Models For Interconnection Networks Research Articles

Dynamics of memristor coupled discrete fractional symmetric neural network model

Neural networks, also known as artificial neural networks (ANNs), represent innovative computational models inspired by the functioning of biological neurons in the human body. Currently, neural network models are employed to address intricate real-world challenges. This article focuses on constructing and dynamically analyzing interconnected symmetric neural network models inspired by the Hopfield type. These models incorporate discrete fractional memristor elements featuring quadratic memductance. The primary objective is to comprehend system characteristics by introducing nonlinearity to the inter-neuron weights in a functional manner. Additionally, the study explores the influence of electromagnetic radiation on neurons. Bifurcation diagrams, considering fractional order and Lyapunov exponents, illustrate the chaotic nature of the interconnected neural network model. The investigation delves into coexisting system states, examining coexisting bifurcations and attractors. The article offers potential for developing bio-inspired, energy-efficient, and adaptive neural network architectures, thereby contributing to advancements in artificial intelligence and neuromorphic applications.

Pilot Protection of AC System in AC-DC Interconnected Grid Based on Traveling Wave Refraction and Reflection

To solve the problem that the voltage travelling wave protection at the AC bus is difficult to detect in the AC/DC interconnection network, a frequency protection principle of the line waveguide using the phenomenon of travelling wave catadioptric is proposed in this paper. According to the catadioptric phenomenon when the discontinuity of traveling wave impedance meets the wave, the fault area is identified by using the different refraction and catadioptric coefficients of faults inside and outside the region. In PSCAD/EMTDC environment, the AC-DC interconnection network model is established, and the protection principle is verified by MATLAB.

3-path-connectivity of Cayley graphs generated by transposition trees

For a graph G=(V,E) and a set S⊆V(G) of size at least 2, a path in G is said to be an S-path if it connects all vertices of S. Two S-paths P1 and P2 are said to be internally disjoint if E(P1)∩E(P2)=0̸ and V(P1)∩V(P2)=S. Let πG(S) denote the maximum number of internally disjoint S-paths in G. The k-path-connectivityπk(G) of G is then defined as the minimum πG(S), where S ranges over all k-subsets of V(G). Cayley graphs often make good models for interconnection networks. In this paper, we consider the 3-path-connectivity of Cayley graphs generated by transposition trees Γn. We find that Γn always has a nice structure connecting any 3-subset S of V(Γn), according to the parity of n. Thereby, we show that π3Γn=⌊3n4⌋−1, for any n≥3.

Novel Concepts in Rough Cayley Fuzzy Graphs with Applications

Today, fuzzy graphs (FGs) have a variety of applications in other fields of study, including medicine, engineering, and psychology, and for this reason, many researchers around the world are trying to identify their properties and use them in computer sciences as well as finding the smallest problem in a network. The concept of a Cayley fuzzy graph has become a standard part of the toolkit used to investigate and describe groups. Also, Cayley fuzzy graphs are good models for interconnection networks, and they are useful in semigroup theory for establishing which elements are ℓ and R related. The previous definition limitations in the FGs have directed us to offer a new classification in terms of Cayley fuzzy graphs. So, in this paper, two new definitions of Cayley fuzzy graphs (CFGs) and pseudo-Cayley fuzzy graphs (PCFGs) are discussed and their rough approximations are studied. Also, some properties of fuzzy rough sets (FRSs) in CFGs and PCFGs have been investigated. Finally, we presented the determination of the most effective person in the Water and Sewerage Organization and the importance of using refereeing facilities in football matches between club teams, by using CFG in the presented applications.

Fault-tolerant Hamiltonian connectivity of 2-tree-generated networks

Interconnection networks are often modeled by finite graphs. The vertices of the graph represent the nodes of the network (processing elements, memory modules or switches), and the edges correspond to communication lines. There are many advantages in using Cayley graphs as models for interconnection networks. In this paper we consider a class of Cayley graphs that are generated by certain 3-cycles on the alternating group An. These graphs are generalizations of the alternating group graph AGn. We look at the case when the 3-cycles form a “tree-like structure”, and analyze the fault-Hamiltonian connectivity of such graphs. We prove that these graphs are (2n−7)-fault-tolerant Hamiltonian connected.

