8 resultados para mean-field theory

em Université de Lausanne, Switzerland


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Particle physics studies highly complex processes which cannot be directly observed. Scientific realism claims that we are nevertheless warranted in believing that these processes really occur and that the objects involved in them really exist. This dissertation defends a version of scientific realism, called causal realism, in the context of particle physics. I start by introducing the central theses and arguments in the recent philosophical debate on scientific realism (chapter 1), with a special focus on an important presupposition of the debate, namely common sense realism. Chapter 2 then discusses entity realism, which introduces a crucial element into the debate by emphasizing the importance of experiments in defending scientific realism. Most of the chapter is concerned with Ian Hacking's position, but I also argue that Nancy Cartwright's version of entity realism is ultimately preferable as a basis for further development. In chapter 3,1 take a step back and consider the question whether the realism debate is worth pursuing at all. Arthur Fine has given a negative answer to that question, proposing his natural ontologica! attitude as an alternative to both realism and antirealism. I argue that the debate (in particular the realist side of it) is in fact less vicious than Fine presents it. The second part of my work (chapters 4-6) develops, illustrates and defends causal realism. The key idea is that inference to the best explanation is reliable in some cases, but not in others. Chapter 4 characterizes the difference between these two kinds of cases in terms of three criteria which distinguish causal from theoretical warrant. In order to flesh out this distinction, chapter 5 then applies it to a concrete case from the history of particle physics, the discovery of the neutrino. This case study shows that the distinction between causal and theoretical warrant is crucial for understanding what it means to "directly detect" a new particle. But the distinction is also an effective tool against what I take to be the presently most powerful objection to scientific realism: Kyle Stanford's argument from unconceived alternatives. I respond to this argument in chapter 6, and I illustrate my response with a discussion of Jean Perrin's experimental work concerning the atomic hypothesis. In the final part of the dissertation, I turn to the specific challenges posed to realism by quantum theories. One of these challenges comes from the experimental violations of Bell's inequalities, which indicate a failure of locality in the quantum domain. I show in chapter 7 how causal realism can further our understanding of quantum non-locality by taking account of some recent experimental results. Another challenge to realism in quantum mechanics comes from delayed-choice experiments, which seem to imply that certain aspects of what happens in an experiment can be influenced by later choices of the experimenter. Chapter 8 analyzes these experiments and argues that they do not warrant the antirealist conclusions which some commentators draw from them. It pays particular attention to the case of delayed-choice entanglement swapping and the corresponding question whether entanglement is a real physical relation. In chapter 9,1 finally address relativistic quantum theories. It is often claimed that these theories are incompatible with a particle ontology, and this calls into question causal realism's commitment to localizable and countable entities. I defend the commitments of causal realism against these objections, and I conclude with some remarks connecting the interpretation of quantum field theory to more general metaphysical issues confronting causal realism.

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The complex network dynamics that arise from the interaction of the brain's structural and functional architectures give rise to mental function. Theoretical models demonstrate that the structure-function relation is maximal when the global network dynamics operate at a critical point of state transition. In the present work, we used a dynamic mean-field neural model to fit empirical structural connectivity (SC) and functional connectivity (FC) data acquired in humans and macaques and developed a new iterative-fitting algorithm to optimize the SC matrix based on the FC matrix. A dramatic improvement of the fitting of the matrices was obtained with the addition of a small number of anatomical links, particularly cross-hemispheric connections, and reweighting of existing connections. We suggest that the notion of a critical working point, where the structure-function interplay is maximal, may provide a new way to link behavior and cognition, and a new perspective to understand recovery of function in clinical conditions.

