Pattern theory, formulated by Ulf Grenander, is a mathematical formalism to describe knowledge of the world as patterns. It differs from other approaches to artificial intelligence in that it does not begin by prescribing algorithms and machinery to recognize and classify patterns; rather, it prescribes a vocabulary to articulate and recast the pattern concepts in precise language. Broad in its mathematical coverage, Pattern Theory spans algebra and statistics, as well as local topological and global entropic properties. In addition to the new algebraic vocabulary, its statistical approach is novel in its aim to: Identify the hidden variables of a data set using real world data rather than artificial stimuli, which was previously commonplace. Formulate prior distributions for hidden variables and models for the observed variables that form the vertices of a Gibbs-like graph. Study the randomness and variability of these graphs. Create the basic classes of stochastic models applied by listing the deformations of the patterns. Synthesize (sample) from the models, not just analyze signals with them. The Brown University Pattern Theory Group was formed in 1972 by Ulf Grenander. Many mathematicians are currently working in this group, noteworthy among them being the Fields Medalist David Mumford. Mumford regards Grenander as his "guru" in Pattern Theory.
TimeTiger
TimeTiger is a time and project tracking app developed by Indigo Technologies Ltd. in Toronto, Ontario, Canada. Indigo was founded in 1997 and initially released TimeTiger in 1998. == Company == The company was incorporated in 1997 and began operations as a custom software developer. TimeTiger (internally called TaskMaster) was developed as a tool to help with Indigo's own project planning and estimating. After releasing TimeTiger as a commercial product in 1998, Indigo shifted its focus to time and project management solutions. TimeTiger first introduced support for web-based time logging in 2000, to appeal to workers who were not already tracking their time for billing reasons. Subsequent development emphasized project analysis tools. == Features == Web-based electronic time log "To Do" list to monitor project and non-project activities Pivot table report designer Role-based access control == Software integration == Reports can be exported to Microsoft Excel or saved as Excel-compatible HTML files. Microsoft Project files can be imported and exported. A Software Development Kit is available.
Mini-STX
Mini-STX (mSTX, Mini Socket Technology EXtended, originally "Intel 5x5") is a computer motherboard form factor that was released by Intel in 2015 (as "Intel 5x5"). These motherboards measure 147mm by 140mm (5.8" x 5.5"), making them larger than "4x4" NUC (102x102mm / 4.01" x 4.01" inches) and Nano-ITX (120x120mm / 4.7" x 4.7") boards, but notably smaller than the more common Mini-ITX (170x170mm / 6.7" x 6.7") boards. Unlike these standards, which use a square shape, the Mini-STX form factor is 7mm longer from front-to-rear, making it slightly rectangular. == Mini-STX design elements == The Mini-STX design suggests (but does not require) support for: Socketed processors (e.g. LGA or PGA CPUs) Onboard power regulation circuitry, enabling direct DC power input IO ports embedded on the front and rear of the motherboard (akin to NUC, but unlike typical motherboards which often use headers instead to connect built-in ports on enclosures) == Adoption by manufacturers == This motherboard form factor is still not in particularly common use with consumer-PC manufacturers, although there are a few offerings: ASRock offers both DeskMini kits (that use mini-STX boards) and standalone motherboards, Asus offer VivoMini kits (that use mini-STX boards) and standalone motherboards, Gigabyte offers a few motherboards, and industrial PC suppliers (e.g. Kontron, Iesy, ASRock Industrial) also provide some options for mini-STX equipment. == Derivatives == ASRock developed a derivative of mini-STX, dubbed micro-STX, for their 'DeskMini GTX/RX' small form-factor PCs and industrial motherboards. Micro-STX adds an MXM slot which allows the use of special PCI Express expansion cards, including graphics or machine learning accelerators, but increases the width of the board to be extended two inches, resulting in measurements of 147 x 188 mm (5.8" x 7.4")
Computer aided transceiver
