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T-theory
T-theory is a branch of discrete mathematics dealing with analysis of trees and discrete metric spaces. General history T-theory originated from a question raised by Manfred Eigen in the late 1970s. He was trying to fit twenty distinct t-RNA molecules of the ''Escherichia coli'' bacterium into a tree. An important concept of T-theory is the tight span of a metric space. If ''X'' is a metric space, the tight span ''T''(''X'') of ''X'' is, up to isomorphism, the unique minimal injective metric space that contains ''X''. John Isbell was the first to discover the tight span in 1964, which he called the injective envelope. Andreas Dress independently constructed the same construct, which he called the tight span. Application areas * Phylogenetic analysis, which is used to create phylogenetic trees. * Online algorithm In computer science, an online algorithm is one that can process its input piece-by-piece in a serial fashion, i.e., in the order that the input is fed to the algori ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Tight Span
In metric geometry, the metric envelope or tight span of a metric space ''M'' is an injective metric space into which ''M'' can be embedded. In some sense it consists of all points "between" the points of ''M'', analogous to the convex hull of a point set in a Euclidean space. The tight span is also sometimes known as the injective envelope or hyperconvex hull of ''M''. It has also been called the injective hull, but should not be confused with the injective hull of a module in algebra, a concept with a similar description relative to the category of ''R''-modules rather than metric spaces. The tight span was first described by , and it was studied and applied by Holsztyński in the 1960s. It was later independently rediscovered by and ; see for this history. The tight span is one of the central constructions of T-theory. Definition The tight span of a metric space can be defined as follows. Let (''X'',''d'') be a metric space, and let ''T''(''X'') be the set of extremal funct ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Andreas Dress
Andreas Dress (26 August 1938 – 23 February 2024) was a German mathematician specialising in geometry, combinatorics and mathematical biology. Biography Dress earned his PhD from the University of Kiel in 1962, under the supervision of Friedrich Bachmann and Karl-Heinrich Weise. His thesis is entitled ''Konstruktion metrischer Ebenen''. Dress was a professor of mathematics at the University of Bielefeld beginning in 1969. He was the first director of the Max Planck Partner Institute for Computational Biology in Shanghai. In 1998 he was an Invited Speaker of the International Congress of Mathematicians in Berlin. Dress died on 23 February 2024, at the age of 85. See also * Split networks *SplitsTree *T-theory *Tight span In metric geometry, the metric envelope or tight span of a metric space ''M'' is an injective metric space into which ''M'' can be embedded. In some sense it consists of all points "between" the points of ''M'', analogous to the convex hull of a po ... R ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Phylogenetic Tree
A phylogenetic tree or phylogeny is a graphical representation which shows the evolutionary history between a set of species or taxa during a specific time.Felsenstein J. (2004). ''Inferring Phylogenies'' Sinauer Associates: Sunderland, MA. In other words, it is a branching diagram or a tree showing the evolutionary relationships among various biological species or other entities based upon similarities and differences in their physical or genetic characteristics. In evolutionary biology, all life on Earth is theoretically part of a single phylogenetic tree, indicating common ancestry. Phylogenetics is the study of phylogenetic trees. The main challenge is to find a phylogenetic tree representing optimal evolutionary ancestry between a set of species or taxa. Computational phylogenetics (also phylogeny inference) focuses on the algorithms involved in finding optimal phylogenetic tree in the phylogenetic landscape. Phylogenetic trees may be rooted or unrooted. In a ''rooted'' p ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Discrete Mathematics
Discrete mathematics is the study of mathematical structures that can be considered "discrete" (in a way analogous to discrete variables, having a bijection with the set of natural numbers) rather than "continuous" (analogously to continuous functions). Objects studied in discrete mathematics include integers, Graph (discrete mathematics), graphs, and Statement (logic), statements in Mathematical logic, logic. By contrast, discrete mathematics excludes topics in "continuous mathematics" such as real numbers, calculus or Euclidean geometry. Discrete objects can often be enumeration, enumerated by integers; more formally, discrete mathematics has been characterized as the branch of mathematics dealing with countable sets (finite sets or sets with the same cardinality as the natural numbers). However, there is no exact definition of the term "discrete mathematics". The set of objects studied in discrete mathematics can be finite or infinite. The term finite mathematics is sometime ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Commentarii Mathematici Helvetici
The ''Commentarii Mathematici Helvetici'' is a quarterly peer-reviewed scientific journal in mathematics. The Swiss Mathematical Society (SMG) started the journal in 1929 after a meeting in May of the previous year. The Swiss Mathematical Society still owns and operates the journal; the publishing is currently handled on its behalf by the European Mathematical Society. The scope of the journal includes research articles in all aspects in mathematics. The editors-in-chief have been Rudolf Fueter (1929–1949), J.J. Burckhardt (1950–1981), P. Gabriel (1982–1989), H. Kraft (1990–2005), and Eva Bayer-Fluckiger (2006–present). Abstracting and indexing The journal is abstracted and indexed in: According to the ''Journal Citation Reports'', the journal has a 2019 impact factor of 0.854. History The idea for a society-owned research journal emerged in June 1926, when the SMG petitioned the Swiss Confederation for a CHF 3,500 subsidy "to establish its own scientific jour ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
European Journal Of Combinatorics
