a data bearing approach for pilot embedding frameworks in space time coded mimo systems space time st coded mimo systems employing coherent detectors crucially require channel state information this paper presents a novel pilot embedding framework for channel estimation and data detection by exploiting the null space property and the orthogonality property of the data bearer and pilot matrices the st data matrix is firstly projected onto the data bearer matrix which is a null space of the pilot matrix and the resulting matrix and the pilot matrix are combined for transmitting the data and pilot extractions are achieved independently through linear transformations by exploiting the null space property the unconstrained maximum likelihood ml and linear minimum mean squared error lmmse estimators are explored for channel estimation then the ml approach for data detection is developed by exploiting the orthogonality property the mean squared error mse of channel estimation cramer rao lower bound crlb and the chernoff s bound of a pair wise error probability for st codes are analyzed for examining the performance of the proposed scheme the optimum power allocation scheme for data and pilot parts is also considered three data bearer and pilot structures including time multiplexing tm based st block code stbc based and code multiplexing cm based are proposed simulation results show that the cm based structure provides superior performance for nonquasi static flat rayleigh fading channels while these three structures yield similar performances for quasi static flat rayleigh fading channels

the milne and kramers problems for the boltzmann equation of a hard sphere gas existence uniqueness and properties of asymptotic behavior are proved for solutions of the milne and kramers problems for the linearized boltzmann equation for a gas of hard spheres the proof uses energy like estimates and follows the analysis of bardos santos and sentis for the equations of neutron transport

milne problem for the linear and linearized boltzmann equations relevant to a binary gas mixture abstract a stationary boundary value problem for the boltzmann equation in a half space is considered for a binary mixture of gases when the indata on the boundary are given for the both species under the assumption that one of the species is dominant and close to equilibrium but the density of the other is small the problem is decomposed into two half space problems the so called milne problem for the linearized boltzmann equation with a source term for the dominant species and that for the linear boltzmann equation for the low density species the two problems are coupled in such a way that the source term in the former is specified by the solution of the latter the existence and uniqueness of the solutions to the two problems are proved and their accurate asymptotic behavior in the far field is obtained in particular the precise rate of approach of the solution to the state at infinity is expressed in terms of the decay rate in the molecular velocity of the boundary data for both species

optimal training sequences for large scale mimo ofdm systems this paper considers the optimal design of training sequences for channel estimation in large scale multiple input multiple output orthogonal frequency division multiplexing systems the application scenario of interest is when the number of transmit antennas for the downlink or the number of receive antennas for the uplink is large but not large enough to benefit the asymptotical optimality of using equipower training sequences e g due to practical constraints on deployment costs space and antenna size under the criterion of minimizing the mean square error of the channel estimate the optimal design of training sequences for such systems poses a truly large scale optimization problem to which existing optimization solvers are not applicable we develop a fast convex programming fcp procedure to find its global optimal solution in each iteration of the proposed fcp procedure a solution is found in a scalable and closed form the singularity and ill conditionedness of the channel correlation matrices are also exploited to improve the computation efficiency furthermore we also examine the design of reduced length training sequences and develop a successive quadratic programming procedure to find the solutions intensive simulation results are provided to illustrate the performance of our methods

estimation for the linear model with uncertain covariance matrices we derive a maximum a posteriori estimator for the linear observation model where the signal and noise covariance matrices are both uncertain the uncertainties are treated probabilistically by modeling the covariance matrices with prior inverse wishart distributions the nonconvex problem of jointly estimating the signal of interest and the covariance matrices is tackled by a computationally efficient fixed point iteration as well as an approximate variational bayes solution the statistical performance of estimators is compared numerically to state of the art estimators from the literature and shown to perform favorably

