identification of influential nodes in complex networks method from spreading probability viewpoint abstract the problem of identifying influential nodes in complex networks has attracted much attention owing to its wide applications including how to maximize the information diffusion boost product promotion in a viral marketing campaign prevent a large scale epidemic and so on from spreading viewpoint the probability of one node propagating its information to one other node is closely related to the shortest distance between them the number of shortest paths and the transmission rate however it is difficult to obtain the values of transmission rates for different cases to overcome such a difficulty we use the reciprocal of average degree to approximate the transmission rate then a semi local centrality index is proposed to incorporate the shortest distance the number of shortest paths and the reciprocal of average degree simultaneously by implementing simulations in real networks as well as synthetic networks we verify that our proposed centrality can outperform well known centralities such as degree centrality betweenness centrality closeness centrality k shell centrality and nonbacktracking centrality in particular our findings indicate that the performance of our method is the most significant when the transmission rate nears to the epidemic threshold which is the most meaningful region for the identification of influential nodes

maximal subgroups of gl1 d abstract let d be a division algebra of degree m over its center f herstein has shown that any finite normal subgroup of d gl 1 d is central here as a generalization of this result it is shown that any finitely generated normal subgroup of d is central this also solves a problem raised by akbari and mahdavi hezavehi proc amer math soc to appear for finite dimensional division algebras the structure of maximal multiplicative subgroups of an arbitrary division ring d is then investigated given a maximal subgroup m of d whose center is algebraic over f it is proved that if m satisfies a multilinear polynomial identity over f then d f

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

an optimum strategy for detection in the presence of random transient disturbance and white gaussian noise detection of a deterministic signal is considered because of the presence of the transient disturbance the traditional totally probabilistic criteria are no longer appropriate since they cannot be related to the physical reality as in the case of stationary ergodic noise only a mixed strategy is proposed for the detection where the disturbance is treated as a semideterministic object while white gaussian noise is treated as a genuinely random object specifically the author uses as the detection statistic the log likelihood ratio of two conditional probability measures corresponding to the signal presence and the signal absence hypotheses given the disturbance in which the disturbance is replaced by its maximum a posteriori likelihood estimate the detection statistic takes the generalized in function space form of a soft limiter or a blanker followed by the matched filter it is an explicit detection algorithm though improvement in computational efficiency is much desired

nonparametric multiuser detection in non gaussian channels existing multiuser detection techniques in wireless systems are based on the assumption that some information on the parameters of the probability density function pdf of ambient noise is available such information may not be available in all cases particularly for non gaussian and impulsive noises or may change depending on circumstances in this paper we present a technique for multiuser detection that does not require any a priori knowledge about the noise parameters this method is based on using pseudo norms for linear nonparametric regression analytical and simulation results show that the proposed method offers an improved or at least comparable performance over existing robust techniques in the absence of any information on the nature of noise in the environment the increased computational complexity is marginal compared to existing parametric detectors in addition the proposed nonparametric detector is portable in the sense that it does not need to be tuned for different noise models without any considerable degradation of performance we also show that in non gaussian noise the performance of blind adaptive nonparametric multiuser detectors is better than that of robust multiuser detectors

analysis of the effect of impulse noise on multicarrier and single carrier qam systems the paper first shows the equivalence of the bernoulli gaussian impulse noise model in the discrete time domain to the continuous time model of poisson arriving delta functions with random area distributed according to the power rayleigh probability density function this equivalence is then used to develop a closed form expression for the probability of error for single carrier qam that is easily evaluated furthermore the performance of multicarrier modulation mcm is also analyzed using the same impulse noise model and it is shown that in most cases mcm performs better than single carrier systems specifically when the probability of an impulse is not too high and the impulse power is moderate

nilpotent and polycyclic by finite maximal subgroups of skew linear groups abstract let d be an infinite division ring n a natural number and n a subnormal subgroup of gl n d such that n 1 or the center of d contains at least five elements this paper contains two main results in the first one we prove that each nilpotent maximal subgroup of n is abelian this generalizes the result in ebrahimian 2004 3 which asserts that each maximal subgroup of gl n d is abelian and a result in ramezan nassab and kiani 2013 12 in the second one we show that a maximal subgroup of gl n d cannot be polycyclic by finite

locally optimum detection in moving average non gaussian noise detection algorithms that are locally optimum bayes and also asymptotically optimum are developed for both coherent and incoherent signaling for arbitrary interference and signal waveforms when the dependence in the noise samples is represented by a moving average model this leads to receiver structures which are prewhitened versions of the locally optimum detectors in the independent case a probability of error expression in the ideal observer symmetric case the processing gain and the minimum detectable signal are derived in both cases these demonstrate by means of an expression comparing performance between this and the independent case that for the same large sample size n 1 an improvement in performance is always achieved when the noise samples are dependent without any additional complexity in receiver structure

pseudo likelihood methods for community detection in large sparse networks many algorithms have been proposed for fitting network models with communities but most of them do not scale well to large networks and often fail on sparse networks here we propose a new fast pseudo likelihood method for fitting the stochastic block model for networks as well as a variant that allows for an arbitrary degree distribution by conditioning on degrees we show that the algorithms perform well under a range of settings including on very sparse networks and illustrate on the example of a network of political blogs we also propose spectral clustering with perturbations a method of independent interest which works well on sparse networks where regular spectral clustering fails and use it to provide an initial value for pseudo likelihood we prove that pseudo likelihood provides consistent estimates of the communities under a mild condition on the starting value for the case of a block model with two communities