Computer aided transceiver (CAT) is a non-generic serial protocol used by radio amateurs for (remotely) controlling a transceiver radio receiver equipment using a computer. Conventional transmitters are manually controlled and used to transmit voice using buttons, dials, etc. However, advances in electronics have come to market devices that can be controlled by a computer and allow digital modes such as packet radio and also the use of satellite tracking, because it can continuously change the device's frequency according to the Doppler effect. This is done by connecting a Radio receiver and a PC using a CAT interface and a CAT Program Additionally, CAT interfaces can also be used to position tracking antennas, in controllers. As a satellite moves overhead. A CAT interface is a piece of hardware that connects the PC and radio that provides a connection to allows the radio and the PC to communicate with each other. The CAT interface provides the signals to and fro via correct voltage levels and in the case of a Universal Serial Bus (USB) CAT interface it requires a "protocol" for communication but communication itself is down to the radio and the software on the PC. Software that may be called a CAT program allows a radio to be controlled through the PC. Changes made on the radio through user interactions on the CAT Program are (generally) shown on the PC's screen. The functionality of CAT equipment (software & interface) depends on the radio and what features the software writers included in the CAT software. Modern radio systems do have more CAT functionality If you run a logging program that supports CAT, then that software may take advantage of the CAT system by retrieving information from the radio to help fill in log details, such as the frequency that the contact was made. CAT is also useful on many radios where there are many sub-menus in the radios menu system, and many of the sub-menu items can be easily changed via the PC. On many HF radios, the CAT system is also used to program the memories on the radio, but you would need to use appropriate programming software. A CAT interface does not receive or transmit any DATA mode, that is the purpose of a DATA interface. Although, both may be used at the same time with the correct CAT Equipment. DATA modes, and getting audio to and from the PC is the function of a DATA interface. A completely different thing but it is easier and more useful when CAT and DATA are used at the same time. Wouldn't it be nice to have an interface that could operate Frequency-shift keying (FSK), Audio FSK (AFSK), (real) Morse Code (CW), with a CAT interface and its own sound card..... (eg. The DigiMaster Pro3).
Kimchi (software)
Kimchi is a web management tool to manage Kernel-based Virtual Machine (KVM) infrastructure. Developed with HTML5, Kimchi is developed to intuitively manage KVM guests, create storage pools, manage network interfaces (bridges, VLANs, NAT), and perform other related tasks. The name is an extended acronym for KVM infrastructure management. It is an Apache-licensed project hosted on GitHub, and incubated by oVirt.org.
Kolmogorov–Arnold Networks
Kolmogorov–Arnold Networks (KANs) are a type of artificial neural network architecture inspired by the Kolmogorov–Arnold representation theorem, also known as the superposition theorem. Unlike traditional multilayer perceptrons (MLPs), which rely on fixed activation functions and linear weights, KANs replace each weight with a learnable univariate function, often represented using splines. == History == KANs (Kolmogorov–Arnold Networks) were proposed by Liu et al. (2024) as a generalization of the Kolmogorov–Arnold representation theorem (KART), aiming to outperform MLPs in small-scale AI and scientific tasks. Before KANs, numerous studies explored KART's connections to neural networks or used it as a basis for designing new network architectures. In the 1980s and 1990s, early research applied KART to neural network design. Kůrková et al. (1992), Hecht-Nielsen (1987), and Nees (1994) established theoretical foundations for multilayer networks based on KART. Igelnik et al. (2003) introduced the Kolmogorov Spline Network using cubic splines to model complex functions. Sprecher (1996, 1997) introduced numerical methods for building network layers, while Nakamura et al. (1993) created activation functions with guaranteed approximation accuracy. These works linked KART's theoretical potential with practical neural network implementation. KART has also been used in other computational and theoretical fields. Coppejans (2004) developed nonparametric regression estimators using B-splines, Bryant (2008) applied it to high-dimensional image tasks, Liu (2015) investigated theoretical applications in optimal transport and image encryption, and more recently, Polar and Poluektov (2021) used Urysohn operators for efficient KART construction, while Fakhoury et al. (2022) introduced ExSpliNet, integrating KART with probabilistic trees and multivariate B-splines for improved