robustness analysis of network controllability abstract structural controllability which is an interesting property of complex networks attracts many researchers from various fields the maximum matching algorithm was recently applied to explore the minimum number of driver nodes where control signals are injected for controlling the whole network here we study the controllability of directed erdos renyi and scale free networks under attacks and cascading failures results show that degree based attacks are more efficient than random attacks on network structural controllability cascade failures also do great harm to network controllability even if they are triggered by a local node failure

representations of sl 2 c and unimodal polynomials on montre que les representations de sl 2 c et les polynomes unimodaux sont la meme chose

dominating communities for hierarchical control of complex networks abstract well selected nodes driven by external signals in complex networks are of great importance for a dynamic system s structural controllability which can also be achieved by selecting nodes in the minimum dominating set mds of the networks as driver nodes however hierarchical structures such as communities are widely observed in complex networks which motivates us to develop the hierarchical control of complex networks by dominating communities and the control over whole networks is transformed into that within communities i e a non driver node is effectively controlled by its driver node if they belong to the same community for the hierarchical control we propose the structure driven minimum dominating set sd mds which assumes that a driver node can control a non driver node if the link between them belongs to a cyclic structure of the networks we further investigate the impact of community dynamics on our framework the results show that it is easier to control the networks with stronger communities and more heterogeneous community sizes and the sd mds achieves more effective control for non driver nodes than the mds this work also indicates that the number of driver nodes for the sd mds is associated with the degree distribution of the network

modular lie representations of groups of prime order let k be a field of prime characteristic p and let g be a group of order p for any finite dimensional kg module v and any positive integer n let ln v denote the nth homogeneous component of the free lie k algebra generated by a basis of v then ln v can be considered as a kg module called the nth lie power of v the main result of the paper is a formula which describes the module structure of ln v up to isomorphism

epidemic spreading in correlated complex networks we study a dynamical model of epidemic spreading on complex networks in which there are explicit correlations among the node s connectivities for the case of markovian complex networks showing only correlations between pairs of nodes we find an epidemic threshold inversely proportional to the largest eigenvalue of the connectivity matrix that gives the average number of links which from a node with connectivity k go to nodes with connectivity k ensuremath numerical simulations on a correlated growing network model provide support for our conclusions

optimizing the controllability of arbitrary networks with genetic algorithm abstract recently as the controllability of complex networks attracts much attention how to optimize networks controllability has become a common and urgent problem in this paper we develop an efficient genetic algorithm oriented optimization tool to optimize the controllability of arbitrary networks consisting of both state nodes and control nodes under popov belevitch hautus rank condition the experimental results on a number of benchmark networks show the effectiveness of this method and the evolution of network topology is captured furthermore we explore how network structure affects its controllability and find that the sparser a network is the more control nodes are needed to control it and the larger the differences between node degrees the more control nodes are needed to achieve the full control our framework provides an alternative to controllability optimization and can be applied to arbitrary networks without any limitations

losses in the pemc boundary perfect electromagnetic conductor pemc was recently introduced to generalize both the perfect electric conductor pec and the perfect magnetic conductor pmc which are used as boundary material in this paper an extension of pemc boundary conditions is made to a more realistic model with small losses good electromagnetic conductor it is shown that the antisymmetric boundary impedance dyadic defining the ideal pemc boundary cannot alone carry any losses and a symmetric component must be added that actually dominates the lossy behavior of the boundary as an example a slab of low loss gyrotropic wave guiding material is studied and shown to represent the lossy counterpart of the pemc boundary the effect of losses is demonstrated by considering plane wave reflection from an imperfect pemc plane

studies on controllability of directed networks with extremal optimization abstract almost all natural social and man made engineered systems can be represented by a complex network to describe their dynamic behaviors to make a real world complex network controllable with its desired topology the study on network controllability has been one of the most critical and attractive subjects for both network and control communities in this paper based on a given directed weighted network with both state and control nodes a novel optimization tool with extremal dynamics to generate an optimal network topology with minimum control nodes and complete controllability under kalman s rank condition has been developed the experimental results on a number of popular benchmark networks show the proposed tool is effective to identify the minimum control nodes which are sufficient to guide the whole network s dynamics and provide the evolution of network topology during the optimization process we also find the conclusion the sparse networks need more control nodes than the dense and the homogeneous networks need fewer control nodes compared to the heterogeneous liu et al 2011 18 is also applicable to network complete controllability these findings help us to understand the network dynamics and make a real world network under the desired control moreover compared with the relevant research results on structural controllability with minimum driver nodes the proposed solution methodology may also be applied to other constrained network optimization problems beyond complete controllability with minimum control nodes

