Mechanisms inducing parallel computation in a model of physarum polycephalum transport networks

The giant amoeboid organism true slime mould Physarum polycephalum dynamically adapts its body plan in response to changing environmental conditions and its protoplasmic transport network is used to distribute nutrients within the organism. These networks are efficient in terms of network length and network resilience and are parallel approximations of a range of proximity graphs and plane division problems. The complex parallel distributed computation exhibited by this simple organism has since served as an inspiration for intensive research into distributed computing and robotics within the last decade. P. polycephalum may be considered as a spatially represented parallel unconventional computing substrate, but how can this ‘computer’ be programmed? In this paper we examine and catalogue individual low-level mechanisms which may be used to induce network formation and adaptation in a multi-agent model of P. polycephalum. These mechanisms include those intrinsic to the model (particle sensor angle, rotation angle, and scaling parameters) and those mediated by the environment (stimulus location, distance, angle, concentration, engulfment and consumption of nutrients, and the presence of simulated light irradiation, repellents and obstacles). The mechanisms induce a concurrent integration of chemoattractant and chemorepellent gradients diffusing within the 2D lattice upon which the agent population resides, stimulating growth, movement, morphological adaptation and network minimisation. Chemoattractant gradients, and their modulation by the engulfment and consumption of nutrients by the model population, represent an efficient outsourcing of spatial computation. The mechanisms may prove useful in understanding the search strategies and adaptation of distributed organisms within their environment, in understanding the minimal requirements for complex adaptive behaviours, and in developing methods of spatially programming parallel unconventional computers and robotic devices

Bessel bridges decomposition with varying dimension. Applications to finance

We consider a class of stochastic processes containing the classical and well-studied class of Squared Bessel processes. Our model, however, allows the dimension be a function of the time. We first give some classical results in a larger context where a time-varying drift term can be added. Then in the non-drifted case we extend many results already proven in the case of classical Bessel processes to our context. Our deepest result is a decomposition of the Bridge process associated to this generalized squared Bessel process, much similar to the much celebrated result of J. Pitman and M. Yor. On a more practical point of view, we give a methodology to compute the Laplace transform of additive functionals of our process and the associated bridge. This permits in particular to get directly access to the joint distribution of the value at t of the process and its integral. We finally give some financial applications to illustrate the panel of applications of our results

Reducing nonideal to ideal coupling in random matrix description of chaotic scattering: Application to the time-delay problem

We write explicitly a transformation of the scattering phases reducing the problem of quantum chaotic scattering for systems with M statistically equivalent channels at nonideal coupling to that for ideal coupling. Unfolding the phases by their local density leads to universality of their local fluctuations for large M. A relation between the partial time delays and diagonal matrix elements of the Wigner-Smith matrix is revealed for ideal coupling. This helped us in deriving the joint probability distribution of partial time delays and the distribution of the Wigner time delay.Comment: 4 pages, revtex, no figures; published versio

AC resistivity of d-wave ceramic superconductors

We model d-wave ceramic superconductors with a three-dimensional lattice of randomly distributed $\pi$ Josephson junctions with finite self-inductance. The linear and nonlinear ac resistivity of the d-wave ceramic superconductors is obtained as function of temperature by solving the corresponding Langevin dynamical equations. We find that the linear ac resistivity remains finite at the temperature $T_p$ where the third harmonics of resistivity has a peak. The current amplitude dependence of the nonlinear resistivity at the peak position is found to be a power law. These results agree qualitatively with experiments. We also show that the peak of the nonlinear resistivity is related to the onset of the paramagnetic Meissner effect which occurs at the crossover temperature $T_p$, which is above the chiral glass transition temperature $T_{cg}$.Comment: 7 eps figures, Phys. Rev. B (in press

Charge and spin Drude weight of the one-dimensional extended Hubbard model at quarter-filling

We calculate the charge and spin Drude weight of the one-dimensional extended Hubbard model with on-site repulsion $U$ and nearest-neighbor repulsion $V$ at quarter filling using the density-matrix renormalization group method combined with a variational principle. Our numerical results for the Hubbard model (V=0) agree with exact results obtained from the Bethe ansatz solution. We obtain the contour map for both Drude weights in the $UV$-parameter space for repulsive interactions. We find that the charge Drude weight is discontinuous across the Kosterlitz-Thouless transition between the Luttinger liquid and the charge-density-wave insulator, while the spin Drude weight varies smoothly and remains finite in both phases. Our results can be generally understood using bosonization and renormalization group results. The finite-size scaling of the charge Drude weight is well fitted by a polynomial function of the inverse system size in the metallic region. In the insulating region we find an exponential decay of the finite-size corrections with the system size and a universal relation between the charge gap $\Delta_c$ and the correlation length $\xi$ which controls this exponential decay.Comment: 10 pages, 9 figure

Universal computation with limited resources: Belousov-Zhabotinsky and Physarum computers

Using the examples of an excitable chemical system (Belousov-Zhabotinsky medium) and plasmodium of Physarum polycephalum we show that universal computation in a geometrically unconstrained medium is only possible when resources (excitability or concentration of nutrients) are limited. In situations of limited resources the systems studied develop travelling localizations. The localizations are elementary units of dynamical logical circuits in collision-based computing architectures.Comment: Int. J. Bifurcation and Chaos (2008), accepte

Gate-induced band ferromagnetism in an organic polymer

We propose that a chain of five-membered rings (polyaminotriazole) should be ferromagnetic with an appropriate doping that is envisaged to be feasible with an FET structure. The ferromagnetism is confirmed by a spin density functional calculation, which also shows that ferromagnetism survives the Peierls instability. We explain the magnetism in terms of Mielke and Tasaki's flat-band ferromagnetism with the Hubbard model. This opens a new possibility of band ferromagnetism in purely organic polymers.Comment: 4 pages, 7 figure

Fermi Surface of 3d^1 Perovskite CaVO3 Near the Mott Transition

We present a detailed de Haas van Alphen effect study of the perovskite CaVO3, offering an unprecedented test of electronic structure calculations in a 3d transition metal oxide. Our experimental and calculated Fermi surfaces are in good agreement -- but only if we ignore large orthorhombic distortions of the cubic perovskite structure. Subtle discrepancies may shed light on an apparent conflict between the low energy properties of CaVO3, which are those of a simple metal, and high energy probes which reveal strong correlations that place CaVO3 on the verge of a metal-insulator transition.Comment: 4 pages, 4 figures (REVTeX