transmit signal design for optimal estimation of correlated mimo channels we address optimal estimation of correlated multiple input multiple output mimo channels using pilot signals assuming knowledge of the second order channel statistics at the transmitter assuming a block fading channel model and minimum mean square error mmse estimation at the receiver we design the transmitted signal to optimize two criteria mmse and the conditional mutual information between the mimo channel and the received signal our analysis is based on the recently proposed virtual channel representation which corresponds to beamforming in fixed virtual directions and exposes the structure and the true degrees of freedom in the correlated channel however our design framework is applicable to more general channel models which include known channel models such as the transmit and receive correlated model as special cases we show that optimal signaling is in a block form where the block length depends on the signal to noise ratio snr as well as the channel correlation matrix the block signal corresponds to transmitting beams in successive symbol intervals along fixed virtual transmit angles whose powers are determined by nonidentical water filling solutions based on the optimization criteria our analysis shows that these water filling solutions identify exactly which virtual transmit angles are important for channel estimation in particular at low snr the block length reduces to one and all the power is transmitted on the beam corresponding to the strongest transmit angle whereas at high snr the block length has a maximum length equal to the number of active virtual transmit angles and the power is assigned equally to all active transmit angles consequently from a channel estimation viewpoint a faster fading rate can be tolerated at low snrs relative to higher snrs

a model framework for the enhancement of community detection in complex networks abstract community detection is an important data analysis problem in many different areas and how to enhance the quality of community detection in complicated real applications is still a challenge current community detection enhancement methods often take the enhancement as a preprocess of community detection they mainly focus on how to design the suitable topological similarity of nodes to adjust the original network but did not consider how to make use of this topological similarity more effectively in order to better utilize the similarity information we propose a model framework which integrates the enhancement into the whole community detection procedure first we calculate the structural similarity of nodes based on network topology second we present a stochastic model to describe the community memberships of nodes we then model the strong constraint based on structural similarity i e we make each node have the same community membership distribution with its most similar neighbors and then we model the weak constraint i e if two nodes have a high similarity we will make their community membership distributions close otherwise we will make them not close finally we present a nonnegative matrix factorization approach to learn the model parameters we evaluate our method on both synthetic and real world networks with ground truths and compare it with five comparable methods the experimental results demonstrate the superior performance of our new method over the competing ones for community detection and enhancement

identifying and ranking influential spreaders in complex networks with consideration of spreading probability abstract identifying the influential spreaders in complex network has great theoretical and practical significance in order to evaluate the spreading ability of the nodes some centrality measures are usually computed which include degree centrality dc betweenness centrality bc closeness centrality cc k shell centrality ks and local centrality lc however we observe that the performance of different centrality measures may change when these measures are used in a real network with different spreading probabilities specifically dc performs well for small spreading probabilities and lc is more suitable for larger ones to alleviate the sensitivity of these centrality measures to the spreading probability we modify lc and then integrate it with dc by considering the spreading probability we call the proposed measure hybrid degree centrality hc hc can take the advantages of dc or lc depending on the given spreading probability we use sir model to evaluate the performance of hc in both real networks and artificial networks experimental results show that hc performs robustly under different spreading probabilities compared with these known centrality measures such as dc lc bc cc and ks hc can evaluate the spreading ability of the nodes more accurately on most range of spreading probabilities furthermore we show that our method can better distinguish the spreading ability of nodes

an efficient community detection algorithm using greedy surprise maximization community detection is an important and crucial problem in complex network analysis although classical modularity function optimization approaches are widely used for identifying communities the modularity function q suffers from its resolution limit recently the surprise function s was experimentally proved to be better than the q function however up until now there has been no algorithm available to perform searches to directly determine the maximal surprise values in this paper considering the superiority of the s function over the q function we propose an efficient community detection algorithm called agso algorithm based on greedy surprise optimization and its improved version fagso fast agso which are based on greedy surprise optimization and do not suffer from the resolution limit in addition f agso does not need the number of communities k to be specified in advance tests on experimental networks show that f agso is able to detect optimal partitions in both simple and even more complex networks moreover algorithms based on surprise maximization perform better than those algorithms based on modularity maximization including blondel guillaume lambiotte lefebvre bgll clauset newman moore cnm and the other state of the art algorithms such as infomap order statistics local optimization method oslom and label propagation algorithm lpa

