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We study the motion of a particle in spatially periodic potentials with broken mirror symmetry under the influence of white a-stable Levy noises. We consider both time-independent and fluctuating potentials. We focus on cases in which the spatial asymmetry of the potential is due not to a difference between the distances from an absolute minimum to the absolute maximum on its left and to the absolute maximum on its right but only to the curvatures of the potential profiles. The analysis is performed using the fractional Fokker-Planck formalism. Consistent results from Langevin simulations are also presented. We analyze the influence of the symmetry properties of the potentials in combination with the fluctuating characteristics of the system in the determination of the current. We find different situations in which both the absolute value and the direction of the current depend not only on the properties of the potential but also on the parameters characterizing the α-stable Lévy noise. Among other features, we analyze the case of supersymmetric potentials. In particular, we show that a static supersymmetric potential produces no current, and we analyze the conditions for observing a nonvanishing current when the potential fluctuates between different supersymmetric profiles.e [ABSTRACT FROM AUTHOR]

The marginal correlation between two variables is a measure of the linear dependence of one variable on the other. The two original variables need not interact directly, because marginal correlation may arise from the mediation of other variables in the system. The underlying network of direct interactions can be captured by a weighted graphical model. The connection between two variables can be weighted by their partial correlation, defined as the residual correlation left after accounting for the linear effects of mediating variables. While matrix inversion can be used to obtain marginal correlations from partial correlations, in large systems this approach does not reveal how the former emerge from the latter. Here we present an expansion of marginal correlations in terms of partial correlations, which shows that the effect of mediating variables can be quantified by the weight of the paths in the graphical model that connect the original pair of variables. The expansion is proved to converge for arbitrary probability distributions. The graphical interpretation reveals a close connection between the topology of the graph and the marginal correlations. Moreover, the expansion shows how marginal correlations change when some variables are severed from the graph, and how partial correlations change when some variables are marginalized out from the description. It also establishes the minimum number of latent variables required to replicate the exact effect of a collection of variables that are marginalized out, ensuring that the partial and marginal correlations of the remaining variables remain unchanged. Notably, the number of latent variables may be significantly smaller than the number of variables that they effectively replicate. Finally, for Gaussian variables, marginal correlations are shown to be related to the efficacy with which information propagates along the paths in the graph.

After mating, the physiology of Drosophila females undergo several important changes, some of which are reflected in their rest-activity cycles. To explore the hypothesis that mating modifies the temporal organization of locomotor activity patterns, we recorded fly activity by a video tracking method. Monitoring rest-activity patterns under light/dark (LD) cycles indicated that mated females lose their ability to anticipate the night-day transition, in stark contrast to males and virgins. This postmating response is mediated by the activation of the sex peptide receptor (SPR) mainly on pickpocket (ppk) expressing neurons, since reducing expression of this receptor in these neurons restores the ability to anticipate the LD transition in mated females. Furthermore, we provide evidence of connectivity between ppk+ neurons and the pigment-dispersing factor (PDF)-positive ventral lateral neurons (sLNv), which play a central role in the temporal organization of daily activity. Since PDF has been associated to the generation of the morning activity peak, we hypothesized that the mating signal could modulate PDF levels. Indeed, we confirm that mated females have reduced PDF levels at the dorsal protocerebrum; moreover, SPR downregulation in ppk+ neurons mimics PDF levels observed in males. In sum, our results are consistent with a model whereby mating-triggered signals reach clock neurons in the fly central nervous system to modulate the temporal organization of circadian behavior according to the needs of the new status., Competing Interests: The authors have declared that no competing interests exist., (Copyright: © 2022 Riva et al. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.)