message passing approach for recurrent state epidemic models on networks epidemic processes are common out of equilibrium phenomena of broad interdisciplinary interest recently dynamic message passing dmp has been proposed as an efficient algorithm for simulating epidemic models on networks and in particular for estimating the probability that a given node will become infectious at a particular time to date dmp has been applied exclusively to models with one way state changes as opposed to models like sis and sirs where nodes can return to previously inhabited states because many real world epidemics can exhibit such recurrent dynamics we propose a dmp algorithm for complex recurrent epidemic models on networks our approach takes correlations between neighboring nodes into account while preventing causal signals from backtracking to their immediate source and thus avoids echo chamber effects where a pair of adjacent nodes each amplify the probability that the other is infectious we demonstrate that this approach well approximates results obtained from monte carlo simulation and that its accuracy is often superior to the pair approximation which also takes second order correlations into account moreover our approach is more computationally efficient than the pair approximation especially for complex epidemic models the number of variables in our dmp approach grows as 2mk where m is the number of edges and k is the number of states as opposed to mk 2 for the pair approximation we suspect that the resulting reduction in computational effort as well as the conceptual simplicity of dmp will make it a useful tool in epidemic modeling especially for high dimensional inference tasks

exact results for the kuramoto model with a bimodal frequency distribution we analyze a large system of globally coupled phase oscillators whose natural frequencies are bimodally distributed the dynamics of this system has been the subject of long standing interest in 1984 kuramoto proposed several conjectures about its behavior ten years later crawford obtained the first analytical results by means of a local center manifold calculation nevertheless many questions have remained open especially about the possibility of global bifurcations here we derive the system s stability diagram for the special case where the bimodal distribution consists of two equally weighted lorentzians using an ansatz recently discovered by ott and antonsen we show that in this case the infinite dimensional problem reduces exactly to a flow in four dimensions depending on the parameters and initial conditions the long term dynamics evolves to one of three states incoherence where all the oscillators are desynchronized partial synchrony where a macroscopic group of phase locked oscillators coexists with a sea of desynchronized ones and a standing wave state where two counter rotating groups of phase locked oscillators emerge analytical results are presented for the bifurcation boundaries between these states similar results are also obtained for the case in which the bimodal distribution is given by the sum of two gaussians

predicting epidemic threshold of correlated networks a comparison of methods abstract being able to theoretically predict the outbreak threshold of an epidemic is essential in disease control real world correlated networks are ubiquitous and their topological structure strongly affects the prediction accuracy of present day theoretical methods quantifying their accuracy and fitness in predicting outbreak thresholds of correlated networks is thus essential we use a susceptible infected removed sir model to examine four widely used theoretical methods the heterogeneous mean field h m f quenched mean field q m f dynamical message passing d m p and connectivity matrix c m methods to predict the outbreak threshold of a correlated network the potential topological structure of correlated network impacts on prediction accuracy of these four methods we emphasize that the quantitative changes of degree correlation degree distribution exponent and network size strongly affect the outbreak of sir spreading dynamics and compare the simulation results with the theoretical ones obtained from these four methods the extensive experiments in synthetic networks show that a the increasing degree correlation coefficients reduce outbreak threshold and suppress outbreak size b the increasing degree distribution exponents raise outbreak threshold but suppress outbreak size c the increasing network sizes decrease outbreak threshold but do not affect outbreak size d as for four theoretical methods c m and d m p are more likely to precisely predict outbreak threshold because they to some extent incorporate network topology with dynamical correlations the experimental results in 50 real world networks also prove the above conclusions

spread spectrum multiple access performance of orthogonal codes linear receivers this paper analyzes a direct sequence spread spectrum multiple access ssma communication system which assigns a set of m orthogonal sequences to each user with all direct sequence ssma systems k users share a channel by phase modulating their transmissions with signature sequences however the users of our system transmit log 2 m bits of information sequence this contrasts classical ssma schemes which use a pair of antipodal sequences and transmit 1 bit sequence in this paper we assume that the channel noise is a combination of additive white gaussian noise awgn and multiple access interference we employ the optimum single user demodulator for orthogonal signals in gaussian noise the multiple user performance of this receiver is analyzed we obtain approximations for the multiuser probability of error by using a gaussian approximation for the multiple access interference we also obtain an upper bound on the exact probability by using characteristic functions our ssma system is well suited for application at the lower radio frequencies therefore a companion paper describes a realistic model for low frequency radio noise modifies the receiver to include a zero memory nonlinearity and studies the performance of the nonlinear receiver

spread spectrum multiple access performance of orthogonal codes impulsive noise a direct sequence spread spectrum multiple access ssma communication system that assigned a set of m orthogonal sequences to each user is analyzed an accurate model is incorporated for the impulsive noise that characterizes the lf and mf bands so that the ssma receiver operates in a combination of multiple access interference and impulsive atmospheric noise the performance of a linear receiver operating in such an environment is analyzed and probability of error curves are presented the presence of impulsive noise motivates the derivation and analysis of a nonlinear receiver that use a variable gain stage to suppress noise impulses this receiver is effectively optimum when the signal amplitudes are below a certain bound and when the noise and interference samples are independent or nearly so however the gain stage of this nearly optimum receiver depends on the noise model parameters including the various user delays consequently a nonparametric receiver that incorporates a simple clipper is also analyzed the asymptotic relative efficiency of both receivers is determined

