Related papers: Approximate Capacities of Two-Dimensional Codes by…
We present new bounds on the existence of general quantum maximum distance separable codes (QMDS): the length $n$ of all QMDS codes with local dimension $D$ and distance $d \geq 3$ is bounded by $n \leq D^2 + d - 2$. We obtain their weight…
We find many tight codes in compact spaces, i.e., optimal codes whose optimality follows from linear programming bounds. In particular, we show the existence (and abundance) of several hitherto unknown families of simplices in quaternionic…
In recent years, there has been increasing attention to the spatial dimensions of residential segregation, such as the spatial arrangement of segregated neighborhoods and the geographic scale or relative size of segregated areas. However,…
In this paper, we provide a family of dynamic programming based algorithms to sample nearly-shortest self avoiding walks between two points of the integer lattice $\mathbb{Z}^2$. We show that if the shortest path of between two points has…
We provide a rigorous mathematical treatment to the crowding issue in data visualization when high dimensional data sets are projected down to low dimensions for visualization. By properly adjusting the capacity of high dimensional balls,…
The metric capacitated facility location is a well-studied problem for which, while constant factor approximations are known, no efficient relaxation with constant integrality gap is known. The question whether there is such a relaxation is…
This manuscript provides a model to characterize the energy savings of network coded storage (NCS) in storage area networks (SANs). We consider blocking probability of drives as our measure of performance. A mapping technique to analyze…
Neural Architecture Search (NAS) has emerged as a favoured method for unearthing effective neural architectures. Recent development of large models has intensified the demand for faster search speeds and more accurate search results.…
We show the existence of rigid combinatorial objects which previously were not known to exist. Specifically, for a wide range of the underlying parameters, we show the existence of non-trivial orthogonal arrays, $t$-designs, and $t$-wise…
The Wasserstein barycenter problem seeks a probability measure that minimizes the weighted average of the Wasserstein distances to a given collection of probability measures. We study the discrete setting, where each measure has finite…
Spatially coupled, parallel concatenated codes (SC-PCCs) have been shown to approach channel capacity when decoded using optimal iterative methods. However, under complexity constraints such decoding strategies can result in unacceptable…
The use of automatic methods, often referred to as Neural Architecture Search (NAS), in designing neural network architectures has recently drawn considerable attention. In this work, we present an efficient NAS approach, named HM- NAS,…
For many mixed-integer programming (MIP) problems, high-quality dual bounds can be obtained either through advanced formulation techniques coupled with a state-of-the-art MIP solver, or through semidefinite programming (SDP) relaxation…
Search spaces hallmark the advancement of Neural Architecture Search (NAS). Large and complex search spaces with versatile building operators and structures provide more opportunities to brew promising architectures, yet pose severe…
We study strength of inequalities used in mixed-integer programming, and in branch-and-cut algorithms that solve such problems. Strength is an ethereal property lacking good formal definition, but crucial for computational speed. We review…
First, we study geometric variants of the standard set cover motivated by assignment of directional antenna and shipping with deadlines, providing the first known polynomial-time exact solutions. Next, we consider the following general…
We consider the problem of tracking one solution path defined by a polynomial homotopy on a parallel shared memory computer. Our robust path tracker applies Newton's method on power series to locate the closest singular parameter value. On…
We consider the following problem: given a program, find tight asymptotic bounds on the values of some variables at the end of the computation (or at any given program point) in terms of its input values. We focus on the case of…
Codes in the sum-rank metric have received many attentions in recent years, since they have wide applications in the multishot network coding, the space-time coding and the distributed storage. Fundamental bounds, some explicit or…
Spatial coupling was proved to improve the belief-propagation (BP) performance up to the maximum-a-posteriori (MAP) performance. This paper addresses an extended class of spatially coupled (SC) systems. A potential function is derived for…