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We use anticommuting variables to study probability distributions of random variables that are solutions of Langevin's equation.We showthat the probability density always enjoys 'worldpoint supersymmetry'. The partition function, however, may not. We find that the domain of integration can acquire a boundary, which implies that the auxiliary field has a non-zero expectation value, signalling spontaneous supersymmetry breaking. This is due to the presence of 'fermionic' zeromodes, whose contribution cannot be canceled by a surface term. This we prove by an explicit calculation of the regularized partition function, as well as by computing the moments of the auxiliary field and checking whether they satisfy the identities implied by Wick's theorem. Nevertheless, supersymmetry manifests itself in the identities that are satisfied by the moments of the scalar, whose expressions we can calculate for all values of the coupling constant. We also provide some quantitative estimates concerning the visibility of supersymmetry breaking effects in the identities for the moments and remark that the shape of the distribution of the auxiliary field can influence quite strongly how easy it would be to mask them, since the expectation value of the auxiliary field does not coincide with its typical value. [ABSTRACT FROM AUTHOR]

Activity rhythms in animal groups arise both from external changes in the environment, as well as from internal group dynamics. These cycles are reminiscent of physical and chemical systems with quasiperiodic and even chaotic behavior resulting from "autocatalytic" mechanisms. We use nonlinear differential equations to model how the coupling between the self-excitatory interactions of individuals and external forcing can produce four different types of activity rhythms: quasiperiodic, chaotic, phase locked, and displaying over or under shooting. At the transition between quasiperiodic and chaotic regimes, activity cycles are asymmetrical, with rapid activity increases and slower decreases and a phase shift between external forcing and activity. We find similar activity patterns in ant colonies in response to varying temperature during the day. Thus foraging ants operate in a region of quasiperiodicity close to a cascade of transitions leading to chaos. The model suggests that a wide range of temporal structures and irregularities seen in the activity of animal and human groups might be accounted for by the coupling between collectively generated internal clocks and external forcings. [ABSTRACT FROM AUTHOR]

The recent turbulence on the world's stock markets has reinvigorated the attack on classical economic models of stock market fluctuations. The key problem is determining a dynamic model, which is consistent with observed fluctuations and which reflects investor behavior. Here, we use a novel equation-free approach developed in nonlinear dynamics literature to identify the salient statistical features of fluctuations of the Dow Jones Industrial Average over the past 80 years. We then develop a minimal dynamical model in the form of a stochastic differential equation involving both additive and multiplicative system-noise couplings, which captures these features and whose parameterization on a time scale of days can be used to capture market distributions up to a time scale of months. The terms in the model can be directly linked to "herding" behavior on the part of traders. However, we show that parameters in this model have changed over a number of decades producing different market regimes. This result partially explains how, during some periods of history, "classic" economic models may work well and at other periods "econo-physics" models prove better. [ABSTRACT FROM AUTHOR]

An approach aiming to quantify the dynamics of information within a population is developed based on the mapping of the processes underlying the system's evolution into a birth and death type stochastic process and the derivation of a balance equation for the information entropy. Information entropy flux and information entropy production are identified and their time-dependent properties, as well as their dependence on the parameters present in the problem, are analyzed. States of minimum information entropy production are shown to exist for appropriate parameter values. Furthermore, uncertainty and information production are transiently intensified when the population traverses the inflexion point stage of the logisticlike growth process. [ABSTRACT FROM AUTHOR]

Amplifying communications are a ubiquitous characteristic of group-living animals. This work is concerned with their role in the processes of food recruitment and resource exploitation by social insects. The collective choices made by ants faced with different food sources are analyzed using both a mean field description and a stochastic approach. Emphasis is placed on the possibility of optimizing the recruitment and exploitation strategies through an appropriate balance between individual variability, cooperative interactions and environmental constraints. [ABSTRACT FROM AUTHOR]

model for the kinetics of aggregation in social insects which accounts for stochastic effects arising from individual variability and covers both the early and the mature stages of the process is developed. Different aggregation scenarios are studied, depending on the degree of cooperativity and the mean population density. It is shown that under certain conditions, the system evolves slowly to a single cluster incorporating all individuals, or to two coexisting clusters of similar sizes. [ABSTRACT FROM AUTHOR]

A two-variable bistable system modeling the selection between competing options is considered in the presence of additive white noise, representing environmental or internal variability. It is shown that when the strengths of the noises acting on the evolution equations of the two variables are different a symmetry-breaking process takes place, whereby the state in which the excess variable is perturbed by the strongest noise becomes predominant. [ABSTRACT FROM AUTHOR]

At short time scales, the inertia term becomes relevant for the magnetization dynamics of ferromagnets and leads to nutation for the magnetization vector. For the case of spatially extended magnetic systems, for instance, Heisenberg spin chains with the isotropic spin-exchange interaction, this leads to the appearance of a collective excitation, the "nutation wave," whose properties are elucidated by analytical arguments and numerical studies. The one-particle excitations can be identified as relativistic massive particles. These particles, the "nutatons," acquire their mass via the Brout–Englert–Higgs mechanism, through the interaction of the wave with an emergent topological gauge field. This spin excitation would appear as a peak in the spectrum of the scattering structure factor in inelastic neutron scattering experiments. The high frequency and speed of the nutation wave can open paths for realizing ultrafast spin dynamics. [ABSTRACT FROM AUTHOR]

We propose a stochastic approach for the description of the time evolution of the magnetization of nanomagnets, that interpolates between the Landau–Lifshitz–Gilbert and the Landau–Lifshitz–Bloch approximations, by varying the strength of the noise. In addition, we take into account the autocorrelation time of the noise and explore the consequences, when it is finite, on the scale of the response of the magnetization, i.e. when it may be described as colored, rather than white, noise and non-Markovian features become relevant. We close the hierarchy for the moments of the magnetization, by introducing a suitable truncation scheme, whose validity is tested by direct numerical solution of the moment equations and compared to the average deduced from a numerical solution of the corresponding stochastic Langevin equation. In this way we establish a general framework that allows both coarse-graining simulations and faster calculations beyond the truncation approximation used here. [ABSTRACT FROM AUTHOR]

The development and maintenance of most tissues and organs require the presence of multipotent and unipotent stem cells that have the ability of self-renewal as well as of generating committed, further differentiated cell types. The transcription factor Sox2 is essential for embryonic development and maintains pluripotency and self-renewal in embryonic stem cells. It is expressed in immature osteoblasts/osteoprogenitors in vitro and in vivo and is induced by fibroblast growth factor signaling, which stimulates osteoblast proliferation and inhibits differentiation. Sox2 overexpression can by itself inhibit osteoblast differentiation. To elucidate its function in the osteoblastic lineage, we generated mice with an osteoblast-specific, Cre-mediated knockout of Sox2. These mice are small and osteopenic, and mosaic for Sox2 inactivation. However, culturing calvarial osteoblasts from the mutant mice for 2–3 passages failed to yield any Sox2-null cells. Inactivation of the Sox2 gene by Cre-mediated excision in cultured osteoblasts showed that Sox2-null cells could not survive repeated passage in culture, could not form colonies, and arrested their growth with a senescent phenotype. In addition, expression of Sox2-specific shRNAs in independent osteoblastic cell lines suppressed their proliferative ability. Osteoblasts capable of forming ‘osteospheres’ are greatly enriched in Sox2 expression. These data identify a novel function for Sox2 in the maintenance of self-renewal in the osteoblastic lineage. [ABSTRACT FROM AUTHOR]