A well-posedness theory in measures for some kinetic models of collective motion

We present existence, uniqueness and continuous dependence results for some kinetic equations motivated by models for the collective behavior of large groups of individuals. Models of this kind have been recently proposed to study the behavior of large groups of animals, such as flocks of birds, swarms, or schools of fish. Our aim is to give a well-posedness theory for general models which possibly include a variety of effects: an interaction through a potential, such as a short-range repulsion and long-range attraction; a velocity-averaging effect where individuals try to adapt their own velocity to that of other individuals in their surroundings; and self-propulsion effects, which take into account effects on one individual that are independent of the others. We develop our theory in a space of measures, using mass transportation distances. As consequences of our theory we show also the convergence of particle systems to their corresponding kinetic equations, and the local-in-time convergence to the hydrodynamic limit for one of the models.

Lp theory for the multidimensional aggregation equation

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Interactive Epistemology and Reasoning: On the Foundations of Game Theory

Game theory describes and analyzes strategic interaction. It is usually distinguished between static games, which are strategic situations in which the players choose only once as well as simultaneously, and dynamic games, which are strategic situations involving sequential choices. In addition, dynamic games can be further classified according to perfect and imperfect information. Indeed, a dynamic game is said to exhibit perfect information, whenever at any point of the game every player has full informational access to all choices that have been conducted so far. However, in the case of imperfect information some players are not fully informed about some choices. Game-theoretic analysis proceeds in two steps. Firstly, games are modelled by so-called form structures which extract and formalize the significant parts of the underlying strategic interaction. The basic and most commonly used models of games are the normal form, which rather sparsely describes a game merely in terms of the players' strategy sets and utilities, and the extensive form, which models a game in a more detailed way as a tree. In fact, it is standard to formalize static games with the normal form and dynamic games with the extensive form. Secondly, solution concepts are developed to solve models of games in the sense of identifying the choices that should be taken by rational players. Indeed, the ultimate objective of the classical approach to game theory, which is of normative character, is the development of a solution concept that is capable of identifying a unique choice for every player in an arbitrary game. However, given the large variety of games, it is not at all certain whether it is possible to device a solution concept with such universal capability. Alternatively, interactive epistemology provides an epistemic approach to game theory of descriptive character. This rather recent discipline analyzes the relation between knowledge, belief and choice of game-playing agents in an epistemic framework. The description of the players' choices in a given game relative to various epistemic assumptions constitutes the fundamental problem addressed by an epistemic approach to game theory. In a general sense, the objective of interactive epistemology consists in characterizing existing game-theoretic solution concepts in terms of epistemic assumptions as well as in proposing novel solution concepts by studying the game-theoretic implications of refined or new epistemic hypotheses. Intuitively, an epistemic model of a game can be interpreted as representing the reasoning of the players. Indeed, before making a decision in a game, the players reason about the game and their respective opponents, given their knowledge and beliefs. Precisely these epistemic mental states on which players base their decisions are explicitly expressible in an epistemic framework. In this PhD thesis, we consider an epistemic approach to game theory from a foundational point of view. In Chapter 1, basic game-theoretic notions as well as Aumann's epistemic framework for games are expounded and illustrated. Also, Aumann's sufficient conditions for backward induction are presented and his conceptual views discussed. In Chapter 2, Aumann's interactive epistemology is conceptually analyzed. In Chapter 3, which is based on joint work with Conrad Heilmann, a three-stage account for dynamic games is introduced and a type-based epistemic model is extended with a notion of agent connectedness. Then, sufficient conditions for backward induction are derived. In Chapter 4, which is based on joint work with Jérémie Cabessa, a topological approach to interactive epistemology is initiated. In particular, the epistemic-topological operator limit knowledge is defined and some implications for games considered. In Chapter 5, which is based on joint work with Jérémie Cabessa and Andrés Perea, Aumann's impossibility theorem on agreeing to disagree is revisited and weakened in the sense that possible contexts are provided in which agents can indeed agree to disagree.