function approximation. == Architecture == KANs are based on the Kolmogorov–Arnold representation theorem, which was linked to the 13th Hilbert problem. Given x = ( x 1 , x 2 , … , x n ) {\displaystyle x=(x_{1},x_{2},\dots ,x_{n})} consisting of n variables, a multivariate continuous function f ( x ) {\displaystyle f(x)} can be represented as: f ( x ) = f ( x 1 , … , x n ) = ∑ q = 1 2 n + 1 Φ q ( ∑ p = 1 n φ q , p ( x p ) ) {\displaystyle f(x)=f(x_{1},\dots ,x_{n})=\sum _{q=1}^{2n+1}\Phi _{q}\left(\sum _{p=1}^{n}\varphi _{q,p}(x_{p})\right)} (1) This formulation contains two nested summations: an outer and an inner sum. The outer sum ∑ q = 1 2 n + 1 {\displaystyle \sum _{q=1}^{2n+1}} aggregates 2 n + 1 {\displaystyle 2n+1} terms, each involving a function Φ q : R → R {\displaystyle \Phi _{q}:\mathbb {R} \to \mathbb {R} } . The inner sum ∑ p = 1 n {\displaystyle \sum _{p=1}^{n}} computes n terms for each q, where each term φ q , p : [ 0 , 1 ] → R {\displaystyle \varphi _{q,p}:[0,1]\to \mathbb {R} } is a continuous function of the single variable x p {\displaystyle x_{p}} . The inner continuous functions φ q , p {\displaystyle \varphi _{q,p}} are universal, independent of f {\displaystyle f} , while the outer functions Φ q {\displaystyle \Phi _{q}} depend on the specific function f {\displaystyle f} being represented. The representation (1) holds for all multivariate functions f {\displaystyle f} as proved in . If f {\displaystyle f} is continuous, then the outer functions Φ q {\displaystyle \Phi _{q}} are continuous; if f {\displaystyle f} is discontinuous, then the corresponding Φ q {\displaystyle \Phi _{q}} are generally discontinuous, while the inner functions φ q , p {\displaystyle \varphi _{q,p}} remain the same universal functions. Liu et al. proposed the name KAN. A general KAN network consisting of L layers takes x to generate the output as: K A N ( x ) = ( Φ L − 1 ∘ Φ L − 2 ∘ ⋯ ∘ Φ 1 ∘ Φ 0 ) x {\displaystyle \mathrm {KAN} (x)=(\Phi ^{L-1}\circ \Phi ^{L-2}\circ \cdots \circ \Phi ^{1}\circ \Phi ^{0})x} (3) Here, Φ l {\displaystyle \Phi ^{l}} is the function matrix of the l-th KAN layer or a set of pre-activations. Let i denote the neuron of the l-th layer and j the neuron of the (l+1)-th layer. The activation function φ j , i l {\displaystyle \varphi _{j,i}^{l}} connects (l, i) to (l+1, j): φ j , i l , l = 0 , … , L − 1 , i = 1 , … , n l , j = 1 , … , n l + 1 {\displaystyle \varphi _{j,i}^{l},\quad l=0,\dots ,L-1,\;i=1,\dots ,n_{l},\;j=1,\dots ,n_{l+1}} (4) where nl is the number of nodes of the l-th layer. Thus, the function matrix Φ l {\displaystyle \Phi ^{l}} can be represented as an n l + 1 × n l {\displaystyle n_{l+1}\times n_{l}} matrix of activations: x l + 1 = ( φ 1 , 1 l ( ⋅ ) φ 1 , 2 l ( ⋅ ) ⋯ φ 1 , n l l ( ⋅ ) φ 2 , 1 l ( ⋅ ) φ 2 , 2 l ( ⋅ ) ⋯ φ 2 , n l l ( ⋅ ) ⋮ ⋮ ⋱ ⋮ φ n l + 1 , 1 l ( ⋅ ) φ n l + 1 , 2 l ( ⋅ ) ⋯ φ n l + 1 , n l l ( ⋅ ) ) x l {\displaystyle x^{l+1}={\begin{pmatrix}\varphi _{1,1}^{l}(\cdot )&\varphi _{1,2}^{l}(\cdot )&\cdots &\varphi _{1,n_{l}}^{l}(\cdot )\\\varphi _{2,1}^{l}(\cdot )&\varphi _{2,2}^{l}(\cdot )&\cdots &\varphi _{2,n_{l}}^{l}(\cdot )\\\vdots &\vdots &\ddots &\vdots \\\varphi _{n_{l+1},1}^{l}(\cdot )&\varphi _{n_{l+1},2}^{l}(\cdot )&\cdots &\varphi _{n_{l+1},n_{l}}^{l}(\cdot )\end{pmatrix}}x^{l}} == Implementations == To make the KAN layers optimizable, the inner function is formed by the combination of spline and basic functions as the formula: φ ( x ) = w b b ( x ) + w s spline ( x ) {\displaystyle \varphi (x)=w_{b}\,b(x)+w_{s}\,{\text{spline}}(x)} where b ( x ) {\displaystyle b(x)} is the basic function, usually defined as s i l u ( x ) = x / ( 1 + e x ) {\displaystyle silu(x)=x/(1+e^{x})} and w b {\displaystyle w_{b}} is the base weight matrix. Also, w s {\displaystyle w_{s}} is the spline weight matrix and spline ( x ) {\displaystyle {\text{spline}}(x)} is the spline function. The spline function can be a sum of B-splines. spline ( x ) = ∑ i c i B i ( x ) {\displaystyle {\text{spline}}(x)=\sum _{i}c_{i}B_{i}(x)} Many studies suggested to use other polynomial and curve functions instead of B-spline to create new KAN variants. == Functions used == The choice of functional basis strongly influences the performance of KANs. Common function families include: B-splines: Provide locality, smoothness, and interpretability; they are the most widely used in current implementations. RBFs (include Gaussian RBFs): Capture localized features in data and are effective in approximating functions with non-linear or clustered structures. Chebyshev polynomials: Offer efficient approximation with minimized error in the maximum norm, making them useful for stable function representation. Rational