Network Diameter Research Articles

Identification and estimation of linear social interaction models

This paper has two parts. The first part derives the identification conditions for higher-order social interaction models. In the case where social effects depend on the distance between individuals, the upper bounds on the network diameters for non-identified models are derived. Many network properties of non-identified models in the literature can be derived from these upper bounds. This part analyzes which fixed effect elimination methods require less restrictive identification conditions. The second part considers estimation with panel data. This part develops an estimator which is computationally simple and asymptotically as efficient as the maximum likelihood estimator under normality.

Exact results for the first-passage properties in a class of fractal networks.

In this work, we consider a class of recursively grown fractal networks Gn(t) whose topology is controlled by two integer parameters, t and n. We first analyse the structural properties of Gn(t) (including fractal dimension, modularity, and clustering coefficient), and then we move to its transport properties. The latter are studied in terms of first-passage quantities (including the mean trapping time, the global mean first-passage time, and Kemeny's constant), and we highlight that their asymptotic behavior is controlled by the network's size and diameter. Remarkably, if we tune n (or, analogously, t) while keeping the network size fixed, as n increases (t decreases) the network gets more and more clustered and modular while its diameter is reduced, implying, ultimately, a better transport performance. The connection between this class of networks and models for polymer architectures is also discussed.

The k-interchange-constrained diameter of a transit network: a connectedness indicator that accounts for travel convenience

ABSTRACTWe study two variants of the shortest path problem. Given an integer , the -color-constrained and the -interchange-constrained shortest path problems, respectively, seek a shortest path that uses no more than colors and one that makes no more than alternations of colors. We show that the former problem is NP-hard, when the latter is tractable. The study of these problems is motivated by some limitations in the use of diameter-based metrics to evaluate the topological structure of transit networks. We notably show that indicators such as the diameter or directness of a transit network fail to adequately account for travel convenience in measuring the connectivity of a network and propose a new network indicator, based on solving the -interchange-constrained shortest path problem, that aims at alleviating these limitations.

Effects of residual lignin on composition, structure and properties of mechanically defibrillated cellulose fibrils and films

This study investigated effects of residual lignin on composition, structure and properties of cellulose fibrils and cellulose fibril-based films by comparing two groups of cellulose fibrils which contained different amounts of lignin (15% and 2%, respectively) but were similar in cellulose to hemicellulose ratio. The results showed that lignin affected the size and content of nanofibril in cellulose fibrils through initially delaying but ultimately facilitating the mechanical defibrillation. Due to higher thermal stability and strong UV absorption capability, lignin enhanced the thermal stability and UV blocking properties of cellulose fibril-based film. Hydrophobic lignin also improved the dewatering of cellulose fibrils and the hydrophobicity of cellulose fibril-based film. Lignin interfered with the interfibrillar hydrogen bonding and therefore increased the mesopore diameter of cellulose fibril network. Lignin acting as a cement in cellulose fibril-based film made the film with a more densely packed structure, a higher density and a smoother surface. However, lignin decreased the transparency of cellulose fibril-based film due to its chromophore groups and impaired the mechanical strength of cellulose fibril-based film through interfering with the interfibrillar hydrogen bonding.

On the Interaction between Small Decay, Agent Heterogeneity and Diameter of Minimal Strict Nash Networks in Two-way Flow Model: A Note

On the Interaction between Small Decay, Agent Heterogeneity and Diameter of Minimal Strict Nash Networks in Two-way Flow Model: A Note

Nanodiamonds reinforced titanium matrix nanocomposites with network architecture

The conflict between strength and ductility is vital problem for the metals. Titanium matrix composites (TMCs) have high strength but usually with a severe room temperature brittleness. Herein, a network distribution of nanodiamond (ND) reinforcements in the TMCs was achieved for the first time. The phases, microstructure, mechanical properties and strengthening mechanisms of the TMCs with network architectures were systemically studied. Experimental results showed that the reinforcements had a network distribution in the Ti matrix and the diameter of networks was 100–200 μm. Higher tensile yield strength (σ0.2) with excellent ductility (ε) can be obtained in the nanocomposites. The in-situ formed TiC and residual NDs in the network boundary played the role of reinforcing phases, while the internal matrix of the network still maintained high ductility of the pure Ti. Eventually, the conflicts between strength and ductility of the TMCs have been reconciled effectively by the controllable spatial network distribution of the nano-reinforcements.

