A swarm pattern transformation method based on macroscopic parameter operations

The work reported in this paper is motivated by biomimetic inspiration - the transformation of patterns. The major issue addressed is the development of feasible methods for transformation based on a macroscopic tool. The general requirement for the feasibility of the transformation method is determined by classifying pattern formation approaches an their characteristics. A formal definition for pattern transformation is provided and four special cases namely, elementary and geometric transformation based on repositioning all and some robotic agents are introduced. A feasible method for transforming patterns geometrically, based on the macroscopic parameter operation of a swarm is considered. The transformation method is applied to a swarm model which lends itself to the transformation technique. Simulation studies are developed to validate the feasibility of the approach, and do indeed confirm the approach.

A framework towards multi-modal fingerprinting scheme for multimedia assets

Fingerprinting is a well known approach for identifying multimedia data without having the original data present but what amounts to its essence or ”DNA”. Current approaches show insufficient deployment of three types of knowledge that could be brought to bear in providing a finger printing framework that remains effective, efficient and can accommodate both the whole as well as elemental protection at appropriate levels of abstraction to suit various Foci of Interest (FoI) in an image or cross media artefact. Thus our proposed framework aims to deliver selective composite fingerprinting that remains responsive to the requirements for protection of whole or parts of an image which may be of particularly interest and be especially vulnerable to attempts at rights violation. This is powerfully aided by leveraging both multi-modal information as well as a rich spectrum of collateral context knowledge including both image-level collaterals as well as the inevitably needed market intelligence knowledge such as customers’ social networks interests profiling which we can deploy as a crucial component of our Fingerprinting Collateral Knowledge. This is used in selecting the special FoIs within an image or other media content that have to be selectively and collaterally protected.

Investigating feasible tools for swarm pattern transformation

Abstract-The work reported in this paper is motivated by the need for developing swarm pattern transformation methodologies. Two methods, namely a macroscopic method and a mathematical method are investigated for pattern transformation. The first method is based on macroscopic parameters while the second method is based on both microscopic and macroscopic parameters. A formal definition to pattern transformation considering four special cases of transformation is presented. Simulations on a physics simulation engine are used to confirm the feasibility of the proposed transformation methods. A brief comparison between the two methods is also presented.

Modeling and simulating a mathematical tool for multi-robot pattern transformation

The work reported in this paper is motivated by the need to investigate general methods for pattern transformation. A formal definition for pattern transformation is provided and four special cases namely, elementary and geometric transformation based on repositioning all and some agents in the pattern are introduced. The need for a mathematical tool and simulations for visualizing the behavior of a transformation method is highlighted. A mathematical method based on the Moebius transformation is proposed. The transformation method involves discretization of events for planning paths of individual robots in a pattern. Simulations on a particle physics simulator are used to validate the feasibility of the proposed method.

Parallel Hybrid Monte Carlo Algorithms for Matrix Computations

In this paper we consider hybrid (fast stochastic approximation and deterministic refinement) algorithms for Matrix Inversion (MI) and Solving Systems of Linear Equations (SLAE). Monte Carlo methods are used for the stochastic approximation, since it is known that they are very efficient in finding a quick rough approximation of the element or a row of the inverse matrix or finding a component of the solution vector. We show how the stochastic approximation of the MI can be combined with a deterministic refinement procedure to obtain MI with the required precision and further solve the SLAE using MI. We employ a splitting A = D – C of a given non-singular matrix A, where D is a diagonal dominant matrix and matrix C is a diagonal matrix. In our algorithm for solving SLAE and MI different choices of D can be considered in order to control the norm of matrix T = D –1C, of the resulting SLAE and to minimize the number of the Markov Chains required to reach given precision. Further we run the algorithms on a mini-Grid and investigate their efficiency depending on the granularity. Corresponding experimental results are presented.

