Initial Frequency Distribution Research Articles

Traffic-driven explosive synchronization with adaptive local routing in complex networks

Despite extensive researches on explosive synchronization, the interplay between it and traffic dynamics has not received enough attentions. In this paper, we develop a traffic-driven Kuramoto-like synchronization model, in which pathway and strength of synchronization are determined by directed flow between the oscillator and its neighbors. We show how combining this model with an adaptive traffic routing based on local dynamic information of phase mismatches induces the explosive synchronization with hysteresis loop, width of which is produced by the difference between forward and backward critical coupling strengths and can be maximized by adjustable routing factors. We demonstrate the validity of such a mechanism in producing explosive synchronization phenomenon for different traffic flow levels, initial frequency distributions, network structures, as well as for both homogeneous and heterogeneous networks. Interestingly, it is found that the critical strength of forward coupling is easily affected by these factors, but backward transition behavior is robust with respect to them. All results indicate that our study can provide a new insight for the control of synchronization behavior in the real-world complex systems.

Explosive synchronization of weighted mobile oscillators

In recent years, explosive synchronization (ES) has attracted extensive interest due to its great significance in the study of epileptic seizures and cascading failures in the real world. In this paper, a weighting method based on the frequency mismatches and distances between linked oscillators is proposed to construct a Kuramoto-like model to study ES of mobile oscillators. An interesting phenomenon that the weighting of oscillators can induce a sudden and irreversible synchronization transition with hysteresis loop is revealed. The transition between continuous synchronization and ES can be tuned by the weighting factors. Moreover, it is found that the critical coupling strength and hysteresis loop width are affected by the initial frequency distribution, the number of oscillators, the communication radius, the setting of boundary conditions and the constant absolute velocity of oscillators.

Spatial gene drives and pushed genetic waves

Gene drives have the potential to rapidly replace a harmful wild-type allele with a gene drive allele engineered to have desired functionalities. However, an accidental or premature release of a gene drive construct to the natural environment could damage an ecosystem irreversibly. Thus, it is important to understand the spatiotemporal consequences of the super-Mendelian population genetics before potential applications. Here, we use a reaction-diffusion model for sexually reproducing diploid organisms to study how a locally introduced gene drive allele spreads to replace the wild-type allele, although it possesses a selective disadvantage s > 0. Using methods developed by Barton and collaborators, we show that socially responsible gene drives require 0.5 < s < 0.697, a rather narrow range. In this "pushed wave" regime, the spatial spreading of gene drives will be initiated only when the initial frequency distribution is above a threshold profile called "critical propagule," which acts as a safeguard against accidental release. We also study how the spatial spread of the pushed wave can be stopped by making gene drives uniquely vulnerable ("sensitizing drive") in a way that is harmless for a wild-type allele. Finally, we show that appropriately sensitized drives in two dimensions can be stopped, even by imperfect barriers perforated by a series of gaps.

Explosive synchronization in weighted complex networks

The emergence of dynamical abrupt transitions in the macroscopic state of a system is currently a subject of the utmost interest. Given a set of phase oscillators networking with a generic wiring of connections and displaying a generic frequency distribution, we show how combining dynamical local information on frequency mismatches and global information on the graph topology suggests a judicious and yet practical weighting procedure which is able to induce and enhance explosive, irreversible, transitions to synchronization. We report extensive numerical and analytical evidence of the validity and scalability of such a procedure for different initial frequency distributions, for both homogeneous and heterogeneous networks, as well as for both linear and nonlinear weighting functions. We furthermore report on the possibility of parametrically controlling the width and extent of the hysteretic region of coexistence of the unsynchronized and synchronized states.

Optimization of Resource Allocation Can Explain the Temporal Dynamics and Honesty of Sexual Signals

In species in which males are free to dynamically alter their allocation to sexual signaling over the breeding season, the optimal investment in signaling should depend on both a male's state and the level of competition he faces at any given time. We developed a dynamic optimization model within a game-theoretical framework to explore the resulting signaling dynamics at both individual and population levels and tested two key model predictions with empirical data on three-spined stickleback (Gasterosteus aculeatus) males subjected to dietary manipulation (carotenoid availability): (1) fish in better nutritional condition should be able to maintain their signal for longer over the breeding season, resulting in an increasingly positive correlation between nutritional status and signal (i.e., increasing signal honesty), and (2) female preference for more ornamented males should thus increase over the breeding season. Both predictions were supported by the experimental data. Our model shows how such patterns can emerge from the optimization of resource allocation to signaling in a competitive situation. The key determinants of the honesty and dynamics of sexual signaling are the condition dependency of male survival, the initial frequency distribution of nutritional condition in the male population, and the cost of signaling.

