
Peer reviewed

Peer reviewed

Charlier, Emilie
In this talk I presented the results of the paper "On a group theoretic generalization of the MorseHedlund theorem", which is a joint work with Svetlana Puzynina and Luca Zamboni. In this paper, we give a broad unified framework via group actions for constructing complexity functions of infinite words. Factor complexity, Abelian complexity and cyclic complexity are all particular cases of this general construction.

Demeulenaere, Loïc
The diametral dimension is a topological invariant which characterizes Schwartz and
nuclear spaces. However, there exists another diametral dimension which was conjectured
by Bessaga, Mityagin, Pełczynski, and Rolewicz to be equal to the first one in
Fréchet spaces.
In this talk, we describe some conditions which assure the equality of the two diametral
dimensions in metrizable locally convex spaces. Besides, we explain why such an
equality is generally impossible in nonmetrizable spaces.

Catalan, Eugène
Cinquième édition, revue

Catalan, Eugène
Quatrième édition, revue et augmentée

Nguyen, Ngan Giang

Kleyntssens, Thomas; Esser, Céline; Nicolay, Samuel
Peer reviewed

Nguyen, Ngan Giang; Gilot, Marguerite

Nguyen, Ngan Giang; SchneiderGilot, Marguerite

Demeulenaere, Loïc
The diametral dimension is a topological invariant on the class of topological vector spaces. Besides, there exists another diametral dimension which was claimed to be equal to the first one in Fréchet(Schwartz) spaces. However, this equality has never been proved. In this talk, we make some reminders about Functional Analysis and some related concepts (seminorms, locally convex spaces, etc.) and we insist on some notions linked to compactness. We also introduce the associated notions of Montel spaces and Schwartz spaces.
Then, we introduce the question about the equality of the two diametral dimensions and we explain why this is directly solved...

McKeague, Ian; Peköz, Erol; Swan, Yvik
Peer reviewed

Blondin Massé, Alexandre; de Carufel, Julien; Goupil, Alain; Lapointe, Mélodie; Nadeau, Emile; Vandomme, Elise
Let G be a simple graph of n vertices. We consider the problem ISil of deciding whether there exists an induced subtree with exactly i ≤ n vertices and l leaves in G. We also study the associated optimization problem, that consists in computing the maximal number of leaves, denoted by L_G(i), realized by an induced subtree with i vertices, for 2 ≤ i ≤ n. We compute the values of the map L_G for some classical families of graphs and in particular for the ddimensional hypercubic graphs Q_d , d ≤ 6. Then we prove that the ISil problem...

Vander Haegen, Marie

Hoyoux, Renaud
Mémoire défendu en vue de l'obtention du titre de Master en sciences mathématiques portant sur les théorèmes d'incomplétude et constitué de quatre chapitres : le premier est un rappel des bases en logique formelle et en théorie des fonctions récursives; le second est consacré aux théorèmes d'incomplétude de Gödel; le troisième présente un exemple détaillé d'un énoncé aisé à comprendre mais néanmoins indémontrable dans l'arithmétique de Peano; le dernier explorant les possibilités de "mesure" des théorèmes indémontrables.

Aerts, Stéphanie; Wilms, Ines
Quadratic and Linear Discriminant Analysis (QDA/LDA) are the most often applied classification rules under normality. In QDA, a separate covariance matrix is estimated for each group. If there are more variables than observations in the groups, the usual estimates are singular and cannot be used anymore. Assuming homoscedasticity, as in LDA, reduces the number of parameters to estimate. This rather strong assumption is however rarely verified in practice. Regularized discriminant techniques that are computable in highdimension and cover the path between the two extremes QDA and LDA have been proposed in the literature. However, these procedures rely on sample covariance...

Demeulenaere, Loïc
Spaces Snu are metrizable sequence spaces defined by Jaffard in the context of multifractal analysis and signal treatment. From a functional analysis point of view, the study of these spaces points out some topological properties, such as the facts they are locally pseudoconvex in general and locally pconvex in certain cases, Schwartz, and nonnuclear.
In this talk, we focus on two topological invariants, namely the diametral dimension (Bessaga, Mityagin, Pelczynski, Rolewicz) and the property "Omega Bar" (Vogt, Wagner). Firstly, we revisit a result of Aubry and Bastin giving the diametral dimension of locally pconvex spaces Snu and extend it to some...

Vandomme, Elise; Gravier, Sylvain
Peer reviewed

Charlier, Emilie
The theorem of BüchiBruyère states that a subset of N^d is brecognizable if and only if it is bdefinable. As a corollary, the firstorder theory of (N,+,V_b) is decidable (where V_b(n) is the largest power of the base b dividing n). This classical result is a powerful tool in order to show that many properties of bautomatic sequences are decidable. The first part of my lecture will be devoted to presenting this result and its applications to bautomatic sequences. Then I will move to bregular sequences, which can be viewed as a generalization of bautomatic sequences to integervalued sequences. I...

The series of international conferences on Developments in Language Theory provides a forum for presenting current developments in formal languages and automata. Its scope is very general and includes, among others, the following topics and areas: combinatorial and algebraic properties of words and languages; grammars, acceptors and transducers for strings, trees, graphs, arrays; algebraic theories for automata and languages; codes; efficient text algorithms; symbolic dynamics; decision problems; relationships to complexity theory and logic; picture description and analysis; polyominoes and bidimensional patterns; cryptography; concurrency; cellular automata; bioinspired computing; quantum computing. The papers submitted to DLT 2017 were from 19 countries including...