Election results and the Sznajd model on Barabasi network

The network of Barabasi and Albert, a preferential growth model where a new node is linked to the old ones with a probability proportional to their connectivity, is applied to Brazilian election results. The application of the Sznajd rule, that only agreeing pairs of people can convince their neighbours, gives a vote distribution in good agreement with reality.Comment: 7 pages including two figures, for Eur. Phys. J.

Pacific bonito management information document

Management of Pacific bonito in California is examined in this Management Information Document by a State-Federal team of scientists. Abundance of Pacific bonito in southern California has fallen dramatically between the 1963-1969 period and the 1974-1977 period. Since 1976 the commercia1 fleet has found few large fish in southern California, and has caught fish in the size range of 15 to 57 cm (1.2 to 4.7 pounds). This fact, coupled with the low abundance indices, point out the need for a more active management regime. To develop management measures for the California bonito fishery both a surplus yield analysis and a yield-per-recruit analysis were performed. A maximum sustained yield of 10,000 short tons was estimated for the fishery in southern California, while the whole fishery, including Baja California, has an estimated MSY of 13,000 tons. In order to achieve this level of catch, however, the stock abundance must be increased by a factor of five. Yield-per-recruit considerations suggest that a minimum size limit in the commercial fishery has two important effects. A three-pound size limit could result in a slight increase in yield-per-recruit. If the size limit is increased to 5 or 7.5 lbs, the yield-per-recruit would fall significantly. Offsetting the effect on yield-per-recruit, however, would be a substantial increase in average amount of spawning per recruit which should result in a proportional increase in recruitment. With the current depressed stock abundance both a reduced annual take and a minimum size limit on commercial catch would confer substantial benefits in the form of an increase in the future stock size. After considering seven different types of management measures, the team finds that three types -- an annual commercial catch quota, a commercial size limit, and a recreational bag limit -- appear desirable. Re-establishment of the stock in southern California was the major consideration in this evaluation because the stock is currently depressed. All segments of the fishery will benefit from a more abundant resource. The difficult issues for policy, however, concern the rate of rebuilding, the degree of risk that is acceptable, and the distribution of benefits among user groups. By judicious choice among the options discussed here, a variety of positions can be established with respect to these issues. The greater the size limit, for instance, the more benefit is provided the recreational sector while difficulties are imposed upon commercial fishermen. The higher the quotas adopted, the slower the stock rebuilding and the greater the risk of continued stock depletion. A final reconciliation of the management options involves social, political and legal considerations which must be thoroughly incorporated by decision-makers before adoption of a management plan. (93pp.

Number of spanning clusters at the high-dimensional percolation thresholds

A scaling theory is used to derive the dependence of the average number of spanning clusters at threshold on the lattice size L. This number should become independent of L for dimensions d<6, and vary as log L at d=6. The predictions for d>6 depend on the boundary conditions, and the results there may vary between L^{d-6} and L^0. While simulations in six dimensions are consistent with this prediction (after including corrections of order loglog L), in five dimensions the average number of spanning clusters still increases as log L even up to L = 201. However, the histogram P(k) of the spanning cluster multiplicity does scale as a function of kX(L), with X(L)=1+const/L, indicating that for sufficiently large L the average will approach a finite value: a fit of the 5D multiplicity data with a constant plus a simple linear correction to scaling reproduces the data very well. Numerical simulations for d>6 and for d=4 are also presented.Comment: 8 pages, 11 figures. Final version to appear on Physical Review

Colloids with key-lock interactions: non-exponential relaxation, aging and anomalous diffusion

The dynamics of particles interacting by key-lock binding of attached biomolecules are studied theoretically. Experimental realizations of such systems include colloids grafted with complementary single-stranded DNA (ssDNA), and particles grafted with antibodies to cell-membrane proteins. Depending on the coverage of the functional groups, we predict two distinct regimes. In the low coverage localized regime, there is an exponential distribution of departure times. As the coverage is increased the system enters a diffusive regime resulting from the interplay of particle desorption and diffusion. This interplay leads to much longer bound state lifetimes, a phenomenon qualitatively similar to aging in glassy systems. The diffusion behavior is analogous to dispersive transport in disordered semiconductors: depending on the interaction parameters it may range from a finite renormalization of the diffusion coefficient to anomalous, subdiffusive behavior. We make connections to recent experiments and discuss the implications for future studies.Comment: v2: substantially revised version, new treatment of localized regime, 19 pages, 10 figure