function: Useful for approximating functions with singularities or sharp variations, as they can model asymptotic behavior better than polynomials. Fourier series: Capture periodic patterns effectively and are particularly useful in domains such as physics-informed machine learning. Wavelet functions (DoG, Mexican hat, Morlet, and Shannon): Used for feature extraction as they can capture both high-frequency and low-frequency data components. Piecewise linear functions: Provide efficient approximation for multivariate functions in KANs. == Usage == In some modern neural architectures like convolutional neural networks (CNNs), recurrent neural networks (RNNs), and Transformers, KANs are typically used as drop-in substitutes for MLP layers. Despite KANs' general-purpose design, researchers have created and used them for a number of tasks: Scientific machine learning (SciML): Function fitting, partial differential equations (PDEs) and physical/mathematical laws. Continual learning: KANs better preserve previously learned information during incremental updates, avoiding catastrophic forgetting due to the locality of spline adjustments. Graph neural networks: Extensions such as Kolmogorov–Arnold Graph Neural Networks (KA-GNNs) integrate KAN modules into message-passing architectures, showing improvements in molecular property prediction tasks. Sensor data processing: Kolmogorov–Arnold Networks (KANs) have recently been applied to sensor data processing due to their ability to model complex nonlinear relationships with relatively few parameters and improved interpretability compared to conventional multilayer perceptrons. Applications include industrial soft sensors, biomedical signal analysis, remote sensing, and environmental monitoring systems. == Drawbacks == KANs can be computationally intensive and require a large number of parameters due to their use of polynomial functions to capture data.
GPU switching
GPU switching is a mechanism used on computers with multiple graphic controllers. This mechanism allows the user to either maximize the graphic performance or prolong battery life by switching between the graphic cards. It is mostly used on gaming laptops which usually have an integrated graphic device and a discrete video card. == Basic components == Most computers using this feature contain integrated graphics processors and dedicated graphics cards that applies to the following categories. === Integrated graphics === Also known as: Integrated graphics, shared graphics solutions, integrated graphics processors (IGP) or unified memory architecture (UMA). This kind of graphics processors usually have much fewer processing units and share the same memory with the CPU. Sometimes the graphics processors are integrated onto a motherboard. It is commonly known as: on-board graphics. A motherboard with on-board graphics processors doesn't require a discrete graphics card or a CPU with graphics processors to operate. === Dedicated graphics cards === Also known as: discrete graphics cards. Unlike integrated graphics, dedicated graphics cards have much more processing units and have its own RAM with much higher memory bandwidth. In some cases, a dedicated graphics chip can be integrated onto the motherboards, B150-GP104 for example. Regardless of the fact that the graphics chip is integrated, it is still counted as a dedicated graphics cards system because the graphics chip is integrated with its own memory. == Theory == Most Personal Computers have a motherboard that uses a Southbridge and Northbridge structure. === Northbridge control === The Northbridge is one of the core logic chipset that handles communications between the CPU, GPU, RAM and the Southbridge. The discrete graphics card is usually installed onto the graphics card slot such as PCI-Express and the integrated graphics is integrated onto the CPU itself or occasionally onto the Northbridge. The Northbridge is the most responsible for switching between GPUs. The way how it works usually has the following process (refer to the Figure 1. on the right): The Northbridge receives input from Southbridge through the internal bus. The Northbridge signals to CPU through the Front-side bus. The CPU runs the task assignment application (usually the graphics card driver) to determine which GPU core to use. The CPU passes down the command to the Northbridge. The Northbridge passes down the command to the according GPU core. The GPU core processes the command and returns the rendered data back to the Northbridge. The Northbridge sends the rendered data back to Southbridge. === Southbridge control === The Southbridge is a set of integrated circuits such Intel's I/O Controller Hub (ICH). It