Stability and Diversity in Collective Adaptation

We derive a class of macroscopic differential equations that describe collective adaptation, starting from a discrete-time stochastic microscopic model. The behavior of each agent is a dynamic balance between adaptation that locally achieves the best action and memory loss that leads to randomized behavior. We show that, although individual agents interact with their environment and other agents in a purely self-interested way, macroscopic behavior can be interpreted as game dynamics. Application to several familiar, explicit game interactions shows that the adaptation dynamics exhibits a diversity of collective behaviors. The simplicity of the assumptions underlying the macroscopic equations suggests that these behaviors should be expected broadly in collective adaptation. We also analyze the adaptation dynamics from an information-theoretic viewpoint and discuss self-organization induced by information flux between agents, giving a novel view of collective adaptation.Comment: 22 pages, 23 figures; updated references, corrected typos, changed conten

Fokker-Planck equations for nonlinear dynamical systems driven by non-Gaussian Levy processes

The Fokker-Planck equations describe time evolution of probability densities of stochastic dynamical systems and are thus widely used to quantify random phenomena such as uncertainty propagation. For dynamical systems driven by non-Gaussian L\'evy processes, however, it is difficult to obtain explicit forms of Fokker-Planck equations because the adjoint operators of the associated infinitesimal generators usually do not have exact formulation. In the present paper, Fokker- Planck equations are derived in terms of infinite series for nonlinear stochastic differential equations with non-Gaussian L\'evy processes. A few examples are presented to illustrate the method.Comment: 14 page

A quick-retrieval high-speed digital framing camera

A new high-speed digital framing camera is described. The design is built around a rotating polygon mirror that provides a framing rate of 24 000 frames/s. The camera electronics digitizes an image into a 32×104 grid of pixels, where the second dimension of the grid can be varied and is determined by the 8 bit computer-aided measurement and control digitizer sampling rate. Available digitizer memory provides for 314 frames at this horizontal resolution. The advantages over other available high-speed framing cameras are (1) low cost of the system provided the digitizers are available, (2) rapid retrieval of a recorded event, and (3) the ease with which the system can be used. Sample results from an application in high-power arc photography are given to illustrate the system's spatial and temporal resolution

Solitons and Almost-Intertwining Matrices

We define the set of almost-intertwining matrices to be all triples(X,Y,Z) of n x n matrices for which XZ=YX+T for some rank one matrix T. A surprisingly simple formula is given for tau-functions of the KP hierarchy in terms of such triples. The tau-functions produced in this way include the soliton and vanishing rational solutions. The induced dynamics of the eigenvalues of the matrix X are considered, leading in special cases to the Ruijsenaars-Schneider particle system

R-parity violating supersymmetric contributions to the neutron beta decay

We investigate the contribution to the angular correlation coefficients of the neutron beta decay within the R-parity violating (RPV) minimal supersymmetric standard model (MSSM). The RPV effects contribute to the scalar interaction at the tree level. The effective scalar interaction of the neutron beta decay is constructed by making use of the relation between isospin asymmetries and the proton-neutron mass difference. On the basis of the recent update of the analyses of the superallowed Fermi transitions and the recent measurement of transverse polarization of the emitted electrons at PSI, we deduce new upper limits on the RPV couplings. We also point out the existence of new types of angular correlations which are sensitive to the RPV interactions.Comment: 11 pages, 2 figures, minor errors corrected, references adde

Growth of Single Unit-Cell Superconducting La2−x_{2-x}Srx_xCuO4_{4} Films

We have developed an approach to grow high quality ultrathin films of La$_{2-x}$Sr$_x$CuO$_{4}$ with molecular beam epitaxy, by adding a homoepitaxial buffer layer in order to minimize the degradation of the film structure at the interface. The advantage of this method is to enable a further reduction of the minimal thickness of a superconducting La$_{1.9}$Sr$_{0.1}$CuO$_{4}$ film. The main result of our work is that a single unit cell (only two copper oxide planes) grown on a SrLaAlO$_4$ substrate exhibits a superconducting transition at 12.5 K (zero resistance) and an in-plane magnetic penetration depth $\lambda_{ab}(0)$ = 535 nm.Comment: to be published in "Solid State Electonics" special issue, conference proceedings of the 9th Workshop on Oxide Electronics, St-Pete Beach, FL, 20-23 november 2002 : 12 pages 4 figures in preprint versio