In order to interpret animal behavior we need to understand how they see the world. As directly testing color discrimination in animals is difficult and time consuming, it is important to develop theoretical models based in the properties of visual systems. One of the most successful for the prediction of color discrimination behavior is the receptor noise-limited (RNL) model, which depends only on the level of noise in photoreceptors and opponent mechanisms. Here a complementary approach to model construction is used, and optimal color discrimination properties are obtained using information theoretical tools, for the early stages of visual systems. It is shown here that, for most biologically relevant conditions the optimal discrimination function of an ideal observer coincides with the one obtained with the RNL model. Furthermore, within this framework the influence of opponency can be studied by considering models with and without that mechanism but with exactly the same parameters at the level of photoreceptors. As an example, it is shown here that opponency is necessary to explain the discrimination of monochromatic stimuli in honeybees, but not in budgerigars. Since this is a consequence of the narrowing of absorption spectra of photoreceptors, produced by the presence of oil droplets, this could also be true for most other species of birds. This suggests that in order to study opponency in birds, stimuli should have a relatively wide spectrum., Competing Interests: Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper., (Copyright © 2021 Elsevier Ltd. All rights reserved.)

In many animals the circadian rhythm of locomotor activity is controlled by an endogenous circadian clock. Using custom made housing and video tracking software in order to obtain high spatial and temporal resolution, we studied the statistical properties of the locomotor activity of wild type and two clock mutants of Drosophila melanogaster. We show here that the distributions of activity and quiescence bouts for the clock mutants in light-dark conditions (LD) are very different from the distributions obtained when there are no external cues from the environment (DD). In the wild type these distributions are very similar, showing that the clock controls this aspect of behavior in both regimes (LD and DD). Furthermore, the distributions are very similar to those reported for Wistar rats. For the timing of events we also observe important differences, quantified by how the event rate distributions scale for increasing time windows. We find that for the wild type these distributions can be rescaled by the same function in DD as in LD. Interestingly, the same function has been shown to rescale the rate distributions in Wistar rats. On the other hand, for the clock mutants it is not possible to rescale the rate distributions, which might indicate that the extent of circadian control depends on the statistical properties of activity and quiescence., Competing Interests: The authors have declared that no competing interests exist.

Head lice infest millions of school-age children every year, both in developed and developing countries. However, little is known about the number of lice transferred among children during school activities, because direct methods to study this are almost impossible to implement. This issue has been addressed following an indirect method, which consist in collecting data of real infestation from several children groups and using a mathematical model of lice colonies to infer how the infestation observed might have evolved. By determining the events that would most likely lead to infestations as those observed, we find that severe infestations are most likely initiated by a relatively large number of lice transferred at the same moment or within relatively short time spans. In turn, analysis of the data obtained from screenings of the same groups of children a few days apart shows evidence of such transmission events. Interestingly, only children with severe infestations could harbor the lice necessary for this type of transmission. Thus, they play the same role as 'superspreaders' in epidemiology. As part of our experimental study it is also shown that a simple procedure of combing can be very effective to remove all mobile lice, and thus could be used as an effective preventive measure against those severe infestations that are responsible for the spread of pediculosis.

Circadian systems enable organisms to synchronize their physiology to daily and seasonal environmental changes relying on endogenous pacemakers that oscillate with a period close to 24 h even in the absence of external timing cues. The oscillations are achieved by intracellular transcriptional/translational feedback loops thoroughly characterized for many organisms, but still little is known about the presence and characteristics of circadian clocks in fungi other than Neurospora crassa. We sought to characterize the circadian system of a natural isolate of Aureobasidium pullulans, a cold-adapted yeast bearing great biotechnological potential. A. pullulans formed daily concentric rings that were synchronized by light/dark cycles and were also formed in constant darkness with a period of 24.5 h. Moreover, these rhythms were temperature compensated, as evidenced by experiments conducted at temperatures as low as 10 °C. Finally, the expression of clock-essential genes, frequency, white collar-1, white collar-2 and vivid was confirmed. In summary, our results indicate the existence of a functional circadian clock in A. pullulans, capable of sustaining rhythms at very low temperatures and, based on the presence of conserved clock-gene homologues, suggest a molecular and functional relationship to well-described circadian systems.

