Universal multifractal approach to intermittency in high energy physics

A new stochastic approach to intermittency in high energy physics is proposed. It yields to intermittency exponents defined independently of phase-space dimensions; their role in the calculation of generalized moments is discussed. A straightforward application of universal multifractals is suggested and a new parametric technique for phase-space analysis is provided.     

Statistical physics of inference: thresholds and algorithms

Many questions of fundamental interest in today's science can be formulated as inference problems: some partial, or noisy, observations are performed over a set of variables and the goal is to recover, or infer, the values of the variables based on the indirect information contained in the measurements. For such problems, the central scientific questions are: Under what conditions is the information contained in the measurements sufficient for a satisfactory inference to be possible? What are the most efficient algorithms for this task? A growing body of work has shown that often we can understand and locate these fundamental barriers by thinking of them as phase transitions in the sense of statistical physics. Moreover, it turned out that we can use the gained physical insight to develop new promising algorithms. The connection between inference and statistical physics is currently witnessing an impressive renaissance and we review here the current state-of-the-art, with a pedagogical focus on the Ising model which, formulated as an inference problem, we call the planted spin glass. In terms of applications we review two classes of problems: (i) inference of clusters on graphs and networks, with community detection as a special case and (ii) estimating a signal from its noisy linear measurements, with compressed sensing as a case of sparse estimation. Our goal is to provide a pedagogical review for researchers in physics and other fields interested in this fascinating topic.     

Statistical physics of media processes: Mediaphysics

The processes of mass communications in complicated social or sociobiological systems such as marketing, economics, politics, animal populations, etc. as a subject for the special scientific subbranch—“mediaphysics”—are considered in its relation with sociophysics. A new statistical physics approach to analyze these phenomena is proposed. A keystone of the approach is an analysis of population distribution between two or many alternatives: brands, political affiliations, or opinions. Relative distances between a state of a “person's mind” and the alternatives are measures of propensity to buy (to affiliate, or to have a certain opinion). The distribution of population by those relative distances is time dependent and affected by external (economic, social, marketing, natural) and internal (influential propagation of opinions, “word of mouth”, etc.) factors, considered as fields. Specifically, the interaction and opinion-influence field can be generalized to incorporate important elements of Ising-spin-based sociophysical models and kinetic-equation ones. The distributions were described by a Schrödinger-type equation in terms of Green's functions. The developed approach has been applied to a real mass-media efficiency problem for a large company and generally demonstrated very good results despite low initial correlations of factors and the target variable.     

Statistical physics of crime: A review

Containing the spread of crime in urban societies remains a major challenge. Empirical evidence suggests that, if left unchecked, crimes may be recurrent and proliferate. On the other hand, eradicating a culture of crime may be difficult, especially under extreme social circumstances that impair the creation of a shared sense of social responsibility. Although our understanding of the mechanisms that drive the emergence and diffusion of crime is still incomplete, recent research highlights applied mathematics and methods of statistical physics as valuable theoretical resources that may help us better understand criminal activity. We review different approaches aimed at modeling and improving our understanding of crime, focusing on the nucleation of crime hotspots using partial differential equations, self-exciting point process and agent-based modeling, adversarial evolutionary games, and the network science behind the formation of gangs and large-scale organized crime. We emphasize that statistical physics of crime can relevantly inform the design of successful crime prevention strategies, as well as improve the accuracy of expectations about how different policing interventions should impact malicious human activity that deviates from social norms. We also outline possible directions for future research, related to the effects of social and coevolving networks and to the hierarchical growth of criminal structures due to self-organization.     

Statistical physics for cosmic structures

The recent observations of galaxy and dark matter clumpy distributions have provided new elements to the understanding of the problem of cosmological structure formation. The strong clumping characterizing galaxy structures seems to be present in the overall mass distribution and its relation to the highly isotropic Cosmic Microwave Background Radiation represents a fundamental problem. The extension of structures, the formation of power-law correlations characterizing the strongly clustered regime and the relation between dark and visible matter are the key problems both from an observational and a theoretical point of view. We discuss recent progresses in the studies of structure formation by using concepts and methods of statistical physics.     

Algebraic approaches in nuclear physics

I critically discuss the various algebraic approaches in nuclear physics, looking for limitations and successes. Special emphasis is placed on open problems and active research areas. Presented at the International Conference on “Atomic Nuclei and Metallic Clusters”, Prague, September 1–5, 1997.     

Classical field theory methods in laser physics II. Statistical methods of laser physics

The second part of our work continues the analysis of the problem studied in the first par [J. Russ. Laser Res.,17, 205 (1996)]. We seek an answer to the following question: What is laser radiation from the viewpoint of the classical theory of wave fields? Here, we consider the statistical aspect of the problem. Moveover, we show how this aspect is connected with the formation of laser radiation from the level of spontaneous noise and how it governs the quality of laser radiation.     

