spectra of complex networks we propose a general approach to the description of spectra of complex networks for the spectra of networks with uncorrelated vertices and a local treelike structure exact equations are derived these equations are generalized to the case of networks with correlations between neighboring vertices the tail of the density of eigenvalues ensuremath rho ensuremath lambda at large ensuremath lambda is related to the behavior of the vertex degree distribution p k at large k in particular as p k ensuremath sim k ensuremath ensuremath gamma ensuremath rho ensuremath lambda ensuremath sim ensuremath lambda 1 ensuremath 2 ensuremath gamma we propose a simple approximation which enables us to calculate spectra of various graphs analytically we analyze spectra of various complex networks and discuss the role of vertices of low degree we show that spectra of locally treelike random graphs may serve as a starting point in the analysis of spectral properties of real world networks e g of the internet

typical local measurements in generalized probabilistic theories emergence of quantum bipartite correlations what singles out quantum mechanics as the fundamental theory of nature here we study local measurements in generalized probabilistic theories gpts and investigate how observational limitations affect the production of correlations we find that if only a subset of typical local measurements can be made then all the bipartite correlations produced in a gpt can be simulated to a high degree of accuracy by quantum mechanics our result makes use of a generalization of dvoretzky s theorem for gpts the tripartite correlations can go beyond those exhibited by quantum mechanics however

distance dissimilarity index and network community structure we address the question of finding the community structure of a complex network in an earlier effort h zhou phys rev e 67 041908 2003 the concept of network random walking is introduced and a distance measure defined here we calculate based on this distance measure the dissimilarity index between nearest neighboring vertices of a network and design an algorithm to partition these vertices into communities that are hierarchically organized each community is characterized by an upper and a lower dissimilarity threshold the algorithm is applied to several artificial and real world networks and excellent results are obtained in the case of artificially generated random modular networks this method outperforms the algorithm based on the concept of edge betweenness centrality for yeast s protein protein interaction network we are able to identify many clusters that have well defined biological functions

exponential stability of discrete time switched linear positive systems with time delay abstract this paper addresses the exponential stability problem for a class of discrete time switched linear positive systems dslpss with time delay firstly an exponential stability criterion for a non switched delay positive system is proposed then by constructing a suitable co positive type lyapunov krasovskii functional an exponential stability criterion for switched delay positive systems is derived via the average dwell time approach and a stability criterion for switched positive systems with multiple delays is stated and its proof is sketched finally a numerical example is given to illustrate the obtained results

comments on hastings additivity counterexamples hastings 12 recently provided a proof of the existence of channels which violate the additivity conjecture for minimal output entropy in this paper we present an expanded version of hastings proof in addition to a careful elucidation of the details of the proof we also present bounds for the minimal dimensions needed to obtain a counterexample

spectra and eigenvectors of scale free networks we study the spectra and eigenvectors of the adjacency matrices of scale free networks when bidirectional interaction is allowed so that the adjacency matrix is real and symmetric the spectral density shows an exponential decay around the center followed by power law long tails at both spectrum edges the largest eigenvalue ensuremath lambda 1 depends on system size n as ensuremath lambda 1 ensuremath sim n 1 4 for large n and the corresponding eigenfunction is strongly localized at the hub the vertex with largest degree the component of the normalized eigenfunction at the hub is of order unity we also find that the mass gap scales as n ensuremath 0 68

on the minimum output entropy of random orthogonal quantum channels we consider the sequences of random quantum channels defined by using the stinespring formula with haar distributed random orthogonal matrices for any fixed sequence of input states we study the asymptotic eigenvalue distribution of the outputs through the tensor powers of random channels we show that the input states achieving minimum output entropy are tensor products of maximally entangled states bell states when the tensor power is even this phenomenon is completely different from the one for random quantum channels constructed from haar distributed random unitary matrices which leads us to formulate some conjectures about the regularized minimum output entropy

partial transpose of random quantum states exact formulas and meanders we investigate the asymptotic behavior of the empirical eigenvalues distribution of the partial transpose of a random quantum state the limiting distribution was previously investigated via wishart random matrices indirectly by approximating the matrix of trace 1 by the wishart matrix of random trace and shown to be the semicircular distribution or the free difference of two free poisson distributions depending on how dimensions of the concerned spaces grow our use of wishart matrices gives exact combinatorial formulas for the moments of the partial transpose of the random state we find three natural asymptotic regimes in terms of geodesics on the permutation groups two of them correspond to the above two cases the third one turns out to be a new matrix model for the meander polynomials moreover we prove the convergence to the semicircular distribution together with its extreme eigenvalues under weaker assumptions and show large deviation bound for the latter

hierarchical sequencing of online social graphs abstract in online communications patterns of conduct of individual actors and use of emotions in the process can lead to a complex social graph exhibiting multilayered structure and mesoscopic communities using simplicial complexes representation of graphs we investigate in depth topology of the online social network constructed from myspace dialogs which exhibits original community structure a simulation of emotion spreading in this network leads to the identification of two emotion propagating layers three topological measures are introduced referred to as the structure vectors which quantify graph s architecture at different dimension levels notably structures emerging through shared links triangles and tetrahedral faces frequently occur and range from tree like to maximal 5 cliques and their respective complexes on the other hand the structures which spread only negative or only positive emotion messages appear to have much simpler topology consisting of links and triangles the node s structure vector represents the number of simplices at each topology level in which the node resides and the total number of such simplices determines what we define as the node s topological dimension the presented results suggest that the node s topological dimension provides a suitable measure of the social capital which measures the actor s ability to act as a broker in compact communities the so called simmelian brokerage we also generalize the results to a wider class of computer generated networks investigating components of the node s vector over network layers reveals that same nodes develop different socio emotional relations and that the influential nodes build social capital by combining their connections in different layers

eigenvalue spectra of complex networks we examine the eigenvalue spectrum of the adjacency matrix of a random scale free network with an average of p edges per vertex using the replica method we show how in the dense limit when p one can obtain two relatively simple coupled equations whose solution yields for an arbitrary complex network for scale free graphs with degree distribution exponent we obtain an exact expression for the eigenvalue spectrum when 3 and show that 1 2 1 for large in the limit we recover known results for the erdos renyi random graph

