Nonnegative integral subset representations of integer sets

We consider an integer-subset representation problem motivated by a medical application in radiation therapy. We prove NP-completeness, derive nontrivial bounds, and report on the performance of a greedy heuristic.     

Accurate Depth of Field Simulation in Real Time

We present a new post processing method of simulating depth of field based on accurate calculations of circles of confusion. Compared to previous work, our method derives actual scene depth information directly from the existing depth buffer, requires no specialized rendering passes, and allows easy integration into existing rendering applications. Our implementation uses an adaptive, two‐pass filter, producing a high quality depth of field effect that can be executed entirely on the GPU, taking advantage of the parallelism of modern graphics cards and permitting real time performance when applied to large numbers of pixels.     

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.     

Optimal implementations of UPGMA and other common clustering algorithms

In this work we consider hierarchical clustering algorithms, such as UPGMA, which follow the closest-pair joining scheme. We survey optimal O(n²)-time implementations of such algorithms which use a ‘locally closest’ joining scheme, and specify conditions under which this relaxed joining scheme is equivalent to the original one (i.e. ‘globally closest’).     

Approximation algorithms for minimizing segments in radiation therapy

Intensity modulated radiation therapy (IMRT) is one of the most effective modalities for modern cancer treatment. The key to successful IMRT treatment hinges on the delivery of a two-dimensional discrete radiation intensity matrix using a device called a multileaf collimator (MLC). Mathematically, the delivery of an intensity matrix using an MLC can be viewed as the problem of representing a non-negative integral matrix (i.e., the intensity matrix) by a linear combination of certain special non-negative integral matrices called segments, where each such segment corresponds to one of the allowed states of the MLC. The problem of representing the intensity matrix with the minimum number of segments is known to be NP-complete. In this paper, we present two approximation algorithms for this matrix representation problem. To the best of our knowledge, these are the first algorithms to achieve non-trivial performance guarantees for multi-row intensity matrices.     

Real-time homogenous translucent material editing

This paper presents a novel method for real-time homogenous translucent material editing under fixed illumination. We consider the complete analytic BSSRDF model proposed by Jensen et al. [ [JMLH01] ], including both multiple scattering and single scattering. Our method allows the user to adjust the analytic parameters of BSSRDF and provides high-quality, real-time rendering feedback. Inspired by recently developed Precomputed Radiance Transfer (PRT) techniques, we approximate both the multiple scattering diffuse reflectance function and the single scattering exponential attenuation function in the analytic model using basis functions, so that re-computing the outgoing radiance at each vertex as parameters change reduces to simple dot products. In addition, using a non-uniform piecewise polynomial basis, we are able to achieve smaller approximation error than using bases adopted in previous PRT-based works, such as spherical harmonics and wavelets. Using hardware acceleration, we demonstrate that our system generates images comparable to [ [JMLH01] ]at real-time frame-rates.     

An actor-critic algorithm for constrained Markov decision processes

An actor-critic type reinforcement learning algorithm is proposed and analyzed for constrained controlled Markov decision processes. The analysis uses multiscale stochastic approximation theory and the envelope theorem' of mathematical economics.     

Networks for sorting multitonic sequences

Lee and Batcher have designed networks that efficiently merge k separately provided sorted sequences of known lengths totalling n. We show that the design is still possible, and in fact easier to describe, if we do not make use of the lengths, or even the directions of monotonicity, of the individual sequences—the sequences can be provided in a single undelimited concatenation of length n. The depth of the simplest resulting network to sort sequences that are “k-tonic” and of length n is , generalizing Batcher's 1968 results for the extreme values of k (k=2 corresponding to merging, and k=n/2 corresponding to general sorting).The exposition is self-contained and can serve even as an introduction to sorting networks and Batcher's results.     

MALTING AND BREWING SCIENCE: CHALLENGES AND OPPORTUNITIES*,†

Molecular technologies have been developed for the transformation of barley. These technologies complement current methods of barley breeding. In addition, they offer the potential of altering specific components in barley that affect malting quality and of introducing foreign genes, controlling desirable traits, into barley. Application of genetic engineering to improving malt quality factors such as cell wall degradation, protein modification, starch hydrolysis and flavour stability, is discussed. Limitations to the use of this technology for improving malt-related functional properties of barley components such as cell walls and starch granules are also evaluated. Some possible constraints to the utilization of genetic engineering for malt quality improvements are identified.     

A fast digital Radon transform—An efficient means for evaluating the Hough transform

A fast digital Radon transform based on recursively defined digital straight lines is described, which has the sequential complexity of N² log N additions for an N × N image. This transform can be used to evaluate the Hough transform to detect straight lines in a digital image. Whilst a parallel implementation of the Hough transform algorithm is difficult because of global memory access requirements, the fast digital Radon transform is vectorizable and therefore well suited for parallel computation. The structure of the fast algorithm is shown to be quite similar to the FFT algorithm for decimation in frequency. It is demonstrated that even for sequential computation the fast Radon transform is an attractive alternative to the classical Hough transform algorithm.