detection in multivariate non gaussian noise the applications of multivariate edgeworth series and higher order statistics to the discrete time detection of a known constant signal in multivariate non gaussian noise are considered a technique to derive suboptimum detectors from the neyman pearson optimum and locally optimum detectors is described a numerical algorithm based on knowledge of the noise cumulants is presented in order to analyze the finite sample size performance of the suboptimum detectors as an example the performance of the detectors as compared with the linear detector in multivariate gaussian gaussian mixture noise is presented via receiver operating characteristic curves numerical results indicate that the suboptimum detectors when exploiting knowledge of the dependence structure of the noise can have very good performance with respect to the linear detector

optimal and robust memoryless discrimination from dependent observations discrimination is considered between two possible sources based on dependent observations of their output the discrimination problem is modeled by means of a general binary hypothesis test the main emphasis being on situations that cannot be modeled as signals in additive noise the observations are modeled as stationary m dependent or rho mixing processes the structure of the discriminator is such that the observations are passed through a memoryless nonlinearity summed up to form a test statistic which is then compared to a threshold only fixed sample size tests are considered four different performance measures which resemble the signal to noise ratios encountered in the signal in additive noise problems are derived under different problem formulations the optimal nonlinearities for each of the performance measures are derived as solutions to various integral equations for three of the four performance measures the authors have successfully obtained robust nonlinearities for uncertainty in the marginal and the joint probability density functions of the observations computer simulation results that demonstrate the advantage of using these nonlinearities over the i i d nonlinearity under the probability of error criterion are presented

mean first passage times for two biased walks on the weighted rose networks abstract compared with traditional random walk biased walks have been studied extensively over the past decade especially in the transport and communication networks in this paper we first introduce the weighted rose networks then for the weighted rose networks we focus on two biased walks maximal entropy walk and weight dependent walk and obtain the exact expressions of their stationary distributions and mean first passage times finally we find that the average receiving time for maximal entropy walk is a quadratic function of the weight parameter r while the average receiving time for weighted dependent walk is a linear function of the weight parameter r meanwhile for the maximal entropy walk the smaller the value of r is the more efficient the trapping process is for the weighted dependent walk the larger the value of r r r 0 2 6 is the more efficient for the weighted dependent walk the smaller the value of r r r 0 2 6 is the more efficient for the weight dependent walk

spectra of random graphs with given expected degrees in the study of the spectra of power law graphs there are basically two competing approaches one is to prove analogues of wigner s semicircle law whereas the other predicts that the eigenvalues follow a power law distribution although the semicircle law and the power law have nothing in common we will show that both approaches are essentially correct if one considers the appropriate matrices we will prove that under certain mild conditions the eigenvalues of the normalized laplacian of a random power law graph follow the semicircle law whereas the spectrum of the adjacency matrix of a power law graph obeys the power law our results are based on the analysis of random graphs with given expected degrees and their relations to several key invariants of interest are a number of new values for the exponent where phase transitions for eigenvalue distributions occur the spectrum distributions have direct implications to numerous graph algorithms such as for example randomized algorithms that involve rapidly mixing markov chains

performance evaluation of m ary qprs schemes in severe impulsive noise environments the performance of multilevel quadrature partial response systems qprs in the presence of an additive combination of gaussian and impulsive noise is analytically evaluated by means of the fourier bessel series expansion method the model of the impulsive noise used which closely models atmospheric and or man made electromagnetic interference consists of a stream of poisson impulses with areas distributed according to a power rayleigh probability density function analytical performance evaluation results are presented for 9 49 and 225 qpr systems the results indicate severe system performance degradation especially for highly bandwidth efficient systems e g 225 qprs mostly due to the long error bursts caused by the impulsive noise tails however a qualitative comparison between these results and the corresponding performance results of equivalent qam schemes demonstrates that 49 qprs could be a suitable choice for microwave radio or hdtv satellite links operating in pure impulsive noise environments

synchronization in symmetric bipolar population networks we analyze populations of kuramoto oscillators with a particular distribution of natural frequencies inspired by networks where there are two groups of nodes with opposite behaviors as for instance in power grids where energy is either generated or consumed at different locations we assume that the frequencies can take only two different values correlations between the value of the frequency of a given node and its topological localization are considered in both regular and random topologies synchronization is enhanced when nodes are surrounded by nodes of the opposite frequency the theoretical result presented in this paper is an analytical estimation for the minimum value of the coupling strength between oscillators that guarantees the achievement of a globally synchronized state this analytical estimation which is in a very good agreement with numerical simulations provides a better understanding of the effect of topological localization of natural frequencies on synchronization dynamics

leveraging percolation theory to single out influential spreaders in networks among the consequences of the disordered interaction topology underlying many social technological and biological systems a particularly important one is that some nodes just because of their position in the network may have a disproportionate effect on dynamical processes mediated by the complex interaction pattern for example the early adoption of a commercial product by an opinion leader in a social network may change its fate or just a few superspreaders may determine the virality of a meme in social media despite many recent efforts the formulation of an accurate method to optimally identify influential nodes in complex network topologies remains an unsolved challenge here we present the exact solution of the problem for the specific but highly relevant case of the susceptible infected removed sir model for epidemic spreading at criticality by exploiting the mapping between bond percolation and the static properties of the sir model we prove that the recently introduced nonbacktracking centrality is the optimal criterion for the identification of influential spreaders in locally tree like networks at criticality by means of simulations on synthetic networks and on a very extensive set of real world networks we show that the nonbacktracking centrality is a highly reliable metric to identify top influential spreaders also in generic graphs not embedded in space and for noncritical spreading

