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Benjamin Weiss (Debug Magazine)
Benjamin Weiss ( he, בנימין ווייס; born 1941) is an American-Israeli mathematician known for his contributions to ergodic theory, topological dynamics, probability theory, game theory, and descriptive set theory. Biography Benjamin ("Benjy") Weiss was born in New York City. In 1962 he received B.A. from Yeshiva University and M.A. from the Graduate School of Science, Yeshiva University. In 1965, he received his Ph.D. from Princeton under the supervision of William Feller. Academic career Between 1965 and 1967, Weiss worked at the IBM Research. In 1967, he joined the faculty of the Hebrew University of Jerusalem; and since 1990 occupied the Miriam and Julius Vinik Chair in Mathematics (Emeritus since 2009). Weiss held visiting positions at Stanford, MSRI, and IBM Research Center. Weiss published over 180 papers in ergodic theory, topological dynamics, orbit equivalence, probability, information theory, game theory, descriptive set theory; with notable contributi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematics
Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics with the major subdisciplines of number theory, algebra, geometry, and analysis, respectively. There is no general consensus among mathematicians about a common definition for their academic discipline. Most mathematical activity involves the discovery of properties of abstract objects and the use of pure reason to prove them. These objects consist of either abstractions from nature orin modern mathematicsentities that are stipulated to have certain properties, called axioms. A ''proof'' consists of a succession of applications of deductive rules to already established results. These results include previously proved theorems, axioms, andin case of abstraction from naturesome basic properties that are considered true starting poin ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Orbit Equivalence
In celestial mechanics, an orbit is the curved trajectory of an object such as the trajectory of a planet around a star, or of a natural satellite around a planet, or of an artificial satellite around an object or position in space such as a planet, moon, asteroid, or Lagrange point. Normally, orbit refers to a regularly repeating trajectory, although it may also refer to a non-repeating trajectory. To a close approximation, planets and satellites follow elliptic orbits, with the center of mass being orbited at a focal point of the ellipse, as described by Kepler's laws of planetary motion. For most situations, orbital motion is adequately approximated by Newtonian mechanics, which explains gravity as a force obeying an inverse-square law. However, Albert Einstein's general theory of relativity, which accounts for gravity as due to curvature of spacetime, with orbits following geodesics, provides a more accurate calculation and understanding of the exact mechanics of orbital ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
American Academy Of Arts And Sciences
The American Academy of Arts and Sciences (abbreviation: AAA&S) is one of the oldest learned societies in the United States. It was founded in 1780 during the American Revolution by John Adams, John Hancock, James Bowdoin, Andrew Oliver, and other Founding Fathers of the United States. It is headquartered in Cambridge, Massachusetts. Membership in the academy is achieved through a thorough petition, review, and election process. The academy's quarterly journal, '' Dædalus'', is published by MIT Press on behalf of the academy. The academy also conducts multidisciplinary public policy research. History The Academy was established by the Massachusetts legislature on May 4, 1780, charted in order "to cultivate every art and science which may tend to advance the interest, honor, dignity, and happiness of a free, independent, and virtuous people." The sixty-two incorporating fellows represented varying interests and high standing in the political, professional, and commerc ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Rice University
William Marsh Rice University (Rice University) is a private research university in Houston, Texas. It is on a 300-acre campus near the Houston Museum District and adjacent to the Texas Medical Center. Rice is ranked among the top universities in the United States. Opened in 1912 as the Rice Institute after the murder of its namesake William Marsh Rice, Rice is a research university with an undergraduate focus. Its emphasis on undergraduate education is demonstrated by its 6:1 student-faculty ratio. The university has a very high level of research activity, with $156 million in sponsored research funding in 2019. Rice is noted for its applied science programs in the fields of artificial heart research, structural chemical analysis, signal processing, space science, and nanotechnology. Rice has been a member of the Association of American Universities since 1985 and is classified among "R1: Doctoral Universities – Very high research activity". The university is orga ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Conference Board Of Mathematical Sciences
A conference is a meeting of two or more experts to discuss and exchange opinions or new information about a particular topic. Conferences can be used as a form of group decision-making, although discussion, not always decisions, are the main purpose of conferences. History The first known use of "conference" appears in 1527, meaning "a meeting of two or more persons for discussing matters of common concern". It came from the word "confer", which means "to compare views or take counsel". However the idea of a conference far predates the word. Arguably, as long as there have been people, there have been meetings and discussions between people. Evidence of ancient forms of conference can be seen in archaeological ruins of common areas where people would gather to discuss shared interests such as "hunting plans, wartime activities, negotiations for peace or the organisation of tribal celebrations". Since the 1960s, conferences have become a lucrative sector of the tourism indu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
International Congress Of Mathematicians
The International Congress of Mathematicians (ICM) is the largest conference for the topic of mathematics. It meets once every four years, hosted by the International Mathematical Union (IMU). The Fields Medals, the Nevanlinna Prize (to be renamed as the IMU Abacus Medal), the Gauss Prize, and the Chern Medal are awarded during the congress's opening ceremony. Each congress is memorialized by a printed set of Proceedings recording academic papers based on invited talks intended to be relevant to current topics of general interest. Being invited to talk at the ICM has been called "the equivalent ... of an induction to a hall of fame". History Felix Klein and Georg Cantor are credited with putting forward the idea of an international congress of mathematicians in the 1890s.A. John Coleman"Mathematics without borders": a book review ''CMS Notes'', vol 31, no. 3, April 1999, pp. 3-5 The University of Chicago, which had opened in 1892, organized an International Mathematical Con ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fields Medal