Construction and analysis of graph models for multiprocessor interconnection networks

A graph G can serve as a model for the Multiprocessor Interconnection Networks (MINs) in which the vertices represent the processors, while the edges represent connections between processors. This paper presents several graphs that could qualify as models for efficient MINs based on the small values of the graph tightness previously introduced by Cvetkovic and Davidovic in 2008. These graphs are constructed using some well-known and widely used graph operations. The tightness values of these graphs range from O(4?N) to O(?N), where N is the order of the graph under consideration. Also, two new graph tightness values, namely Third type mixed tightness t3(G) and Second type of Structural tightness t4(G) are defined in this paper. It has been shown that these tightness types are easier to calculate than the others for the considered graphs. Moreover, their values are significantly smaller.

Multidimensional Computer Interconnection Networks with the Virtual Cut–Through Routing

A theoretical model of an n-dimensional toroidal interconnection network with the virtual cut-through routing is developed. The network performance is characterized as a function of the message load for various values of the network and communication parameters. An exact analytical expression for the saturation point has been obtained. The method of statistical physics known as the mean field theory approximation has been used in order to derive analytical expressions of latency as a function of message generation rate for the full range of the network load. The saturation point has been found proportional to the number of the torus dimensions and inversely proportional to the message length and to the length of the path from the source to the destination. It was found that the transition to the saturation state is a second-order (continuous) phase transition with a critical exponent equal to 1.

K-Banhatti Invariants Empowered Topological Investigation of Bridge Networks

Any number that can be uniquely determined by a graph is called graph invariants. During the most recent twenty years’ innumerable numerical graph invariants have been described and used for correlation analysis. In the fast and advanced environment of manufacturing of networks and other products which used different networks, no dependable assessment has been embraced to choose, how much these invariants are connected with a network graph or molecular graph. In this paper, it will talk about three distinct variations of bridge networks with great capability of expectation in the field of computer science, chemistry, physics, drug industry, informatics, and mathematics in setting with physical and synthetic constructions and networks, since K-Banhatti invariants are newly introduced and have various forecast characteristics for various variations of bridge graphs or networks. The review settled the topology of bridge graph/networks of three unique sorts with three types of K-Banhatti Indices. These concluded outcomes can be utilized for the modeling of interconnection networks of Personal computers (PC), networks like Local area network (LAN), Metropolitan area network (MAN) and Wide area network (WAN), the spine of internet and different networks/designs of PCs, power generation interconnection, bio-informatics and chemical structures.

Study of Communication Structural Relationship between Processors of Parallel and Distributed System

Communication Complexity, Data Structures and its structural relationship are the key parameters for study of architecture in any interconnection Network. This paper reveals that the study of data structures in Perfect Difference Interconnection Network have some structural relationship between nodes or processors. In the Perfect Difference Network (PDN) with processors as a nodes and links between the processors or processing elements as an edge represents graphical Model for interconnection networks. The relationship between each processor is connected with some mapping functions to map data according to the topology of the PDN

Fibonacci-run graphs I: Basic properties

Among the classical models for interconnection networks are hypercubes and Fibonacci cubes. Fibonacci cubes are induced subgraphs of hypercubes obtained by restricting the vertex set to those binary strings which do not contain consecutive 1s, counted by Fibonacci numbers. Another set of binary strings which are counted by Fibonacci numbers are those with a restriction on the runlengths. Induced subgraphs of the hypercube on the latter strings as vertices define Fibonacci-run graphs. They have the same number of vertices as Fibonacci cubes, but fewer edges and different graph theoretical properties.We obtain properties of Fibonacci-run graphs including the number of edges, the analogue of the fundamental recursion, the average degree of a vertex, Hamiltonicity, special degree sequences, and the number of hypercubes they contain. A detailed study of the degree sequences of Fibonacci-run graphs is interesting in its own right and is reported in a companion paper.

The median of Sierpiński graphs

The median of a graph consists of those vertices which minimize the average distance to all other vertices. It plays an important role in optimization scenarios like facility location problems. Sierpiński graphs are the state graphs of the Switching Tower of Hanoi problem, a variant of the Tower of Hanoi game. They also provide optimum models for interconnection networks. In this study, we present our observations on the median of Sierpiński graphs. We conjecture that the number of median vertices in S 3 n is always 12, if n ≥ 3 , and that they lie around the inner ring of the standard drawing.

