It has been published six times a year since 1985 and is indexed in Scopus and SSCI. It is accessible to a wide range of professional legal and IT practitioners, businesses, academics, researchers, libraries and organisations in both the public and private sectors. The journal regularly covers: CLSR Briefing with special emphasis on UK/US developments European Union update National news from 10 European jurisdictions Pacific rim news column Refereed practitioner and academic papers on topics such as Web 2.0, IT security, Identity management, ID cards, RFID, interference with privacy, Internet law, telecoms regulation, online broadcasting, intellectual property, software law, e-commerce, outsourcing, data protection and freedom of information and many other topics. The Journal's Correspondent Panel includes more than 40 specialists in IT law and security. Each issue contains articles, case law analysis and current news on information and communications technology. Special Features High quality peer reviewed papers from internationally renowned practitioner and academic experts Latest developments reported in situ by more than 20 leading law firms from around the world Highly experienced and respected editor and correspondents panel Online access to all 23 volumes of CLSR with embedded web links to primary sources Contact details of all authors A pool of expertise that can collectively identify the key topics that need to be examined.

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  • Database virtualization

    Database virtualization

    Database virtualization is the decoupling of the database layer, which lies between the storage and application layers within the application stack. Virtualization of the database layer enables a shift away from the physical, toward the logical or virtual. Virtualization enables compute and storage resources to be pooled and allocated on demand. This enables both the sharing of single server resources for multi-tenancy, as well as the pooling of server resources into a single logical database or cluster. In both cases, database virtualization provides increased flexibility, more granular and efficient allocation of pooled resources, and more scalable computing. == Virtual data partitioning == The act of partitioning data stores as a database grows has been in use for several decades. There are two primary ways that data has been partitioned inside legacy data management systems: Shared-data databases: an architecture that assumes all database cluster nodes share a single partition. Inter-node communications are used to synchronize update activities performed by different nodes on the cluster. Shared-data data management systems are limited to single-digit node clusters. Shared-nothing databases: an architecture in which all data is segregated to internally managed partitions with clear, well-defined data location boundaries. Shared-nothing databases require manual partition management. In virtual partitioning, logical data is abstracted from physical data by autonomously creating and managing large numbers of data partitions (100s to 1000s). Because they are autonomously maintained, the resources required to manage the partitions are minimal. This kind of massive partitioning results in: Partitions that are small, efficiently managed, and load-balanced. Systems that do not require re-partitioning events to define additional partitions, even when the hardware is changed. “Shared-data” and “shared-nothing” architectures allow scalability through multiple data partitions and cross-partition querying and transaction processing without full partition scanning. == Horizontal data partitioning == Partitioning database sources from consumers is a fundamental concept. With greater numbers of database sources, inserting a horizontal data virtualization layer between the sources and consumers helps address this complexity. Rick van der Lans, the author of multiple books on SQL and relational databases, has defined data virtualization as "the process of offering data consumers a data access interface that hides the technical aspects of stored data, such as location, storage structure, API, access language, and storage technology." == Advantages == Added flexibility and agility for existing computing infrastructure. Enhanced database performance. Pooling and sharing computing resources, either splitting them (multi-tenancy) or combining them (clustering). Simplification of administration and management. Increased fault tolerance.

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  • Apptek

    Apptek

    Applications Technology (AppTek) is a U.S. company headquartered in McLean, Virginia that specializes in artificial intelligence and machine learning for human language technologies. The company provides both managed and professional services for natural language processing (NLP) technologies including automatic speech recognition (ASR), neural machine translation (MT), natural-language understanding (NLU) and neural speech synthesis. AppTek's Head of Science, Prof. Dr. -Ing Hermann Ney, was awarded the IEEE James L. Flanagan Speech and Audio Processing Award in 2019 and the ISCA Medal for Scientific Achievement in 2021 for his work in natural language processing. == History == AppTek was acquired in 1998 by Lernout & Hauspie (at the time a NASDAQ publicly traded company), AppTek organized a management buy-out and went private again in 2001. In 2014, the company sold its hybrid machine translation technology to eBay and has since rebuilt the platform to modern neural-based approaches for machine translation. In 2020, SOSi acquired non-controlling interest in AppTek and became an exclusive reseller of AppTek products for U.S. federal, state, and local government entities.

