Multilevel Monte Carlo simulation for Levy processes based on the Wiener-Hopf factorisation

In Kuznetsov et al. (2011) a new Monte Carlo simulation technique was introduced for a large family of Levy processes that is based on the Wiener-Hopf decomposition. We pursue this idea further by combining their technique with the recently introduced multilevel Monte Carlo methodology. Moreover, we provide here for the first time a theoretical analysis of the new Monte Carlo simulation technique in Kuznetsov et al. (2011) and of its multilevel variant for computing expectations of functions depending on the historical trajectory of a Levy process. We derive rates of convergence for both methods and show that they are uniform with respect to the "jump activity" (e.g. characterised by the Blumenthal-Getoor index). We also present a modified version of the algorithm in Kuznetsov et al. (2011) which combined with the multilevel methodology obtains the optimal rate of convergence for general Levy processes and Lipschitz functionals. This final result is only a theoretical one at present, since it requires independent sampling from a triple of distributions which is currently only possible for a limited number of processes

Robust estimation based on one-shot device test data under log-normal lifetimes

In this paper we present robust estimators for one-shot device test data under lognormal lifetimes. Based on these estimators, confidence intervals and Wald-type tests are also developed. Their robustness feature is illustrated through a simulation study and two numerical examples

Is the phase transition in the Heisenberg model described by the (2+ϵ)(2+\epsilon)-expansion of the nonlinear σ\sigma-model?

Nonlinear $\sigma$-model is an ubiquitous model. In this paper, the $O(N)$ model where the $N$-component spin is a unit vector, ${\bf S}^2=1$,is considered. The stability of this model with respect to gradient operators $(\partial_{\mu}{\bf S}\cdot \partial_{\nu}{\bf S})^s$, where the degree $s$ is arbitrary, is discussed. Explicit two-loop calculations within the scheme of $\epsilon$-expansion, where $\epsilon=(d-2)$, leads to the surprising result that these operators are relevant. In fact, the relevancy increases with the degree $s$. We argue that this phenomenon in the $O(N)$-model actually reflects the failure of the perturbative analysis, that is, the $(2+\epsilon)$-expansion. It is likely that it is necessary to take into account non-perturbative effects if one wants to describe the phase transition of the Heisenberg model within the context of the non-linear $\sigma$-model. Thus, uncritical use of the $(2+\epsilon)$-expansion may be misleading, especially for those cases for which there are not many independent checks.Comment: RevTex, 33 pages, figures embedde

Metabolic Changes Following Perinatal Asphyxia: Role of Astrocytes and Their Interaction with Neurons

Perinatal Asphyxia (PA) represents an important cause of severe neurological deficits including delayed mental and motor development, epilepsy, major cognitive deficits and blindness. The interaction between neurons, astrocytes and endothelial cells plays a central role coupling energy supply with changes in neuronal activity. Traditionally, experimental research focused on neurons, whereas astrocytes have been more related to the damage mechanisms of PA. Astrocytes carry out a number of functions that are critical to normal nervous system function, including uptake of neurotransmitters, regulation of pH and ion concentrations, and metabolic support for neurons. In this work, we aim to review metabolic neuron-astrocyte interactions with the purpose of encourage further research in this area in the context of PA, which is highly complex and its mechanisms and pathways have not been fully elucidated to this day.Fil: Logica Tornatore, Tamara Maite Ayelén. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Houssay. Instituto de Investigaciones Cardiológicas. Universidad de Buenos Aires. Facultad de Medicina. Instituto de Investigaciones Cardiológicas; ArgentinaFil: Riviere, Stephanie. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Houssay. Instituto de Investigaciones Cardiológicas. Universidad de Buenos Aires. Facultad de Medicina. Instituto de Investigaciones Cardiológicas; ArgentinaFil: Holubiec, Mariana Ines. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Houssay. Instituto de Investigaciones Cardiológicas. Universidad de Buenos Aires. Facultad de Medicina. Instituto de Investigaciones Cardiológicas; ArgentinaFil: Castilla Lozano, Maria del Rocio. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Houssay. Instituto de Investigaciones Cardiológicas. Universidad de Buenos Aires. Facultad de Medicina. Instituto de Investigaciones Cardiológicas; ArgentinaFil: Barreto, George E.. Pontificia Universidad Javeriana; ColombiaFil: Capani, Francisco. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Houssay. Instituto de Investigaciones Cardiológicas. Universidad de Buenos Aires. Facultad de Medicina. Instituto de Investigaciones Cardiológicas; Argentina. Universidad Argentina "John F. Kennedy"; Argentina. Universidad Autónoma de Chile; Chil

On the Specification of Non-functional Properties of Systems by Observation

Domain specific languages play a cornerstone role in Model-Driven Engineering (MDE) for representing models and metamodels. So far, most of the MDE community efforts have focused on the specification of the functional properties of systems. However, the correct and complete specification of some of their non-functional properties is critical in many important distributed application domains, such as embedded systems, multimedia applications or e-commerce services. In this paper we present an approach to specify QoS requirements, based on the observation of the system actions and of the state of its objects. We show how this approach can be used to extend languages which specify behavior in terms of rules, and how QoS characteristics can be easily expressed and reused across models. We show as well how this approach enables the specification of other important properties of systems, such as automatic reconfiguration of the system when some of the QoS properties change.Ministerio de Ciencia e Innovación TIN2008-031087Junta de Andalucía P07-TIC-0318