, first industrial usage of time-series constraints and thus valorise them, and 2) highlight weak sides in the propagation of time-series constraints and thus inspire future work. 17.2.4.2 Feature Extraction and Time-Series Generation with Time-Series Constraints Time series are common in many applications in different areas such as

, Time-series constraints could be used in these contexts for extracting symbolic features in time series, e.g. the number of peaks in a time series, and then generating time series with the same values of considered features, but optimising a certain quantity

, elles ont été conçues, mais ne peuvent pas du tout être réutilisées pour tout autre problème, ou bien exigent un effort important d'adaptation. D'où la nécessité de développer des méthodes systématiques afin de synthétiser des objets combinatoires

, Cette thèse étudie une famille de contraintes, nommées contraintes sur les séries temporelles. Ces contraintes sont définies d'une façon compositionnelle

, X n i, dite série temporelle, qui représente des mesures prises au fil du temps. Par exemple, R pourrait être le nombre de paires de variables consécutives hX i ,X i+1 i de X tel que X i <X, Une contrainte sur les séries temporelles ?(X, R) restreint la variable R, dite valeur de résultat de ?, à être le résultat des calculs faits à partir de la séquence des variables entières X = hX 1

. Une-caractéristique, Un motif est une forme régulière de sous-séquences, qui, est d'un point de vue formel, est caractérisée par une expression régulière sur l'alphabet de trois lettres {'<', '=', '>'}. Par exemple, le motif DECREASING_SEQUENCE, qui correspond à toute sous-séquence monotone maximale décroissante hX i ,X i+1, Nous donnons quelques exemples d'utilisations possibles des contraintes sur les séries temporelles : ? L'analyse

, À partir des courbes de production connues des centrales électriques, on peut extraire un modèle en utilisant les contraintes sur les séries temporelles, puis générer une ou plusieurs courbes de production similaires satisfaisantes des restrictions supplémentaires pour la centrale considérée

, Le problème consiste à couvrir la demande de la main-d'oeuvre donnée variant au fil du temps, tout en minimisant le coût global des ressources, et en satisfaisant les contraintes sur les séries temporelles données qui correspondent à des processus d'affaires

, ? La fouille de données dans le contexte de la gestion de l'alimentation pour systèmes distribués à grande échelle, vol.26

?. , analyse de trace pour le fournisseur d'Internet afin de tester la bande passante de la connexion de l'utilisateur, vol.66

, ? La prise de décision en temps réel, par exemple lorsqu'il faut analyser des flux de données afin d'ajuster certains paramètres

, En effet, d'un point de vue compositionnel, les formules peuvent être utilisées conjointement et avec plusieurs techniques de résolution telles que la PPC ou la PM, ce qui s'avère beaucoup plus difficile dans le contexte des algorithmes. Un autre avantage des objets combinatoires est la synergie entre eux, c'est-à-dire que nous pouvons les composer. Des objets combinatoires différents combinés ensemble ont une meilleure performance que lorsqu'ils sont utilisés séparément. Un bon exemple d'une telle synergie est l'interaction entre des bornes précises sur la valeur de résultat d'une contrainte sur les séries temporelles ?, nous nous concentrons d'abord sur la construction de méthodes systématiques pour synthétiser des objets combinatoires compositionnels tels que des bornes précises, des invariants linéaires, des automates

, ctr_date (nb_peak

, Based on the \\ hyperlink{Ppeak}{\\ pattern{peak}} pattern

[. Ctr_arguments-(nb_peak and . &apos;v-a-l-u-e-&apos;?-dvar,

&. Value&apos;-=-0, VALUE' >=0 , 'VALUE'= < markup ( max ( 0 , ( sv ?1) / 2 ) ,1) , required

, ctr_typical (nb_peak ,[ size ('VARIABLES') >2,range('VARIABLES'^var) >1])

?. , ?. , ?. , ?. , and ?. ). , automaton_with_signature ( nb_peak_a_s) ]). ? series ctr_cond_imply, checker ( nb_peak_c ) , automaton ( nb_peak_a1 ) , automaton ( nb_peak_a ) , automaton_with_signature (nb_peak_a1_s)

_. Default, _. Clast, and R. Dlast, Value ) :? !, Value is RLast+CLast. nb_peak_c

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X. |. Xi, ]. Xs, C. Default, D. , R. et al.,

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