The FCLT with Dependent Errors: an Helicopter Tour of the Quality of the Approximation

This note investigates the adequacy of the finite-sample approximation provided by the Functional Central Limit Theorem (FCLT) when the errors are allowed to be dependent. We compare the distribution of the scaled partial sums of some data with the distribution of the Wiener process to which it converges. Our setup is purposely very simple in that it considers data generated from an ARMA(1,1) process. Yet, this is sufficient to bring out interesting conclusions about the particular elements which cause the approximations to be inadequate in even quite large sample sizes.Cette note examine la pertinence de l'approximation en échantillon fini donnée par le théorème de la limite centrale fonctionnelle quand les erreurs sont dépendantes. Nous comparons la distribution des sommes partielles échelonnées de quelques donnés avec la distribution du processus de Wiener sur lequel elle converge. Notre modèle est intentionnellement très simple, compte tenu qu'il considère les donnés générées à partir d'un processus ARMA(1,1). Cependant, c'est suffisant pour obtenir des conclusions intéressantes sur les éléments particuliers qui causent des approximations inadéquates même en larges échantillons

La dynamique des attracteurs comme base de génération de comportements en robotique mobile autonome

L’hypothèse centrale de l’approche dynamique en robotique mobile autonome (Schöner et Dose, 1992 ; Schöner, Dose et Engels, 1995 ; Bicho et Schöner, 1997 ; Steinhage et Schöner, 1998 ; Large, Christensen et Bajcy, 1999 ; Bicho, Mallet et Schöner, 2000) est que le comportement moteur ainsi que les représentations pertinentes nécessaires à sa réalisation doivent, d’une part, être générés de façon continue dans le temps, et, d’autre part, résister aux fluctuations ou perturbations auxquelles tout système réel est exposé. Cela conduit à une conception dans laquelle le comportement et les représentations sont les solutions stables (ou attracteurs) d’un ensemble de systèmes dynamiques, qui traduisent en temps réel l’information sensorielle en contraintes graduées et intégrables. De multiples attracteurs peuvent co-exister en présence de la même situation sensorielle. C’est l’état interne du système autonome qui décidera quel attracteur sera choisi. Le changement du nombre et/ou de la nature des attracteurs à travers des instabilités (ou bifurcations) permet au système autonome de se configurer de manière flexible selon le contexte sensoriel instantané. L’approche est ici présentée au niveau de la génération de comportements moteurs. Dans ce cas, des variables « comportementales » représentent directement un continuum d’états physiques du système qui sont générés par des systèmes de contrôle conventionnels. Par exemple, une variable représentant la direction dans laquelle un véhicule se déplace, peut évoluer dans le temps grâce à un système dynamique qui intègre les contraintes « acquisition de cibles » et « évitement d’obstacles ». La fusion ou sélection parmi ces contraintes est réalisée au moyen d’une dynamique non linéaire bien maîtrisée

Maxwell-Garnett mixing rule in the presence of multiple scattering: Derivation and accuracy

We give a rigorous and original derivation of the Maxwell-Garnett mixing rule in the dynamical regime for a composite dielectric random medium with small spherical inclusions. For certain configurations of scatterers, we show that contrarily to the common belief, the Maxwell-Garnett formula can remain very accurate at a high concentration of scatterers and incorporate multiple-scattering effects as well as attenuation of the mean field. We provide a realistic numerical example for which this is the case

Effective-medium theory for finite-size aggregates

We propose an effective-medium theory for random aggregates of small spherical particles that accounts for the finite size of the embedding volume. The technique is based on the identification of the first two orders of the Born series within a finite volume for the coherent field and the effective field. Although the convergence of the Born series requires a finite volume, the effective constants that are derived through this identification are shown to admit of a large-scale limit. With this approach we recover successively, and in a simple manner, some classical homogenization formulas: the Maxwell Garnett mixing rule, the effective-field approximation, and a finite-size correction to the quasi-crystalline approximation (QCA). The last formula is shown to coincide with the usual low-frequency QCA in the limit of large volumes, while bringing substantial improvements when the dimension of the embedding medium is of the order of the probing wavelength. An application to composite spheres is discussed

The Roles of the Creditor and Debtor in the Settlement Process of the Debtor\u27s Financial Obligations Under the Debtor\u27s Insolvency Law No. 19 of 2019

The UAE Cabinet approved a federal law to regulate cases of insolvency of natural persons or individuals. In 2016, the UAE government had adopted a similar insolvency law for companies which was widely welcomed by businesses and financial institutions. The legal framework for insolvency for both companies and individuals are expected to improve the competitiveness and the ease of doing business of the UAE. Debt restructuring for individuals under legal protection is widely seen as a great step forward in helping those who are unable to pay their debts from going bankrupt. “The approval of a new federal law to regulate the cases of personal insolvency is a step forward in improving the ease of doing business for both debtors and creditors. A legal framework for addressing debts and financial difficulties will help them reschedule their debts and provide them with the opportunity to be granted new concessional loans. “The introduction of any form of personal insolvency regime is a critical step in both enhancing and rounding out the already improved UAE insolvency provisions. In this article we will present the role of the civil debtor and the creditor in the period of debt restructuring. We will start with the role of the debtor as soon as debt restructuring is requested, then its role during the preparation of the debt restructuring, then its role in the execution of the plan and finally its role with the end of the plan. In the second part we will examine the role of the creditor in the preparation of the debt restructuring plan then its role in the execution of the plan finally we will study its role in the end of the plan. We will present in our conclusion the results of our research and the recommendations

