Constant Node Degree Research Articles

Computational neuronal correlation with enhanced synchronized activity in the basal ganglia and the slowing of thalamic theta and alpha rhythms in Parkinson's disease.

The aim of this work is computationally to correlate the synchronized neuronal activity of basal ganglia and slowing in theta and alpha rhythms in electroencephalogram (EEG) signal in thalamic region in case of dopamine depletion and decrease of synaptic connections. The used network topology is a scale-free network with constant node degree. The dopamine-modulated type Izikhevich neuron model is used for modeling the striatal region, consisting of fast-spiking interneurons, D1 and D2 type dopamine expressing medium spiny neurons. On the other hand, the ordinary Izikhevich neuron model is used in the modeling of extrastriatal basal ganglia (BG) regions where globus pallidus (GP) subregion neurons have also dopamine-dependent parameters. The thalamic region of the network is mass modeled including inhibitory input from basal ganglia. Depending on the decrease of synaptic connections and dopamine level, the synchronization among basal ganglia neuron populations is investigated. The effect of synaptic delay on synchronization is also considered. It is observed that the decrease of dopamine neurotransmitter and decrease in the number of synaptic connections cause an increased synchronous activity in BG. Also, slowing in theta and alpha bands in thalamus EEG signals is observed. This shows the causal relation between synchronization and power shifting to lower frequency components in the case of neurodegenerative diseases such as Parkinson's disease (PD).

Midimew Connected Torus Network for Next Generation Massively Parallel Computer System

Important scientific and engineering applications need high performance computing. This can be provided by massively parallel computer (MPC) systems. A sensitive step of maintaining such systems is the interconnection network used to interconnect the computing nodes. The topology used effects the network costs and performance significantly. Hierarchal interconnection networks (HIN) were introduced having several attractive features including low latency, low cost, and high fault tolerance. This paper proposes a new HIN called Midimew connect Torus Network (MTN) that provides constant node degree, high arc connectivity, high fault tolerance and a reasonable bisection width. Static network performance evaluation for the proposed MTN has been conducted and compared with other networks. The comparison included conventional topologies such as 2D Mesh and 2D Torus and hierarchal ones which are TESH and TTN. The comparison of result shows that with the cost of extra communication links MTN attains higher fault tolerance than that of TESH and mesh networks, and equal to that of TTN, and less than that of torus network. Also, the hierarchical networks such as MTN, TTN, and TESH yield moderate bisection width; and the bisection width of MTN is lower than that of mesh and torus networks. This paper shows the superiority of the proposed MTN by comparative study of static network performance.

Network science applied to forest megaplots: tropical tree species coexist in small-world networks

Network analysis is an important tool to analyze the structure of complex systems such as tropical forests. Here, we infer spatial proximity networks in tropical forests by using network science. First, we focus on tree neighborhoods to derive spatial tree networks from forest inventory data. In a second step, we construct species networks to describe the potential for interactions between species. We find remarkably similar tree and species networks among tropical forests in Panama, Sri Lanka and Taiwan. Across these sites only 32 to 51% of all possible connections between species pairs were realized in the species networks. The species networks show the common small-world property and constant node degree distributions not yet described and explained by network science. Our application of network analysis to forest ecology provides a new approach in biodiversity research to quantify spatial neighborhood structures for better understanding interactions between tree species. Our analyses show that details of tree positions and sizes have no important influence on the detected network structures. This suggests existence of simple principles underlying the complex interactions in tropical forests.

HTM: a new hierarchical interconnection network for future generation parallel computers

ABSTRACTIn this paper, we have discussed the architectural structure, static network performance, and dynamic communication performance of a new hierarchical interconnection network called hierarchical Tori connected mesh network (HTM). For the exploration of static network performance, we have evaluated degree, diameter, cost, average distance, arc-connectivity, bisection width, and wiring complexity. We have also evaluated the dynamic communication performance of HTM, its counter rival H3DM, and conventional mesh and torus networks using a deadlock-free dimension order routing using two virtual channels under uniform and non-uniform traffic patterns. The dynamic communication performance is evaluated using computer simulation. We discovered that the HTM has a number of lucrative properties. These include constant node degree, small diameter, low cost, small average distance, moderate (neither too low, nor too high) bisection width, and less wiring complexity. HTM also yields high throughput per link and very low zero load latency, which provide better dynamic communication performance than that of H3DM, mesh, and torus networks.