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  • Stencil buffer

    Stencil buffer

    A stencil buffer is an extra data buffer, in addition to the color buffer and Z-buffer, found on modern graphics hardware. The buffer is per pixel and works on integer values, usually with a depth of one byte per pixel. The Z-buffer and stencil buffer often share the same area in the RAM of the graphics hardware. In the simplest case, the stencil buffer is used to limit the area of rendering (stenciling). More advanced usage of the stencil buffer makes use of the strong connection between the Z-buffer and the stencil buffer in the rendering pipeline. For example, stencil values can be automatically increased/decreased for every pixel that fails or passes the depth test. The simple combination of depth test and stencil modifiers make a vast number of effects possible (such as stencil shadow volumes, Two-Sided Stencil, compositing, decaling, dissolves, fades, swipes, silhouettes, outline drawing, or highlighting of intersections between complex primitives) though they often require several rendering passes and, therefore, can put a heavy load on the graphics hardware. The most typical application is still to add shadows to 3D applications. It is also used for planar reflections. Other rendering techniques, such as portal rendering, use the stencil buffer in other ways; for example, it can be used to find the area of the screen obscured by a portal and re-render those pixels correctly. The stencil buffer and its modifiers can be accessed in computer graphics by using APIs like OpenGL, Direct3D, Vulkan or Metal. == Architecture == The stencil buffer typically shares the same memory space as the Z-buffer, and typically the ratio is 24 bits for Z-buffer + 8 bits for stencil buffer or, in the past, 15 bits for Z-buffer + 1 bit for stencil buffer. Another variant is 4 + 24, where 28 of the 32 bits are used and 4 ignored. Stencil and Z-buffers are part of the frame buffer, coupled to the color buffer. The first chip available to a wider market was 3Dlabs' Permedia II, which supported a one-bit stencil buffer. The bits allocated to the stencil buffer can be used to represent numerical values in the range [0, 2n-1], and also as a Boolean matrix (n is the number of allocated bits), each of which may be used to control the particular part of the scene. Any combination of these two ways of using the available memory is also possible. == Stencil test == Stencil test or stenciling is among the operations on the pixels/fragments (Per-pixel operations), located after the alpha test, and before the depth test. The stencil test ensures undesired pixels do not reach the depth test. This saves processing time for the scene. Similarly, the alpha test can prevent corresponding pixels to reach the stencil test. The test itself is carried out over the stencil buffer to some value in it, or altered or used it, and carried out through the so-called stencil function and stencil operations. The stencil function is a function by which the stencil value of a certain pixel is compared to a given reference value. If this comparison is logically true, the stencil test passes. Otherwise not. In doing so, the possible reaction caused by the result of comparing three different state-depth and stencil buffer: Stencil test is not passed Stencil test is passed but not the depth test Both tests are passed (or stencil test is passed, and the depth is not enabled) For each of these cases, different operations can be set over the examined pixel. In the OpenGL stencil functions, the reference value and mask, respectively, define the function glStencilFunc. In Direct3D each of these components is adjusted individually using methods SetRenderState devices currently in control. This method expects two parameters, the first of which is a condition that is set and the other its value. In the order that was used above, these conditions are called D3DRS_STENCILFUNC, D3DRS_STENCILREF, and D3DRS_STENCILMASK. Stencil operations in OpenGL adjust glStencilOp function that expects three values. In Direct3D, again, each state sets a specific method SetRenderState. The three states that can be assigned to surgery are called D3DRS_STENCILFAIL, D3DRENDERSTATE_STENCILZFAIL, and D3DRENDERSTATE_STENCILPASS. == Z-fighting == Due to the lack of precision in the Z-buffer, coplanar polygons that are short-range, or overlapping, can be portrayed as a single plane with a multitude of irregular cross-sections. These sections can vary depending