In computer science, learning vector quantization (LVQ) is a prototype-based supervised classification algorithm. LVQ is the supervised counterpart of vector quantization systems. LVQ can be understood as a special case of an artificial neural network, more precisely, it applies a winner-take-all Hebbian learning-based approach. It is a precursor to self-organizing maps (SOM) and related to neural gas and the k-nearest neighbor algorithm (k-NN). LVQ was invented by Teuvo Kohonen. == Definition == An LVQ system is represented by prototypes W = ( w ( i ) , . . . , w ( n ) ) {\displaystyle W=(w(i),...,w(n))} which are defined in the feature space of observed data. In winner-take-all training algorithms one determines, for each data point, the prototype which is closest to the input according to a given distance measure. The position of this so-called winner prototype is then adapted, i.e. the winner is moved closer if it correctly classifies the data point or moved away if it classifies the data point incorrectly. An advantage of LVQ is that it creates prototypes that are easy to interpret for experts in the respective application domain. LVQ systems can be applied to multi-class classification problems in a natural way. A key issue in LVQ is the choice of an appropriate measure of distance or similarity for training and classification. Recently, techniques have been developed which adapt a parameterized distance measure in the course of training the system, see e.g. (Schneider, Biehl, and Hammer, 2009) and references therein. LVQ can be a valuable aid in classifying text documents. == Algorithm == The algorithms are presented as in. Set up: Let the data be denoted by x i ∈ R D {\displaystyle x_{i}\in \mathbb {R} ^{D}} , and their corresponding labels by y i ∈ { 1 , 2 , … , C } {\displaystyle y_{i}\in \{1,2,\dots ,C\}} . The complete dataset is { ( x i , y i ) } i = 1 N {\displaystyle \{(x_{i},y_{i})\}_{i=1}^{N}} . The set of code vectors is w j ∈ R D {\displaystyle w_{j}\in \mathbb {R} ^{D}} . The learning rate at iteration step t {\displaystyle t} is denoted by α t {\displaystyle \alpha _{t}} . The hyperparameters w {\displaystyle w} and ϵ {\displaystyle \epsilon } are used by LVQ2 and LVQ3. The original paper suggests ϵ ∈ [ 0.1 , 0.5 ] {\displaystyle \epsilon \in [0.1,0.5]} and w ∈ [ 0.2 , 0.3 ] {\displaystyle w\in [0.2,0.3]} . === LVQ1 === Initialize several code vectors per label. Iterate until convergence criteria is reached. Sample a datum x i {\displaystyle x_{i}} , and find out the code vector w j {\displaystyle w_{j}} , such that x i {\displaystyle x_{i}} falls within the Voronoi cell of w j {\displaystyle w_{j}} . If its label y i {\displaystyle y_{i}} is the same as that of w j {\displaystyle w_{j}} , then w j ← w j + α t ( x i − w j ) {\displaystyle w_{j}\leftarrow