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Persistent Homology
In topological data analysis, persistent homology is a method for computing topological features of a space at different spatial resolutions. More persistent features are detected over a wide range of spatial scales and are deemed more likely to represent true features of the underlying space rather than artifacts of sampling, noise, or particular choice of parameters. To find the persistent homology of a space, the space must first be represented as a simplicial complex. A distance function on the underlying space corresponds to a filtration of the simplicial complex, that is a nested sequence of increasing subsets. One common method of doing this is via taking the sublevel filtration of the distance to a point cloud, or equivalently, the offset filtration on the point cloud and taking its nerve in order to get the simplicial filtration known as Čech filtration. A similar construction uses a nested sequence of Vietoris–Rips complexes known as the Vietoris–Rips filtration. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Homology (mathematics)
In mathematics, the term homology, originally introduced in algebraic topology, has three primary, closely-related usages. The most direct usage of the term is to take the ''homology of a chain complex'', resulting in a sequence of Abelian group, abelian groups called ''homology groups.'' This operation, in turn, allows one to associate various named ''homologies'' or ''homology theories'' to various other types of mathematical objects. Lastly, since there are many homology theories for Topological space, topological spaces that produce the same answer, one also often speaks of the ''homology of a topological space''. (This latter notion of homology admits more intuitive descriptions for 1- or 2-dimensional topological spaces, and is sometimes referenced in popular mathematics.) There is also a related notion of the cohomology of a Cochain complexes, cochain complex, giving rise to various cohomology theories, in addition to the notion of the cohomology of a topological space. Ho ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
GPLv3
The GNU General Public Licenses (GNU GPL or simply GPL) are a series of widely used free software licenses, or ''copyleft'' licenses, that guarantee end users the freedom to run, study, share, or modify the software. The GPL was the first copyleft license available for general use. It was originally written by Richard Stallman, the founder of the Free Software Foundation (FSF), for the GNU Project. The license grants the recipients of a computer program the rights of the Free Software Definition. The licenses in the GPL series are all copyleft licenses, which means that any derivative work must be distributed under the same or equivalent license terms. The GPL is more restrictive than the GNU Lesser General Public License, and even more distinct from the more widely used permissive software licenses such as BSD, MIT, and Apache. Historically, the GPL license family has been one of the most popular software licenses in the free and open-source software (FOSS) domain. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
MIT License
The MIT License is a permissive software license originating at the Massachusetts Institute of Technology (MIT) in the late 1980s. As a permissive license, it puts very few restrictions on reuse and therefore has high license compatibility. Unlike copyleft software licenses, the MIT License also permits reuse within proprietary software, provided that all copies of the software or its substantial portions include a copy of the terms of the MIT License and also a copyright notice. In 2015, the MIT License was the most popular software license on GitHub, and was still the most popular in 2025. Notable projects that use the MIT License include the X Window System, Ruby on Rails, Node.js, Lua (programming language), Lua, jQuery, .NET, Angular (web framework), Angular, and React (JavaScript library), React. License terms The MIT License has the identifier MIT in the SPDX License List. It is also known as the "#Ambiguity and variants, Expat License". It has the following terms: Co ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
French Institute For Research In Computer Science And Automation
The National Institute for Research in Digital Science and Technology (Inria) () is a French national research institution focusing on computer science and applied mathematics. It was created under the name French Institute for Research in Computer Science and Automation (IRIA) () in 1967 at Rocquencourt near Paris, part of Plan Calcul. Its first site was the historical premises of SHAPE (central command of NATO military forces), which is still used as Inria's main headquarters. In 1980, IRIA became INRIA. Since 2011, it has been styled ''Inria''. Inria is a Public Scientific and Technical Research Establishment (EPST) under the double supervision of the French Ministry of National Education, Advanced Instruction and Research and the Ministry of Economy, Finance and Industry. Administrative status Inria has nine research centers distributed across France (in Bordeaux, Grenoble- Inovallée, Lille, Lyon, Nancy, Paris- Rocquencourt, Rennes, Saclay, and Sophia Antipolis) an ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Python (programming Language)
Python is a high-level programming language, high-level, general-purpose programming language. Its design philosophy emphasizes code readability with the use of significant indentation. Python is type system#DYNAMIC, dynamically type-checked and garbage collection (computer science), garbage-collected. It supports multiple programming paradigms, including structured programming, structured (particularly procedural programming, procedural), object-oriented and functional programming. It is often described as a "batteries included" language due to its comprehensive standard library. Guido van Rossum began working on Python in the late 1980s as a successor to the ABC (programming language), ABC programming language, and he first released it in 1991 as Python 0.9.0. Python 2.0 was released in 2000. Python 3.0, released in 2008, was a major revision not completely backward-compatible with earlier versions. Python 2.7.18, released in 2020, was the last release of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