handles all of a computer's I/O functions, such as receiving the keyboard input and outputting the data onto the screen. The way how it usually works usually has two steps: Take in the user input and pass it down to the Northbridge. (Optional) Receive the rendered data from the Northbridge and output it. The reason why the second step can be optional is that sometimes the rendered the data is outputted directly from the discrete graphics card which is located on the graphics card slot so there is no need to output the data through the Southbridge. == Main purpose == GPU switching is mostly used for saving energy by switching between graphic cards. The dedicated graphics cards consume much more power than integrated graphics but also provides higher 3D performances, which is needed for a better gaming and CAD experience. Following is a list of the TDPs of the most popular CPU with integrated graphics and dedicated graphics cards. The dedicated graphics cards exhibit much higher power consumption than the integrated graphics on both platforms. Disabling them when no heavy graphics processing is needed can significantly lower the power consumption. == Technologies == === Nvidia Optimus === Nvidia Optimus™ is a computer GPU switching technology created by Nvidia that can dynamically and seamlessly switch between two graphic cards based on running programs. === AMD Enduro === AMD Enduro™ is a collective brand developed by AMD that features many new technologies that can significantly save power. It was previously named as: PowerXpress and Dynamic Switchable Graphics (DSG). This technology implements a sophisticated system to predict the potential usage need for graphics cards and switch between graphics cards based on predicted need. This technology also introduces a new power control plan that allows the discrete graphics cards consume no energy when idling. == Manufacturers == === Integrated graphics === In personal computers, the IGP (integrated graphics processors) are mostly manufactured by Intel and AMD and are integrated onto their CPUs. They are commonly known as: Intel HD and Iris Graphics - also called HD series and Iris series AMD Accelerated Processing Unit (APU) - also formerly known as: fusion === Dedicated graphics cards === The most popular dedicated graphics cards are manufactured by AMD and Nvidia. They are commonly known as: AMD Radeon Nvidia GeForce == Drivers and OS support == Most common operating systems have built-in support for this feature. However, the users may download the updated drivers from Nvidia or AMD for better experience. === Windows support === Windows 7 has built-in support for this feature. The system automatically switches between GPUs depending on the program that's running. However, the user may switch the GPUs manually through device manager or power manager. === Linux === Modern Linux systems handle hybrid graphics in two parts: power/control for the inactive GPU, and optional render offloading for individual applications. vga_switcheroo (in the kernel since 2.6.34) coordinates power and mux control on systems with multiple GPUs. It was designed primarily for muxed designs (hardware display switch), and on muxless laptops it is typically used only for power control. A display server restart is no longer required for offloading on muxless systems. DRI PRIME (Mesa) enables per-process render offload on muxless systems: an app renders on the discrete GPU and the integrated GPU presents the result. Users can opt in via the DRI_PRIME environment variable (e.g., DRI_PRIME=1) or desktop integration. On GNOME, the switcheroo-control service exposes the discrete GPU to the shell, adding a “Launch using Discrete Graphics Card” entry to app menus on supported systems (Wayland or Xorg), which invokes render offload under the hood. With the proprietary Nvidia driver, render offload is provided as PRIME Render Offload (supported since driver 435.xx). Distributions commonly ship a helper like prime-run or desktop menu entries that set the required environment for offloading. ==== Notes and limitations (Linux) ==== On muxless systems the internal display is hard-wired to the integrated GPU; the discrete GPU cannot directly drive that panel and instead renders offscreen for composition by the iGPU. External displays connected to the dGPU may allow direct output depending on the laptop’s wiring. Power-saving behavior varies by driver and distro defaults. Some setups need explicit configuration to power down the inactive GPU when idle. Desktop integrations (e.g., GNOME's menu item) simply opt an app into offload; they do not "auto-switch" the whole session. Users can still launch apps on either GPU as needed.