spacing ratio characterization of the spectra of directed random networks previous literature on random matrix and network science has traditionally employed measures derived from nearest neighbor level spacing distributions to characterize the eigenvalue statistics of random matrices this approach however depends crucially on eigenvalue unfolding procedures which in many situations represent a major hindrance due to constraints in the calculation especially in the case of complex spectra here we study the spectra of directed networks using the recently introduced ratios between nearest and next to nearest eigenvalue spacing thus circumventing the shortcomings imposed by spectral unfolding specifically we characterize the eigenvalue statistics of directed erd ifmmode mbox h o else h o fi s r enyi er random networks by means of two adjacency matrix representations namely 1 weighted non hermitian random matrices and 2 a transformation on non hermitian adjacency matrices which produces weighted hermitian matrices for both representations we find that the distribution of spacing ratios becomes universal for a fixed average degree in accordance with undirected random networks furthermore by calculating the average spacing ratio as a function of the average degree we show that the spectral statistics of directed er random networks undergoes a transition from poisson to ginibre statistics for model 1 and from poisson to gaussian unitary ensemble statistics for model 2 eigenvector delocalization effects of directed networks are also discussed

nonbacktracking expansion of finite graphs message passing equations yield a sharp percolation transition in finite graphs as an artifact of the locally treelike approximation for an arbitrary finite connected undirected graph we construct an infinite tree having the same local structural properties as this finite graph when observed by a nonbacktracking walker formally excluding the boundary this infinite tree is a generalization of the bethe lattice we indicate an infinite locally treelike random network whose local structure is exactly given by this infinite tree message passing equations for various cooperative models on this construction are the same as for the original finite graph but here they provide the exact solutions of the corresponding cooperative problems these solutions are good approximations to observables for the models on the original graph when it is sufficiently large and not strongly correlated we show how to express these solutions in the critical region in terms of the principal eigenvector components of the nonbacktracking matrix as representative examples we formulate the problems of the random and optimal destruction of a connected graph in terms of our construction the nonbacktracking expansion we analyze the limitations and the accuracy of the message passing algorithms for different classes of networks and compare the complexity of the message passing calculations to that of direct numerical simulations notably in a range of important cases simulations turn out to be more efficient computationally than the message passing

maximal subgroups of sln d abstract given a non commutative f central division ring d n a subnormal subgroup of g l n d and m a non abelian maximal subgroup of n if m is a non abelian soluble maximal subgroup of n then n 1 and d is cyclic of prime degree p with a maximal cyclic subfield k f such that the groups g a l k f and m k m are isomorphic furthermore for any x m k we have x p f and d f m i 1 p k x i

stochastic geometry modeling and performance evaluation of mimo cellular networks using the equivalent in distribution eid based approach the equivalent in distribution eid based approach to the analysis of single input single output siso cellular networks for transmission over rayleigh fading channels has recently been introduced 1 its rationale relies upon formulating the aggregate other cell interference in terms of an infinite summation of independent and conditionally distributed gaussian random variables rvs this approach leads to exact integral expressions of the error probability for arbitrary bi dimensional modulations in this paper the eid based approach is generalized to the performance analysis of multiple input multiple output mimo cellular networks for transmission over rayleigh fading channels the proposed mathematical formulation allows us to study a large number of mimo arrangements including receive diversity spatial multiplexing orthogonal space time block coding zero forcing reception and zero forcing precoding depending on the mimo setup either exact or approximate integral expressions of the error probability are provided in the presence of other cell interference and noise the error probability is formulated in terms of a two fold integral in interference limited cellular networks the mathematical framework simplifies to a single integral expression as a byproduct the proposed approach enables us to study siso cellular networks for transmission over nakagami m fading channels the mathematical analysis is substantiated with the aid of extensive monte carlo simulations

combined binary pulse position modulation biorthogonal modulation for direct sequence code division multiple access a novel modulation format is proposed for cellular direct sequence cdma systems where a user specific spreading sequence is binary pulse position and biorthogonally modulated to form a set of biorthogonal spreading sequences the modulation scheme trades the signal space used for spreading sequences with that for modulation while a global space is fixed the interference is mainly determined by the cross correlation properties among sequences but also affected by modulation the effect is taken into account to evaluate the multi user performance of the combined modulation compared to m ary orthogonal modulation the performance is shown to be almost the same while resulting in a simpler receiver structure

locally soluble by locally finite maximal subgroups of gln d abstract let d be a non commutative division ring and m a maximal subgroup of gl n d n 2 this paper continues the ongoing effort to show that the structure of maximal subgroups of gl n d is similar in some sense to the structure of gl n d it is known that every locally soluble normal subgroup of gl n d is abelian here among other results we prove that if either i d is finite dimensional over its center or ii the center of d contains at least five elements and m is soluble by finite or iii char d 0 and m is locally soluble by finite then every locally soluble normal subgroup of m is abelian

free subgroups in maximal subgroups of gl1 d abstract let d be a division algebra of finite dimension over its center f given a noncommutative maximal subgroup m of d gl 1 d it is proved that either m contains a noncyclic free subgroup or there exists a maximal subfield k of d which is galois over f such that k is normal in m and m k gal k f using this result it is shown in particular that if d is a noncrossed product division algebra then m does not satisfy any group identity