The ''European Journal of Combinatorics'' is an international peer-reviewed scientific journal that specializes in combinatorics. The journal primarily publishes papers dealing with mathematical structures within combinatorics and/or establishing direct links between combinatorics and the theories of computing. The journal includes full-length research papers, short notes, and research problems on several topics. This journal has been founded in 1980 by Michel Deza, Michel Las Vergnas and Pierre Rosenstiehl. The current editor-in-chief is Patrice Ossona de Mendez and the vice editor-in-chief is Marthe Bonamy. Abstracting and indexing The journal is abstracted and indexed in *MathSciNet, *Science Citation Index Expanded, *Scopus Scopus is a scientific abstract and citation database, launched by the academic publisher Elsevier as a competitor to older Web of Science in 2004. The ensuing competition between the two databases has been characterized as "intense" and is c . ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Advances In Mathematics
''Advances in Mathematics'' is a peer-reviewed scientific journal covering research on pure mathematics. It was established in 1961 by Gian-Carlo Rota. The journal publishes 18 issues each year, in three volumes. At the origin, the journal aimed at publishing articles addressed to a broader "mathematical community", and not only to mathematicians in the author's field. Herbert Busemann writes, in the preface of the first issue, "The need for expository articles addressing either all mathematicians or only those in somewhat related fields has long been felt, but little has been done outside of the USSR. The serial publication ''Advances in Mathematics'' was created in response to this demand." Abstracting and indexing The journal is abstracted and indexed in: * [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
University Of California, Berkeley
The University of California, Berkeley (UC Berkeley, Berkeley, Cal, or California), is a Public university, public Land-grant university, land-grant research university in Berkeley, California, United States. Founded in 1868 and named after the Anglo-Irish philosopher George Berkeley, it is the state's first land-grant university and is the founding campus of the University of California system. Berkeley has an enrollment of more than 45,000 students. The university is organized around fifteen schools of study on the same campus, including the UC Berkeley College of Chemistry, College of Chemistry, the UC Berkeley College of Engineering, College of Engineering, UC Berkeley College of Letters and Science, College of Letters and Science, and the Haas School of Business. It is Carnegie Classification of Institutions of Higher Education, classified among "R1: Doctoral Universities – Very high research activity". Lawrence Berkeley National Laboratory was originally founded as par ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bernd Sturmfels
Bernd Sturmfels (born March 28, 1962, in Kassel, West Germany) is a Professor of Mathematics and Computer Science at the University of California, Berkeley and is a director of the Max Planck Institute for Mathematics in the Sciences in Leipzig since 2017. Education and career He received his PhD in 1987 from the University of Washington and the Technische Universität Darmstadt. After two postdoctoral years at the Institute for Mathematics and its Applications in Minneapolis, Minnesota, and the Research Institute for Symbolic Computation in Linz, Austria, he taught at Cornell University, before joining University of California, Berkeley in 1995. His Ph.D. students include Melody Chan, Jesús A. De Loera, Mike Develin, Diane Maclagan, Rekha R. Thomas, Caroline Uhler, and Cynthia Vinzant. Contributions Bernd Sturmfels has made contributions to a variety of areas of mathematics, including algebraic geometry, commutative algebra, discrete geometry, Gröbner bases, toric varie ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
K-server Problem
The -server problem is a problem of theoretical computer science in the category of online algorithms, one of two abstract problems on metric spaces that are central to the theory of competitive analysis (the other being metrical task systems). In this problem, an online algorithm must control the movement of a set of ''k'' ''servers'', represented as points in a metric space, and handle ''requests'' that are also in the form of points in the space. As each request arrives, the algorithm must determine which server to move to the requested point. The goal of the algorithm is to keep the total distance all servers move small, relative to the total distance the servers could have moved by an optimal adversary who knows in advance the entire sequence of requests. The problem was first posed by Mark Manasse, Lyle A. McGeoch and Daniel Sleator (1988). The most prominent open question concerning the ''k''-server problem is the so-called ''k''-server conjecture, also posed by Manasse ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Online Algorithm
In computer science, an online algorithm is one that can process its input piece-by-piece in a serial fashion, i.e., in the order that the input is fed to the algorithm, without having the entire input available from the start. In contrast, an offline algorithm is given the whole problem data from the beginning and is required to output an answer which solves the problem at hand. In operations research Operations research () (U.S. Air Force Specialty Code: Operations Analysis), often shortened to the initialism OR, is a branch of applied mathematics that deals with the development and application of analytical methods to improve management and ..., the area in which online algorithms are developed is called online optimization. As an example, consider the sorting algorithms selection sort and insertion sort: selection sort repeatedly selects the minimum element from the unsorted remainder and places it at the front, which requires access to the entire input; it is thus a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
John Isbell
John Rolfe Isbell (October 27, 1930 – August 6, 2005) was an American mathematician. For many years he was a professor of mathematics at the University at Buffalo (SUNY). Biography Isbell was born in Portland, Oregon, the son of an army officer from Isbell, a town in Franklin County, Alabama... He attended several undergraduate institutions, including the University of Chicago, where professor Saunders Mac Lane was a source of inspiration. He began his graduate studies in mathematics at Chicago, briefly studied at Oklahoma A&M University and the University of Kansas, and eventually completed a Ph.D. in game theory at Princeton University in 1954 under the supervision of Albert W. Tucker. After graduation, Isbell was drafted into the U.S. Army, and stationed at the Aberdeen Proving Ground. In the late 1950s he worked at the Institute for Advanced Study in Princeton, New Jersey, from which he then moved to the University of Washington and Case Western Reserve University. He join ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
