Related papers: Towards an Operational Definition of Group Network…
Coding theory is a central discipline underpinning wireline and wireless modems that are the workhorses of the information age. Progress in coding theory is largely driven by individual human ingenuity with sporadic breakthroughs over the…
Link and node failures are two common fundamental problems that affect operational networks. Protection of communication networks against such failures is essential for maintaining network reliability and performance. Network protection…
A novel implementation of a special class of Galois ring, in which the multiplication can be realized by a cyclic convolution, is applied to the construction of network codes. The primitive operations involved are byte-wise shifts and…
We analyze a distributed information network in which each node has access to the information contained in a limited set of nodes (its neighborhood) at a given time. A collective computation is carried out in which each node calculates a…
Understanding neurocognitive computations will require not just localizing cognitive information distributed throughout the brain but also determining how that information got there. We review recent advances in linking empirical and…
Boolean functions have important applications in cryptography and coding theory. Two famous classes of binary codes derived from Boolean functions are the Reed-Muller codes and Kerdock codes. In the past two decades, a lot of progress on…
Intersession network coding (NC) can provide significant performance benefits via mixing packets at wireless routers; these benefits are especially pronounced when NC is applied in conjunction with intelligent link scheduling. NC however…
Task taxonomies for graph and network visualizations focus on tasks commonly encountered when analyzing graph connectivity and topology. However, in many application fields such as the social sciences (social networks), biology (protein…
Depthwise convolution and grouped convolution has been successfully applied to improve the efficiency of convolutional neural network (CNN). We suggest that these models can be considered as special cases of a generalized convolution…
We present our ongoing work on understanding the limitations of graph convolutional networks (GCNs) as well as our work on generalizations of graph convolutions for representing more complex node attribute dependencies. Based on an analysis…
In this work, we propose novel families of positional encodings tailored to graph neural networks obtained with quantum computers. These encodings leverage the long-range correlations inherent in quantum systems that arise from mapping the…
How do neural networks trained over sequences acquire the ability to perform structured operations, such as arithmetic, geometric, and algorithmic computation? To gain insight into this question, we introduce the sequential group…
We discuss quantum two-block codes, a large class of CSS codes constructed from two commuting square matrices.Interesting families of such codes are generalized-bicycle (GB) codes and two-block group-algebra (2BGA) codes, where a cyclic…
We introduce partial differential encodings of Boolean functions as a way of measuring the complexity of Boolean functions. These encodings enable us to derive from group actions non-trivial bounds on the Chow-Rank of polynomials used to…
The notion of 'presentation', as used in combinatorial group theory, is applied to coded character sets(CCSs) - sets which facilitate the interchange of messages in a digital computer network(DCN) . By grouping each element of the set into…
Cayley graphs have a number of useful features: the ability to graphically represent finitely generated group elements and their relations; to name all vertices relative to a point; and the fact that they have a well-defined notion of…
By defining projective error models we study the mathematical structure of Clifford codes and stabilizer codes using tools from projective representation theory. Furthermore, we introduce a new class of codes which we have called weak…
Link and node failures are common two fundamental problems that affect operational networks. Hence, protection of communication networks is essential to increase their reliability, performance, and operations. Much research work has been…
We consider the locality of encoding and decoding operations in distributed storage systems (DSS), and propose a new class of codes, called locally encodable and decodable codes (LEDC), that provides a higher degree of operational locality…
Functionals are an important research subject in Mathematics and Computer Science as well as a challenge in Information Technologies where the current programming paradigm states that only symbolic computations are possible on higher order…