Generation of interface for an Allen-Cahn equation with nonlinear diffusion

In this note, we consider a nonlinear diffusion equation with a bistable reaction term arising in population dynamics. Given a rather general initial data, we investigate its behavior for small times as the reaction coefficient tends to infinity: we prove a generation of interface property

Quantum Cosmology and Conformal Invariance

According to Belinsky, Khalatnikov and Lifshitz, gravity near a space-like singularity reduces to a set of decoupled one-dimensional mechanical models at each point in space. We point out that these models fall into a class of conformal mechanical models first introduced by de Alfaro, Fubini and Furlan (DFF). The deformation used by DFF to render the spectrum discrete corresponds to a negative cosmological constant. The wave function of the universe is the zero-energy eigenmode of the Hamiltonian, also known as the spherical vector of the representation of the conformal group SO(1,2). A new class of conformal quantum mechanical models is constructed, based on the quantization of nilpotent coadjoint orbits, where the conformal group is enhanced to an ADE non-compact group for which the spherical vector is known.Comment: 4 pages, latex2e, uses revtex

The Large-NN Limit of the Two-Hermitian-matrix model by the hidden BRST method

This paper discusses the large N limit of the two-Hermitian-matrix model in zero dimensions, using the hidden BRST method. A system of integral equations previously found is solved, showing that it contained the exact solution of the model in leading order of large $N$.Comment: 19 pages, Latex,CERN--TH-6531/9

An Algorithm for Probabilistic Alternating Simulation

In probabilistic game structures, probabilistic alternating simulation (PA-simulation) relations preserve formulas defined in probabilistic alternating-time temporal logic with respect to the behaviour of a subset of players. We propose a partition based algorithm for computing the largest PA-simulation, which is to our knowledge the first such algorithm that works in polynomial time, by extending the generalised coarsest partition problem (GCPP) in a game-based setting with mixed strategies. The algorithm has higher complexities than those in the literature for non-probabilistic simulation and probabilistic simulation without mixed actions, but slightly improves the existing result for computing probabilistic simulation with respect to mixed actions.Comment: We've fixed a problem in the SOFSEM'12 conference versio

Electric Dipole Moments and Polarizability in the Quark-Diquark Model of the Neutron

For a bound state internal wave function respecting parity symmetry, it can be rigorously argued that the mean electric dipole moment must be strictly zero. Thus, both the neutron, viewed as a bound state of three quarks, and the water molecule, viewed as a bound state of ten electrons two protons and an oxygen nucleus, both have zero mean electric dipole moments. Yet, the water molecule is said to have a nonzero dipole moment strength $d=e\Lambda$ with $\Lambda_{H_2O} \approx 0.385\ \dot{A}$. The neutron may also be said to have an electric dipole moment strength with $\Lambda_{neutron} \approx 0.612\ fm$. The neutron analysis can be made experimentally consistent, if one employs a quark-diquark model of neutron structure.Comment: four pages, two figure

Discounting in LTL

In recent years, there is growing need and interest in formalizing and reasoning about the quality of software and hardware systems. As opposed to traditional verification, where one handles the question of whether a system satisfies, or not, a given specification, reasoning about quality addresses the question of \emph{how well} the system satisfies the specification. One direction in this effort is to refine the "eventually" operators of temporal logic to {\em discounting operators}: the satisfaction value of a specification is a value in $[0,1]$, where the longer it takes to fulfill eventuality requirements, the smaller the satisfaction value is. In this paper we introduce an augmentation by discounting of Linear Temporal Logic (LTL), and study it, as well as its combination with propositional quality operators. We show that one can augment LTL with an arbitrary set of discounting functions, while preserving the decidability of the model-checking problem. Further augmenting the logic with unary propositional quality operators preserves decidability, whereas adding an average-operator makes some problems undecidable. We also discuss the complexity of the problem, as well as various extensions

Imitation in Large Games

In games with a large number of players where players may have overlapping objectives, the analysis of stable outcomes typically depends on player types. A special case is when a large part of the player population consists of imitation types: that of players who imitate choice of other (optimizing) types. Game theorists typically study the evolution of such games in dynamical systems with imitation rules. In the setting of games of infinite duration on finite graphs with preference orderings on outcomes for player types, we explore the possibility of imitation as a viable strategy. In our setup, the optimising players play bounded memory strategies and the imitators play according to specifications given by automata. We present algorithmic results on the eventual survival of types

Field-enlarging transformations and chiral theories

A field-enlarging transformation in the chiral electrodynamics is performed. This introduces an additional gauge symmetry to the model that is unitary and anomaly-free and allows for comparison of different models discussed in the literature. The problem of superfluous degrees of freedom and their influence on quantization is discussed. Several "mysteries" are explained from this point of view.Comment: 14 pages, LaTeX-file, BI-TP 93/0