Electrical Network Theory Research Articles

Computation of resistance distance and Kirchhoff index of the two classes of silicate networks

The resistance distance between two vertices of a simple connected graph G is equal to the resistance between two equivalent points on an electrical network, constructed so as to correspond to G, with each edge being replaced by a unit resistor. The Kirchhoff index of G is the sum of resistance distances between all pairs of vertices in G. In this paper, the resistance distance between any two arbitrary vertices of a chain silicate network and a cyclic silicate network was procured by utilizing techniques from the theory of electrical networks, i.e., the series and parallel principles, the principle of elimination, the star-triangle transformation and the delta-wye transformation. Two closed formulae for the Kirchhoff index of the chain silicate network and the cyclic silicate network were obtained respectively.

Applications of matroids in electric network theory

Professor Masao Iri and his students had several important contributions to the theory of electric networks. He was one of the first scientists who recognized the importance of matroid theory in studying the qualitative problems of electric networks. The present paper summarizes his results in the unique solvability of linear active networks and in the existence of hybrid immittance description of linear multiports. Then his contribution to the proper understanding of the duality principle in electric network theory is presented. The last two sections are strongly related to the concept of genericity, leading to some results in the qualitatively reliable synthesis of linear multiports and to some considerations on how to store the data of linear multiports. These applications require a broad spectrum of matroidal tools, like the matroid partition, intersection and parity algorithms and concepts like matroid union, gammoids, transversal matroids, etc. The survey is extended by some more recent results showing that the influence of Professor Iri to the younger generation of researchers will be thriving for many years to come.

Comparison of exclusion, imputation and modelling of missing binary outcome data in frequentist network meta-analysis

BackgroundMissing participant outcome data (MOD) are ubiquitous in systematic reviews with network meta-analysis (NMA) as they invade from the inclusion of clinical trials with reported participant losses. There are available strategies to address aggregate MOD, and in particular binary MOD, while considering the missing at random (MAR) assumption as a starting point. Little is known about their performance though regarding the meta-analytic parameters of a random-effects model for aggregate binary outcome data as obtained from trial-reports (i.e. the number of events and number of MOD out of the total randomised per arm).MethodsWe used four strategies to handle binary MOD under MAR and we classified these strategies to those modelling versus excluding/imputing MOD and to those accounting for versus ignoring uncertainty about MAR. We investigated the performance of these strategies in terms of core NMA estimates by performing both an empirical and simulation study using random-effects NMA based on electrical network theory. We used Bland-Altman plots to illustrate the agreement between the compared strategies, and we considered the mean bias, coverage probability and width of the confidence interval to be the frequentist measures of performance.ResultsModelling MOD under MAR agreed with exclusion and imputation under MAR in terms of estimated log odds ratios and inconsistency factor, whereas accountability or not of the uncertainty regarding MOD affected intervention hierarchy and precision around the NMA estimates: strategies that ignore uncertainty about MOD led to more precise NMA estimates, and increased between-trial variance. All strategies showed good performance for low MOD (<5%), consistent evidence and low between-trial variance, whereas performance was compromised for large informative MOD (> 20%), inconsistent evidence and substantial between-trial variance, especially for strategies that ignore uncertainty due to MOD.ConclusionsThe analysts should avoid applying strategies that manipulate MOD before analysis (i.e. exclusion and imputation) as they implicate the inferences negatively. Modelling MOD, on the other hand, via a pattern-mixture model to propagate the uncertainty about MAR assumption constitutes both conceptually and statistically proper strategy to address MOD in a systematic review.

Towards a Simplified Estimation of Muscle Activation Pattern from MRI and EMG Using Electrical Network and Graph Theory.

Muscle functional MRI (mfMRI) is an imaging technique that assess muscles’ activity, exploiting a shift in the T2-relaxation time between resting and active state on muscles. It is accompanied by the use of electromyography (EMG) to have a better understanding of the muscle electrophysiology; however, a technique merging MRI and EMG information has not been defined yet. In this paper, we present an anatomical and quantitative evaluation of a method our group recently introduced to quantify its validity in terms of muscle pattern estimation for four subjects during four isometric tasks. Muscle activation pattern are estimated using a resistive network to model the morphology in the MRI. An inverse problem is solved from sEMG data to assess muscle activation. The results have been validated with a comparison with physiological information and with the fitting on the electrodes space. On average, over 90% of the input sEMG information was able to be explained with the estimated muscle patterns. There is a match with anatomical information, even if a strong subjectivity is observed among subjects. With this paper we want to proof the method’s validity showing its potential in diagnostic and rehabilitation fields.