symmetric powers of the p 1 dimensional indecomposable module of a cyclic p group and the λ structure of its green ring let k be a field of order p and let g be a cyclic group of order pk k 2 we explicitly decompose the symmetric powers of the indecomposable kg module of dimension p 1 into indecomposable kg modules using this result for every odd prime p we give a negative answer to the conjecture posed by kouwenhoven f m kouwenhoven the structure of the green rings of cyclic p groups proc sympos pure math 47 1987 451 466

general representations for wavefield modeling and inversion in geophysics acoustic electromagnetic elastodynamic poroelastic and electroseismic waves are all governed by a unified matrix vector wave equation the matrices in this equation obey the same symmetry properties for each of these wave phenomena this implies that the wave vectors for each of these phenomena obey the same reciprocity theorems by substituting green s matrices in these reciprocity theorems unified wavefield representations are obtained analogous to the well known acoustic wavefield representations these unified representations find applications in geophysical modeling migration inversion multiple elimination and interferometry

controllability of multiplex multi time scale networks the paradigm of layered networks is used to describe many real world systems from biological networks to social organizations and transportation systems while recently there has been much progress in understanding the general properties of multilayer networks our understanding of how to control such systems remains limited one fundamental aspect that makes this endeavor challenging is that each layer can operate at a different time scale thus we cannot directly apply standard ideas from structural control theory of individual networks here we address the problem of controlling multilayer and multi time scale networks focusing on two layer multiplex networks with one to one interlayer coupling we investigate the practically relevant case when the control signal is applied to the nodes of one layer we develop a theory based on disjoint path covers to determine the minimum number of inputs n i necessary for full control we show that if both layers operate on the same time scale then the network structure of both layers equally affect controllability in the presence of time scale separation controllability is enhanced if the controller interacts with the faster layer n i decreases as the time scale difference increases up to a critical time scale difference above which n i remains constant and is completely determined by the faster layer we show that the critical time scale difference is large if layer i is easy and layer ii is hard to control in isolation in contrast control becomes increasingly difficult if the controller interacts with the layer operating on the slower time scale and increasing time scale separation leads to increased n i again up to a critical value above which n i still depends on the structure of both layers this critical value is largely determined by the longest path in the faster layer that does not involve cycles by identifying the underlying mechanisms that connect time scale difference and controllability for a simplified model we provide crucial insight into disentangling how our ability to control real interacting complex systems is affected by a variety of sources of complexity

community detection in complex networks using extremal optimization we propose a method to find the community structure in complex networks based on an extremal optimization of the value of modularity the method outperforms the optimal modularity found by the existing algorithms in the literature giving a better understanding of the community structure we present the results of the algorithm for computer simulated and real networks and compare them with other approaches the efficiency and accuracy of the method make it feasible to be used for the accurate identification of community structure in large complex networks

green s function extraction for interfaces with impedance boundary conditions theory and experiments to obtain the response between two receivers from cross correlations of wave fields recorded at these receivers are well established the principle relies on mutually spatial and temporal uncorrelated contributions from sources on a boundary enclosing the two receivers which upon cross correlation interfere only constructively for signals traveling between the two receivers it has therefore become generally known as interferometry the theory includes situations with flow mechanical and electromagnetic field fluctuations and their mutual coupling here we present an electromagnetic theory for green s function retrieval from cross correlations that incorporates general bianisotropic media in which interfaces are present where bianisotropic impedance boundary conditions apply the derived green s function representation shows that in lossless media and for interfaces with lossless impedance boundary conditions the green s function between two receivers is obtained by cross correlating the recordings of these receivers from sources on a boundary enclosing them we show numerical examples in 2 d where proper solutions are numerically tractable and practical approximations illustrate that numerically less intensive algorithms lead to acceptable results and accurate extraction of reflections from impedance boundary surfaces because the method is data driven it is suitable for experimental green s function extraction from measured data

