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The Generalized Area Theorem and Some of its Consequences
Transmission of binary binary files
2015/8/21
There is a fundamental relationship between belief propagation and maximum a posteriori decoding. The case of transmission over the binary erasure channel was investigated in detail in a companion pap...
The moduli space of curves has proven itself a central object in geometry. The past
decade has seen substantial progress in understanding the moduli space of curves, involving ideas, for example, fro...
Deterministic Construction of an Approximate M-Ellipsoid and its Application to Derandomizing Lattice Algorithms
Approximate M-Ellipsoid Lattice Algorithms Computational Complexity
2011/10/9
Abstract: We give a deterministic O(log n)^n algorithm for the {\em Shortest Vector Problem (SVP)} of a lattice under {\em any} norm, improving on the previous best deterministic bound of n^O(n) for g...
On the approximation of a polytope by its dual $L_{p}$-centroid bodies
centroid bodies floating bodies polytopes Lp Brunn Minkowski theory
2011/9/14
Abstract: We show that the rate of convergence on the approximation of volumes of a convex symmetric polytope P in R^n by its dual L_{p$-centroid bodies is independent of the geometry of P. In particu...
The AKNS Hierarchy Integrability Analysis Revisited: The Vertex Operator Approach and its Lie-Algebraic Structure
the AKNS hierarchy Lax type integrability Lie-algebraic approach
2011/3/2
A regular approach to studying the Lax type integrability of the AKNS hierarchy of nonlinear Lax type integrable dynamical systems in the vertex operator representation is devised.
The AKNS Hierarchy Integrability Analysis Revisited: The Vertex Operator Approach and its Lie-Algebraic Structure
the AKNS hierarchy Lax type integrability Lie-algebraic approach vertex operators
2010/12/28
A regular approach to studying the Lax type integrability of the AKNS hierarchy of nonlinear Lax type integrable dynamical systems in the vertex operator representation is devised.