Symmetric Interconnection Research Articles

Depressed MEG causality analysis based on polynomial kernel Granger causality

In this study, we employ the Granger causality of a polynomial kernel to identify the coupling causality of depressed magnetoencephalography (MEG). We collect MEG under positive, neutral, and negative emotional stimuli and focus on the β-band activities. According to test results, depressed people display stronger left–right symmetrical interconnection in their prefrontal and occipital lobes under nonpositive stimuli(namely neutral and negative stimuli), indicating that they are more sensitive to nonpositive stimuli. The intensity of the right occipital information flow is higher in depressed people. We also see the Granger causality index increased in the occipital–frontal areas of depressed patients under negative stimuli. In general, detecting the polynomial kernel Granger causality of the MEG can effectively characterize the strength of the interconnected brain regions in depressed patients, which can be used as a clinical diagnosis aid.

Subspace Aided Fault-tolerant Control for Distributed Homogeneous Systems with Symmetric Interconnection Pattern

Subspace Aided Fault-tolerant Control for Distributed Homogeneous Systems with Symmetric Interconnection Pattern

Electromechanical behavior of 3-3 piezoelectric star-shaped metamaterial with four types of connection

This study presents the complete electromechanical properties of 3-3 piezoelectric metamaterial based on variants of star-shaped cellular structure. Four types of three-dimensional piezoelectric star-shaped metamaterial (3D PSSM) with different connection modes (with symmetric interconnects, with asymmetric horizontal interconnects, with asymmetric vertical interconnects and without any interconnects) are introduced. Periodic boundary conditions are applied to unit cell of 3D PSSM. And the finite element analysis is implemented to investigate the effect of different structural parameters and poling directions (longitudinal and transverse) on the effective electromechanical response. Compared with the monolithic piezoelectric materials, different connection modes of the 3D PSSM show different combinations of enhanced electromechanical response and figures of merit. For example, longitudinally poled 3D PSSM with symmetric interconnects has both higher hydrostatic strain coefficient (dh) and hydrostatic figure of merit (dh•gh), and lower acoustic impedance (Z), indicating it is more suitable for the design of hydrophones; longitudinally poled 3D PSSM with asymmetric interconnects has higher piezoelectric coupling constant (kt), indicating that this structure is more suitable for the design of energy harvesters.

Electromechanical behavior of piezoelectric metamaterial with negative Poisson’s ratios for three kinds of connection

In this paper, the complete electromechanical properties of the cellular-materials-based piezoelectric metamaterial are obtained by using micromechanical modeling method on the basis of the finite element. This study considers the piezoelectric star-shaped cellular structures (PSSCSs) with three connection modes (with symmetric interconnects, with asymmetric interconnects, and without any interconnects) and two poling directions (longitudinal and transverse). The representative volume units of three types of PSSCSs are established respectively, and the finite element analysis is implemented to the effect of different structural length parameters on the effective electromechanical response and the applicability of specific engineering applications. Compared with the monolithic piezoelectric materials, the PSSCSs show an enhanced performance combination. Besides, the results show that PSSCSs have adjustable electromechanical properties.

BSN MOT: A Fast and Cost-efficient Optoelectronic Architecture

Recently, an efficient recursive and symmetrical optoelectronic interconnection network based on biswapped framework named “Biswapped-Hyper Hexa-Cell (BSN HHC)” is reported. In spite of containing a prime advantage concerning network diameter compared to its competitive Biswapped-Mesh (BSN Mesh) optoelectronic architecture; a major limitation of the network is its high cost. In a search for a competitive alternative variation of this network, a fast and a cost-efficient member of biswapped family named “Biswapped-Mesh of Trees (BSN MOT)” is proposed here. The suggested BSN MOT optoelectronic network claims to be a better alternative of counter-part OTIS-Mesh of Trees (OTIS MOT) optoelectronic network, claims advantages concerning diameter, minimum node degree, and network total and optical cost (total cost drops about 10–30% and optical cost drops about 50%). More specifically, compared to competitive Biswapped-Mesh and BSN HHC optoelectronic networks, the proposed network has a major advantage concerning network diameter. Moreover, BSN MOT is a cost-efficient architecture, where total network cost drops about 30–45% than that of BSN HHC. Besides, it is a better alternative for processing numerical problems that require network with “low static maximum node degree”. Thus, on the basis of above-mentioned properties, the proposed network claims to be the most economical and the fastest variation of biswapped framework.

