Number Of Discrete States Research Articles

An Evolutionary Computing Approach to Probabilistic Reasoning on Bayesian Networks

Bayesian belief networks can be used to represent and to reason about complex systems with uncertain or incomplete information. Bayesian networks are graphs capable of encoding and quantifying probabilistic dependence and conditional independence among variables. Diagnostic reasoning, also referred to as abductive inference, determining the most probable explanation (MPE), or finding the maximum a posteriori instantiation (MAP), involves determining the global most probable system description given the values of any subset of variables. In some cases abductive inference can be performed with exact algorithms using distributed network computations, but the problem is NP-hard, and complexity increases significantly with the presence of undirected cycles, the number of discrete states per variable, and the number of variables in the network. This paper describes an approximate method composed of a graph-based evolutionary algorithm that uses nonbinary alphabets, graphs instead of strings, and graph operators to perform abductive inference on multiply connected networks for which systematic search methods are not feasible. The motivation, basis, and adequacy of the method are discussed, and experimental results are presented.

Rydberg-atom stabilization against photoionization: An analytically solvable model with resonance

Stimulated by a recent experiment [L. D. Noordam et al., Phys. Rev. Lett. 68, 1496 (1992)], we present a model of Rydberg-atom photoionization whose essential feature is the resonance between the initially populated Rydberg state and an additional state lying below Rydberg quasicontinuum. Despite the infinite number of discrete states involved in our model we have obtained the expressions for photoionization yield and discrete-state populations in completely analytical form. These expressions cover both short- and long-time scales, i.e., when laser-pulse duration is shorter or longer than the classical round-trip time of the Rydberg electron. The short-time scale corresponds to the conditions met in the experiment of Noordam et al. and, on the basis of our expressions, we have gained at least qualitative understanding of their observations. In the case of long pulses, which in our considerations are never longer than 54 ps, near resonance is shown to be the origin of a profound ionization suppression, particularly for some specific frequencies, which we identify as those ensuring the formation of a perfectly dark dressed state of zero width and thus unionizable. This dark state is shown to be populated with a probability increasing when laser gets stronger. We discuss the connection between stabilization and formation of this perfectly dark state as well as of additional dressed states, which are dark in the sense that they have the property of becoming very narrow as laser intensity increases. The undamped perfectly dark state, created at specific laser frequencies, has given us rise to introduce what we call the zero-pole approximation for ionization yield, which, as we have shown, works well if duration and intensity of laser pulse are appropriately combined.

Multilevel light-induced continuum structure: limitations of adapted Fano theory

An analytical, time-dependent, fully nonperturbative solution of a general model of a light-induced continuum structure, in which a dense Rydberg-like quasi-continuum is laser-embedded into a previously structureless atomic continuum, is reported. On the basis of this solution we point to the limitations of Fano theory, which was originally formulated for an analogous problem of a number of discrete states and one continuum with configuration interaction, when this theory is adapted to the problem of multilevel light-induced continuum structures.

Fano effect studied with use of the recursion method.

We treat the classical problem of a number of discrete states interacting with continua (Fano effect), by means of the recursion method. We first map a continuum of states on an equivalent semi-infinite linear chain; then we take advantage of the concepts and properties of the interaction and dipole carrying states to calculate the absorption spectrum. Our approach leads to a significant simplification of calculations without introducing approximations to the original problem

Optimal Operation of Multipurpose Pool of Elk City Lake

A stochastic dynamic programming is used to develop optimal policies for operating the multipurpose pool of the Elk City Lake in Kansas with serially correlated inflows. The model determines a long‐term operating policy to minimize the expected average annual loss. Using the developed optimal policy to operate the lake from 1967 through 1977 shows a marked reduction in the expected annual losses as compared with the historical operation. The sensitivity of the optimal policy and computation effort to the number of discrete states used is also investigated.

Discrete representation of storage for stochastic reservoir optimization

In explicit stochastic dynamic programing optimization of storage reservoirs the ‘curse of dimensionality’ dictates the adoption of the smallest possible number of discrete states to represent the range of reservoir storage. This pressure makes it imperative to understand clearly the consequences of pushing the limit too far. It is shown that the number of storage states is subject to some absolute constraints and that it must increase linearly with the reservoir storage capacity in order that comparability of results be assured. It is demonstrated, both theoretically and with the aid of a numerical example, that a too coarse discrete storage representation can not only impede accuracy but may completely distort reality in most unexpected ways. Finally, charts are presented giving the numbers of storage states necessary to obtain stationary probabilities of reservoir emptiness and/or fullness with an error e ≤ 0.1% for log normal and normal input distributions.