In this thesis, we focus on design of a highly e cient parallel algorithm for solving the radiosity method. The presented parallel algorithm is based on the progressive radiosity method. We use asynchronous message passing model in combination with communication-thread in order to overlap communication with computation. This approach allows us to take a di erent numerical approach to the proble...

Stein’s method provides a way of bounding the distance of a probability distribution to a target distribution μ. Here we develop Stein’s method for the class of discrete Gibbs measures with a density e , where V is the energy function. Using size bias couplings, we treat an example of Gibbs convergence for strongly correlated random variables due to Chayes and Klein [Helv. Phys. Acta 67 (1994) ...

In 1981, S. Maslov has proposed a new iterative method for solving propositional satissability problems. The 1981{87 results related to this method were described in the present book. In this chapter, we brieey recall the origins of Maslov's method, and describe further results and ideas related to this method. 1. 1979{81: The Origins of S. Maslov's Iterative Method 1.1. Freedom of choice is ne...

We extend the TSE [14] timing analysis algorithm into the symbolic domain, that is, we allow symbolic variables to be used to specify unknown parameters of the model (essentially, unknown delays) and verification algorithms which are capable of identifying not just failure or success, but also the constraints on these symbolic variables which will ensure successful verification. The two main co...

Recently, there have been many studies on artificial neural network models with nonequilibrium dynamics. For example, Ishii et al.’s model, which is an improvement version of Kaneko’s globally coupled map (GCM) model, is called globally coupled map using the symmetric map (SGCM). A new learning method for S-GCM is proposed in this paper. In the proposed method, we use modified saprse matrix for...

Fixed point equations X = f (X) over ω-continuous semirings are a natural mathematical foundation of interprocedural program analysis. Generic algorithms for solving these equations are based on Kleene’s theorem, which states that the sequence 0, f (0), f (f (0)), . . . converges to the least fixed point. However, this approach is often inefficient. We report on recent work in which we extend N...

We give a proof that Total Variation {a,,(.)} < 1 can be replaced by Sup{u,(.)} e 1 in Glimm's method whenever a coordinate system of Riemann invariants is present. The argument is somewhat simpler but in the same spirit as that given by Glimm in his celebrated paper of 1965. 0 1990 Academic Press, Inc. We consider the Cauchy problem u, + F(u), = 0, (1) 4-G 0) = u,(x), (2) where (1) denotes a s...

A parametric approach is developed to the method of S-tree diagrams and its generalization for investigation of the hierarchical substructure of N-body nonlinearly interacting systems (e.g., clusters of galaxies). The introduction of a parametric function allows us to take into account the individual features of the particles which do not have a direct influence on the dynamics of the system bu...

In this report, we present a simple geometric generation principle for the fractal that is obtained when applying Newton's method to nd the roots of a general complex polynomial with real coee-cients. For the case of symmetric polynomials z ? 1, the generation mechanism is derived from rst principles. We discuss the case of a general cubic and are able to give a description of the arising fract...