stability analysis for continuous time positive systems with time varying delays this note addresses the stability problem of continuous time positive systems with time varying delays it is shown that such a system is asymptotically stable for any continuous and bounded delay if and only if the sum of all the system matrices is a hurwitz matrix the result is a time varying version of the widely known asymptotic stability criterion for constant delay positive systems a numerical example illustrates the correctness of our result

local random quantum circuits are approximate polynomial designs we prove that local random quantum circuits acting on n qubits composed of o t10n2 many nearest neighbor two qubit gates form an approximate unitary t design previously it was unknown whether random quantum circuits were a t design for any t 3 the proof is based on an interplay of techniques from quantum many body theory representation theory and the theory of markov chains in particular we employ a result of nachtergaele for lower bounding the spectral gap of frustration free quantum local hamiltonians a quasi orthogonality property of permutation matrices a result of oliveira which extends to the unitary group the path coupling method for bounding the mixing time of random walks and a result of bourgain and gamburd showing that dense subgroups of the special unitary group composed of elements with algebraic entries are copy tensor product expanders we also consider pseudo randomness properties of local random quantum circuits of small depth and prove that circuits of depth o t10n constitute a quantum t copy tensor product expander the proof also rests on techniques from quantum many body theory in particular on the detectability lemma of aharonov arad landau and vazirani we give applications of the results to cryptography equilibration of closed quantum dynamics and the generation of topological order in particular we show the following pseudo randomness property of generic quantum circuits almost every circuit u of size o nk on n qubits cannot be distinguished from a haar uniform unitary by circuits of size o n k 9 11 that are given oracle access to u

absolute exponential l1 gain analysis and synthesis of switched nonlinear positive systems with time varying delay this paper investigates absolute exponential stability and stabilization with l1 gain performance of switched nonlinear positive systems with time varying delay nonlinear functions considered in the paper are located in a sector field and the time varying delay is unknown but bounded the notion of absolute exponential l1 stability of switched nonlinear positive systems is first introduced a nonlinear lyapunov krasovskii functional is constructed for the underlying systems by using the lyapunov krasovskii functional a sufficient condition for absolute exponential l1 stability of the systems is established in terms of linear programming then absolute exponential l1 control synthesis of the systems is addressed a feedback control law containing nonlinear functions and a state feedback control law are designed respectively by comparing with existing results it is shown that the present design is less conservative finally an illustrative example is provided to illustrate the effectiveness of the results

hastings s additivity counterexample via dvoretzky s theorem the goal of this note is to show that hastings s counterexample to the additivity of minimal output von neumann entropy can be readily deduced from a sharp version of dvoretzky s theorem

random positive operator valued measures we introduce several notions of random positive operator valued measures povms and we prove that some of them are equivalent we then study statistical properties of the effect operators for the canonical examples starting from the limiting eigenvalue distribution we derive the large system limit for several quantities of interest in quantum information theory such as the sharpness the noise content and the probability range finally we study different compatibility criteria and we compare them for generic povms

are random pure states useful for quantum computation we show the following a randomly chosen pure state as a resource for measurement based quantum computation is with overwhelming probability of no greater help to a polynomially bounded classical control computer than a string of random bits thus unlike the familiar cluster states the computing power of a classical control device is not increased from p to bqp bounded error quantum polynomial time but only to bpp bounded error probabilistic polynomial time the same holds if the task is to sample from a distribution rather than to perform a bounded error computation furthermore we show that our results can be extended to states with significantly less entanglement than random states

centrality measures for networks with community structure understanding the network structure and finding out the influential nodes is a challenging issue in large networks identifying the most influential nodes in a network can be useful in many applications like immunization of nodes in case of epidemic spreading during intentional attacks on complex networks a lot of research is being done to devise centrality measures which could efficiently identify the most influential nodes in a network there are two major approaches to this problem on one hand deterministic strategies that exploit knowledge about the overall network topology while on the other end random strategies are completely agnostic about the network structure centrality measures that can deal with a limited knowledge of the network structure are of prime importance indeed in practice information about the global structure of the overall network is rarely available or hard to acquire even if available the structure of the network might be too large that it is too much computationally expensive to calculate global centrality measures to that end a centrality measure is proposed here that requires information only at the community level indeed most of the real world networks exhibit a community structure that can be exploited efficiently to discover the influential nodes we performed a comparative evaluation of prominent global deterministic strategies together with stochastic strategies an available and the proposed deterministic community based strategy effectiveness of the proposed method is evaluated by performing experiments on synthetic and real world networks with community structure in the case of immunization of nodes for epidemic control

analysis of weighted networks the connections in many networks are not merely binary entities either present or not but have associated weights that record their strengths relative to one another recent studies of networks have by and large steered clear of such weighted networks which are often perceived as being harder to analyze than their unweighted counterparts here we point out that weighted networks can in many cases be analyzed using a simple mapping from a weighted network to an unweighted multigraph allowing us to apply standard techniques for unweighted graphs to weighted ones as well we give a number of examples of the method including an algorithm for detecting community structure in weighted networks and a simple proof of the maximum flow minimum cut theorem

exponential stabilization of switched time varying systems with delays and disturbances abstract this paper deals with exponential stabilization for a class of switched time varying systems by taking time varying delays and nonlinear disturbances into consideration time dependent switching signals have been characterized in terms of metzler matrices such that the resulting system is globally exponentially stable compared with preceding works we introduce a model transformation and an approach without involving the lyapunov krasovskii functional to derive new exponential stability criteria for switched time varying systems under the average dwell time switching numerical examples show that the obtained theoretical results can be applied to some cases not covered by some existing results

spectra of modular random graphs we compute spectra of symmetric random matrices defined on graphs exhibiting a modular structure modules are initially introduced as fully connected sub units of a graph by contrast inter module connectivity is taken to be incomplete two different types of inter module connectivities are considered one where the number of intermodule connections per node diverges and one where this number remains finite in the infinite module size limit in the first case the results can be understood as a perturbation of a superposition of semicircular spectral densities one would obtain for uncoupled modules in the second case matters can be more involved and depend in detail on inter module connectivities for suitable parameters we even find near triangular shaped spectral densities similar to those observed in certain scale free networks in a system consisting of just two coupled modules analytic results are presented for the infinite module size limit they are well corroborated by numerical simulations