Aspects of Iwasawa theory over function fields

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Generic Nekhoroshev theory without small divisors

In this article, we present a new approach of Nekhoroshev theory for a generic unperturbed Hamiltonian which completely avoids small divisors problems. The proof is an extension of a method introduced by P. Lochak which combines averaging along periodic orbits with simultaneous Diophantine approximation and uses geometric arguments designed by the second author to handle generic integrable Hamiltonians. This method allows to deal with generic non-analytic Hamiltonians and to obtain new results of generic stability around linearly stable tori.

Conflict prevention and decentralized governance: some remarks about the state of the art in theory and practice

Is there a link between decentralized governance and conflict prevention? This article tries to answer the question by presenting the state of the art of the intersection of both concepts. Provided that social conflict is inevitable and given the appearance of new threats and types of violence, as well as new demands for security based on people (human security), our societies should focus on promoting peaceful changes. Through an extensive analysis of the existing literature and the study of several cases, this paper suggests that decentralized governance can contribute to these efforts by transforming conflicts, bringing about power-sharing and inclusion incentives of minority groups. Albeit the complexity of assessing its impact on conflict prevention, it can be contended that decentralized governance might have very positive effects on the reduction of causes that bring about conflicts due to its ability to foster the creation of war/violence preventors. More specifically, this paper argues that decentralization can have a positive impact on the so-called triggers and accelerators (short- and medium-term causes).

A critical application of securitization theory: overcoming the normative dilemma of writing security

This article addresses the normative dilemma located within the application of `securitization,’ as a method of understanding the social construction of threats and security policies. Securitization as a theoretical and practical undertaking is being increasingly used by scholars and practitioners. This scholarly endeavour wishes to provide those wishing to engage with securitization with an alternative application of this theory; one which is sensitive to and self-reflective of the possible normative consequences of its employment. This article argues that discussing and analyzing securitization processes have normative implications, which is understood here to be the negative securitization of a referent. The negative securitization of a referent is asserted to be carried out through the unchallenged analysis of securitization processes which have emerged through relations of exclusion and power. It then offers a critical understanding and application of securitization studies as a way of overcoming the identified normative dilemma. First, it examines how the Copenhagen School’s formation of securitization theory gives rise to a normative dilemma, which is situated in the performative and symbolic power of security as a political invocation and theoretical concept. Second, it evaluates previous attempts to overcome the normative dilemma of securitization studies, outlining the obstacles that each individual proposal faces. Third, this article argues that the normative dilemma of applying securitization can be avoided by firstly, deconstructing the institutional power of security actors and dominant security subjectivities and secondly, by addressing countering or alternative approaches to security and incorporating different security subjectivities. Examples of the securitization of international terrorism and immigration are prominent throughout.

On problems of calculating energy expenditure and substrate utilization from respiratory exchange data.

