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.

Identification of nonlinear systems using generalized kernel models

Nonlinear system identification is considered using a generalized kernel regression model. Unlike the standard kernel model, which employs a fixed common variance for all the kernel regressors, each kernel regressor in the generalized kernel model has an individually tuned diagonal covariance matrix that is determined by maximizing the correlation between the training data and the regressor using a repeated guided random search based on boosting optimization. An efficient construction algorithm based on orthogonal forward regression with leave-one-out (LOO) test statistic and local regularization (LR) is then used to select a parsimonious generalized kernel regression model from the resulting full regression matrix. The proposed modeling algorithm is fully automatic and the user is not required to specify any criterion to terminate the construction procedure. Experimental results involving two real data sets demonstrate the effectiveness of the proposed nonlinear system identification approach.

A fast identification algorithm for Box-Cox transformation based radial basis function neural network

In this letter, a Box-Cox transformation-based radial basis function (RBF) neural network is introduced using the RBF neural network to represent the transformed system output. Initially a fixed and moderate sized RBF model base is derived based on a rank revealing orthogonal matrix triangularization (QR decomposition). Then a new fast identification algorithm is introduced using Gauss-Newton algorithm to derive the required Box-Cox transformation, based on a maximum likelihood estimator. The main contribution of this letter is to explore the special structure of the proposed RBF neural network for computational efficiency by utilizing the inverse of matrix block decomposition lemma. Finally, the Box-Cox transformation-based RBF neural network, with good generalization and sparsity, is identified based on the derived optimal Box-Cox transformation and a D-optimality-based orthogonal forward regression algorithm. The proposed algorithm and its efficacy are demonstrated with an illustrative example in comparison with support vector machine regression.

Modified radial basis function neural network using output transformation

A modified radial basis function (RBF) neural network and its identification algorithm based on observational data with heterogeneous noise are introduced. The transformed system output of Box-Cox is represented by the RBF neural network. To identify the model from observational data, the singular value decomposition of the full regression matrix consisting of basis functions formed by system input data is initially carried out and a new fast identification method is then developed using Gauss-Newton algorithm to derive the required Box-Cox transformation, based on a maximum likelihood estimator (MLE) for a model base spanned by the largest eigenvectors. Finally, the Box-Cox transformation-based RBF neural network, with good generalisation and sparsity, is identified based on the derived optimal Box-Cox transformation and an orthogonal forward regression algorithm using a pseudo-PRESS statistic to select a sparse RBF model with good generalisation. The proposed algorithm and its efficacy are demonstrated with numerical examples.

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.

Generalized matching networks and their properties

In this paper, we introduce two kinds of graphs: the generalized matching networks (GMNs) and the recursive generalized matching networks (RGMNs). The former generalize the hypercube-like networks (HLNs), while the latter include the generalized cubes and the star graphs. We prove that a GMN on a family of k-connected building graphs is -connected. We then prove that a GMN on a family of Hamiltonian-connected building graphs having at least three vertices each is Hamiltonian-connected. Our conclusions generalize some previously known results.

Minimum neighborhood in a generalized cube

Generalized cubes are a subclass of hypercube-like networks, which include some hypercube variants as special cases. Let theta(G)(k) denote the minimum number of nodes adjacent to a set of k vertices of a graph G. In this paper, we prove theta(G)(k) >= -1/2k(2) + (2n - 3/2)k - (n(2) - 2) for each n-dimensional generalized cube and each integer k satisfying n + 2 <= k <= 2n. Our result is an extension of a result presented by Fan and Lin [J. Fan, X. Lin, The t/k-diagnosability of the BC graphs, IEEE Trans. Comput. 54 (2) (2005) 176-184]. (c) 2005 Elsevier B.V. All rights reserved.

Generalized honeycomb torus is Hamiltonian

Generalized honeycomb torus is a candidate for interconnection network architectures, which includes honeycomb torus, honeycomb rectangular torus, and honeycomb parallelogramic torus as special cases. Existence of Hamiltonian cycle is a basic requirement for interconnection networks since it helps map a "token ring" parallel algorithm onto the associated network in an efficient way. Cho and Hsu [Inform. Process. Lett. 86 (4) (2003) 185-190] speculated that every generalized honeycomb torus is Hamiltonian. In this paper, we have proved this conjecture. (C) 2004 Elsevier B.V. All rights reserved.

A lower bound on the size of k-neighborhood in generalized cubes

The determination of the minimum size of a k-neighborhood (i.e., a neighborhood of a set of k nodes) in a given graph is essential in the analysis of diagnosability and fault tolerance of multicomputer systems. The generalized cubes include the hypercube and most hypercube variants as special cases. In this paper, we present a lower bound on the size of a k-neighborhood in n-dimensional generalized cubes, where 2n + 1 <= k <= 3n - 2. This lower bound is tight in that it is met by the n-dimensional hypercube. Our result is an extension of two previously known results. (c) 2005 Elsevier Inc. All rights reserved.

A novel radix-3/9 algorithm for type-III generalized discrete Hartley transform

A novel radix-3/9 algorithm for type-III generalized discrete Hartley transform (GDHT) is proposed, which applies to length-3(P) sequences. This algorithm is especially efficient in the case that multiplication is much more time-consuming than addition. A comparison analysis shows that the proposed algorithm outperforms a known algorithm when one multiplication is more time-consuming than five additions. When combined with any known radix-2 type-III GDHT algorithm, the new algorithm also applies to length-2(q)3(P) sequences.

A numerical scheme for two-dimensional, open channel flows with non-rectangular geometries

An algorithm based on flux difference splitting is presented for the solution of two-dimensional, open channel flows. A transformation maps a non-rectangular, physical domain into a rectangular one. The governing equations are then the shallow water equations, including terms of slope and friction, in a generalized coordinate system. A regular mesh on a rectangular computational domain can then be employed. The resulting scheme has good jump capturing properties and the advantage of using boundary/body-fitted meshes. The scheme is applied to a problem of flow in a river whose geometry induces a region of supercritical flow.

Transformation of plant cells

Plant cells are transformed by bringing them into contact with a a multiplicity of needle-like bodies on which the cells may be impaled. This causes a rupture in the cell wall allowing entry of transforming DNA either from a surrounding liquid medium or of DNA previously bound to or otherwise entrapped in the needle-like projections.