Related papers: Characteristic-Dependent Linear Rank Inequalities …
Nowadays, feature selection is frequently used in machine learning when there is a risk of performance degradation due to overfitting or when computational resources are limited. During the feature selection process, the subset of features…
Neural networks posses the crucial ability to generate meaningful representations of task-dependent features. Indeed, with appropriate scaling, supervised learning in neural networks can result in strong, task-dependent feature learning.…
We study the rank weight hierarchy of linear codes which are stable under a linear endomorphism defined over the base field, in particular when the endomorphism is cyclic. In this last case, we give a necessary and sufficient condition for…
It is known a vector linear solution may exist if and only if the characteristic of the finite field belongs to a certain set of primes. But, can increasing the message dimension make a network vector linearly solvable over a larger set of…
Network analysis is often focused on characterizing the dependencies between network relations and node-level attributes. Potential relationships are typically explored by modeling the network as a function of the nodal attributes or by…
We prove an elementary yet useful inequality bounding the maximal value of certain linear programs. This leads directly to a bound on the martingale difference for arbitrarily dependent random variables, providing a generalization of some…
In this paper, we introduce a graph structure called linear dependence graph of a finite dimensional vector space over a finite field. Some basic properties of the graph like connectedness, completeness, planarity, clique number, chromatic…
Feature models are widely used to capture the configuration space of software systems. Although automated reasoning has been studied for detecting problematic features and supporting configuration tasks, significantly less attention has…
In this paper, we consider networks with multiple unicast sessions. Generally, non-linear network coding is needed to achieve the whole rate region of network coding. Yet, there exist networks for which routing is sufficient to achieve the…
In this paper, we obtain the upper and lower bounds for two inequalities related to the range statistics. The first one is concerning the one-variable case and the second one is about the bivariate case.
We study a model for cascade effects over finite networks based on a deterministic binary linear threshold model. Our starting point is a networked coordination game where each agent's payoff is the sum of the payoffs coming from pairwise…
This paper is concerned with cross-sectional dependence arising because observations are interconnected through an observed network. Following Doukhan and Louhichi (1999), we measure the strength of dependence by covariances of nonlinearly…
This paper aims at comparing two coupling approaches as basic layers for building clustering criteria, suited for modularizing and clustering very large networks. We briefly use "optimal transport theory" as a starting point, and a way as…
We consider the long-standing question of finding a parameter of a class of probability distributions that characterizes its PAC learnability. We provide a rather surprising answer - no such parameter exists. Our techniques allow us to show…
This paper investigates the theory of sum-rank metric codes for which the individual matrix blocks may have different sizes. Various bounds on the cardinality of a code are derived, along with their asymptotic extensions. The duality theory…
We determine the rank of a random matrix A over a finite field with prescribed numbers of non-zero entries in each row and column. As an application we obtain a formula for the rate of low-density parity check codes. This formula verifies a…
In this paper, we study the redundancy of linear codes with graph constraints. First we consider linear parity check codes based on bipartite graphs with diversity and with generalized graph constraints. We describe sufficient conditions on…
Motivated by communication through a network employing linear network coding, capacities of linear operator channels (LOCs) with arbitrarily distributed transfer matrices over finite fields are studied. Both the Shannon capacity $C$ and the…
The problem of maximum rate achievable with analog network coding for a unicast communication over a layered wireless relay network with directed links is considered. A relay node performing analog network coding scales and forwards the…
We consider multi-commodity network design models, where capacity can be added to the arcs of the network using multiples of facilities that may have different capacities. This class of mixed-integer optimization models appears frequently…