link prediction based on local information considering preferential attachment abstract link prediction in complex networks has attracted much attention in many fields in this paper a common neighbors plus preferential attachment index is presented to estimate the likelihood of the existence of a link between two nodes based on local information of the nearest neighbors numerical experiments on six real networks demonstrated the high effectiveness and efficiency of the new index compared with five well known and widely accepted indices the common neighbors resource allocation index preferential attachment index local path index and katz index the new index provides competitively accurate prediction with local path index and katz index while has less computational complexity and is more accurate than the other two indices

stabilization of rayleigh benard convection by means of mode reduction a method is developed to suppress the intensity of the rayleigh benard convection by adjusting the heat flux distribution at the bottom boundary under the constraint of constant heat input to the system the appropriate profile of heat flux which is changing continually in accordance with the shape of convection cells in the domain is determined by the model predictive control the optimal control strategy given by the model predictive control is implemented efficiently by employing the karhunen loeve galerkin procedure through which the boussinesq equation is reduced to a low dimensional dynamic model this method is found to yield accurate results with a decent requirement of computer time

radial structure of the internet the structure of the internet at the autonomous system as level has been studied by the physics mathematics and computer science communities we extend this work to include features of the core and the periphery taking a radial perspective on as network structure new methods for plotting as data are described and they are used to analyse datasets that have been extended to contain edges missing from earlier collections the average distance from one vertex to the rest of the network is used as the baseline metric for investigating radial structure common vertex specific quantities are plotted against this metric to reveal distinctive characteristics of central and peripheral vertices two datasets are analysed

percolation theory and fragmentation measures in social networks abstract we study the statistical properties of a recently proposed social networks measure of fragmentation f after removal of a fraction q of nodes or links from the network the measure f is defined as the ratio of the number of pairs of nodes that are not connected in the fragmented network to the total number of pairs in the original fully connected network we compare this measure with the one traditionally used in percolation theory p the fraction of nodes in the largest cluster relative to the total number of nodes using both analytical and numerical methods we study erd s renyi er and scale free sf networks under various node removal strategies we find that for a network obtained after removal of a fraction q of nodes above criticality p 1 f 1 2 for fixed p and close to criticality we show that 1 f better reflects the actual fragmentation for a given p 1 f has a broad distribution and thus one can improve significantly the fragmentation of the network we also study and compare the fragmentation measure f and the percolation measure p for a real national social network of workplaces linked by the households of the employees and find similar results

the iterative method for solving nonlinear matrix equation xs a x ta q abstract nonlinear matrix equation x s a x t a q where q is an hermitian positive definite matrix a is the conjugate transpose of the matrix a and both of s and t are positive integers has widely applied background in this paper necessary conditions and sufficient conditions for the existence of hermitian positive definite solutions of this equation are derived an iterative method for obtaining hermitian positive definite solutions is proposed moreover a perturbation bound for the hermitian positive definite solutions is given

spin glass model for the c dismantling problem c dismantling cd problem aims at finding the minimum vertex set d of a graph g v e after removing which the remaining graph will break into connected components with the size not larger than c in this paper we introduce a spin glass model with c 1 integer value states into the cd problem and then study the properties of this spin glass model by the belief propagation bp equations under the replica symmetry ansatz we give the lower bound rho c of the relative size of d with finite c on regular random graphs and erdos renyi random graphs we find rho c will decrease gradually with growing c and it converges to rho infty as c to infty the cd problem is called dismantling problem when c is a small finite fraction of v therefore rho infty is also the lower bound of the dismantling problem when v to infty to reduce the computation complexity of the bp equations taking the knowledge of the probability of a random selected vertex belonging to a remaining connected component with the size a the original bp equations can be simplified to one with only three states when c to infty the simplified bp equations are very similar to the bp equations of the feedback vertex set spin glass model h j zhou eur phys j b 86 455 2013 at last we develop two practical belief propagation guide decimation algorithms based on the original bp equations cd bpd and the simplified bp equations scd bpd to solve the cd problem on a certain graph our bpd algorithms and two other state of art heuristic algorithms are applied on various random graphs and some real world networks computation results show that the cd bpd is the best in all tested algorithms in the case of small c but considering the performance and computation consumption we recommend using scd bpd for the network with small clustering coefficient when c is large