w_{j}+\alpha _{t}(x_{i}-w_{j})} , otherwise, w j ← w j − α t ( x i − w j ) {\displaystyle w_{j}\leftarrow w_{j}-\alpha _{t}(x_{i}-w_{j})} . === LVQ2 === LVQ2 is the same as LVQ3, but with this sentence removed: "If w j {\displaystyle w_{j}} and w k {\displaystyle w_{k}} and x i {\displaystyle x_{i}} have the same class, then w j ← w j − α t ( x i − w j ) {\displaystyle w_{j}\leftarrow w_{j}-\alpha _{t}(x_{i}-w_{j})} and w k ← w k + α t ( x i − w k ) {\displaystyle w_{k}\leftarrow w_{k}+\alpha _{t}(x_{i}-w_{k})} .". If w j {\displaystyle w_{j}} and w k {\displaystyle w_{k}} and x i {\displaystyle x_{i}} have the same class, then nothing happens. === LVQ3 === Initialize several code vectors per label. Iterate until convergence criteria is reached. Sample a datum x i {\displaystyle x_{i}} , and find out two code vectors w j , w k {\displaystyle w_{j},w_{k}} closest to it. Let d j := ‖ x i − w j ‖ , d k := ‖ x i − w k ‖ {\displaystyle d_{j}:=\|x_{i}-w_{j}\|,d_{k}:=\|x_{i}-w_{k}\|} . If min ( d j d k , d k d j ) > s {\displaystyle \min \left({\frac {d_{j}}{d_{k}}},{\frac {d_{k}}{d_{j}}}\right)>s} , where s = 1 − w 1 + w {\displaystyle s={\frac {1-w}{1+w}}} , then If w j {\displaystyle w_{j}} and x i {\displaystyle x_{i}} have the same class, and w k {\displaystyle w_{k}} and x i {\displaystyle x_{i}} have different classes, then w j ← w j + α t ( x i − w j ) {\displaystyle w_{j}\leftarrow w_{j}+\alpha _{t}(x_{i}-w_{j})} and w k ← w k − α t ( x i − w k ) {\displaystyle w_{k}\leftarrow w_{k}-\alpha _{t}(x_{i}-w_{k})} . If w k {\displaystyle w_{k}} and x i {\displaystyle x_{i}} have the same class, and w j {\displaystyle w_{j}} and x i {\displaystyle x_{i}} have different classes, then w j ← w j − α t ( x i − w j ) {\displaystyle w_{j}\leftarrow w_{j}-\alpha _{t}(x_{i}-w_{j})} and w k ← w k + α t ( x i − w k ) {\displaystyle w_{k}\leftarrow w_{k}+\alpha _{t}(x_{i}-w_{k})} . If w j {\displaystyle w_{j}} and w k {\displaystyle w_{k}} and x i {\displaystyle x_{i}} have the same class, then w j ← w j − ϵ α t ( x i − w j ) {\displaystyle w_{j}\leftarrow w_{j}-\epsilon \alpha _{t}(x_{i}-w_{j})} and w k ← w k + ϵ α t ( x i − w k ) {\displaystyle w_{k}\leftarrow w_{k}+\epsilon \alpha _{t}(x_{i}-w_{k})} . If w k {\displaystyle w_{k}} and x i {\displaystyle x_{i}} have different classes, and w j {\displaystyle w_{j}} and x i {\displaystyle x_{i}} have different classes, then the original paper simply does not explain what happens in this case, but presumably nothing happens in this case. Otherwise, skip. Note that condition min ( d j d k , d k d j ) > s {\displaystyle \min \left({\frac {d_{j}}{d_{k}}},{\frac {d_{k}}{d_{j}}}\right)>s} , where s = 1 − w 1 + w {\displaystyle s={\frac {1-w}{1+w}}} , precisely means that the point x i {\displaystyle x_{i}} falls between two Apollonian spheres.