An exchanged folded hypercube‐based topology structure for interconnection networks

SummaryThis paper focuses on the topology structure of interconnection networks. To overcome drawbacks in the existing hypercube structure, we present an exchanged folded hypercube (EFH) structure, which is an improvement of the exchanged hypercube. Compared with the existing hypercube structures, EFH shows better performance in terms of many metrics such as smaller diameter, lower cost factor, and constant node degree. In this paper, we first introduce the structure of an EFH; then, we propose a routing algorithm and a load‐balancing algorithm for EFHs. Finally, we analyze the fault tolerance characteristics of EFHs including fault diameter and the cost effectiveness factor. Copyright © 2015 John Wiley & Sons, Ltd.

On the resistance of overlay networks against bandwidth exhaustion attacks

In order to perform private communication over public networks, such as the Internet, several different kinds of virtual overlay networks emerged. Examples are the well known Virtual Private Networks, Darknets, and anonymizing networks like Tor. All of these networks are designed to provide data delivery that is confidential, authentic and integrity protected. Nonetheless, for a secure operation also the availability must be taken into account, especially as these structures turn into vital targets for Denial-of-Service attacks. Within this article we present metrics to rate different network topologies with regard to their resistance against botnets, whose available attack bandwidth is not a limiting factor. The presented metrics consider random, greedy, and optimally operating attackers, and are used to derive several properties that very resilient overlay topologies must have. In particular a low constant node degree and high girth are identified. The results are validated by a simulation study.

High and stable performance under adverse traffic patterns of tori-connected torus network

A Tori-connected Torus Network (TTN) is a scalable network constructed from hierarchically-interconnected 2D-torus networks. Static network performance of fixed size TTN and dynamic communication performance under very common traffic patterns have been evaluated in our previous study. A generalized study of static network performance of TTN of any size and dynamic communication performance under adverse traffic patterns are the main focus of this paper. The TTN possesses several attractive features, including constant node degree, small diameter, low cost, small average distance, moderate bisection width, and better fault-tolerant performance than other networks. We compared with hierarchical TESH and MH3DT and conventional mesh and torus networks, and found that under adverse traffic patterns, the TTN yields high throughput and low latency, providing better dynamic communication performance compared to those networks. Also, the adverse traffic patterns have more stable throughput than uniform traffic in the TTN.

Symmetric and Folded Tori Connected Torus Network

Hierarchical interconnection networks provide high performance at low cost by exploring the locality that exists in the communication patterns of massively parallel computers. A Symmetric Tori connected Torus Network (STTN) is a 2D-torus network of multiple basic modules, in which the basic modules are 2D-torus networks that are hierarchically interconnected for higher-level networks. We also fold the STTN to minimize the length of the longest wire of STTN. The folded network is called Folded Tori connected Torus Network (FTTN). In this paper, we present the architecture of the STTN and FTTN, addressing of node, routing of message, and evaluate the static network performance of STTN, FTTN, TTN, TESH, mesh, and torus networks. It is shown that both the STTN and FTTN possess several attractive features, including constant node degree, small diameter, low cost, small average distance, moderate bisection width, and high fault tolerant performance than that of other conventional and hierarchical interconnection networks. We further evaluate the longest wire length of FTTN and compare it with other networks. We found that the longest wire length of the FTTN is far lower than that of other networks considered in this paper while keeping good static network performance. It is just about (1 / 2 m th) of its rival STTN.