Designing of hydraulic systems on computer models

Project of a heat network combining two sources of centralized heat supply has been completed with the help of the developed mathematical and computer model. The model is based on the electrohydraulic analogy of electrical potentials distribution in conductors and liquid pressure in piping systems is described by the same differential equations. To build a model of a hydraulic system, the Kirchhoff’s laws were applied for the calculation of electrical networks. The research carried out using the model made it possible to determine the optimal parameters of the equipment, its position in the heat network scheme, the lengths and diameters of the pipelines, etc. due to the criteria of the specifications for design and constructions.

Nano-microscale porosity and pore size distribution in aggregates of paddy soil as affected by long-term mineral and organic fertilization under rice-wheat cropping system

The soil porosity and pore size distribution are useful indicators for understanding the impact of fertilization practice on soil quality. In this study, a combined approach of nitrogen gas adsorption (NA), mercury intrusion porosimetry (MIP) and synchrotron radiation X-ray computed microtomography (SR-mCT) was used to study the impact of mineral and organic fertilization on the pore structure in aggregates of paddy soils (porosity, pore size distribution, pore morphology, and pore network). The paddy soil was treated with long-term mineral and organic fertilization (control (CK), chemical fertilizers (NPK), pig manure (PM), and pig manure plus chemical fertilizers (PM + NPK)) under rice-wheat cropping system. The total pore volume estimated by NA method was significantly (p > 0.05) lower in PM than in NPK and CK treatments. The PM treatment significantly increased the total pore volume (TPV) determined by both MIP and SR-mCT methods, while the NPK treatment showed no statistically significant difference relative to the CK treatment. The long-term fertilization greatly affected soil pore size distribution, particularly PM treatment increasing the volumes of macro-, meso-, and micropores, while decreasing the volumes of ultramicro- and cryptopores. The PM treatment significantly increased degree of anisotropy (DA), and elongated pore fraction, and decreased regular pore fraction compared with the CK treatment, while the NKP treatment no significant difference. The NPK and PM treatments significantly affected pore network structure, PM treatment increasing throat area, channel length, key node pores, path length, and network diameter compared with CK treatment, while the verse was true for the NPK treatment. The 3D SR-mCT visualization on aggregates revealed that mineral and organic fertilization affected the pore spatial distribution within the aggregate. The long-term application of mineral fertilizer would deteriorate pore structure by affecting the pore morphology and network structure. Our results was helpful for understanding the impact of fertilization practice on soil quality and illustrating the importance of pore network structure in evaluating the response of soils to fertilization management.

Mesh-of-Torus: a new topology for server-centric data center networks

Various topologies have been proposed for high-performance computing (HPC), i.e., fat-tree, Torus topology. Compared with conventional fat-tree topology, Torus performs much better when applied in HPC. Unfortunately, due to its wraparound links, Torus topology naturally has the tendency to trigger deadlock incidents inside the network. Researchers solve this problem by means of virtual channel, but this approach will also restrict the routing of message. In this paper, we propose a deadlock-free topology for HPC, called Mesh-of-Torus, which incarnates the good characteristics of Mesh and Torus topology. Comparing with mesh, Mesh-of-Torus has shorter network diameter. Furthermore, we have proposed a corresponding port assignment rules in consideration of complicated internal arbitration or scheduling mechanism incurred by the employment of virtual channel. Deadlock avoidance can be achieved when dimension-order routing algorithm and our port assignment rules are applied to Mesh-of-Torus. Finally, simulations and mathematical analysis have shown that Mesh-of-Torus outperforms Mesh in terms of average end-to-end latency and network load distribution.

