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Prediction of time series by statistical learning: general losses and fast rates

Pierre Alquier, Xiaoyin Li, Olivier Wintenberger (2013)

Dependence Modeling

We establish rates of convergences in statistical learning for time series forecasting. Using the PAC-Bayesian approach, slow rates of convergence √ d/n for the Gibbs estimator under the absolute loss were given in a previous work [7], where n is the sample size and d the dimension of the set of predictors. Under the same weak dependence conditions, we extend this result to any convex Lipschitz loss function. We also identify a condition on the parameter space that ensures similar rates for the...

Predictive control for trajectory tracking and decentralized navigation of multi-agent formations

Ionela Prodan, Sorin Olaru, Cristina Stoica, Silviu-Iulian Niculescu (2013)

International Journal of Applied Mathematics and Computer Science

This paper addresses a predictive control strategy for a particular class of multi-agent formations with a time-varying topology. The goal is to guarantee tracking capabilities with respect to a reference trajectory which is pre-specified for an agent designed as the leader. Then, the remaining agents, designed as followers, track the position and orientation of the leader. In real-time, a predictive control strategy enhanced with the potential field methodology is used in order to derive a feedback...

Preface

Christian Choffrut, Juhani Karhumäki (1994)

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

Preface

Markus Holzer, Bianca Truthe (2014)

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

Preface

Didier Caucal, Anne Siegel (2008)

RAIRO - Theoretical Informatics and Applications

Preface

J. Berstel, T. Harju, J. Karhumäki (2008)

RAIRO - Theoretical Informatics and Applications

Preliminaries to Classical First Order Model Theory

Marco Caminati (2011)

Formalized Mathematics

First of a series of articles laying down the bases for classical first order model theory. These articles introduce a framework for treating arbitrary languages with equality. This framework is kept as generic and modular as possible: both the language and the derivation rule are introduced as a type, rather than a fixed functor; definitions and results regarding syntax, semantics, interpretations and sequent derivation rules, respectively, are confined to separate articles, to mark out the hierarchy...

Prescribed ultrametrics

J. Higgins, D. Campbell (1993)

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

Presentations of finite simple groups: a computational approach

Robert Guralnick, William M. Kantor, Martin Kassabov, Alexander Lubotzky (2011)

Journal of the European Mathematical Society

All finite simple groups of Lie type of rank n over a field of size q , with the possible exception of the Ree groups 2 G 2 ( q ) , have presentations with at most 49 relations and bit-length O ( 𝚕𝚘𝚐 n + 𝚕𝚘𝚐 q ) . Moreover, A n and S n have presentations with 3 generators; 7 relations and bit-length O ( 𝚕𝚘𝚐 n ) , while 𝚂𝙻 ( n , q ) has a presentation with 6 generators, 25 relations and bit-length O ( 𝚕𝚘𝚐 n + 𝚕𝚘𝚐 q ) .

Preservation of properties of fuzzy relations during aggregation processes

Józef Drewniak, Urszula Dudziak (2007)

Kybernetika

Diverse classes of fuzzy relations such as reflexive, irreflexive, symmetric, asymmetric, antisymmetric, connected, and transitive fuzzy relations are studied. Moreover, intersections of basic relation classes such as tolerances, tournaments, equivalences, and orders are regarded and the problem of preservation of these properties by n -ary operations is considered. Namely, with the use of fuzzy relations R 1 , ... , R n and n -argument operation F on the interval [ 0 , 1 ] , a new fuzzy relation R F = F ( R 1 , ... , R n ) is created. Characterization...

Prime ideal theorem for double Boolean algebras

Léonard Kwuida (2007)

Discussiones Mathematicae - General Algebra and Applications

Double Boolean algebras are algebras (D,⊓,⊔,⊲,⊳,⊥,⊤) of type (2,2,1,1,0,0). They have been introduced to capture the equational theory of the algebra of protoconcepts. A filter (resp. an ideal) of a double Boolean algebra D is an upper set F (resp. down set I) closed under ⊓ (resp. ⊔). A filter F is called primary if F ≠ ∅ and for all x ∈ D we have x ∈ F or x ⊲ ∈ F . In this note we prove that if F is a filter and I an ideal such that F ∩ I = ∅ then there is a primary filter G containing F such that G...

Primitive substitutive numbers are closed under rational multiplication

Pallavi Ketkar, Luca Q. Zamboni (1998)

Journal de théorie des nombres de Bordeaux

Let M ( r ) denote the set of real numbers α whose base- r digit expansion is ultimately primitive substitutive, i.e., contains a tail which is the image (under a letter to letter morphism) of a fixed point of a primitive substitution. We show that the set M ( r ) is closed under multiplication by rational numbers, but not closed under addition.

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