on the camera position and other parameters and are rapidly changing. This is called Z-fighting. There exist multiple solutions to this issue: - Bring the far plane closer to restrict the scene's depth, thus increasing the accuracy of the Z-buffer, or reducing the distance at which objects are visible in the scene. - Increase the number of bits allocated to the Z-buffer, which is possible at the expense of memory for the stencil buffer. - Move polygons farther apart from one another, which restricts the possibilities for the artist to create an elaborate scene. All of these approaches to the problem can only reduce the likelihood that the polygons will experience Z-fighting, and do not guarantee a definitive solution in the general case. A solution that includes the stencil buffer is based on the knowledge of which polygon should be in front of the others. The silhouette of the front polygon is drawn into the stencil buffer. After that, the rest of the scene can be rendered only where the silhouette is negative, and so will not clash with the front polygon. == Shadow volume == Shadow volume is a technique used in 3D computer graphics to add shadows to a rendered scene. They were first proposed by Frank Crow in 1977 as the geometry describing the 3D shape of the region occluded from a light source. A shadow volume divides the virtual world in two: areas that are in shadow and areas that are not. The stencil buffer implementation of shadow volumes is generally considered among the most practical general-purpose real-time shadowing techniques for use on modern 3D graphics hardware. It has been popularised by the video game Doom 3, and a particular variation of the technique used in this game has become known as Carmack's Reverse. == Reflections == Reflection of a scene is drawn as the scene itself transformed and reflected relative to the "mirror" plane, which requires multiple render passes and using of stencil buffer to restrict areas where the current render pass works: Draw the scene excluding mirror areas – for each mirror lock the Z-buffer and color buffer Render visible part of the mirror Depth test is set up so that each pixel is passed to enter the maximum value and always passes for each mirror: Depth test is set so that it passes only if the distance of a pixel is less than the current (default behavior) The matrix transformation is changed to reflect the scene relative to the mirror plane Unlock the Z-buffer and color buffer Draw the scene, but only the part of it that lies between the mirror plane and the camera. In other words, a mirror plane is also a clipping plane Again locks color buffer, depth test is set so that it always passes, reset stencil for the next mirror. == Planar Shadows == While drawing a plane of shadows, there are two dominant problems: The first concerns the problem of deep struggle in case the flat geometry is not awarded on the part covered with the shadow of shadows and outside. See the section that relates to this. Another problem relates to the extent of the shadows outside the area where the plane there. Another problem, which may or may not appear, depending on the technique, the design of more polygons in one part of the shadow, resulting in darker and lighter parts of the same shade. All three problems can be solved geometrically, but because of the possibility that hardware acceleration is directly used, it is a far more elegant implementation using the stencil buffer: 1. Enable lights and the lights 2. Draw a scene without any polygon that should be projected shadows 3. Draw all polygons which should be projected shadows, but without lights. In doing so, the stencil buffer, the pixel of each polygon to be assigned to a specific value for the ground to which they belong. The distance between these values should be at least two, because for each plane to be used two values for two states: in the shadows and bright. 4. Disable any global illumination (to ensure that the next steps will affect only individual selected light) For each plane: For each light: 1. Edit a stencil buffer and only the pixels that carry a specific value for the selected level. Increase the value of all the pixels that are projected objects between the date of a given level and bright. 2. Allow only selected light for him to draw level at which part of her specific value was not changed. == Spatial shadows == Stencil buffer implementation of spatial drawing shadows is any shadow of a geometric body that its volume includes part of the scene that is