Algebraic approaches in nuclear physics

In these lectures I discuss algebraic approaches in nuclear physics. The emphasis is on aspects that can not be found in the same form in other publications of the subject. We discuss the relation between bosons and fermions, as well as some of the standard formalism underlying all algebraic models in nuclear physics. We then contrast fermionic and bosonic models. We end with a case study on supersymmetry in superdeformed nuclei. Dedicated to the memory of Prof. P.W.M. Glaudemans, 1931–1998. Lecture given at the 10th Indian-Summer School of Nuclear Physics: “Theory of Many-Fermion Systems”, Prague, September 8–12, 1997.     

Statistical physics, optimization and source coding

The combinatorial problem of satisfying a given set of constraints that depend on N discrete variables is a fundamental one in optimization and coding theory. Even for instances of randomly generated problems, the question “does there exist an assignment to the variables that satisfies all constraints?” may become extraordinarily difficult to solve in some range of parameters where a glass phase sets in. We shall provide a brief review of the recent advances in the statistical mechanics approach to these satisfiability problems and show how the analytic results have helped to design a new class of message-passing algorithms — the survey propagation (SP) algorithms — that can efficiently solve some combinatorial problems considered intractable. As an application, we discuss how the packing properties of clusters of solutions in randomly generated satisfiability problems can be exploited in the design of simple lossy data compression algorithms.     

Book review:Statistical physics II: Nonequilibrium statistical mechanics

Journal of Statistical Physics -     

Statistical physics of shear flow: a non-equilibrium problem

Complex fluids are easily and reproducibly driven into non-equilibrium steady states by the action of shear flow. The statistics of the microstructure of non-equilibrium fluids is important to the material properties of every complex fluid that flows, e.g. axle grease on a rotating bearing; blood circulating in capillaries; molten plastic flowing into a mould; the non-equilibrium onion phase of amphiphiles used for drug delivery; the list is endless. Such states are as diverse and interesting as equilibrium states, but are not governed by the same statistics as equilibrium materials. I review some recently discovered principles governing the probabilities of various types of molecular re-arrangements taking place within a sheared fluid. As well as providing new foundations for the study of non-equilibrium matter, the principles are applied to some simple models of particles interacting under flow, showing that the theory exhibits physically convincing behaviour.     

Adirectional temporal zones in quantum physics and brain physiology

Change in space and time of an observed object creates a logistical problem for our brain because the temporal central availability is undefined. As solution we claim the existence of elementary integration units (EIUs) which are defined as zones of simultaneity; i.e., within such an EIU the before-after relationship has to be abandoned. Experimental evidence points to a duration of the EIUs of the order of 30 msec. In considering a delayed choice experiment in physics, we propose that a similar renunciation of the before-after relation leads to a deeper understanding of the individuality of processes in quantum theory. In short, time may be more momentous than its usual appearance as a real-valued parameter demonstrates.     

Statistical physics approach to graphical games: local and global interactions

In a graphical game agents play with their neighbors on a graph to achieve an appropriate state of equilibrium. Here relevant problems are characterizing the equilibrium set and discovering efficient algorithms to find such an equilibrium (solution). We consider a representation of games that extends over graphical games to deal conveniently with both local a global interactions and use the cavity method of statistical physics to study the geometrical structure of the equilibria space. The method also provides a distributive and local algorithm to find an equilibrium. For simplicity we consider only pure Nash equilibria but the methods can as well be extended to deal with (approximated) mixed Nash equilirbia.     

统计物理和复杂系统专题编者按

从20世纪中叶至今,复杂系统研究迅速发展,成为了引人注目并具有广泛应用的新领域.复杂系统要么具有结构的复杂性,要么具有演化的复杂性,在多数情况下二者兼具.不同于传统物理学通常处理的规则介质,许多复杂系统具有复杂结构,近年来受到极大关注的复杂网络结构就是其中最典型的代表.同时复杂系统也可表现为演化行为的多样性和复杂性.即便系统结构并不复杂,系统中的非线性相互作用可能产生复杂的演化行为,包括:形形色色的不稳定性;丰富的斑图动力学;各种各样的自组织、涌现及进化行为等等.物理学从一开始就深深进入了复杂系统研究领域,其中统计物理无疑是研究和理解复杂系统最主要的工具.     

Statistical physics and practical training of soft-committee machines

Equilibrium states of large layered neural networks with differentiable activation function and a single, linear output unit are investigated using the replica formalism. The quenched free energy of a student network with a very large number of hidden units learning a rule of perfectly matching complexity is calculated analytically. The system undergoes a first order phase transition from unspecialized to specialized student configurations at a critical size of the training set. Computer simulations of learning by stochastic gradient descent from a fixed training set demonstrate that the equilibrium results describe quantitatively the plateau states which occur in practical training procedures at sufficiently small but finite learning rates. Received 16 December 1998     

Statistical physics and fluctuations in ballistic non-equilibrium systems

In nonequilibrium systems in the ballistic transport regime, every point of the system contains particles arriving from different regions-each of them at different temperatures-and there are only few collisions, in such a way that equilibrium between the different populations will be reached very slowly. Here, we tentatively approach the local distribution function by a superposition of local-equilibrium distribution functions with different temperatures, corresponding to the different starting positions of the particles. In a second-order expansion, we find a distribution function which depends not only on the Hamiltonian H but also on H², and we study the additional contribution to energy fluctuations.