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arXiv2008

Ensembles related to the rich-club coefficient for non-evolving networks

In complex networks the rich nodes are the subset of nodes with high degree. These well connected nodes tend to dominate the organisation of the network's structure. In non-evolving networks, a reference network has been used to detect if the connectivity between the rich nodes is due to chance or caused by an unknown mechanism. Chance is represented as a reference network obtained from an ensemble of networks. When compared with the original network the reference network discounts suggests the existence of a well connected rich club beyond structural constraints. Here we revise some of the properties of the ensemble obtained by conserving only the degree distribution and introduce two new reference networks to study the importance of the rich nodes as organisers of the network structure. The first reference network is obtained from an ensemble of networks where all the members of the ensemble have the same rich--club coefficient. The reference network obtained from the ensemble is assortative. We propose that this reference network can be used to study networks where assortativness is a fundamental property, a common case in many social networks. The second reference network is obtained from an ensemble where the members of the ensemble all have the same probability degree distribution and rich-club coefficient. The reference network obtained from this ensemble has a very similar structure to the original network. This ensemble can be used to quantify correlations between the rich nodes and pinpoint which links are the backbone of the network's structure.

physics.soc-ph↗

arXiv2008

How markets slowly digest changes in supply and demand

In this article we revisit the classic problem of tatonnement in price formation from a microstructure point of view, reviewing a recent body of theoretical and empirical work explaining how fluctuations in supply and demand are slowly incorporated into prices. Because revealed market liquidity is extremely low, large orders to buy or sell can only be traded incrementally, over periods of time as long as months. As a result order flow is a highly persistent long-memory process. Maintaining compatibility with market efficiency has profound consequences on price formation, on the dynamics of liquidity, and on the nature of impact. We review a body of theory that makes detailed quantitative predictions about the volume and time dependence of market impact, the bid-ask spread, order book dynamics, and volatility. Comparisons to data yield some encouraging successes. This framework suggests a novel interpretation of financial information, in which agents are at best only weakly informed and all have a similar and extremely noisy impact on prices. Most of the processed information appears to come from supply and demand itself, rather than from external news. The ideas reviewed here are relevant to market microstructure regulation, agent-based models, cost-optimal execution strategies, and understanding market ecologies.

q-fin.TR↗

arXiv2009

Non-sequential recursive pair substitutions and numerical entropy estimates in symbolic dynamical systems

We numerically test the method of non-sequential recursive pair substitutions to estimate the entropy of an ergodic source. We compare its performance with other classical methods to estimate the entropy (empirical frequencies, return times, Lyapunov exponent). We considered as a benchmark for the methods several systems with different statistical properties: renewal processes, dynamical systems provided and not provided with a Markov partition, slow or fast decay of correlations. Most experiments are supported by rigorous mathematical results, which are explained in the paper.

cond-mat.stat-mech↗

arXiv2010

Stability of Maximum likelihood based clustering methods: exploring the backbone of classifications (Who is keeping you in that community?)

Components of complex systems are often classified according to the way they interact with each other. In graph theory such groups are known as clusters or communities. Many different techniques have been recently proposed to detect them, some of which involve inference methods using either Bayesian or Maximum Likelihood approaches. In this article, we study a statistical model designed for detecting clusters based on connection similarity. The basic assumption of the model is that the graph was generated by a certain grouping of the nodes and an Expectation Maximization algorithm is employed to infer that grouping. We show that the method admits further development to yield a stability analysis of the groupings that quantifies the extent to which each node influences its neighbors group membership. Our approach naturally allows for the identification of the key elements responsible for the grouping and their resilience to changes in the network. Given the generality of the assumptions underlying the statistical model, such nodes are likely to play special roles in the original system. We illustrate this point by analyzing several empirical networks for which further information about the properties of the nodes is available. The search and identification of stabilizing nodes constitutes thus a novel technique to characterize the relevance of nodes in complex networks.

physics.soc-ph↗

arXiv2010

Minimum-Free-Energy Distribution of RNA Secondary Structures: Entropic and Thermodynamic Properties of Rare Events

We study the distribution of the minimum free energy (MFE) for the Turner model of pseudoknot free RNA secondary structures over ensembles of random RNA sequences. In particular, we are interested in those rare and intermediate events of unexpected low MFEs. Generalized ensemble Markov-chain Monte Carlo methods allow us to explore the rare-event tail of the MFE distribution down to probabilities like $10^{-70}$ and to study the relationship between the sequence entropy and structural properties for sequence ensembles with fixed MFEs. Entropic and structural properties of those ensembles are compared with natural RNA of the same reduced MFE (z-score).