The Fields Medal is a prize awarded to two, three, or four mathematicians under 40 years of age at the International Congress of the International Mathematical Union (IMU), a meeting that takes place every four years. The name of the award honours the Canadian mathematician John Charles Fields. The Fields Medal is regarded as one of the highest honors a mathematician can receive, and has been described as the Nobel Prize of Mathematics, although there are several major differences, including frequency of award, number of awards, age limits, monetary value, and award criteria. According to the annual Academic Excellence Survey by ARWU, the Fields Medal is consistently regarded as the top award in the field of mathematics worldwide, and in another reputation survey conducted by IREG in 2013–14, the Fields Medal came closely after the Abel Prize as the second most prestigious international award in mathematics. The prize includes a monetary award which, since 2006, has bee ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Roy Adler
Roy Lee Adler (February 22, 1931 – July 26, 2016) was an American mathematician. Adler earned his Ph.D. in 1961 from Yale University under the supervision of Shizuo Kakutani (''On some algebraic aspects of measure preserving transformations''). He then worked as a mathematician for IBM at the Thomas J. Watson Research Center. Adler studies dynamical systems, ergodic theory, symbolic and topological dynamics and coding theory. The road coloring problem that was solved by Avraham Trakhtman in 2007 came from him, along with L. W. Goodwyn and Benjamin Weiss. He was a fellow of the American Mathematical Society. A paper was written on his work and the impact of his work by Bruce Kitchens and others. Writings *With Brian Marcus: ''Topological entropy and equivalence of dynamical systems''. Memoirs of the American Mathematical Society. 20 (1979), no 219. *With Benjamin Weiss: ''Similarity of automorphisms of the torus'', Memoirs of the American Mathematical Society (1970), no 9 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Road Coloring Problem
In graph theory the road coloring theorem, known previously as the road coloring conjecture, deals with synchronized instructions. The issue involves whether by using such instructions, one can reach or locate an object or destination from any other point within a network (which might be a representation of city streets or a maze). In the real world, this phenomenon would be as if you called a friend to ask for directions to his house, and he gave you a set of directions that worked no matter where you started from. This theorem also has implications in symbolic dynamics. The theorem was first conjectured by Roy Adler and Benjamin Weiss. It was proved by Avraham Trahtman. Example and intuition The image to the right shows a directed graph on eight vertices in which each vertex has out-degree 2. (Each vertex in this case also has in-degree 2, but that is not necessary for a synchronizing coloring to exist.) The edges of this graph have been colored red and blue to crea ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sofic Subshift
In symbolic dynamics and related branches of mathematics, a shift space or subshift is a set of infinite words that represent the evolution of a discrete system. In fact, shift spaces and '' symbolic dynamical systems'' are often considered synonyms. The most widely studied shift spaces are the subshifts of finite type. Notation Let ''A'' be a finite set of states. An ''infinite'' (respectively ''bi-infinite'') ''word'' over ''A'' is a sequence \mathbf x=(x_n)_, where M=\mathbb N (respectively M=\mathbb Z) and x_n is in ''A'' for any n \in M. The shift operator \sigma acts on an infinite or bi-infinite word by shifting all symbols to the left, i.e., :\sigma(\mathbf x)_n=x_ for all ''n''. In the following we choose M=\mathbb N and thus speak of infinite words, but all definitions are naturally generalizable to the bi-infinite case. Definition A set of infinite words over ''A'' is a ''shift space'' (or ''subshift'') if it is closed with respect to the natural product topology o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mean Dimension
In mathematics, the mean (topological) dimension of a topological dynamical system is a non-negative extended real number that is a measure of the complexity of the system. Mean dimension was first introduced in 1999 by Gromov. Shortly after it was developed and studied systematically by Lindenstrauss and Weiss. In particular they proved the following key fact: a system with finite topological entropy has zero mean dimension. For various topological dynamical systems with infinite topological entropy, the mean dimension can be calculated or at least bounded from below and above. This allows mean dimension to be used to distinguish between systems with infinite topological entropy. Mean dimension is also related to the problem of embedding topological dynamical systems in shift spaces (over Euclidean cubes). General definition A topological dynamical system consists of a compact Hausdorff topological space \textstyle X and a continuous self-map \textstyle T:X\rightarrow X. Let ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Amenable Group
In mathematics, an amenable group is a locally compact topological group ''G'' carrying a kind of averaging operation on bounded functions that is invariant under translation by group elements. The original definition, in terms of a finitely additive measure (or mean) on subsets of ''G'', was introduced by John von Neumann in 1929 under the German name "messbar" ("measurable" in English) in response to the Banach–Tarski paradox. In 1949 Mahlon M. Day introduced the English translation "amenable", apparently as a pun on "''mean''". The amenability property has a large number of equivalent formulations. In the field of analysis, the definition is in terms of linear functionals. An intuitive way to understand this version is that the support of the regular representation is the whole space of irreducible representations. In discrete group theory, where ''G'' has the discrete topology, a simpler definition is used. In this setting, a group is amenable if one can say what ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