controllability and modularity of complex networks two primary properties of complex networks controllability and modularity not only are closely related to each other but also play an important role in understanding the networks characteristics in this paper we discuss an elastic model to enhance the control of undirected networks and study the controllability of random networks with built in gradually varied modularity as well as real world networks to elaborate the correlation between the networks controllability and modularity the results show that it is easier to control the networks with stronger modularity than that of weaker modularity and the networks with larger size communities probably need more driver nodes to control than that of smaller size communities when we fix both the number of nodes and the number of links of the networks in addition the robustness analysis indicates that the model enhances the resistance of networks against link failure this work shows that the controllability of complex networks is highly associated with the networks degree distribution as well as the networks modularity which gives a new insight into the understanding of controllability and modularity of complex networks

variability analysis of complex networks measures based on stochastic distances abstract complex networks can model the structure and dynamics of different types of systems it has been shown that they are characterized by a set of measures in this work we evaluate the variability of complex network measures face to perturbations and for this purpose we impose controlled perturbations and quantify their effect we analyze theoretical models random small world and scale free and real networks a collaboration network and a metabolic networks along with the shortest path length vertex degree local cluster coefficient and betweenness centrality measures in such an analysis we propose the use of three stochastic quantifiers the kullback leibler divergence and the jensen shannon and hellinger distances the sensitivity of these measures was analyzed with respect to the following perturbations edge addition edge removal edge rewiring and node removal all of them applied at different intensities the results reveal that the evaluated measures are influenced by these perturbations additionally hypotheses tests were performed to verify the behavior of the degree distribution to identify the intensity of the perturbations that leads to break this property

implementation of method of moments for numerical analysis of corrugated surfaces with impedance boundary condition a method of moments formulation is developed to analyze the scattering of corrugated surfaces by using an impedance boundary condition the numerical analysis of the impedance surface is done using closed form formulae and accurate numerical integration the studied formulation greatly decreases the computational resources required to study corrugated structures

scale free networks via attaching to random neighbors abstract preferential attachment is considered one of the key factors in the formation of scale free networks however complete random attachment without a preferential mechanism can also generate scale free networks in nature such as protein interaction networks in cells this article presents a new scale free network model that applies the following general mechanisms i networks expand continuously by the addition of new vertices and ii new vertices attach to random neighbors of random vertices that are already well connected the proposed model does not require global based preferential strategies and utilizes only the random attachment method theoretical analysis and numerical simulation results denote that the proposed model has steady scale free network characteristics and random attachment without a preferential mechanism may generate scale free networks

generalized soft and hard surface soft and hard surface shs is a mathematical idealization of the tuned corrugated boundary the boundary conditions are defined by a single real vector parallel to the corrugations the shs boundary was recently generalized by replacing the real vector by a complex vector and its conjugate see lindell i v proc inst elect eng microw antenna propagat vol 147 p 495 9 2000 the shs boundary is generalized one step further by defining it in terms of two complex vectors tangential to the surface it is shown that analogous to the previous special cases there exist two eigenpolarizations te and tm with respect to the two vectors for plane waves of any angle of incidence these two specially polarized waves see the boundary as a simple perfect magnetic or electric conductor surface respectively because the same is true for te and tm parts of fields radiated by finite sources it is possible to apply the classical image theory for the computation of fields in the presence of a planar generalized shs boundary a principle of realization of such a boundary is briefly discussed if the two vectors defining the boundary can be realized in practice a device transforming any given polarization to any other polarization in reflection appears feasible

