Related papers: Induced Weights on Quotient Modules and an Applica…
For many optimization problems it is possible to define a distance metric between problem variables that correlates with the likelihood and strength of interactions between the variables. For example, one may define a metric so that the…
Many results related to quantitative problems in the metric theory of Diophantine approximation are asymptotic, such as the number of rational solutions to certain inequalities grows with the same rate almost everywhere modulo an asymptotic…
Linear programming approaches have been applied to derive upper bounds on the size of classical codes and quantum codes. In this paper, we derive similar results for general quantum codes with entanglement assistance, including nonadditive…
This paper focuses on a class of inclusion problems of maximal monotone operators in a multi-agent network, where each agent is characterized by an operator that is not available to any other agents, but the agents can cooperate by…
A classic result of Cook et al. (1986) bounds the distances between optimal solutions of mixed-integer linear programs and optimal solutions of the corresponding linear relaxations. Their bound is given in terms of the number of variables…
The rapid growth of multimodal intelligence on resource-constrained and heterogeneous domestic hardware exposes critical bottlenecks: multimodal feature heterogeneity, real-time requirements in dynamic scenarios, and hardware-specific…
Series of maximum distance quantum error-correcting codes are developed and analysed. For a given rate and given error-correction capability, quantum error-correcting codes with these specifications are constructed. The codes are explicit…
We show that solving a multiple-unicast network coding problem can be reduced to solving a single-unicast network error correction problem, where an adversary may jam at most a single edge in the network. Specifically, we present an…
In this paper, orthogonal to the existing data and model studies, we instead resort our efforts to investigate the potential of loss function in a new perspective and present our belief ``Random Weights Networks can Be Acted as Loss Prior…
The problem of error-control in random linear network coding is considered. A ``noncoherent'' or ``channel oblivious'' model is assumed where neither transmitter nor receiver is assumed to have knowledge of the channel transfer…
Long quantum codes using projective Reed-Muller codes are constructed. Projective Reed-Muller codes are evaluation codes obtained by evaluating homogeneous polynomials at the projective space. We obtain asymmetric and symmetric quantum…
Linear network coding transmits information in terms of a basis of a vector space and the information is received as a basis of a possible altered vectorspace. Ralf Koetter and Frank R. Kschischang in Coding for errors and erasures in…
Machine learning techniques have received growing attention as an alternative strategy for developing general-purpose density functional approximations, augmenting the historically successful approach of human designed functionals derived…
In this paper, we give error bounds for the distance distribution of Reed-Muller codes, extending prior work on the distance distribution of Reed-Solomon codes. This is equivalent to the problem of counting multivariate polynomials over a…
The potential of quantum computers to outperform classical ones in practically useful tasks remains challenging in the near term due to scaling limitations and high error rates of current quantum hardware. While quantum error correction…
Quantization is essential for Neural Network (NN) compression, reducing model size and computational demands by using lower bit-width data types, though aggressive reduction often hampers accuracy. Mixed Precision (MP) mitigates this…
We investigate the asymptotic density of error-correcting codes with good distance properties and prescribed linearity degree, including sublinear and nonlinear codes. We focus on the general setting of finite translation-invariant metric…
Orthogonal geometric constructions are the basis of many many quantum error-correcting codes (QEC), but strict orthogonality constraints limit design flexibility and resource efficiency. We introduce a quasi-orthogonal geometric framework…
For a bounded metric space X, we define a metric on the set of all finite subsets of X. This generalizes the sequence-subset distance introduced by Wentu Song, Kui Cai and Kees A. Schouhamer Immink to study error correcting codes for DNA…
Embedding probability distributions into reproducing kernel Hilbert spaces (RKHS) has enabled powerful nonparametric methods such as the maximum mean discrepancy (MMD), a statistical distance with strong theoretical and computational…