The Strange Man in Random Networks of Automata

We have performed computer simulations of Kauffman's automata on several graphs such as the regular square lattice and invasion percolation clusters in order to investigate phase transitions, radial distributions of the mean total damage (dynamical exponent $z$) and propagation speeds of the damage when one adds a damaging agent, nicknamed "strange man". Despite the increase in the damaging efficiency, we have not observed any appreciable change at the transition threshold to chaos neither for the short-range nor for the small-world case on the square lattices when the strange man is added in comparison to when small initial damages are inserted in the system. The propagation speed of the damage cloud until touching the border of the system in both cases obeys a power law with a critical exponent $\alpha$ that strongly depends on the lattice. Particularly, we have ckecked the damage spreading when some connections are removed on the square lattice and when one considers special invasion percolation clusters (high boundary-saturation clusters). It is seen that the propagation speed in these systems is quite sensible to the degree of dilution.Comment: AMS-LaTeX v1.2, 7 pages with 14 figures Encapsulated Postscript, to be publishe

Model for Cumulative Solar Heavy Ion Energy and Linear Energy Transfer Spectra

A probabilistic model of cumulative solar heavy ion energy and LET spectra is developed for spacecraft design applications. Spectra are given as a function of confidence level, mission time period during solar maximum and shielding thickness. It is shown that long-term solar heavy ion fluxes exceed galactic cosmic ray fluxes during solar maximum for shielding levels of interest. Cumulative solar heavy ion fluences should therefore be accounted for in single event effects rate calculations and in the planning of space missions

The Kauffman model on Small-World Topology

We apply Kauffman's automata on small-world networks to study the crossover between the short-range and the infinite-range case. We perform accurate calculations on square lattices to obtain both critical exponents and fractal dimensions. Particularly, we find an increase of the damage propagation and a decrease in the fractal dimensions when adding long-range connections.Comment: AMS-LaTeX v1.2, 8 pages with 8 figures Encapsulated Postscript, to be published in Physica

Gaussian model of explosive percolation in three and higher dimensions

The Gaussian model of discontinuous percolation, recently introduced by Ara\'ujo and Herrmann [Phys. Rev. Lett., 105, 035701 (2010)], is numerically investigated in three dimensions, disclosing a discontinuous transition. For the simple-cubic lattice, in the thermodynamic limit, we report a finite jump of the order parameter, $J=0.415 \pm 0.005$. The largest cluster at the threshold is compact, but its external perimeter is fractal with fractal dimension $d_A = 2.5 \pm 0.2$. The study is extended to hypercubic lattices up to six dimensions and to the mean-field limit (infinite dimension). We find that, in all considered dimensions, the percolation transition is discontinuous. The value of the jump in the order parameter, the maximum of the second moment, and the percolation threshold are analyzed, revealing interesting features of the transition and corroborating its discontinuous nature in all considered dimensions. We also show that the fractal dimension of the external perimeter, for any dimension, is consistent with the one from bridge percolation and establish a lower bound for the percolation threshold of discontinuous models with finite number of clusters at the threshold

Probability distribution of persistent spins in a Ising chain

We study the probability distribution $Q(n,t)$ of $n(t)$, the fraction of spins unflipped till time $t$, in a Ising chain with ferromagnetic interactions. The distribution shows a peak at $n=n_{max}$ and in general is non-Gaussian and asymmetric in nature. However for $n>n_{max}$ it shows a Gaussian decay. A data collapse can be obtained when $Q(n,t)/L^{\alpha}$ versus $(n-n_{max})L^{\beta}$ is plotted with $\alpha \sim 0.45$ and $\beta \sim 0.6$. Interestingly, $n_{max}(t)$ shows a different behaviour compared to $= P(t)$, the persistence probability which follows the well-known behaviour $P(t)\sim t^{-\theta}$. A quantitative estimate of the asymmetry and non-Gaussian nature of $Q(n,t)$ is made by calculating its skewness and kurtosis.Comment: 4 pages, submitted to J. Phys