Applying Mean-Field Approximation to Continuous Time Markov Chains

The mean-field analysis technique is used to perform analysis of a system with a large number of components to determine the emergent deterministic behaviour and how this behaviour modifies when its parameters are perturbed. The computer science performance modelling and analysis community has found the mean-field method useful for modelling large-scale computer and communication networks. Applying mean-field analysis from the computer science perspective requires the following major steps: (1) describing how the agent populations evolve by means of a system of differential equations, (2) finding the emergent deterministic behaviour of the system by solving such differential equations, and (3) analysing properties of this behaviour. Depending on the system under analysis, performing these steps may become challenging. Often, modifications of the general idea are needed. In this tutorial we consider illustrating examples to discuss how the mean-field method is used in different application areas. Starting from the application of the classical technique, moving to cases where additional steps have to be used, such as systems with local communication. Finally, we illustrate the application of existing model checking analysis techniques

Stochastic population growth in spatially heterogeneous environments

Classical ecological theory predicts that environmental stochasticity increases extinction risk by reducing the average per-capita growth rate of populations. To understand the interactive effects of environmental stochasticity, spatial heterogeneity, and dispersal on population growth, we study the following model for population abundances in $n$ patches: the conditional law of $X_{t+dt}$ given $X_t=x$ is such that when $dt$ is small the conditional mean of $X_{t+dt}^i-X_t^i$ is approximately $[x^i\mu_i+\sum_j(x^j D_{ji}-x^i D_{ij})]dt$, where $X_t^i$ and $\mu_i$ are the abundance and per capita growth rate in the $i$-th patch respectivly, and $D_{ij}$ is the dispersal rate from the $i$-th to the $j$-th patch, and the conditional covariance of $X_{t+dt}^i-X_t^i$ and $X_{t+dt}^j-X_t^j$ is approximately $x^i x^j \sigma_{ij}dt$. We show for such a spatially extended population that if $S_t=(X_t^1+...+X_t^n)$ is the total population abundance, then $Y_t=X_t/S_t$, the vector of patch proportions, converges in law to a random vector $Y_\infty$ as $t\to\infty$, and the stochastic growth rate $\lim_{t\to\infty}t^{-1}\log S_t$ equals the space-time average per-capita growth rate \sum_i\mu_i\E[Y_\infty^i] experienced by the population minus half of the space-time average temporal variation \E[\sum_{i,j}\sigma_{ij}Y_\infty^i Y_\infty^j] experienced by the population. We derive analytic results for the law of $Y_\infty$, find which choice of the dispersal mechanism $D$ produces an optimal stochastic growth rate for a freely dispersing population, and investigate the effect on the stochastic growth rate of constraints on dispersal rates. Our results provide fundamental insights into "ideal free" movement in the face of uncertainty, the persistence of coupled sink populations, the evolution of dispersal rates, and the single large or several small (SLOSS) debate in conservation biology.Comment: 47 pages, 4 figure

Influence of opinion dynamics on the evolution of games

Under certain circumstances such as lack of information or bounded rationality, human players can take decisions on which strategy to choose in a game on the basis of simple opinions. These opinions can be modified after each round by observing own or others payoff results but can be also modified after interchanging impressions with other players. In this way, the update of the strategies can become a question that goes beyond simple evolutionary rules based on fitness and become a social issue. In this work, we explore this scenario by coupling a game with an opinion dynamics model. The opinion is represented by a continuous variable that corresponds to the certainty of the agents respect to which strategy is best. The opinions transform into actions by making the selection of an strategy a stochastic event with a probability regulated by the opinion. A certain regard for the previous round payoff is included but the main update rules of the opinion are given by a model inspired in social interchanges. We find that the dynamics fixed points of the coupled model is different from those of the evolutionary game or the opinion models alone. Furthermore, new features emerge such as the resilience of the fraction of cooperators to the topology of the social interaction network or to the presence of a small fraction of extremist players.Comment: 7 pages, 5 figure

Echelles fonctionnelles et évaluation des fonctions motrices dans la Sclérose Latérale Amyotrophique [Functional scales and motor assessment in amyotrophic lateral sclerosis]