iterative methods for nonlinear matrix equations x a x αa i abstract the present paper treats iterative methods for a class of nonlinear matrix equations x a x a i with two cases 1 and 0 a is nonsingular we will derive the necessary and sufficient conditions for the existence of positive definite solutions

on matrix equations x a x 2a i the two matrix equations x a x 2 a i and x a x 2 a i are studied we construct iterative methods for obtaining positive definite solutions of these equations sufficient conditions for the existence of two different solutions of the equation x a x 2 a i are derived sufficient conditions for the existence of positive definite solutions of the equation x a x 2 a i are given numerical experiments are discussed 2001 elsevier science

coauthorship networks and patterns of scientific collaboration by using data from three bibliographic databases in biology physics and mathematics respectively networks are constructed in which the nodes are scientists and two scientists are connected if they have coauthored a paper we use these networks to answer a broad variety of questions about collaboration patterns such as the numbers of papers authors write how many people they write them with what the typical distance between scientists is through the network and how patterns of collaboration vary between subjects and over time we also summarize a number of recent results by other authors on coauthorship patterns

mixing patterns in networks we study assortative mixing in networks the tendency for vertices in networks to be connected to other vertices that are like or unlike them in some way we consider mixing according to discrete characteristics such as language or race in social networks and scalar characteristics such as age as a special example of the latter we consider mixing according to vertex degree i e according to the number of connections vertices have to other vertices do gregarious people tend to associate with other gregarious people we propose a number of measures of assortative mixing appropriate to the various mixing types and apply them to a variety of real world networks showing that assortative mixing is a pervasive phenomenon found in many networks we also propose several models of assortatively mixed networks both analytic ones based on generating function methods and numerical ones based on monte carlo graph generation techniques we use these models to probe the properties of networks as their level of assortativity is varied in the particular case of mixing by degree we find strong variation with assortativity in the connectivity of the network and in the resilience of the network to the removal of vertices

on the existence of a positive definite solution of the matrix equation x atx 1a i the question is raised under which conditions on the real square matrix a the matrix equation x atx 1a i has a real symmetric positive definite solution x both necessary and sufficient solvability conditions on a are derived moreover we give an algorithm to calculate the solution for a number of special cases we also present an analytic solution

investigations on boundary temperature control analysis considering a moving body based on the adjoint variable and the fictitious domain finite element methods summary this paper presents an examination of moving boundary temperature control problems with a moving boundary problem a finite element mesh is generated at each time step to express the position of the boundary on the other hand if an overlapped domain that is comprising foreground and background meshes is prepared the moving boundary problem can be solved without mesh generation at each time step by using the fictitious domain method in this study boundary temperature control problems with a moving boundary are formulated using the finite element the adjoint variable and the fictitious domain methods and several numerical experiments are carried out copyright 2015 john wiley sons ltd

correlations in complex networks under attack for any initially correlated network after any kind of attack where either nodes or edges are removed we obtain general expressions for the degree degree probability matrix and degree distribution we show that the proposed analytical approach predicts the correct topological changes after the attack by comparing the evolution of the assortativity coefficient for different attack strategies and intensities in theory and simulations we find that it is possible to turn an initially assortative network into a disassortative one and vice versa by fine tuning removal of either nodes or edges for an initially uncorrelated network on the other hand we discover that only a targeted edge removal attack can induce such correlations

bridges in complex networks a bridge in a graph is an edge whose removal disconnects the graph and increases the number of connected components we calculate the fraction of bridges in a wide range of real world networks and their randomized counterparts we find that real networks typically have more bridges than their completely randomized counterparts but they have a fraction of bridges that is very similar to their degree preserving randomizations we define an edge centrality measure called bridgeness to quantify the importance of a bridge in damaging a network we find that certain real networks have a very large average and variance of bridgeness compared to their degree preserving randomizations and other real networks finally we offer an analytical framework to calculate the bridge fraction and the average and variance of bridgeness for uncorrelated random networks with arbitrary degree distributions

on the positive definite solutions of the matrix equations xs atx ta in abstract the two matrix equations x s a t x t a i n and x s a t x t a i n are studied based on the fixed point theory the existence of the symmetric positive definite solutions are proved sensitivity analysis of the maximal solution is presented some elegant estimates of the positive definite solutions are obtained three iterative methods for computing the positive solutions are proposed

graph partitioning induced phase transitions we study the percolation properties of graph partitioning on random regular graphs with n vertices of degree k optimal graph partitioning is directly related to optimal attack and immunization of complex networks we find that for any partitioning process even if nonoptimal that partitions the graph into essentially equal sized connected components clusters the system undergoes a percolation phase