Target Set Selection on generalized pancake graphs

Target Set Selection (TSS) was initially proposed to study the problem of the spread of information, ideas or influence through a social network and had formulated many problems arising in various practical applications. We consider a particular type of graphs, namely n-dimensional m-sided pancake graph mPn, which is one class of Cayley graphs and is widely used in the symmetric interconnection networks. We establish a bound of TSS on mPn by the minimum feedback vertex set.

Complete stability of feedback CNNs with dynamic memristors and second‐order cells

SummaryThe paper considers a feedback cellular neural network (CNN) obtained by interconnecting elementary cells with an ideal capacitor and an ideal flux‐controlled memristor. It is supposed that during the analogue computation of the CNN the memristors behave as dynamic elements, so that each dynamic memristor (DM)‐CNN cell is described by a second‐order differential system in the state variables given by the capacitor voltage and the memristor flux. The proposed networks are called DM‐CNNs, that is CNNs using a dynamic (D) memristor (M). After giving a foundation to the DM‐CNN model, the paper establishes a fundamental result on complete stability, that is convergence of solutions toward equilibrium points, when the DM‐CNN has symmetric interconnections. Because of the presence of dynamic memristors, a DM‐CNN displays peculiar and basically different dynamic properties with respect to standard CNNs. First of all a DM‐CNN computes during the time evolution of the memristor fluxes, instead of the capacitor voltages as for a standard CNN. Furthermore, when a steady state is reached, the memristors keep in memory the result of the computation, that is the limiting values of the fluxes, while all memristor currents and voltages, as well as all currents, voltages, and power in the DM‐CNN vanish. Instead, for standard CNNs, currents, voltages, and power do not drop off when a steady state is reached. Copyright © 2016 John Wiley & Sons, Ltd.

Decentralized [formula omitted]-infinity control of complex systems with delayed feedback

The paper studies the problem of decentralized H∞ fault tolerant state feedback control design for a class of continuous-time complex systems composed of identical subsystems and symmetric interconnections. We consider a time-varying interval-bounded delay in the feedback of each channel. Single delay as well as multiple delay cases is considered. By exploiting a particular structure of the systems, sufficient conditions are derived for the gain matrix selection. The controller design is performed using a reduced-order system under linear matrix inequality approach constraints. The asymptotic stability with disturbance attenuation γ of the overall multiple delay closed-loop system is guaranteed when synthesizing the gain matrix into the decentralized controller. Moreover, sufficient conditions for the H∞ bound tolerance under local control channel failures of the overall closed-loop system are derived. The tolerance can be easily tested on several low-order systems. A numerical example illustrates the effectiveness of the proposed method.

Edge disjoint Hamiltonian cycles in Eisenstein–Jacobi networks

Many communication algorithms in parallel systems can be efficiently solved by obtaining edge disjoint Hamiltonian cycles in the interconnection topology of the network. The Eisenstein–Jacobi (EJ) network generated by α=a+bρ, where ρ=(1+i3)/2, is a degree six symmetric interconnection network. The hexagonal network is a special case of the EJ network that can be obtained by α=a+(a+1)ρ. Generating three edge disjoint Hamiltonian cycles in the EJ network with generator α=a+bρ for gcd(a,b)=1 has been shown before. However, this problem has not been solved when gcd(a,b)=d>1. In this paper, some results to this problem are given.

Control of Heterogeneous Groups of Systems Interconnected Through Directed and Switching Topologies

This note presents a technique to synthesize distributed controllers for the control of heterogeneous systems interconnected through switching directed interaction topologies. Groups of subsystems are defined with undirected interaction within, but directed interconnections between each other. This allows to construct a virtual symmetric interconnection matrix representation of the graph topology. The symmetry guarantees the existence of a diagonalizing transformation, which renders both analysis and synthesis problems particularly simple. Structural constraints on multipliers are used to reduce the complexity of the resulting coupled matrix inequalities to be of the order of a single subsystem times the number of groups. The problem can then be essentially solved by linear fractional transformation (LFT)-based linear parameter-varying (LPV) gain-scheduling synthesis methods, in which the possibly time-varying eigenvalues of the interconnection matrix act as the scheduling variables of the transformed problem.