dynamics of directed graphs the world wide web we introduce and simulate a growth model of the world wide web based on the dynamics of outgoing links that is motivated by the conduct of the agents in the real web to update outgoing links re directing them towards constantly changing selected nodes emergent statistical correlation between the distributions of outgoing and incoming links is a key feature of the dynamics of the web the growth phase is characterized by temporal fractal structures which are manifested in the hierarchical organization of links we obtain quantitative agreement with the recent empirical data in the real web for the distributions of in and out links and for the size of the connected component in a fully grown network of n nodes we study the structure of connected clusters of nodes that are accessible along outgoing links from a randomly selected node the distributions of size and depth of the connected clusters with a giant component exhibit supercritical behavior by decreasing the control parameter average fraction of updated and added links per time step towards c n 10 the web can resume a critical structure with no giant component in it we find a different universality class when the updates of links are not allowed i e for 0 corresponding to the network of science citations

laplacian spectra as a diagnostic tool for network structure and dynamics we examine numerically the three way relationships among structure laplacian spectra and frequency synchronization dynamics on complex networks we study the effects of clustering degree distribution and a particular type of coupling asymmetry input normalization all of which are known to have effects on the synchronizability of oscillator networks we find that these topological factors produce marked signatures in the laplacian eigenvalue distribution and in the localization properties of individual eigenvectors using a set of coordinates based on the laplacian eigenvectors as a diagnostic tool for synchronization dynamics we find that the process of frequency synchronization can be visualized as a series of quasi independent transitions involving different normal modes particular features of the partially synchronized state can be understood in terms of the behavior of particular modes or groups of modes for example there are important partially synchronized states in which a set of low lying modes remain unlocked while those in the main spectral peak are locked we find therefore that spectra are correlated with dynamics in ways that go beyond results relating a single threshold to a single extremal eigenvalue

geometry of complex networks and topological centrality abstract we explore the geometry of complex networks in terms of an n dimensional euclidean embedding represented by the moore penrose pseudo inverse of the graph laplacian l the squared distance of a node i to the origin in this n dimensional space l i i yields a topological centrality index defined as c i 1 l i i in turn the sum of reciprocals of individual node centralities i 1 c i i l i i or the trace of l yields the well known kirchhoff index k an overall structural descriptor for the network to put into context this geometric definition of centrality we provide alternative interpretations of the proposed indices that connect them to meaningful topological characteristics first as forced detour overheads and frequency of recurrences in random walks that has an interesting analogy to voltage distributions in the equivalent electrical network and then as the average connectedness of i in all the bi partitions of the graph these interpretations respectively help establish the topological centrality c i of node i as a measure of its overall position as well as its overall connectedness in the network thus reflecting the robustness of i to random multiple edge failures through empirical evaluations using synthetic and real world networks we demonstrate how the topological centrality is better able to distinguish nodes in terms of their structural roles in the network and along with kirchhoff index is appropriately sensitive to perturbations re wirings in the network

large deviation bounds for k designs we present a technique for de randomizing large deviation bounds of functions on the unitary group we replace the haar measure with a pseudo random distribution a k design k designs have the first k moments equal to those of the haar measure the advantage of this is that approximate k designs can be implemented efficiently whereas haar random unitaries cannot we find large deviation bounds for unitaries chosen from a k design and then illustrate this general technique with three applications we first show that the von neumann entropy of a pseudo random state is almost maximal then we show that if the dynamics of the universe produces a k design then suitably sized subsystems will be in the canonical state as predicted by statistical mechanics finally we show that pseudo random states are useless for measurement based quantum computation

on dvoretzky s theorem for subspaces of lp abstract we prove that for any 2 p and for every n dimensional subspace x of l p represented on r n whose unit ball b x is in lewis position one has the following two level gaussian concentration inequality p z e z e e z c exp c min p e 2 n e n 2 p 0 e 1 where z is the standard n dimensional gaussian vector p 0 is a constant depending only on p and c c 0 are absolute constants as a consequence we show optimal lower bound on the dimension of random almost spherical sections for these spaces in particular for any 2 p and every n dimensional subspace x of l p the euclidean space l 2 k can be 1 e embedded into x with k c p min e 2 n e n 2 p where c p 0 is a constant depending only on p this improves upon the previously known estimate due to figiel lindenstrauss and milman

eigenvalue distributions of reduced density matrices given a random quantum state of multiple distinguishable or indistinguishable particles we provide an effective method rooted in symplectic geometry to compute the joint probability distribution of the eigenvalues of its one body reduced density matrices as a corollary by taking the distribution s support which is a convex moment polytope we recover a complete solution to the one body quantum marginal problem we obtain the probability distribution by reducing to the corresponding distribution of diagonal entries i e to the quantitative version of a classical marginal problem which is then determined algorithmically this reduction applies more generally to symplectic geometry relating invariant measures for the coadjoint action of a compact lie group to their projections onto a cartan subalgebra and can also be quantized to provide an efficient algorithm for computing bounded height kronecker and plethysm coefficients

temporal quantum correlations and leggett garg inequalities in multilevel systems we show that the quantum bound for temporal correlations in a leggett garg test analogous to the tsirelson bound for spatial correlations in a bell test strongly depends on the number of levels n that can be accessed by the measurement apparatus via projective measurements we provide exact bounds for small n that exceed the known bound for the leggett garg inequality and we show that in the limit n the leggett garg inequality can be violated up to its algebraic maximum

search and topology aspects in transport on scale free networks abstract using a recently proposed model physica a 332 2004 566 of information transport on complex networks we study the role of network substrates on the statistics of queuing times and correlations in traffic streams when navigation with an enlarged information horizon is applied the waiting time distribution on structured networks has a power law tail which can be parametrized by 1 1 q where the respective value of the non extensivity parameter q increases systematically with increasing graph complexity the corresponding distribution on the small world graph appears to be a stretched exponential function that cannot be classified within the same scheme we further demonstrate by looking at the anti persistence in flow time series and the transit time distributions how traffic efficiency increases with an extended information horizon a horizon of two layers approaches the critical horizon on the correlated cyclic scale free graph suggesting that the mechanisms of signaling over two to three layers ensure efficient transport processes on networks with this organizational complexity