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

finitely generated subnormal subgroups of gln d are central abstract let d be an infinite division algebra of finite dimension over its center assume that n is a subnormal subgroup of gln d with n 1 it is shown that if n is finitely generated then n is central

design and analysis of trellis codes for orthogonal signal sets this paper studies trellis codes to be used with orthogonal signal constellations the intended application is in direct sequence code division multiple access communication systems the problem of designing good codes is addressed showing how to construct trellis codes from block codes with good burst error detecting capabilities several examples are given resulting in codes equivalent to those found previously by computer search ryan and wilson 1991 the procedure presented can be done by hand and is applicable for designing codes with long constraint lengths and large signal sets where a computer search becomes prohibitive performance of such coded systems can be determined through transfer functions of the specific codes used a general transfer function is given which provides a reasonable approximation to the actual transfer function of good codes thus a first order approximation to the performance of a given system can be determined without actually going through the process of designing and analyzing a specific code

bit to bit error dependence in slotted ds ssma packet systems with random signature sequences a technique is developed to find an accurate approximation to the probability of data bit error and the probability of packet success in a direct sequence spread spectrum multiple access ds ssma packet radio system with random signature sequences an improved gaussian approximation to the probability of data bit error is performed packet performance is analyzed by using the theory of moment spaces to gain insight into the effect of bit to bit error dependence caused by interfering signal relative delays and phases which are assumed constant over the duration of a desired packet numerical results show that if no error control exists in the desired packet or if block error control is used when multiple access interference is high the error dependence increases the average probability of packet success beyond that predicted by models which use independent bit errors however when block error control is used and the multiple access interference is low the bit error dependencies cause a reduction in packet error performance

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

detection in impulsive noise based on robust whitening despite the widespread use of the additive gaussian noise model it has long been recognized that many important environments are distinctly nongaussian the authors present a detector which is designed to operate in a correlated plus impulsive noise environment the detector robustly whitens the data and then uses a two sided threshold test to determine the presence of impulsive samples the impulsive samples are discarded and the remaining samples are used to detect the presence or absence of a signal using a matched filter an approximate analysis is presented and simulations are used to demonstrate the effectiveness of this approach

frustration tuning and perfect phase synchronization in the kuramoto sakaguchi model we present an analysis of conditions under which the dynamics of a frustrated kuramoto or kuramoto sakaguchi model on sparse networks can be tuned to enhance synchronization using numerical optimization techniques linear stability and dimensional reduction analysis a simple tuning scheme for setting node specific frustration parameters as functions of native frequencies and degrees is developed finite size scaling analysis reveals that even partial application of the tuning rule can significantly reduce the critical coupling for the onset of synchronization in the second part of the paper a codynamics is proposed which allows a dynamic tuning of frustration parameters simultaneously with the ordinary kuramoto dynamics we find that such codynamics enhance synchronization when operating on slow time scales and impede synchronization when operating on fast time scales relative to the kuramoto dynamics

error probability for direct sequence spread spectrum multiple access communications part ii approximations approximations are obtained for the average probability of error in an asynchronous direct sequence spread spectrum multiple access communications system both binary and quaternary systems are considered and the chip waveforms are allowed to be arbitrary time limited waveforms with time duration equal to the inverse of the chip rate the approximation is based on the integration of the characteristic function of the multiple access interference the amount of computation required to evaluate this approximation grows only linearly with the product of the number of simultaneous transmitters and the number of chips per bit the accuracy of the approximation is extremely good in most cases but it can be improved if necessary by an application of a series expansion numerical results are presented for specific chip waveforms and signature sequences

spectra of random graphs with arbitrary expected degrees we study random graphs with arbitrary distributions of expected degree and derive expressions for the spectra of their adjacency and modularity matrices we give a complete prescription for calculating the spectra that is exact in the limit of large network size and large vertex degrees we also study the effect on the spectra of hubs in the network vertices of unusually high degree and show that these produce isolated eigenvalues outside the main spectral band akin to impurity states in condensed matter systems with accompanying eigenvectors that are strongly localized around the hubs we give numerical results that confirm our analytic expressions

the maximality of monomial subgroups of linear groups over division rings abstract the monomial subgroups are proved to be maximal in gl n k or sl n k for arbitrary division rings k with some exceptions

a reduced state ungerboeck type map receiver with bidirectional decision feedback for m ary quasi orthogonal signaling in this paper we propose a generic receiver based on optimum maximum likelihood sequence estimation mlse employing a generalized ungerboeck metric with significantly reduced complexity for the general class of m ary quasi orthogonal signaling mos in severe multipath fading channels first by using the factor graph fg of the obtained generalized ungerboeck metric for mos and sum product algorithm spa framework a highly efficient reduced state sequence estimation rsse algorithm is proposed that operates on forward and backward directions and is directly applied to unwhitened channel matched filter cmf and code matched filter outputs at symbol rate the proposed structure generating the a posteriori probabilities app by bidirectional rsse recursions are substantiated with symbol rate bidirectional decision feedback bdf based on surviving paths in order to eliminate the post and pre cursor inter symbol interference isi as well as multi code interference mci due to the non ideal properties of the signaling waveforms and multipath channel it appears as the unification of ungerboeck type reduced trellis equalization framework for mos and achieves near optimum performance especially for channels with large dispersion second we identify a bias term through an error probability analysis which helps us improve the proposed receiver s performance furthermore a tight approximation for the bit error rate ber of the proposed receiver is derived these analyses lead to significant insight on the selection of system parameters and clearly demonstrate the high performance and efficiency of the proposed scheme by a proper choice of the signaling parameters

on the α nonbacktracking centrality for complex networks existence and limit cases abstract nonbactracking centrality was introduced as an attempt to correct some deficiencies of eigenvector centrality in this work the nonbacktracking centrality is introduced as an extension that interpolates between the nonbacktracking centrality of the edges of a directed network and the eigenvector centrality of the corresponding directed line graph the existence of this new nonbacktracking centrality is proved in terms of the connectivity of the original network we prove that the limit of the nonbacktracking centrality when decreases to zero exists and is well defined moreover it coincides with the nonbacktracking centrality when this measure is defined with the same techniques we also prove the convergence of pagerank vectors to the eigenvector centrality vector when the damping factor tends to 1

