ORBi Collection: Mathematics
http://hdl.handle.net/2268/153
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Impact of dependency on the distribution of p-value
http://hdl.handle.net/2268/213661
Title: Impact of dependency on the distribution of p-value
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<br/>Author, co-author: Ernst, Marie; Swan, Yvik
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<br/>Abstract: We study the impact of dependence assumptions on the distribution of p-values and quantiles for repeated testing on dependent data. This leads us to considering the general problem of the quality of a binomial approximation to the distribution of a sum of dependent indicator variables. Whenever possible we use classical and adhoc versions of Stein’s method to provide tight bounds on classical probability distances. In many cases, however, the relevant expressions are intractable and we resort to empirical analysis by extensive simulations. We apply our findings to a realistic real-life scenario.Second-order moment of the first passage time of a quasi-Hamiltonian oscillator with stochastic parametric and forcing excitations (under review)
http://hdl.handle.net/2268/213521
Title: Second-order moment of the first passage time of a quasi-Hamiltonian oscillator with stochastic parametric and forcing excitations (under review)
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<br/>Author, co-author: Vanvinckenroye, Hélène; Denoël, VincentLinearization and quadratization techniques for 0-1 optimization problems
http://hdl.handle.net/2268/213515
Title: Linearization and quadratization techniques for 0-1 optimization problems
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<br/>Author, co-author: Rodriguez Heck, Elisabeth; Crama, YvesA class of valid inequalities for multilinear 0-1 optimization problems
http://hdl.handle.net/2268/213514
Title: A class of valid inequalities for multilinear 0-1 optimization problems
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<br/>Author, co-author: Rodriguez Heck, Elisabeth; Crama, YvesMéditations expérimenées sur la TSUM (Transition Secondaire-Université en Mathématiques)
http://hdl.handle.net/2268/213509
Title: Méditations expérimenées sur la TSUM (Transition Secondaire-Université en Mathématiques)
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<br/>Author, co-author: Bair, Jacques
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<br/>Abstract: L’objectif de ce travail est de mettre par écrit quelques idées personnelles à propos de l’enseignement des mathématiques dans une première année de l’enseignement supérieur et ainsi de réfléchir à propos de la transition entre le secondaire et l’Université (TSU, en abrégé) pour un cours de mathématiques. A cet effet, on compare les enseignements secondaire et universitaire, on précise une certaine conception des mathématiques et de leur enseignement au niveau de la TSU. Dans une première annexe se trouve également une étude plus théorique et technique sur la métacognition.
Une particularité de ce travail est probablement de relier des idées issues de la littérature spécialisée relative à trois thèmes qui sont souvent développés indépendamment les uns des autres, à savoir l’épistémologie des mathématiques, la pédagogie universitaire et la didactique des mathématiques, le tout étant agencé d’après des convictions personnelles et des expériences professionnelles.Du calcul infinitésimal à l'analyse mathématique
http://hdl.handle.net/2268/212878
Title: Du calcul infinitésimal à l'analyse mathématique
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<br/>Author, co-author: Schneider, Maggy; Balhan, Kevin; Gérard, Isaline; Henrotay, PierreUn dispositif de formation initiale des enseignants en didactique des mathématiques au niveau du secondaire supérieur en Belgique francophone
http://hdl.handle.net/2268/212867
Title: Un dispositif de formation initiale des enseignants en didactique des mathématiques au niveau du secondaire supérieur en Belgique francophone
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<br/>Author, co-author: Balhan, Kevin; Gérard, Isaline; Nguyen, Giang; Schneider, Maggy
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<br/>Abstract: L'article présenté lors du symposium fédère plusieurs recherches menées dans notre laboratoire de didactique des mathématiques : le « Ladimath », autour de la formation initiale des enseignants de mathématique au niveau du lycée et, plus particulièrement, autour d’une question de recherche qui concerne une dimension particulière de la « réflexivité » : « les mathématiques comme problème professionnel ». Nous y décrivons le dispositif mis en place dans la formation initiale des enseignants en mathématique à l’Université de Liège, celui-ci étant alimenté de différentes manières selon l’épistémologie du savoir mathématique questionné lors de la formation. Dans cet article, nous l’illustrons sur trois thèmes différents : celui de l’analyse mathématique, de la géométrie, et des probabilités/statistiques.Characterising Industrial Sites' Flexibility with Reservoir Models
http://hdl.handle.net/2268/212703
Title: Characterising Industrial Sites' Flexibility with Reservoir Models
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<br/>Author, co-author: Cuvelier, Thibaut
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<br/>Abstract: Electro-intensive industrial sites are very dependent on electricity prices to remain competitive. Nevertheless, they can often tune their processes in order to decrease their electricity consumption during the most critical periods, for example by using decision support systems based on mathematical modelling of their processes. Our goal is to estimate the flexibility potential of a complete site, not to tune each process very precisely.