on the existence of quantum representations for two dichotomic measurements under which conditions do outcome probabilities of measurements possess a quantum mechanical model this kind of problem is solved here for the case of two dichotomic von neumann measurements which can be applied repeatedly to a quantum system with trivial dynamics the solution uses methods from the theory of operator algebras and the theory of moment problems the ensuing conditions reveal surprisingly simple relations between certain quantum mechanical probabilities it also shown that generally none of these relations holds in general probabilistic models this result might facilitate further experimental discrimination between quantum mechanics and other general probabilistic theories

stabilization of switched positive system with impulse and marginally stable subsystems a mode dependent dwell time method abstract in this article the problem of stabilization for the switched positive linear system spls with impulse and marginally stable subsystems is studied in which both the continuous time case and the discrete time case are taken into account by the usage of a piecewise weak linear copositive lyapunov function lclf and the mode dependent dwell time mdt time dependent switching control laws are designed to guarantee the asymptotic stability of the system furthermore based on the comparison principal for positive systems the main results are generalized to the time variant spls two examples are worked out to indicate that our results have advantages over some known results in the literature

constrained control of positive systems with delays this technical note addresses controller design for continuous time delayed linear systems the control is under positivity constraint which means that the resulting closed loop systems are not only stable but also positive bounded control is also considered further requiring that the trajectory of the closed loop system is bounded by a prescribed boundary if the initial condition is bounded by the same boundary the contribution lies in three aspects first some necessary and sufficient conditions are presented for the existence of controllers satisfying the positivity constraint second a necessary and sufficient condition is established determining whether the trajectory of a positive system can be bounded by a prescribed boundary provided that the initial condition is bounded by the same boundary third a sufficient condition is presented for bounded control and it is shown to be also necessary if asymptotic stability is not required

quantum channels with polytopic images and image additivity we study quantum channels with respect to their image i e the image of the set of density operators under the action of the channel we first characterize the set of quantum channels having polytopic images and show that additivity of the minimal output entropy can be violated in this class we then provide a complete characterization of quantum channels t that are universally image additive in the sense that for any quantum channel s the image of t otimes s is the convex hull of the tensor product of the images of t and s these channels turn out to form a strict subset of entanglement breaking channels with polytopic images and a strict superset of classical quantum channels

on linear copositive lyapunov functions and the stability of switched positive linear systems we consider the problem of common linear copositive lyapunov function existence for positive switched linear systems in particular we present a necessary and sufficient condition for the existence of such a function for switched systems with two constituent linear time invariant systems several applications of this result are also given

a tutorial on the positive realization problem this paper is a tutorial on the positive realization problem that is the problem of finding a positive state space representation of a given transfer function and characterizing existence and minimality of such representation this problem goes back to the 1950s and was first related to the identifiability problem for hidden markov models then to the determination of internal structures for compartmental systems and later embedded in the more general framework of positive systems theory within this framework developing some ideas sprang in the 1960s during the 1980s the positive realization problem was reformulated in terms of a geometric condition which was recently exploited as a tool for finding the solution to the existence problem and providing partial answers to the minimality problem in this paper the reader is carried through the key ideas which have proved to be useful in order to tackle this problem in order to illustrate the main results contributions and open problems several motivating examples and a comprehensive bibliography on positive systems organized by topics are provided

sequences of projective measurements in generalized probabilistic models we define a simple rule that allows us to describe sequences of projective measurements for a broad class of generalized probabilistic models this class embraces quantum mechanics and classical probability theory but for example also the hypothetical popescu rohrlich box for quantum mechanics the definition yields the established luders rule which is the standard rule for updating the quantum state after a measurement for the general case it can be seen as being the least disturbing or most coherent way of performing sequential measurements we show as an example that the spekkens toy model spekkens 2007 phys rev a 75 032110 provides an instance of our definition we also demonstrate the possibility of strong postquantum correlations as well as the existence of triple slit correlations for certain nonquantum toy models

spectra of real world graphs beyond the semicircle law results on the spectra of adjacency matrices corresponding to models of real world graphs we find that when the number of links grows as the number of nodes the spectral density of uncorrelated random matrices does not converge to the semicircle law furthermore the spectra of real world graphs have specific features depending on the details of the corresponding models in particular scale free graphs develop a trianglelike spectral density with a power law tail while small world graphs have a complex spectral density consisting of several sharp peaks these and further results indicate that the spectra of correlated graphs represent a practical tool for graph classification and can provide useful insight into the relevant structural properties of real networks

exact evaluation of the causal spectrum and localization properties of electronic states on a scale free network abstract a deterministic network with tree structure is considered for which the spectrum of its adjacency matrix can be exactly evaluated by a recursive renormalization approach it amounts to successively increasing number of contributions at any finite step of construction of the tree resulting in a causal chain the resulting eigenvalues can be related the full energy spectrum of a nearest neighbor tight binding model defined on this structure given this association it turns out that further properties of the eigenvectors can be evaluated like the degree of quantum localization of the tight binding eigenstates expressed by the inverse participation ratio ipr it happens that for the current model the ipr s are also suitable to be analytically expressed in terms in corresponding eigenvalue chain the resulting ipr scaling behavior is expressed by the tails of eigenvalue chains as well

metric and classical fidelity uncertainty relations for random unitary matrices we analyze uncertainty relations on finite dimensional hilbert spaces expressed in terms of classical fidelity which are stronger than metric uncertainty relations introduced by fawzi hayden and sen we establish the validity of fidelity uncertainty relations for random unitary matrices with optimal parameters up to universal constants which improves upon known results for the weaker notion of metric uncertainty this result is then applied to locking classical information in quantum states and allows to obtain optimal locking in hellinger distance improving upon previous results on locking in the total variation distance both by strengthening the metric used and by improving the dependence on parameters we also show that general probabilistic estimates behind the main theorem can be used to prove existence of data hiding schemes with bayesian type guarantees as a byproduct of our approach we obtain existence of almost euclidean subspaces of the matrix spaces with a better dimension distortion dependence than allowed in previously known constructions