There is a need of standardized and quantitative clinical assessments of ALS patients receiving new treatments. Some clinical scales, that are based on patients interviews and/or on physical examination, allow to quantify the patient functional status over time. The ALSFRS has been validated for that purpose and is one the most commonly used scales in clinical trials. Its revised version (the ALSFRS-R) has recently shown excellent metric properties. Functional scales are part of the clinical evaluation of ALS patients, and complete the quantitative assessment of muscle strength, that includes the Manual Muscular Testing (MMT) and the Maximal Voluntary Isometric Contraction (MVIC). Readers will find in this article a (non-exhaustive) listing of functional and motor scales that can be useful both in clinical trials of experimental agents and in daily practice

Place du traitement interdisciplinaire intensif dans la lombalgie chronique [Place of interdisciplinary treatments in chronic low back pain]

The treatment of chronic lumbar pain patients needs a global interdisciplinary approach when traditional conservative treatments do not fulfil their aims. One of the most efficient ways to proceed is using an interdisciplinary treatment program, including physiotherapeutic measures, occupational therapy and psychological support for 3 weeks. It is important that people in conflicts with insurances companies should be excluded from these treatments. It is also important that the reconditioning should continue over a long term to have a sustainable result

Gestion des scores cliniques multidimensionnels: quelles solutions pour l'agrégation des items? [Management of multidimensional clinical scores: which solutions for items aggregation?]

Clinical evaluation is a multifactorial process producing as many clinical scores as there are clinical dimensions. For a medicoeconomical analysis however, a single global score would be most useful. The aim of this work was to examine methods allowing relative quantification of items on multidimensional clinical scores in order to determine an appropriate solution for weighted items aggregation. Several techniques for item weighting, developed as part of a multi-criteria decision-making tool (AMCD Aide Multi-Critère à la Décision), were examined. Two methods were applied to multidimensional assessment of disability in order to estimate the weight that should be assigned to each of its six items before aggregation in a unique score. The AHP method was used with an interview of 20 functional rehabilitation specialists. The Diakoulaki method was based on the observation of thirty patients with chronic back pain and in thirty patients with vascular hemiplegia. The three weighting schemes were very different from the uniform weighting and were not correlated with each other. The items best weighted by the AHP method were "physical independence" and "mobility". For the Diakoulaki method, they were "social integration" and "economic independence" for the chronic back pain patients, and "awareness of the outside world" and "economic independence" for the vascular hemiplegia patients. Application of these three weighting schemes to theoretical patients produced very different assessments of global disability. Weighting schemes are useful to quantify the relative importance of individual clinical items. The choice of the weighting method is determinant and depends on the objective of the investigator. If the objective is a global score, the first step is to estimate the weight of the individual items, either when applying a validation process for a new multidimensional clinical score, or secondarily to adapt a validated score to a particular protocol

Spirometry and provocation tests for vocal fold dysfunction diagnosis: a retrospective case series.

Vocal cord dysfunction (VCD) is characterised by paradoxical inspiratory laryngeal motion and is often misdiagnosed as asthma. Definitive diagnosis of VCD is difficult, because laryngoscopy is positive only during symptomatic episodes or upon provocation with exercise or inhaled irritants. The aims of the study were to better characterise the symptomatology of patients with VCD and to evaluate the potential usefulness of less-invasive diagnostic tools, namely provocation tests and spirometry. Retrospective case series of 84 patients with a typical clinical history of VCD, in whom at least one of the three following diagnostic tests were performed: laryngoscopy, provocation testing, or spirometry. The mean age of the patients was 51 years and 74% were women. The principal comorbidities were rhinosinusitis (60%), gastro-oesophageal reflux disease (56%) and atopy (54%). Diagnosis of VCD was confirmed in 73/84 cases (87%), by laryngoscopy (8%), spirometry (84%) and/or provocation tests (68%). VCD remains an underdiagnosed condition. A negative finding on laryngoscopy can lead to false negative diagnosis if it is done when the patient is asymptomatic. Here we show that a clinical suspicion of VCD, evoked by medical history, can be confirmed in many cases by less invasive diagnostic tools such as spirometry and provocation tests. Future well-conducted prospective case-control studies are needed to draw firmer conclusions and to improve the diagnostic accuracy of this condition. &nbsp