On the construction of all shortest vertex-disjoint paths in Cayley graphs of abelian groups

Cayley graphs provide a group-theoretic model for designing and analyzing symmetric interconnection networks. In this paper, we give a sufficient condition for the existence of m vertex-disjoint shortest paths from one source vertex to other m (not necessarily distinct) destination vertices in a Cayley graph of an abelian group, where m≤n and n is the cardinality of a (group) generator of the abelian group. In addition, when the condition holds, the m vertex-disjoint shortest paths can be constructed in O(mn) time, which is optimal in the worst case when O(n) ≤ the order of diameter. By applying our results, we can easily obtain the necessary and sufficient conditions, which can be verified in nearly optimal time, for the existence of all shortest vertex-disjoint paths in generalized hypercubes and odd tori. In the situation that all of the source vertex and destination vertices are mutually distinct, brute-force computations show that the probability of the existence of the m vertex-disjoint shortest paths in an r-dimensional generalized hypercube with r coordinates each of order k is greater than 94%, 70%, 96%, 99%, and 99% for (k,r,m)=(2,7,7),(3,4,8),(4,3,6),(5,3,6), and (6,3,6), respectively.

A novel FPGA-programmable switch matrix interconnection element in quantum-dot cellular automata

The Quantum-dot cellular automata (QCA) is a novel nanotechnology, promising extra low-power, extremely dense and very high-speed structure for the construction of logical circuits at a nanoscale. In this paper, initially previous works on QCA-based FPGA’s routing elements are investigated, and then an efficient, symmetric and reliable QCA programmable switch matrix (PSM) interconnection element is introduced. This element has a simple structure and offers a complete routing capability. It is implemented using a bottom-up design approach that starts from a dense and high-speed 2:1 multiplexer and utilise it to build the target PSM interconnection element. In this study, simulations of the proposed circuits are carried out using QCAdesigner, a layout and simulation tool for QCA circuits. The results demonstrate high efficiency of the proposed designs in QCA-based FPGA routing.

하프팬케익 그래프의 다양한 성질 분석

The Pancake graph is node symmetric and useful interconnection network in the field of data sorting algorithm. The Half Pancake graph is a new interconnection network that reduces the degree of the Pancake graph by approximately half and improves the network cost of the Pancake graph. In this paper, we analyze topological properties of the Half Pancake graph . Fist, we prove that has maximally fault tolerance and recursive scalability. In addition, we show that in , there are isomorphic graphs of low-dimensional . Also, we propose that the Bubblesort can be embedded into Half Pancake with dilation 5, expansion 1. These results mean that various algorithms designed for the Pancake graph and the Bubble sort graph can be executed on efficiently.

Convergence of Type-Symmetric and Cut-Balanced Consensus Seeking Systems

We consider continuous-time consensus seeking systems whose time-dependent interactions are cut-balanced, in the following sense: if a group of agents influences the remaining ones, the former group is also influenced by the remaining ones by at least a proportional amount. Models involving symmetric interconnections and models in which a weighted average of the agent values is conserved are special cases. We prove that such systems always converge. We give a sufficient condition on the evolving interaction topology for the limit values of two agents to be the same. Conversely, we show that if our condition is not satisfied, then these limits are generically different. These results allow treating systems where the agent interactions are a priori unknown, being for example random or determined endogenously by the agent values.

Electromechanical response of piezoelectric foams

A three-dimensional finite element model is developed to completely characterize the elastic, dielectric, and piezoelectric properties of piezoelectric foam structures. Three kinds of 3-3 type piezoelectric foam structures (i.e. with asymmetric interconnects, with symmetric interconnects, and without any interconnects) are identified and their electromechanical properties are characterized as a function of the interconnect geometry and architecture and benchmarked with that of long porous 3-1 type piezoelectric materials over a range of volume fractions/foam densities. In general, at a particular volume fraction a majority of the elasticity constants (with the exception of C55 and C13) of the 3-3 type open foam structures are lower than that of the 3-1 type long porous structure. Amongst the 3-3 type foam structures the sparsely packed foam structures (with longer and thicker interconnects) display higher coupling constants and acoustic impedance as compared to close-packed foam structures (with shorter and thinner interconnects). The piezoelectric charge coefficients (dh), the hydrostatic voltage coefficients (gh) and the hydrostatic figures of merit (dhgh) are observed to be significantly higher for the 3-3 type (PZT-7A) piezoelectric foam structures as compared with that of the 3-1 type (PZT-7A) long porous materials. For example, at about 3% volume fraction, the dh, gh, and dhgh figures of merit are 360%, 1000% and 5000% higher, respectively, for the interconnect-free foam structure compared with the 3-1 type long porous materials. Amongst the 3-3 type piezoelectric foam structures those that are close packed exhibit higher piezoelectric charge coefficients, while the sparsely packed structures exhibit higher hydrostatic voltage coefficients and hydrostatic figures of merit.