Effect of Hybrid Particles of Nano-Micron Sizes on Electrical Transport of Silver-Epoxy Composites

Electrically Conductive Adhesive’s (ECAs) mainly consist of a polymer as matrix and binder to filler as conductor. The performance of electrical properties in ECAs strongly depends on the concentration (volume fraction) of the metal filler, morphology of the filler, filler distribution within the polymer matrix, the interaction between filler surface, and the contact resistance between adjacent particles. In this work, the characteristics of electrical transport of ECA's systems on Ag-Epoxy composites are containing either micro or nano fillers are studied by the electric static network theory using FEM. The hybrid system will be formed for considering influence electrical transport properties. The spherical Silver (Ag) used 80 nm and 2 μm in diameter in this study. Two particles chain forming electrically transport with some number of particles and reach a conductivity value of ECA's. The result indicated that nano size silver usually lower its conductivity than micron size. During simulation, it has been shown the correlation between nano and micron size demonstrated a increasing in the electrical transport when the hybrid system performed.

Stability Analysis of Multi-Inverters Grid-Connected System Using Improved Current Source Impedance Ratio Criterion

Stability analysis of multi-inverters grid-connected system in electric vehicles power station is presented in this paper. An equivalent circuit model of the multi-inverters grid-connected system is built based on electrical network theory. Then an improved current source impedance criterion is proposed to analyse the stability of the system which is mainly related to the number of grid connected inverters, grid impedance and output impedance of the inverters. Finally, simulation results are given to verify the effectiveness of the multi-inverters model and the improved current source impedance criterion. DOI: 10.5755/j01.eie.25.2.23198

Biophysical implications of Maxwell stress in electric field stimulated cellular microenvironment on biomaterial substrates

A number of experimental studies have established the critical role of electric field stimulation on cell functionality modulation of various cell types on a wide range of biomaterial platforms in vitro. In particular, cell fate processes, morphological changes and electroporation are significantly modulated over a narrow range of electric field stimulation conditions. Although a few studies using electrical network theory, first principle simulations and electrohydrodynamic models are reported in the literature, the present study establishes a theoretical foundation to a new perspective that bioelectric stress can significantly influence cell morphological changes/electroporation and in a broader sense, the cell response to electric field on biomaterial substrates. A single cell is modelled as a spherical membrane separating the culture medium and the cytoplasm having different dielectric properties. The analytical solutions to the Laplace equation and Poisson equation for the system are adopted to quantitatively capture the potential distribution in the cellular microenvironment for different cases. These include a cell on a conducting substrate, on an insulating substrate and a cell with surface charge density, in electric field stimulated cellular microenvironment. The biophysical significance of the normal stress distribution has been discussed in terms of the variation in the cellular deformation, depending on the frequency of the electric field and substrate conductivity. A significant difference has been observed in the deformation behavior at higher frequencies (>109 Hz) compared to low frequency and DC electric fields. This theoretical study therefore unravels the significance of substrate conductivity in synergy with electric field parameters to modulate cell response. In addition, the tangential component of the Maxwell stress tensor (shear stress), a measure of the stretching force on the membrane, has been used to obtain estimates of the critical electric field required for membrane rupture. It has been predicted that a cell with surface charge density requires electric fields of the order of 10 kV/mm in order to undergo membrane rupture, which is in line with the experimental observations reported in the literature. Taken together, the presented analysis is expected to provide guidelines to develop next generation biomaterials and biomedical devices for regenerative medicine and cancer treatments.

Robust Determination of Protein Allosteric Signaling Pathways.