K-Fibonacci Cubes: A Family of Subgraphs of Fibonacci Cubes

Hypercubes and Fibonacci cubes are classical models for interconnection networks with interesting graph theoretic properties. We consider [Formula: see text]-Fibonacci cubes, which we obtain as subgraphs of Fibonacci cubes by eliminating certain edges during the fundamental recursion phase of their construction. These graphs have the same number of vertices as Fibonacci cubes, but their edge sets are determined by a parameter [Formula: see text]. We obtain properties of [Formula: see text]-Fibonacci cubes including the number of edges, the average degree of a vertex, the degree sequence and the number of hypercubes they contain.

Inferring essential proteins from centrality in interconnected multilayer networks

Computational tool for inferring essential genes and their coding essential proteins based on its topological features in biological network is crucial for insights into vital and disease mechanism of organisms. The problem of how to quantify this correspondence via network centralities in an incomplete protein interaction network (PIN), such as that of human, remains open. Here we develop Random Walk Occupation (RWO) augmented method in interconnected multilayer network model to disclose topological characteristics of essential proteins. The peculiar non-hub essential proteins can be revealed in yeast–human interconnected networks. Statistically RWO augmented method performs well, and improves the prediction results in incomplete human PIN and maintains noticeable performance in well-tested yeast PIN. Biologically, the detected non-hub essential proteins really participate in some vital biological function. Overall, we present a systematic method for deeper understanding and effective identification of essential proteins.

Similarities and Variations in Stepfamily Dynamics among Selected Asian Societies

Stepfamilies, an emerging family form in Asia, are gaining growing academic and social attention in Asia. This paper presents an overview of stepfamilies in Asia, based primarily on research findings in Japan, which suggest underlying two competing stepfamily models as key factors in understanding stepfamily dynamics: the “scrap and build” household model versus the expanded and interconnected network model. The findings in Japan are, then, juxtaposed with existing research findings on stepfamilies in East Asia and Singapore in terms of (a) cultural views on stepfamilies; (b) values of grandparenting, mothering, and fathering; and (c) family law and policies. Some commonalities are found in remaining influence of the “scrap and build” household model and in recent policy changes toward the expanded and interconnected network model, along with some variations, across these societies. Evidently, more studies across Asian societies are needed to obtain a clearer picture of stepfamilies in Asia.

Structure connectivity and substructure connectivity of bubble-sort star graph networks

The bubble-sort star graph, denoted BSn, is an interconnection network model for multiprocessor systems, which has attracted considerable interest since its first proposal in 1996 [5]. In this paper, we study the problem of structure/substructure connectivity in bubble-sort star networks. Two basic but important structures, namely path Pi and cycle Ci, are studied. Let T be a connected subgraph of graph G. The T-structure connectivity κ(G; T) of G is the cardinality of a minimum set of subgraphs in G, whose deletion disconnects G and every element in the set is isomorphic to T. The T-substructure connectivity κs(G; T) of G is the cardinality of a minimum set of subgraphs in G, whose deletion disconnects G and every element in the set is isomorphic to a connected subgraph of T. Both T-structure connectivity and T-substructure connectivity are a generalization of the classic notion of node-connectivity. We will prove that for P2k+1, a path on odd nodes (resp. P2k, a path on even nodes), κ(BSn;P2k+1)=κs(BSn;P2k+1)=⌈2n−3k+1⌉ for n ≥ 4 and k+1≤2n−3 (resp. κ(BSn;P2k)=κs(BSn;P2k)=⌈2n−3k⌉ for n ≥ 5 and k≤2n−3). For a cycle on 2k nodes C2k (there are only cycles on even nodes in BSn), κ(BSn;C2k)=κs(BSn;C2k)=⌈2n−3k⌉ for n ≥ 5 and 2≤k≤n−1.

Understanding the survival of Zika virus in a vector interconnected sexual contact network

The recent outbreaks of the insect-vectored Zika virus have demonstrated its potential to be sexually transmitted, which complicates modeling and our understanding of disease dynamics. Autochthonous outbreaks in the US mainland may be a consequence of both modes of transmission, which affect the outbreak size, duration, and virus persistence. We propose a novel individual-based interconnected network model that incorporates both insect-vectored and sexual transmission of this pathogen. This model interconnects a homogeneous mosquito vector population with a heterogeneous human host contact network. The model incorporates the seasonal variation of mosquito abundance and characterizes host dynamics based on age group and gender in order to produce realistic projections. We use a sexual contact network which is generated on the basis of real world sexual behavior data. Our findings suggest that for a high relative transmissibility of asymptomatic hosts, Zika virus shows a high probability of sustaining in the human population for up to 3 months without the presence of mosquito vectors. Zika outbreaks are strongly affected by the large proportion of asymptomatic individuals and their relative transmissibility. The outbreak size is also affected by the time of the year when the pathogen is introduced. Although sexual transmission has a relatively low contribution in determining the epidemic size, it plays a role in sustaining the epidemic and creating potential endemic scenarios.

