Exact extreme, order, and sum statistics in a class of strongly correlated systems.

Even though strongly correlated systems are abundant, only a few exceptional cases admit analytical solutions. In this paper we present a large class of solvable systems with strong correlations. We consider a set of N independent and identically distributed random variables {X_{1},X_{2},.

Extreme Statistics and Spacing Distribution in a Brownian Gas Correlated by Resetting.

We study a one-dimensional gas of N Brownian particles that diffuse independently, but are simultaneously reset to the origin at a constant rate r. The system approaches a nonequilibrium stationary state with long-range interactions induced by the simultaneous resetting. Despite the presence of strong correlations, we show that several observables can be computed exactly, which include the global average density, the distribution of the position of the kth rightmost particle, and the spacing distribution between two successive particles.

Modeling the role of police corruption in the reduction of organized crime: Mexico as a case study.

Among all types of corruption, police corruption is probably the one that most directly hurts society, as those trusted with protecting the people either side with the criminals that victimize the citizens, or are themselves, criminals. However, both corruption and its effects are very difficult to measure quantitatively other than by perception surveys, but the perception that citizens have of this phenomenon may be different from reality. Using a simple agent-based model, we analyze the effect on crime rates as a result of both corruption and the perception of corruption within law-enforcement corporations.

First-passage probabilities and mean number of sites visited by a persistent random walker in one- and two-dimensional lattices.

We study the first passage probability and mean number of sites visited by a discrete persistent random walker on a lattice in one and two dimensions. This is performed by using the multistate formulation of the process. We obtain explicit expressions for the generating functions of these quantities.

Delay in the dispersal of flocks moving in unbounded space using long-range interactions.

Since the pioneering work by Vicsek and his collaborators on the motion of self-propelled particles, most of the subsequent studies have focused on the onset of ordered states through a phase transition driven by particle density and noise. Usually, the particles in these systems are placed within periodic boundary conditions and interact via short-range velocity alignment forces. However, when the periodic boundaries are eliminated, letting the particles move in open space, the system is not able to organize into a coherently moving group since even small amounts of noise cause the flock to break apart.

Giant Catalytic Effect of Altruists in Schelling's Segregation Model.

We study the effect of introducing altruistic agents in a Schelling-like model of residential segregation. We find that even an infinitesimal proportion of altruists has dramatic catalytic effects on the collective utility of the system. Altruists provide pathways that move the system away from the suboptimal equilibrium it would reach if the system included only egoist agents, allowing it to reach the optimal steady state.

Multiple scaling behaviour and nonlinear traits in music scores.

We present a statistical analysis of music scores from different composers using detrended fluctuation analysis (DFA). We find different fluctuation profiles that correspond to distinct autocorrelation structures of the musical pieces. Further, we reveal evidence for the presence of nonlinear autocorrelations by estimating the DFA of the magnitude series, a result validated by a corresponding study of appropriate surrogate data.

Stochastic resonance at criticality in a network model of the human cortex.

Stochastic resonance is a phenomenon in which noise enhances the response of a system to an input signal. The brain is an example of a system that has to detect and transmit signals in a noisy environment, suggesting that it is a good candidate to take advantage of stochastic resonance. In this work, we aim to identify the optimal levels of noise that promote signal transmission through a simple network model of the human brain.

A detailed heterogeneous agent model for a single asset financial market with trading via an order book.

We present an agent based model of a single asset financial market that is capable of replicating most of the non-trivial statistical properties observed in real financial markets, generically referred to as stylized facts. In our model agents employ strategies inspired on those used in real markets, and a realistic trade mechanism based on a double auction order book. We study the role of the distinct types of trader on the return statistics: specifically, correlation properties (or lack thereof), volatility clustering, heavy tails, and the degree to which the distribution can be described by a log-normal.

Ballistic annihilation with superimposed diffusion in one dimension.

We consider a one-dimensional system with particles having either positive or negative velocity, and these particles annihilate on contact. Diffusion is superimposed on the ballistic motion of the particle. The annihilation may represent a reaction in which the two particles yield an inert species.

Evaluation of children with ADHD on the Ball-Search Field Task.

Searching, defined for the purpose of the present study as the displacement of an individual to locate resources, is a fundamental behavior of all mobile organisms. In humans this behavior underlies many aspects of everyday life, involving cognitive processes such as sustained attention, memory and inhibition. We explored the performance of 36 treatment-free children diagnosed with attention-deficit hyperactivity disorder (ADHD) and 132 children from a control school sample on the ecologically based ball-search field task (BSFT), which required them to locate and collect golf balls in a large outdoor area.

Analysis of México's Narco-War Network (2007-2011).

Since December 2006, more than a thousand cities in México have suffered the effects of the war between several drug cartels, amongst themselves, as well as with Mexican armed forces. Sources are not in agreement about the number of casualties of this war, with reports varying from 30 to 100 thousand dead; the economic and social ravages are impossible to quantify. In this work we analyze the official report of casualties in terms of the location and the date of occurrence of the homicides.

Temperature gradients in equilibrium: Small microcanonical systems in an external field.

