ORBi Collection: Mathematics
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Parameter estimation and inference in dynamic systems described by linear partial differential equations
http://hdl.handle.net/2268/188416
Title: Parameter estimation and inference in dynamic systems described by linear partial differential equations
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<br/>Author, co-author: Frasso, Gianluca; Jeager, Jonathan; Lambert, Philippe
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<br/>Abstract: Differential equations (DEs) are commonly used to describe dynamic sys-
tems evolving in one (ordinary differential equations or ODEs) or in more than one
dimensions (partial differential equations or PDEs). In real data applications, the para-
meters involved in the DE models are usually unknown and need to be estimated from
the available measurements together with the state function. In this paper, we present
frequentist and Bayesian approaches for the joint estimation of the parameters and of
the state functions involved in linear PDEs. We also propose two strategies to include
state (initial and/or boundary) conditions in the estimation procedure. We evaluate the
performances of the proposed strategy through simulated examples and a real data
analysis involving (known and necessary) state conditions.Damage modeling of composites and reliability analysis
http://hdl.handle.net/2268/188122
Title: Damage modeling of composites and reliability analysis
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<br/>Author, co-author: Zein, Samih; Bruyneel, MichaëlOptimization of composite structures with curved fiber trajectories
http://hdl.handle.net/2268/188121
Title: Optimization of composite structures with curved fiber trajectories
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<br/>Author, co-author: Bruyneel, Michaël; Zein, Samih; Lemaire, EtienneReducing overdesign with predictive performance and producibility simulation of composite structures
http://hdl.handle.net/2268/188118
Title: Reducing overdesign with predictive performance and producibility simulation of composite structures
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<br/>Author, co-author: Hudson, Leigh; Bruyneel, Michaël; Lemaire, EtienneA two-step solution procedure for composite structures optimization including geometric non-linear behaviour, design rules and manufacturing constraints
http://hdl.handle.net/2268/188117
Title: A two-step solution procedure for composite structures optimization including geometric non-linear behaviour, design rules and manufacturing constraints
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<br/>Author, co-author: Bruyneel, Michaël; Zein, Samih; Grihon, StéphaneOptimal design of composite structures with curved fiber trajectories
http://hdl.handle.net/2268/188116
Title: Optimal design of composite structures with curved fiber trajectories
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<br/>Author, co-author: Lemaire, Etienne; Zein, Samih; DUYSINX, Pierre; Bruyneel, MichaëlComportement asymptotique des morphismes et théorème de Cobham pour les morphismes effaçants
http://hdl.handle.net/2268/187943
Title: Comportement asymptotique des morphismes et théorème de Cobham pour les morphismes effaçants
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<br/>Author, co-author: Stipulanti, ManonA stochastic analysis of some two-person sports
http://hdl.handle.net/2268/187474
Title: A stochastic analysis of some two-person sports
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<br/>Author, co-author: Swan, Yvik; Paindaveine, DavyExcursions le long de la Gaussienne
http://hdl.handle.net/2268/187469
Title: Excursions le long de la Gaussienne
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<br/>Author, co-author: Swan, YvikEntropy and the fourth moment phenomenon
http://hdl.handle.net/2268/187468
Title: Entropy and the fourth moment phenomenon
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<br/>Author, co-author: Swan, Yvik; Peccati, Giovanni; Nourdin, IvanParametric Stein operators and variance bounds
http://hdl.handle.net/2268/187467
Title: Parametric Stein operators and variance bounds
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<br/>Author, co-author: Swan, Yvik; Ley, ChristopheParametric Polyhedra with at least k Lattice Points: Their Semigroup Structure and the k-Frobenius Problem
http://hdl.handle.net/2268/187396
Title: Parametric Polyhedra with at least k Lattice Points: Their Semigroup Structure and the k-Frobenius Problem
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<br/>Author, co-author: Aliev, Iskander; De Loera, Jesus; Louveaux, Quentin
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<br/>Abstract: The well-studied semigroup Sg(A) = {b : b = Ax; x in Z^n; x >= 0} can be
stratified by the sizes of the polyhedral fibers IPA(b) = {x : Ax = b; x >= 0; x in Z^n}. The
key theme of this paper is a structure theory that characterizes precisely the set Sg_k(A) of
all vectors b in Sg(A) such that their fiber IPA(b) has at least k-solutions. We demonstrate
that this set is finitely generated, a union of translated copies of a semigroup which can be
computed explicitly via Hilbert bases computations. Related results can be derived for those
right-hand-side vectors b for which IPA(b) has exactly k solutions or fewer than k solutions.
We also show that, when n, k are fixed natural numbers, one can compute in polynomial time
an encoding of Sg_k(A) as a generating function, using a short sum of rational functions.
As a consequence, one can identify all right-hand-side vectors that have at least k solutions.
Using this tool we prove that for fixed n; k the k-Frobenius number can be computed in
polynomial time, generalizing a well-known result of R. Kannan.A Quantitative Doignon-Bell-Scarf theorem
http://hdl.handle.net/2268/187395
Title: A Quantitative Doignon-Bell-Scarf theorem
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<br/>Author, co-author: Aliev, Iskander; Bassett, Robert; De Loera, Jesus; Louveaux, Quentin
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<br/>Abstract: The famous Doignon-Bell-Scarf theorem is a Helly-type result about the existence of integer solutions to systems of linear inequalities. The purpose of this paper is to present the following quantitative generalization: Given an integer k, we prove that there exists a constant c(n,k), depending only on the dimension n and on the number k, such that if a bounded polyhedron {x in R^n : Ax <= b} contains exactly k integer points, then there exists a subset of the rows, of cardinality no more than c(n,k), defining a polyhedron that contains exactly the same k integer points.