analysis of the dynamics and topology dependencies of small perturbations in electric transmission grids we study the phase dynamics in power grids in response to small disturbances and how this depends on the grid topology to this end we consider the swing equations in linear order in phase disturbances and solve the resulting linear wave equation deriving the eigenmodes of the weighted graph laplacian a linear response expression for the deviation of frequency is given in terms of these eigenvalues and eigenvectors which it is argued to be the basis for future power system stabilizers and other control measures in power systems as an example we present results for random networks based on the watts strogatz model where we observe a transition to localized eigenstates as the randomness in the degree distribution grows moreover it is found that localization leads to faster decay rates thereby disturbances are found to remain localized on a few nodes where they decay faster finally we also consider the german transmission grid topology where the eigenstate of the lowest eigenfrequency the fiedler vector is found to be extended with large intensities at the northwestern and southern boundaries

noise benefits to robust m estimation of location in dependent observations abstract in the presence of weakly dependent noise we analyze the asymptotic efficiency of robust maximum likelihood type estimators m estimators for location estimation we observe the noise enhanced asymptotic efficiency effect by tuning the background noise level for a single m estimator we also theoretically derive the asymptotic efficiency of a parallel array of m estimators and illustrate the possibility of the noise enhancement of the asymptotic efficiency by injecting extra additive noise components these obtained results enrich the research of noise benefits for the robust estimation of location from the dependent observations

robust locally optimum detection of signals in dependent noise a robust locally optimum detector of a signal embedded in additive dependent nongaussian noise is presented the performance criterion is bayes risk the sample size is finite and the uncertainty class of multivariate inputs is the in contamination model the locally optimum detector is shown to be a censored version of the nominal likelihood ratio

insight into detection of deterministic and gaussian signals in correlated plus impulsive noise environments the authors present a different view of the discrete time detection problem in impulsive noise the approach used is to examine the geometry from a subspace viewpoint of two detectors the clairvoyant matched filter and the clairvoyant power detector they are clairvoyant in that the locations of the impulses in the received data sample are assumed known in the presence of impulses both detectors use this knowledge for properly weighting these samples to reduce the effects of the impulses unfortunately since it is never reasonable to assume that the impulse locations are known these are unrealizable detectors however these clairvoyant detectors provide insight into the problem of detection in an impulsive environment when the nominal component is correlated and suggest detectors which are realizable the results can be used as a theoretical justification of preprocessing the data to eliminate impulsive samples prior to detection

on the radicality of maximal subgroups in gln d abstract a division ring d is weakly locally finite if for every finite subset s of d the division subring of d generated by s is centrally finite we previously introduced this notion bui xuan hai mai hoang bien trinh thanh deo on linear groups over weakly locally finite division rings algebra colloq in press and proved that the class of weakly locally finite division rings strictly contains the class of locally finite division rings in this paper for a weakly locally finite division ring d we investigate the structure of maximal subgroups of gl n d that are radical over the center of d our results generalize previous results pertaining to the centrally finite case

corrigendum to the proofs of some theorems in the article on the radicality of maximal subgroups in gln d j algebra 365 2012 42 49 abstract in the proofs of theorems 2 2 and 2 7 in t t deo et al 2012 3 there are some mistakes here we shall give the corrections of these proofs

on the performance of a novel quasi synchronous trellis coded cdma system we introduce a novel signal set defined over a signal space that consists of l l spl ges 2 orthogonal planes and a quasi synchronous trellis coded code division multiple access tc cdma system based on it the proposed scheme makes efficient use of the available processing gain to improve power and or bandwidth efficiency for practical multiuser interference environments having a multiplanar signal constellation structure the proposed scheme provides several options for a given required data rate which makes it better adapted to dynamic channel conditions analytical bounds and simulation results indicate that at practical error rates and 2 b s hz the proposed scheme is approximately 1 2 db better than a tc cdma system based on 8 psk and 3 db better at 3 b s hz compared to tc cdma using 16 qam additionally the proposed system is approximately 1 db better than a multicoded system using two signature sequences per user

trellis coded direct sequence spread spectrum communications this paper considers the application of trellis coding techniques to direct sequence spread spectrum multiple access ds ssma communication the unique feature of the trellis codes considered is that they are constructed over the set of possible signature sequences rather than over some standard 2 d signal constellation the resulting codes have a small number of signals per dimension we present several examples of these trellis codes and suggest possible methods of implementation we also present a detailed error analysis for this system which employs techniques developed by lehnert and pursley 1987 1989 to accurately model the multiple access interference we generate numerical results for several examples and conclude that the proposed trellis coded systems yield significant performance improvements over binary antipodal ds ssma systems in addition the new trellis codes perform better than standard error control techniques with the same complexity and code rate analytic results are verified with simulations

extracting topological features from dynamical measures in networks of kuramoto oscillators the kuramoto model for an ensemble of coupled oscillators provides a paradigmatic example of nonequilibrium transitions between an incoherent and a synchronized state here we analyze populations of almost identical oscillators in arbitrary interaction networks our aim is to extract topological features of the connectivity pattern from purely dynamical measures based on the fact that in a heterogeneous network the global dynamics is not only affected by the distribution of the natural frequencies but also by the location of the different values in order to perform a quantitative study we focused on a very simple frequency distribution considering that all the frequencies are equal but one that of the pacemaker node we then analyze the dynamical behavior of the system at the transition point and slightly above it as well as very far from the critical point when it is in a highly incoherent state the gathered topological information ranges from local features such as the single node connectivity to the hierarchical structure of functional clusters and even to the entire adjacency matrix