entanglement thresholds for random induced states for a random quantum state on h c d otimes c d obtained by partial tracing a random pure state on h otimes c s we consider the whether it is typically separable or typically entangled for this problem we show the existence of a sharp threshold s 0 s 0 d of order roughly d 3 more precisely for any a 0 and for d large enough such a random state is entangled with very large probability when s 1 a s 0 one consequence of this result is as follows for a system of n identical particles in a random pure state there is a threshold k 0 k 0 n sim n 5 such that two subsystems of k particles each typically share entanglement if k k 0 and typically do not share entanglement if k k 0 our methods work also for multipartite systems and for unbalanced systems such as c d otimes c d d neq d the arguments rely on random matrices classical convexity high dimensional probability and geometry of banach spaces some of the auxiliary results may be of reference value a high level non technical overview of the results of this paper and of a related article arxiv 1011 0275 can be found in arxiv 1112 4582

spectral and dynamical properties in classes of sparse networks with mesoscopic inhomogeneities we study structure eigenvalue spectra and random walk dynamics in a wide class of networks with subgraphs modules at mesoscopic scale the networks are grown within the model with three parameters controlling the number of modules their internal structure as scale free and correlated subgraphs and the topology of connecting network within the exhaustive spectral analysis for both the adjacency matrix and the normalized laplacian matrix we identify the spectral properties which characterize the mesoscopic structure of sparse cyclic graphs and trees the minimally connected nodes the clustering and the average connectivity affect the central part of the spectrum the number of distinct modules leads to an extra peak at the lower part of the laplacian spectrum in cyclic graphs such a peak does not occur in the case of topologically distinct tree subgraphs connected on a tree whereas the associated eigenvectors remain localized on the subgraphs both in trees and cyclic graphs we also find a characteristic pattern of periodic localization along the chains on the tree for the eigenvector components associated with the largest eigenvalue lambda l 2 of the laplacian further differences between the cyclic modular graphs and trees are found by the statistics of random walks return times and hitting patterns at nodes on these graphs the distribution of first return times averaged over all nodes exhibits a stretched exponential tail with the exponent sigma approximately 1 3 for trees and sigma approximately 2 3 for cyclic graphs which is independent of their mesoscopic and global structure

laplacian spectra of and random walks on complex networks are scale free architectures really important we study the laplacian operator of an uncorrelated random network and as an application consider hopping processes diffusion random walks signal propagation etc on networks we develop a strict approach to these problems we derive an exact closed set of integral equations which provide the averages of the laplacian operator s resolvent this enables us to describe the propagation of a signal and random walks on the network we show that the determining parameter in this problem is the minimum degree q m of vertices in the network and that the high degree part of the degree distribution is not that essential the position of the lower edge of the laplacian spectrum c appears to be the same as in the regular bethe lattice with the coordination number q m namely c 0 if q m 2 and c 0 if q m 2 in both of these cases the density of eigenvalues p 0 as c 0 but the limiting behaviors near c are very different in terms of a distance from a starting vertex the hopping propagator is a steady moving gaussian broadening with time this picture qualitatively coincides with that for a regular bethe lattice our analytical results include the spectral density p near c and the long time asymptotics of the autocorrelator and the propagator

capacity bounds via operator space methods we prove that for generalized dephasing channels the coherent information and reverse coherent information coincides it also implies an alternative approach for the strong super additivity and strong converse of generalized dephasing channels using the operator space technique our argument is based on an improved renyi relative entropy estimate via analyzing the channel s stinespring space we also apply this estimate to new examples of quantum channels arising from quantum group co representation and kitave s quantum computation model in particular we find concrete examples of non degradable channels that our estimates are tight and give a formula of nontrivial quantum capacity we prove that for generalized dephasing channels the coherent information and reverse coherent information coincides it also implies an alternative approach for the strong super additivity and strong converse of generalized dephasing channels using the operator space technique our argument is based on an improved renyi relative entropy estimate via analyzing the channel s stinespring space we also apply this estimate to new examples of quantum channels arising from quantum group co representation and kitave s quantum computation model in particular we find concrete examples of non degradable channels that our estimates are tight and give a formula of nontrivial quantum capacity

on the geometry of projective tensor products abstract in this work we study the volume ratio of the projective tensor products l p n l q n l r n with 1 p q r we obtain asymptotic formulas that are sharp in almost all cases as a consequence of our estimates these spaces allow for a nearly euclidean decomposition of kasin type whenever 1 p q r 2 or 1 p 2 r and q 2 also from the bourgain milman bound on the volume ratio of banach spaces in terms of their cotype 2 constant we obtain information on the cotype of these 3 fold projective tensor products our results naturally generalize to k fold products l p 1 n l p k n with k n and 1 p 1 p k

asymptotic behavior of switched delay systems with nonlinear disturbances the objective of this paper is to study the asymptotic behavior of switched delay systems with nonlinear disturbances by establishing a new delay gronwall bellman integral inequality and an elementary inequality we obtain some asymptotic results for the systems under arbitrary switching laws which extend some existing results in the literature to the more general nonlinear case finally two examples are provided to illustrate the effectiveness of our results

nonadditivity of renyi entropy and dvoretzky s theorem the goal of this note is to show that the analysis of the minimum output p renyi entropy of a typical quantum channel essentially amounts to applying milman s version of dvoretzky s theorem about almost euclidean sections of high dimensional convex bodies this conceptually simplifies the nonconstructive argument by hayden winter disproving the additivity conjecture for the minimal output p renyi entropy for p 1

symmetry constraints on temporal order in measurement based quantum computation we discuss the interdependence of resource state measurement setting and temporal order in measurement based quantum computation the possible temporal orders of measurement events are constrained by the principle that the randomness inherent in quantum measurement should not affect the outcome of the computation we provide a classification for all temporal relations among measurement events compatible with a given initial stabilizer state and measurement setting in terms of a matroid conversely we show that classical processing relations necessary for turning the local measurement outcomes into computational output determine the resource state and measurement setting up to local equivalence further we find a symmetry transformation related to local complementation that leaves the temporal relations invariant