a new numerical method for the boundary optimal control problems of the heat conduction equation a new numerical method is developed for the boundary optimal control problems of the heat conduction equation in the present paper when the boundary optimal control problem is solved by minimizing the objective function employing a conjugate gradient method the most crucial step is the determination of the gradient of objective function usually employing either the direct differentiation method or the adjoint variable method the direct differentiation method is simple to implement and always yields accurate results but consumes a large amount of computational time although the adjoint variable method is computationally very efficient the adjoint variable does not have sufficient regularity at the boundary for the boundary optimal control problems as a result a large numerical error is incurred in the evaluation of the gradient function resulting in premature termination of the conjugate gradient iteration in the present investigation a new method is developed that circumvents this difficulty with the adjoint variable method by introducing a partial differential equation that describes the temporal and spatial dynamics of the control variable at the boundary the present method is applied to the neumann and dirichlet boundary optimal control problems respectively and is found to solve the problems efficiently with sufficient accuracy

the extremal solution of the matrix equation x s a x q a i in this paper the distribution of the positive definite solution of the nonlinear equation x s a x qa i is deduced the existence of the maximal solution and the minimal solution is discussed and two new iterative algorithms for obtaining these solutions are proposed these algorithms avoid matrix inversion

optimization of random searches on defective lattice networks we study the general problem of how to search efficiently for targets randomly located on defective lattice networks i e regular lattices which have some fraction of its nodes randomly removed we consider large but finite triangular lattices and assume for the search dynamics that the walker chooses steps lengths lj from the power law distribution p lj approximately lj mu with the exponent mu regulating the strategy of the search process at each step lj the searcher moves in straight lines and constantly looks within a detection radius of vision rv for the targets along the way if there is contact with a defect the movement stops and a new step length is chosen hence the presence of defects decreases the efficiency of the overall process we study numerically how three different aspects of the lattice influence the optimization of the search efficiency i the type of boundary conditions ii the concentration of targets and defects and iii the category or class of search destructive nondestructive or regenerative motivated by the results we develop a type of mean field model for the problem and obtain an analytical approximation for the search efficiency function finally we discuss in the context of searches how defective lattices compare with perfect lattices and with continuous environments

attack vulnerability of complex networks we study the response of complex networks subject to attacks on vertices and edges several existing complex network models as well as real world networks of scientific collaborations and internet traffic are numerically investigated and the network performance is quantitatively measured by the average inverse geodesic length and the size of the largest connected subgraph for each case of attacks on vertices and edges four different attacking strategies are used removals by the descending order of the degree and the betweenness centrality calculated for either the initial network or the current network during the removal procedure it is found that the removals by the recalculated degrees and betweenness centralities are often more harmful than the attack strategies based on the initial network suggesting that the network structure changes as important vertices or edges are removed furthermore the correlation between the betweenness centrality and the degree in complex networks is studied

predicting percolation thresholds in networks we consider different methods which do not rely on numerical simulations of the percolation process to approximate percolation thresholds in networks we perform a systematic analysis on synthetic graphs and a collection of 109 real networks to quantify their effectiveness and reliability as prediction tools our study reveals that the inverse of the largest eigenvalue of the nonbacktracking matrix of the graph often provides a tight lower bound for true percolation threshold however in more than 40 of the cases this indicator is less predictive than the naive expectation value based solely on the moments of the degree distribution we find that the performance of all indicators becomes worse as the value of the true percolation threshold grows thus none of them represents a good proxy for the robustness of extremely fragile networks

robustness of network controllability in cascading failure controllability of networks widely existing in real life systems have been a critical and attractive research subject for both network science and control systems communities research in network controllability has mostly focused on the effects of the network structure on its controllability and some studies have begun to investigate the controllability robustness of complex networks cascading failure is common phenomenon in many infrastructure networks which largely affect normal operation of networks and sometimes even lead to collapse resulting in considerable economic losses the robustness of network controllability against the cascading failure is studied by a linear load capacity model with a breakdown probability in this paper the controllability of canonical model networks under different node attack strategies is investigated random failure and malicious attack it is shown by numerical simulations that the tolerant parameter of load capacity model has an important role in the emergence of cascading failure independent to the types of network the networks with moderate average degree are more vulnerable to the cascading failure while these with high average degree are very robust in particular betweenness attack strategy is more harmful to the network controllability than degree attack one especially for the scale free networks