To this end, we propose a generic paradigm to help conceiving such models: reservoirs are the basic building block, which allows for great expressiveness while being close to the physics. More specifically, we do not need very precise models for our purposes, but ones that can be efficiently included in optimisation models.
Our first results show that the obtained reservoir models can give sufficiently good approximations for metallurgical processes (more precisely, electric-arc and ladle furnaces).What is the best approach to analyze longitudinal bounded scores? Application to Quality of Life Data.
http://hdl.handle.net/2268/212624
Title: What is the best approach to analyze longitudinal bounded scores? Application to Quality of Life Data.
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<br/>Author, co-author: Donneau, Anne-Françoise; Russo, Cibele; Dardenne, Nadia; Mauer, Murielle; Coens, Corneel; Bottomley, Andrew; Lesaffre, EmmanuelLogic, Decidability and Numeration Systems
http://hdl.handle.net/2268/212572
Title: Logic, Decidability and Numeration Systems
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<br/>Author, co-author: Charlier, Emilie
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<br/>Abstract: The theorem of Büchi-Bruyère states that a subset of N^d is b-recognizable if and only if it is b-definable. As a corollary, the first-order 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 b-automatic sequences are decidable. The first part of my lecture will be devoted to presenting this result and its applications to b-automatic sequences. Then I will move to b-regular sequences, which can be viewed as a generalization of b-automatic sequences to integer-valued sequences. I will explain how first-order logic can be used to show that many enumeration problems of b-automatic sequences give rise to corresponding b-regular sequences. Finally, I will consider more general frameworks than integer bases and (try to) give a state of the art of the research in this domain.
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<br/>Commentary: This is a 3-hour mini-course. Part of it was on the blackboard (no slides). The first hour was videotaped : https://www.youtube.com/watch?v=U9t10GAsn1k.Holomorphic cohomological convolution
http://hdl.handle.net/2268/212432
Title: Holomorphic cohomological convolution
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<br/>Author, co-author: Dubussy, Christophe
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<br/>Abstract: In his thesis, T. Pohlen succeeded in defining a Hadamard product between holomorphic functions defined on star-eligible subsets of the Riemann sphere. We show how this theory is actually a particular case of the holomorphic cohomological convolution, defined in a general way thanks to the integration map on complex Lie groups.Developments in Language Theory
http://hdl.handle.net/2268/212280
Title: Developments in Language Theory
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<br/>Editor: Charlier, Emilie; Leroy, Julien; Rigo, Michel
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<br/>Abstract: 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; bio-inspired computing; quantum computing. The papers submitted to DLT 2017 were from 19 countries including Belgium, Canada, Czech Republic, France, Germany, Hungary, India, Italy, Japan, The Netherlands, Poland, Portugal, Republic of Korea, Russia, Slovakia, South Africa, Thailand and USA.Balanced sequences of complexity 2n+1
http://hdl.handle.net/2268/212151
Title: Balanced sequences of complexity 2n+1
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<br/>Author, co-author: Cassaigne, Julien; Labbé, Sébastien; Leroy, JulienFirst-order Logic and Numeration Systems
http://hdl.handle.net/2268/212150
Title: First-order Logic and Numeration Systems
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<br/>Author, co-author: Charlier, Emilie
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<br/>Abstract: The Büchi-Bruyère theorem states that a multidimensional set of non-negative integers is b-recognizable if and only if it is b-definable. This result is a powerful tool for showing that many properties of b-automatic sequences are decidable. Going a step further, first-order logic can be used to show that many enumeration problems of b-automatic sequences can be described by b-regular sequences. The latter sequences can be viewed as a generalization of b-automatic sequences to integer-valued sequences. These techniques were extended to two wider frameworks: U-recognizable multidimensional sets of non-negative integers and multidimensional beta-recognizable sets of reals. In the second case, real numbers are represented by infinite words, and hence, the notion of beta-recognizability is defined by means of Büchi automata. Again, logic-based characterizations of $U$-recognizable (resp. beta-recognizable) sets allows us to obtain various decidability results. The aim of this chapter is to present a survey of this very active research domain.An efficient algorithm to decide periodicity of b-recognisable sets using MSDF convention
http://hdl.handle.net/2268/212135
Title: An efficient algorithm to decide periodicity of b-recognisable sets using MSDF convention
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<br/>Author, co-author: Boigelot, Bernard; Mainz, Isabelle; Marsault, Victor; Rigo, Michel
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<br/>Abstract: Given an integer base b>1, a set of integers is represented in base b by a language over {0,1,...,b-1}. The set is said to be b-recognisable if its representation is a regular language. It is known that eventually periodic sets are b-recognisable in every base b, and Cobham's theorem implies the converse: no other set is b-recognisable in every base b.