Topological properties and routing algorithm for semi-diagonal torus networks

To improve the scalability and reduce the implementation complexity of Mesh and Mesh-like networks, the semi-diagonal Torus (SD-Torus) network, a regular and symmetrical interconnection network is proposed. The SD-Torus network is a combination of a typical 2D-Torus network with two extra diagonal links from northwest to southeast direction for each node. The topological properties of SD-Torus networks are discussed, and a load balanced routing algorithm for SD-Torus is presented. System-C based simulation result shows that, compared with diagonal Mesh (DMesh), diagonal Torus (DTorus) and XMesh networks, the SD-Torus network can achieve high performance with a lower network cost. It makes the SD-Torus network a powerful candidate for the high performance interconnection networks.

Existence and robustness of phase-locking in coupled Kuramoto oscillators under mean-field feedback

Motivated by the recent development of Deep Brain Stimulation (DBS) for neurological diseases, we study a network of interconnected oscillators under the influence of mean-field feedback and analyze the robustness of its phase-locking with respect to general inputs. Under standard assumptions, this system can be reduced to a modified version of the Kuramoto model of coupled nonlinear oscillators. In the first part of the paper we present an analytical study on the existence of phase-locked solutions under generic interconnection and feedback configurations. In particular we show that, in general, no oscillating phase-locked solutions can co-exist with any non-zero proportional mean-field feedback. In the second part we prove some robustness properties of phase-locked solutions (namely total stability). This general result allows in particular to justify the persistence of practically phase-locked states if sufficiently small feedback gains are applied, and to give explicit necessary conditions on the intensity of a desynchronizing mean-field feedback. Furthermore, the Lyapunov function used in the analysis provides a new characterization of the robust phase-locked configurations in the Kuramoto system with symmetric interconnections.

Łojasiewicz inequality and exponential convergence of the full-range model of CNNs

This paper considers the Full-range (FR) model of Cellular Neural Networks (CNNs) in the case where the signal range is delimited by an ideal hard-limiter nonlinearity with two vertical segments in the i−v characteristic. A Łojasiewicz inequality around any equilibrium point, for a FRCNN with a symmetric interconnection matrix, is proved. It is also shown that the Łojasiewicz exponent is equal to **image**. The main consequence is that any forward solution of a symmetric FRCNN has finite length and is exponentially convergent toward an equilibrium point, even in degenerate situations where the FRCNN possesses non-isolated equilibrium points. The obtained results are shown to improve the previous results in literature on convergence or almost convergence of symmetric FRCNNs. Copyright © 2010 John Wiley & Sons, Ltd.

On the surface area of the [formula omitted]-star graph

We present an explicit formula for the surface area of the ( n , k ) -star graph, i.e., the number of nodes at a certain distance from the identity node in the graph, by identifying the unique cycle structures associated with the nodes in the graph, deriving a distance expression in terms of such structures between the identity node of the graph and any other node, and enumerating those cycle structures satisfying the distance restriction. The above surface area derivation process can also be applied to some of the other node symmetric interconnection structures defined on the symmetric group, when the aforementioned distance expression is available.

Analysis of Scale Effects in Peer-to-Peer Networks

In this paper, we study both positive and negative scale effects on the operations of peer-to-peer (P2P) file sharing networks and propose the optimal sizing (number of peers) and grouping (number of directory intermediary) decisions. Using analytical models and simulation, we evaluate various performance metrics to investigate the characteristics of a P2P network. Our results show that increasing network scale has a positive effect on the expected content availability and transmission cost, but a negative effect on the expected provision and search costs. We propose an explicit expression for the overall utility of a content sharing P2P community that incorporates tradeoffs among all of the performance measures. This utility function is maximized numerically to obtain the optimal network size (or scale). We also investigate the impact of various P2P network parameters on the performance measures as well as optimal scaling decisions. Furthermore, we extend the model to examine the grouping decision in networks with symmetric interconnection structures and compare the performance between random- and location-based grouping policies.