The stochastic Boltzmann equation and hydrodynamic fluctuations

Based on the assumption of a kinetic equation in space, a stochastic differential equation of the one-particle distribution is derived without the use of the linear approximation. It is just the Boltzmann equation with a Langevin-fluctuating force term. The result is the general form of the linearized Boltzmann equation with fluctuations found by Bixon and Zwanzig and by Fox and Uhlenbeck. It reduces to the general Landau-Lifshitz equations of fluid dynamics in the presence of fluctuations in a similar hydrodynamic approximation to that used by Chapman and Enskog with respect to the Boltzmann equation.This work received financial support from the Alexander von Humboldt Foundation.     

A parallel implementation of the COLUMBUS multireference configuration interaction program

Summary In this work a parallel implementation of the COLUMBUS MRSDCI program system is presented. A coarse grain parallelization approach using message passing via the portable toolkit TCGMSG is used. The program is very well portable and runs on shared memory machines like the Cray Y-MP, Alliant FX/2800 or Convex C2 and on distributed memory machines like the iPSC/860. Further implementations on a network of workstations and on the Intel Touchstone Delta are in progress. Overall, results are quite satisfactory considering the complexity and the prodigious requirements, especially the I/O bandwidth, of MRCI programs in general. For our largest test case we obtain a speedup of a factor of 7.2 on an eight processor Cray Y-MP for that section of the program (hamiltonian matrix times trial vector product) which has been parallelized. The speedup for one complete diagonalization iteration amounts to 5.9. An absolute speed close to 1 GFLOPS is found. Results for the iPSC/860 show that ordinary disk I/O is certainly not sufficient in order to guarantee a satisfactory performance. As a solution for that problem, the implementation of a fully asynchronous distributed-memory model for certain data files is in preparation. On leave from: Bereich Informatik, Universität Leipzig, Augustusplatz 10/11, O-7010 Leipzig, Germany     

Perfect equilibria in stochastic games

We examine stochastic games with finite state and action spaces. For the -discounted case, as well as for the irreducible limiting average case, we show the existence of trembling-hand perfect equilibria and give characterizations of those equilibria. In the final section, we give an example which illustrates that the existence of stationary limiting average equilibria in a nonirreducible stochastic game does not imply the existence of a perfect limiting average equilibrium.Support was provided by the Netherlands Organization for Scientific Research NWO via the Netherlands Foundation for Mathematics SMC, Project 10-64-10.     

On the convergence of the affine-scaling algorithm

The affine-scaling algorithm, first proposed by Dikin, is presently enjoying great popularity as a potentially effective means of solving linear programs. An outstanding question about this algorithm concerns its convergence in the presence of degeneracy. In this paper, we give new convergence results for this algorithm that do not require any non-degeneracy assumption on the problem. In particular, we show that if the stepsize choice of either Dikin or Barnes or Vanderbei, et al. is used, then the algorithm generates iterates that converge at least linearly with a convergence ratio of , wheren is the number of variables and (0,1] is a certain stepsize ratio. For one particular stepsize choice which is an extension of that of Barnes, we show that the cost of the limit point is within O(/(1–)) of the optimal cost and, for sufficiently small (roughly, proportional to how close the cost of the nonoptimal vertices are to the optimal cost), is exactly optimal. We prove the latter result by using an unusual proof technique, that of analyzing the ergodic convergence of the corresponding dual vectors. For the special case of network flow problems with integer data, we show that it suffices to take = 1/(6mC), wherem is the number of constraints andC is the sum of the cost coefficients, to attain exact optimality.This research is partially supported by the U.S. Army Research Office, contract DAAL03-86-K-0171 (Center for Intelligent Control Systems), by the National Science Foundation, grant NSF-ECS-8519058, and by the Science and Engineering Research Board of McMaster University.     