cond-mat.dis-nn↗

arXiv2008

Melting at the absolute zero of temperature: Quantum phase transitions in condensed matter

We dedicate this article to our father, Prof. Dr. Guenter Vojta, on the occasion of his 80th birthday. While colleagues appreciate him as an excellent scientist with widespread interests and an amazingly broad knowledge, we see in him the father, teacher, friend, and much more. Thanks to him, we grew up immersed in the fascinating world of physics from an early age. His example and encouragement have crucially influenced our own lives.

cond-mat.str-el↗

arXiv2008

A Control Variate Approach for Improving Efficiency of Ensemble Monte Carlo

In this paper we present a new approach to control variates for improving computational efficiency of Ensemble Monte Carlo. We present the approach using simulation of paths of a time-dependent nonlinear stochastic equation. The core idea is to extract information at one or more nominal model parameters and use this information to gain estimation efficiency at neighboring parameters. This idea is the basis of a general strategy, called DataBase Monte Carlo (DBMC), for improving efficiency of Monte Carlo. In this paper we describe how this strategy can be implemented using the variance reduction technique of Control Variates (CV). We show that, once an initial setup cost for extracting information is incurred, this approach can lead to significant gains in computational efficiency. The initial setup cost is justified in projects that require a large number of estimations or in those that are to be performed under real-time constraints.

cs.CE↗

arXiv2008

Aspects of quantum phase transitions

A unified description of i) classical phase transitions and their remnants in finite systems and ii) quantum phase transitions is presented. The ensuing discussion relies on the interplay between, on the one hand, the thermodynamic concepts of temperature and specific heat and on the other, the quantal ones of coupling strengths in the Hamiltonian. Our considerations are illustrated in an exactly solvable model of Plastino and Moszkowski [Il Nuovo Cimento {\bf 47}, 470 (1978)].

quant-ph↗

arXiv2008

The role of the extra cellular matrix on memory

We expose first a biological model of memory based on one hand of the mechanical oscillations of axons during action potential and on the other hand on the changes in the extra cellular matrix composition when a mechanical strain is applied on it. Due to these changes, the stiffness of the extra cellular matrix along the most excited neurons will increase close to these neurons due to the growth of astrocytes around them and to the elastoplastic behavior of collagen. This will create preferential paths linked to a memory effect. In a second part, we expose a physical model based on random walk of the action potential on the array composed of dendrites and axons. This last model shows that repetition of the same event leads to long time memory of this event and that paradoxical sleep leads to the linking of different events put into memory.

cond-mat.soft↗

arXiv2008

Ultracold Feshbach Molecules

In this Chapter, we give an introduction into experiments with Feshbach molecules and their applications. In particular, we discuss the various creation and detection methods, and the internal-state manipulation of such molecules. We highlight two topics, namely Feshbach molecules in the halo regime and the application of Feshbach molecule to achieve ultracold gases of molecules in the rovibrational ground state. Our illustrative examples are mainly based on work performed at Innsbruck University.

cond-mat.other↗

arXiv2009

Exactness of the replica method in perturbation

The replica method for a quenched disordered system is considered in a perturbative field theory. Since correction in a finite-order perturbation is given in a polynomial of the replica number $n$, the zero-replica limit $n \to 0$ is regarded as extracting the constant term from the polynomial, which mathematically makes sense. The meaning of the extraction is clarified comparing with a direct calculation.

cond-mat.dis-nn↗

arXiv2008

Schwinger Bosons Approaches to Quantum Antiferromagnetism

These lectures review the large N Schwinger Bosons Mean Field approach to the quantum Heisenberg model. The method applies to ordered and disordered phases in all dimensions, at zero and at finite temperature. Extension to frustrated models is explained. An example for an experimentally useful application, is the temperature dependent staggered magnetization of the layered antiferromagnet.

cond-mat.str-el↗

arXiv2008

Accounting for monopole configurations in Yang-Mills theory in three Euclidean dimensions