Neural radiance field
A neural radiance field (NeRF) is a neural field for reconstructing a three-dimensional representation of a scene from two-dimensional images. The NeRF model enables downstream applications of novel view synthesis, scene geometry reconstruction, and obtaining the reflectance properties of the scene. Additional scene properties such as camera poses may also be jointly learned. First introduced in 2020, it has since gained significant attention for its potential applications in computer graphics and content creation. == Algorithm == The NeRF algorithm represents a scene as a radiance field parametrized by a deep neural network (DNN). The network predicts a volume density and view-dependent emitted radiance given the spatial location ( x , y , z ) {\displaystyle (x,y,z)} and viewing direction in Euler angles ( θ , Φ ) {\displaystyle (\theta ,\Phi )} of the camera. By sampling many points along camera rays, traditional volume rendering techniques can produce an image. === Data collection === A NeRF needs to be retrained for each unique scene. The first step is to collect images of the scene from different angles and their respective camera pose. These images are standard 2D images and do not require a specialized camera or software. Any camera is able to generate datasets, provided the settings and capture method meet the requirements for SfM (Structure from Motion). This requires tracking of the camera position and orientation, often through some combination of SLAM, GPS, or inertial estimation. Researchers often use synthetic data to evaluate NeRF and related techniques. For such data, images (rendered through traditional non-learned methods) and respective camera poses are reproducible and error-free. === Training === For each sparse viewpoint (image and camera pose) provided, camera rays are marched through the scene, generating a set of 3D points with a given radiance direction (into the camera). For these points, volume density and emitted radiance are predicted using the multi-layer perceptron (MLP). An image is then generated through classical volume rendering. Because this process is fully differentiable, the error between the predicted image and the original image can be minimized with gradient descent over multiple viewpoints, encouraging the MLP to develop a coherent model of the scene. == Variations and improvements == Early versions of NeRF were slow to optimize and required that all input views were taken with the same camera in the same lighting conditions. These performed best when limited to orbiting around individual objects, such as a drum set, plants or small toys. Since the original paper in 2020, many improvements have been made to the NeRF algorithm, with variations for special use cases. === Fourier feature mapping === In 2020, shortly after the release of NeRF, the addition of Fourier Feature Mapping improved training speed and image accuracy. Deep neural networks struggle to learn high frequency functions in low dimensional domains; a phenomenon known as spectral bias. To overcome this shortcoming, points are mapped to a higher dimensional feature space before being fed into the MLP. γ ( v ) = [ a 1 cos ( 2 π B 1 T v ) a 1 sin ( 2 π B 1 T v ) ⋮ a m cos ( 2 π B m T v ) a m sin ( 2 π B m T v ) ] {\displaystyle \gamma (\mathrm {v} )={\begin{bmatrix}a_{1}\cos(2{\pi }{\mathrm {B} }_{1}^{T}\mathrm {v} )\\a_{1}\sin(2\pi {\mathrm {B} }_{1}^{T}\mathrm {v} )\\\vdots \\a_{m}\cos(2{\pi }{\mathrm {B} }_{m}^{T}\mathrm {v} )\\a_{m}\sin(2{\pi }{\mathrm {B} }_{m}^{T}\mathrm {v} )\end{bmatrix}}} Where v {\displaystyle \mathrm {v} } is the input point, B i {\displaystyle \mathrm {B} _{i}} are the frequency vectors, and a i {\displaystyle a_{i}} are coefficients. This allows for rapid convergence to high frequency functions, such as pixels in a detailed image. === Bundle-adjusting neural radiance fields === One limitation of NeRFs is the requirement of knowing accurate camera poses to train the model. Often times, pose estimation methods are not completely accurate, nor is the camera pose even possible to know. These imperfections result in artifacts and suboptimal convergence. So, a method was developed to optimize the camera pose along with the volumetric function itself. Called Bundle-Adjusting Neural Radiance Field (BARF), the technique uses a dynamic low-pass filter (DLPF) to go from coarse to fine adjustment, minimizing error by finding the geometric transformation to the desired image. This corrects imperfect camera poses and greatly improves the quality of NeRF renders. === Multiscale representation === Conventional NeRFs struggle to represent detail at all viewing distances, producing blurry images up close and overly aliased images from distant views. In 2021, researchers introduced a technique to improve the sharpness of details at different viewing scales known as mip-NeRF (comes from mipmap). Rather than sampling a single ray per pixel, the technique fits a gaussian to the conical frustum cast by the camera. This improvement effectively anti-aliases across all viewing scales. mip-NeRF also reduces overall image error and is faster to converge at about half the size of ray-based NeRF. === Learned initializations === In 2021, researchers applied meta-learning to assign initial weights to the MLP. This rapidly speeds up convergence by effectively giving the network a head start in gradient descent. Meta-learning also allowed the MLP to learn an underlying representation of certain scene types. For example, given a dataset of famous tourist landmarks, an initialized NeRF could