Percolation in living neural networks

We study living neural networks by measuring the neurons' response to a global electrical stimulation. Neural connectivity is lowered by reducing the synaptic strength, chemically blocking neurotransmitter receptors. We use a graph-theoretic approach to show that the connectivity undergoes a percolation transition. This occurs as the giant component disintegrates, characterized by a power law with critical exponent $\beta \simeq 0.65$ is independent of the balance between excitatory and inhibitory neurons and indicates that the degree distribution is gaussian rather than scale freeComment: PACS numbers: 87.18.Sn, 87.19.La, 64.60.Ak http://www.weizmann.ac.il/complex/tlusty/papers/PhysRevLett2006.pd

Thermodynamics and structure of self-assembled networks

We study a generic model of self-assembling chains which can branch and form networks with branching points (junctions) of arbitrary functionality. The physical realizations include physical gels, wormlike micells, dipolar fluids and microemulsions. The model maps the partition function of a solution of branched, self-assembling, mutually avoiding clusters onto that of a Heisenberg magnet in the mathematical limit of zero spin components. The model is solved in the mean field approximation. It is found that despite the absence of any specific interaction between the chains, the entropy of the junctions induces an effective attraction between the monomers, which in the case of three-fold junctions leads to a first order reentrant phase separation between a dilute phase consisting mainly of single chains, and a dense network, or two network phases. Independent of the phase separation, we predict the percolation (connectivity) transition at which an infinite network is formed that partially overlaps with the first-order transition. The percolation transition is a continuous, non thermodynamic transition that describes a change in the topology of the system. Our treatment which predicts both the thermodynamic phase equilibria as well as the spatial correlations in the system allows us to treat both the phase separation and the percolation threshold within the same framework. The density-density correlation correlation has a usual Ornstein-Zernicke form at low monomer densities. At higher densities, a peak emerges in the structure factor, signifying an onset of medium-range order in the system. Implications of the results for different physical systems are discussed.Comment: Submitted to Phys. Rev.

Where are they all from? - sources and sustainability in the ornamental freshwater fish trade

The global trade in ornamental fish involves c. 125 countries worldwide and is worth c. US $15-30 billion each year. This total is dominated (90%) by freshwater fishes, most of which are sourced from breeding facilities located in developing countries, typically in Asia or South America, but also in Israel, USA and Europe. Some fish are obtained from natural (wild) sources in Asia and South America, but the exact percentage of wild-caught fish is difficult to quantify given a lack of reliable data. Although c. 1000 species of freshwater fishes are widely available (from a total of > 5300 on sale), the most dominant freshwater fishes in the market comprise only 30 species from the orders Cyprinodontiformes, Perciformes, Characiformes and Siluriformes. In this perspectives review, illustrative example case studies of wild-fish collecting (Barcelos and Rio Xingu, Brazil) and breeding projects (Java, Indonesia) are described. In addition, wild-collecting expeditions to West Papua, Indonesia are discussed, focused on discovering novel species of rainbowfish (Melanotaeniidae) for breeding in captivity. Sustainability of the aquarium industry is considered in its broadest sense. The aquarium industry has been portrayed as both a major threat to natural ecosystems, but also as being part of the solution in terms of helping to maintain species when they have gone extinct in the wild or offering an income to impoverished citizens who might otherwise engage in much more destructive practices

Thermal bremsstrahlung probing the thermodynamical state of multifragmenting systems

Inclusive and exclusive hard-photon (E$_\gamma >$ 30 MeV) production in five different heavy-ion reactions ($^{36}$Ar+$^{197}$Au, $^{107}$Ag, $^{58}$Ni, $^{12}$C at 60{\it A} MeV and $^{129}$Xe+$^{120}$Sn at 50{\it A} MeV) has been studied coupling the TAPS photon spectrometer with several charged-particle multidetectors covering more than 80% of 4$\pi$. The measured spectra, slope parameters and source velocities as well as their target-dependence, confirm the existence of thermal bremsstrahlung emission from secondary nucleon-nucleon collisions that accounts for roughly 20% of the total hard-photon yield. The thermal slopes are a direct measure of the temperature of the excited nuclear systems produced during the reaction.Comment: 4 pages, 3 figures, Proceedings CRIS 2000, 3rd Catania Relativistic Ion Studies, "Phase Transitions in Strong Interactions: Status and Perspectives", Acicastello, Italy, May 22-26, 2000 (to be published in Nuc. Phys. A

