Analytic reconstruction of some dynamical systems

We propose a reconstruction of the initial system of ordinary differential equations from a single observed variable. The suggested approach is applied to a certain class of systems which includes, in particular, the Rössler system and other chaotic systems. We develop relations and a method to pass from a model that involves the observable and its time derivatives to a real original system. To this end, we first find a set of candidates of the system in an analytic way. After that, by additionally studying the system, we make a choice for the sought system.     

Cross-entropic learning of a machine for the decision in a partially observable universe

In this paper, we are interested in optimal decisions in a partially observable universe. Our approach is to directly approximate an optimal strategic tree depending on the observation. This approximation is made by means of a parameterized probabilistic law. A particular family of Hidden Markov Models (HMM), with input and output, is considered as a model of policy. A method for optimizing the parameters of these HMMs is proposed and applied. This optimization is based on the cross-entropic (CE) principle for rare events simulation developed by Rubinstein.     

系综Monte Carlo方法

本文系统地给出了Monte Carlo模拟的一般方法在各种系综条件下的表述以及它们的算法。     

Maximal integral over observable measures

Let f be a continuous transformation on a compact,finite-dimensional manifold M,andψa continuous function on M.This paper establishes the following formula:ess sup lim sup n→∞ 1/n ψ_n(x)=sup{∫ψdμ︱μ∈O_f}≤lim sup n→∞ 1/n ess sup ψ_n(x),where ess sup denotes the essential supremum taken against the Lebesgue measure,ψ_n(x)=n-1 ∑ i=0 ψ(f~ix) and O_f is the set of observable measures.Examples are provided to illustrate that the inequality could be an equality or strict.Moreover,if μ is the unique maximizing observable measure for ψ,it is weakly statistical stable.     

The intersection operation in light of joint observables and Bell inequalities in operational probability theory

Operational probability theory appears as a smooth extension of classical probability theory that fulfills quantum physics needs. In this paper, we, first, explain the need to extend the concept of the intersection operation in the light of the concept of joint observables. Then, we tried to determine the basic features that characterize any possible definition of the intersection operation. Furthermore, we tried to know if there is a relation between the definitions of the intersection operation of both fuzzy and operational probability theories. These relations are used, first, to find a suitable suggestion to define the intersection operation. Second, they are used, besides the studies made on Bell inequalities in fuzzy probability theory, to find the conditions that should be satisfied by the intersection operation to ensure the possibility of the violation of Bell inequalities in operational probability theory.     

Volatility skews and extensions of the Libor market model

The paper considers extensions of the Libor market model to markets with volatility skews in observable option prices. The family of forward rate processes is expanded to include diffusions with non-linear forward rate dependence, and efficient techniques for calibration to quoted prices of caps and swaptions are discussed. Special emphasis is put on generalized CEV processes for which closed-form expressions for cap and swaption prices are derived. Modifications of the CEV process which exhibit more appealing growth and boundary characteristics are also discussed. The proposed models are investigated numerically through Crank–Nicholson finite difference schemes and Monte Carlo simulations.     

Observable Correlations in Two-Qubit States

The total correlations in a bipartite quantum state are well quantified by the quantum mutual information, the amount of which is not necessarily fully extractable by local measurements. The observable correlations are the maximal correlations that can be extracted via local measurements, and have an intuitive interpretation as a measure of classical correlations. We evaluate the observable correlations for generic two-qubit states and obtain analytical expressions in some particular cases. The intricate and subtle relationships among the total, quantum and classical correlations are illustrated in terms of observable correlations. In the course, we also disprove an intuitive conjecture of Lindblad which states that the classical correlations account for at least half of the total correlations, or equivalently, correlations are more classical than quantum.     

Time and Dirac Observables in Friedmann Cosmologies

A cosmological time variable is emerged from the Hamiltonian formulation of Friedmann model to measure the evolution of dynamical observables in the theory. A set of observables has been identified for the theory on the null hypersurfaces that its evolution is with respect to the volume clock introduced by the cosmological time variable.     

The Galois Correspondence in Field Algebra of G-spin Model

Suppose that G is a finite group and D（G） the double algebra of G. For a given subgroup H of G, there is a sub-Hopf algebra D（G; H） of D（G）. This paper gives the concrete construction of a D（G; H）-invariant subspace AH in field algebra of G-spin model and proves that if H is a normal subgroup of G, then AH is Galois closed.     

Normal covariant quantization maps

We consider questions related to quantizing complex valued functions defined on a locally compact topological group. In the case of bounded functions, we generalize R. Werner's approach to prove the characterization of the associated normal covariant quantization maps.