nilpotent maximal subgroups of gln d abstract in s akbari j algebra 217 1999 422 433 it has been conjectured that if d is a noncommutative division ring then d contains no nilpotent maximal subgroup in connection with this conjecture we show that if gln d contains a nilpotent maximal subgroup say m then m is abelian provided d is infinite this extends one of the main results appeared in s akbari j algebra 259 2003 201 225 theorem 4

on signal detection in the presence of weakly correlated noise over fading channels in cognitive radio networks in order to avoid interference form secondary users to the primary license holders of the spectrum reliable spectrum sensing is necessary in scenarios where the noise samples are correlated the spectrum sensing methods optimized considering impairment by independent noise samples will not provide optimum performances to address this issue a locally optimum detection method for random signals under a weakly correlated noise model over fading channels is proposed the probabilities of false alarm and detection of the proposed detector in the low signal to noise ratio regime are analyzed the average probabilities are calculated over different channel gains numerical and simulation results demonstrate the superiority of the proposed method over the known energy detection method with comparable complexities furthermore we consider the scenario where the estimated correlation is different from the real correlation and investigate the effect of this correlation mismatch on the probabilities of false alarm and detection of the proposed method

locally optimal detection in multivariate non gaussian noise the detection of a vanishingly small known signal in multi variate noise is considered efficacy is used as a criterion of detector performance and the locally optimal detector lod for multivariate noise is derived it is shown that this is a generalization of the well known lod for independent identically distributed i i d noise several characterizations of multivariate noise are used as examples these include specific examples and some general methods of density generation in particular the class of multivariate densities generated by a zero memory nonlinear transformation of a correlated gaussian source is discussed in some detail the detector structure is derived and practical aspects of obtaining detector subsystems are considered through the use of monte carlo simulations the performance of this system if compared to that of the matched filter and of the i i d lod finally the class of multivariate densities generated by a linear transformation of an i i d noise source is described and its lod is shown to be a form frequently suggested to deal with multivariate non gaussian noise a linear filter followed by a memoryless nonlinearity and a correlator

maximal subgroups of gln d abstract in this paper we study the structure of locally solvable solvable locally nilpotent and nilpotent maximal subgroups of skew linear groups in s akbari et al j algebra 217 1999 422 433 it has been conjectured that if d is a division ring and m a nilpotent maximal subgroup of d then d is commutative in connection with this conjecture we show that if f m f contains an algebraic element over f then m is an abelian group also we show that c c j is a solvable maximal subgroup of real quaternions and so give a counterexample to conjecture 3 of s akbari et al j algebra 217 1999 422 433 which states that if d is a division ring and m a solvable maximal subgroup of d then d is commutative also we completely determine the structure of division rings with a non abelian algebraic locally solvable maximal subgroup which gives a full solution to both cases given in theorem 8 of s akbari et al j algebra 217 1999 422 433 ultimately we extend our results to the general skew linear groups

random graphs with arbitrary degree distributions and their applications recent work on the structure of social networks and the internet has focused attention on graphs with distributions of vertex degree that are significantly different from the poisson degree distributions that have been widely studied in the past in this paper we develop in detail the theory of random graphs with arbitrary degree distributions in addition to simple undirected unipartite graphs we examine the properties of directed and bipartite graphs among other results we derive exact expressions for the position of the phase transition at which a giant component first forms the mean component size the size of the giant component if there is one the mean number of vertices a certain distance away from a randomly chosen vertex and the average vertex vertex distance within a graph we apply our theory to some real world graphs including the worldwide web and collaboration graphs of scientists and fortune 1000 company directors we demonstrate that in some cases random graphs with appropriate distributions of vertex degree predict with surprising accuracy the behavior of the real world while in others there is a measurable discrepancy between theory and reality perhaps indicating the presence of additional social structure in the network that is not captured by the random graph

localization of eigenvector centrality in networks with a cut vertex we show that eigenvector centrality exhibits localization phenomena on networks that can be easily partitioned by the removal of a vertex cut set the most extreme example being networks with a cut vertex three distinct types of localization are identified in these structures one is related to the well established hub node localization phenomenon and the other two are introduced and characterized here we gain insights into these problems by deriving the relationship between eigenvector centrality and katz centrality this leads to an interpretation of the principal eigenvector as an approximation to more robust centrality measures which exist in the full span of an eigenbasis of the adjacency matrix

on the robust estimation of the autocorrelation coefficients of stationary sequences this paper discusses methods for the estimation of the autocorrelation coefficients of a finite dependent stationary random sequence three estimators are examined the sample average and two proposed approaches namely the pseudo maximum likelihood pseudo ml estimator and the pseudo m estimator the latter scheme is found as a solution of a fredholm integral equation all three estimators are first studied for specific distribution models then the existence of a minimax robust design is proved and a suboptimally robust scheme is proposed simulation results illustrate the theoretical foundations of the methods and indicate that the pseudo m estimator achieves significantly better performance than the other two schemes when tested against dependent data and in the presence of outliers finally the results may also be applied to the estimation of a location parameter of a dependent random sequence

