Topic
Character (mathematics)
About: Character (mathematics) is a research topic. Over the lifetime, 46723 publications have been published within this topic receiving 411412 citations.
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TL;DR: Using parsimony to reconstruct ancestral character states on a phylogenetic tree has become a popular method for testing ecological and evolutionary hypotheses, but recent research suggests that parsimony reconstructions are often sensitive to violations of the almost universal assumption of equal probabilities of gains and losses.
Abstract: Using parsimony to reconstruct ancestral character states on a phylogenetic tree has become a popular method for testing ecological and evolutionary hypotheses. Despite its popularity, the assumptions and uncertainties of reconstructing the ancestral states of a single character have received less attention than the much less challenging endeavor of reconstructing phylogenetic trees from many characters. Recent research suggests that parsimony reconstructions are often sensitive to violations of the almost universal assumption of equal probabilities of gains and losses. In addition, maximum likelihood has been developed as an alternative to parsimony reconstruction, and has also revealed a surprising amount of uncertainty in ancestral reconstructions.
485 citations
Book•
01 Aug 1976
TL;DR: The number of points in a variety over finite fields is a constant in algebraic geometry as mentioned in this paper, and the number of vertices in a manifold is a function of the cardinality of the vertices.
Abstract: Equations yd=f(x) and yq?y=f(x)- Character sums and exponential sums- Absolutely irreducible equations f(x,y)=0- Equations in many variables- Absolutely irreducible equations f(x1,,xn)=0- Rudiments of algebraic geometry The number of points in varieties over finite fields
471 citations
Journal Article•
468 citations
Book•
07 Nov 2007
TL;DR: In this article, the authors propose a character formula of the highest weight modules, based on Hecke Algebras and Hodge Modules, which they call the Character Formula of Highest Weight Modules.
Abstract: D-Modules and Perverse Sheaves.- Preliminary Notions.- Coherent D-Modules.- Holonomic D-Modules.- Analytic D-Modules and the de Rham Functor.- Theory of Meromorphic Connections.- Regular Holonomic D-Modules.- Riemann-Hilbert Correspondence.- Perverse Sheaves.- Representation Theory.- Algebraic Groups and Lie Algebras.- Conjugacy Classes of Semisimple Lie Algebras.- Representations of Lie Algebras and D-Modules.- Character Formula of HighestWeight Modules.- Hecke Algebras and Hodge Modules.
461 citations
01 Dec 1996
460 citations