Computation of efficient solutions of discretely distributed stochastic optimization problems

In engineering and economics often a certain vectorx of inputs or decisions must be chosen, subject to some constraints, such that the expected costs (or loss) arising from the deviation between the outputA() x of a stochastic linear systemxA()x and a desired stochastic target vectorb() are minimal. Hence, one has the following stochastic linear optimization problem minimizeF(x)=Eu(A()x b()) s.t.xD, (1) whereu is a convex loss function on ^m , (A(), b()) is a random (m,n + 1)-matrix, E denotes the expectation operator andD is a convex subset of ⁿ . Concrete problems of this type are e.g. stochastic linear programs with recourse, error minimization and optimal design problems, acid rain abatement methods, problems in scenario analysis and non-least square regression analysis.Solving (1), the loss functionu should be exactly known. However, in practice mostly there is some uncertainty in assigning appropriate penalty costs to the deviation between the outputA ()x and the targetb(). For finding in this situation solutions hedging against uncertainty a set of so-called efficient points of (1) is defined and a numerical procedure for determining these compromise solutions is derived. Several applications are discussed.     

KEADA: Identifying Key Classes in Software Systems Using Dynamic Analysis and Entropy-Based Metrics

Software maintenance is indispensable in the software development process. Developers need to spend a lot of time and energy to understand the software when maintaining the software, which increases the difficulty of software maintenance. It is a feasible method to understand the software through the key classes of the software. Identifying the key classes of the software can help developers understand the software more quickly. Existing techniques on key class identification mainly use static analysis techniques to extract software structure information. Such structure information may contain redundant relationships that may not exist when the software runs and ignores the actual interaction times between classes. In this paper, we propose an approach based on dynamic analysis and entropy-based metrics to identify key classes in the Java GUI software system, called KEADA (identifying KEy clAsses based on Dynamic Analysis and entropy-based metrics). First, KEADA extracts software structure information by recording the calling relationship between classes during the software running process; such structure information takes into account the actual interaction of classes. Second, KEADA represents the structure information as a weighted directed network and further calculates the importance of each node using an entropy-based metric OSE (One-order Structural Entropy). Third, KEADA ranks classes in descending order according to their OSE values and selects a small number of classes as the key class candidates. In order to verify the effectiveness of our approach, we conducted experiments on three Java GUI software systems and compared them with seven state-of-the-art approaches. We used the Friedman test to evaluate all approaches, and the results demonstrate that our approach performs best in all software systems.     

一类利用回归关系的计量指标抽样方案

在产品质量判定的抽样检验问题中,当目标指标需用破坏性试验才能得其值时,更为常用的是用非破坏性试验可得量值的协变指标量来预报它。但在产品抽样验收问题上,未能形成理论较为严密的方法,这是由于预报误差这个关键问题的处理尚未解决得好,即给不出抽样方案的功效计算的正确或是近似性较好的公式。本文通过建立合理的数学模型,把对目标指标的质量要求化为对协变指标量的统计要求,从而利用两者的回归关系,结合两种复杂的抽样方案,给出功效函数的计算公式和计算方法,并进行了分析。     

Important unanswered questions—1970

This paper was given as the opening address at the 1970 Albany International Conference on Radiation Effects in Semiconductors, and it attempts to establish a general overview of the field by concentrating on recent research developments and important unanswered questions. The continuing importance of impurity-defect interactions, of microscopic defect identification, and of the necessity for more theoretical calculations are emphasized. The rapid development of the field of ion implantation and its close relationship with radiation effects studies are pointed out. It is predicted that research in compound semiconductors will increase rapidly with close beneficial interaction with ion implantation studies.     

Note on the Design Differentiability of the Static Response of Elastic Structures

This paper provides a new proof of design sensitivity of the static response of some typical structures. These structures (beams, plates, and plane elastic solids) have been described previously. A proof of design sensitivity of the inverse state operator was provided there, and design sensitivity of static response was derived. The proof presented here is simpler and self-contained.     

Joint distribution of direction and length of typical I-segment in a homogeneous random planar tessellation stable under iteration

The paper deals with homogeneous random planar tessellations stable under iteration (random STIT tessellations). The length distribution of the typical I-segment is already known in the isotropic case [8]. In the present paper, the anisotropic case is treated. Then also the direction of the typical I-segment is of interest. The joint distribution of direction and length of the typical I-segment is evaluated. As a first step, the corresponding joint distribution for the so-called typical remaining I-segment is derived. Dedicated to the 80th birthday of Klaus Krickeberg