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  • Line Drawing System-1

    Line Drawing System-1

    LDS-1 (Line Drawing System-1) was a calligraphic (vector, rather than raster) display processor and display device created by Evans & Sutherland in 1969. This model was known as the first graphics device with a graphics processing unit. == Features == It was controlled by a variety of host computers. Straight lines were smoothly rendered in real-time animation. General principles of operation were similar to the systems used today: 4x4 transformation matrices, 1x4 vertices. Possible uses included flight simulation (in the product brochure there are screenshots of landing on a carrier), scientific imaging and GIS systems. == History == The first LDS-1 was shipped to the customer (BBN) in August 1969. Only a few of these systems were ever built. One was used by the Los Angeles Times as their first typesetting/layout computer. One went to NASA Ames Research Center for Human Factors Research. Another was bought by the Port Authority of New York to develop a tugboat pilot trainer for navigation in the harbor. The MIT Dynamic Modeling had one, and there was a program for viewing an ongoing game of Maze War.

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  • Stop Motion Studio

    Stop Motion Studio

    Stop Motion Studio is a stop motion animation software developed by Cateater LLC. It is available as both an app for iOS and Android and as a software for Windows and Mac. Two versions of the software exist, the standard Stop Motion Studio for free, and the paid Stop Motion Studio Pro, which contains extra, more advanced features. The software is commonly used in brickfilming.

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  • PDE surface

    PDE surface

    PDE surfaces are used in geometric modelling and computer graphics for creating smooth surfaces conforming to a given boundary configuration. PDE surfaces use partial differential equations to generate a surface which usually satisfy a mathematical boundary value problem. PDE surfaces were first introduced into the area of geometric modelling and computer graphics by two British mathematicians, Malcolm Bloor and Michael Wilson. == Technical details == The PDE method involves generating a surface for some boundary by means of solving an elliptic partial differential equation of the form ( ∂ 2 ∂ u 2 + a 2 ∂ 2 ∂ v 2 ) 2 X ( u , v ) = 0. {\displaystyle \left({\frac {\partial ^{2}}{\partial u^{2}}}+a^{2}{\frac {\partial ^{2}}{\partial v^{2}}}\right)^{2}X(u,v)=0.} Here X ( u , v ) {\displaystyle X(u,v)} is a function parameterised by the two parameters u {\displaystyle u} and v {\displaystyle v} such that X ( u , v ) = ( x ( u , v ) , y ( u , v ) , z ( u , v ) ) {\displaystyle X(u,v)=(x(u,v),y(u,v),z(u,v))} where x {\displaystyle x} , y {\displaystyle y} and z {\displaystyle z} are the usual cartesian coordinate space. The boundary conditions on the function X ( u , v ) {\displaystyle X(u,v)} and its normal derivatives ∂ X / ∂ n {\displaystyle \partial {X}/\partial {n}} are imposed at the edges of the surface patch. With the above formulation it is notable that the elliptic partial differential operator in the above PDE represents a smoothing process in which the value of the function at any point on the surface is, in some sense, a weighted average of the surrounding values. In this way, a surface is obtained as a smooth transition between the chosen set of boundary conditions. The parameter a {\displaystyle a} is a special design parameter which controls the relative smoothing of the surface in the u {\displaystyle u} and v {\displaystyle v} directions. When a = 1 {\displaystyle a=1} , the PDE is the biharmonic equation: X u u u u + 2 X u u v v + X v v v v = 0 {\displaystyle X_{uuuu}+2X_{uuvv}+X_{vvvv}=0} . The biharmonic equation is the equation produced by applying the Euler-Lagrange equation to the simplified thin plate energy functional X u u 2 + 2 X u v 2 + X v v 2 {\displaystyle X_{uu}^{2}+2X_{uv}^{2}+X_{vv}^{2}} . So solving the PDE with a = 1 {\displaystyle a=1} is equivalent to minimizing the thin plate energy functional subject to the same boundary conditions. == Applications == PDE surfaces can be used in many application areas. These include computer-aided design, interactive design, parametric design, computer animation, computer-aided physical analysis and design optimisation. == Related publications == M.I.G. Bloor and M.J. Wilson, Generating Blend Surfaces using Partial Differential Equations, Computer Aided Design, 21(3), 165–171, (1989). H. Ugail, M.I.G. Bloor, and M.J. Wilson, Techniques for Interactive Design Using the PDE Method, ACM Transactions on Graphics, 18(2), 195–212, (1999). J. Huband, W. Li and R. Smith, An Explicit Representation of Bloor-Wilson PDE Surface Model by using Canonical Basis for Hermite Interpolation, Mathematical Engineering in Industry, 7(4), 421-33 (1999). H. Du and H. Qin, Direct Manipulation and Interactive Sculpting of PDE surfaces, Computer Graphics Forum, 19(3), C261-C270, (2000). H. Ugail, Spine Based Shape Parameterisations for PDE surfaces, Computing, 72, 195–204, (2004). L. You, P. Comninos, J.J. Zhang, PDE Blending Surfaces with C2 Continuity, Computers and Graphics, 28(6), 895–906, (2004).