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DNA condensation observed in vitro with the addition of polyvalent counterions is due to intermolecular attractive forces. We introduce a quantitative model of these forces in a Brownian dynamics simulation in addition to a standard mean-field Poisson-Boltzmann repulsion. The comparison of a theoretical value of the effective diameter calculated from the second virial coefficient in cylindrical geometry with some experimental results allows a quantitative evaluation of the one-parameter attractive potential. We show afterward that with a sufficient concentration of divalent salt (typically approximately 20 mM MgCl(2)), supercoiled DNA adopts a collapsed form where opposing segments of interwound regions present zones of lateral contact. However, under the same conditions the same plasmid without torsional stress does not collapse. The condensed molecules present coexisting open and collapsed plectonemic regions. Furthermore, simulations show that circular DNA in 50% methanol solutions with 20 mM MgCl(2) aggregates without the requirement of torsional energy. This confirms known experimental results. Finally, a simulated DNA molecule confined in a box of variable size also presents some local collapsed zones in 20 mM MgCl(2) above a critical concentration of the DNA. Conformational entropy reduction obtained either by supercoiling or by confinement seems thus to play a crucial role in all forms of condensation of DNA.

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Brain fluctuations at rest are not random but are structured in spatial patterns of correlated activity across different brain areas. The question of how resting-state functional connectivity (FC) emerges from the brain's anatomical connections has motivated several experimental and computational studies to understand structure-function relationships. However, the mechanistic origin of resting state is obscured by large-scale models' complexity, and a close structure-function relation is still an open problem. Thus, a realistic but simple enough description of relevant brain dynamics is needed. Here, we derived a dynamic mean field model that consistently summarizes the realistic dynamics of a detailed spiking and conductance-based synaptic large-scale network, in which connectivity is constrained by diffusion imaging data from human subjects. The dynamic mean field approximates the ensemble dynamics, whose temporal evolution is dominated by the longest time scale of the system. With this reduction, we demonstrated that FC emerges as structured linear fluctuations around a stable low firing activity state close to destabilization. Moreover, the model can be further and crucially simplified into a set of motion equations for statistical moments, providing a direct analytical link between anatomical structure, neural network dynamics, and FC. Our study suggests that FC arises from noise propagation and dynamical slowing down of fluctuations in an anatomically constrained dynamical system. Altogether, the reduction from spiking models to statistical moments presented here provides a new framework to explicitly understand the building up of FC through neuronal dynamics underpinned by anatomical connections and to drive hypotheses in task-evoked studies and for clinical applications.

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Regulatory gene networks contain generic modules, like those involving feedback loops, which are essential for the regulation of many biological functions (Guido et al. in Nature 439:856-860, 2006). We consider a class of self-regulated genes which are the building blocks of many regulatory gene networks, and study the steady-state distribution of the associated Gillespie algorithm by providing efficient numerical algorithms. We also study a regulatory gene network of interest in gene therapy, using mean-field models with time delays. Convergence of the related time-nonhomogeneous Markov chain is established for a class of linear catalytic networks with feedback loops.

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Pierre Bourdieu's field theory is a strong account of how human action can be understood based on the principle that negotiates between structural, relational, and cognitive dimensions within the social world. With his central notion of fields, Bourdieu provides social scientists and economists, a way to transcend the dichotomies that shape theoretical thinking about human conduct and its innovative potentials. This chapter is dedicated to locate the position of the notion of field with respect to major schools of thought, and in particular to the embeddedness tradition that addresses similar questions on the social structuring of human behavior.

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Despite the considerable evidence showing that dispersal between habitat patches is often asymmetric, most of the metapopulation models assume symmetric dispersal. In this paper, we develop a Monte Carlo simulation model to quantify the effect of asymmetric dispersal on metapopulation persistence. Our results suggest that metapopulation extinctions are more likely when dispersal is asymmetric. Metapopulation viability in systems with symmetric dispersal mirrors results from a mean field approximation, where the system persists if the expected per patch colonization probability exceeds the expected per patch local extinction rate. For asymmetric cases, the mean field approximation underestimates the number of patches necessary for maintaining population persistence. If we use a model assuming symmetric dispersal when dispersal is actually asymmetric, the estimation of metapopulation persistence is wrong in more than 50% of the cases. Metapopulation viability depends on patch connectivity in symmetric systems, whereas in the asymmetric case the number of patches is more important. These results have important implications for managing spatially structured populations, when asymmetric dispersal may occur. Future metapopulation models should account for asymmetric dispersal, while empirical work is needed to quantify the patterns and the consequences of asymmetric dispersal in natural metapopulations.