Reasoning about Action: An Argumentation - Theoretic Approach

We present a uniform non-monotonic solution to the problems of reasoning about action on the basis of an argumentation-theoretic approach. Our theory is provably correct relative to a sensible minimisation policy introduced on top of a temporal propositional logic. Sophisticated problem domains can be formalised in our framework. As much attention of researchers in the field has been paid to the traditional and basic problems in reasoning about actions such as the frame, the qualification and the ramification problems, approaches to these problems within our formalisation lie at heart of the expositions presented in this paper

The Role of Surface Entropy in Statistical Emission of Massive Fragments from Equilibrated Nuclear Systems

Statistical fragment emission from excited nuclear systems is studied within the framework of a schematic Fermi-gas model combined with Weisskopf's detailed balance approach. The formalism considers thermal expansion of finite nuclear systems and pays special attention to the role of the diffuse surface region in the decay of hot equilibrated systems. It is found that with increasing excitation energy, effects of surface entropy lead to a systematic and significant reduction of effective emission barriers for fragments and, eventually, to the vanishing of these barriers. The formalism provides a natural explanation for the occurrence of negative nuclear heat capacities reported in the literature. It also accounts for the observed linearity of pseudo-Arrhenius plots of the logarithm of the fragment emission probability {\it versus} the inverse square-root of the excitation energy, but does not predict true Arrhenius behavior of these emission probabilities

Dynamical heterogeneities in a two dimensional driven glassy model: current fluctuations and finite size effects

In this article, we demonstrate that in a transport model of particles with kinetic constraints, long-lived spatial structures are responsible for the blocking dynamics and the decrease of the current at strong driving field. Coexistence between mobile and blocked regions can be anticipated by a first-order transition in the large deviation function for the current. By a study of the system under confinement, we are able to study finite-size effects and extract a typical length between mobile regions

Timeless path integral for relativistic quantum mechanics

Starting from the canonical formalism of relativistic (timeless) quantum mechanics, the formulation of timeless path integral is rigorously derived. The transition amplitude is reformulated as the sum, or functional integral, over all possible paths in the constraint surface specified by the (relativistic) Hamiltonian constraint, and each path contributes with a phase identical to the classical action divided by $\hbar$. The timeless path integral manifests the timeless feature as it is completely independent of the parametrization for paths. For the special case that the Hamiltonian constraint is a quadratic polynomial in momenta, the transition amplitude admits the timeless Feynman's path integral over the (relativistic) configuration space. Meanwhile, the difference between relativistic quantum mechanics and conventional nonrelativistic (with time) quantum mechanics is elaborated on in light of timeless path integral.Comment: 41 pages; more references and comments added; version to appear in CQ

Thermodynamic formalism for dissipative quantum walks

We consider the dynamical properties of dissipative continuous-time quantum walks on directed graphs. Using a large-deviation approach we construct a thermodynamic formalism allowing us to define a dynamical order parameter, and to identify transitions between dynamical regimes. For a particular class of dissipative quantum walks we propose a quantum generalization of the the classical PageRank vector, used to rank the importance of nodes in a directed graph. We also provide an example where one can characterize the dynamical transition from an effective classical random walk to a dissipative quantum walk as a thermodynamic crossover between distinct dynamical regimes.Comment: 8 page

Survival benefits in mimicry: a quantitative framework

Mimicry is a resemblance between species that benefits at least one of the species. It is a ubiquitous evolutionary phenomenon particularly common among prey species, in which case the advantage involves better protection from predation. We formulate a mathematical description of mimicry among prey species, to investigate benefits and disadvantages of mimicry. The basic setup involves differential equations for quantities representing predator behavior, namely, the probabilities for attacking prey at the next encounter. Using this framework, we present new quantitative results, and also provide a unified description of a significant fraction of the quantitative mimicry literature. The new results include `temporary' mutualism between prey species, and an optimal density at which the survival benefit is greatest for the mimic. The formalism leads naturally to extensions in several directions, such as the evolution of mimicry, the interplay of mimicry with population dynamics, etc. We demonstrate this extensibility by presenting some explorations on spatiotemporal pattern dynamics.Comment: 9 pages, 7 figure

First-passage method for the study of the efficiency of a two-channel reaction on a lattice

We study the efficiency of a two-channel reaction between two walkers on a finite one-dimensional periodic lattice. The walkers perform a combination of synchronous and asynchronous jumps on the lattice and react instantaneously when they meet at the same site (first channel) or upon position exchange (second channel). We develop a method based on a conditional first-passage problem to obtain exact results for the mean number of time steps needed for the reaction to take place as well as for higher order moments. Previous results obtained in the framework of a difference equation approach are fully confirmed, including the existence of a parity effect. For even lattices the maximum efficiency corresponds to a mixture of synchronous events and a small amount of asynchronous events, while for odd lattices the reaction time is minimized by a purely synchronous process. We provide an intuitive explanation for this behavior. In addition, we give explicit expressions for the variance of the reaction time. The latter displays a similar even-odd behavior, suggesting that the parity effect extends to higher order moments.Comment: 17 pages, 2 tables, 6 figures, revtex

Diffraction 2000: New Scaling Laws in Shadow Dynamics

New scaling structure for the shadow corrections in elastic scattering from deuteron at high energies has been presented and discussed. It is shown that this structure corresponds to the experimental data on proton(antiproton)-deuteron total cross sections. The effect of weakening for the inelastic screening at superhigh energies has been theoretically predicted.Comment: LaTex2e, espcrc2.sty, 2 figures, Contribution to the Workshop "Diffraction 2000", Cetraro, Ialy, Sept. 2-7, 2000, to be published in proceedings of the Worksho

Mean Escape Time in a System with Stochastic Volatility

We study the mean escape time in a market model with stochastic volatility. The process followed by the volatility is the Cox Ingersoll and Ross process which is widely used to model stock price fluctuations. The market model can be considered as a generalization of the Heston model, where the geometric Brownian motion is replaced by a random walk in the presence of a cubic nonlinearity. We investigate the statistical properties of the escape time of the returns, from a given interval, as a function of the three parameters of the model. We find that the noise can have a stabilizing effect on the system, as long as the global noise is not too high with respect to the effective potential barrier experienced by a fictitious Brownian particle. We compare the probability density function of the return escape times of the model with those obtained from real market data. We find that they fit very well.Comment: 9 pages, 9 figures, to be published in Phys. Rev.