Computer Science Algorithms Research Articles

Characterizing complex particle morphologies through shape matching: Descriptors, applications, and algorithms

Many standard structural quantities, such as order parameters and correlation functions, exist for common condensed matter systems, such as spherical and rod-like particles. However, these structural quantities are often insufficient for characterizing the unique and highly complex structures often encountered in the emerging field of nano and microscale self-assembly, or other disciplines involving complex structures such as computational biology. Computer science algorithms known as “shape matching” methods pose a unique solution to this problem by providing robust metrics for quantifying the similarity between pairs of arbitrarily complex structures. This pairwise matching operation, either implicitly or explicitly, lies at the heart of most standard structural characterization schemes for particle systems. By substituting more robust “shape descriptors” into these schemes we extend their applicability to structures formed from more complex building blocks. Here, we describe several structural characterization schemes and shape descriptors that can be used to obtain various types of structural information about particle systems. We demonstrate the application of shape matching algorithms to a variety of example problems, for topics including local and global structure identification and classification, automated phase diagram mapping, and the construction of spatial and temporal correlation functions. The methods are applicable to a wide range of systems, both simulated and experimental, provided particle positions are known or can be accurately imaged.

On aggregation of normed structures

In 1981, Borsik and Doboš studied in depth the problem of how to merge, by means of a function, a collection (not necessarily finite) of distance spaces in order to obtain a single one as a result [J. Borsik, J. Doboš, On a product of metric spaces, Math. Slovaca 31 (1981) 193–205]. Later on, Herburt and Moszyńska studied the same problem for the case of normed linear spaces, inspired by the fact that every norm induces in a natural way a distance on a linear space, and analyzed the relationship between the both aforenamed problems [I. Herburt, M. Moszyńska, On metric products, Colloq. Math. 62 (1991) 121–133]. More recently, Romaguera and Schellekens introduced a mathematical approach, based on the notions of asymmetric distance and asymmetric normed linear space, which is suitable for the complexity analysis of programs and algorithms in Computer Science [S. Romaguera, M. Schellekens, Quasi-metric properties of complexity spaces, Topology Appl. 98 (1999) 311–322]. In this paper, motivated by the importance of the information fusion techniques in Artificial Intelligence and by the utility of asymmetric distances and asymmetric norms in Computer Science, we study the Herburt and Moszyńska problem for asymmetric normed linear spaces. In particular we give a general description of how to combine a collection (not necessarily finite) of asymmetric normed linear spaces in order to obtain a single one as output and, in addition, we clear up the relationship between this problem and its analogous of combining asymmetric distance spaces which has been already explored by Mayor and Valero [G. Mayor, O. Valero, Aggregation of asymmetric distances in computer science, Inform. Sci. 180 (2010) 803–812]. Furthermore, it is shown that the asymmetric norms employed, in the spirit of Romaguera and Schellekens, in complexity analysis can be retrieved as a particular case of the developed theory. The last fact opens the possibility of applying a wide range of properties from the general aggregation theory in Artificial Intelligence to the complexity analysis of programs and algorithms in Computer Science.

Certain summation formulas involving harmonic numbers and generalized harmonic numbers

Abstract Harmonic numbers and generalized harmonic numbers have been studied since the distant past and involved in a wide range of diverse fields such as analysis of algorithms in computer science, various branches of number theory, elementary particle physics and theoretical physics. Here we aim at presenting further interesting identities about certain finite or infinite series involving harmonic numbers and generalized harmonic numbers by applying an algorithmic method to a known summation formula for the hypergeometric function 5 F 4 (1).

Convex Geometry and its Applications

The geometry of convex domains in Euclidean space plays a central role in several branches of mathematics: functional and harmonic analysis, the theory of PDE, linear programming and, increasingly, in the study of other algorithms in computer science. High-dimensional geometry, both the discrete and convex branches of it, has experienced a striking series of developments in the past 10 years. Several examples were presented at this meeting, for example the work of Rudelson et al. on conjunction matrices and their relation to confidential data analysis, that of Litvak et al. on remote sensing and a series of results by Nazarov and Ryabogin et al. on Mahler’s conjecture for the volume product of domains and their polars.

Formal Correctness Proof for DPLL Procedure

The DPLL procedure for the SAT problem is one of the fundamental algorithms in computer science, with many applications in a range of domains, including software and hardware verification. Most of the modern SAT solvers are based on this procedure, extending it with different heuristics. In this paper we present a formal proof that the DPLL procedure is correct. As far as we know, this is the first such proof. The proof was formalized within the Isabelle/Isar proof assistant system. This proof adds to the growing body of formalized mathematical knowledge and it also provides a number of lemmas relevant for proving correctness of modern SAT and SMT solvers.