modularity and extreme edges of the internet we study the spectral properties of a diffusion process taking place on the internet network focusing on the slowest decaying modes these modes identify an underlying modular structure roughly corresponding to individual countries for instance in the slowest decaying mode the diffusion current flows from russia to u s military sites quantitatively the modular structure manifests itself in a 10 times larger participation ratio of its slow decaying modes compared to a random scale free network we propose to use the fraction of nodes participating in slow decaying modes as a general measure of the modularity of a network for the 100 slowest decaying modes of the internet this fraction is 30 finally we suggest that the degree of isolation of an individual module can be assessed by comparing its participation in different diffusion modes

signal detection in the presence of weakly dependent noise i optimum detection the problem of designing robust systems for detecting constant signals in the presence of weakly dependent noise with uncertain statistics is considered as in part i of this study which treated optimum detection in weakly dependent noise a moving average representation is used to model the dependence structure of the noise process with the degree of dependence being parameterized by the averaging weights weak dependence is then modeled as the situation in which quantities depending to second or higher order on the averaging weights can be considered to be negligible uncertainty in the noise statistics is introduced within this framework by allowing a general type of uncertainty in the univariate statistics of the independent sequence that drives the moving average to find robust detectors for signals in this type of weakly dependent noise environment related results concerning robust location estimation in an analogous dependent situation are applied to modify a robust detection system for the corresponding independent noise case it is argued here that a robust detector for this dependent noise model is characterized by a least favorable noise distribution which coincides with the distribution that is least favorable for the corresponding independent noise case however the resulting detector design for dependent noise differs from that for independent noise in particular the robust detector for dependent noise is based on a linearly corrected version of the influence curve that defines the independent noise robust detector the worst case performance of the proposed robust detector relative to that of the independent noise robust detector is also analyzed with the conclusion that the performance of the proposed technique is better to first order in the averaging weights in this respect a modification of this robust detector is also proposed which eliminates some practical disadvantages of this system while retaining equivalent performance to first order the specific situation of contaminated gaussian noise is treated in order to illustrate the analysis

tits alternative for maximal subgroups of gln d let d be a noncommutative division algebra of finite dimension over its centre f g iven a maximal subgroup m of gln d with n 1 it is proved that either m contains a noncyclic free subgroup or there exists a finite family ki r of fields properly containing f with k i m for all 1 i r such that m a is finite if char f 0a ndm a is locally finite if char f p 0 where a k k r

on the exponential generating function for non backtracking walks we derive an explicit formula for the exponential generating function associated with non backtracking walks around a graph we study both undirected and directed graphs our results allow us to derive computable expressions for non backtracking versions of network centrality measures based on the matrix exponential we find that eliminating backtracking walks in this context does not significantly increase the computational expense we show how the new measures may be interpreted in terms of standard exponential centrality computation on a certain multilayer network insights from this block matrix interpretation also allow us to characterize centrality measures arising from general matrix functions rigorous analysis on the star graph illustrates the effect of non backtracking and shows that unwanted localization effects can be eliminated when we restrict to non backtracking walks we also investigate the localization issue on synthetic networks

on maximal subgroups of the multiplicative group of a division algebra abstract the question of existence of a maximal subgroup in the multiplicative group d of a division algebra d finite dimensional over its center f is investigated we prove that if d has no maximal subgroup then deg d is not a power of 2 f 2 is divisible and for each odd prime p dividing deg d there exist noncyclic division algebras of degree p over f

localization and centrality in networks eigenvector centrality is a common measure of the importance of nodes in a network here we show that under common conditions the eigenvector centrality displays a localization transition that causes most of the weight of the centrality to concentrate on a small number of nodes in the network in this regime the measure is no longer useful for distinguishing among the remaining nodes and its efficacy as a network metric is impaired as a remedy we propose an alternative centrality measure based on the nonbacktracking matrix which gives results closely similar to the standard eigenvector centrality in dense networks where the latter is well behaved but avoids localization and gives useful results in regimes where the standard centrality fails

optimum detection of a weak signal with minimal knowledge of dependency the optimum nonlinearity is defined for detection of a weak signal when minimal knowledge of the dependency structure of the observations is available specifically it is assumed that the observations form a one dependent strictly stationary sequence of random variables and that only a finite number of moments of the marginal density and the correlation coefficient between consecutive observations are known it is assumed that the bivariate densities involved can be represented as diagonal series using orthonormal polynomials using efficacy as a performance measure the optimum nonlinearity is required to satisfy a saddle point condition over this class of bivariate densities

optimal synchronization of kuramoto oscillators a dimensional reduction approach a recently proposed dimensional reduction approach for studying synchronization in the kuramoto model is employed to build optimal network topologies to favor or to suppress synchronization the approach is based in the introduction of a collective coordinate for the time evolution of the phase locked oscillators in the spirit of the ott antonsen ansatz we show that the optimal synchronization of a kuramoto network demands the maximization of the quadratic function t l where stands for the vector of the natural frequencies of the oscillators and l for the network laplacian matrix many recently obtained numerical results can be reobtained analytically and in a simpler way from our maximization condition a computationally efficient hill climb rewiring algorithm is proposed to generate networks with optimal synchronization properties our approach can be easily adapted to the case of the kuramoto models with both attractive and repulsive interactions and again many recent numerical results can be rederived in a simpler and clearer analytical manner

stability in linear detection the stability of linear detectors for signals nominally known except for amplitude in correlated nominally gaussian noise is considered stability is defined in terms of bounds on the distribution of the test statistic as the true probability measure on the observation space varies in a prokhorov neighborhood of the nominal the derived stability index is independent of the neighborhood size an optimization problem is formulated and solved to give the most stable linear detector meeting a constraint on the nominal level of detectability