A gauge transformation provided by the three eigenfunctions of $\B^a(x) \cdot \B^b(x)$ (where $\B^a(x)$, with a=1,2,3, are the non-Abelian magnetic fields) exposes the topological configurations of the Yang-Mills fields. In particular, it gives Dirac monopoles interacting with `photons' and massless charged vector bosons. A magnetic dipole field at each monopole corresponds to infinitesimal translation of the monopole, and provides the functional measure a la collective coordinates. The grand canonical partition function of the monopole plasma is exactly equivalent to a local field theory with certain scalar fields interacting with the Yang-Mills fields. This integrates topological degrees of freedom with perturbation theory.

hep-th↗

arXiv2008

General properties of the boundary renormalization group flow for supersymmetric systems in 1+1 dimensions

We consider the general supersymmetric one-dimensional quantum system with boundary, critical in the bulk but not at the boundary. The renormalization group flow on the space of boundary conditions is generated by the boundary beta functions β^{a}(λ) for the boundary coupling constants λ^{a}. We prove a gradient formula \partial\ln z/\partialλ^{a} =-g_{ab}^{S}β^{b} where z(λ) is the boundary partition function at given temperature T=1/β, and g_{ab}^{S}(λ) is a certain positive-definite metric on the space of supersymmetric boundary conditions. The proof depends on canonical ultraviolet behavior at the boundary. Any system whose short distance behavior is governed by a fixed point satisfies this requirement. The gradient formula implies that the boundary energy, -\partial\ln z/\partialβ= -Tβ^{a}\partial_{a}\ln z, is nonnegative. Equivalently, the quantity \ln z(λ) decreases under the renormalization group flow.

hep-th↗

arXiv2009

Information Geometry of q-Gaussian Densities and Behaviors of Solutions to Related Diffusion Equations

This paper presents new geometric aspects of the behaviors of solutions to the porous medium equation (PME) and its associated equation. First we discuss the Legendre structure with information geometry on the manifold of generalized exponential densities. Next by considering such a structure in particular on the q-Gaussian densities, we derive several physically and geometrically interesting properties of the solutions. They include, for example, characterization of the moment-conserving projection of a solution, evaluation of evolutional velocities of the second moments and the convergence rate to the manifold in terms of the geodesic curves, divergence and so on.

cond-mat.stat-mech↗

arXiv2008

A moment approach to analytic time-dependent solutions of the Fokker-Planck equation with additive and multiplicative noise

An efficient method is presented as a means of an approximate, analytic time-dependent solution of the Fokker-Planck equation (FPE) for the Langevin model subjected to additive and multiplicative noise. We have assumed that the dynamical probability distribution function has the same structure as the exact stationary one and that its parameters are expressed in terms of first and second moments, whose equations of motion are determined by the FPE. Model calculations have shown that dynamical distributions in response to applied signal and force calculated by our moment method are in good agreement with those obtained by the partial difference equation method. As an application of our method, we present the time-dependent Fisher information for the inverse-gamma distribution which is realized in the FPE including multiplicative noise only.

cond-mat.stat-mech↗

arXiv2010

The synchronization transition in correlated oscillator populations

The synchronization transition of correlated ensembles of coupled Kuramoto oscillators on sparse random networks is investigated. Extensive numerical simulations show that correlations between the native frequencies of adjacent oscillators on the network systematically shift the critical point as well as the critical exponents characterizing the transition. Negative correlations imply an onset of synchronization for smaller coupling, whereas positive correlations shift the critical coupling towards larger interaction strengths. For negatively correlated oscillators the transition still exhibits critical behaviour similar to the all-to-all coupled Kuramoto system, while positive correlations change the universality class of the transition depending on the correlation strength. Crucially, the paper demonstrates that the synchronization behaviour is not only determined by the coupling architecture, but is also strongly influenced by the oscillator placement on the coupling network.

cond-mat.stat-mech↗

arXiv2008

Breakdown of large-N reduction in the quenched Eguchi-Kawai model

We study the validity of the large-N equivalence between four-dimensional SU(N) lattice gauge theory and its momentum quenched version -- the Quenched Eguchi-Kawai (QEK) model. We have found strong evidence that this equivalence does not hold in the weak-coupling regime (and thus in the continuum limit). This is based on weak-coupling analytic arguments and Monto-Carlo simulations at intermediate couplings with 20 <= N <= 200. Since detailed expositions of our arguments, methods and results have already appeared in Phys. Rev. D78:034507 (2008) and Phys. Rev. D78:074503 (2008), we attempt here to give a more intuitive explanation of our results. The breakdown of reduction that we find is due to a dynamically generated correlation between different Euclidean components of the gauge fields.

hep-lat↗