To understand how protein function changes upon an allosteric perturbation, such as ligand binding and mutation, significant progress in characterizing allosteric network from molecular dynamics (MD) simulations has been made. However, determining which amino acid(s) play an essential role in the propagation of signals may prove challenging, even when the location of the source and sink is known for a protein or protein complex. This challenge is mainly due to the large fluctuations in protein dynamics that cause instability of the network topology within a single trajectory or between multiple replicas. To solve this problem, we introduce the current-flow betweenness scheme, originated from electrical network theory, to protein dynamical network analysis. To demonstrate the benefit of this new method, we chose a prototypic allosteric enzyme (IGPS or HisH-HisF dimer) as our benchmark system. Using multiple replicas of simulations and multiple network topology comparison metrics (edge ranking, path length, and node frequency), we show that the current-flow betweenness provides a significant improvement in the convergence of the allosteric networks. The improved stability of the network topology allows us to generate a delta-network between the apo and holo forms of the protein. We illustrated that the delta-network is a more rigorous way to capture the subtle changes in the networks that would otherwise be neglected by comparing node usage frequencies alone. We have also investigated the use of a linear smoothing function to improve the stability of the contact map. The methodology presented here is general and may be applied to other topology and weighting schemes. We thus conclude that, for determining protein signaling pathways between the pair(s) of source and sink, multiple MD simulation replicas are necessary, and the current-flow betweenness scheme introduced here provides a more robust approach than the geodesic scheme based on correlation edge weighting.

Somatosensory stimulation treatments for postoperative analgesia of mixed hemorrhoids: Protocol for a systematic review and network meta-analysis.

Background:Pain after hemorrhoidal surgery bothers both clinicians and patients. Somatosensory stimulation treatments have shown promising effect on the pain after hemorrhoidal surgery, but the comparative effectiveness between them has not been studied. We aim to determine the relative effectiveness among these treatments on pain relief after hemorrhoidal surgery by using network meta-analysis.Method:We will search the following electronic databases: MEDLINE, EMBASE, the Cochrane library, Chinese Biomedicine database (CBM), China National Knowledge Infrastructure (CNKI). We will include randomized controlled trials (RCTs) that examine the effect of somatosensory stimulation treatments on pain after hemorrhoidal surgery. The primary outcome will be the responder rate after treatment. The secondary outcomes will include the assessments with pain intensity scales (visual analog scale, numeric rating scale, or other scales) on day 1 to 7 after surgery. Two independent reviewers will extract needed information from eligible trials using standardized electronic forms. Network meta-analysis will be performed using a frequentist framework based on electrical network theory. The relative effectiveness of the treatments will be ranked by using P score, which is the mean probability of a treatment ranking the best in all treatments. Meta-regression will be performed to assess the impact of surgery type, anesthesia methods, and funding source on the treatment ranking. The quality of the eligible RCTs will be evaluated by the Cochrane risk of bias tool.Ethics and dissemination:The result of this network meta-analysis will clarify which is the relatively best somatosensory-stimulation treatment in relieving postoperative pain caused by hemorrhoidal surgery, and the review will, therefore, guide the management of postoperative pain after hemorrhoidal surgery for clinicians and patients. This review does not require ethical approval and will be reported in a peer-reviewed journal.Trial registration number:PROSPERO CRD42018115558.

Cover Time in Edge-Uniform Stochastically-Evolving Graphs

We define a general model of stochastically-evolving graphs, namely the edge-uniform stochastically-evolving graphs. In this model, each possible edge of an underlying general static graph evolves independently being either alive or dead at each discrete time step of evolution following a (Markovian) stochastic rule. The stochastic rule is identical for each possible edge and may depend on the past k ≥ 0 observations of the edge’s state. We examine two kinds of random walks for a single agent taking place in such a dynamic graph: (i) The Random Walk with a Delay (RWD), where at each step, the agent chooses (uniformly at random) an incident possible edge, i.e., an incident edge in the underlying static graph, and then, it waits till the edge becomes alive to traverse it. (ii) The more natural Random Walk on what is Available (RWA), where the agent only looks at alive incident edges at each time step and traverses one of them uniformly at random. Our study is on bounding the cover time, i.e., the expected time until each node is visited at least once by the agent. For RWD, we provide a first upper bound for the cases k = 0 , 1 by correlating RWD with a simple random walk on a static graph. Moreover, we present a modified electrical network theory capturing the k = 0 case. For RWA, we derive some first bounds for the case k = 0 , by reducing RWA to an RWD-equivalent walk with a modified delay. Further, we also provide a framework that is shown to compute the exact value of the cover time for a general family of stochastically-evolving graphs in exponential time. Finally, we conduct experiments on the cover time of RWA in edge-uniform graphs and compare the experimental findings with our theoretical bounds.