Protecting the Privacy of the Worker in light of the Development of Modern Means of Communication: A Comparative Study of the UAE and French Laws

The concept of privacy has evolved a lot due to the tremendous scientific development that humanity has achieved in recent decades. The massive use of computers and the Internet in all areas has given rise to new aspects of privacy. This concept now concerns calls, personal photos, recordings, the use of social networks and personal conversations. Through this research, we want to inform the reader about the rules governing the protection of the privacy of an employee in the field of computer science in the light of the legal texts applied in UAE laws, or at least clarify the positions of French law and the judicial authority in this regard, especially since they have made significant progress in this area. Failure to respect the sanctity of privacy in modern areas of communication goes beyond the traditional problems that dealt with the sanctity of privacy. These legal studies and legal scientific theses focused mainly on the classic concept of the right to private life of an employee, and very few of them highlighted the lack of respect for the employee\u27s privacy when using computer tools at work. The technological revolution has allowed the emergence of new forms that violate the privacy of the employee in our Arab societies and which deserve to be clarified. Through this research, we want to know the obligations of the employer when monitoring its employees especially when this monitoring affects the work tools and the use of employees of the Internet. We also want to identify cases in which an employee is considered to be beyond the scope of his or her work privacy to the point of harming the employer. Thus, cases where the employer has the right to dismiss the employee because of a serious fault. We believe that the absence of special legal texts that govern these issues demonstrates a profound legal vacuum in these areas. Key words: Privacy, French law, UAE labor law, employer authority, modern means of communication, the worker

Bacterivory by benthic organisms in sediment: quantification using 15N enriched bacteria

International audienceThe fate of benthic bacterial biomass in benthic food webs is a topic of major importance but poorly described. This paper describes an alternative method for evaluation of bacterial grazing rate by meiofauna and macrofauna using bacteria pre-enriched with stable isotopes. Natural bacteria from the sediment of an intertidal mudflat were cultured in a liquid medium enriched with 15NH4Cl. Cultured bacteria contained 2.9 % of 15N and were enriched sufficiently to be used as tracers during grazing experiments. Cultured-bacteria presented a biovolume (0.21 µm3) and a percentage of actively respiring bacteria (10 %) similar to those found in natural communities. The number of Operational Taxon Units found in cultures fluctuated between 56 and 75 % of that found in natural sediment. Despite this change in community composition, the bacterial consortium used for grazing experiments exhibited characteristics of size, activity and diversity more representative of the natural community than usually noticed in many other grazing studies. The bacterial ingestion rates of three different grazers were in the range of literature values resulting from other methods: 1149 ngC ind-1 h-1 for the mud snail Hydrobia ulvae, 0.027 ngC ind-1 h-1 for the nematode community, and 0.067 ngC ind-1 h-1 for the foraminifera Ammonia tepida. The alternative method described in this paper overcomes some past limitations and it presents interesting advantages such as short time incubation and in situ potential utilisation

The Roles of the Creditor and Debtor in the Settlement Process of the Debtor\u27s Financial Obligations Under the Debtor\u27s Insolvency Law No. 19 of 2019

The UAE Cabinet approved a federal law to regulate cases of insolvency of natural persons or individuals. In 2016, the UAE government had adopted a similar insolvency law for companies which was widely welcomed by businesses and financial institutions. The legal framework for insolvency for both companies and individuals are expected to improve the competitiveness and the ease of doing business of the UAE. Debt restructuring for individuals under legal protection is widely seen as a great step forward in helping those who are unable to pay their debts from going bankrupt. “The approval of a new federal law to regulate the cases of personal insolvency is a step forward in improving the ease of doing business for both debtors and creditors. A legal framework for addressing debts and financial difficulties will help them reschedule their debts and provide them with the opportunity to be granted new concessional loans. “The introduction of any form of personal insolvency regime is a critical step in both enhancing and rounding out the already improved UAE insolvency provisions. In this article we will present the role of the civil debtor and the creditor in the period of debt restructuring. We will start with the role of the debtor as soon as debt restructuring is requested, then its role during the preparation of the debt restructuring, then its role in the execution of the plan and finally its role with the end of the plan. In the second part we will examine the role of the creditor in the preparation of the debt restructuring plan then its role in the execution of the plan finally we will study its role in the end of the plan. We will present in our conclusion the results of our research and the recommendations