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The year 2000 in science and technology involved some significant events.
In graph theory, an expander graph is a sparse graph that has strong connectivity properties, quantified using vertex, edge or spectral expansion. Expander constructions have spawned research in pure and applied mathematics, with several applications to complexity theory, design of robust computer networks, and the theory of error-correcting codes.
1931 (MCMXXXI) was a common year starting on Thursday of the Gregorian calendar, the 1931st year of the Common Era (CE) and Anno Domini (AD) designations, the 931st year of the 2nd millennium, the 31st year of the 20th century, and the 2nd year of the 1930s decade.
Steven Weinberg was an American theoretical physicist and Nobel laureate in physics for his contributions with Abdus Salam and Sheldon Glashow to the unification of the weak force and electromagnetic interaction between elementary particles.
The year 1934 in science and technology involved some significant events, listed below.
The year 1998 in science and technology involved many events, some of which are included below.
The year 2004 in science and technology involved some significant events.
The year 1997 in science and technology involved many significant events, listed below.
The year 1933 in science and technology involved some significant events, listed below.
Moscow Institute of Physics and Technology, is a public research university located in Moscow Oblast, Russia. It prepares specialists in theoretical and applied physics, applied mathematics and related disciplines.
The year 2005 in science and technology involved some significant events.
In combinatorial mathematics, rotation systems encode embeddings of graphs onto orientable surfaces by describing the circular ordering of a graph's edges around each vertex. A more formal definition of a rotation system involves pairs of permutations; such a pair is sufficient to determine a multigraph, a surface, and a 2-cell embedding of the multigraph onto the surface.
Robert Allan Weinberg is a biologist, Daniel K. Ludwig Professor for Cancer Research at Massachusetts Institute of Technology (MIT), director of the Ludwig Center of the MIT, and American Cancer Society Research Professor. His research is in the area of oncogenes and the genetic basis of human cancer.
Avi Wigderson is an Israeli computer scientist and mathematician. He is the Herbert H. Maass Professor in the school of mathematics at the Institute for Advanced Study in Princeton, New Jersey, United States of America. His research interests include complexity theory, parallel algorithms, graph theory, cryptography, distributed computing, and neural networks. Wigderson received the Abel Prize in 2021 for his work in theoretical computer science. He also received the 2023 Turing Award for his contributions to the understanding of randomness in the theory of computation.
Omer Reingold is an Israeli computer scientist. He is the Rajeev Motwani professor of Computer Science in the Computer Science Department at Stanford University and the director of the Simons Collaboration on the Theory of Algorithmic Fairness. He received a PhD in computer science at Weizmann in 1998 under Moni Naor. He received the 2005 Grace Murray Hopper Award for his work in finding a deterministic logarithmic-space algorithm for st-connectivity in undirected graphs. He, along with Avi Wigderson and Salil Vadhan, won the Gödel Prize (2009) for their work on the zig-zag product. He became a Fellow of the Association for Computing Machinery in 2014 "For contributions to the study of pseudorandomness, derandomization, and cryptography."
In the mathematical field of graph theory, graph operations are operations which produce new graphs from initial ones. They include both unary and binary operations.
A symmetric Turing machine is a Turing machine which has a configuration graph that is undirected.
In graph theory, the zig-zag product of regular graphs , denoted by , is a binary operation which takes a large graph and a small graph and produces a graph that approximately inherits the size of the large one but the degree of the small one. An important property of the zig-zag product is that if is a good expander, then the expansion of the resulting graph is only slightly worse than the expansion of .
In mathematics, a rotation map is a function that represents an undirected edge-labeled graph, where each vertex enumerates its outgoing neighbors. Rotation maps were first introduced by Reingold, Vadhan and Wigderson in order to conveniently define the zig-zag product and prove its properties. Given a vertex and an edge label , the rotation map returns the 'th neighbor of and the edge label that would lead back to .
The hallmarks of cancer were originally six biological capabilities acquired during the multistep development of human tumors and have since been increased to eight capabilities and two enabling capabilities. The idea was coined by Douglas Hanahan and Robert Weinberg in their paper "The Hallmarks of Cancer" published January 2000 in Cell.
Douglas Hanahan is an American biologist, professor and director emeritus of the Swiss Institute for Experimental Cancer Research at EPFL in Lausanne, Switzerland. He is currently member of the Lausanne branch of the Ludwig Institute.