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  • Tandem Money

    Tandem Money

    Tandem is one of the UK's original challenger banks. Tandem is a digital bank with a mobile app, and no branches. The acquisition of Harrods Bank in 2017 allowed the company to provide services using the former's banking licence. Tandem Bank Limited is authorised by the Prudential Regulation Authority and regulated by the Financial Conduct Authority. Tandem has offices across the UK in Blackpool, Cardiff, Durham and London, employing over 500 people. == History == The company was founded by Ricky Knox, Matt Cooper and Michael Kent in 2014. In December 2016, Tandem announced that it had secured a £35 million investment from The Sanpower Group, the Chinese company that also owned the department store House of Fraser; however, £29 million of this investment was later revoked by Sanpower over concerns that the Chinese Government would object to the investment following increased restrictions on outbound investment in China. This resulted in a delay in the launch of Tandem's savings products, which, at the time of the revocation, was expected imminently and, more importantly, meant that Tandem volunteered the return of their banking license but retained all other permissions. In April 2018, Tandem launched fixed-term savings accounts, offering one-, two- and three-year terms through its app. === Acquisitions === In August 2017, it was announced that Tandem would fully acquire Harrods Bank, founded in 1893, in a deal that would bring a near-£200m loan book, over £300m of deposits and nearly £80 million of capital. Prior to its sale to Tandem Money, Harrods Bank catered for high-net-worth (HNW) individuals and operated from the Harrods store in Knightsbridge, London. It offered a variety of personal and business current and savings accounts, mortgages, foreign currency and gold bullion trading services. On 7 August 2017, Tandem Money Limited announced a deal to acquire 100% of Harrods Bank Limited shares. The purchase deal closed successfully on 11 January 2018. In March 2018, Tandem agreed to acquire Pariti Technologies Limited, developers of the Pariti money management application. In August 2020 Tandem acquired green home improvement loan specialists Allium Lending Group. It was announced on 8 February 2021 that Tandem had agreed to purchase the mortgage book from private bank Bank and Clients, consisting of 300 B&C customers for an undisclosed amount. In January 2022 Tandem Bank acquired consumer lender Oplo, creating a combined business with £1.2 billion of total assets. In April 2023, it was announced that Tandem had acquired money-sharing app Loop Money. At the time of the purchase, one of Loop's founders – Paul Pester – was also chairman at Tandem. == Features == Tandem Bank offers customers savings, mortgages, personal and secured loans, green home improvement loans and motor finance. In November 2022, the bank launched its new Tandem Marketplace, providing information and resources to help promote greener living.

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  • Hit-testing

    Hit-testing

    In computer graphics programming, hit-testing (hit detection, picking, or pick correlation) is the process of determining whether a user-controlled cursor (such as a mouse cursor or touch-point on a touch-screen interface) intersects a given graphical object (such as a shape, line, or curve) drawn on the screen. Hit-testing may be performed on the movement or activation of a mouse or other pointing device. Hit-testing is used by GUI environments to respond to user actions, such as selecting a menu item or a target in a game based on its visual location. In web programming languages such as HTML, SVG, and CSS, this is associated with the concept of pointer-events (e.g. user-initiated cursor movement or object selection). Collision detection is a related concept for detecting intersections of two or more different graphical objects, rather than intersection of a cursor with one or more graphical objects. == Algorithm == There are many different algorithms that may be used to perform hit-testing, with different performance or accuracy outcomes. One common hit-test algorithm for axis aligned bounding boxes. A key idea is that the box being tested must be either entirely above, entirely below, entirely to the right or left of the current box. If this is not possible, they are colliding. Example logic is presented in the pseudo-code below: In Python:

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