Indirect calorimetry based on respiratory exchange measurement has been successfully used from the beginning of the century to obtain an estimate of heat production (energy expenditure) in human subjects and animals. The errors inherent to this classical technique can stem from various sources: 1) model of calculation and assumptions, 2) calorimetric factors used, 3) technical factors and 4) human factors. The physiological and biochemical factors influencing the interpretation of calorimetric data include a change in the size of the bicarbonate and urea pools and the accumulation or loss (via breath, urine or sweat) of intermediary metabolites (gluconeogenesis, ketogenesis). More recently, respiratory gas exchange data have been used to estimate substrate utilization rates in various physiological and metabolic situations (fasting, post-prandial state, etc.). It should be recalled that indirect calorimetry provides an index of overall substrate disappearance rates. This is incorrectly assumed to be equivalent to substrate "oxidation" rates. Unfortunately, there is no adequate golden standard to validate whole body substrate "oxidation" rates, and this contrasts to the "validation" of heat production by indirect calorimetry, through use of direct calorimetry under strict thermal equilibrium conditions. Tracer techniques using stable (or radioactive) isotopes, represent an independent way of assessing substrate utilization rates. When carbohydrate metabolism is measured with both techniques, indirect calorimetry generally provides consistent glucose "oxidation" rates as compared to isotopic tracers, but only when certain metabolic processes (such as gluconeogenesis and lipogenesis) are minimal or / and when the respiratory quotients are not at the extreme of the physiological range. However, it is believed that the tracer techniques underestimate true glucose "oxidation" rates due to the failure to account for glycogenolysis in the tissue storing glucose, since this escapes the systemic circulation. A major advantage of isotopic techniques is that they are able to estimate (given certain assumptions) various metabolic processes (such as gluconeogenesis) in a noninvasive way. Furthermore when, in addition to the 3 macronutrients, a fourth substrate is administered (such as ethanol), isotopic quantification of substrate "oxidation" allows one to eliminate the inherent assumptions made by indirect calorimetry. In conclusion, isotopic tracers techniques and indirect calorimetry should be considered as complementary techniques, in particular since the tracer techniques require the measurement of carbon dioxide production obtained by indirect calorimetry. However, it should be kept in mind that the assessment of substrate oxidation by indirect calorimetry may involve large errors in particular over a short period of time. By indirect calorimetry, energy expenditure (heat production) is calculated with substantially less error than substrate oxidation rates.

Theory of mind tasks and executive functions: A systematic review of group studies in neurology.

A growing number of studies have been addressing the relationship between theory of mind (TOM) and executive functions (EF) in patients with acquired neurological pathology. In order to provide a global overview on the main findings, we conducted a systematic review on group studies where we aimed to (1) evaluate the patterns of impaired and preserved abilities of both TOM and EF in groups of patients with acquired neurological pathology and (2) investigate the existence of particular relations between different EF domains and TOM tasks. The search was conducted in Pubmed/Medline. A total of 24 articles met the inclusion criteria. We considered for analysis classical clinically accepted TOM tasks (first- and second-order false belief stories, the Faux Pas test, Happe's stories, the Mind in the Eyes task, and Cartoon's tasks) and EF domains (updating, shifting, inhibition, and access). The review suggests that (1) EF and TOM appear tightly associated. However, the few dissociations observed suggest they cannot be reduced to a single function; (2) no executive subprocess could be specifically associated with TOM performances; (3) the first-order false belief task and the Happe's story task seem to be less sensitive to neurological pathologies and less associated to EF. Even though the analysis of the reviewed studies demonstrates a close relationship between TOM and EF in patients with acquired neurological pathology, the nature of this relationship must be further investigated. Studies investigating ecological consequences of TOM and EF deficits, and intervention researches may bring further contributions to this question.

Dietary supplements utilization: an explanatory survey among Swiss consumers

Dietary supplement (DS) use increased rapidly over the last years. However evidence of benefits of many DS for healthy users are scarce and may not equate known risks of overdose, drug interaction and recently discovered negative long-term effects. Therefore this study aimed to investigate perceptions and motivations of DS users in Lausanne, Switzerland. Method A convenience sample was recruited at the entrance of local sales points. Data were collected in on-site semi-structured interviews to assess dietary supplementation habits. Results The 119 participants provided information on 147 users. Among 273 declared products, the majority were mixed products, containing minerals and vitamins (78), mineral products (69), and herbal products (28). 55% of DS users took more than one product simultaneously. Seventy five percent of participants indicated that DS use presents no risk or nearly no risk and about half (49%) of participants did not inform their physician about their consumption. Male participants reported to share this information with their physicians significantly less frequently than female participants (p = 0.008). About half of participants looked for information on potential risks of DS, men significantly more often than women (p=0.001). Discussion According to other studies in the US, our study shows that, in Lausanne (Switzerland), DS are commonly used as mixed products. Risk perception seems generally low among DS users. Implications Physicians should be trained to evaluate patientsʼ health behaviour and needs in order to provide good evidence based information or propose alternatives to DS use.