Virendra C. Bhavsar

Fractals from z ← zα + c in the complex c-plane

Abstract The self-squared function z ← z 2 + c , has been discussed extensively in the literature for generating fractals. In this article, we consider the generalized transformation function z ← z α + c for generating fractal images. A multitude of interesting, intriguing, and rich families of fractals are generated by changing a single parameter α. Direct relationships are observed between α and the visual characteristics of the fractal images in the c -plane. The exponent α can be represented as α = ± ( η + ϵ ), where η and ϵ are the integer and fractional parts, respectively. It is found that when α is a positive integer number, the resulting image contains lobular structures. The number of major lobes equals ( η − 1). When α is a negative integer number, the generated fractal image is a planetary structure consisting of overlapping central planets surrounded by satellite structures. The number of satellite structures equals ( η + 1). A continuous variation of α between two consecutive integers results into a continuous proportional change between the two limiting fractal images. Several conjuctures about the visual characteristics of the images and the value of α are stated.

Fractal images from z ← zα + c in the complex z-plane

Abstract The transformation function z ← zα + c is used for generating fractal images in the complex z-plane. When α is a positive integer the fractal image has a lobular structure with α major lobes. When α is a negative integer the image has a planetary configuration consisting of a central planet with |α| major satellite structures. For noninteger values of α, additional embryonic lobular/satellite structures, proportional in size to the fractional part of α, are observed. Based on the extensive experimentation, six conjectures regarding the number of major as well as embryonic lobular/satellite structures, their positions, and angular spaces are formulated.

Relationships between selected software measures and latent bug-density: guidelines for improving quality

It is cost-effective for software practitioners to monitor and control the quality of software from the early phases of development. To address this issue, a study aimed at investigating relationships between fifteen predictive design/code measures and bug-density was undertaken. Thirty projects having varied characteristics were chosen. An experimental analysis was performed. It was discovered that most of the metrics considered in the study have strong relationship with bug-density. On the other hand, few metrics do not demonstrate any remarkable relationship. The study provides invaluable lessons that should facilitate software engineers to administer quality from the early phases of development. Some of the major contributions of the work are: investigation of a large number of software projects, consideration of a large number of predictive software measures in one study, comparison of the results of these measures on a common platform, and lessons learned for controlling quality from early stages of software development.

Can a vector space based learning model discover inductive class generalization in a symbolic environment

Abstract We outline a general framework for inductive learning based on the recently proposed evolving transformation system model. Mathematical foundations of this framework include two basic components: a set of operations (on objects) and the corresponding geometry defined by means of these operations. According to the framework, to perform inductive learning in a symbolic environment, the set of operations (class features) may need to be dynamically updated, and this requires that the geometric component allows for an evolving topology. In symbolic systems, as defined in this paper, the geometric component allows for a dynamic change in topology, whereas finite-dimensional numeric systems (vector spaces) can essentially have only one natural topology. This fact should form the basis of a complete formal proof that, in a symbolic setting, the vector space based models, e. g. artificial neural networks, cannot capture inductive generalization. Since the presented argument indicates that the symbolic learning process is more powerful than the numeric process, it appears that only the former should be properly called an inductive learning process.

Proceedings. 19th IEEE International Parallel and Distributed Processing Symposium

HIPS-HPGC 2005 is a full-day workshop, focusing on high-performance grid computing and high-level parallel programming models. The papers deal with component models and service-based systems for grids, emphasizing on experiences with existing systems. Also the papers report on the state of the art of grid applications, both for academic and industrial problems

Towards a weighted-tree similarity algorithm for RNA secondary structure comparison

A tree similarity algorithm for RNA (ribonucleic acid) secondary structure comparison is presented. The elements (nucleotides and nucleotide-pairs) of an RNA secondary structure are represented as normalized node-weighted trees. We show that our weighted tree representations of RNA secondary structures are informative and useful. Based on this unique representation for RNA secondary structure, we propose a weighted-tree similarity algorithm for computing the similarity between RNA secondary structures. The algorithm is justified by computing similarities among several well-known RNA secondary structures. For a given RNA secondary structure, the proposed algorithm provides a ranked list of RNA structures in a database according to their similarity values with the query RNA. Hence, our algorithm is helpful in predicting the functions and the class of a newly discovered RNA

A Performance Evaluation of the Acorn Architecture

ACORN (Agent-based Community Oriented Retrieval Network) is a multi-agent system which uses agents to provide information across internet/intranet networks. In this report, we adapt the ACORN architecture for its performance evaluation on single and multiple servers, running on single and multiple machines. In order to evaluate the performance of ACORN, we introduce a novel concept of multiple autonomous virtual users. The concept of multiple autonomous virtual users and our testing philosophy is applicable to the performance evaluation of other client/server based multi-agent systems. The modified ACORN architecture has been ported to different machines and experimental results on single processors obtained. The processing time required by ACORN is found to be a nonlinear function of the number of agents.

Training artificial neural networks using variable precision incremental communication

We have earlier proposed incremental inter-node communication to reduce the communication cost as well as time of the learning process in artificial neural networks. In the incremental communication, instead of communicating the full magnitude of an input (output) variable of a neuron, only the increment/decrement to the previous value of the variable, using reduced precision, is sent on a communication link. In this paper, a variable precision incremental communication scheme is proposed. Variable precision, which can be implemented in either hardware or software, can further reduce the complexity of intercommunication and speed up the computations in massively parallel computers. This scheme is applied to the multilayer feedforward networks and simulation studies are carried out. The results of our simulations reveal that, regardless of the degree of the complexity of the problems used, variable precision scheme has stable convergence behavior and shows considerable degree of saving in terms of the number of bits used for communications.<<ETX>>

Vectorization of generation of fractals from z ← z2 + c on IBM 3090/180VF

Abstract Algebraic fractals generated from the self-squared transformation function z ← z 2 + c , where z and c are complex quantities, have been discussed extensively in the literature. The process of generating these fractal images, being iterative in nature, is computationally intensive. In this paper we propose and study three vectorization techniques for generating algebraic fractals from z ← z 2 + c , namely, use of long vectors, short vectors, and short vectors with replenishment. The speedups obtained by vectorization of all these techniques on IBM 3090-180VF, which has a vector facility, are presented. It is observed that the technique of using short vectors with replenishment is the best.

iC2mpi: A Platform for Parallel Execution of Graph-Structured Iterative Computations

Parallelization of sequential programs is often daunting because of the substantial development cost involved. Previous solutions have not always been successful, partly because many try to address all types of applications. We propose a platform for parallelization of a class of applications that have similar computational structure, namely graph-structured iterative applications. iC2mpi is a unique proof-of-concept prototype platform that provides relatively easy parallelization of existing sequential programs and facilitates experimentation with static partitioning and dynamic load balancing schemes. We demonstrate with various generic application graph topologies that our platform can produce good performance with very little effort. The iC2mpi platform has a good potential for further performance improvements and for extensions to related classes of application domains.