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Jaroslav Nešetřil
Jaroslav (Jarik) Nešetřil (; born March 13, 1946 in Brno) is a Czech mathematician, working at Charles University in Prague. His research areas include combinatorics (structural combinatorics, Ramsey theory), graph theory (coloring problems, sparse structures), algebra (representation of structures, categories, homomorphisms), posets (diagram and dimension problems), computer science (complexity, NP-completeness). Education and career Nešetřil received his Ph.D. from Charles University in 1973 under the supervision of Aleš Pultr and Gert Sabidussi. He is responsible for more than 300 publications. Since 2006, he is chairman of the Committee of Mathematics of Czech Republic (the Czech partner of IMU). Jaroslav Nešetřil is Editor in Chief of ''Computer Science Review'' and ''INTEGERS: the Electronic Journal of Combinatorial Number Theory''. He is also honorary editor of ''Electronic Journal of Graph Theory and Applications''. Since 2008, Jaroslav Nešetřil belongs to th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Brno, Czech Republic
Brno ( , ; german: Brünn ) is a city in the South Moravian Region of the Czech Republic. Located at the confluence of the Svitava and Svratka rivers, Brno has about 380,000 inhabitants, making it the second-largest city in the Czech Republic after the capital, Prague, and one of the 100 largest cities of the EU. The Brno metropolitan area has almost 700,000 inhabitants. Brno is the former capital city of Moravia and the political and cultural hub of the South Moravian Region. It is the centre of the Czech judiciary, with the seats of the Constitutional Court, the Supreme Court, the Supreme Administrative Court, and the Supreme Public Prosecutor's Office, and a number of state authorities, including the Ombudsman, and the Office for the Protection of Competition. Brno is also an important centre of higher education, with 33 faculties belonging to 13 institutes of higher education and about 89,000 students. Brno Exhibition Centre is among the largest exhibition ce ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Combinatorics
Combinatorics is an area of mathematics primarily concerned with counting, both as a means and an end in obtaining results, and certain properties of finite structures. It is closely related to many other areas of mathematics and has many applications ranging from logic to statistical physics and from evolutionary biology to computer science. Combinatorics is well known for the breadth of the problems it tackles. Combinatorial problems arise in many areas of pure mathematics, notably in algebra, probability theory, topology, and geometry, as well as in its many application areas. Many combinatorial questions have historically been considered in isolation, giving an ''ad hoc'' solution to a problem arising in some mathematical context. In the later twentieth century, however, powerful and general theoretical methods were developed, making combinatorics into an independent branch of mathematics in its own right. One of the oldest and most accessible parts of combinatorics is gra ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Academia Sinica
Academia Sinica (AS, la, 1=Academia Sinica, 3=Chinese Academy; ), headquartered in Nangang, Taipei, is the national academy of Taiwan. Founded in Nanking, the academy supports research activities in a wide variety of disciplines, ranging from mathematical and physical sciences to life sciences, and to humanities and social sciences. As an educational institute, it provides PhD training and scholarship through its English-language Taiwan International Graduate Program in biology, agriculture, chemistry, physics, informatics, and earth and environmental sciences. Academia Sinica is ranked 144th in Nature Publishing Index - 2014 Global Top 200 and 18th in Reuters World's Most Innovative Research Institutions of 2019. The current president since 2016 is James C. Liao, an expert in metabolic engineering, systems biology and synthetic biology. History Academia Sinica, which means "Chinese Academy", was founded in 1928 in Nanking, then capital of the Republic of China, wit ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Elsevier
Elsevier () is a Dutch academic publishing company specializing in scientific, technical, and medical content. Its products include journals such as ''The Lancet'', ''Cell'', the ScienceDirect collection of electronic journals, '' Trends'', the '' Current Opinion'' series, the online citation database Scopus, the SciVal tool for measuring research performance, the ClinicalKey search engine for clinicians, and the ClinicalPath evidence-based cancer care service. Elsevier's products and services also include digital tools for data management, instruction, research analytics and assessment. Elsevier is part of the RELX Group (known until 2015 as Reed Elsevier), a publicly traded company. According to RELX reports, in 2021 Elsevier published more than 600,000 articles annually in over 2,700 journals; as of 2018 its archives contained over 17 million documents and 40,000 e-books, with over one billion annual downloads. Researchers have criticized Elsevier for its high profit marg ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
International Mathematical Union
The International Mathematical Union (IMU) is an international non-governmental organization devoted to international cooperation in the field of mathematics across the world. It is a member of the International Science Council (ISC) and supports the International Congress of Mathematicians. Its members are national mathematics organizations from more than 80 countries. The objectives of the International Mathematical Union (IMU) are: promoting international cooperation in mathematics, supporting and assisting the International Congress of Mathematicians (ICM) and other international scientific meetings/conferences, acknowledging outstanding research contributions to mathematics through the awarding of scientific prizes, and encouraging and supporting other international mathematical activities, considered likely to contribute to the development of mathematical science in any of its aspects, whether pure, applied, or educational. The IMU was established in 1920, but dissolved in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
P = NP Problem