pod and cvt based reduced order modeling of navier stokes flows abstract a discussion of reduced order modeling for complex systems such as fluid flows is given to provide a context for the construction and application of reduced order bases reviews of the pod proper orthogonal decomposition and cvt centroidal voronoi tessellation approaches to reduced order modeling are provided including descriptions of pod and cvt reduced order bases their construction from snapshot sets and their application to the low cost simulation of the navier stokes system some concrete incompressible flow examples are used to illustrate the construction and use of pod and cvt reduced order bases and to compare and contrast the two approaches to reduced order modeling

solutions and perturbation estimates for the matrix equations x a x n a q in this paper we investigate the equations x a x na q for the existence of positive definite solutions and perturbation bounds for these solutions are derived a sufficient condition for uniqueness of a unique positive definite solution of the equation x a x na q is given the results are illustrated by using numerical examples

on positive definite solutions of the nonlinear matrix equations x a x q a q in this paper we investigate the nonlinear matrix equations x a x q a q 0 q 1 and x a x q a q q 1 necessary and sufficient conditions for the unique existence of hermitian positive definite solutions of these equations are derived effective iterative algorithms are also provided to obtain the unique solution of x a x q a q 0 q 1 and the minimal and maximal hermitian positive definite solutions of x a x q a q q 1 numerical examples are included to illustrate the efficiency of the presented iteration algorithms

on positive definite solutions of the nonlinear matrix equation x a x n a i in this paper some properties of a positive definite solution of the nonlinear matrix equation x a x na i are discussed effective iterative methods to obtain the smallest positive definite solution are established moreover the necessary and sufficient conditions for existence the smallest positive definite solution are obtained finally some numerical results are given

enhancing robustness and immunization in geographical networks we find that different geographical structures of networks lead to varied percolation thresholds although these networks may have similar abstract topological structures thus strategies for enhancing robustness and immunization of a geographical network are proposed using the generating function formalism we obtain an explicit form of the percolation threshold q c for networks containing arbitrary order cycles for three cycles the dependence of q c on the clustering coefficients is ascertained the analysis substantiates the validity of the strategies with analytical evidence

exact controllability stabilization and perturbations for distributed systems exact controllability is studied for distributed systems of hyperbolic type or for petrowsky systems like plate equations the control is a boundary control or a local distributed control exact controllability consists in trying to drive the system to rest in a given finite time the solution of the problems depends on the function spaces where the initial data are taken and also depends on the function space where the control can be chosen a systematic method named hum for hilbert uniqueness method is introduced as the terminology indicates it is based on uniqueness results classical or new and on hilbert spaces constructed in infinitely many ways by using uniqueness a number of applications are indicated having a general method for exact controllability implies having a general method for stabilization this leads to new and complicated nonlinear riccati s type pdes to be compared with direct methods when available in the last part of the paper we consider how all this behaves fo

effect of edge removal on topological and functional robustness of complex networks abstract we study the robustness of several network models subject to edge removal the robustness is measured by the statistics of network breakdowns where a breakdown is defined as the destroying of the total connectedness of a network rather than the disappearance of the giant component we introduce a simple traffic dynamics as the function of a network topology and the total connectedness can be destroyed in the sense of either the topology or the function the overall effect of the topological breakdown and the functional breakdown as well as the relative importance of the topological robustness and the functional robustness are studied under two edge removal strategies

centroidal voronoi tessellation based reduced order modeling of complex systems noindent a reduced order modeling methodology based on centroidal voronoi tessellations cvts is introduced cvts are special voronoi tessellations for which the generators of the voronoi diagram are also the centers of mass means of the corresponding voronoi cells for discrete data sets cvts are closely related to the h means and k means clustering techniques a discussion of reduced order modeling for complex systems such as fluid flows is given to provide a context for the application of reduced order bases then detailed descriptions of cvt based reduced order bases and how they can be constructed from snapshot sets and how they can be applied to the low cost simulation of complex systems are given subsequently some concrete incompressible flow examples are used to illustrate the construction and use of cvt based reduced order bases the cvt based reduced order modeling methodology is shown to be effective for these examples

