相关论文: Thorup-Zwick Emulators are Universally Optimal Hop…

The note is concerned with inductive systems of Toeplitz algebras and their $*$-homomorphisms over arbitrary partially ordered sets. The Toeplitz algebra is the reduced semigroup $C^*$-algebra for the additive semigroup of non-negative…

We introduce the effectual topological complexity (ETC) of a $G$-space $X$. This is a $G$-equivariant homotopy invariant sitting in between the effective topological complexity of the pair $(X,G)$ and the (regular) topological complexity of…

We study vertex sparsification for preserving distances in planar graphs. Given an edge-weighted planar graph with $k$ terminals, the goal is to construct an emulator, which is a smaller edge-weighted planar graph that contains the…

Graphlets are induced subgraphs of a large network and are important for understanding and modeling complex networks. Despite their practical importance, graphlets have been severely limited to applications and domains with relatively small…

The paper presents a topology optimization approach that designs an optimal structure, called a self-supporting structure, which is ready to be fabricated via additive manufacturing without the usage of additional support structures. Such…

The beta transformation is the iterated map $\beta x\,\mod1$; it generates the base-$\beta$ expansion of a real number x. Every iterated piece-wise monotonic map is topologically conjugate to the beta transformation. For all but a countable…

Transitivity, the existence of periodic points and positive topological entropy can be used to characterize complexity in dynamical systems. It is known that for graphs that are not trees, for every $\varepsilon>0,$ there exist (complicate)…

Enhanced tensor field theories (eTFT) have dominant graphs that differ from the melonic diagrams of conventional tensor field theories. They therefore describe pertinent candidates to escape the so-called branched polymer phase, the…

We give an algorithmic proof for the existence of tight Hamilton cycles in a random r-uniform hypergraph with edge probability p=n^{-1+eps} for every eps>0. This partly answers a question of Dudek and Frieze [Random Structures Algorithms],…

We consider a compact metric graph of size $\varepsilon$, and attach to it several edges (leads) of length of order one (or of infinite length). As $\varepsilon$ goes to zero, the graph $\mathcal{G}^\varepsilon$ obtained in this way looks…

A celebrated conjecture of Zs. Tuza says that in any (finite) graph, the minimum size of a cover of triangles by edges is at most twice the maximum size of a set of edge-disjoint triangles. Resolving a recent question of Bennett, Dudek, and…

We study finite loop models on a lattice wrapped around a cylinder. A section of the cylinder has N sites. We use a family of link modules over the periodic Temperley-Lieb algebra EPTL_N(\beta, \alpha) introduced by Martin and Saleur, and…

Previous works have shown the universality of allometric scalings under density and total value at city level, but our understanding about the size effects of regions on them is still poor. Here, we revisit the scaling relations between…

We develop a statistically robust framework for reconstructing metal--semiconductor contact regions using topological gradients. The inverse problem is formulated as the identification of an unknown contact region from boundary measurements…

Node embedding is the task of extracting informative and descriptive features over the nodes of a graph. The importance of node embeddings for graph analytics, as well as learning tasks such as node classification, link prediction and…

Topological descriptors, such as the Euler characteristic function and the persistence diagram, have grown increasingly popular for representing complex data. Recent work showed that a carefully chosen set of these descriptors encodes all…

We present a general method for counting and packing Hamilton cycles in dense graphs and oriented graphs, based on permanent estimates. We utilize this approach to prove several extremal results. In particular, we show that every nearly…

We aim to revive Thorup's conjecture [Thorup, WG'92] on the existence of reachability shortcuts with ideal size-diameter tradeoffs. Thorup originally asked whether, given any graph $G=(V,E)$ with $m$ edges, we can add $m^{1+o(1)}$…

We extend the use of random evolving sets to time-varying conductance models and utilize it to provide tight heat kernel upper bounds. It yields the transience of any uniformly lazy random walk, on Z^d, d>=3, equipped with uniformly bounded…

Consider a set of terminal nodes K that belong to a network whose nodes are connected by links that fail independently with known probabilities. We introduce a method for estimating any performability measure that depends on the hop…