Fast Four‐Way Parallel Radix Sorting on GPUs

Abstract Efficient sorting is a key requirement for many computer science algorithms. Acceleration of existing techniques as well as developing new sorting approaches is crucial for many real‐time graphics scenarios, database systems, and numerical simulations to name just a few. It is one of the most fundamental operations to organize and filter the ever growing massive amounts of data gathered on a daily basis. While optimal sorting models for serial execution on a single processor exist, efficient parallel sorting remains a challenge. In this paper, we present a hardware‐optimized parallel implementation of the radix sort algorithm that results in a significant speed up over existing sorting implementations. We outperform all known General Processing Unit (GPU) based sorting systems by about a factor of two and eliminate restrictions on the sorting key space. This makes our algorithm not only the fastest, but also the first general GPU sorting solution.

Combinatorial algorithms for computational science and engineering

We discuss recent activities in the SciDAC Applied Mathematics Institute for Combinatorial Scientific Computing and Petascale Simulations (CSCAPES).

A cross-domain visual learning engine for interactive generation of instructional materials

We present the design and development of a Visual Learning Engine, a tool that can form the basis for interactive development of visually rich teaching and learning modules across multiple disciplines. The engine has three key features that makes it powerful and cross-disciplinary, (1) it is based on a finite state machine model, that supports concepts presented in any defined sequence, (2) instructional modules are designed and generated interactively using graphical interface widgets, facilitating non-programmers to use the system, and (3) ability to simultaneously present concepts and their visual representation that allows for a more intuitive and exploratory learning experience. We demonstrate a prototype of the learning engine by testing it on examples from Computer Science(sorting)algorithms, recursion) and Electrical Engineering (signal manipulations).

Leaf‐sequencing for intensity‐modulated arc therapy using graph algorithms

Intensity-modulated arc therapy (IMAT) is a rotational IMRT technique. It uses a set of overlapping or nonoverlapping arcs to create a prescribed dose distribution. Despite its numerous advantages, IMAT has not gained widespread clinical applications. This is mainly due to the lack of an effective IMAT leaf-sequencing algorithm that can convert the optimized intensity patterns for all beam directions into IMAT treatment arcs. To address this problem, we have developed an IMAT leaf-sequencing algorithm and software using graph algorithms in computer science. The input to our leaf-sequencing software includes (1) a set of (continuous) intensity patterns optimized by a treatment planning system at a sequence of equally spaced beam angles (typically 10 degrees apart), (2) a maximum leaf motion constraint, and (3) the number of desired arcs, k. The output is a set of treatment arcs that best approximates the set of optimized intensity patterns at all beam angles with guaranteed smooth delivery without violating the maximum leaf motion constraint. The new algorithm consists of the following key steps. First, the optimized intensity patterns are segmented into intensity profiles that are aligned with individual MLC leaf pairs. Then each intensity profile is segmented into k MLC leaf openings using a k-link shortest path algorithm. The leaf openings for all beam angles are subsequently connected together to form 1D IMAT arcs under the maximum leaf motion constraint using a shortest path algorithm. Finally, the 1D IMAT arcs are combined to form IMAT treatment arcs of MLC apertures. The performance of the implemented leaf-sequencing software has been tested for four treatment sites (prostate, breast, head and neck, and lung). In all cases, our leaf-sequencing algorithm produces efficient and highly conformal IMAT plans that rival their counterpart, the tomotherapy plans, and significantly improve the IMRT plans. Algorithm execution times ranging from a few seconds to 2 min are observed on a laptop computer equipped with a 2.0 GHz Pentium M processor.

Three‐dimensional reconstruction of seed implants by randomized rounding and visual evaluation

The development of efficient 3D seed reconstruction algorithms is an ongoing and vivid research topic. Since the 1980s many publications about seed assignment were published. In this paper a novel mathematical approach is described to solve the 3D assignment problem for the reconstruction of seeds with radiographs: we present a fast linear programming approach together with afterwards applying the so-called randomized rounding scheme to compute good (possibly partial) assignments. We apply a visualization software that allows user interaction to check the solution given by the algorithm and to augment partial assignments. The second step is justified as the randomized algorithm already returns optimal solutions is many cases, and in cases with partial assignments it fails to match only a very small number of seed images. Our algorithm transfers ideas from recent breakthrough research work on the design of efficient randomized algorithms in discrete optimization and computer science to the seed reconstruction problem.