partially reconstruct a scene given one image. === NeRF in the wild === Conventional NeRFs are vulnerable to slight variations in input images (objects, lighting) often resulting in ghosting and artifacts. As a result, NeRFs struggle to represent dynamic scenes, such as bustling city streets with changes in lighting and dynamic objects. In 2021, researchers at Google developed a new method for accounting for these variations, named NeRF in the Wild (NeRF-W). This method splits the neural network (MLP) into three separate models. The main MLP is retained to encode the static volumetric radiance. However, it operates in sequence with a separate MLP for appearance embedding (changes in lighting, camera properties) and an MLP for transient embedding (changes in scene objects). This allows the NeRF to be trained on diverse photo collections, such as those taken by mobile phones at different times of day. === Relighting === In 2021, researchers added more outputs to the MLP at the heart of NeRFs. The output now included: volume density, surface normal, material parameters, distance to the first surface intersection (in any direction), and visibility of the external environment in any direction. The inclusion of these new parameters lets the MLP learn material properties, rather than pure radiance values. This facilitates a more complex rendering pipeline, calculating direct and global illumination, specular highlights, and shadows. As a result, the NeRF can render the scene under any lighting conditions with no re-training. === Plenoctrees === Although NeRFs had reached high levels of fidelity, their costly compute time made them useless for many applications requiring real-time rendering, such as VR/AR and interactive content. Introduced in 2021, Plenoctrees (plenoptic octrees) enabled real-time rendering of pre-trained NeRFs through division of the volumetric radiance function into an octree. Rather than assigning a radiance direction into the camera, viewing direction is taken out of the network input and spherical radiance is predicted for each region. This makes rendering over 3000x faster than conventional NeRFs. === Sparse Neural Radiance Grid === Similar to Plenoctrees, this method enabled real-time rendering of pretrained NeRFs. To avoid querying the large MLP for each point, this method bakes NeRFs into Sparse Neural Radiance Grids (SNeRG). A SNeRG is a sparse voxel grid containing opacity and color, with learned feature vectors to encode view-dependent information. A lightweight, more efficient MLP is then used to produce view-dependent residuals to modify the color and opacity. To enable this compressive baking, small changes to the NeRF architecture were made, such as running the MLP once per pixel rather than for each point along the ray. These improvements make SNeRG extremely efficient, outperforming Plenoctrees. === Instant NeRFs === In 2022, researchers at Nvidia enabled real-time training of NeRFs through a technique known as Instant Neural Graphics Primitives. An innovative input encoding reduces computation, enabling real-time training of a NeRF, an improvement orders of magnitude above previous methods. The speedup stems from the use of spatial hash functions, which have O ( 1 ) {\displaystyle O(1)} access times, and parallelized architectures which run fast on modern GPUs. == Related techniques == === Plenoxels === Plen
Graphics address remapping table
The graphics address remapping table (GART), also known as the graphics aperture remapping table, or graphics translation table (GTT), is an I/O memory management unit (IOMMU) used by Accelerated Graphics Port (AGP) and PCI Express (PCIe) graphics cards. The GART allows the graphics card direct memory access (DMA) to the host system memory, through which buffers of textures, polygon meshes and other data are loaded. AMD later reused the same mechanism for I/O virtualization with other peripherals including disk controllers and network adapters. A GART is used as a means of data exchange between the main memory and video memory through which buffers (i.e. paging/swapping) of textures, polygon meshes and other data are loaded, but can also be used to expand the amount of video memory available for systems with only integrated or shared graphics (i.e. no discrete or inbuilt graphics processor), such as Intel HD Graphics processors. However, this type of memory (expansion) remapping has a caveat that affects the entire system: specifically, any GART, pre-allocated memory becomes pooled and cannot be utilised for any other purposes but graphics memory and display rendering. Since PCI Express, the GART is extended to the GTT (Graphics Translation Table), which act as a buffer or cache between system memory and graphics card, and in PCI Express, the GTT buffer size is changeable by the GPU driver. == Operating system support == === Windows === Support for AGP GART was added since Windows 95 OSR2. Later, support for GTT was added since Windows XP SP2 and Windows Vista. === Linux === Jeff Hartmann served as the primary maintainer of the Linux kernel's agpgart driver, which began as part of Brian Paul's Utah GLX accelerated Mesa 3D driver project. The developers primarily targeted Linux 2.4.x kernels, but made patches available against older 2.2.x kernels. Dave Jones heavily reworked agpgart for the Linux 2.6.x kernels, along with more contributions from Jeff Hartmann. === FreeBSD === In FreeBSD, the agpgart driver appeared in its 4.1 release. === Solaris === AGPgart support was introduced into Solaris Express Developer Edition as of its 7/05 release.