The P versus NP problem is a major unsolved problem in theoretical computer science. In informal terms, it asks whether every problem whose solution can be quickly verified can also be quickly solved. The informal term ''quickly'', used above, means the existence of an algorithm solving the task that runs in polynomial time, such that the time to complete the task varies as a polynomial function on the size of the input to the algorithm (as opposed to, say, exponential time). The general class of questions for which some algorithm can provide an answer in polynomial time is " P" or "class P". For some questions, there is no known way to find an answer quickly, but if one is provided with information showing what the answer is, it is possible to verify the answer quickly. The class of questions for which an answer can be ''verified'' in polynomial time is NP, which stands for "nondeterministic polynomial time".A nondeterministic Turing machine can move to a state that is not d ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Computational Complexity Theory
In theoretical computer science and mathematics, computational complexity theory focuses on classifying computational problems according to their resource usage, and relating these classes to each other. A computational problem is a task solved by a computer. A computation problem is solvable by mechanical application of mathematical steps, such as an algorithm. A problem is regarded as inherently difficult if its solution requires significant resources, whatever the algorithm used. The theory formalizes this intuition, by introducing mathematical models of computation to study these problems and quantifying their computational complexity, i.e., the amount of resources needed to solve them, such as time and storage. Other measures of complexity are also used, such as the amount of communication (used in communication complexity), the number of gates in a circuit (used in circuit complexity) and the number of processors (used in parallel computing). One of the roles of computationa ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Computer Science
Computer science is the study of computation, automation, and information. Computer science spans theoretical disciplines (such as algorithms, theory of computation, information theory, and automation) to Applied science, practical disciplines (including the design and implementation of Computer architecture, hardware and Computer programming, software). Computer science is generally considered an area of research, academic research and distinct from computer programming. Algorithms and data structures are central to computer science. The theory of computation concerns abstract models of computation and general classes of computational problem, problems that can be solved using them. The fields of cryptography and computer security involve studying the means for secure communication and for preventing Vulnerability (computing), security vulnerabilities. Computer graphics (computer science), Computer graphics and computational geometry address the generation of images. Progr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Order Dimension
In mathematics, the dimension of a partially ordered set (poset) is the smallest number of total orders the intersection of which gives rise to the partial order. This concept is also sometimes called the order dimension or the Dushnik–Miller dimension of the partial order. first studied order dimension; for a more detailed treatment of this subject than provided here, see . Formal definition The dimension of a poset ''P'' is the least integer ''t'' for which there exists a family :\mathcal R=(<_1,\dots,<_t) of s of ''P'' so that, for every ''x'' and ''y'' in ''P'', ''x'' precedes ''y'' in ''P'' if and only if it precedes ''y'' in all of the linear extensions. That is, : An alternative definition of order dimension is the minimal number of |
Partially Ordered Sets
In mathematics, especially order theory, a partially ordered set (also poset) formalizes and generalizes the intuitive concept of an ordering, sequencing, or arrangement of the elements of a set. A poset consists of a set together with a binary relation indicating that, for certain pairs of elements in the set, one of the elements precedes the other in the ordering. The relation itself is called a "partial order." The word ''partial'' in the names "partial order" and "partially ordered set" is used as an indication that not every pair of elements needs to be comparable. That is, there may be pairs of elements for which neither element precedes the other in the poset. Partial orders thus generalize total orders, in which every pair is comparable. Informal definition A partial order defines a notion of comparison. Two elements ''x'' and ''y'' may stand in any of four mutually exclusive relationships to each other: either ''x'' ''y'', or ''x'' and ''y'' are ''incom ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Graph Homomorphism
In the mathematical field of graph theory, a graph homomorphism is a mapping between two graphs that respects their structure. More concretely, it is a function between the vertex sets of two graphs that maps adjacent vertices to adjacent vertices. Homomorphisms generalize various notions of graph colorings and allow the expression of an important class of constraint satisfaction problems, such as certain scheduling or frequency assignment problems. The fact that homomorphisms can be composed leads to rich algebraic structures: a preorder on graphs, a distributive lattice, and a category (one for undirected graphs and one for directed graphs). The computational complexity of finding a homomorphism between given graphs is prohibitive in general, but a lot is known about special cases that are solvable in polynomial time. Boundaries between tractable and intractable cases have been an active area of research. Definitions In this article, unless stated otherwise, ''graphs'' are fi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Category Theory
Category theory is a general theory of mathematical structures and their relations that was introduced by Samuel Eilenberg and Saunders Mac Lane in the middle of the 20th century in their foundational work on algebraic topology. Nowadays, category theory is used in almost all areas of mathematics, and in some areas of computer science. In particular, many constructions of new mathematical objects from previous ones, that appear similarly in several contexts are conveniently expressed and unified in terms of categories. Examples include quotient spaces, direct products, completion, and duality. A category is formed by two sorts of objects: the objects of the category, and the morphisms, which relate two objects called the ''source'' and the ''target'' of the morphism. One often says that a morphism is an ''arrow'' that ''maps'' its source to its target. Morphisms can be ''composed'' if the target of the first morphism equals the source of the second one, and morphism compos ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