Protein interaction network underpins concordant prognosis among heterogeneous breast cancer signatures

Characterizing the biomolecular systems’ properties underpinning prognosis signatures derived from gene expression profiles remains a key clinical and biological challenge. In breast cancer, while different “poor-prognosis” sets of genes have predicted patient survival outcome equally well in independent cohorts, these prognostic signatures have surprisingly little genetic overlap. We examine 10 such published expression-based signatures that are predictors or distinct breast cancer phenotypes, uncover their mechanistic interconnectivity through a protein–protein interaction network, and introduce a novel cross-“gene expression signature” analysis method using (i) domain knowledge to constrain multiple comparisons in a mechanistically relevant single-gene network interactions and (ii) scale-free permutation re-sampling to statistically control for hubness (SPAN – Single Protein Analysis of Network with constant node degree per protein). At adjusted p-values<5%, 54-genes thus identified have a significantly greater connectivity than those through meticulous permutation re-sampling of the context-constrained network. More importantly, eight of 10 genetically non-overlapping signatures are connected through well-established mechanisms of breast cancer oncogenesis and progression. Gene Ontology enrichment studies demonstrate common markers of cell cycle regulation. Kaplan–Meier analysis of three independent historical gene expression sets confirms this network-signature’s inherent ability to identify “poor outcome” in ER(+) patients without the requirement of machine learning. We provide a novel demonstration that genetically distinct prognosis signatures, developed from independent clinical datasets, occupy overlapping prognostic space of breast cancer via shared mechanisms that are mediated by genetically different yet mechanistically comparable interactions among proteins of differentially expressed genes in the signatures. This is the first study employing a networks’ approach to aggregate established gene expression signatures in order to develop a phenotype/pathway-based cancer roadmap with the potential for (i) novel drug development applications and for (ii) facilitating the clinical deployment of prognostic gene signatures with improved mechanistic understanding of biological processes and functions associated with gene expression changes. http://www.lussierlab.org/publication/networksignature/

The 2D digraph-based NoCs: attractive alternatives to the 2D mesh NoCs

This paper proposes two-dimensional directed graphs (or digraphs for short) as a promising alternative to the popular 2D mesh topology for networks-on-chip (NoCs). Mesh is the most popular topology for the NoCs, mainly due to its suitability for on-chip implementation and low cost. However, the fact that a digraph offers a lower diameter than its equivalent linear array of equal cost motivated us to evaluate digraphs as the underlying topology of NoCs. This paper introduces a family of NoC topologies based on three well-known digraphs, namely de Bruijn, shuffle-exchange, and Kautz. We study topological properties of the proposed topologies. We show that the proposed digraph-based topologies have several attractive features including constant node degree, low diameter and cost, and low zero load latency which result in superior performance over the mesh. We introduce a deadlock-free routing algorithm for the proposed NoC topologies and compare NoCs employing the proposed topologies and the mesh topology in terms of power consumption and performance. Simulation results also reveal that the proposed NoC topologies offer higher performance and consume lower power than the mesh NoC.

TTN: A High Performance Hierarchical Interconnection Network for Massively Parallel Computers

Interconnection networks play a crucial role in the performance of massively parallel computers. Hierarchical interconnection networks provide high performance at low cost by exploring the locality that exists in the communication patterns of massively parallel computers. A Tori connected Torus Network (TTN) is a 2D-torus network of multiple basic modules, in which the basic modules are 2D-torus networks that are hierarchically interconnected for higher-level networks. This paper addresses the architectural details of the TTN and explores aspects such as node degree, network diameter, cost, average distance, arc connectivity, bisection width, and wiring complexity. We also present a deadlock-free routing algorithm for the TTN using four virtual channels and evaluate the network's dynamic communication performance using the proposed routing algorithm under uniform and various non-uniform traffic patterns. We evaluate the dynamic communication performance of TTN, TESH, MH3DT, mesh, and torus networks by computer simulation. It is shown that the TTN possesses several attractive features, including constant node degree, small diameter, low cost, small average distance, moderate (neither too low, nor too high) bisection width, and high throughput and very low zero load latency, which provide better dynamic communication performance than that of other conventional and hierarchical networks.

A Hypercube-based Scalable Interconnection Network for Massively Parallel Computing

An important issues in the design of interconnection networks for massively parallel computers is scalability. A new scalable interconnection network topology, called Double-Loop Hypercube (DLH), is proposed. The DLH network combines the positive features of the hypercube topology, such as small diameter, high connectivity, symmetry and simple routing, and the scalability and constant node degree of a new double-loop topology. The DLH network can maintain a constant node degree regardless of the increase in the network size. The nodes of the DLH network adopt the hybrid coding combining Johnson code and Gray code. The hybrid coding scheme can make routing algorithms simple and efficient. Both unicasting and broadcasting routing algorithms are designed for the DLH network, and it is based on the hybrid coding scheme. A detailed analysis shows that the DLH network is a better interconnection network in the properties of topology and the performance of communication. Moreover, it also adopts a three-dimensional optical design methodology based on free-space optics. The optical implementation has totally space-invariant connection patterns at every node, which enables the DLH to be highly amenable to optical implementation using simple and efficient large space-bandwidth product space-invariant optical elements.

