Related papers: Degenerate flag varieties in network coding

A Viterbi-like decoding algorithm is proposed in this paper for generalized convolutional network error correction coding. Different from classical Viterbi algorithm, our decoding algorithm is based on minimum error weight rather than the…

Deep convolutional neural networks have been successfully applied to image classification tasks. When these same networks have been applied to image retrieval, the assumption has been made that the last layers would give the best…

Maximum Hermitian rank metric codes were introduced by Schmidt in 2018 and in this paper we propose both interpolation-based encoding and decoding algorithms for this family of codes when the length and the minimum distance of the code are…

Given a finite field F_q and a positive integer n, a flag is a sequence of nested F_q-subspaces of a vector space F_q^n and a flag code is a nonempty collection of flags. The projected codes of a flag code are the constant dimension codes…

Non-local self-similarity is well-known to be an effective prior for the image denoising problem. However, little work has been done to incorporate it in convolutional neural networks, which surpass non-local model-based methods despite…

Networks are a useful representation for data on connections between units of interests, but the observed connections are often noisy and/or include missing values. One common approach to network analysis is to treat the network as a…

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…

Many real-world networks exhibit a high degeneracy at few eigenvalues. We show that a simple transformation of the network's adjacency matrix provides an understanding of the origins of occurrence of high multiplicities in the networks…

Finding optimal correction of errors in generic stabilizer codes is a computationally hard problem, even for simple noise models. While this task can be simplified for codes with some structure, such as topological stabilizer codes,…

This article offers an empirical exploration on the use of character-level convolutional networks (ConvNets) for text classification. We constructed several large-scale datasets to show that character-level convolutional networks could…

Deep linear networks trained with gradient descent yield low rank solutions, as is typically studied in matrix factorization. In this paper, we take a step further and analyze implicit rank regularization in autoencoders. We show greedy…

We consider the ubiquitous technique of VByte compression, which represents each integer as a variable length sequence of bytes. The low 7 bits of each byte encode a portion of the integer, and the high bit of each byte is reserved as a…

In this work we present error-correcting codes for random network coding based on rank- metric codes, Ferrers diagrams, and puncturing. For most parameters, the constructed codes are larger than all previously known codes.

Scalable coding, which can adapt to channel bandwidth variation, performs well in today's complex network environment. However, most existing scalable compression methods face two challenges: reduced compression performance and insufficient…

A classification of double flag varieties of complexity 0 and 1 is obtained. An application of this problem to decomposing tensor products of irreducible representations of semisimple Lie groups is considered.

We use some moment graph techniques, recently introduced by Lanini and P\"utz, to provide a combinatorial description of the smooth locus in flat linear degenerations of flag varieties, generalizing a result proved by Cerulli Irelli, Feigin…

Parallel tensor network contraction algorithms have emerged as the pivotal benchmarks for assessing the classical limits of computation, exemplified by Google's demonstration of quantum supremacy through random circuit sampling. However,…

Network embedding has attracted an increasing attention over the past few years. As an effective approach to solve graph mining problems, network embedding aims to learn a low-dimensional feature vector representation for each node of a…

Coding schemes for several problems in network information theory are constructed starting from point-to-point channel codes that are designed for symmetric channels. Given that the point-to-point codes satisfy certain properties pertaining…

The present work discusses the use of a weakly-supervised deep learning algorithm that reduces the cost of labelling pixel-level masks for complex radio galaxies with multiple components. The algorithm is trained on weak class-level labels…