asymptotic estimates for efficiency vulnerability and cost for random networks an investigation both analytical and numerical of the values of efficiency vulnerability and cost functions is provided several comparisons among these functions are made following a pairwise strategy and taking into account different efficiency vulnerability and cost functions it is shown in all cases that these magnitudes display strong correlations which are typically piecewise linear in log space as well as universal i e independent of the number of nodes n to a great extent the analytical part of the work develops explicit bounds linking all pairs of such parameters these results are numerically compared with the result of a random testing for erdos renyi networks

on equations that are equivalent to the nonlinear matrix equation x a x α a q the nonlinear matrix equation x 1 a x aa q 0 email protected 1 is equivalent to the nonlinear matrix equation x a x aa q 0 email protected 1 the nonlinear matrix equation x 1 axa 1 a q 1 a is equivalent to the nonlinear matrix equation x 1 a x aa q 1 a the necessary and sufficient conditions for the existence of a positive definite solution of x 1 a x aa q 0 email protected 1 and x 1 axa 1 a q 1 a are given in the process two iterative algorithms are obtained estimations of the errors of the iterative algorithms are derived two numerical examples are given that demonstrate that the iterative algorithms are applicable

reduced order modeling of time dependent pdes with multiple parameters in the boundary data abstract the computational approximation of solutions to nonlinear partial differential equations pdes such as the navier stokes equations is often a formidable task for this reason there is significant interest in the development of very low dimensional models that can be used to determine reasonably accurate approximations in simulation and control problems for pdes many concrete tests have been reported on in the literature that show that several classes of reduced order models roms are effective i e an accurate approximate solution can be obtained using very low dimensional roms most of these tests involved problems for which the solution depends on only a single parameter appearing in the boundary data the extension of the techniques used in those tests to the case of multiple parameters is not a straightforward matter here we present test and compare two methods for treating within the context of a class of roms inhomogeneous dirichlet type boundary conditions that contain multiple parameters in this study we focus on the proper orthogonal decomposition pod approach to rom however the issues and results discussed here in the pod context apply equally well to other rom approaches

contractive maps on normed linear spaces and their applications to nonlinear matrix equations in this paper we will give necessary and sufficient conditions under which a map is a contraction on a certain subset of a normed linear space these conditions are already well known for maps on intervals in r using the conditions and banach s fixed point theorem we can prove a fixed point theorem for operators on a normed linear space the fixed point theorem will be applied to the matrix equation x in a f x a where f is a map on the set of positive definite matrices induced by a real valued map on 0 this will give conditions on a and f under which the equation has a unique solution in a certain set we will consider two examples of f in detail in one example the application of the fixed point theorem is the first step in proving that the equation has a unique positive definite solution under the conditions on a

positive solutions to x a bx 1 b abstract we study the positive semidefinite solutions to the matrix equation x a bx 1 b under the assumption that a 0 we show that a positive solution exists if and only if a certain block tridiagonal operator is positive in which case the solution is given by the shorted operator or generalized schur complement of that operator

necessary and sufficient conditions for the existence of a positive definite solution of the matrix equation x a x 1a q abstract we consider the problem of when the matrix equation x a x 1 a q has a positive definite solution here q is positive definite we study both the real and the complex case this equation plays a crucial role in solving a special case of the discrete time riccati equation we present both necessary and sufficient conditions for its solvability this result is obtained by using an analytic factorization approach moreover we present algebraic recursive algorithms to compute the largest and smallest the solution of the equation respectively finally we discuss the number of solutions

solvability and sensitivity analysis of polynomial matrix equation xs atxta q abstract in this paper we present a sufficient condition for the existence of the symmetric positive definite solution of polynomial matrix equation x s a t x t a q where s t are both nonnegative integers a q r n n and q 0 we firstly define the condition number of the unique spd solution and reduce its representation form we also give the algebraic perturbation analysis of the unique spd solutions with respect to perturbations of matrices a and q

positive definite solutions of the matrix equations x a x q a q q 1 in this paper we investigate nonlinear matrix equations x a x qa q where q 1 we derive necessary conditions and sufficient conditions for the existence of positive definite solutions for these equations we provide a sufficient condition for the equation x a x qa q to have two different positive definite solutions and several sufficient conditions for the equation x a x qa q to have a unique positive definite solution we also propose iterative methods for obtaining positive definite solutions of these equations numerical examples are given to illustrate the effectiveness of the methods