Modelling snow melt and snowcover depletion in a small alpine cirque, Canadian Rocky Mountains

AbstractSpatial and temporal patterns of areal snowcover depletion (SCD) were studied over a small (&lt;0·6 km2) alpine cirque within the Canadian Rocky Mountains using a combined approach of daily acquisition of remotely sensed imagery, together with meteorological observations and snowmelt modelling. Digital terrestrial photographs were georeferenced using a novel software tool together with a high‐resolution digital elevation model and used to derive measurements of fractional snowcovered area (SCA) over the cirque. Manual snow surveys carried out in the pre‐melt period were used to describe the initial frequency distribution of snow water equivalent (SWE) values over the cirque, and indicated a lognormal distribution of SWE when surveys were stratified by terrain features. Rates of snowmelt were simulated using a physically based snowmelt energy balance model, Snobal, driven by observed meteorological conditions at a nearby station, which were adjusted for slope orientation and exposure by making corrections to observed incoming shortwave and longwave radiation components in the cold regions hydrological model platform. Simulated melt rates were then applied to the approximated SWE distributions to model the decline in SCA over the spring. The model was found to perform well for the simulation of snowmelt based on point observations of SWE at the meteorological station, and produced a close correspondence between simulated and observed SCD curves representing two opposing slopes within the cirque. The results show that both the pre‐melt distributions of SWE and the spring melt rates exhibit considerable spatial variability between distinct slope units within the cirque, and that this variability has a significant impact on simulated SCD. Assuming a unimodal pre‐melt frequency distribution and conditions of spatially uniform snowmelt over complex terrain such as this can lead to large errors in the simulation results. It is suggested that modelling applications intended to represent snowmelt dynamics and areal SCD in similar alpine environments consider the effects of spatial variation in SWE distribution and melt energetics between slopes. Copyright © 2009 John Wiley &amp; Sons, Ltd.

Reconstruction of electron-phonon interaction function from temperature dependence of electrical resistivity for metals

The determination of the electron phonon interaction function (EPIF) from the temperature dependence of the electrical resistivity (TDER) for metals within a selected moderate temperature range is numerically demonstrated based on the general theory of the amplitude phase retrieval problem and an iterative algorithm. From the model calculation, the convergent solution can be obtained; however,the profile of the recovered EPIF depends on the initial frequency distribution used in the algorithm since this inversion problem is inherently ill posed. In order to get reasonable result,it is necessary to introduce additional information about the feature of the EPIF for guiding the choice of the initial distribution. The algorithm can also furnish a robust reconstruction of EPIF from TDER contaminated with random noise. It means that this algorithm is relatively stable and insensitive to external perturbation; therefore in a sense, the presented algorithm overcomes the ill posedness of the inversion problem.

Orbital decay of protostellar binaries in molecular clouds

The evolution of a protostellar binary system is investigated while it is embedded in its parent molecular cloud core and acted upon by gas drag due to dynamical friction. Approximate analytical results are obtained for the energy and angular momentum evolution of the orbit in the limiting cases, where the velocity is much smaller than, and much larger than the velocity dispersion of the gas. The general case is solved numerically. Dissipation causes a decay of the orbit to smaller separations and orbital eccentricity increases with time. As a binary probably spends about a few $10^6$ years embedded in the cloud, significant evolution of the orbit is expected before the dispersal of the cloud. Binary populations have been statistically generated and evolved for comparison with observations of MS and PMS binaries. Dynamical friction changes the initial frequency distribution with period of the binaries, and a maximum is obtained in the distribution as seen observationally. Decay of the orbit due to gas drag causes an evolution of long-period orbits to shorter periods and thus enables the formation of close binaries.

Investigations of the recovery of the phonon density of states from specific heat: numerical study

An iterative algorithm for the determination of the phonon density of states (DOS) from the specific heat is presented based on the general theory of the amplitude-phase retrieval problem. From the model calculation, it is found that a convergent solution can always be obtained. However, the profile of the recovered DOS depends on the initial frequency distribution used in the algorithm since the inverse problem is inherently ill-posed. In order to obtain the ideal reconstruction of the DOS, it is necessary to introduce additional information about the character of the DOS to guide the choice of the initial distribution. The algorithm can also give a robust reconstruction of the DOS from specific heat data contaminated with random noise. The recovery of the DOS based on specific heat data in a confined temperature range has also been examined in detail.

Models of long term artificial selection in finite population

SummaryThe effects of population size and selection intensity, which are in the breeder's control, are investigated for ranges of values of quantities outside his control, namely the number, initial distribution of frequencies and effects of genes influencing the trait. Two alleles are assumed to be initially segregating at each locus, with no linkage, dominance or epistasis. The effects are assumed to follow a gamma distribution, using a wide range of its two parameters which specify both mean gene effect or selective value and the shape of the distribution, or the ratio of Wright's effective number to actual number of genes. The initial gene frequencies (q) are assumed to be either 0·5 at all loci, uniformly distributed over the range 0–1, or to have a U-shaped distribution, proportional to [q(1 −q)]−1such as derives from neutral mutation, with gene effect and frequency distributions independent. The mean and variance of selection response and limits, in the absence of new mutation, are derived.The shape of the distribution of effects is not usually important even up to the selection limit. With appropriate parametrization, the influence of the initial frequency distribution is small over a wide range of parameters. For reasonable choices of parameters, the effects of changing population size from those typically used in animal breeding programmes are likely to be small, but not negligible. For the initial U-shaped frequency distribution, further increases in population size are always expected to give a greater limit, regardless of present value, but not for the other distributions.