In the fruit fly, circadian behavior is controlled by a small number of specialized neurons, whose molecular clocks are relatively well known. However, much less is known about how these neurons communicate among themselves. In particular, only 1 circadian neuropeptide, pigment-dispersing factor (PDF), has been identified, and most aspects of its interaction with the molecular clock remain to be elucidated. Furthermore, it is speculated that many other peptides should contribute to circadian communication. We have developed a relatively detailed model of the 2 main groups of circadian pacemaker neurons (sLNvs and LNds) to investigate these issues. We have proposed many possible mechanisms for the interaction between the synchronization factors and the molecular clock, and we have compared the outputs with the experimental results reported in the literature both for the wild-type and PDF-null mutant. We have studied how different the properties of each neuron should be to account for the observations reported for the sLNvs in the mutant. We have found that only a few mechanisms, mostly related to the slowing down of nuclear entry of a circadian protein, can synchronize neurons that present these differences. Detailed immunofluorescent recordings have suggested that, whereas in the mutant, LNd neurons are synchronized, in the wild-type, a subset of the LNds oscillate faster than the rest. With our model, we find that a more likely explanation for the same observations is that this subset is being driven outside its synchronization range and displays therefore a complex pattern of oscillation.

Intransitivity is a property of connected, oriented graphs representing species interactions that may drive their coexistence even in the presence of competition, the standard example being the three species Rock-Paper-Scissors game. We consider here a generalization with four species, the minimum number of species allowing other interactions beyond the single loop (one predator, one prey). We show that, contrary to the mean field prediction, on a square lattice the model presents a transition, as the parameter setting the rate at which one species invades another changes, from a coexistence to a state in which one species gets extinct. Such a dependence on the invasion rates shows that the interaction graph structure alone is not enough to predict the outcome of such models. In addition, different invasion rates permit to tune the level of transitiveness, indicating that for the coexistence of all species to persist, there must be a minimum amount of intransitivity., (Copyright © 2012 Elsevier Ltd. All rights reserved.)

It is by now well known that, at the molecular level, the core of the circadian clock of most living species is a negative feedback loop where some proteins inhibit their own transcription. However, it has recently been shown that post-translational processes, such as phosphorylations, are essential for a correct timing of the clock. Depending on which sites of a circadian protein are phosphorylated, different properties such as degradation, nuclear localization and repressing power can be altered. Furthermore, phosphorylation domains can be related in a positive way, giving rise to consecutive phosphorylations, or in a negative way, hindering phosphorylation at other domains. Here we present a simple mathematical model of a circadian protein having two mutually exclusive domains of phosphorylation. We show that the system has limit cycles that arise from a unique fixed point through a Hopf bifurcation. We find a set of parameters, with realistic values, for which the limit cycle has the same period as the wild type circadian oscillations of the fruit fly. The domains act as a switch, in the sense that alterations in their phosphorylation can alter the period of circadian oscillation in opposite ways, increasing or decreasing the period of the wild type oscillations. In particular, we show that our model is able to reproduce some of the experimental results found for switch-like phosphorylations of the PER protein of the circadian clock of the fly Drosophila melanogaster., (Copyright © 2012 Elsevier Ltd. All rights reserved.)

Network epidemiology often assumes that the relationships defining the social network of a population are static. The dynamics of relationships is only taken indirectly into account by assuming that the relevant information to study epidemic spread is encoded in the network obtained, by considering numbers of partners accumulated over periods of time roughly proportional to the infectious period of the disease. On the other hand, models explicitly including social dynamics are often too schematic to provide a reasonable representation of a real population, or so detailed that no general conclusions can be drawn from them. Here, we present a model of social dynamics that is general enough so its parameters can be obtained by fitting data from surveys about sexual behaviour, but that can still be studied analytically, using mean-field techniques. This allows us to obtain some general results about epidemic spreading. We show that using accumulated network data to estimate the static epidemic threshold lead to a significant underestimation of that threshold. We also show that, for a dynamic network, the relative epidemic threshold is an increasing function of the infectious period of the disease, implying that the static value is a lower bound to the real threshold. A practical example is given of how to apply the model to the study of a real population.