stability and continuity of centrality measures in weighted graphs this paper presents a formal definition of stability for node centrality measures in weighted graphs it is shown that the commonly used measures of degree closeness and eigenvector centrality are stable whereas betweenness centrality is not an alternative definition of the latter that preserves the same centrality notion while satisfying the stability criteria is introduced continuity is presented as a less stringent alternative to stability betweenness centrality is shown to be not only unstable but discontinuous numerical experiments in synthetic random networks and real world data show that in practice stability and continuity imply different levels of robustness in the presence of noisy data in particular the stable betweenness centrality is shown to exhibit resilience against noise that is absent in the discontinuous and unstable standard betweenness centrality while preserving a similar notion of centrality

numerical solution of a flow control problem vorticity reduction by dynamic boundary action in order to laminarize an unsteady internal flow the vorticity field is minimized in a least squares sense using an optimal control approach the flow model is the navier stokes equation for a viscous incompressible fluid and the flow is controlled by suction and blowing on a part of the boundary a quasi newton method is used for the minimization of a quadratic objective function involving a measure of the vorticity and a regularization term the navier stokes equations are approximated using a finite difference scheme in time and finite element approximations in space accurate expressions for the gradient of the discrete objective function are needed to obtain a satisfactory convergence rate of the minimization algorithm therefore first order necessary conditions for a minimizer of the objective function are derived in the fully discrete case a memory saving device is discussed without which problems of any realistic size especially in three space dimensions would remain computationally intractable the feasibility of the optimal control approach for flow control problems is demonstrated by numerical experiments for a two dimensional flow in a rectangular cavity at a reynolds number high enough for nonlinear effects to be important

a comparative analysis of network robustness against different link attacks abstract recently the study of optimizing network robustness has attracted increasing attentions and the constraint that every node s degree cannot be changed is considered although this constraint maintains the node degree distribution consistently in order to reserve the structure of networks it makes the network structure be lack of flexibility since many network structure always transform in the modern society given this consideration in this paper we analyze the robustness of networks through setting a new constraint that is only the number of edges should be unchanged then we use the link robustness index r l as the measure of the network robustness against either random failures or intentional attacks and make a comparative analysis of network robustness against different types of link attacks moreover we use four types of networks as initial networks namely scale free networks random networks regular networks and small world networks the experimental results show that the values of robustness measures for the optimized networks starting from different initial networks are similar under different link attacks but the network topologies may be different that is to say networks with different topologies may have similar robustness in terms of the robustness measures we also find that the optimized networks obtained by one link attack may not robust against other link attacks sometimes even weaker than the original networks therefore before building networks it is better to study which type of link attacks may happen

positive definite solutions of the nonlinear matrix equation x a xqa q q 0 abstract in this paper the nonlinear matrix equation x a x q a q q 0 is investigated some necessary and sufficient conditions for existence of hermitian positive definite solutions of the nonlinear matrix equations are derived an effective iterative method to obtain the positive definite solution is presented some numerical results are given to illustrate the effectiveness of the iterative methods

iterative methods for the extremal positive definite solution of the matrix equation x a x αa q in this paper the inversion free variant of the basic fixed point iteration methods for obtaining the maximal positive definite solution of the nonlinear matrix equation x a x aa q with the case 0 1 are proposed some necessary conditions and sufficient conditions for the existence of positive definite solutions for the matrix equation are derived numerical examples to illustrate the behavior of the considered algorithms are also given

current flow efficiency of networks abstract many real world networks from infrastructure networks to social and communication networks can be formulated as flow networks how to realistically measure the transport efficiency of these networks is of fundamental importance the shortest path based efficiency measurement has limitations as it assumes that flow travels only along those shortest paths here we propose a new metric named current flow efficiency in which we calculate the average reciprocal effective resistance between all pairs of nodes in the network this metric takes the multipath effect into consideration and is more suitable for measuring the efficiency of many real world flow equilibrium networks moreover this metric can handle a disconnected graph and can thus be used to identify critical nodes and edges from the efficiency loss perspective we further analyze how the topological structure affects the current flow efficiency of networks based on some model and real world networks our results enable a better understanding of flow networks and shed light on the design and improvement of such networks with higher transport efficiency

properties of positive definite solutions of the equation x a x 2a i abstract in this paper we discuss some properties of a positive definite solution of the matrix equation x a x 2 a i two effective iterative methods for computing a positive definite solution of this equation are proposed necessary and sufficient conditions for existence of a positive definite solution are derived numerical experiments are executed with these methods