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

Combinatorics Quantum Physics 05C50, 05C10, 81P45

TWEETS

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

TWEETS

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

TWEETS

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

TWEETS

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

Combinatorics

TWEETS

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

TWEETS

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

TWEETS

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

Dynamical Systems Mathematical Physics Analysis of PDEs Mathematical Physics

TWEETS

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

TWEETS

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

Number Theory Mathematical Physics Mathematical Physics 11M26, 11M50

TWEETS