Building the foundations for a market-oriented planning system in Bulgaria

Planning is highly conditioned by the relationships between the market, state and politics. This becomes particularly clear in looking at the changes taking place in the countries of the former Communist block as they attempt to establish a new set of relationships. The old power structures have been dislodged and old laws discarded. This paper examines the situation in Bulgaria and explores the preconditions for setting up a new planning system there. The first section outlines the political changes since 1989 and shows how political instability has effected the pace of change. The establishment of a market in land and property is a second precondition for the planning system there and moves in this direction are presented, including restitution policies. Finally the issues raised by the early attempts towards a new planning system are discussed. This paper is the first of a series looking at the countries of Eastern Europe and the author would welcome comments from others working in this field.

Exact error estimates and optimal randomized algorithms for integration

Exact error estimates for evaluating multi-dimensional integrals are considered. An estimate is called exact if the rates of convergence for the low- and upper-bound estimate coincide. The algorithm with such an exact rate is called optimal. Such an algorithm has an unimprovable rate of convergence. The problem of existing exact estimates and optimal algorithms is discussed for some functional spaces that define the regularity of the integrand. Important for practical computations data classes are considered: classes of functions with bounded derivatives and Holder type conditions. The aim of the paper is to analyze the performance of two optimal classes of algorithms: deterministic and randomized for computing multidimensional integrals. It is also shown how the smoothness of the integrand can be exploited to construct better randomized algorithms.

Parallel Monte Carlo approach for integration of the rendering equation

This paper is addressed to the numerical solving of the rendering equation in realistic image creation. The rendering equation is integral equation describing the light propagation in a scene accordingly to a given illumination model. The used illumination model determines the kernel of the equation under consideration. Nowadays, widely used are the Monte Carlo methods for solving the rendering equation in order to create photorealistic images. In this work we consider the Monte Carlo solving of the rendering equation in the context of the parallel sampling scheme for hemisphere. Our aim is to apply this sampling scheme to stratified Monte Carlo integration method for parallel solving of the rendering equation. The domain for integration of the rendering equation is a hemisphere. We divide the hemispherical domain into a number of equal sub-domains of orthogonal spherical triangles. This domain partitioning allows to solve the rendering equation in parallel. It is known that the Neumann series represent the solution of the integral equation as a infinity sum of integrals. We approximate this sum with a desired truncation error (systematic error) receiving the fixed number of iteration. Then the rendering equation is solved iteratively using Monte Carlo approach. At each iteration we solve multi-dimensional integrals using uniform hemisphere partitioning scheme. An estimate of the rate of convergence is obtained using the stratified Monte Carlo method. This domain partitioning allows easy parallel realization and leads to convergence improvement of the Monte Carlo method. The high performance and Grid computing of the corresponding Monte Carlo scheme are discussed.

Parallel Monte Carlo sampling scheme for sphere and hemisphere

The sampling of certain solid angle is a fundamental operation in realistic image synthesis, where the rendering equation describing the light propagation in closed domains is solved. Monte Carlo methods for solving the rendering equation use sampling of the solid angle subtended by unit hemisphere or unit sphere in order to perform the numerical integration of the rendering equation. In this work we consider the problem for generation of uniformly distributed random samples over hemisphere and sphere. Our aim is to construct and study the parallel sampling scheme for hemisphere and sphere. First we apply the symmetry property for partitioning of hemisphere and sphere. The domain of solid angle subtended by a hemisphere is divided into a number of equal sub-domains. Each sub-domain represents solid angle subtended by orthogonal spherical triangle with fixed vertices and computable parameters. Then we introduce two new algorithms for sampling of orthogonal spherical triangles. Both algorithms are based on a transformation of the unit square. Similarly to the Arvo's algorithm for sampling of arbitrary spherical triangle the suggested algorithms accommodate the stratified sampling. We derive the necessary transformations for the algorithms. The first sampling algorithm generates a sample by mapping of the unit square onto orthogonal spherical triangle. The second algorithm directly compute the unit radius vector of a sampling point inside to the orthogonal spherical triangle. The sampling of total hemisphere and sphere is performed in parallel for all sub-domains simultaneously by using the symmetry property of partitioning. The applicability of the corresponding parallel sampling scheme for Monte Carlo and Quasi-D/lonte Carlo solving of rendering equation is discussed.

Parallel performance and scalability experiments with the Danish Eulerian Model on the EPCC supercomputers

The Danish Eulerian Model (DEM) is a powerful air pollution model, designed to calculate the concentrations of various dangerous species over a large geographical region (e.g. Europe). It takes into account the main physical and chemical processes between these species, the actual meteorological conditions, emissions, etc.. This is a huge computational task and requires significant resources of storage and CPU time. Parallel computing is essential for the efficient practical use of the model. Some efficient parallel versions of the model were created over the past several years. A suitable parallel version of DEM by using the Message Passing Interface library (AIPI) was implemented on two powerful supercomputers of the EPCC - Edinburgh, available via the HPC-Europa programme for transnational access to research infrastructures in EC: a Sun Fire E15K and an IBM HPCx cluster. Although the implementation is in principal, the same for both supercomputers, few modifications had to be done for successful porting of the code on the IBM HPCx cluster. Performance analysis and parallel optimization was done next. Results from bench marking experiments will be presented in this paper. Another set of experiments was carried out in order to investigate the sensitivity of the model to variation of some chemical rate constants in the chemical submodel. Certain modifications of the code were necessary to be done in accordance with this task. The obtained results will be used for further sensitivity analysis Studies by using Monte Carlo simulation.

A collaborative working environment for a large scale environmental model

Large scientific applications are usually developed, tested and used by a group of geographically dispersed scientists. The problems associated with the remote development and data sharing could be tackled by using collaborative working environments. There are various tools and software to create collaborative working environments. Some software frameworks, currently available, use these tools and software to enable remote job submission and file transfer on top of existing grid infrastructures. However, for many large scientific applications, further efforts need to be put to prepare a framework which offers application-centric facilities. Unified Air Pollution Model (UNI-DEM), developed by Danish Environmental Research Institute, is an example of a large scientific application which is in a continuous development and experimenting process by different institutes in Europe. This paper intends to design a collaborative distributed computing environment for UNI-DEM in particular but the framework proposed may also fit to many large scientific applications as well.

Examining random number generators used in stochastic iteration algorithms

This paper investigates random number generators in stochastic iteration algorithms that require infinite uniform sequences. We take a simple model of the general transport equation and solve it with the application of a linear congruential generator, the Mersenne twister, the mother-of-all generators, and a true random number generator based on quantum effects. With this simple model we show that for reasonably contractive operators the theoretically not infinite-uniform sequences perform also well. Finally, we demonstrate the power of stochastic iteration for the solution of the light transport problem.