Analysis of social interaction network properties and growth on Twitter

The complex topology of real networks allows its actors to change their functional behavior. Network models provide better understanding of the evolutionary mechanisms being accountable for the growth of such networks by capturing the dynamics in the ways network agents interact and change their behavior. Considerable amount of research efforts is required for developing novel network modeling techniques to understand the structural properties of such networks, reproducing similar properties based on empirical evidence, and designing such networks efficiently. In this study, we first demonstrate how to construct social interaction networks using social media data and then present the key findings obtained from the network analytics. We analyze the characteristics and growth of online social interaction networks, examine the network properties and derive important insights based on the theories of network science literature. We observed that the degree distributions of such networks follow power-law that is indicative of the existence of fewer nodes in the network with higher levels of interactions, and many other nodes with less interaction. While the network elements and average user degree grow linearly each day, densities of such networks tend to become zero. Largest connected components exhibit higher connectivity (density) when compared with the whole graph. Network radius and diameter become stable over time evidencing the small-world property. We also observe increased transitivity and higher stability of the power-law exponents as the networks grow. Since the data is specific to the Purdue University community, we also observe two very big events, namely Purdue Day of Giving and Senator Bernie Sanders’ visit to Purdue University as part of Indiana Primary Election 2016. The social interaction network properties that are revealed in this study can be useful in disseminating targeted information during planned special events.

The Relationship Between P-Dominance and Stochastic Stability

This paper examines the properties of networks that determine the uniqueness of long-run equilibria emerging from symmetric coordination games when players are myopic best responders. We identify the contagion threshold and the network diameter as two measures of finite networks that determine when strategies in the minimal p-best response set of a coordination game are uniquely stochastically stable. We show that when the contagion threshold is greater or equal to p, strategies in the minimal p-best response set are uniquely stochastically stable in strongly connected networks with diameter greater or equal to seven. The contagion threshold and the network diameter are easy to compute and their values are unique for every strongly connected network.

A new routing strategy limited by heterogeneous link bandwidth

Traffic capacity of a network is very vital to a variety of complex networks, such as communication networks and road networks, in which the bandwidth of every link is limited or finite. In this work, inspired by the deployment process of nodes and links in real networks, we assume the bandwidth of every link is composed of a constant part and a degree-related one that can be updated iteratively with the network hardware update. We propose a link bandwidth-based routing mechanism to enhance the network traffic capacity. Extensive simulations in both scale-free networks and random networks are done to confirm the effectiveness of our proposed method. Comparing results with the shortest path routing and a weighted routing, our method achieves better network traffic capacity among all used routing strategies without obvious extra cost including the network diameter, average path length and average packet traveling time. Our work studies network routing from a very new perspective and might have potential applications in real network systems such as the communication networks.

The pressure drop across combined polydisperse spherical particle – Cylindrical fiber networks

In the fibrous filtration of particles in gas and liquid flows, loading is the act of particles depositing onto fibers. Loaded particles alter the filter microstructure and can have a profound influence on the pressure drop across a filter medium. Of interest is therefore a simple approach to predict the pressure drop across a loaded filter, accounting for both fibers and loaded, spherical particles. In the present study, we use computational fluid dynamics simulations to develop a simple predictive model for the pressure drop across fibrous media composed of a combination of cylindrical fibers and spherical particles. Specifically, the pressure drop is calculated via an in-house written code to solve the incompressible viscous flow equations in a periodic domain, with the particles and fibers accounted for via the immersed boundary method. For calculations, we generate randomly oriented three-dimensional virtual fibrous networks with prescribed microstructures, including network total solidity, fiber orientation angle distribution, fiber radius distribution, and particle radius distribution (both polydisperse). We find that irrespective of network geometry, by defining a single effective network diameter, the product of the dimensionless pressure drop per unit length and the Reynolds number can be expressed solely a function of the total solidity of the network (particle solidity plus fiber solidity) for fiber solidities in 0.03–0.20 range and particle solidities in the 0.0–0.08 range. The effective diameter, employed in both non-dimensionalization of the pressure drop and the Reynolds number definition, is found to depend upon the first and second moments of the fiber diameter distribution functions, and the second and third moments of the particle diameter distribution functions. We develop a regression equation to fit calculation results; the functional form of the equation is based upon a linear combination of the low and high solidity limits for the permeability term in Darcy’s Law. We additionally apply this pressure drop relationship in loading simulations to examine the evolution of filter pressure drop and figure of merit as loading proceeds. Test results on model filters show that the pressure drop increases significantly as loading proceeds, with loading of the front regions of filters contributing most significantly to the pressure drop. Interestingly, model results suggest that the figure of merit first increases upon loading and then decreases, justifying preloading of filters to increase performance.

