Handling congestion in crowd motion modeling

We address here the issue of congestion in the modeling of crowd motion, in the non-smooth framework: contacts between people are not anticipated and avoided, they actually occur, and they are explicitly taken into account in the model. We limit our approach to very basic principles in terms of behavior, to focus on the particular problems raised by the non-smooth character of the models. We consider that individuals tend to move according to a desired, or spontanous, velocity. We account for congestion by assuming that the evolution realizes at each time an instantaneous balance between individual tendencies and global constraints (overlapping is forbidden): the actual velocity is defined as the closest to the desired velocity among all admissible ones, in a least square sense. We develop those principles in the microscopic and macroscopic settings, and we present how the framework of Wasserstein distance between measures allows to recover the sweeping process nature of the problem on the macroscopic level, which makes it possible to obtain existence results in spite of the non-smooth character of the evolution process. Micro and macro approaches are compared, and we investigate the similarities together with deep differences of those two levels of description

Long-Term Values in Markov Decision Processes and Repeated Games, and a New Distance for Probability Spaces

We study long-term Markov decision processes (MDPs) and gambling houses, with applications to any partial observation MDPs with finitely many states and zero-sum repeated games with an informed controller. We consider a decision maker who is maximizing the weighted sum 11t 65 1 trt, where rt is the expected reward of the t-th stage. We prove the existence of a very strong notion of long-term value called general uniform value, representing the fact that the decision maker can play well independently of the evaluations (t)t 65 1 over stages, provided the total variation (or impatience) 11t 651 23 23\u3b8t+1 12\u3b8t 23 23 is small enough. This result generalizes previous results of the literature that focus on arithmetic means and discounted evaluations. Moreover, we give a variational characterization of the general uniform value via the introduction of appropriate invariant measures for the decision problems, generalizing the fundamental theorem of gambling or the Aumann\u2013Maschler cav(u) formula for repeated games with incomplete information. Apart the introduction of appropriate invariant measures, the main innovation in our proofs is the introduction of a new metric, d*, such that partial observation MDPs and repeated games with an informed controller may be associated with auxiliary problems that are nonexpansive with respect to d*. Given two Borel probabilities over a compact subset X of a normed vector space, we define d 17(u,v)=supf 08D1 23 23u(f) 12v(f) 23 23, where D1 is the set of functions satisfying 00 x, y 08 X, 00 a, b 65 0, af(x) 12 bf(y) 64 \u2016ax 12 by\u2016. The particular case where X is a simplex endowed with the L1-norm is particularly interesting: d* is the largest distance over the probabilities with finite support over X, which makes every disintegration nonexpansive. Moreover, we obtain a Kantorovich\u2013Rubinstein-type duality formula for d*(u, v), involving couples of measures (\u3b1, \u3b2) over X 7 X such that the first marginal of \u3b1 is u and the second marginal of \u3b2 is v

The underestimated effects of nanoplastics on living organisms

International audienceScientific SessionsS-31 | Micro- and nanoplastics (MNPs) and human healt

Lymphoscintigraphy in limb lymphoedema: Current methodology and interests

International audienceLymphoscintigraphy is a physiological method for the assessment of the lymphatic system. Routinely used for the localisation of sentinel nodes, it is not commonly performed to explore lymphoedema. We report the practical interest of lymphoscintigraphy in the study of limb lymphedoema from a population of 100 patients investigated during an 18-month period. After recalling the pathophysiology of lymphoedema and describing our acquisition and interpretation protocol, we present the practical interest of lymphoscintigraphy from the analysis of response to questions raised by the requesting physician. In our experience, lymphoscintigraphy was useful for the diagnosis of lymphoedema in clinically doubtful cases, the discussion of oedema pathophysiology, for the identification of the lymphatic component in lymphovenous oedema, and for the management of lymphoedema. The quality of information provided by lymphoscintigraphy depends on the rigour of the protocol, the overall data analysis and the integration of clinical data

Secularization or a return to religion? The religiosity of immigrants and their descendants

International audienceLike most European societies, France has become a predominantly secular country. Moreover, with the affirmation of the political creed of laïcité in the last decade, the expression of religion in public life, Islam especially, is under a strict scrutiny. The trends towards more secularism vary greatly, however, across religious denominations: not only are people educated in a Christian family more likely than the others to report not having a religion, but they also report a lower level of religiosity. Conversely, religious reproduction is more prevalent in Muslim’s families, and levels of religiosity are much higher among self-reported Muslims. This chapter analyses original data from the TeO survey, one of the few French surveys to provide detailed information on religious affiliation and its transmission among families. We compare the situation of Catholics, Protestants, Muslims and non-affiliated people, and discuss trends in religiosity over time. We also cover the specificities of social relations and intermarriage among religious groups, and develop an analysis of the link between religion and experiences of discrimination and exclusion