Related papers: Constrained Codes for Rank Modulation

Exploiting permutation invariance to reduce the exponential scaling of semidefinite programs in quantum information has emerged as a powerful computational technique. In this work, we develop a systematic framework for using this reduction…

We investigate refined algebraic quantisation within a family of classically equivalent constrained Hamiltonian systems that are related to each other by rescaling a momentum-type constraint. The quantum constraint is implemented by a…

A Genome rearrangement problem studies large-scale mutations on a set of DNAs in living organisms. Various rearrangements like reversals, transpositions, translocations, fissions, fusions, and combinations and different variations have been…

This work studies the (non)robustness of two-layer neural networks in various high-dimensional linearized regimes. We establish fundamental trade-offs between memorization and robustness, as measured by the Sobolev-seminorm of the model…

We consider the effect on the mixing properties of a piecewise smooth interval map $f$ when its domain is divided into $N$ equal subintervals and $f$ is composed with a permutation of these. The case of the stretch-and-fold map $f(x)=mx…

For each integer k >= 2, let F(k) denote the largest n for which there exists a permutation \sigma \in S_n, all of whose patterns of length k are distinct. We prove that F(k) = k + \lfloor \sqrt{2k-3} \rfloor + e_k, where e_k \in {-1,0} for…

The capacity of a class of Interference Relay Channels (IRC) -the Injective Semideterministic IRC where the relay can only observe one of the sources- is investigated. We first derive a novel outer bound and two inner bounds which are based…

Chance constraints are frequently used to limit the probability of constraint violations in real-world optimization problems where the constraints involve stochastic components. We study chance-constrained submodular optimization problems,…

Permutation of any two hidden units yields invariant properties in typical deep generative neural networks. This permutation symmetry plays an important role in understanding the computation performance of a broad class of neural networks…

In this work, we consider the Submodular Maximization under Knapsack (SMK) constraint problem over the ground set of size $n$. The problem recently attracted a lot of attention due to its applications in various domains of combination…

Tandem duplication in DNA is the process of inserting a copy of a segment of DNA adjacent to the original position. Motivated by applications that store data in living organisms, Jain {\em et al.} (2016) proposed the study of codes that…

We consider avoidance of permutation patterns with designated gap sizes between pairs of consecutive letters. We call the patterns having such constraints distant patterns (DPs) and we show their relation to other pattern notions…

Transformer architectures have achieved state-of-the-art results on a variety of sequence modeling tasks. However, their attention mechanism comes with a quadratic complexity in sequence lengths, making the computational overhead…

We study random string-duplication systems, which we call P\'olya string models. These are motivated by DNA storage in living organisms, and certain random mutation processes that affect their genome. Unlike previous works that study the…

We investigate the clustering transition undergone by an exemplary random constraint satisfaction problem, the bicoloring of $k$-uniform random hypergraphs, when its solutions are weighted non-uniformly, with a soft interaction between…

Let S=K[x_1,...,x_n] be a polynomial ring and R=S/I be a graded K-algebra where I is a graded ideal in S. Herzog, Huneke and Srinivasan have conjectured that the multiplicity of R is bounded above by a function of the maximal shifts in the…

We study randomized algorithms for constrained optimization, in abstract frameworks that include, in strictly increasing generality: convex programming; LP-type problems; violator spaces; and a setting we introduce, consistent spaces. Such…

Combinatorial reconfiguration is a growing research field studying problems on the transformability between a pair of solutions of a search problem. We consider the approximability of optimization variants of reconfiguration problems; e.g.,…

The problem of maximizing a constrained monotone set function has many practical applications and generalizes many combinatorial problems. Unfortunately, it is generally not possible to maximize a monotone set function up to an acceptable…

We consider the decoding of rank metric codes assuming the error matrix is symmetric. We prove two results. First, for rates $<1/2$ there exists a broad family of rank metric codes for which any symmetric error pattern, even of maximal rank…