BSD Licenses
BSD licenses are a family of permissive free software licenses, imposing minimal restrictions on the use and distribution of covered software. This is in contrast to copyleft licenses, which have share-alike requirements. The original BSD license was used for its namesake, the Berkeley Software Distribution (BSD), a Unix-like operating system. The original version has since been revised, and its descendants are referred to as modified BSD licenses. BSD is both a license and a class of license (generally referred to as BSD-like). The modified BSD license (in wide use today) is very similar to the license originally used for the BSD version of Unix. The BSD license is a simple license that merely requires that all code retain the BSD license notice if redistributed in source code format, or reproduce the notice if redistributed in binary format. The BSD license (unlike some other licenses e.g. GPL) does not require that source code be distributed at all. Terms In addition to ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Java (programming Language)
Java is a High-level programming language, high-level, General-purpose programming language, general-purpose, Memory safety, memory-safe, object-oriented programming, object-oriented programming language. It is intended to let programmers ''write once, run anywhere'' (Write once, run anywhere, WORA), meaning that compiler, compiled Java code can run on all platforms that support Java without the need to recompile. Java applications are typically compiled to Java bytecode, bytecode that can run on any Java virtual machine (JVM) regardless of the underlying computer architecture. The syntax (programming languages), syntax of Java is similar to C (programming language), C and C++, but has fewer low-level programming language, low-level facilities than either of them. The Java runtime provides dynamic capabilities (such as Reflective programming, reflection and runtime code modification) that are typically not available in traditional compiled languages. Java gained popularity sh ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
CUDA
In computing, CUDA (Compute Unified Device Architecture) is a proprietary parallel computing platform and application programming interface (API) that allows software to use certain types of graphics processing units (GPUs) for accelerated general-purpose processing, an approach called general-purpose computing on GPUs. CUDA was created by Nvidia in 2006. When it was first introduced, the name was an acronym for ''Compute Unified Device Architecture'', but Nvidia later dropped the common use of the acronym and now rarely expands it. CUDA is a software layer that gives direct access to the GPU's virtual instruction set and parallel computational elements for the execution of compute kernels. In addition to drivers and runtime kernels, the CUDA platform includes compilers, libraries and developer tools to help programmers accelerate their applications. CUDA is designed to work with programming languages such as C, C++, Fortran, Python and Julia. This accessibility makes ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Matlab
MATLAB (an abbreviation of "MATrix LABoratory") is a proprietary multi-paradigm programming language and numeric computing environment developed by MathWorks. MATLAB allows matrix manipulations, plotting of functions and data, implementation of algorithms, creation of user interfaces, and interfacing with programs written in other languages. Although MATLAB is intended primarily for numeric computing, an optional toolbox uses the MuPAD symbolic engine allowing access to symbolic computing abilities. An additional package, Simulink, adds graphical multi-domain simulation and model-based design for dynamic and embedded systems. , MATLAB has more than four million users worldwide. They come from various backgrounds of engineering, science, and economics. , more than 5000 global colleges and universities use MATLAB to support instruction and research. History Origins MATLAB was invented by mathematician and computer programmer Cleve Moler. The idea for MATLAB was base ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Apache 2
APACHE II ("Acute Physiology and Chronic Health Evaluation II") is a severity-of-disease classification system, one of several ICU scoring systems. It is applied within 24 hours of admission of a patient to an intensive care unit (ICU): an integer score from 0 to 71 is computed based on several measurements; higher scores correspond to more severe disease and a higher risk of death. The first APACHE model was presented by Knaus et al. in 1981. Application APACHE II was designed to measure the severity of disease for adult patients admitted to intensive care units. It has not been validated for use in children or young people aged under 16. This scoring system is used in many ways which include: # Some procedures or some medicine is only given to patients with a certain APACHE II score # APACHE II score can be used to describe the morbidity of a patient when comparing the outcome with other patients. # Predicted mortalities are averaged for groups of patients in order to spec ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lipschitz Map
In mathematical analysis, Lipschitz continuity, named after German mathematician Rudolf Lipschitz, is a strong form of uniform continuity for functions. Intuitively, a Lipschitz continuous function is limited in how fast it can change: there exists a real number such that, for every pair of points on the graph of this function, the absolute value of the slope of the line connecting them is not greater than this real number; the smallest such bound is called the ''Lipschitz constant'' of the function (and is related to the '' modulus of uniform continuity''). For instance, every function that is defined on an interval and has a bounded first derivative is Lipschitz continuous. In the theory of differential equations, Lipschitz continuity is the central condition of the Picard–Lindelöf theorem which guarantees the existence and uniqueness of the solution to an initial value problem. A special type of Lipschitz continuity, called contraction, is used in the Banach fixed-point the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
