Self-Assembling of Networks in an Agent-Based Model

We propose a model to show the self-assembling of network-like structures between a set of nodes without using preexisting positional information or long-range attraction of the nodes. The model is based on Brownian agents that are capable of producing different local (chemical) information and respond to it in a non-linear manner. They solve two tasks in parallel: (i) the detection of the appropriate nodes, and (ii) the establishment of stable links between them. We present results of computer simulations that demonstrate the emergence of robust network structures and investigate the connectivity of the network by means of both analytical estimations and computer simulations. PACS: 05.65.+b, 89.75.Kd, 84.30.Bv, 87.18.SnComment: 10 pages, 8 figures. A video of the computer simulations can be found at http://www.ais.fhg.de/~frank/network.html. After publication, this paper was also included in: Virtual Journal of Biological Physics Research 4/5 (September 1, 2002) and Virtual Journal of Nanoscale Science & Technology 6/10 (September 2, 2002). For related work, see also http://www.ais.fhg.de/~frank/active.htm

Uphill Motion of Active Brownian Particles in Piecewise Linear Potentials

We consider Brownian particles with the ability to take up energy from the environment, to store it in an internal depot, and to convert internal energy into kinetic energy of motion. Provided a supercritical supply of energy, these particles are able to move in a ``high velocity'' or active mode, which allows them to move also against the gradient of an external potential. We investigate the critical energetic conditions of this self-driven motion for the case of a linear potential and a ratchet potential. In the latter case, we are able to find two different critical conversion rates for the internal energy, which describe the onset of a directed net current into the two different directions. The results of computer simulations are confirmed by analytical expressions for the critical parameters and the average velocity of the net current. Further, we investigate the influence of the asymmetry of the ratchet potential on the net current and estimate a critical value for the asymmetry in order to obtain a positive or negative net current.Comment: accepted for publication in European Journal of Physics B (1999), for related work see http://summa.physik.hu-berlin.de/~frank/active.htm

Directed motion of Brownian particles with internal energy depot

A model of Brownian particles with the ability to take up energy from the environment, to store it in an internal depot, and to convert internal energy into kinetic energy of motion, is discussed. The general dynamics outlined in Sect. 2 is investigated for the deterministic and stochastic particle's motion in a non-fluctuating ratchet potential. First, we discuss the attractor structure of the ratchet system by means of computer simulations. Dependent on the energy supply, we find either periodic bound attractors corresponding to localized oscillations, or one/two unbound attractors corresponding to directed movement in the ratchet potential. Considering an ensemble of particles, we show that in the deterministic case two currents into different directions can occur, which however depend on a supercritical supply of energy. Considering stochastic influences, we find the current only in one direction. We further investigate how the current reversal depends on the strength of the stochastic force and the asymmetry of the potential. We find both a critical value of the noise intensity for the onset of the current and an optimal value where the net current reaches a maximum. Eventually, the dynamics of our model is compared with other ratchet models previously suggested.Comment: 24 pages, 11 Figs., For related work see http://summa.physik.hu-berlin.de/~frank/active.htm

Statistical Mechanics of Canonical-Dissipative Systems and Applications to Swarm Dynamics

We develop the theory of canonical-dissipative systems, based on the assumption that both the conservative and the dissipative elements of the dynamics are determined by invariants of motion. In this case, known solutions for conservative systems can be used for an extension of the dynamics, which also includes elements such as the take-up/dissipation of energy. This way, a rather complex dynamics can be mapped to an analytically tractable model, while still covering important features of non-equilibrium systems. In our paper, this approach is used to derive a rather general swarm model that considers (a) the energetic conditions of swarming, i.e. for active motion, (b) interactions between the particles based on global couplings. We derive analytical expressions for the non-equilibrium velocity distribution and the mean squared displacement of the swarm. Further, we investigate the influence of different global couplings on the overall behavior of the swarm by means of particle-based computer simulations and compare them with the analytical estimations.Comment: 14 pages incl. 13 figures. v2: misprints in Eq. (40) corrected, ref. updated. For related work see also: http://summa.physik.hu-berlin.de/~frank/active.htm

Generalized Force Model of Traffic Dynamics

Floating car data of car-following behavior in cities were compared to existing microsimulation models, after their parameters had been calibrated to the experimental data. With these parameter values, additional simulations have been carried out, e.g. of a moving car which approaches a stopped car. It turned out that, in order to manage such kinds of situations without producing accidents, improved traffic models are needed. Good results have been obtained with the proposed generalized force model.Comment: For related work see http://www.theo2.physik.uni-stuttgart.de/helbing.htm

Connecting Anxiety and Genomic Copy Number Variation: A Genome-Wide Analysis in CD-1 Mice.

Genomic copy number variants (CNVs) have been implicated in multiple psychiatric disorders, but not much is known about their influence on anxiety disorders specifically. Using next-generation sequencing (NGS) and two additional array-based genotyping approaches, we detected CNVs in a mouse model consisting of two inbred mouse lines showing high (HAB) and low (LAB) anxiety-related behavior, respectively. An influence of CNVs on gene expression in the central (CeA) and basolateral (BLA) amygdala, paraventricular nucleus (PVN), and cingulate cortex (Cg) was shown by a two-proportion Z-test (p = 1.6 x 10-31), with a positive correlation in the CeA (p = 0.0062), PVN (p = 0.0046) and Cg (p = 0.0114), indicating a contribution of CNVs to the genetic predisposition to trait anxiety in the specific context of HAB/LAB mice. In order to confirm anxiety-relevant CNVs and corresponding genes in a second mouse model, we further examined CD-1 outbred mice. We revealed the distribution of CNVs by genotyping 64 CD 1 individuals using a high-density genotyping array (Jackson Laboratory). 78 genes within those CNVs were identified to show nominally significant association (48 genes), or a statistical trend in their association (30 genes) with the time animals spent on the open arms of the elevated plus-maze (EPM). Fifteen of them were considered promising candidate genes of anxiety-related behavior as we could show a significant overlap (permutation test, p = 0.0051) with genes within HAB/LAB CNVs. Thus, here we provide what is to our knowledge the first extensive catalogue of CNVs in CD-1 mice and potential corresponding candidate genes linked to anxiety-related behavior in mice

Genomic positions of CNVs on chromosome 3.

<p>The chromosome is indicated by a thick horizontal line (grey). Depending on the detection method, CNVs in HAB/LAB mice are depicted in orange (aCGH), dark red (JaxMDGA) and red (NGS), respectively. Data displayed above the grey line represent a copy number gain in HAB vs. LAB animals, data below a copy number loss. Data printed on the grey line show CNVs in 64 CD-1 mice, with those highlighted in color that could be associated with anxiety-related behavior (time on the open arm of EPM) with a nominal <i>p</i>-value less than 0.1 (light blue) or less than 0.05 (blue). Start points of CNVs are marked by dots and lines are drawn to the end points.</p