Connectivity in a Karst System Using Electrical Resistivity Tomography and Network Theory.

The Ring of Cenotes (RC) is an alignment of numerous cenotes (sinkholes) in a semicircular form (with a radius of 100 km) located in northwestern Yucatán, México. The formation roughly coincides with a concentric ring that corresponds to a buried structure, which has been identified as the product of a meteor impact, known as the Chicxulub crater. Secondary permeability generated by the fracturing and faulting of the sedimentary sequence in the Chicxulub crater has favored the karstification process and therefore the development of underground rivers that transport water from the mainland to the sea. This study implements the network theory to study the hydrological connectivity between a group of 11 cenotes within the RC. Eight electrical resistivity tomography transects were used as an empirical basis. Each transect was acquired directly in the field using the SuperSting R1/IP equipment with a dipole-dipole configuration. An adapted version of the reliability algorithm for communication networks was used as a theoretical model. We found evidence of the existence of water cavities in the study area. We made a network from the data and assigned connection probabilities among cenotes as a function of the separation length and the number of water cavities, as well as their size.

Impulse Grounding Resistance of Graphite Flexible Grounding Material under Spark Effect

Graphite flexible grounding material is an environmentally friendly material with corrosion resistant, non-magnetic and flexible characteristic, which is gradually applied to grounding of transmission lines in recent years. In order to provide a reference for grounding grid design and impulse resistance measurement, an iterative calculation method based on electric-network theory is proposed. The equivalent method of the equivalent time-varying radius and influence of different iteration methodsonthe calculation resultsare discussed. Furthermore the accuracy of this method is compared with that of traditional ones in regulations. In the end the impulse grounding resistance of three kinds of grounding grids are calculated with this method and the empirical formulas of impulse coefficient are built. The results show that it can be considered that there is reference value in the calculation results obtained by the method in this paper, and the calculation accuracy improved as well. It obtains three typical grid structures under the impulse coefficient experience formula, and the grounding grid design and impulse resistance measurements of flexible graphite grounding electrode can provide reference. Flexible graphite grounding material has a broad application prospect in the power system grounding technology.

Symmetry in the Green’s Function for Birth-death Chains

A symmetric relation in the probabilistic Green’s function for birth-death chains is explored. Two proofs are given, each of which makes use of the known symmetry of the Green’s functions in other contexts. The first uses as primary tool the local time of Brownian motion, while the second uses the reciprocity principle from electric network theory. We also show that the the second proof extends easily to cover birth-death chains (a.k.a. state-dependent random walks) on trees, and can be adapted in order to derive hitting times on trees.

On the number of spanning trees, the Laplacian eigenvalues, and the Laplacian Estrada index of subdivided-line graphs

Abstract As a generalization of the Sierpiński-like graphs, the subdivided-line graph Г(G) of a simple connected graph G is defined to be the line graph of the barycentric subdivision of G. In this paper we obtain a closed-form formula for the enumeration of spanning trees in Г(G), employing the theory of electrical networks. We present bounds for the largest and second smallest Laplacian eigenvalues of Г(G) in terms of the maximum degree, the number of edges, and the first Zagreb index of G. In addition, we establish upper and lower bounds for the Laplacian Estrada index of Г(G) based on the vertex degrees of G. These bounds are also connected with the number of spanning trees in Г(G).

Using electric network theory to model the spread of oak processionary moth, Thaumetopoea processionea, in urban woodland patches

Context Habitat fragmentation is increasing as a result of anthropogenic activities, especially in urban areas. Dispersal through fragmented habitats is key for species to spread, persist in metapopulations and shift range in response to climate change. However, high habitat connectivity may also hasten the spread of invasive species. Objective To develop a model of spread in fragmented landscapes and apply it to the spread of an invasive insect in urban woodland. Methods We applied a patch-based model, based on electric network theory, to model the current and predicted future spread of oak processionary moth (OPM: Thaumetopoea processionea) from its source in west London. We compared the pattern of ‘effective distance’ from the source (i.e. the patch ‘voltage’ in the model) with the observed spread of the moth from 2006 to 2012. Results We showed that ‘effective distance’ fitted current spread of OPM. Patches varied considerably in their ‘current’ and ‘power’ (metrics from the model), which is an indication of their importance in the future spread of OPM. Conclusions Patches identified as ‘important’ are potential ‘pinch points’ and regions of high ‘flow’, where resources for detection and management will be most cost-effectively deployed. However, data on OPM dispersal and the distribution of oak trees limited the strength of our conclusions, so should be priorities for further data collection. This application of electric network theory can be used to inform landscape-scale conservation initiatives both to reduce the spread of invasives and to facilitate large-scale species’ range shifts in response to climate change.