on the distributions of laplacian eigenvalues versus node degrees in complex networks abstract in this paper the important issue of laplacian eigenvalue distributions is investigated through theory guided extensive numerical simulations for four typical complex network models namely the er random graph networks ws and nw small world networks and ba scale free networks it is found that these four types of complex networks share some common features particularly similarities between the laplacian eigenvalue distributions and the node degree distributions

spectra of modular and small world matrices we compute spectra of symmetric random matrices describing graphs with general modular structure and arbitrary inter and intra module degree distributions subject only to the constraint of finite mean connectivities we also evaluate spectra of a certain class of small world matrices generated from random graphs by introducing shortcuts via additional random connectivity components both adjacency matrices and the associated graph laplacians are investigated for the laplacians we find lifshitz type singular behaviour of the spectral density in a localized region of small values in the case of modular networks we can identify contributions of local densities of state from individual modules for small world networks we find that the introduction of short cuts can lead to the creation of satellite bands outside the central band of extended states exhibiting only localized states in the band gaps results for the ensemble in the thermodynamic limit are in excellent agreement with those obtained via a cavity approach for large finite single instances and with direct diagonalization results

stability theory for nonnegative and compartmental dynamical systems with time delay abstract nonnegative and compartmental dynamical system models are derived from mass and energy balance considerations and involve the exchange of nonnegative quantities between subsystems or compartments these models are widespread in biological and physical sciences and play a key role in understanding these processes a key physical limitation of such systems is that transfers between compartments is not instantaneous and realistic models for capturing the dynamics of such systems should account for material in transit between compartments in this paper we present necessary and sufficient conditions for stability of nonnegative and compartmental dynamical systems with time delay specifically asymptotic stability conditions for linear and nonlinear nonnegative dynamical systems with time delay are established using linear lyapunov krasovskii functionals

topos logic in measurement based quantum computation we report first steps towards elucidating the relationship between contextuality measurement based quantum computation mbqc and the non classical logic of a topos associated with the computation we show that in a class of mbqc classical universality requires non classical logic which is consumed during the course of the computation thereby pinpointing another potential quantum computational resource

on the multiplicity of laplacian eigenvalues and fiedler partitions abstract in this paper we investigate the relation between eigenvalue distribution and graph structure of two classes of graphs the m k stars and l dependent graphs we give conditions on the topology and edge weights in order to get values and multiplicities of laplacian matrix eigenvalues we prove that a vertex set reduction on graphs with m k star subgraphs is feasible keeping the same eigenvalues with reduced multiplicity moreover some useful eigenvectors properties are derived up to a product with a suitable matrix finally we relate these results with fiedler spectral partitioning of the graph and the physical relevance of the results is shortly discussed

dynamic output feedback control for continuous time interval positive systems under l1 performance this paper is concerned with the design of l1 induced dynamic output feedback controller for continuous time positive systems with interval uncertainties a necessary and sufficient condition for stability and l1 induced performance of positive linear systems is proposed in terms of linear inequalities based on this conditions for the existence of robust dynamic output feedback controllers are established and an iterative convex optimization approach is developed to solve the conditions one illustrative example is provided to show the effectiveness and applicability of the theoretical results

improved delay dependent stability criteria for time delay systems this note provides an improved asymptotic stability condition for time delay systems in terms of a strict linear matrix inequality unlike previous methods the mathematical development avoids bounding certain cross terms which often leads to conservatism when time varying norm bounded uncertainties appear in a delay system an improved robust delay dependent stability condition is also given examples are provided to demonstrate the reduced conservatism of the proposed conditions

channel capacities via p summing norms abstract in this paper we show how the metric theory of tensor products developed by grothendieck perfectly fits in the study of channel capacities a central topic in shannon s information theory furthermore in the last years shannon s theory has been fully generalized to the quantum setting and revealed qualitatively new phenomena in comparison in this paper we consider the classical capacity of quantum channels with restricted assisted entanglement these capacities include the classical capacity and the unlimited entanglement assisted classical capacity of a quantum channel our approach to restricted capacities is based on tools from functional analysis and in particular the notion of p summing maps going back to grothendieck s work pisier s noncommutative vector valued l p spaces allow us to establish the new connection between functional analysis and information theory in the quantum setting

delay dependent robust stabilization of uncertain state delayed systems this paper concerns a problem of robust stabilization of uncertain state delayed systems a new delay dependent stabilization condition using a memoryless controller is formulated in terms of matrix inequalities an algorithm involving convex optimization is proposed to design a controller guaranteeing a suboptimal maximal delay such that the system can be stabilized for all admissible uncertainties

revisiting additivity violation of quantum channels we prove additivity violation of minimum output entropy of quantum channels by straightforward application of epsilon net argument and levy s lemma the additivity conjecture was disproved initially by hastings later a proof via asymptotic geometric analysis was presented by aubrun szarek and werner which uses dudley s bound on gaussian process or dvoretzky s theorem with schechtman s improvement in this paper we develop another proof along dvoretzky s theorem in milman s view showing additivity violation in broader regimes than the existing proofs importantly dvoretzky s theorem works well with norms to give strong statements but these techniques can be extended to functions which have norm like structures positive homogeneity and triangle inequality then a connection between hastings method and ours is also discussed in addition we make some comments on relations between regularized minimum output entropy and classical capacity of quantum channels

analysis of heat kernel highlights the strongly modular and heat preserving structure of proteins abstract in this paper we study the structure and dynamical properties of protein contact networks with respect to other biological networks together with simulated archetypal models acting as probes we consider both classical topological descriptors such as modularity and statistics of the shortest paths and different interpretations in terms of diffusion provided by the discrete heat kernel which is elaborated from the normalized graph laplacians a principal component analysis shows high discrimination among the network types by considering both the topological and heat kernel based vector characterizations furthermore a canonical correlation analysis demonstrates the strong agreement among those two characterizations providing thus an important justification in terms of interpretability for the heat kernel finally and most importantly the focused analysis of the heat kernel provides a way to yield insights on the fact that proteins have to satisfy specific structural design constraints that the other considered networks do not need to obey notably the heat trace decay of an ensemble of varying size proteins denotes subdiffusion a peculiar property of proteins