Observations in using parallel and sequential evolutionary algorithms for automatic software testing

In this paper we analyze the application of parallel and sequential evolutionary algorithms (EAs) to the automatic test data generation problem. The problem consists of automatically creating a set of input data to test a program. This is a fundamental step in software development and a time consuming task in existing software companies. Canonical sequential EAs have been used in the past for this task. We explore here the use of parallel EAs. Evidence of greater efficiency, larger diversity maintenance, additional availability of memory/CPU, and multi-solution capabilities of the parallel approach, reinforce the importance of the advances in research with these algorithms. We describe in this work how canonical genetic algorithms (GAs) and evolutionary strategies (ESs) can help in software testing, and what the advantages are (if any) of using decentralized populations in these techniques. In addition, we study the influence of some parameters of the proposed test data generator in the results. For the experiments we use a large benchmark composed of twelve programs that includes fundamental algorithms in computer science.

Computer-Aided Model Based Analysis for Design and Operation of a Copolymerization Process

The advances in computer science and computational algorithms for process modelling, process simulation, numerical methods and design/synthesis algorithms, makes it advantageous and helpful to employ computer-aided modelling systems and tools for integrated process analysis. This is illustrated through the study of a copolymerization process, where operational problems due to their complex nonlinear behaviour are usually encountered, indicating thereby, the need for the development of an appropriate process model that can describe the dynamic behaviour over the complete range of conversion. This will allow analysis of the process behaviour, contribute to a better understanding of the polymerization process, help to avoid unsafe conditions of operation, and to develop operational and optimizing control strategies. In this work, through a computer-aided modeling system ICAS-MoT, two first-principles models have been investigated with respect to design and operational issues for solution copolymerization reactors in general, and for the methyl methacrylate/vinyl acetate system in particular. The Model 1 is taken from literature and is commonly used for low conversion region, while the Model 2 has been derived in this work and covers the complete range of conversion. The performances of the two models are compared with respect to the steady state and dynamic behaviour of the polymerization process. The model analyses highlight the influence of the reaction mechanism, the transport phenomena, the process design and conditions of operation on the polymer grade and the production rate.

The Optimality of a Simple Market Mechanism

Strategic behavior in a finite market can cause inefficiency in the allocation, and market mechanisms differ in how successfully they limit this inefficiency. A method for ranking algorithms in computer science is adapted here to rank market mechanisms according to how quickly inefficiency diminishes as the size of the market increases. It is shown that trade at a single market-clearing price in the k-double auction is worst-case asymptotic optimal among all plausible mechanisms: evaluating mechanisms in their least favorable trading environments for each possible size of the market, the k-double auction is shown to force the worst-case inefficiency to zero at the fastest possible rate.

Phase transition in a random fragmentation problem with applications to computer science

We study a fragmentation problem where an initial object of size x is broken into m random pieces provided x>x_0 where x_0 is an atomic cut-off. Subsequently the fragmentation process continues for each of those daughter pieces whose sizes are bigger than x_0. The process stops when all the fragments have sizes smaller than x_0. We show that the fluctuation of the total number of splitting events, characterized by the variance, generically undergoes a nontrivial phase transition as one tunes the branching number m through a critical value m=m_c. For m<m_c, the fluctuations are Gaussian where as for m>m_c they are anomalously large and non-Gaussian. We apply this general result to analyze two different search algorithms in computer science.

Data Structures in the Design of Interfaces

Computer science algorithms can be used to improve user interfaces. Using data structures as a source of design ideas, a new interface was constructed for a cellular telephone handset. Once implemented, a user experiment was conducted which showed that predicted improvements in usability were confirmed with real users doing realistic tasks.

Algorithmic aspects in speech recognition

Speech recognition is an area with a considerable literature, but there is little discussion of the topic within the computer science algorithms literature. Many computer scientists, however, are interested in the computational problems of speech recognition. This paper presents the field of speech recognition and describes some of its major open problems from an algorithmic viewpoint. Our goal is to stimulate the interest of algorithm designers and experimenters to investigate the algorithmic problems of effective automatic speech recognition.

Critical Behavior in the Satisfiability of Random Boolean Expressions

Determining the satisfiability of randomly generated Boolean expressions with k variables per clause is a popular test for the performance of search algorithms in artificial intelligence and computer science. It is known that for k = 2, formulas are almost always satisfiable when the ratio of clauses to variables is less than 1; for ratios larger than 1, the formulas are almost never satisfiable. Similar sharp threshold behavior is observed for higher values of k. Finite-size scaling, a method from statistical physics, can be used to characterize size-dependent effects near the threshold. A relationship can be drawn between thresholds and computational complexity.

Multiprocessors and run‐time compilation

AbstractRun‐time preprocessing plays a major role in many efficient algorithms in computer science, as well as playing an important role in exploiting multiprocessor architectures. We give examples that elucidate the importance of run‐time preprocessing and show how these optimizations can be integrated into compilers. To support our arguments, we describe transformations implemented in prototype multiprocessor compilers and present benchmarks from the iPSC2/860, the CM‐2 and the Encore Multimax/320.