A series RCL circuit theory for analyzing non-steady-state water uptake of maize plants.

Understanding water uptake and transport through the soil-plant continuum is vital for ecosystem management and agricultural water use. Plant water uptake under natural conditions is a non-steady transient flow controlled by root distribution, plant configuration, soil hydraulics, and climatic conditions. Despite significant progress in model development, a mechanistic description of transient water uptake has not been developed or remains incomplete. Here, based on advanced electrical network theory (RLC circuit theory), we developed a non-steady state biophysical model to mechanistically analyze the fluctuations of uptake rates in response to water stress. We found that the non-steady-state model captures the nature of instantaneity and hysteresis of plant water uptake due to the considerations of water storage in plant xylem and coarse roots (capacitance effect), hydraulic architecture of leaf system (inductance effect), and soil-root contact (fuse effect). The model provides insights into the important role of plant configuration and hydraulic heterogeneity in helping plants survive an adverse environment. Our tests against field data suggest that the non-steady-state model has great potential for being used to interpret the smart water strategy of plants, which is intrinsically determined by stem size, leaf size/thickness and distribution, root system architecture, and the ratio of fine-to-coarse root lengths.

An Upper Bound on the Convergence Time for Quantized Consensus of Arbitrary Static Graphs

We analyze a class of distributed quantized consensus algorithms for arbitrary static networks. In the initial setting, each node in the network has an integer value. Nodes exchange their current estimate of the mean value in the network, and then update their estimation by communicating with their neighbors in a limited capacity channel in an asynchronous clock setting. Eventually, all nodes reach consensus with quantized precision. We analyze the expected convergence time for the general quantized consensus algorithm proposed by Kashyap et al. (“Quantized consensus,” Automatica, 2007). We use the theory of electric networks, random walks, and couplings of Markov chains to derive an O(N <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sup> log N) upper bound for the expected convergence time on an arbitrary graph of size N, improving on the state of art bound of O(N <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">5</sup> ) for quantized consensus algorithms. Our result is not dependent on graph topology. Example of complete graphs is given to show how to extend the analysis to graphs of given topology. This is consistent with the analysis in “Convergence speed of binary interval consensus,” (M. Draief and M. Vojnovic, SIAM J. Control and Optimization, 2012.

Application on State Evaluation of the Grounding Conductor Based on Fault Diagnosis Method

In this paper, fault diagnosis model of grounding grid is established combining electrical network theory with sensitivity analysis. A new method which is used to select the node pairs to calculate the corrosion situation of grounding grid is presented. Based on this method, the fault branch of grounding grid can be efficiently judged through topology diagram and port resistance without power failure and the excavation of large area. Field test was carried out at 220 kV electrical substations using the diagnosis method. The conductors diagnosed as severely corroded was excavated. The result was identical to the diagnosis results, indicating that this diagnosis method has engineering practicality.

On a new cyclicity measure of graphs—The global cyclicity index

Being motivated in terms of mathematical concepts from the theory of electrical networks, Klein and Ivanciuc introduced and studied a new graph-theoretic cyclicity index—the global cyclicity index (Klein, Ivanciuc, 2001). In this paper, by utilizing techniques from graph theory, electrical network theory and real analysis, we obtain some further results on this new cyclicity measure, including the strictly monotone increasing property, some lower and upper bounds, and some Nordhaus–Gaddum-type results. In particular, we establish a relationship between the global cyclicity index C(G) and the cyclomatic number μ(G) of a connected graph G with n vertices and m edges: mn−1μ(G)≤C(G)≤n2μ(G).

Time-Domain Synthesis Problem involving I-Function of Several Variables

The object of this paper is to evaluate an integral involving Bessel polynomial and I-function of several variables and employ it to obtain a particular solution of the general solution derived in this paper of the classical problem known as the, Time-domain Synthesis Problem, occurring in electrical network theory.