A framework towards a multi-modal fingerprinting scheme for multimedia assets

Fingerprinting is a well known approach for identifying multimedia data without having the original data present but instead what amounts to its essence or 'DNA'. Current approaches show insufficient deployment of various types of knowledge that could be brought to bear in providing a fingerprinting framework that remains effective, efficient and can accommodate both the whole as well as elemental protection at appropriate levels of abstraction to suit various Zones of Interest (ZoI) in an image or cross media artefact. The proposed framework aims to deliver selective composite fingerprinting that is powerfully aided by leveraging both multi-modal information as well as a rich spectrum of collateral context knowledge including both image-level collaterals and also the inevitably needed market intelligence knowledge such as customers' social networks interests profiling which we can deploy as a crucial component of our fingerprinting collateral knowledge.

Monte Carlo methods for matrix computations on the grid

Many scientific and engineering applications involve inverting large matrices or solving systems of linear algebraic equations. Solving these problems with proven algorithms for direct methods can take very long to compute, as they depend on the size of the matrix. The computational complexity of the stochastic Monte Carlo methods depends only on the number of chains and the length of those chains. The computing power needed by inherently parallel Monte Carlo methods can be satisfied very efficiently by distributed computing technologies such as Grid computing. In this paper we show how a load balanced Monte Carlo method for computing the inverse of a dense matrix can be constructed, show how the method can be implemented on the Grid, and demonstrate how efficiently the method scales on multiple processors. (C) 2007 Elsevier B.V. All rights reserved.

A sparse parallel hybrid Monte Carlo algorithm for matrix computations

In this paper we introduce a new algorithm, based on the successful work of Fathi and Alexandrov, on hybrid Monte Carlo algorithms for matrix inversion and solving systems of linear algebraic equations. This algorithm consists of two parts, approximate inversion by Monte Carlo and iterative refinement using a deterministic method. Here we present a parallel hybrid Monte Carlo algorithm, which uses Monte Carlo to generate an approximate inverse and that improves the accuracy of the inverse with an iterative refinement. The new algorithm is applied efficiently to sparse non-singular matrices. When we are solving a system of linear algebraic equations, Bx = b, the inverse matrix is used to compute the solution vector x = B(-1)b. We present results that show the efficiency of the parallel hybrid Monte Carlo algorithm in the case of sparse matrices.

Error analysis of a Monte Carlo algorithm for computing bilinear forms of matrix powers

In this paper we present error analysis for a Monte Carlo algorithm for evaluating bilinear forms of matrix powers. An almost Optimal Monte Carlo (MAO) algorithm for solving this problem is formulated. Results for the structure of the probability error are presented and the construction of robust and interpolation Monte Carlo algorithms are discussed. Results are presented comparing the performance of the Monte Carlo algorithm with that of a corresponding deterministic algorithm. The two algorithms are tested on a well balanced matrix and then the effects of perturbing this matrix, by small and large amounts, is studied.

A review and implementation of swarm pattern formation and transformation models

Purpose: The purpose of this paper is to address a classic problem – pattern formation identified by researchers in the area of swarm robotic systems – and is also motivated by the need for mathematical foundations in swarm systems. Design/methodology/approach: The work is separated out as inspirations, applications, definitions, challenges and classifications of pattern formation in swarm systems based on recent literature. Further, the work proposes a mathematical model for swarm pattern formation and transformation. Findings: A swarm pattern formation model based on mathematical foundations and macroscopic primitives is proposed. A formal definition for swarm pattern transformation and four special cases of transformation are introduced. Two general methods for transforming patterns are investigated and a comparison of the two methods is presented. The validity of the proposed models, and the feasibility of the methods investigated are confirmed on the Traer Physics and Processing environment. Originality/value: This paper helps in understanding the limitations of existing research in pattern formation and the lack of mathematical foundations for swarm systems. The mathematical model and transformation methods introduce two key concepts, namely macroscopic primitives and a mathematical model. The exercise of implementing the proposed models on physics simulator is novel.