In this paper we use detailed data about the biology of the head louse (pediculus humanus capitis) to build a model of the evolution of head lice colonies. Using theory and computer simulations, we show that the model can be used to assess the impact of the various strategies usually applied to eradicate head lice, both conscious (treatments) and unconscious (grooming). In the case of treatments, we study the difference in performance that arises when they are applied in systematic and non-systematic ways. Using some reasonable simplifying assumptions (as random mixing of human groups and the same mobility for all life stages of head lice other than eggs) we model the contagion of pediculosis using only one additional parameter. It is shown that this parameter can be tuned to obtain collective infestations whose characteristics are compatible with what is given in the literature on real infestations. We analyze two scenarios: One where group members begin treatment when a similar number of lice are present in each head, and another where there is one individual who starts treatment with a much larger threshold ("superspreader"). For both cases we assess the impact of several collective strategies of treatment.

We study the effects of switching social contacts as a strategy to control epidemic outbreaks. Connections between susceptible and infective individuals can be broken by either individual, and then reconnected to a randomly chosen member of the population. It is assumed that the reconnecting individual has no previous information on the epidemiological condition of the new contact. We show that reconnection can completely suppress the disease, both by continuous and discontinuous transitions between the endemic and the infection-free states. For diseases with an asymptomatic phase, we analyze the conditions for the suppression of the disease, and show that-even when these conditions are not met-the increase of the endemic infection level is usually rather small. We conclude that, within some simple epidemiological models, contact switching is a quite robust and effective control strategy. This suggests that it may also be an efficient method in more complex situations.

We perform an extensive numerical investigation on the retrieval dynamics of the synchronous Hopfield model, also known as Little-Hopfield model, up to sizes of 2(18) neurons. Our results correct and extend much of the early simulations on the model. We find that the average convergence time has a power law behavior for a wide range of system sizes, whose exponent depends both on the network loading and the initial overlap with the memory to be retrieved. Surprisingly, we also find that the variance of the convergence time grows as fast as its average, making it a non-self-averaging quantity. Based on the simulation data we differentiate between two definitions for memory retrieval time, one that is mathematically strict, tau(c), the number of updates needed to reach the attractor whose properties we just described, and a second definition correspondent to the time tau(eta) when the network stabilizes within a tolerance threshold eta such that the difference of two consecutive overlaps with a stored memory is smaller that eta. We show that the scaling relationships between tau(c) and tau(eta) and the typical network parameters as the memory load alpha or the size of the network N vary greatly, being tau(eta) relatively insensitive to system sizes and loading. We propose tau(eta) as the physiological realistic measure for the typical attractor network response.

We study the properties of random graphs where for each vertex a neighborhood has been previously defined. The probability of an edge joining two vertices depends on whether the vertices are neighbors or not, as happens in small-world graphs (SWG's). But we consider the case where the average degree of each node is of order of the size of the graph (unlike SWG's, which are sparse). This allows us to calculate the mean distance and clustering, which are qualitatively similar (although not in such a dramatic scale range) to the case of SWG's. We also obtain analytically the distribution of eigenvalues of the corresponding adjacency matrices. This distribution is discrete for large eigenvalues and continuous for small eigenvalues. The continuous part of the distribution follows a semicircle law, whose width is proportional to the "disorder" of the graph, whereas the discrete part is simply a rescaling of the spectrum of the substrate. We apply our results to the calculation of the mixing rate and the synchronizability threshold.

A random walk is performed on a disordered landscape composed of N sites randomly and uniformly distributed inside a d-dimensional hypercube. The walker hops from one site to another with probability proportional to exp[-betaE(D)], where beta=1/T is the inverse of a formal temperature and E(D) is an arbitrary cost function which depends on the hop distance D. Analytic results indicate that, if E(D)=D(d) and N--> infinity, there exists a glass transition at beta(d)=pi(d/2)/[(d/2)Gamma(d/2)]. Below T(d), the average trapping time diverges and the system falls into an out-of-equilibrium regime with aging phenomena. A Lévy flight scenario and applications of exploratory behavior are considered.