We are interested in deciding whether a $b$-recognisable set of integers (given as a finite automaton) is eventually periodic. Honkala showed that this problem is decidable in 1986 and recent developments give efficient decision algorithms. However, they only work when the integers are written with the least significant digit first.
In this work, we consider the natural order of digits (Most Significant Digit First) and give a quasi-linear algorithm to solve the problem in this case.
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<br/>Commentary: Long version at : https://arxiv.org/abs/1702.03715Permutations and negative beta-shifts
http://hdl.handle.net/2268/212122
Title: Permutations and negative beta-shifts
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<br/>Author, co-author: Charlier, Emilie; Steiner, Wolfgang
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<br/>Abstract: Elizalde (2011) characterized which permutations can be obtained by ordering consecutive elements in the trajectories of (positive) beta-transformations and beta-shifts. We prove similar results for negative bases beta.
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<br/>Commentary: Paper submitted in February 2017.Rigidity and substitutive tree words
http://hdl.handle.net/2268/212025
Title: Rigidity and substitutive tree words
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<br/>Author, co-author: Berthé, Valérie; Dolce, Francesco; Durand, Fabien; Leroy, Julien; Perrin, DominiqueDiametral dimension(s) and prominent bounded sets
http://hdl.handle.net/2268/211982
Title: Diametral dimension(s) and prominent bounded sets
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<br/>Author, co-author: Demeulenaere, Loïc
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<br/>Abstract: The classical diametral dimension (Bessaga, Mityagin, Pelczynski, Rolewicz), denoted by "Delta", is a topological invariant which can be used to characterize Schwartz and nuclear locally convex spaces. Mityagin also introduced a variant of this diametral dimension, denoted by "Delta_b", using bounded sets in its definition, contrary to "Delta". In this talk, we present some conditions assuring the equality of these two diametral dimensions for Fréchet spaces. Among these conditions, there is the notion of existence of prominent bounded sets, due to Terzioglu. In fact, it appears that the existence of prominent sets is implied by the property "Omega Bar" of Vogt and Wagner. Finally, we describe a construction which gives Schwartz and nuclear non-Fréchet spaces E verifying "Delta_b(E) = \Delta(E)".Assessing quality of life using structural equation modeling
http://hdl.handle.net/2268/211926
Title: Assessing quality of life using structural equation modeling
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<br/>Author, co-author: Dardenne, Nadia; Pétré, Benoît; Husson, Eddy; Guillaume, Michèle; Donneau, Anne-FrançoiseGeneralized Pascal triangles for binomial coefficients of finite words
http://hdl.handle.net/2268/211880
Title: Generalized Pascal triangles for binomial coefficients of finite words
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<br/>Author, co-author: Stipulanti, Manon
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<br/>Abstract: We introduce a generalization of Pascal triangle based on binomial coefficients of finite words. These coefficients count the number of times a finite word appears as a subsequence of another finite word. Similarly to the Sierpiński gasket that can be built as the limit set, for the Hausdorff distance, of a convergent sequence of normalized compact blocks extracted from Pascal triangle modulo 2, we describe and study the first properties of the subset of [0, 1] × [0, 1] associated with this extended Pascal triangle modulo a prime p. Then we create a new sequence from this extended Pascal triangle that counts, on each row of this triangle, the number of positive binomial coefficients. We show that this sequence is 2-regular. To extend our work, we construct a Pascal triangle using the Fibonacci representations of all the nonnegative integers and we define the corresponding sequence of which we study the regularity. This regularity is an extension of the classical k-regularity of sequences.
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<br/>Commentary: Work in collaboration with Julien Leroy (ULg, j.leroy@ulg.ac.be) and Michel Rigo (ULg, m.rigo@ulg.ac.be). // Travail en collaboration avec Julien Leroy (ULg, j.leroy@ulg.ac.be) et Michel Rigo (ULg, m.rigo@ulg.ac.be).