Incidence cuts and connectivity in fuzzy incidence graphs

Fuzzy incidence graphs can be used as models for nondeterministic interconnection networks having extra node-edgerelationships. For example, ramps in a highway system may be modeled as a fuzzy incidence graph so that unexpectedflow between cities and highways can be effectively studied and controlled. Like node and edge connectivity in graphs,node connectivity and arc connectivity in fuzzy incidence graphs are introduced in this article. Their relationships withfuzzy connectivity parameters are discussed and results similar to Whitney’s theorems are obtained. Also, the incidenceis used to model flows in human trafficking networks.

Computer interconnection networks with virtual cut-through routing

This paper considers a model of a toroidal computer interconnection network with the virtual cut-through routing. The interrelationships between network parameters, load and performance are analyzed. An exact analytical expression for the saturation point and expressions for the latency as a function of the message generation rate under the mean field theory approximation have been obtained. The theoretical results have been corroborated with the results of simulation experiments for various values of network parameters. The network behavior has been found not depending on the torus linear dimensions provided that they are at least twice as large as the message path length. The saturation point has been found to be inversely proportional to the message length in good agreement with the analytical results. A good agreement with Little’s theorem has been found if the network remains in the steady state during the experiment.

Structure Connectivity and Substructure Connectivity of $k$ -Ary $n$ -Cube Networks

We present new results on the fault tolerability of k-ary n-cube (denoted Q n k ) networks. Q n k is a topological model for interconnection networks that has been extensively studied since proposed, and this paper is concerned with the structure/substructure connectivity of Q n k networks, for paths and cycles, two basic yet important network structures. Let G be a connected graph and T a connected subgraph of G. The T-structure connectivity κ(G; T) of G is the cardinality of a minimum set of subgraphs in G, such that each subgraph is isomorphic to T, and the set's removal disconnects G. The T -substructure connectivity κ s (G; T) of G is the cardinality of a minimum set of subgraphs in G, such that each subgraph is isomorphic to a connected subgraph of T, and the set's removal disconnects G. In this paper, we study κ(Q n k ; T) and κ s (Q n k ; T) for T = P i , a path on i nodes (resp. T = C i , a cycle on i nodes). Lv et al. determined κ(Q n k ; T) and κ s (Q n k ; T) for T ∈ {P 1 , P 2 , P 3 }. Our results generalize the preceding results by determining κ(Q n k ; P i ) and κ s (Q n k ; P i ). In addition, we have also established κ(Q n k ; C i ) and κs(Q n k ; C i ).

Invariance of Water Permeance through Size-Differentiated Graphene Oxide Laminates.

Laminates made of graphene oxide nanosheets have been shown to exhibit high water permeance and salt rejection and, therefore, have generated immense interest from the scientific community due to their potential in separation applications. However, there is no clear consensus on the water-transport pathways through such laminates. In this study, we synthesized chemically identical graphene oxide nanosheets with 2 orders of magnitude difference in lateral sizes and measured water permeance through laminates of different thicknesses fabricated by pressure-assisted deposition of these nanosheets. Our results reveal that water permeance through these laminates is nearly the same despite such massive difference in lateral sheet size. Furthermore, we simulated fluid flow through laminates using an interconnected nanochannel network model for comparison with experiments. The simulations in combination with the experimental data show that it is unlikely that the dominant fluid transport pathway is a circuitous, lateral pathway around individual sheets, as has been proposed in some studies. Rather, nonideal factors including trans-sheet flow through pinhole defects in sheet interiors and/or flow-through regions arising from imperfect stacking in the laminates can significantly affect the fluid transport pathways. The presence of such nonidealities is also supported by thickness- and time-dependent measurements of permeance and by infrared spectroscopy, which indicates that water predominantly adopts a bulk-like structure in the laminates. These analyses are significant steps toward understanding water transport through graphene oxide laminates and provide further insight toward the structure of water inside these materials, which could have immense potential in next-generation separation applications.