A study of the robustness of optical networks under massive failures

In this paper, we provide a comparative analysis of network robustness for different synthetic and real optical network topologies under various types of massive failures using the Girona Network Robustness Simulator (GNRS). We model massive failures as random, targeted, and epidemic, the later of which has not yet been considered in the context of robustness. Results indicate that, in addition to the presence of hub nodes, which are critical for targeted attacks, the network diameter limiting the distance between hubs plays an important role in network robustness under epidemic massive failures.

A cost-effective low-latency overlaid torus-based data center network architecture

In this paper, we present the design, analysis, and implementation of a novel data center network architecture named CLOT, which delivers significant reduction in the network diameter, network latency, and infrastructure cost. CLOT is built based on a switchless torus topology by adding only a number of most beneficial low-end switches in a proper way. Forming the servers in close proximity of each other in torus topology well implements the network locality. The extra layer of switches largely shortens the average routing path length of torus network, which increases the communication efficiency. We show that CLOT can achieve lower latency, smaller routing path length, higher bisection bandwidth and throughput, and better fault tolerance compared to both conventional hierarchical data center networks as well as the recently proposed CamCube network. Coupled with the coordinate based geographical addresses and credit based flow control, the specially designed POW routing algorithm helps CLOT achieve its maximum theoretical performance. Besides, an automatic address configuration mechanism and malfunction detection mechanism are provided to facilitate the network deployment and configuration. The sufficient mathematical analysis and theoretical derivation prove both guaranteed and ideal performance of CLOT.

A possible optimal design of one-way Hamming network H(n, 3) based on the minimum transmission latency

One-way Hamming network H(n, 3), namely directed Hamming network, is the cartesian product of n complete graphs $$K_{3}$$ and has been widely used in hypercube parallel computer for its high communication rate and availability. As one of the critical parameters for evaluating the one-way Hamming network performance, the transmission latency which is the time for the information transmits from the source to the destination is proportional to the network diameter, and it can be reduced by optimizing the network diameter, especially, the minimum transmission latency corresponds to the oriented diameter which is the minimum diameter of one-way network. Currently, although the problems in the design and optimization of H(n, 2) with the oriented diameter and the minimum transmission latency have been solved, studies on the one-way Hamming network H(n, 3) are not found the best of our knowledge. This paper studies the one-way Hamming network H(n, 3) with the possible oriented diameter and the possible minimum transmission latency. Specifically, we first present a lemma and a mathematical model for the one-way Hamming network H(n, 3) with the possible oriented diameter and the possible minimum transmission latency, and then propose a recursive method to obtain $$n\le \overrightarrow{d}(H(n,3))\le n+1$$, where $$\overrightarrow{d}(H(n,3))$$ denotes the oriented diameter of H(n, 3). Finally, a practical example is utilized to intuitively describe such a method in this paper. Results show that the optimal design of the one-way Hamming network H(n, 3) helps reduce the information transmission latency by $$100\%$$ as n tends to infinity when 2n is the baseline.

Technical and Economic Synergetic Effect in Conditions of Innovative Transformation of Water Supply and Sewerage Economy

There has been conducted a study of interdependence between technical and economic researches of diameters calculation of water pressure supply and sewerage networks. There has been offered the method to calculate the optimal diameter of water pressure supply and sewerage networks made of polymeric pipes. This qualitative and quantity methodology includes, firstly, the observation review of Ukrainian water supply and sewerage networks and, secondly, the survey of financial and economic documents of water supply and sewerage economy. The factual basis of the study is the initial data of statistical monitoring of work conditions of water pressure supply and sewerage networks. The paper proposes using the net present value (NPV) to calculate the optimal diameter of water pressure pipes made of polymeric materials, which, finally, decreases capital and exploiting expenditures and considers the maximum income for water supply and sewerage economy (WSE).