Rules for biological regulation based on error minimization

The control of gene expression involves complex mechanisms that show large variation in design. For example, genes can be turned on either by the binding of an activator (positive control) or the unbinding of a repressor (negative control). What determines the choice of mode of control for each gene? This study proposes rules for gene regulation based on the assumption that free regulatory sites are exposed to nonspecific binding errors, whereas sites bound to their cognate regulators are protected from errors. Hence, the selected mechanisms keep the sites bound to their designated regulators for most of the time, thus minimizing fitness-reducing errors. This offers an explanation of the empirically demonstrated Savageau demand rule: Genes that are needed often in the natural environment tend to be regulated by activators, and rarely needed genes tend to be regulated by repressors; in both cases, sites are bound for most of the time, and errors are minimized. The fitness advantage of error minimization appears to be readily selectable. The present approach can also generate rules for multi-regulator systems. The error-minimization framework raises several experimentally testable hypotheses. It may also apply to other biological regulation systems, such as those involving protein-protein interactions.Comment: biological physics, complex networks, systems biology, transcriptional regulation http://www.weizmann.ac.il/complex/tlusty/papers/PNAS2006.pdf http://www.pnas.org/content/103/11/3999.ful

Nematic-Wetted Colloids in the Isotropic Phase: Pairwise Interaction, Biaxiality and Defects

We calculate the interaction between two spherical colloidal particles embedded in the isotropic phase of a nematogenic liquid. The surface of the particles induces wetting nematic coronas that mediate an elastic interaction. In the weak wetting regime, we obtain exact results for the interaction energy and the texture, showing that defects and biaxiality arise, although they are not topologically required. We evidence rich behaviors, including the possibility of reversible colloidal aggregation and dispersion. Complex anisotropic self-assembled phases might be formed in dense suspensions.Comment: 4 pages, 6 figure

On the bistable zone of milling processes

A modal-based model of milling machine tools subjected to time-periodic nonlinear cutting forces is introduced. The model describes the phenomenon of bistability for certain cutting parameters. In engineering, these parameter domains are referred to as unsafe zones, where steady-state milling may switch to chatter for certain perturbations. In mathematical terms, these are the parameter domains where the periodic solution of the corresponding nonlinear, time-periodic delay differential equation is linearly stable, but its domain of attraction is limited due to the existence of an unstable quasi-periodic solution emerging from a secondary Hopf bifurcation. A semi-numerical method is presented to identify the borders of these bistable zones by tracking the motion of the milling tool edges as they might leave the surface of the workpiece during the cutting operation. This requires the tracking of unstable quasi-periodic solutions and the checking of their grazing to a time-periodic switching surface in the infinite-dimensional phase space. As the parameters of the linear structural behaviour of the tool/machine tool system can be obtained by means of standard modal testing, the developed numerical algorithm provides efficient support for the design of milling processes with quick estimates of those parameter domains where chatter can still appear in spite of setting the parameters into linearly stable domains

Evidence for Thermal Equilibration in Multifragmentation Reactions probed with Bremsstrahlung Photons

The production of nuclear bremsstrahlung photons (E$_{\gamma}>$ 30 MeV) has been studied in inclusive and exclusive measurements in four heavy-ion reactions at 60{\it A} MeV. The measured photon spectra, angular distributions and multiplicities indicate that a significant part of the hard-photons are emitted in secondary nucleon-nucleon collisions from a thermally equilibrated system. The observation of the thermal component in multi-fragment $^{36}$Ar+$^{197}$Au reactions suggests that the breakup of the thermalized source produced in this system occurs on a rather long time-scale.Comment: Revised version, accepted for publication in Physical Review Letters. 4 pages, 4 fig

A molecular dynamics study on the equilibrium magnetization properties and structure of ferrofluids

We investigate in detail the initial susceptibility, magnetization curves, and microstructure of ferrofluids in various concentration and particle dipole moment ranges by means of molecular dynamics simulations. We use the Ewald summation for the long-range dipolar interactions, take explicitly into account the translational and rotational degrees of freedom, coupled to a Langevin thermostat. When the dipolar interaction energy is comparable with the thermal energy, the simulation results on the magnetization properties agree with the theoretical predictions very well. For stronger dipolar couplings, however, we find systematic deviations from the theoretical curves. We analyze in detail the observed microstructure of the fluids under different conditions. The formation of clusters is found to enhance the magnetization at weak fields and thus leads to a larger initial susceptibility. The influence of the particle aggregation is isolated by studying ferro-solids, which consist of magnetic dipoles frozen in at random locations but which are free to rotate. Due to the artificial suppression of clusters in ferro-solids the observed susceptibility is considerably lowered when compared to ferrofluids.Comment: 33 pages including 12 figures, requires RevTex