Distinguishable interfaces
Distinguishable interfaces use computer graphic principles to automatically generate easily distinguishable appearance for computer data. Although the desktop metaphor revolutionized user interfaces, there is evidence that a spatial layout alone does little to help in locating files and other data; distinguishable appearance is also required. Studies have shown that average users have considerable difficulty finding files on their personal computers, even ones that they created the same day. Search engines do not always help, since it has been found that users often know of the existence of a file without being able to specify relevant search terms. On the contrary, people appear to incrementally search for files using some form of context. Recently researchers and web developers have argued that the problem is the lack of distinguishable appearance: in the traditional computer interface most objects and locations appear identical. This problem rarely occurs in the real world, where both objects and locations generally have easily distinguishable appearance. Discriminability was one of the recommendations in the ISO 9241-12 recommendation on presentation of information on visual displays (part of the overall report on Ergonomics of Human System Interaction), however it was assumed in that report that this would be achieved by manual design of graphical symbols. == VisualIDs, semanticons, and identicons == The mass availability of computer graphics supported the introduction of approaches that make better use of the brain's "visual hardware", by providing individual files and other abstract data with distinguishable appearance. This idea initially appeared in strictly academic VisualIDs and Semanticons works, but the web community has explored and rapidly adopted similar ideas, such as the Identicon. The VisualIDs project automatically generated icons for files or other data based on a hash of the data identifier, so the icons had no relation to the content or meaning of the data. It was argued not only that generating meaningful icons is unnecessary (their user study showed rapid learning of the arbitrary icons), but also that basing icons on content is actually incorrect ("contrasting visualization with visual identifiers"). The Semanticons project developed by Setlur et al. demonstrated an algorithm to create icons that reflect the content of files. In this work the name, location and content of a file are parsed and used to retrieve related image(s) from an image database. These are then processed using a Non-photorealistic rendering technique in order to generate graphical icons. Developer Don Park introduced the identicon library for making a visual icon from a hash of a data identifier. This initial public implementation has spawned a large number of implementations for various environments. In particular, identicons are now being used as default visual user identifiers (avatars) for several widely used systems. They are also used as a complement to Gravatars, which are pre-existing avatar images created or chosen by users, instead of automatically generated images. (see #External links). == Current research == While current web practice has followed the semantics-free approach of VisualIDs, recent research has followed the semantics-based approach of Semanticons. Examples include using data mining principles to automatically create "intelligent icons" that reflect the contents of files and creating icons for music files that reflect audio characteristics or affective content.
