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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.
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...
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...
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.
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.
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...
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.
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 ...
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...
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...
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...
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...

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