Traces of harmonic functions,capacities, and traces of symmetric Markov processes

We derive explicit isomorphism formulas between weighted Dirichlet integrals for harmonic functions and boundary Dirichlet forms. Applications yield results on traces of Markov processes and convergence quasieverywhere of harmonic functions.     

Validation and verification of social processes within agent-based computational organization models

The use of simulation modeling in computational analysis of organizations is becoming a prominent approach in social science research. However, relying on simulations to gain intuition about social phenomena has significant implications. While simulations may give rise to interesting macro-level phenomena, and sometimes even mimic empirical data, the underlying micro and macro level processes may be far from realistic. Yet, this realism may be important to infer results that are relevant to existing theories of social systems and to policy making. Therefore, it is important to assess not only predictive capability but also explanation accuracy of formal models in terms of the degree of realism reflected by the embedded processes. This paper presents a process-centric perspective for the validation and verification (V&V) of agent-based computational organization models. Following an overview of the role of V&V within the life cycle of a simulation study, emergent issues in agent-based organization model V&V are outlined. The notion of social contract that facilitates capturing micro level processes among agents is introduced to enable reasoning about the integrity and consistency of agent-based organization designs. Social contracts are shown to enable modular compositional verification of interaction dynamics among peer agents. Two types of consistency are introduced: horizontal and vertical consistency. It is argued that such local consistency analysis is necessary, but insufficient to validate emergent macro processes within multi-agent organizations. As such, new formal validation metrics are introduced to substantiate the operational validity of emergent macro-level behavior. Levent Yilmaz is Assistant Professor of Computer Science and Engineering in the College of Engineering at Auburn University and co-founder of the Auburn Modeling and Simulation Laboratory of the M&SNet. Dr. Yilmaz received his Ph.D. and M.S. degrees from Virginia Polytechnic Institute and State University (Virginia Tech). His research interests are on advancing the theory and methodology of simulation modeling, agent-directed simulation (to explore dynamics of socio-technical systems, organizations, and human/team behavior), and education in simulation modeling. Dr. Yilmaz is a member of ACM, IEEE Computer Society, Society for Computer Simulation International, and Upsilon Pi Epsilon. URL: http://www.eng.auburn.edu/~yilmaz     

SPAR: stochastic programming with adversarial recourse

We consider a general adversarial stochastic optimization model. Our model involves the design of a system that an adversary may subsequently attempt to destroy or degrade. We introduce SPAR, which utilizes mixed-integer programming for the design decision and a Markov decision process (MDP) for the modeling of our adversarial phase.     

Theoretical and computational studies of vectorial processes in biomolecular systems

Efficient vectorial processes such as the transduction of bioenergy and signals are characteristics that strikingly distinguish living systems from inanimate materials. Recent developments in biophysical and biochemical techniques have provided new information about the structure, dynamics and interaction of biomolecules involved in vectorial life processes at multiple length and temporal scales. This wealth of data makes it possible to carry out theoretical and computational studied of key mechanistic questions associated with complex life processes at an unprecedented level. Using two “vectorial biomolecular machines”, myosin and cytochrome c oxidase, as examples, we discuss the identification of interesting and biologically relevant questions that require thorough theoretical analysis. Technical challenges and recent progress related to these theoretical investigations are briefly summarized     

On the Equivalence of Multiparameter Gaussian Processes

Our purpose is to characterize the multiparameter Gaussian processes, that is Gaussian sheets, that are equivalent in law to the Brownian sheet and to the fractional Brownian sheet. We survey multiparameter analogues of the Hitsuda, Girsanov and Shepp representations. As an application, we study a special type of stochastic equation with linear noise.      

Large deviation principle for enhanced Gaussian processes

We study large deviation principles for Gaussian processes lifted to the free nilpotent group of step N. We apply this to a large class of Gaussian processes lifted to geometric rough paths. A large deviation principle for enhanced (fractional) Brownian motion, in Hölder- or modulus topology, appears as special case.     

Effect of a thermal radiation field on the γ-luminescence of alkali-silicate glass

We revealed the changes in the γ-luminescence spectra under the influence of a thermal radiation field on high-purity alkali-silicate glasses (I) and those with addition of Fe³⁺ ions (II). We explain the obtained results within the framework of the L-model of edge absorption and electron-hole recombination processes. Samarkand State University, 15, Universitetskii Bul., Samarkand, 703004, Republic of Uzbekistan. Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 65, No. 3, pp. 453–455, May–June, 1998.     

Symmetric form of the Hudson-Parthasarathy stochastic equation

We prove that the Hudson-Parthasarathy equation corresponds, up to unitary equivalence, to the strong resolvent limit of Schrödinger Hamiltonians in Fock space and that the symmetric form of this equation corresponds to the weak limit of the Schrödinger Hamiltonians.Translated fromMatematicheskie Zametki, Vol. 60, No. 5, pp. 726–750, November, 1996.     

Functional Central Limit Theorems for Triangular Arrays of Function-Indexed Processes under Uniformly Integrable Entropy Conditions

Functional central limit theorems for triangular arrays of rowwise independent stochastic processes are established by a method replacing tail probabilities by expectations throughout. The main tool is a maximal inequality based on a preliminary version proved by P. Gaenssler and Th. Schlumprecht. Its essential refinement used here is achieved by an additional inequality due to M. Ledoux and M. Talagrand. The entropy condition emerging in our theorems was introduced by K. S. Alexander, whose functional central limit theorem for so-calledmeasure-like processeswill be also regained. Applications concern, in particular, so-calledrandom measure processeswhich include function-indexed empirical processes and partial-sum processes (with random or fixed locations). In this context, we obtain generalizations of results due to K. S. Alexander, M. A. Arcones, P. Gaenssler, and K. Ziegler. Further examples include nonparametric regression and intensity estimation for spatial Poisson processes.     

Multiple local solutions to nonlinear control processes

We use the topological tool of Nielsen fixed-point theory to study the controllability of perturbed linear control processes whose control space can be reduced to a finite-dimensional one. These methods produce a lower bound on the number of controls that achieve a given target. We concentrate particularly on the case where the perturbation has sublinear growth, and we exhibit examples of multiple controls of various types that are detected by the Nielsen theory method.This research was partly supported by the Research Grant Teoria del Controllo dei Sistemi Dinamici, Ministero della Pubblica Istruzione, Roma, Italy.