In this case c(n,0)=2^n as in the original case of Doignon-Bell-Scarf for infeasible systems of inequalities.
We work on both upper and lower bounds for the constant c(n,k) and discuss some consequences, including a Clarkson-style algorithm to find the l-th best solution of an integer program with respect to the ordering induced by the objective function.Les Mots des Maths : Trapèze
http://hdl.handle.net/2268/187382
Title: Les Mots des Maths : Trapèze
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<br/>Author, co-author: Dupont, PascalLatex, un peu, beaucoup (9. Figures & tables)
http://hdl.handle.net/2268/187381
Title: Latex, un peu, beaucoup (9. Figures & tables)
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<br/>Author, co-author: Dupont, PascalComputing k-binomial equivalence and avoiding binomial repetitions
http://hdl.handle.net/2268/187305
Title: Computing k-binomial equivalence and avoiding binomial repetitions
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<br/>Author, co-author: Rigo, Michel
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<br/>Abstract: In this talk, I will first recall basic results on binomial coefficients of words, then review the connections and differences with Parikh matrices. As a generalization of abelian equivalence, two words u and v are k-binomially equivalent if every word of length at most k appears as a subword of u exactly as many times as it appears as a subword of v. So a k-binomial square is a word uv where u and v are k-binomially equivalent. We will discuss avoidance of squares and cubes in infinite words (this is a joint word with M. Rao). Finally, I will consider the question of deciding whether or not two finite words are k-binomially equivalent. This problem has recently been shown to be decidable in polynomial time by Freydenberger, Gawrychowski et al.Quadratizations of pseudo-Boolean functions
http://hdl.handle.net/2268/187079
Title: Quadratizations of pseudo-Boolean functions
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<br/>Author, co-author: Crama, Yves
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<br/>Abstract: A pseudo-Boolean function is a real-valued function of 0-1 variables. Every pseudo-Boolean function can be represented by various analytical expressions, e.g., as a polynomial in its variables, or as a polynomial in its variables and in their Boolean complements, or as a disjunctive form, or as pointwise minimum of a family of affine functions, and so forth.
Motivated by the problem of minimizing pseudo-Boolean functions, we consider yet another class of representations. Namely, we say that g(x,y) is a quadratization of the pseudo-Boolean function f(x) if g(x,y) is a quadratic pseudo-Boolean function of x and of m auxiliary binary variables y such that, for all x, f(x) = min g(x,y), where the minimum is taken over all possible values of the y-variables.
It can be shown that every pseudo-Boolean function has at least one, and usually, many quadratizations. In recent years, several authors have proposed to reduce the problem of minimizing an arbitrary function f(x) (say, expressed as a high-degree polynomial) to the (presumably easier) problem of minimizing one of its quadratizations.
In this talk, we discuss the size of ``small'' quadratizations, that is, the number of auxiliary variables required in any quadratization. We provide lower and upper bounds on the number of auxiliary variables for the case of an arbitrary function f(x), as well as for the special case where f(x) is a symmetric function of its variables.Identifying codes in vertex-transitive graphs and strongly regular graphs
http://hdl.handle.net/2268/186885
Title: Identifying codes in vertex-transitive graphs and strongly regular graphs
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<br/>Author, co-author: Gravier, Sylvain; Parreau, Aline; Rottey, Sara; Storme, Leo; Vandomme, Elise
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<br/>Abstract: We consider the problem of computing identifying codes of graphs and its fractional relaxation. The ratio between the size of optimal integer and fractional solutions is between 1 and 2ln(|V|)+1 where V is the set of vertices of the graph. We focus on vertex-transitive graphs for which we can compute the exact fractional solution. There are known examples of vertex-transitive graphs that reach both bounds. We exhibit infinite families of vertex-transitive graphs with integer and fractional identifying codes of order |V|^α with α∈{14,13,25}. These families are generalized quadrangles (strongly regular graphs based on finite geometries). They also provide examples for metric dimension of graphs.On generalized Hölder spaces
http://hdl.handle.net/2268/186554
Title: On generalized Hölder spaces
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<br/>Author, co-author: Kreit, Damien; Nicolay, Samuel
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<br/>Abstract: We introduce generalized pointwise Hölder spaces as the point wise version of generalized uniform Hölder spaces. These last ones can be seen as a special case of generalized Besov spaces.Dynamics of hybrid switching diffusions SIRS model
http://hdl.handle.net/2268/186346
Title: Dynamics of hybrid switching diffusions SIRS model
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<br/>Author, co-author: Settati, Adel; Lahrouz, Aadil; El Jarroudi, Mustapha; El Jarroudi, Moussa
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<br/>Abstract: The main aim of this paper is to study the effect of the environmental noises in the asymptotic properties of a stochastic version of the classical SIRS epidemic model. The model studied here include white noise and telegraph noise modeled by Markovian switching. We obtained conditions for extinction both in probability one and in pth moment. We also established the persistence of disease under different conditions on the intensities of noises, the parameters of the model and the stationary distribution of the Markov chain. The highlight point of our work is that our conditions are sufficient and almost necessary for extinction and persistence of the epidemic. The presented results are demonstrated by numerical simulations.