1,720,983 research outputs found
McKean-Vlasov limits, propagation of chaos and long-time behavior of some mean field interacting particle systems
Full text linkIn this thesis we study mean field interacting particle systems and their McKean-Vlasov limiting processes, in particular we focus on three different interaction mechanisms, mainly emerging from biological modelling. The first type of interaction is given by the so called simultaneous jumps. We consider a system of interacting jump-diffusion processes that interact by means of the discontinuous component: each particle performs a main jump and it simultaneously induces in all the other particles a simultaneous jump whose amplitude is rescaled with the size of the system. This peculiar interaction is motivated by recent neuroscience models and here we depict a general framework for this type of processes. We focus on the well-posedness of the McKean-Vlasov limits of these particle systems under different assumptions on the coefficients and we prove a pathwise propagation of chaos result. The second interaction we consider is an asymmetric one. We describe a system of biased random walks on the positive integers, reflected at zero, where each particle may perform a leftward jump with a rate proportional to the fraction of particles which are strictly at its left. We study the critical interaction strength able to ensure ergodicity to this system, that would be transient in absence of interaction. We compare this model with existing models of diffusions interacting through their CDF and we highlight their differences, mainly caused by the presence of clusters of particles in the discrete model. The third interaction we account for is based on a dynamical version of the generalized Curie-Weiss model. We modify a Langevin dynamics for this model with a dissipative evolution of the interaction component, breaking the reversibility of the system. We prove that, in the mean field limit, this gives rise to stable limit cycles, explaining self-sustained periodic behaviors. In particular, we build a flexible model in which a suitable change in the interaction function can result in a system which, in certain regimes of parameters, displays coexistence of stable periodic orbits
Strong existence and uniqueness of the stationary distribution for a stochastic inviscid dyadic model
Full text linkWe consider an inviscid stochastically forced dyadic model, where the additive noise acts only on the first component. We prove that a strong solution for this problem exists and is unique by means of uniform energy estimates. Moreover, we exploit these results to establish strong existence and uniqueness of the stationary distribution
McKean-Vlasov limit for interacting systems with simultaneous jumps
No full textMotivated by several applications, including neuronal models, we consider the McKean-Vlasov limit for a general class of mean-field systems of interacting diffusions characterized by an interaction via simultaneous jumps. We focus our interest on systems where the rate of the jumps is unbounded, which are rarely treated in the mean-field literature, and we prove well-posedness of the McKean-Vlasov limit together with propagation of chaos via a coupling technique. To highlight the role of simultaneous jumps, we introduce an intermediate process which is close to the original particle system but does not display simultaneous jumps. This shows in particular that the simultaneous jumps contribute to the overall rate of convergence of the -particle empirical measures by a term of order
Pricing reliability options under different electricity price regimes
Full text linkReliability Options are capacity remuneration mechanisms aimed at enhancing security of supply in electricity systems. They can be framed as call options on electricity sold by power producers to System Operators. This paper provides a comprehensive mathematical treatment of Reliability Options. Their value is first derived by means of closed-form pricing formulae, which are obtained under several assumptions about the dynamics of electricity prices and strike prices. Then, the value of the Reliability Option is simulated under a real-market calibration, using data of the Italian power market. We perform sensitivity analyses to highlight the role of the level and volatility of both power and strike price, of the mean reversion speeds and of the correlation coefficient on the Reliability Options' value. Finally, we calculate the parameter model risk to quantify the impact that a model misspecification has on the equilibrium value of the RO
Going Beyond Counting First Authors in Author Co-citation Analysis
Full text linkThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
Ergodicity of a system of interacting random walks with asymmetric interaction
Full text linkWe study N interacting random walks on the positive integers. Each particle has drift δ towards infinity, a reflection at the origin, and a drift towards particles with lower positions. This inhomogeneous mean field system is shown to be ergodic only when the interaction is strong enough. We focus on this latter regime, and point out the effect of piles of particles, a phenomenon absent in models of interacting diffusion in continuous space
Variations on the Author
Full text link“Variations on the Author” discusses two of Eduardo Coutinho’s recent films (Um Dia na Vida, from 2010, and Últimas Conversas, posthumously released in 2015) and their contribution to the general question of documentary authorship. The director’s filmography is characterized by a consistent yet self-effacing form of authorial self-inscription: Coutinho often features as an interviewer that rather than express opinions propels discourses; an interviewer that is good at listening. This mode of self-inscription characterizes him as an author who is not expressive but who is nonetheless markedly present on the screen. In Um Dia na Vida, however, Coutinho is completely absent form the image, while Últimas Conversas, on the contrary, includes a confessional prologue that moves the director from the margins to the center of his films. This article examines the ways in which these works stand out in the filmography of a director who offers new insights into the notion of cinematic authorship
Appropriate Similarity Measures for Author Cocitation Analysis
Full text linkWe provide a number of new insights into the methodological discussion about author cocitation analysis. We first argue that the use of the Pearson correlation for measuring the similarity between authors’ cocitation profiles is not very satisfactory. We then discuss what kind of similarity measures may be used as an alternative to the Pearson correlation. We consider three similarity measures in particular. One is the well-known cosine. The other two similarity measures have not been used before in the bibliometric literature. Finally, we show by means of an example that our findings have a high practical relevance.information science;Pearson correlation;cosine;similarity measure;author cocitation analysis
Dispelling the Myths Behind First-author Citation Counts
Full text linkWe conducted a full-scale evaluative citation analysis study of scholars in the XML research field to explore just how different from each other author rankings resulting from different citation counting methods actually are, and to demonstrate the capability of emerging data and tools on the Web in supporting more realistic citation counting methods. Our results contest some common arguments for the continued
use of first-author citation counts in the evaluation of scholars, such as high correlations between author rankings by first-author citation counts and other citation
counting methods, and high costs of using more realistic citation counting methods that are not well-supported by the ISI databases. It is argued that increasingly available digital full text research papers make it possible for citation analysis studies to go beyond what the ISI databases have directly supported and to employ more
sophisticated methods
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