Related papers: Network Coding Capacity: A Functional Dependence B…
The learnability of different neural architectures can be characterized directly by computable measures of data complexity. In this paper, we reframe the problem of architecture selection as understanding how data determines the most…
One important issue implied by the finite nature of real-world networks regards the identification of their more external (border) and internal nodes. The present work proposes a formal and objective definition of these properties, founded…
Due to structural and functional abnormalities or genetic variations and mutations, there may be dysfunctional molecules within an intracellular signaling network that do not allow the network to correctly regulate its output molecules,…
In this paper, we consider different aspects of the network functional compression problem where computation of a function (or, some functions) of sources located at certain nodes in a network is desired at receiver(s). The rate region of…
Network calculus is an elegant theory which uses envelopes to determine the worst-case performance bounds in a network. Statistical network calculus is the probabilistic version of network calculus, which strives to retain the simplicity of…
Quantum capacities are fundamental quantities that are notoriously hard to compute and can exhibit surprising properties such as superadditivity. Thus, a vast amount of literature is devoted to finding tight and computable bounds on these…
An established measure of the expressive power of a given ReLU neural network is the number of linear regions into which it partitions the input space. There exist many different, non-equivalent definitions of what a linear region actually…
We consider questions related to the computation of the capacity of codes that avoid forbidden difference patterns. The maximal number of $n$-bit sequences whose pairwise differences do not contain some given forbidden difference patterns…
Universal bounds for the potential energy of weighted spherical codes are obtained by linear programming. The universality is in the sense of Cohn-Kumar -- every attaining code is optimal with respect to a large class of potential functions…
It is known that for any finite/co-finite set of primes there exists a network which has a rate $1$ solution if and only if the characteristic of the finite field belongs to the given set. We generalize this result to show that for any…
Sum-networks are networks where all the terminals demand the sum of the symbols generated at the sources. It has been shown that for any finite set/co-finite set of prime numbers, there exists a sum-network which has a vector linear…
We determine both the random code capacity region and the deterministic code capacity region of the arbitrarily varying multiple access channel (AVMAC) under input and state constraints. As in the single user case, the boundary of the…
The empirical results suggest that the learnability of a neural network is directly related to its size. To mathematically prove this, we borrow a tool in topological algebra: Betti numbers to measure the topological geometric complexity of…
We study the problem of communicating over a single-source single-terminal network in the presence of an adversary that may jam a single link of the network. If any one of the edges can be jammed, the capacity of such networks is well…
We consider the problem of computing the capacity of a coded, multicast network over a small alphabet. We introduce a novel approach to this problem based on mixed integer programming. As an application of our approach, we recover, extend…
We examine the issue of separation and code design for networks that operate over finite fields. We demonstrate that source-channel (or source-network) separation holds for several canonical network examples like the noisy multiple access…
We consider transmission over a general memoryless channel, with bounded decoding complexity per bit under message passing decoding. We show that the achievable rate is bounded below capacity if there is a finite success in the decoding in…
Automating the solutions of multiple network information theory problems, stretching from fundamental concerns such as determining all information inequalities and the limitations of linear codes, to applied ones such as designing coded…
In contrast to the network coding problem wherein the sinks in a network demand subsets of the source messages, in a network computation problem the sinks demand functions of the source messages. Similarly, in the functional index coding…
For each integer $m \geq 2$, a network is constructed which is solvable over an alphabet of size $m$ but is not solvable over any smaller alphabets. If $m$ is composite, then the network has no vector linear solution over any $R$-module…