Related papers: Designs, linear codes, plateaued functions, and th…
We employ the notions of `sequential function' and `interrogation' (dialogue) in order to define new partial combinatory algebra structures on sets of functions. These structures are analyzed using J. Longley's preorder-enriched category of…
Plateaued functions as an extension of bent functions play a significant role in cryptography, coding theory, sequences and combinatorics. In \cite{Mesnager9}, Mesnager \emph{et al.} introduced generalized plateaued functions in order to…
Considered two linear regression models of a given response variable with some predictor set and its subset. It is shown that there is a linear relationship between coefficients of these models. Some corollaries of the proved theorem is…
The control approaches generally resort to the tools from the mathematics, but whether and how the mathematics can benefit from the control approaches is unclear. This paper aims to bring the "control design" idea into the mathematics by…
In this work we present the results of several simulations on main-effect factorial designs. The goal of such simulations is to investigate the connections between the $D$-optimality of a design and its geometrical structure. By means of a…
We derive results about geometric means of the Fourier modulus of filters and functions related to refinable distributions with arbitrary dilations and translations. Then we develop multi-scale constructions for dilations by…
Topics concerning metric dimension related invariants in graphs are nowadays intensively studied. This compendium of combinatorial and computational results on this topic is an attempt of surveying those contributions that are of the…
Almost designs ($t$-adesigns) were proposed and discussed by Ding as a certain generalization of combinatorial designs related to almost difference sets. Unlike $t$-designs, it is not clear whether $t$-adesigns need also be $(t-1)$-designs…
A logic calculus is presented that is a conservative extension of linear logic. The motivation beneath this work concerns lazy evaluation, true concurrency and interferences in proof search. The calculus includes two new connectives to deal…
The major challenge in designing a discriminative learning algorithm for predicting structured data is to address the computational issues arising from the exponential size of the output space. Existing algorithms make different assumptions…
Motivated by a fundamental geometrical object, the cut locus, we introduce and study a new combinatorial structure on graphs.
The machine learning community has recently devoted much attention to the problem of inferring causal relationships from statistical data. Most of this work has focused on uncovering connections among scalar random variables. We generalize…
Logical models have been successfully used to describe regulatory and signaling networks without requiring quantitative data. However, existing data is insufficient to adequately define a unique model, rendering the parametrization of a…
Open issues on the structure of multiple interactions are outlined. An improved model is summarized, with a new approach to correlated parton densities in flavour, colour, longitudinal and transverse momenta, for both hard-scattering…
There are several examples of spaces of univariate functions for which we have a characterization of all sets of knots which are poised for the interpolation problem. For the standard spaces of univariate polynomials, or spline functions…
The versatility of data-driven approximation by interpolatory methods, originally settled for model approximation purpose, is illustrated in the context of linear controller design and stability analysis of irrational models. To this aim,…
The concept of spatial coupling is among the most significant breakthroughs in coding theory over the past decade. The excellent waterfall and error floor performance of spatially coupled codes has positioned them as promising coding…
We review the main results of the theory of rank-metric codes, with emphasis on their combinatorial properties. We study their duality theory and MacWilliams identities, comparing in particular rank-metric codes in vector and matrix…
The intersection problem for additive (extended and non-extended) perfect codes, i.e. which are the possibilities for the number of codewords in the intersection of two additive codes C1 and C2 of the same length, is investigated. Lower and…
This work is devoted to the study of integration with respect to binomial measures. We develop interpolatory quadrature rules and study their properties. Local error estimates for these rules are derived in a general framework.