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Structural reliability problems involving the use of advanced finite-element models of real-world structures are usually defined by limit-states expressed as functions (referred to as limit-state functions) of basic random variables used to characterize the pertinent sources of uncertainty. These limit-state functions define hyper-surfaces (referred to as limit-state surfaces) in the high-dimensional spaces of the basic random variables. The hyper-surface topology is of paramount interest, particularly in the failure domain regions with highest probability density. In fact, classical asymptotic reliability methods, such as the first- and second-order reliability method (FORM and SORM), are based on geometric approximations of the limit-state surfaces near the so-called design point(s) (DP). This paper presents a new efficient tool, the multidimensional visualization in the principal planes (MVPP) method, to study the topology of high-dimensional nonlinear limit-state surfaces (LSSs) near their DPs. The MVPP method allows the visualization, in particularly meaningful two-dimensional subspaces denoted as principal planes, of actual high-dimensional nonlinear limit-state surfaces that arise in both time-invariant and time-variant (mean out-crossing rate computation) structural reliability problems. The MVPP method provides, at a computational cost comparable with SORM, valuable insight into the suitability of FORM/SORM approximations of the failure probability for various reliability problems. Several application examples are presented to illustrate the developed MVPP methodology and the value of the information provided by visualization of the LSS. DOI: 10.1061/(ASCE)EM.1943-7889.0000183 CE Database subject headings: Finite element method; Structural reliability; Limit states; Imaging techniques. Author keywords: Nonlinear finite-element method; Structural reliability analysis; Limit-state surface; Hyper-surface topology; Multidimensional visualization.

Genomic duplication-divergence processes are the primary source of new protein functions and thereby contribute to the evolutionary expansion of functional molecular networks. Yet, it is still unclear to what extent such duplication-divergence processes also restrict by construction the emerging properties of molecular networks, regardless of any specific cellular functions. We address this question, here, focusing on the evolution of protein-protein interaction (PPI) networks. We solve a general duplication-divergence model, based on the statistically necessary deletions of protein-protein interactions arising from stochastic duplications at various genomic scales, from single-gene to whole-genome duplications. Major evolutionary scenarios are shown to depend on two global parameters only: (11 a protein conservation index (M), which controls the evolutionary history of PPI networks, and (ii) a distinct topology index (M') controlling their resulting structure. We then demonstrate that conserved, nondense networks, which are of prime biological relevance, are also necessarily scale-free by construction, irrespective of any evolutionary variations or fluctuations of the model parameters. It is shown to result from a fundamental linkage between individual protein conservation and network topology under general duplication-divergence evolution. By contrast, we find that conservation of network motifs with two or more proteins cannot be indefinitely preserved under general duplication-divergence evolution (independently from any network rewiring dynamics), in broad agreement with empirical evidence between phylogenetically distant species. All in all, these evolutionary constraints, inherent to duplication-divergence processes, appear to have largely controlled the overall topology and scale-dependent conservation of PPI networks, regardless of any specific biological function. evolutionary constraint | scale-free graph | functional motif orthology | statistical model

Despite numerous research efforts in matrix converter-based drives, a study of fault-tolerant topology and control strategy for a matrix converter drive has not been presented in the literature. This paper proposes a matrix converter structure and a modulation technique for the remedial operation in case of opened switch faults and single-phase open circuits. The fault compensation is achieved by reconfiguring the matrix converter topology with the help of a connecting device. Based on the redefined converter structure, a fault-tolerant modulation algorithm is developed to reshape output currents of two unfaulty phases for obtaining continuous operation. The proposed method allows improved system reliability and fault-tolerant capability with no backup leg and no parallel redundancy. Simulation and experimental results are shown to demonstrate the feasibility of the proposed fault-tolerant approach to the matrix converter drives. Index Terms--Fault-tolerant strategy, matrix converter, modulation algorithm.

The hybrid cellular automaton method has been successfully applied to topology optimization using a uniform strain energy density distribution approach. In this work, a new set of design rules is derived from the first-order optimality conditions of a multi-objective problem. In this new formulation, the final topology is derived to minimize both mass and strain energy. In the hybrid cellular automaton algorithm, local design rules based on the cellular automaton paradigm are used to efficiently drive the design to optimality. In addition to the control-based techniques previously introduced, a new ratio technique is derived in this investigation. This work also compares the performance of the control strategies and the ratio technique.