We consider the statistical mechanics of a small gaseous system subject to a constant external field. As is well known, in the canonical ensemble, that the system (i) obeys a barometric formula for the density profile, and (ii) the kinetic temperature is independent of height, even when the system is small. We show here that in the microcanonical ensemble the kinetic temperature of the particles affected by the field is not constant with height, but that rather, generally speaking, it decreases with a gradient of order 1/N.

Statistics of the duration time of a random walk given its present position: dating a random walk.

We consider the distribution of the duration time, the time elapsed since it began, of a diffusion process given its present position, under the assumption that the process began at the origin. For unbiased diffusion, the distribution does not exist (it is identically zero) for one- and two-dimensional systems. We find the explicit expression for the distribution for three and higher dimensions and discuss the behavior of the duration time statistics: we find that the expected duration time exists only for dimensions five and higher, whereas the variance becomes finite for seven dimensions and above.

Maximum-entropy distributions of correlated variables with prespecified marginals.

The problem of determining the joint probability distributions for correlated random variables with prespecified marginals is considered. When the joint distribution satisfying all the required conditions is not unique, the "most unbiased" choice corresponds to the distribution of maximum entropy. The calculation of the maximum-entropy distribution requires the solution of rather complicated nonlinear coupled integral equations, exact solutions to which are obtained for the case of Gaussian marginals; otherwise, the solution can be expressed as a perturbation around the product of the marginals if the marginal moments exist.

Pattern recognition in neural networks with competing dynamics: coexistence of fixed-point and cyclic attractors.

We study the properties of the dynamical phase transition occurring in neural network models in which a competition between associative memory and sequential pattern recognition exists. This competition occurs through a weighted mixture of the symmetric and asymmetric parts of the synaptic matrix. Through a generating functional formalism, we determine the structure of the parameter space at non-zero temperature and near saturation (i.

Systems with negative specific heat in thermal contact: violation of the zeroth law.

Using both numerical simulations and exact expressions for the free energy and microcanonical entropy for a modified Hamiltonian mean-field (HMF) model, we show that when two similar systems with the same intensive parameters but with negative specific heat are weakly coupled, they undergo a process in which the total entropy increases irreversibly. We find that the final equilibrium is such that two phases appear at a temperature (equal in both systems) that is generally different from the initial temperature. We corroborate our results using two different kinds of couplings between the HMF systems.

Intrinsic and extrinsic noise effects on phase transitions of network models with applications to swarming systems.

We analyze order-disorder phase transitions driven by noise that occur in two kinds of network models closely related to the self-propelled model proposed by Vicsek [Phys. Rev. Lett.

Violation of the zeroth law of thermodynamics in systems with negative specific heat.

We show that systems with negative specific heat can violate the zeroth law of thermodynamics. By both numerical simulations and by using exact expressions for free energy and microcanonical entropy, it is shown that if two systems with the same intensive parameters but with negative specific heat are thermally coupled, they undergo a process in which the total entropy increases irreversibly. The final equilibrium is such that two phases appear; that is, the subsystems have different magnetizations and internal energies at temperatures which are equal in both systems, but that can be different from the initial temperature.

Phase transitions in systems of self-propelled agents and related network models.

An important characteristic of flocks of birds, schools of fish, and many similar assemblies of self-propelled particles is the emergence of states of collective order in which the particles move in the same direction. When noise is added into the system, the onset of such collective order occurs through a dynamical phase transition controlled by the noise intensity. While originally thought to be continuous, the phase transition has been claimed to be discontinuous on the basis of recently reported numerical evidence.

Scale-free foraging by primates emerges from their interaction with a complex environment.

Scale-free foraging patterns are widespread among animals. These may be the outcome of an optimal searching strategy to find scarce, randomly distributed resources, but a less explored alternative is that this behaviour may result from the interaction of foraging animals with a particular distribution of resources. We introduce a simple foraging model where individual primates follow mental maps and choose their displacements according to a maximum efficiency criterion, in a spatially disordered environment containing many trees with a heterogeneous size distribution.

Occurrence of normal and anomalous diffusion in polygonal billiard channels.

From extensive numerical simulations, we find that periodic polygonal billiard channels with angles which are irrational multiples of pi generically exhibit normal diffusion (linear growth of the mean squared displacement) when they have a finite horizon, i.e., when no particle can travel arbitrarily far without colliding.

Static pairwise annihilation in complex networks.

We study static annihilation on complex networks, in which pairs of connected particles annihilate at a constant rate during time. Through a mean-field formalism, we compute the temporal evolution of the distribution of surviving sites with an arbitrary number of connections. This general formalism, which is exact for disordered networks, is applied to Kronecker, Erdös-Rényi (i.

Metastability for Markov processes with detailed balance.

We present a definition for metastable states applicable to arbitrary finite state Markov processes satisfying detailed balance. In particular, we identify a crucial condition that distinguishes metastable states from other slow decaying modes and which allows us to show that our definition has several desirable properties similar to those postulated in the restricted ensemble approach. The intuitive physical meaning of this condition is simply that the total equilibrium probability of finding the system in the metastable state is negligible.

Phase transitions in scale-free neural networks: departure from the standard mean-field universality class.

We investigate the nature of the phase transition from an ordered to a disordered state that occurs in a family of neural network models with noise. These models are closely related to the majority voter model, where a ferromagneticlike interaction between the elements prevails. Each member of the family is distinguished by the network topology, which is determined by the probability distribution of the number of incoming links.