characterizing the topological and controllability features of u s power transmission networks understanding the controllability of complex networks continues to gain traction across disciplinary fields including the exploration of infrastructure systems such as power grids through topological principles this paper investigates the controllability features of an ensemble of 58 u s city level power transmission networks in seven u s states to perform structural controllability analyses the topological characteristics of the ensemble of networks are first quantified including degree shortest path length clustering coefficient meshedness and betweenness centrality as well as the uncertainty associated with these and related properties then the paper focuses on the controllability features of complex networks so as to detect the minimal sets of driver nodes to possibly control the networks given system linearity assumptions accordingly a node is critical intermittent or redundant if it acts as a driver node in all some or none of the potentially controllable system configurations moreover this paper constructs a new methodology to quantify the probability of being a driver node among the intermittent nodes and reveals the controllability importance of system components results show that a small proportion of driver nodes can provide the conditions for controlling the slow dynamics of entire power transmission networks from a topological perspective despite variations in network sizes and configurations this paper also reveals that the driver nodes tend to avoid high degree nodes and high triangulation sub graph nodes as well as high betweenness centrality nodes the identification of topological differences for different categories of nodes critical intermittent or redundant could help researchers and utilities understand the conditions for future functional controllability of power networks while improving their reliability and resilience as well as facilitating their transition into smart grid systems

pinning control of scale free dynamical networks abstract recently it has been demonstrated that many large complex networks display a scale free feature that is their connectivity distributions have the power law form in the present work control of a scale free dynamical network by applying local feedback injections to a fraction of network nodes is investigated the specifically and randomly pinning schemes are considered the specifically pinning of the most highly connected nodes is shown to require a significantly smaller number of local controllers as compared to the randomly pinning scheme the method is applied to an array of chua s oscillators as an example

symmetrical properties of dyadic green s functions for mixed boundary conditions and integral representations of the electric fields for problems involving a pemc perfect electromagnetic conductor pemc is a recently introduced fundamental medium in which certain linear combinations of electromagnetic fields are required to vanish since electric and magnetic dyadic green s functions are required to satisfy dyadic mixed boundary conditions on pemc surface it is necessary to develop a new classification of electric and magnetic dyadic green s functions based on a parameter m of a pemc boundary this classification while including dyadic dirichlet and neumann boundary conditions should be general as well in this paper a new classification of dyadic green s functions is introduced and symmetrical properties of these functions are presented furthermore integral representations of electric fields in problems of two isotropic media involving a pemc are derived finally using symmetrical properties of the dyadic green s functions the expressions for electric fields are proposed in an appropriate integral form in terms of volume currents and electric and magnetic fields on apertures

tunable path centrality quantifying the importance of paths in networks abstract centrality is a fundamental measure in network analysis specifically centrality of a path describes the importance of the path with respect to the remaining part of the network in this paper we propose a tunable path centrality tpc measure which quantifies the centrality of a path by integrating the path degree pd number of neighbors of the path and the path bridge pb number of bridges in the path with a control parameter considering the complexity of large scale and dynamical topologies of many real world networks both pd and pb are computed with only the local topological structure of a path we demonstrate the distribution of the three path centralities tpc pd and pb in computer generated networks and real world networks furthermore we apply the three path centralities to the network fragility problem and exploit the distribution of the optimal control parameter o p t through simulation and analysis finally the simulation results show that generally tpc is more efficient than pd and pb in the network fragility problem these path centralities are also applicable in many other network problems including spread control prediction and so on

λ ring structure of the green ring of a cyclic p group abstract let f p be a field of order p g a cyclic group of order p k and rs p k the green ring of g over f p this paper concerns the conjecture on the ring structure of a certain quotient ring rs p k i p k of rs p k when k 2 which was originally due to kouwenhoven to be more precise he conjectured that the ideal i p k is closed under the exterior powers and rs p k i p k is equipped with the ring structure for the induced exterior powers we show that kouwenhoven s conjecture turns out to be true when p 2 but false when p 3 for other primes except p 2 3 it will be demonstrated that rs p k i p k cannot have the ring structure for the induced exterior powers

some formulas in invariant theory in an earlier paper 121 the author discussed the relationship between invariants of the group g z pz in characteristic p and the classical covariants of sl 2 k in characteristic zero this is more closely studied here in the corresponding representation rings in characteristic zero the only indecomposable 1 irreducible sl 2 k modules are the r si where r is the set of homogeneous forms of degree n of the polynomial ring r k x y in characteristic p there are p indecomposable g modules i vp the corresponding representation rings are

exterior and symmetric powers of modules for cyclic 2 groups abstract we prove a recursive formula for the exterior and symmetric powers of modules for a cyclic 2 group this makes computation straightforward previously a complete description was only known for cyclic groups of prime order

