Evolutionary quantum minority game: A wireless network application.

The users of wireless communication networks usually face a resources scarcity issue by competing for places in a limited frequency spectrum. This problem is modeled as a quantum minority game with both some dynamic features of the classic minority game and quantum properties. The game is played by agents with memory exploring a finite space of classic and quantum strategies in an evolutionary way. The player actions are based on the m previous outcomes, their insights about other future actions, and their own expectation thresholds.

Chaos in kicked ratchets.

We present a minimal one-dimensional deterministic continuous dynamical system that exhibits chaotic behavior and complex transport properties. Our model is an overdamped rocking ratchet with finite dissipation, that is periodically kicked with a δ function driving force, without finite inertia terms or temporal or spatial stochastic forces. To our knowledge this is the simplest model reported in the literature for a ratchet, with this complex behavior. We develop an analytical approach that predicts many key features of the system, such as current reversals, as well as the presence of chaotic behavior and bifurcation. Our analytical approach allows us to study the transition from regular to chaotic motion as well as a tangent bifurcation associated with this transition. We show that our approach can be easily extended to other types of periodic driving forces. The square wave is shown as an example.

Shock detection in dynamics of single-headed motor proteins KIF1A via Jensen-Shannon divergence.

Information theoretic quantities are useful tools to characterize symbolic sequences. In this paper, we use the Jensen-Shannon divergence to study symbolic binary sequences that represent the stationary state of a lattice-gas model describing the traffic of monomeric kinesin KIF1A. More specifically, the constructed binary sequences represent the state of a microtubule protofilament at different adenosine triphosphate (ATP) and KIF1A motor concentrations in the cytosol. The model presents some stationary regimes with phase coexistence. By using the Jensen-Shannon divergence, we develop a method of analysis that allows us to identify cases in which phase coexistence occurs and, for these cases, to locate the position of the interphase that separates the regions with different phase.

Complex synchronization structure of an overdamped ratchet with discontinuous periodic forcing.

A deterministic overdamped ratchet driven by a periodic square driving force is shown to display chaotic behavior. The system has neither temporal nor quenched noise but the strong nonlinearity of the driving force produces a very rich bifurcation pattern with synchronized as well as chaotic regions. This pattern disappears if a sinusoidal force replaces the square force. This unexpected behavior is explained by decomposing the system into two exactly solvable subsystems, each with its own characteristic transit time, so that the ratio between the period of the driving force and the transit times can be analyzed. The transition from synchronized to chaotic motion can be explained by means of a one-dimensional Poincaré map. Our results can be experimentally confirmed in a number of systems, including the three-junction superconducting quantum interference devices ratchet, the rocking ratchet effect for cold atoms, and the Josephson vortex ratchet.

Formation and growth of lipofuscin in the retinal pigment epithelium cells.

The kinetics of lipofuscin growth in diseased retinal pigment epithelium cells is investigated using Monte Carlo simulations and scaling theory on a cluster aggregation model. The model captures the essential physics of lipofuscin growth in the cells. A remarkable feature is that small particles may be removed from the cells while the larger ones become fixed and grow by aggregation. Model simulations are compared to the number of lipofuscin granules in eyes with early age-related degeneration.

Converting genetic network oscillations into somite spatial patterns.

The segmentation of vertebrate embryos, a process known as somitogenesis, depends on a complex genetic network that generates highly dynamic gene expression in an oscillatory manner. A recent proposal for the mechanism underlying these oscillations involves negative-feedback regulation at transcriptional translational levels, also known as the "delay model" [J. Lewis Curr. Biol. 13, 1398 (2003)]. In addition, in the zebrafish a longitudinal positional information signal in the form of an Fgf8 gradient constitutes a determination front that could be used to transform these coupled intracellular temporal oscillations into the observed spatial periodicity of somites. Here we consider an extension of the delay model by taking into account the interaction of the oscillation clock with the determination front. Comparison is made with the known properties of somite formation in the zebrafish embryo. We also show that the model can mimic the anomalies formed when progression of the determination wave front is perturbed and make an experimental prediction that can be used to test the model.

Trapping mechanism in overdamped ratchets with quenched noise.

A trapping mechanism is observed and proposed as the origin of the anomalous behavior recently discovered in transport properties of overdamped ratchets subject to an external oscillatory drive in the presence of quenched noise. In particular, this mechanism is shown to appear whenever the quenched disorder strength is greater than a threshold value. The minimum disorder strength required for the existence of traps is determined by studying the trap structure in a disorder configuration space. An approximation to the trapping probability density function in a disordered region of finite length included in an otherwise perfect ratchet lattice is obtained. The mean velocity of the particles and the diffusion coefficient are found to have a nonmonotonic dependence on the quenched noise strength due to the presence of the traps.

Chaotic dynamics and control of deterministic ratchets.

Deterministic ratchets, in the inertial and also in the overdamped limit, have a very complex dynamics, including chaotic motion. This deterministically induced chaos mimics, to some extent, the role of noise, changing, on the other hand, some of the basic properties of thermal ratchets; for example, inertial ratchets can exhibit multiple reversals in the current direction. The direction depends on the amount of friction and inertia, which makes it especially interesting for technological applications such as biological particle separation. We overview in this work different strategies to control the current of inertial ratchets. The control parameters analysed are the strength and frequency of the periodic external force, the strength of the quenched noise that models a non-perfectly-periodic potential, and the mass of the particles. Control mechanisms are associated with the fractal nature of the basins of attraction of the mean velocity attractors. The control of the overdamped motion of noninteracting particles in a rocking periodic asymmetric potential is also reviewed. The analysis is focused on synchronization of the motion of the particles with the external sinusoidal driving force. Two cases are considered: a perfect lattice without disorder and a lattice with noncorrelated quenched noise. The amplitude of the driving force and the strength of the quenched noise are used as control parameters.

Quenched disorder effects on deterministic inertia ratchets.

The effect of quenched disorder on the underdamped motion of a periodically driven particle on a ratchet potential is studied. As a consequence of disorder, current reversal and chaotic diffusion may take place on regular trajectories. On the other hand, on some chaotic trajectories disorder induces regular motion. A localization effect similar to the Golosov phenomenon sets in whenever a disorder threshold that depends on the mass of the particle is reached. Possible applications of the localization phenomenon are discussed.

Disorder induced diffusive transport in ratchets.

The effects of quenched disorder on the overdamped motion of a driven particle on a periodic, asymmetric potential are studied. While for the unperturbed potential the transport is due to a regular drift, the quenched disorder induces a significant additional chaotic "diffusive" motion. Possible applications to experiments in nanoscale surfaces and particle separation are discussed.

Wavelet-based fractal analysis of airborne pollen.

The most abundant biological particles in the atmosphere are pollen grains and spores. Self-protection of a pollen allergy is possible through information about future pollen contents in the air. In spite of the importance of airborne pollen concentration forecasting, it has not been possible to predict the pollen concentrations with great accuracy, and about 25% of daily pollen forecasts result in failures. Previous analyses of the dynamic characteristics of atmospheric pollen time series indicate that the system can be described by a low dimensional chaotic map. We apply a wavelet transform to study the multifractal characteristics of an airborne pollen time series. The information and the correlation dimensions correspond to a chaotic system showing a loss of information with time evolution.