# Perfect state transfer in quantum walks on orientable maps

no code yet • 23 Nov 2022

A discrete-time quantum walk is the quantum analogue of a Markov chain on a graph.

Combinatorics Quantum Physics 05C50, 05C10, 81P45

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# MPMICE: A hybrid MPM-CFD model for simulating coupled problems in porous media. Application to earthquake-induced submarine landslides

no code yet • 23 Nov 2022

In this paper, we describe a soil-fluid-structure interaction model that combines soil mechanics (saturated sediments), fluid mechanics (seawater or air), and solid mechanics (structures).

Numerical Analysis Numerical Analysis Computational Physics

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# Improved Lower Bound for the Union-Closed Sets Conjecture

no code yet • 21 Nov 2022

We verify an explicit inequality conjectured recently by Gilmer, thus proving that for any nonempty union-closed family $\mathcal F \subseteq 2^{[n]}$, some $i\in [n]$ is contained in at least $\frac{3-\sqrt{5}}{2} \approx 0. 38$ fraction of the sets in $\mathcal F$.

Combinatorics

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# Approximate union closed conjecture

no code yet • 21 Nov 2022

A set system is called union closed if for any two sets in the set system their union is also in the set system.

Combinatorics

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# An improved lower bound for the union-closed set conjecture

no code yet • 21 Nov 2022

We also disprove a conjecture of Gilmer that would have implied the union-closed set conjecture.

Combinatorics

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# Empirical Bayes estimation: When does $g$-modeling beat $f$-modeling in theory (and in practice)?

no code yet • 23 Nov 2022

For the Poisson model with sample size $n$, assuming $p>1$ (for otherwise triviality arises), we show that the NPMLE with appropriate regularization and truncation achieves a total regret $\tilde \Theta(n^{\frac{3}{2p+1}})$, which is minimax optimal within logarithmic factors.

Statistics Theory Methodology Statistics Theory

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# A knot-theoretic approach to comparing the Grothendieck-Teichmüller and Kashiwara-Vergne groups

no code yet • 21 Nov 2022

The sets of Drinfel'd associators and KV solutions are both bi-torsors, with actions by the pro-unipotent Grothendieck-Teichm\"{u}ller and Kashiwara-Vergne groups, respectively.

Quantum Algebra Algebraic Topology Category Theory Primary 18M85, 57K16, Secondary 18M15, 18M60

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# Mean-Field Coupled Systems and Self-Consistent Transfer Operators: A Review

no code yet • 21 Nov 2022

In this review we survey the literature on mean-field coupled maps.

Dynamical Systems Mathematical Physics Analysis of PDEs Mathematical Physics

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# Exact solution approaches for the discrete $α$-neighbor $p$-center problem

no code yet • 23 Nov 2022

The discrete $\alpha$-neighbor $p$-center problem (d-$\alpha$-$p$CP) is an emerging variant of the classical $p$-center problem which recently got attention in literature.

Optimization and Control Discrete Mathematics 90B80, 90C11

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# Currently there are no reasons to doubt the Riemann Hypothesis

no code yet • 21 Nov 2022

We examine published arguments which suggest that the Riemann Hypothesis may not be true.

Number Theory Mathematical Physics Mathematical Physics 11M26, 11M50

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