controllability of complex networks via pinning we study the problem of controlling a general complex network toward an assigned synchronous evolution by means of a pinning control strategy we define the pinning controllability of the network in terms of the spectral properties of an extended network topology the roles of the control and coupling gains as well as of the number of pinned nodes are also discussed

optimizing controllability of complex networks by minimum structural perturbations to drive a large complex networked dynamical system toward some desired state using as few external signals as possible is a fundamental issue in the emerging field of controlling complex networks optimal control is referred to the situation where such a network can be fully controlled using only one driving signal we propose a general approach to optimizing the controllability of complex networks by judiciously perturbing the network structure the principle of our perturbation method is validated theoretically and demonstrated numerically for homogeneous and heterogeneous random networks and for different types of real networks as well the applicability of our method is discussed in terms of the relative costs of establishing links and imposing external controllers besides the practical usage of our approach its implementation elucidates interestingly the intricate relationship between certain structural properties of the network and its controllability

electromagnetic boundary and its realization with anisotropic metamaterial a set of boundary conditions requiring vanishing of the normal components of the d and b vectors at the boundary surface is introduced and labeled as that of db boundary basic properties of the db boundary are studied in this paper reflection of an arbitrary plane wave incident with a complex propagation vector is analyzed for the planar db boundary it is shown that waves polarized transverse electric te and transverse magnetic tm with respect to the normal of the boundary are reflected as from respective perfect electric conductor and perfect magnetic conductor planes the basic problem of current source above the planar db boundary is solved by applying te and tm decomposition for the source realization of the db boundary in terms of an interface of uniaxially anisotropic metamaterial half space with zero axial medium parameters is considered it is also shown that such a medium with small axial parameters acts as a spatial filter for waves incident at the interface which could be used for narrowing the beam of a directive antenna application of db boundary as an isotropic soft surface with low interaction between antenna apertures also appears possible

transformation method for problems involving perfect electromagnetic conductor pemc structures perfect electric conductor pec and perfect magnetic conductor pmc can be generalized to perfect electromagnetic conductor pemc a medium where certain linear combinations of electromagnetic fields are required to vanish in differential form representation the corresponding medium is characterized as the simplest possible medium it is defined through a scalar admittance parameter whose zero and infinite limits yield the pmc and pec media respectively in this paper a duality transformation is found that has the property of transforming pemc to pec and an isotropic medium to itself thus problems involving pemc objects in air can be transformed to problems with pec objects in air which can be solved through traditional techniques and then transformed back several simple examples are treated to demonstrate the principle pemc has the potential of having similar applications as pmc in antenna engineering and finding structures for its realization is a challenge

effect of degree correlation on exact controllability of multiplex networks abstract it has been proved that the degree correlation can affect the structural controllability of directed networks here we explore the effect of interconnections correlation on the exact controllability of multiplex networks we find that the minimal number of driver nodes decreases with correlation for lower density of interconnections however the controllability of networks with higher density of interconnections shows the contrary tendency for different interconnections correlations controllability of multiplex networks depicts transition with the density of interconnections for lower interconnections density the networks with disassortative coupling patterns are harder to control whereas for higher interconnections density the networks with assortative coupling patterns are harder to control

solving ibc cfie with dual basis functions the surface integral equation method is applied to solve electromagnetic scattering by arbitrarily shaped three dimensional imperfectly conducting objects modeled with the leontovitch impedance boundary condition ibc dual basis functions are used to remove previously reported difficulties associated with the solution of the combined field integral equation for objects with the ibc by expanding the magnetic current with quasi curl conforming dual functions and the electric current with divergence conforming primary rwg functions leads to a stable discretization procedure for the rotation n operator required by the ibc

necklace rings and logarithmic functions in this paper we develop the theory of the necklace ring and the logarithmic function regarding the necklace ring we introduce the necklace ring functor nr from the category of special rings into the category of special rings and then study the associated adams operators as far as the logarithmic function is concerned we generalize the results in bryant s paper free lie algebras and formal power series j algebra 253 1 2002 167 188 to the case of graded lie super algebras with a group action by applying the euler poincare principle