Analysis of transmission-power-grid topology and scalability, the European case study

Topological analyses are crucial when assessing network robustness or generating synthetic power grids. In the case of synthetic power grids, topological considerations may be included during the generation process or they may be used as validation criteria once synthetic networks are generated. These synthetic grids can be used as case studies only if their topology is statistically consistent with real power networks. With a view to looking into power-network topology, we analyze the topology of fifteen European transmission networks by using complex-network metrics. The study includes two voltage levels: 400 kV and 200 kV. We study these levels both independently and as a single combined grid. Degree distribution, characteristic path length, network diameter, betweenness centrality and global clustering coefficient are explored in order to understand network topology and to explain observed differences among countries. We analyze empirically whether those metrics scale or not with network size as well as the characterization of power grids as small-world networks. Our conclusions improve the current understanding of power network topology, which is essential for generating synthetic power grids and in the assessment of network robustness.

Characterizing Aggregate Pore Structure by X‐Ray Micro‐Computed Tomography and a Network Model

Core Ideas Function‐related intra‐aggregate pore structures were investigated for four soils. The network properties of a connected pore system were analyzed. The C/I ratio has potential to predict the functions and properties of aggregates. Spatial variation of the isolated pores affects the potential water retention ability. Information about the influence of intra‐aggregate pore structure on functions and properties of soil aggregates is not fully available or predictable. In this study, the microscale intra‐aggregate pore structure of four soils (Mollisol, Alfisol, Ultisol, and Vertisol) was studied by a synergistic use of synchrotron‐based X‐ray micro‐computed tomography (SR‐mCT) and advanced analytical data methods. Detailed characteristics of the connected and isolated pores of four soils were investigated by a pore network model, a network analysis, and a pore map analysis, respectively. Results indicated that total porosity and the connected/isolated porosity ratio (C/I) could describe the possible function of the soil aggregates. The aggregates with larger total porosity and C/I ratio (such as Mollisol and Alfisol) tend to have better air, water, and nutrient exchangeability as well as balance of water retention and physical C protection; whereas the aggregates with smaller total porosity and C/I ratio (such as Ultisol and Vertisol) tend to reduce air and water exchange but have relatively better water retention ability. The pore map analysis revealed the spatial variations of isolated pores within the aggregates and depending on soil types, may influence greatly water retention and C physical protection in aggregates. The pore network model and the network analysis revealed that Ultisol and Vertisol have a smaller average throat area, an average channel length, a larger network diameter, and an average path length, which could have limited the exchangeability of air, water, and nutrient. Our results indicated that the total porosity and the C/I ratio were effective proxy indicators, which could be used to predict the functions and properties of an aggregate.

Algorithm for complex network diameter based on distance matrix

The network diameter is an important characteristic parameter of a complex network. Calculation for a large-scale complex network's diameter has been an important subject in the study of complex networks. If the network diameter is calculated directly, the problem mainly exists in efficiency for searching and counting the shortest paths. If the network diameter is calculated indirectly by studying the statistical function about the relationship between the network diameter and parameters affecting the diameter, the problems not only exist in the efficiency of statistic, but also exist in the function which may be not applicable to all kinds of networks. An algorithm for the complex network diameter based on the k order distance matrix is proposed with a matrix multiplication approach, and a mathematical proof for the algorithm correctness is given as well. Furthermore, some relevant propositions and deductions for reducing the complexity of this algorithm are put forward. With a good theoretical basis and a simple calculation process, this algorithm can be used to calculate the diameter of a large-scale complex network with small-world effect more accurately and efficiently. Two cases about the advanced research projects agency (ARPA) network model and the Chinese airline network model are adopted to verify the effect of this algorithm.