An oblivious shortest-path routing algorithm for fully connected cubic networks

Fully connected cubic networks (FCCNs) are a class of newly proposed hierarchical interconnection networks for multicomputer systems, which enjoy the strengths of constant node degree and good expandability. The shortest path routing in FCCNs is an open problem. In this paper, we present an oblivious routing algorithm for n-level FCCN with N = 8 n nodes, and prove that this algorithm creates a shortest path from the source to the destination. At the costs of both an O ( N ) -parallel-step off-line preprocessing phase and a list of size N stored at each node, the proposed algorithm is carried out at each related node in O ( n ) time. In some cases the proposed algorithm is superior to the one proposed by Chang and Wang in terms of the length of the routing path. This justifies the utility of our routing strategy.

Optimal all-to-all personalized exchange in self-routable multistage networks

All-to-all personalized exchange is one of the most dense collective communication patterns and occurs in many important applications in parallel computing. Previous all-to-all personalized exchange algorithms were mainly developed for hypercube and mesh/torus networks. Although the algorithms for a hypercube may achieve optimal time complexity, the network suffers from unbounded node degrees and thus has poor scalability in terms of I/O port limitation in a processor. On the other hand, a mesh/torus has a constant node degree and better scalability in this aspect, but the all-to-all personalized exchange algorithms have higher time complexity. In this paper, we propose an alternative approach to efficient all-to-all personalized exchange by considering another important type of networks, multistage networks, for parallel computing systems. We present a new all-to-all personalized exchange algorithm for a class of unique-path, self-routable multistage networks. We first develop a generic method for decomposing all-to-all personalized exchange patterns into some permutations which are realizable in these networks, and then present a new all-to-all personalized exchange algorithm based on this method. The newly proposed algorithm has O(n) time complexity for an n/spl times/n network, which is optimal for all-to-all personalized exchange. By taking advantage of fast switch setting of self-routable switches and the property of a single input/output port per processor in a multistage network, we believe that a multistage network could be a better choice for implementing all-to-all personalized exchange due to its shorter communication latency and better scalability.

A spanning multichannel linked hypercube: a gradually scalable optical interconnection network for massively parallel computing

A new, scalable interconnection topology called the Spanning Multichannel Linked Hypercube (SMLH) is proposed. This proposed network is very suitable to massively parallel systems and is highly amenable to optical implementation. The SMLH uses the hypercube topology as a basic building block and connects such building blocks using two-dimensional multichannel links (similar to spanning buses). In doing so, the SMLH combines positive features of both the hypercube (small diameter, high connectivity, symmetry, simple routing, and fault tolerance) and the spanning bus hypercube (SBH) (constant node degree, scalability, and ease of physical implementation), while at the same time circumventing their disadvantages. The SMLH topology supports many communication patterns found in different classes of computation, such as bus-based, mesh-based, and tree-based problems, as well as hypercube-based problems. A very attractive feature of the SMLH network is its ability to support a large number of processors with the possibility of maintaining a constant degree and a constant diameter. Other positive features include symmetry, incremental scalability, and fault tolerance. It is shown that the SMLH network provides better average message distance, average traffic density, and queuing delay than many similar networks, including the binary hypercube, the SBH, etc. Additionally, the SMLH has comparable performance to other high-performance hypercubic networks, including the Generalized Hypercube and the Hypermesh. An optical implementation methodology is proposed for SMLH. The implementation methodology combines both the advantages of free space optics with those of wavelength division multiplexing techniques. A detailed analysis of the feasibility of the proposed network is also presented.

