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      Cospectral graphs obtained by edge deletion

      February 7, 2023

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      Mathematics
      Combinatorics
      Combinatorics
      Let M∘NM\circ NM∘N denote the Schur product of two matrices MMM and NNN. A graph XXX with adjacency matrix AAA is walk regular if Ak∘IA^k\circ IAk∘I is a constant times III for each k≥0k\ge0k≥0, and XXX is 1-walk-regular if it is walk regular and $A^k\ci...

      ℓp\ell^pℓp metrics on cell complexes

      February 7, 2023

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      Mathematics
      Group Theory
      Metric Geometry
      Group Theory
      Metric Geometry
      Motivated by the observation that groups can be effectively studied using metric spaces modelled on ℓ1\ell^1ℓ1, ℓ2\ell^2ℓ2, and ℓ∞\ell^\inftyℓ∞ geometry, we consider cell complexes equipped with an ℓp\ell^pℓp metric for arbitrary ppp. Under weak co...

      Relativity and decoherence of spacetime superpositions

      February 7, 2023

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      Physics
      General Relativity and Quantum Cosmology
      High Energy Physics - Theory
      Quantum Physics
      General Relativity and Quantum Cosmology
      High Energy Physics - Theory
      Quantum Physics
      It is univocally anticipated that in a theory of quantum gravity, there exist quantum superpositions of semiclassical states of spacetime geometry. Such states could arise for example, from a source mass in a superposition of spatial config...

      Quantum dynamics of coupled excitons and phonons in chain-like systems: tensor train approaches and higher-order propagators

      February 7, 2023

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      Physics
      Quantum Physics
      Quantum Physics
      We investigate tensor-train approaches to the solution of the time-dependent Schr\"{o}dinger equation for chain-like quantum systems with on-site and nearest-neighbor interactions only. Using efficient low-rank tensor train representations,...

      The size of the Betti table of Binomial Edge Ideals

      February 7, 2023

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      Mathematics
      Commutative Algebra
      Commutative Algebra
      Let GGG be a finite simple graph on nnn non-isolated vertices, and let JGJ_GJG​ be its binomial edge ideal. We determine almost all pairs (projdim(JG),reg(JG))(\text{projdim}(J_G),\text{reg}(J_G))(projdim(JG​),reg(JG​)), where GGG ranges over all finite simple graphs on nnn non-isolat...

      A Nonlocal diffusion model with H1H^1H1 convergence for Dirichlet Boundary

      February 7, 2023

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      Mathematics
      Analysis of PDEs
      Analysis of PDEs
      In this paper, we present a nonlocal model for Poisson equation and corresponding eigenproblem with Dirichlet boundary condition. In the direct derivation of the nonlocal model, normal derivative is required which is not known for Dirichlet...

      Label propagation on binomial random graphs

      February 7, 2023

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      Mathematics
      Computer Science
      Probability
      Computational Complexity
      Probability
      Computational Complexity
      We study the behavior of a label propagation algorithm (LPA) on the Erd\H{o}s-R\'enyi random graph G(n,p)\mathcal{G}(n,p)G(n,p). Initially, given a network, each vertex starts with a random label in the interval [0,1][0,1][0,1]. Then, in each round of LPA, e...

      Learning Discretized Neural Networks under Ricci Flow

      February 7, 2023

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      Computer Science
      Mathematics
      Machine Learning
      Information Theory
      Neural and Evolutionary Computing
      Information Theory
      Machine Learning
      Information Theory
      Neural and Evolutionary Computing
      Information Theory
      In this paper, we study Discretized Neural Networks (DNNs) composed of low-precision weights and activations, which suffer from either infinite or zero gradients due to the non-differentiable discrete function during training. Most training...

      Generalized Rindler Wedge and Holographic Observer Concordance

      February 7, 2023

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      Physics
      High Energy Physics - Theory
      General Relativity and Quantum Cosmology
      High Energy Physics - Theory
      General Relativity and Quantum Cosmology
      Defining gravitational subsystems has long been challenging due to the lack of the conventional notion of locality in gravity. In this work, we define gravitational subsystems from the observable spacetime subregions of a set of well-define...

      Extremal graphs for the odd prism

      February 7, 2023

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      Mathematics
      Combinatorics
      The Tur\'an number ex(n,H)\mathrm{ex}(n,H)ex(n,H) of a graph HHH is the maximum number of edges in an nnn-vertex graph which does not contain HHH as a subgraph. The Tur\'{a}n number of regular polyhedrons was widely studied in a series of works due to ...
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