on equivalence and efficiency of certain stability criteria for time delay systems in recent years there have been a number of new delay dependent stability criteria based on linear matrix inequalities published in the literature this note aims to theoretically establish the equivalence of seven of these stability criteria moreover the efficiency of these stability criteria is assessed based on the number of unknowns in the linear matrix inequalities

the ppt square conjecture holds generically for some classes of independent states let be a random pure state on where is a random unit vector uniformly distributed on the sphere in let be a random induced state whose distribution is and let be a random induced state following the same distribution independent of let be a random state induced by the entanglement swapping of and we show that the empirical spectrum of converges almost surely to the marcenko pastur law with parameter c 2 as and as an application we prove that the state is separable generically if are ppt entangled

quantum measuring processes of continuous observables the purpose of this paper is to provide a basis of theory of measurements of continuous observables we generalize von neumann s description of measuring processes of discrete quantum observables in terms of interaction between the measured system and the apparatus to continuous observables and show how every such measuring process determines the state change caused by the measurement we establish a one to one correspondence between completely positive instruments in the sense of davies and lewis and the state changes determined by the measuring processes we also prove that there are no weakly repeatable completely positive instruments of nondiscrete observables in the standard formulation of quantum mechanics so that there are no measuring processes of nondiscrete observables whose state changes satisfy the repeatability hypothesis a proof of the wigner araki yanase theorem on the nonexistence of repeatable measurements of observables not commuting conserved quantities is given in our framework we also discuss the implication of these results for the recent results due to srinivas and due to mercer on measurements of continuous observables

greedy discrete particle swarm optimization for large scale social network clustering social computing is a new paradigm for information and communication technology social network analysis is one of the theoretical underpinnings of social computing community structure detection is believed to be an effective tool for social network analysis uncovering community structures in social networks can be regarded as clustering optimization problems because social networks are characterized by dynamics and huge volumes of data conventional nature inspired optimization algorithms encounter serious challenges when applied to solving large scale social network clustering optimization problems in this study we put forward a novel particle swarm optimization algorithm to reveal community structures in social networks the particle statuses are redefined under a discrete scenario the status updating rules are reconsidered based on the network topology a greedy strategy is designed to drive particles to a promising region to this end a greedy discrete particle swarm optimization framework for large scale social network clustering is suggested to determine the performance of the algorithm extensive experiments on both synthetic and real world social networks are carried out we also compare the proposed algorithm with several state of the art network community clustering methods the experimental results demonstrate that the proposed method is effective and promising for social network clustering

asymptotically well behaved input states do not violate additivity for conjugate pairs of random quantum channels it is now well known that with high probability the additivity of minimum output entropy does not hold for pairs of the random quantum channel and its complex conjugate we investigate asymptotic behavior of output states of r tensor powers of such pairs as the dimension of inputs grows we compute the limit output states for any sequence of well behaved inputs which consist of a large class of input states having a nice set of parameters then we show that among these input states tensor products of bell states give asymptotically the least output entropy giving positive mathematical evidence towards additivity of above pairs of channels

potential output purity of completely positive maps the notion of potential output purity of a completely positive map is introduced as a generalization of the regularized output purity an upper bound is derived for this quantity and for several classes of maps including cq classical quantum qc quantum classical hadamard channels it is shown that potential purity does not exceed the standard output purity as an application the potential purity is used to bound the logarithmic sobolev constant of a product of depolarizing channel semigroups

counterexamples to the maximal p norm multiplicativity conjecture for all p 1 for all p 1 we demonstrate the existence of quantum channels with non multiplicative maximal output p norms equivalently for all p 1 the minimum output renyi entropy of order p of a quantum channel is not additive the violations found are large in all cases the minimum output renyi entropy of order p for a product channel need not be significantly greater than the minimum output entropy of its individual factors since p 1 corresponds to the von neumann entropy these counterexamples demonstrate that if the additivity conjecture of quantum information theory is true it cannot be proved as a consequence of any channel independent guarantee of maximal p norm multiplicativity we also show that a class of channels previously studied in the context of approximate encryption lead to counterexamples for all p 2

graph wavelets for multiscale community mining we develop a signal processing approach to the multiscale detection of communities in networks that is of groups of nodes well connected together the method relies on carefully engineered wavelets on graphs to introduce the notion of scale and to obtain a local view of the graph from each node computing the correlations between wavelets centered at different nodes one has access to a notion of similarity between nodes thereby enabling a clustering procedure that groups nodes according to their community at the scale of analysis by using a collection of random vectors to estimate the correlation between the nodes we show that the method is suitable for the analysis of large graphs furthermore we introduce a notion of partition stability and a statistical test allowing us to assess which scales of analysis of the network are relevant the effectiveness of the method is discussed first on multiscale graph benchmarks then on real data of social networks and on models for signal processing on graphs

separable states are more disordered globally than locally a remarkable feature of quantum entanglement is that an entangled state of two parties alice a and bob b may be more disordered locally than globally that is s a s a b where s is the von neumann entropy it is known that satisfaction of this inequality implies that a state is nonseparable in this paper we prove the stronger result that for separable states the vector of eigenvalues of the density matrix of system ab is majorized by the vector of eigenvalues of the density matrix of system a alone this gives a strong sense in which a separable state is more disordered globally than locally and a new necessary condition for separability of bipartite states in arbitrary dimensions

chain motifs the tails and handles of complex networks a great part of the interest in complex networks has been motivated by the presence of structured frequently nonuniform connectivity because diverse connectivity patterns tend to result in distinct network dynamics and also because they provide the means to identify and classify several types of complex network it becomes important to obtain meaningful measurements of the local network topology in addition to traditional features such as the node degree clustering coefficient and shortest path motifs have been introduced in the literature in order to provide complementary descriptions of the network connectivity the current work proposes a different type of motif namely chains of nodes that is sequences of connected nodes with degree 2 these chains have been subdivided into cords tails rings and handles depending on the type of their extremities e g open or connected a theoretical analysis of the density of such motifs in random and scale free networks is described and an algorithm for identifying these motifs in general networks is presented the potential of considering chains for network characterization has been illustrated with respect to five categories of real world networks including 16 cases several interesting findings were obtained including the fact that several chains were observed in real world networks especially the world wide web books and the power grid the possibility of chains resulting from incompletely sampled networks is also investigated

