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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Topology optimization via implicit neural representations
隐式 神经表示 拓扑优化
2023/4/24
Along with the rapid development of artificial intelligence (AI) technology, scientific research enters a new era of AI. Topology optimization (TO) and AI technology are recently showing a growing tre...
Topological components of spaces of representations
representations Topological components
2015/9/29
Let S be a closed oriented surface of genus g > 1 and let ~r denote its fundamental
group. Let G be a semisimple Lie group. The purpose of this paper is to investigate the global properties of the s...
One of the foundations of oriented matroid theory is the topological representation theorem of Folkman and Lawrence [8]. It says that an oriented (simple) matroid can be realized uniquely as an arrang...
Representations of the Kauffman skein algebra II: punctured surfaces
Representations of the Kauffman skein algebra II punctured surfaces Geometric Topology
2012/6/29
In earlier work, we constructed invariants of irreducible representations of the Kauffman skein algebra of a surface. We introduce here an inverse construction, which to a set of possible invariants a...
Representations of the Kauffman skein algebra I: invariants and miraculous cancellations
Representations of the Kauffman skein algebra I invariants miraculous cancellations Geometric Topology
2012/6/29
We study finite-dimensional representations of the Kauffman skein algebra of a surface S. In particular, we construct invariants of such irreducible representations when the underlying parameter q is ...
Knot state asymptotics II, Witten conjecture and irreducible representations
Knot state asymptotics II Witten conjecture irreducible representations Geometric Topology
2011/8/30
Abstract: This article pursues the study of the knot state asymptotics in the large level limit initiated in "Knot sate Asymptotics I". As a main result, we prove the Witten asymptotic expansion conje...
Knot state asymptotics I, AJ Conjecture and abelian representations
Knot state asymptotics I AJ Conjecture abelian representations Geometric Topology
2011/8/30
Abstract: Consider the Chern-Simons topological quantum field theory with gauge group SU(2) and level k. Given a knot in the 3-sphere, this theory associates to the knot exterior an element in a vecto...
Relative homological algebra in categories of representations of infinite quivers
cover envelope torsion free flat representations of a quiver
2010/11/26
In the first part of this paper, we prove the existence of torsion
free covers in the category of representations of quivers, (Q,R-Mod),for a wide class of quivers included in the class of the so-cal...
Lowest Weight Representations of Super Schrodinger Algebras in One Dimensional Space
Lowest Weight Representations Super Schrodinger One Dimensional Space
2010/11/26
Lowest weight modules, in particular, Verma modules over the N = 1, 2 super Schr¨odinger
algebras in (1+1) dimensional spacetime are investigated. The reducibility of the Verma
modules is analyzed v...
Ambiguities in recurrence-based complex network representations of time series
time series complex network perspective phase-space properties
2010/4/1
Recently, different approaches have been proposed for studying basic properties of time series from a complex network perspective. In this work, the corresponding potentials and limitations of network...
Earlier an arbitrary poset $P$ was proved to be isomorphic to the collection of subsets of a space $M$ with two closures which are closed in the first closure and open in the other. As a space $M$ fo...