Related papers: The local quantization behavior of absolutely cont…
For an increasing monotone graph property $\mP$ the \emph{local resilience} of a graph $G$ with respect to $\mP$ is the minimal $r$ for which there exists of a subgraph $H\subseteq G$ with all degrees at most $r$ such that the removal of…
A regular partition $\mathcal{P}$ for a $3$-uniform hypergraph $H=(V,E)$ consists of a partition $V=V_1\cup \ldots \cup V_t$ and for each $ij\in {[t]\choose 2}$, a partition $K_2[V_i,V_j]=P_{ij}^1\cup \ldots \cup P_{ij}^{\ell}$, such that…
In this paper, we propose a new method for localization of polynomial ideal, which we call "Local Primary Algorithm". For an ideal $I$ and a prime ideal $P$, our method computes a $P$-primary component of $I$ after checking if $P$ is…
Tests of fit to exact models in statistical analysis often lead to rejections even when the model is a useful approximate description of the random generator of the data. Among possible relaxations of a fixed model, the one defined by…
A $d$-dimensional binary Markov random field on a lattice torus is considered. As the size $n$ of the lattice tends to infinity, potentials $a=a(n)$ and $b=b(n)$ depend on $n$. Precise bounds for the probability for local configurations to…
Inertial particle data from three-dimensional direct numerical simulations of particle-laden homogeneous isotropic turbulence at high Reynolds number are analyzed using Voronoi tessellation of the particle positions, considering different…
In this work, we show that the class of multivariate degree-$d$ polynomials mapping $\{0,1\}^{n}$ to any Abelian group $G$ is locally correctable with $\widetilde{O}_{d}((\log n)^{d})$ queries for up to a fraction of errors approaching half…
We consider the power of local algorithms for approximately solving Max $k$XOR, a generalization of two constraint satisfaction problems previously studied with classical and quantum algorithms (MaxCut and Max E3LIN2). In Max $k$XOR each…
In the literature on $K$-locality ($K\geq2$) networks, the local hidden variables are strictly distributed in the specific observers rather than the whole ones. Regarding genuine Bell locality, all local hidden variables, as classical…
In the number partitioning problem (NPP) one aims to partition a given set of $N$ real numbers into two subsets with approximately equal sum. The NPP is a well-studied optimization problem and is famous for possessing a…
We consider the problem of calculating the logical error probability for a stabilizer quantum code subject to random Pauli errors. To access the regime of large code distances where logical errors are extremely unlikely we adopt the…
In this paper, we study the probabilistic local well-posedness of the cubic Schr\"odinger equation (cubic NLS): \[ (i\partial_{t} + \Delta) u = \pm |u|^{2} u \text{ on } [0,T) \times \mathbb{R}^{d}, \] with initial data being a Wiener…
We study the distinguishability norms associated to families of locally restricted POVMs on multipartite systems. These norms (introduced by Matthews, Wehner and Winter) quantify how quantum measurements, subject to locality constraints,…
We study the optimization version of the set partition problem (where the difference between the partition sums are minimized), which has numerous applications in decision theory literature. While the set partitioning problem is NP-hard and…
The conserved probability densities (attributed to the conserved currents derived from relativistic wave equations) should be non-negative and the integral of them over an entire hypersurface should be equal to one. To satisfy these…
We investigate quantization coefficients for self-similar probability measures \mu on limit sets which are generated by systems S of infinitely many contractive similarities and by probabilistic vectors. The theory of quantization…
We prove that with "high probability" a random Kostlan polynomial in $n+1$ many variables and of degree $d$ can be approximated by a polynomial of "low degree" without changing the topology of its zero set on the sphere $S^n$. The…
We consider the root lattice $A_n$ and derive explicit formulae for the moments of its Voronoi cell. We then show that these formulae enable accurate prediction of the error probability of lattice codes constructed from $A_n$.
We establish efficient approximate counting algorithms for several natural problems in local lemma regimes. In particular, we consider the probability of intersection of events and the dimension of intersection of subspaces. Our approach is…
Given a graph $G = (V, E)$, the $3$-path partition problem is to find a minimum collection of vertex-disjoint paths each of order at most $3$ to cover all the vertices of $V$. It is different from but closely related to the well-known…