搜索结果: 1-15 共查到“知识库 代数拓扑学”相关记录72条 . 查询时间(3.725 秒)
切换拓扑一阶积分器网络量化趋同控制
多智能体系统 量化趋同 切换拓扑 收敛时间
2014/3/12
针对数字信道中传输的是经过量化和编码后的数据, 研究了切换拓扑情况下连续时间一阶积分器网络中的量化趋同问题. 通过均匀量化器, 每个智能体将量化后的状态传输给邻居, 并利用所得信息设计协议, 实现量化趋同.在所提出的量化趋同协议下, 所有状态将在有限时间内进入包含状态均值的量化层中. 特别地, 对于通信拓扑是时不变的情况, 给出了实现量化趋同所需时间的上界. 仿真结果验证了所提出算法的有效性.
Sharp vanishing thresholds for cohomology of random flag complexes
Sharp vanishing thresholds cohomology random flag complexes Algebraic Topology
2012/7/11
We exhibit a sharp threshold for vanishing of rational cohomology in random flag complexes, providing a generalization of the Erd\H{o}s-R\'enyi theorem. As a corollary, almost all d-dimensional flag c...
Combinatorial resolutions of multigraded modules and multipersistent homology
Combinatorial resolutions multigraded modules multipersistent homology Algebraic Topology
2012/6/30
Let $ R=k[x_1...x_r]$ and $M$ a multigraded $R-$module. In this work we interpret $M$ as a multipersistent homology module and give a multigraded resolution of it. The construction involves cellular r...
Cutting description of trivial 1-cohomology
Cutting description trivial 1-cohomology Algebraic Topology
2012/6/30
As an exercise in Morse theory and Eilenberg-MacLane spectrum, we propose a topological description of trivial first cohomology in terms of cutting properties of open sets.
Cohomology of Kac-Moody groups over a finite field
Cohomology classifying spaces Kac-Moody groups
2012/6/26
We compute the mod $p$ cohomology algebra of a family of infinite discrete Kac-Moody groups of rank two defined over finite fields of characteristic different from $p$.
Given a homotopy equivalence f between two topological spaces we obtain an explicit formula for a strong deformation retraction of the mapping cylinder of f onto its top.
Multidimensional Interleavings and Applications to Topological Inference
Multidimensional Interleavings Topological Inference Algebraic Topology
2012/6/27
This work concerns the theoretical foundations of persistence-based topological data analysis. We develop theory of topological inference in the multidimensional persistence setting, and directly at t...
Symmetric Squaring in Homology and Bordism
algebraic topology homology theory bordism Cech homology
2012/6/19
Looking at the cartesian product X \times X of a topological space X with itself, a natural map to be considered on that object is the involution that interchanges the coordinates, i.e. that maps (x, ...
Several large classes of homogeneous spaces are known to be formal---in the sense of Rational Homotopy Theory. However, it seems that far fewer examples of non-formal homogeneous spaces are known.
Large self-injective rings and the generating hypothesis
Large self-injective rings the generating hypothesis Algebraic Topology
2012/6/9
We construct a number of different examples of non-Noetherian graded rings that are injective as modules over themselves (or have some related but weaker properties). We discuss how these are related ...
Topological complexity of motion planning in projective product spaces
Topological complexity product projective spaces Euclidean immersions of manifolds generalized axial maps
2012/6/14
We study Farber's topological complexity (TC) of Davis' projective product spaces (PPS's). We show that, in many non-trivial instances, the TC of PPS's coming from at least two sphere factors is (much...
On the algebraic K-theory of truncated polynomial algebras in several variables
algebraic K-theory truncated polynomial algebras several variables Algebraic Topology
2012/6/14
We consider the algebraic K-theory of a truncated polynomial algebra in several commuting variables, K(k[x_1, ..., x_n]/(x_1^a_1, ..., x_n^a_n)). This naturally leads to a new generalization of the bi...
Topological and uniform structures on universal covering spaces
Universal covering maps uniform structures Algebraic Topology
2012/6/7
We discuss various uniform structures and topologies on the universal covering space $\widetilde X$ and on the fundamental group $\pi_1(X,x_0)$. We introduce a canonical uniform structure $CU(X)$ on a...
We introduce a variant of the slice spectral sequence which uses only regular slice cells, and state the precise relationship between the two spectral sequences. We analyze how the slice filtration of...
On Lusternik-Schnirelmann Category of Connected Sums
Lusternik-Schnirelmann Category of Connected Sums Algebraic Topology
2012/5/9
In this paper we estimate the Lusternik-Schnirelmann category of the connected sum of two manifolds through their categories. We achieve a more general result regarding the category of a quotient spac...