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The intrinsic connection between lattice theory and topology is fairly well established, For instance, the collection of open subsets of a topological subspace always forms a distributive lattice. Persistent homology has been one of the…
Lattice-based Cryptography is considered to have the characteristics of classical computers and quantum attack resistance. We will design various graphic lattices and matrix lattices based on knowledge of graph theory and topological…
Inspired by previous work of Shoup, Lenstra-De Smit and Couveignes-Lercier, we give fast algorithms to compute in (the first levels of) the ell-adic closure of a finite field. In many cases, our algorithms have quasi-linear complexity.
Let K be a number field, let A be a finite dimensional semisimple K-algebra and let Lambda be an O_K-order in A. It was shown in previous work that, under certain hypotheses on A, there exists an algorithm that for a given (left)…
Eigenvectors of matrices on a network have been used for understanding spectral clustering and influence of a vertex. For matrices with small geodesic-width, we propose a distributed iterative algorithm in this letter to find eigenvectors…
For causal discovery in the presence of latent confounders, constraints beyond conditional independences exist that can enable causal discovery algorithms to distinguish more pairs of graphs. Such constraints are not well-understood yet. In…
High-order finite-difference methods are commonly used in wave propagators for industrial subsurface imaging algorithms. Computational aspects of the reduced linear elastic vertical transversely isotropic propagator are considered. Thread…
Structural properties of large random maps and lambda-terms may be gleaned by studying the limit distributions of various parameters of interest. In our work we focus on restricted classes of maps and their counterparts in the…
We construct several pairwise-incomparable bounds on the projective dimensions of edge ideals. Our bounds use combinatorial properties of the associated graphs; in particular we draw heavily from the topic of dominating sets. Through…
We give an FPTAS and an efficient sampling algorithm for the high-fugacity hard-core model on bounded-degree bipartite expander graphs and the low-temperature ferromagnetic Potts model on bounded-degree expander graphs. The results apply,…
Coordinated inference problems are being introduced as a basis for a neural network representation of the locality problem in the holographic bulk. It is argued that a type of problem originating in the "prisoners and hats" dilemma involves…
We describe edge labelings of the increasing flip graph of a subword complex on a finite Coxeter group, and study applications thereof. On the one hand, we show that they provide canonical spanning trees of the facet-ridge graph of the…
Suppose we want to construct some structure on a bounded-degree graph, e.g., an almost maximum matching, and we want to decide about each edge depending only on its constant-radius neighborhood. We examine and compare the strengths of…
The Artificial Benchmark for Community Detection (ABCD) graph is a recently introduced random graph model with community structure and power-law distribution for both degrees and community sizes. The model generates graphs with similar…
In this paper we show how graph structure can be used to drastically reduce the computational bottleneck of the Breadth First Search algorithm (the foundation of many graph traversal techniques). In particular, we address parallel…
We utilize the Bruns-Lakser completion to introduce Bruns-Lakser towers of a meet-semilattice. This machinery enables us to develop various hierarchies inside the class of bounded distributive lattices, which measure $\kappa$-degrees of…
We report our experiments in identifying large bipartite subgraphs of simple connected graphs which are based on the sign pattern of eigenvectors belonging to the extremal eigenvalues of different graph matrices: adjacency, signless…
In this work the algorithms of fast multiplication of matrices are considered. To any algorithm there associated a certain group of automorphisms. These automorphism groups are found for some well-known algorithms, including algorithms of…
We propose a new algorithm for solving the graph-fused lasso (GFL), a method for parameter estimation that operates under the assumption that the signal tends to be locally constant over a predefined graph structure. Our key insight is to…
Parameter choosing in classical edge detection algorithms can be a costly and complex task. Choosing the correct parameters can improve considerably the resulting edge-map. In this paper we present a version of Edge Drawing algorithm in…