SHUFFLE-RING: A NEW CONSTANT-DEGREE NETWORK

The hypercube as a parallel interconnection network has been of academic and engineering concern for tens of year due to its many merits. However, its increasing node degree is an obvious weakness. Some networks such as the cube-connected cycles (CCC) and the de Bruijn network have been proposed to overcome the increasing degree of the hypercube. In this paper, we present a new cost-effective network which outperforms the cube network. It can overcome the increasing degree of cube networks while keeping the advantages of the cube network such as logarithmic diameter, easy routing, optimal fault tolerance, and suitability for the ASCEND/DESCEND class of parallel problems. Furthermore, the proposed network achieves the logarithmic diameter with a very small constant node degree, 3 or 4.

Incrementally scalable optical interconnection network with a constant degree and constant diameter for parallel computing

A new scalable interconnection topology called the spanning-bus connected hypercube (SBCH) that is suitable for massively parallel systems is proposed. The SBCH uses the hypercube topology as a basic building block and connects such building blocks by use of multidimensional spanning buses. In doing so, the SBCH combines positive features of both the hypercube (small diameter, high connectivity, symmetry, simple routing, and fault tolerance) and the spanning-bus hypercube (SBH) (constant node degree, scalability, and ease of physical implementation), while at the same time circumventing their disadvantages. The SBCH topology permits the efficient support of many communication patterns found in different classes of computation, such as bus-based, mesh-based, and tree-based problems, as well as hypercube-based problems. A very attractive feature of the SBCH network is its ability to support a large number of processors while maintaining a constant degree and a constant diameter. Other positive features include symmetry, incremental scalability, and fault tolerance. An optical implementation methodology is proposed for the SBCH. The implementation methodology combines the advantages of free-space optics with those of wavelength-division multiplexing techniques. An analysis of the feasibility of the proposed network is also presented.

A spanning bus connected hypercube: a new scalable optical interconnection network for multiprocessors and massively parallel systems

A new scalable interconnection topology suitable for massively parallel systems called the spanning bus connected hypercube (SBCH) is proposed. The SBCH uses the hypercube topology as a basic building block and connects such building blocks using multidimensional spanning buses. In doing so, the SBCH combines positive features of both the hypercube (small diameter, high connectivity, symmetry, simple routing, and fault tolerance) and the spanning bus hypercube (SBH) (constant node degree, scalability, and ease of physical implementation), while at the same time circumventing their disadvantages. The SBCH topology permits the efficient support of many communication patterns found in different classes of computation such as bus-based, mesh-based, tree-based problems as well as hypercube-based problems. A very attractive feature of the SBCH network is its ability to support a large number of processors while maintaining a constant degree and constant diameter. Other positive features include symmetry, incremental scalability, and fault-tolerance. An optical implementation methodology is proposed for SBCH. The implementation methodology combines both the advantages of free space optics with those of wavelength division multiplexing techniques. A detailed analysis of the feasibility of the proposed network is also presented.

Multitriangle: A Constant Node Degree Interconnection Network

We propose a constant node degree network topology, multitriangle, which is hierarchical, recursive, and expansive. First we introduce a corner cutting approach that generates a set of new network topologies (including multitriangles), followed by a formal definition of the multitriangle network and discussion of its properties. The salient features of this network are that it is a constant node degree network and it can be viewed as a hierarchical ring, a popular topology which has been adopted in several commercial systems. Algorithms for node-to-node routing, hierarchical ring routing, optimal ring routing, and broadcasting are presented. The multitriangle network is analyzed in terms of diameter, degree, average distance, and message density, and results are compared with other relevant networks.

Hierarchical optical ring interconnection (HORN): scalable interconnection network for multiprocessors and multicomputers

A new interconnection network for massively parallel computing is introduced. This network is called a hierarchal optical ring interconnection (HORN). The HORN consists of a single-hop, scalable, constant-degree, strictly nonblocking, fault-tolerant interconnection topology that uses wavelength-division multiple access to provide better utilization of the terahertz bandwidth offered by optics. The proposed optical network integrates the attractive features of hierarchical ring interconnections, e.g., a simple node interface, a constant node degree, better support for the locality of reference, and fault tolerance, with the advantages of optics. The HORN topology is presented, its architectural properties are analyzed, and an optical design methodology for it is described. Furthermore, a brief feasibility study of the HORN is conducted. The study shows that the topology is highly amenable to optical implementation with commercially available optical elements.