Related papers: A Computer Search for N1L-Configurations
l1-norm quantile regression is a common choice if there exists outlier or heavy-tailed error in high-dimensional data sets. However, it is computationally expensive to solve this problem when the feature size of data is ultra high. As far…
This paper is an attempt to remedy the problem of slow convergence for first-order numerical algorithms by proposing an adaptive conditioning heuristic. First, we propose a parallelizable numerical algorithm that is capable of solving…
We consider the task of locally correcting, and locally list-correcting, multivariate linear functions over the domain $\{0,1\}^n$ over arbitrary fields and more generally Abelian groups. Such functions form error-correcting codes of…
We consider the sets of dimensions for which there is an optimal sphere packing with special regularity properties (respectively, a lattice, or a periodic set with a given bound on the number of translations, or an arbitrary periodic set).…
We present an algorithm for computing upper bounds for the Online Bin Stretching Problem with a small number of bins and the resulting upper bounds for 4, 5 and 6 bins. This both demonstrates the possibility of using computer search for…
We present a construction scheme for quantum error correcting codes. The basic ingredients are a graph and a finite abelian group, from which the code can explicitly be obtained. We prove necessary and sufficient conditions for the graph…
We study the problem of high-dimensional multiple packing in Euclidean space. Multiple packing is a natural generalization of sphere packing and is defined as follows. Let $ N>0 $ and $ L\in\mathbb{Z}_{\ge2} $. A multiple packing is a set…
Quantum contextuality is a limitation on deterministic hidden variable models, testable in measurement scenarios where outcomes differ under quantum or classical descriptions due to a common set of constraints. When considering measurements…
We present a constraint-coding scheme to correct asymmetric magnitude-$1$ errors in multi-level non-volatile memories. For large numbers of such errors, the scheme is shown to deliver better correction capability compared to known…
The constituent parts of a quantum computer are inherently vulnerable to errors. To this end we have developed quantum error-correcting codes to protect quantum information from noise. However, discovering codes that are capable of a…
Coding theory is very useful for real world applications. A notable example is digital television. Basically, coding theory is to study a way of detecting and/or correcting data that may be true or false. Moreover coding theory is an area…
In this work, we propose constructions that correct duplications of multiple consecutive symbols. These errors are known as tandem duplications, where a sequence of symbols is repeated; respectively as palindromic duplications, where a…
The implicit theory that a simulation represents is precisely not in the individual choices but rather in the 'envelope' of possible trajectories - what is important is the shape of the whole envelope. Typically a huge amount of computation…
The breakthrough of quantum error correction brought with it the picture of quantum information as a sort of combination of two complementary types of classical information, "amplitude" and "phase". Here I show how this intuition can be…
We derive lower bounds on the maximal rates for multiple packings in high-dimensional Euclidean spaces. Multiple packing is a natural generalization of the sphere packing problem. For any $ N>0 $ and $ L\in\mathbb{Z}_{\ge2} $, a multiple…
Hinging on ideas from physical-layer network coding, some promising proposals of coded random access systems seek to improve system performance (while preserving low complexity) by means of packet repetitions and decoding of linear…
The perfectly matched layers (PMLs), as a boundary termination over an unbounded spatial domain, are widely used in numerical simulations of wave propagation problems. Given a set of discretization parameters, a procedure to select the PML…
Active quantum error correction using qubit stabilizer codes has emerged as a promising, but experimentally challenging, engineering program for building a universal quantum computer. In this review we consider the formalism of qubit…
Exactly solving first-order constraints (i.e., first-order formulas over a certain predefined structure) can be a very hard, or even undecidable problem. In continuous structures like the real numbers it is promising to compute approximate…
In this article we obtain linear programming bounds for the maximal sphere packing density of commutative spaces. A special case of our results solves a conjecture by Cohn and Zhao on linear programming bounds for sphere packings in…