Related papers: Three experimental pearls in Costas arrays
On a finite graph, there is a natural family of Boltzmann probability measures on cycle-rooted spanning forests, parametrized by weights on cycles. For a certain subclass of those weights, we construct Gibbs measures in infinite volume, as…
Starting with two supercompact cardinals we produce a generic extension of the universe in which a principle that we call ${\rm GM}^+(\omega_3,\omega_1)$ holds. This principle implies ${\rm ISP}(\omega_2)$ and ${\rm ISP}(\omega_3)$, and…
A simple minimalist argument is given for why some correlations between quantum systems boggle our classical intuition. The argument relies on two elementary physical assumptions, and recovers the standard experimentally-testable Bell…
We report on our first set of results for charm physics, using a mixed-action setup with maximally twisted valence fermions on CLS $N_f=2+1$ ensembles. This setup avoids the need of improvement coefficients to subtract $O(am_c)$ effects.…
The aim of this paper is to present some properties of Choquet maximal Radon probability measures on compact, convex subsets of Hausdorff, locally convex, topological real vector spaces. Theorem 3.12 is the main result of the paper. While…
We review old and new uses of exchangeability, emphasizing the general theme of exchangeable representations of complex random structures. Illustrations of this theme include processes of stochastic coalescence and fragmentation; continuum…
The Weyl semimetals [1-6] are three-dimensional (3D) gapless topological phases with Weyl cones in the bulk band, and host massless quasiparticles known as Weyl fermions which were theorized by Hermann Weyl in the last twenties [7]. The…
We investigate monogamy of correlations and entropy inequalities in the Bloch representation. Here, both can be understood as direct relations between different correlation tensor elements and thus appear intimately related. To that end we…
Quantum-mechanical incompatibility, which precludes the simultaneous precise measurement of non-commuting observables, imposes fundamental limits on the rate at which classical information can be extracted. While the potential to surpass…
We introduce a forcing technique to construct three-dimensional arrays of generic extensions through FS (finite support) iterations of ccc posets, which we refer to as 3D-coherent systems. We use them to produce models of new constellations…
We consider loop ensembles on random trees. The loops are induced by a Poisson process of links sampled on the underlying tree interpreted as a metric graph. We allow two types of links, crosses and double bars. The crosses-only case…
The sequence of the primes $p$ for which a variety over $\mathbb{Q}$ has no $p$-adic point plays a fundamental role in arithmetic geometry. This sequence is deterministic, however, we prove that if we choose a typical variety from a family…
A two-dimensional grid with dots is called a \emph{configuration with distinct differences} if any two lines which connect two dots are distinct either in their length or in their slope. These configurations are known to have many…
A well-known conjecture in analytic number theory states that for every pair of sets $X,Y\subset\mathbb{Z}/p\mathbb{Z}$, each of size at least $\log ^C p$ (for some constant $C$) we have that the number of pairs $(x,y)\in X\times Y$ such…
Every Latin square has three attributes that can be even or odd, but any two of these attributes determines the third. Hence the parity of a Latin square has an information content of 2 bits. We extend the definition of parity from Latin…
We give the first example of a mosaic of three combinatorial designs with distinct parameters $2$-$(13,3,1)$, $2$-$(13,4,2)$, and $2$-$(13,6,5)$. Furthermore, we give examples of mosaics of $2$-$(9,3,2)$ designs that are not resolvable,…
The ellipsoid fitting conjecture of Saunderson, Chandrasekaran, Parrilo and Willsky considers the maximum number $n$ random Gaussian points in $\mathbb{R}^d$, such that with high probability, there exists an origin-symmetric ellipsoid…
Pairing in a population imbalanced Fermi system in a two-dimensional optical lattice is studied using Determinant Quantum Monte Carlo (DQMC) simulations and mean-field calculations. The approximation-free numerical results show a wide range…
Erd\H{o}s proved an upper bound on the number of edges in an $n$-vertex non-Hamiltonian graph with given minimum degree and showed sharpness via two members of a particular graph family. F\"{u}redi, Kostochka and Luo showed that these two…
A new method is used to resolve a long-standing conjecture of Niho concerning the crosscorrelation spectrum of a pair of maximum length linear recursive sequences of length $2^{2 m}-1$ with relative decimation $d=2^{m+2}-3$, where $m$ is…