method to find community structures based on information centrality community structures are an important feature of many social biological and technological networks here we study a variation on the method for detecting such communities proposed by girvan and newman and based on the idea of using centrality measures to define the community boundaries m girvan and m e j newman proc natl acad sci u s a 99 7821 2002 we develop an algorithm of hierarchical clustering that consists in finding and removing iteratively the edge with the highest information centrality we test the algorithm on computer generated and real world networks whose community structure is already known or has been studied by means of other methods we show that our algorithm although it runs to completion in a time o n4 is very effective especially when the communities are very mixed and hardly detectable by the other methods

almost one bit violation for the additivity of the minimum output entropy in a previous paper we proved that in the appropriate asymptotic regime the limit of the collection of possible eigenvalues of output states of a random quantum channel is a deterministic compact set kk t we also showed that the set kk t is obtained up to an intersection as the unit ball of the dual of a free compression norm in this paper we identify the maximum of ell p norms on the set kk t and prove that the maximum is attained on a vector of shape a b b where a b in particular we compute the precise limit value of the minimum output entropy of a single random quantum channel as a corollary we show that for any varepsilon 0 it is possible to obtain a violation for the additivity of the minimum output entropy for an output dimension as low as 183 and that for appropriate choice of parameters the violation can be as large as log 2 varepsilon conversely our result implies that with probability one in the limit one does not obtain a violation of additivity using conjugate random quantum channels and the bell state in dimension 182 and less

weak multiplicativity for random quantum channels it is known that random quantum channels exhibit significant violations of multiplicativity of maximum output p norms for any p 1 in this work we show that a weaker variant of multiplicativity nevertheless holds for these channels for any constant p 1 given a random quantum channel mathcal n i e a channel whose stinespring representation corresponds to a random subspace s we show that with high probability the maximum output p norm of mathcal n otimes n decays exponentially with n the proof is based on relaxing the maximum output norm of mathcal n to the operator norm of the partial transpose of the projector onto s then calculating upper bounds on this quantity using ideas from random matrix theory

delay dependent and decay rate dependent conditions for exponential mean stability and non fragile controller design of positive markov jump linear systems with time delay abstract this paper proposes some new sufficient conditions and necessary conditions for exponential mean stability with prescribed decay rate and sufficient conditions for non fragile controller design of both continuous time and discrete time positive markov jump linear systems with time delay first sufficient stability conditions are derived by constructing novel linear stochastic co positive lyapunov krasovskii functionals second the corresponding necessary conditions are established by applying a model transformation technique and analyzing the relationship between stochastic stability of the transformed systems and exponential mean stability with given decay rate of the original systems compared with the existing conditions the proposed stability conditions are not only delay dependent but also decay rate dependent and the sufficient conditions plus the necessary conditions can be used to judge the system stability more precisely third based on the new sufficient conditions non fragile controllers are designed by solving linear programming problems such that the closed loop systems are positive and exponentially mean stable with an expected decay rate finally by numerical examples the effects of both time delay and decay rate on exponential mean stability are exploited and the validity of the non fragile controller design conditions is demonstrated

modelling conflicts with cluster dynamics in networks abstract we introduce cluster dynamical models of conflicts in which only the largest cluster can be involved in an action this mimics the situations in which an attack is planned by a central body and the largest attack force is used we study the model in its annealed random graph version on a fixed network and on a network evolving through the actions the sizes of actions are distributed with a power law tail however the exponent is non universal and depends on the frequency of actions and sparseness of the available connections between units allowing the network reconstruction over time in a self organized manner e g by adding the links based on previous liaisons between units we find that the power law exponent depends on the evolution time of the network its lower limit is given by the universal value 5 2 derived analytically for the case of random fragmentation processes in the temporal patterns behind the size of actions we find long range correlations in the time series of the number of clusters and the non trivial distribution of time that a unit waits between two actions in the case of an evolving network the distribution develops a power law tail indicating that through repeated actions the system develops an internal structure with a hierarchy of units

positive linear observers for linear compartmental systems linear compartmental systems are mathematical systems that are frequently used in biology and mathematics the inputs states and outputs of such systems are positive because they denote amounts or concentrations of material for linear dynamic systems the observer problem has been solved the purpose of the observer problem is to determine a linear observer such that the state can be approximated the difference between the state and its estimate should converge to zero the interpretation in terms of a physical system requires that an estimate of the state be positive like the state itself in this paper conditions on the system matrices are presented that guarantee that there exists a positive linear observer such that both the error converges to zero and the estimate is positive

highly entangled non random subspaces of tensor products from quantum groups in this paper we describe a class of highly entangled subspaces of a tensor product of finite dimensional hilbert spaces arising from the representation theory of free orthogonal quantum groups we determine their largest singular values and obtain lower bounds for the minimum output entropy of the corresponding quantum channels an application to the construction of d positive maps on matrix algebras is also presented

the stability of stochastic coupled systems with time delays and time varying coupling structure this paper is concerned with the pth moment exponential stability of stochastic coupled systems with time delays and time varying coupling structure sctvcs the coupling structure is time varying first second the method of graph theory has been generalized from a system established on a digraph with constant coupling structure to a digraph with time varying coupling structure successfully combining graph theory with lyapunov method a systematic method is given to construct a lyapunov function for sctvcs several pth moment exponential stability criteria are presented including a lyapunov type theorem and some sufficient criteria in the form of coefficients furthermore the theoretical conclusions are applied to the stochastic coupled oscillators with time varying coupling structure and two stability criteria are obtained finally we give two numerical examples to illustrate the effectiveness of our results

stability of multiagent systems with time dependent communication links we study a simple but compelling model of network of agents interacting via time dependent communication links the model finds application in a variety of fields including synchronization swarming and distributed decision making in the model each agent updates his current state based upon the current information received from neighboring agents necessary and or sufficient conditions for the convergence of the individual agents states to a common value are presented thereby extending recent results reported in the literature the stability analysis is based upon a blend of graph theoretic and system theoretic tools with the notion of convexity playing a central role the analysis is integrated within a formal framework of set valued lyapunov theory which may be of independent interest among others it is observed that more communication does not necessarily lead to faster convergence and may eventually even lead to a loss of convergence even for the simple models discussed in the present paper