A methodology is developed for shape optimization of thin plate and shell structures undergoing large deflections subject to displacement and system stability constraints. The optimization method considers shape parameters and overall thickness of the structure as the design variables and aims to minimize the total mass of the structure subject to stability or displacement constraint. Two optimality criteria based on Karush-Kuhn-Tucker conditions are developed for mass minimization problems. Optimality criteria are combined with nonlinear corotational analysis to optimize structures with geometric nonlinearity. The method is applied to plate and shallow shell structures. The efficiency of the developed design optimization methodology is compared with that of the gradient-based method of optimization (sequential quadratic programming).

The study of cerebral microvascular networks requires high-resolution images. However, to obtain statistically relevant results, a large area of the brain (several square millimeters) must be analyzed. This leads us to consider huge images, too large to be loaded and processed at once in the memory of a standard computer. To consider a large area, a compact representation of the vessels is required. The medial axis is the preferred tool for this application. To extract it, a dedicated skeletonization algorithm is proposed. Numerous approaches already exist which focus on computational efficiency. However, they all implicitly assume that the image can be completely processed in the computer memory, which is not realistic with the large images considered here. We present in this paper a skeletonization algorithm that processes data locally (in subimages) while preserving global properties (i.e., homotopy). We then show some results obtained on a mosaic of three-dimensional images acquired by confocal microscopy. Index Terms--Chamfer map, digital topology, image mosaic, medial axis, skeleton, topological thinning.

This paper reports on a modification of the ordinary density method for solving problems of structural optimization in magnetic fields. The method uses the homogenization design concept. A simple hole is assumed in an element, and the element density is determined according to the size of the hole. The report compares the results based on the modified density method with the results obtained by the homogenization design method (HDM), with special focus on changing the penalization parameter in the density method. The results show different tendencies in magnetic optimization problems compared to those in elastic optimization problems. The results are also discussed according to the global/local definition of the design domain using the density method as well as HDM. Index Terms--Density method, homogenization design method, magnetic fields, magnetic permeability tensor.

This paper presents a class of n-dimensional interconnection topologies with N = [2.sup.n] nodes which we refer to as n-fastcubes. The node degree of the n-fastcube is n and its diameter is [(n + 1)/2], which is substantially smaller than that of the same size hypercube. Topological properties as well as several routing algorithms for fastcubes are developed. In addition, a new methodology for the design and analysis of fastcubes is employed. This methodology is based on modeling interconnection networks as finite state automata. The inputs to these particular automata are routing sequences. The routing and embedding algorithms developed in this paper produce routing sequences. The main characteristic of routing sequences is their node independence. A node independent routing sequence, p(H), produces a path between any pair of nodes with the Hamming distance of H. Thus, these sequences can be used, without modification, at any node to establish paths in a fastcube. Keywords: Interconnection networks; Hypercube; Topology design; Routing

The notion of fuzzy connectedness captures the idea of "hanging-togetherness" of image elements in an object by assigning a strength of connectedness to every possible path between every possible pair of image elements. This concept leads to powerful image segmentation algorithms based on dynamic programming whose effectiveness has been demonstrated on 1,000s of images in a variety of applications. In the previous framework, a fuzzy connected object is defined with a threshold on the strength of connectedness. In this paper, we introduce the notion of relative connectedness that overcomes the need for a threshold and that leads to more effective segmentations. The central idea is that an object gets defined in an image because of the presence of other co-objects. Each object is initialized by a seed element. An image element c is considered to belong to that object with respect to whose reference image element c has the highest strength of connectedness. In this fashion, objects compete among each other utilizing fuzzy connectedness to grab membership of image elements. We present a theoretical and algorithmic framework for defining objects via relative connectedness and demonstrate utilizing the theory that the objects defined are independent of reference elements chosen as long as they are not in the fuzzy boundary between objects. An iterative strategy is also introduced wherein the strongest relative connected core parts are first defined and iteratively relaxed to conservatively capture the more fuzzy parts subsequently. Examples from medical imaging are presented to illustrate visually the effectiveness of relative fuzzy connectedness. A quantitative mathematical phantom study involving 160 images is conducted to demonstrate objectively the effectiveness of relative fuzzy connectedness. Index Terms--Fuzzy connectedness, image segmentation, object definition, digital topology.

Abstract: Several combinatorial geometry properties of convex compact sets are proved by topological methods. It is proved that if K .sub.1,... ,K .sub.n-1 are convex compacta in R.sup.n , then there is an (n-2)-plane E.sup.n such that for each i=1,2,... ,n-1 there exist three (two orthogonal) hyperplanes containing E and dividing .sub.Ki into six (four) parts of equal volume. It is also proved that for every two bounded continuous distributions of masses in R.sup.3 centrally symmetric with respect to the origin there are three planes dividing both masses into eight equal parts. Bibliography: 9 titles. Article History: Registration Date: 20/10/2004