Comparison of operating systems
These tables provide a comparison of operating systems, of computer devices, as listing general and technical information for a number of widely used and currently available PC or handheld (including smartphone and tablet computer) operating systems. The article "Usage share of operating systems" provides a broader, and more general, comparison of operating systems that includes servers, mainframes and supercomputers. Because of the large number and variety of available Linux distributions, they are all grouped under a single entry; see comparison of Linux distributions for a detailed comparison. There is also a variety of BSD and DOS operating systems, covered in comparison of BSD operating systems and comparison of DOS operating systems. == Nomenclature == The nomenclature for operating systems varies among providers and sometimes within providers. For purposes of this article the terms used are; kernel In some operating systems, the OS is split into a low level region called the kernel and higher level code that relies on the kernel. Typically the kernel implements processes but its code does not run as part of a process. hybrid kernel monolithic kernel Nucleus In some operating systems there is OS code permanently present in a contiguous region of memory addressable by unprivileged code; in IBM systems this is typically referred to as the nucleus. The nucleus typically contains both code that requires special privileges and code that can run in an unprivileged state. Typically some code in the nucleus runs in the context of a dispatching unit, e.g., address space, process, task, thread, while other code runs independent of any dispatching unit. In contemporary operating systems unprivileged applications cannot alter the nucleus. License and pricing policies vary widely among different systems. Among others, the tables below use the following terms: BSD BSD licenses are a family of permissive free software licenses, imposing minimal restrictions on the use and distribution of covered software. bundled The fee is included in the price of the hardware == General information == == Technical information == == Security == == Commands == For POSIX compliant (or partly compliant) systems like FreeBSD, Linux, macOS or Solaris, the basic commands are the same because they are standardized. NOTE: Linux systems may vary by distribution which specific program, or even 'command' is called, via the POSIX alias function. For example, if you wanted to use the DOS dir to give you a directory listing with one detailed file listing per line you could use alias dir='ls -lahF' (e.g. in a session configuration file).
MoFA Mitra
MoFA Mitra is a mobile application launched by the Ministry of Foreign Affairs of Nepal to provide digital consular services, emergency support, rescue coordination, and complaint registration facilities for Nepali citizens living and working abroad. The application allows Nepali migrant workers, students, tourists, and Non-Resident Nepalis (NRNs) to access embassy services, emergency help, and official information directly from their smartphones. == Background == The need for a centralized digital support platform for Nepalis abroad had been discussed for several years due to increasing complaints related to labor exploitation, rescue delays, documentation problems, and lack of communication with Nepali diplomatic missions. Media organizations and migrant rights advocates had continuously highlighted issues faced by Nepali workers abroad, including human trafficking, fraudulent recruitment, delayed repatriation, and difficulties in receiving emergency assistance. In response, the Ministry of Foreign Affairs developed the MoFA Mitra app to digitize complaint handling, improve communication between embassies and citizens, and make emergency response faster and more accessible. == Features == The app includes several services and features for Nepali citizens abroad, including complaint registration, rescue coordination, embassy communication, and digital consular support services. Features of the application include: Online complaint registration Emergency rescue request system Direct contact with Nepali embassies and consulates Digital consular information Passport and document-related assistance Labor and migration support information Emergency hotline access Real-time notifications and alerts Location-based embassy information Tracking and coordination support for stranded citizens According to reports, the application was designed to simplify access to diplomatic services and strengthen emergency response coordination for Nepalis abroad. == Launch == The application was officially launched by Nepal’s Ministry of Foreign Affairs in Kathmandu in May 2026. Government officials stated that the app would strengthen Nepal’s digital governance system and improve support mechanisms for Nepali citizens residing overseas. Officials said the platform would help improve communication between Nepali diplomatic missions and citizens during emergencies and rescue operations. == Reception == The launch of the app received positive coverage from Nepali and international media outlets. Commentators described the initiative as a significant step toward modernization of Nepal’s diplomatic and consular services and digital governance infrastructure. Some observers also emphasized the importance of effective implementation, rapid response mechanisms, and continuous monitoring to ensure practical benefits for migrant workers abroad.
Tokken
Tokken is a payment system and mobile app most known for being a legal and secure option for businesses transactions within the cannabis industry, because of its compliance with bank requirements. The startup company was created by Lamine Zarrad, a former regulator at the Office of the Comptroller of the Currency. == Operability == In order for a person to start using the app, they need to provide evidence, in the form of bioidentification data and mobile carrier records, that they can legally purchase weed. After they have been verified, customers can pay directly through the app at any dispensary that is using Tokken. Tokken turns credit card transactions into a digital token, which can be exchanged back for money that can later be deposited into a bank account. All transactions are logged publicly through a blockchain leger, making the process both anonymous and verified. === Banking services === Tokken has a "pay taxes" function which enables dispensaries to pay their taxes directly to the department.