We provide new explicit examples of lattice sphere packings in dimensions 54, 55, 162, 163, 486 and 487 that are the densest known so far, using Kummer families of elliptic curves over global function fields.
In some cases, these families of elliptic curve ...
Euclidean lattices are mathematical objects of increasing interest in the fields of cryptography and error-correcting codes. This doctoral thesis is a study on high-dimensional lattices with the motivation to understand how efficient they are in terms of b ...
obtain algorithmically effective versions of the dense lattice sphere packings constructed from orders in Q-division rings by the first author. The lattices in question are lifts of suitable codes from prime characteristic to orders O in Q-division rings a ...
A correspondence functor is a functor from the category of finite sets and correspondences to the category of k-modules, where k is a commutative ring. By means of a suitably defined duality, new correspondence functors are constructed, having remarkable p ...
We study the elliptic curves given by y(2) = x(3) + bx + t(3n+1) over global function fields of characteristic 3 ; in particular we perform an explicit computation of the L-function by relating it to the zeta function of a certain superelliptic curve u(3) ...
We give a construction of an efficient one-out-of-many proof system, in which a prover shows that he knows the pre-image for one element in a set, based on the hardness of lattice problems. The construction employs the recent zero-knowledge framework of Ly ...
It is generally assumed that the parent-twin interface is a fully invariant plane. The calculations of the rational interfaces of the type I twins and irrational interfaces of the type II twins are based on this hypothesis. Recently, some asymmetric facets ...
We propose an adaptive variance-reduction method, called AdaSpider, for minimization of L-smooth, non-convex functions with a finite-sum structure. In essence, AdaSpider combines an AdaGrad-inspired [Duchi et al., 2011, McMahan & Streeter, 2010], but a fai ...
Let K be a totally real number field of degree n >= 2. The inverse different of K gives rise to a lattice in Rn. We prove that the space of Schwartz Fourier eigenfunctions on R-n which vanish on the "component-wise square root" of this lattice, is infinite ...
We propose a new approach for normalization and simplification of logical formulas. Our approach is based on algorithms for lattice-like structures. Specifically, we present two efficient algorithms for computing a normal form and deciding the word problem ...
The Gray-Wyner network subject to a fidelity criterion is studied. Upper and lower bounds for the trade-offs between the private sum-rate and the common rate are obtained for arbitrary sources subject to mean-squared error distortion. The bounds meet exact ...
Inorganic perovskite solar cells (PSCs) have witnessed extraordinary advances owing to their prominent stability against thermal aging. However, they suffer from a phase transition from black phase to yellow phase under ambient conditions and serious energ ...
We give a direct construction of a specific central idempotent in the endomorphism algebra of a finite lattice T. This idempotent is associated with all possible sublattices of T which are totally ordered. A generalization is considered in a conjectural fa ...
An integer program (IP) is a problem of the form min{f(x):Ax=b,l≤x≤u,x∈Zn}, where A∈Zm×n, b∈Zm, l,u∈Zn, and f:Zn→Z is a separable convex objective function.
The problem o ...
We determine the dimension of every simple module for the algebra of the monoid of all relations on a finite set (i.e. Boolean matrices). This is in fact the same question as the determination of the dimension of every evaluation of a simple correspondence ...
The use of cellular ceramics in enhancing the performance of a high-temperature latent heat thermal energy storage unit was investigated. A detailed design methodology is presented, which consists of a combined analytical-numerical analysis followed by a m ...
The Boolean lattice (2[n],subset of) is the family of all subsets of [n]={1,MIDLINE HORIZONTAL ELLIPSIS,n}, ordered by inclusion. Let P be a partially ordered set. We prove that if n is sufficiently large, then there exists a packing P of copies of P in (2 ...
Solid-like behavior at low energies and long distances is usually associated with the spontaneous breaking of spatial translations at microscopic scales, as in the case of a lattice of atoms. We exhibit three quantum field theories that are renormalizable, ...