realization of impedance boundary impedance boundary is generally considered as an approximate model for material interfaces considering an electromagnetic field in a certain wave guiding anisotropic material it is shown that a slab of such a material backed by a perfect electric conductor pec plane can be exactly represented by impedance boundary conditions as a result of the analysis a novel explicit relation is derived between the surface admittance dyadic of the impedance boundary and the material and geometric parameters of the anisotropic slab which can be used to realize a given admittance dyadic the relation is verified with results known for the perfect electromagnetic pemc boundary and bi axial material considered as special cases of the theory

adams operations on the green ring of a cyclic group of prime power order we consider the green ring r kc for a cyclic p group c over a field k of prime characteristic p and determine the adams operations psi n in the case where n is not divisible by p this gives information on the decomposition into indecomposables of exterior powers and symmetric powers of kc modules

minimum structural controllability problems of complex networks abstract controllability of complex networks has been one of the attractive research areas for both network and control community and has yielded many promising and significant results in minimum inputs and minimum driver vertices however few studies have been devoted to studying the minimum controlled vertex set through which control over the network with arbitrary structure can be achieved in this paper we prove that the minimum driver vertices driven by different inputs are not sufficient to ensure the full control of the network when the associated graph contains the inaccessible strongly connected component which has perfect matching and propose an algorithm to identify a minimum controlled vertex set for network with arbitrary structure using convenient graph and mathematical tools and the simulation results show that the controllability of network is correlated to the number of inaccessible strongly connected components which have perfect matching and these results promote us to better understand the relationship between the network s structural characteristics and its control

controllable subspace of edge dynamics in complex networks abstract for the edge dynamics in some real networks it may be neither feasible nor necessary to be fully controlled an accompanying issue is that when the external signal is applied to a few nodes or even a single node how many edges can be controlled in this paper for the edge dynamics system we propose a theoretical framework to determine the controllable subspace and calculate its generic dimension based on the integer linear programming this framework allows us not only to analyze the control centrality i e the ability of a node to control but also to uncover the controllable centrality i e the propensity of an edge to be controllable the simulation results and analytic calculation show that dense and homogeneous networks tend to have larger control centrality of nodes and controllable centrality of edges but the negatively correlated in and out degrees of nodes or edges can reduce the two centrality the positive correlation between the control centrality of node and its out degree leads to that the distribution of control centrality instead of that of controllable centrality is encoded by the out degree distribution of networks meanwhile the positive correlation indicates that the nodes with high out degree tend to play more important roles in control

elementary divisors of tensor products and p ranks of binomial matrices abstract let f be a field of characteristic p and let a and b be two jordan blocks with nonzero eigenvalues the reduction formulas of c w norman enable us to compute the elementary divisors of a b we investigate connections between the elementary divisors of a b and binomial matrices in particular we show that norman s reduction formulas can be used to compute the p rank of certain binomial matrices

symmetric powers and modular invariants of elementary abelian p groups abstract let e be an elementary abelian p group of order q p n let w be a faithful indecomposable representation of e with dimension 2 over a field k of characteristic p and let v s m w with m q we prove that the rings of invariants k v e are generated by elements of degree q and relative transfers this extends recent work of wehlau 18 on modular invariants of cyclic groups of order p if m p we prove that k v e is generated by invariants of degree 2 q 3 extending a result of fleischmann sezer shank and woodcock 6 for cyclic groups of order p our methods are primarily representation theoretic and along the way we prove that for any d q with d m q s d v is projective relative to the set of subgroups of e with order m and that the sequence s d v d 0 is periodic with period q modulo summands which are projective relative to the same set of subgroups these results extend results of almkvist and fossum 1 on cyclic groups of prime order

measure the structure similarity of nodes in complex networks based on relative entropy abstract similarity of nodes is a basic structure quantification in complex networks lots of methods in research on complex networks are based on nodes similarity such as node s classification network s community structure detection network s link prediction and so on therefore how to measure nodes similarity is an important problem in complex networks in this paper a new method is proposed to measure nodes structure similarity based on relative entropy and each node s local structure in the new method each node s structure feature can be quantified as a special kind of information the quantification of similarity between different pair of nodes can be replaced as the quantification of similarity in structural information then relative entropy is used to measure the difference between each pair of nodes structural information at last the value of relative entropy between each pair of nodes is used to measure nodes structure similarity in complex networks comparing with existing methods the new method is more accuracy to measure nodes structure similarity