ORBi Collection: Mathematics
http://hdl.handle.net/2268/153
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Note sur la projection stéréographique
http://hdl.handle.net/2268/192904
Title: Note sur la projection stéréographique
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<br/>Author, co-author: Catalan, EugèneA contribution to the study of Robbins’ problem
http://hdl.handle.net/2268/192589
Title: A contribution to the study of Robbins’ problem
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<br/>Author, co-author: Swan, YvikIntegration by parts and representation of information functionals
http://hdl.handle.net/2268/192581
Title: Integration by parts and representation of information functionals
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<br/>Author, co-author: Swan, Yvik; Peccati, Giovanni; Nourdin, Ivan
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<br/>Abstract: We introduce a new formalism for computing expectations of functionals of arbitrary random vectors, by using generalised integration by parts formulae. In doing so we extend recent representation formulae for the score function introduced in \cite{nourdin2013entropy} and also provide a new proof of a central identity first discovered in \cite{guo2005mutual}. We derive a representation for the standardised Fisher information of sums of i.i.d. random vectors which {we} use to provide rates of convergence in information theoretic central limit theorems (both in Fisher information distance and in relative entropy) {and a Stein bound for Fisher information distance.}Permutations and negative beta-shifts
http://hdl.handle.net/2268/192558
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.On a group theoretic generalization of the Morse-Hedlund theorem
http://hdl.handle.net/2268/192556
Title: On a group theoretic generalization of the Morse-Hedlund theorem
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<br/>Author, co-author: Charlier, Emilie; Puzynina, Svetlana; Zamboni, Luca
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<br/>Abstract: In their 1938 seminal paper on symbolic dynamics, Morse and Hedlund proved that every aperiodic infinite word contains at least n+ 1 distinct factors of each length n. They further showed that an infinite word has exactly n+ 1 distinct factors of each length n if and only if it is binary, aperiodic and balanced, i.e., it is a Sturmian word. In this paper we obtain a broad generalization of the Morse-Hedlund theorem via group actions.Les algorithmes : entre quotidien et créativité
http://hdl.handle.net/2268/192412
Title: Les algorithmes : entre quotidien et créativité
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<br/>Author, co-author: Nicolay, Samuel; Kleyntssens, Thomas; Mainz, IsabelleUse of the wavelet theory as a tool to investigate the l-abelian complexity of a sequence
http://hdl.handle.net/2268/192410
Title: Use of the wavelet theory as a tool to investigate the l-abelian complexity of a sequence
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<br/>Author, co-author: Kleyntssens, Thomas; Nicolay, Samuel; Vandomme, Elise; Rigo, Michel
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<br/>Abstract: The concept of k-automatic sequences is at the intersection of number theory and formal language theory. It has been generalized by the notion of k-regularity that allows to study sequences with values in a (possibly infinite) ring. This concept provides us with structural information about how the different terms of the sequence are related to each other.
They are many different notions related to the measure of complexity of an infinite sequence w. A classical approach is its factor complexity. In an abelian context, the analogue to the factor complexity is the abelian complexity where the number of distinct factors of length n is counted up to abelian equivalence. The notion of abelian complexity was extended to that of l-abelian complexity.
In this talk, I propose to use tools from the wavelet theory to analyze the l-abelian complexity. For the numerical simulations, I apply the wavelet leaders method that allows to study the pointwise regularity of signals.Contribution à la résolution de la conjecture S-adique
http://hdl.handle.net/2268/192373
Title: Contribution à la résolution de la conjecture S-adique
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<br/>Author, co-author: Leroy, JulienSystèmes de numération en base rationnelle
http://hdl.handle.net/2268/192372
Title: Systèmes de numération en base rationnelle
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<br/>Author, co-author: Leroy, JulienAutour de la conjecture S-adique
http://hdl.handle.net/2268/192371
Title: Autour de la conjecture S-adique
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<br/>Author, co-author: Leroy, JulienInitiation à Sage
http://hdl.handle.net/2268/192370
Title: Initiation à Sage
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<br/>Author, co-author: Leroy, JulienSome improvements of the S-adic conjecture
http://hdl.handle.net/2268/192369
Title: Some improvements of the S-adic conjecture
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<br/>Author, co-author: Leroy, JulienConjecture S-adique
http://hdl.handle.net/2268/192368
Title: Conjecture S-adique
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<br/>Author, co-author: Leroy, JulienThe S-adic conjecture: general case and complexity 2n
http://hdl.handle.net/2268/192367
Title: The S-adic conjecture: general case and complexity 2n
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<br/>Author, co-author: Leroy, JulienConjecture S-adique
http://hdl.handle.net/2268/192366
Title: Conjecture S-adique
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<br/>Author, co-author: Leroy, JulienSome improvements of the S-adic conjecture
http://hdl.handle.net/2268/192365
Title: Some improvements of the S-adic conjecture
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<br/>Author, co-author: Leroy, JulienExamples and counter-examples about the S-adic conjecture
http://hdl.handle.net/2268/192364
Title: Examples and counter-examples about the S-adic conjecture
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<br/>Author, co-author: Leroy, JulienExemples et contre-exemples sur la conjecture S-adique
http://hdl.handle.net/2268/192363
Title: Exemples et contre-exemples sur la conjecture S-adique
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<br/>Author, co-author: Leroy, JulienOverview of the S-adic conjecture
http://hdl.handle.net/2268/192362
Title: Overview of the S-adic conjecture
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<br/>Author, co-author: Leroy, JulienOverview of the S-adic conjecture
http://hdl.handle.net/2268/192359
Title: Overview of the S-adic conjecture
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<br/>Author, co-author: Leroy, Julien