Ergodicity of filtering process by vanishing discount approach

A new approach to study ergodicity of filtering processes is presented. It is based on the vanishing discount approach to discounted functional of filtering process. We show that limit superior of the Cesaro averages of the functionals is the same for all initial conditions from which the uniqueness of invariant measures of filtering processes follows. The approach is based on certain assumption for which we provide a sufficient condition using concavity arguments. In addition we show the existence of solutions to the Poisson equation corresponding to filtering process with concave functional. The assumptions are then extended to the controlled case and using similar concave arguments we obtain the existence of solutions to the Bellman equation corresponding to partially observed average cost per unit time problem.     

Hybrid numerical scheme for time-evolving wave fields

Many problems in geophysics, acoustics, elasticity theory, cancer treatment, food process control and electrodynamics involve study of wave field synthesis (WFS) in some form or another. In the present work, modelling of wave propagation phenomena is studied as a static problem, using finite element method and treating time as an additional spatial dimension. In particular, WFS problems are analysed using discrete methods. It is shown that a fully finite element-based scheme is very natural and effective method for the solution of such problems. Distributed WFS in the context of two-dimensional problems is outlined and incorporation of any geometric or material non-linearities is shown to be straightforward. This has significant implications for problems in geophysics or biological media, where material inhomogeneities are quite prevalent. Numerical results are presented for several problems referring to media with material inhomogeneities and predefined absorption profiles. The method can be extended to three-dimensional problems involving anisotropic media properties in a relatively straightforward manner. Copyright © 2006 John Wiley & Sons, Ltd.     

The problem of demodulating across argument and literal boundaries

This article is the twenty-fourth of a series of articles discussing various open research problems in automated reasoning. The problem proposed for research asks one to find an appropriate theory for modulating across argument and across literal boundaries. Because demodulation has proved so useful—is most cases, even crucial—to automated reasoning, extending this concept to permit canonicalization to be applied at the predicate and at the clause and subclause levels merits exploration. For evaluating a proposed solution to this research problem, we suggest problems from mathematics, logic, program verification, database inquiry, and the world of puzzles.This work was supported by the Applied Mathematical Sciences subprogram of the Office of Energy Research, U.S. Department of Energy, under Contract W-31-109-Eng-38.     

Metaheuristic downhill simplex method in combinatorial optimization

The concept of combinatorial objects is formalized. It allows strict definition of a combinatorial optimization problem (COP). An efficient metaheuristic method to solve COPs (H-method) is considered. It includes stochastic local search algorithms as a built-in procedure. A parallel implementation of the H-method is set forth and analyzed. The results from a numerical experiment and solution of some well-known COPs on personal computers and on the SKIT cluster supercomputer are presented. The study was supported by INTAS (Project 06-1000017-8909). __________ Translated from Kibernetika i Sistemnyi Analiz, No. 6, pp. 70–79, November–December 2007.     

Multicast key distribution schemes based on Stinson-Van Trung designs

The efficiency characteristics of multicast key distribution schemes based on (v, b, r, λ)-designs are investigated. The stability and connectivity of such designs are estimated. These estimates generalize and enhance the well-known estimates for the efficiency characteristics of multicast key distribution schemes based on incomplete block designs. __________ Translated from Kibernetika i Sistemnyi Analiz, No. 3, pp. 100–111, May–June 2007.     

Mathematical modeling and optimization of intratumor drug transport

A pseudohyperbolic problem of optimal control of intratumoral drug distribution is formulated. It takes into account the heterogeneity of tumor tissues and effects of convection diffusion in a fissured porous medium. A mathematical model constructed and the corresponding optimal control problem are shown to be correct. __________ Translated from Kibernetika i Sistemnyi Analiz, No. 6, pp. 147–154, November–December 2007.     

A method for the efficient prioritization of infrastructure renewal projects

The infrastructure renewal program at MIT consists of a large number of projects with an estimated budget that could approach $1 billion. Infrastructure renewal at the Massachusetts Institute of Technology (MIT) is the process of evaluating and investing in the maintenance of facility systems and basic structure to preserve existing campus buildings. The selection and prioritization of projects must be addressed with a systematic method for the optimal allocation of funds and other resources. This paper presents a case study of a prioritization method utilizing multi-attribute utility theory. This method was developed at MIT's Department of Nuclear Engineering and was deployed by the Department of Facilities after appropriate modifications were implemented to address the idiosyncrasies of infrastructure renewal projects and the competing criteria and constraints that influence the judgment of the decision-makers. Such criteria include minimization of risk, optimization of economic impact, and coordination with academic policies, programs, and operations of the Institute. A brief overview of the method is presented, as well as the results of its application to the prioritization of infrastructure renewal projects. Results of workshops held at MIT with the participation of stakeholders demonstrate the feasibility of the prioritization method and the usefulness of this approach.     

Smaller superconcentrators of density 28

An N-superconcentrator is a directed, acyclic graph with N input nodes and N output nodes such that every subset of the inputs and every subset of the outputs of same cardinality can be connected by node-disjoint paths. It is known that linear-size and bounded-degree superconcentrators exist. Here it is proved that such superconcentrators exist (by a random construction of certain expander graphs as building blocks) having density 28 (where the density is the number of edges divided by N). The best known density before this paper was 34.2 [U. Schöning, Construction of expanders and superconcentrators using Kolmogorov complexity, J. Random Structures Algorithms 17 (2000) 64-77] or 33 [L.A. Bassalygo, Personal communication, 2004].     

A note on the first-passage problem and VanMarcke’s approximation — short communication

Given a scalar, stationary, Markov process, this short communication presents a closed-form solution for the first-passage problem for a fixed threshold b. The derivation is based on binary processes and the general formula of Siegert [Siegert AJF. On the first-passage time probability problem. Physical Review 1951; 81:617–23]. The relation for the probability density function of the first-passage time is identical to the commonly used formula that was derived by VanMarcke [VanMarcke E. On the distribution of the first-passage time for normal stationary random processes. Journal of Applied Mechanics ASME 1975; 42:215–20] for Gaussian processes. The present derivation is based on more general conditions and reveals the criteria for the validity of the approximation. Properties of binary processes are also used to derive a hierarchy of upper bounds for any scalar process.     

Using what we know: Consequences of intentionally retrieving gist versus item-specific information.

The effect of a prior gist-based versus item-specific retrieval orientation on recognition of objects and words was examined. Prior item-specific retrieval increased item-specific recognition of episodically related but not previously tested objects relative to both conceptual- and perceptual-gist retrieval. An item-specific retrieval advantage also was found when the stimuli were words (synonyms) rather than objects but not when participants overtly named objects during gist-based recognition testing, which suggests that they did not always label objects under general gist-retrieval instructions. Unlike verbal overshadowing, labeling objects during recognition attenuated (but did not eliminate) test- and interference-related forgetting. A full understanding of how retrieval affects subsequent memory, even for events or facts that are not themselves retrieved, must take into account the specificity with which that retrieval occurs. (PsycINFO Database Record (c) 2010 APA, all rights reserved)