exponential random graph models for networks with community structure although the community structure organization is an important characteristic of real world networks most of the traditional network models fail to reproduce the feature therefore the models are useless as benchmark graphs for testing community detection algorithms they are also inadequate to predict various properties of real networks with this paper we intend to fill the gap we develop an exponential random graph approach to networks with community structure to this end we mainly built upon the idea of blockmodels we consider both the classical blockmodel and its degree corrected counterpart and study many of their properties analytically we show that in the degree corrected blockmodel node degrees display an interesting scaling property which is reminiscent of what is observed in real world fractal networks a short description of monte carlo simulations of the models is also given in the hope of being useful to others working in the field

knudsen layer for gas mixtures the knudsen layer in rarefied gas dynamics is essentially described by a half space boundary value problem of the linearized boltzmann equation in which the incoming data are specified on the boundary and the solution is assumed to be bounded at infinity milne problem this problem is considered for a binary mixture of hard sphere gases and the existence and uniqueness of the solution as well as some asymptotic properties are proved the proof is an extension of that of the corresponding theorem for a single component gas given by bardos caflisch and nicolaenko comm pure appl math 39 323 1986 some estimates on the convergence of the solution in a finite slab to the solution of the milne problem are also obtained

modularity functions maximization with nonnegative relaxation facilitates community detection in networks abstract we show here that the problem of maximizing a family of quantitative functions encompassing both the modularity q measure and modularity density d measure for community detection can be uniformly understood as a combinatoric optimization involving the trace of a matrix called modularity laplacian instead of using traditional spectral relaxation we apply additional nonnegative constraint into this graph clustering problem and design efficient algorithms to optimize the new objective with the explicit nonnegative constraint our solutions are very close to the ideal community indicator matrix and can directly assign nodes into communities the near orthogonal columns of the solution can be reformulated as the posterior probability of corresponding node belonging to each community therefore the proposed method can be exploited to identify the fuzzy or overlapping communities and thus facilitates the understanding of the intrinsic structure of networks experimental results show that our new algorithm consistently sometimes significantly outperforms the traditional spectral relaxation approaches

design of par constrained sequences for mimo channel estimation via majorization minimization communication systems and radars widely employ sequences of low peak to average power ratio par or unimodulus to meet the hardware constraints and maximize the power efficiency numerous works have probed the unimodular sequence design especially attempting to obtain good correlation properties regarding channel estimation however sequences of such properties do not necessarily qualify for the mission and tailored unimodular sequences for the specific criterion concerned are more desirable when we have access to the prior knowledge of the channel impulse response in this paper we formulate the problem of unimodular sequence design by optimizing minimum mean square error and conditional mutual information respectively the problems turn out nonconvex and we develop efficient algorithms based on the majorization minimization framework with convergence guaranteed more general we also examine optimal sequence design with low par constraints numerical examples demonstrate the improved results of mean square error signal to noise ratio and conditional mutual information by using our proposed training sequences with the efficiency of the derived algorithms illustrated

ranking the spreading ability of nodes in complex networks based on local structure abstract ranking nodes by their spreading ability in complex networks is a fundamental problem which relates to wide applications local metric like degree centrality is simple but less effective global metrics such as betweenness and closeness centrality perform well in ranking nodes but are of high computational complexity recently to rank nodes effectively and efficiently a semi local centrality measure has been proposed as a tradeoff between local and global metrics however in semi local centrality only the number of the nearest and the next nearest neighbors of a node is taken into account while the topological connections among the neighbors are neglected in this paper we propose a local structural centrality measure which considers both the number and the topological connections of the neighbors of a node to evaluate the performance of our method we use the susceptible infected recovered sir model to simulate the epidemic spreading process on both artificial and real networks by measuring the rank correlation between the ranked list generated by simulation results and the ones generated by centrality measures we show that our method can rank the spreading ability of nodes more accurately than centrality measures such as degree k shell betweenness closeness and local centrality further we show that our method can better distinguish the spreading ability of nodes

detecting communities in clustered networks based on group action on set abstract in this paper we propose a well targeted algorithm gas algorithm for detecting communities in high clustered networks by presenting group action technology on community division during the processing of this algorithm the underlying community structure of a clustered network emerges simultaneously as the corresponding partition of orbits by the permutation groups acting on the node set are achieved as the derivation of the orbit partition an algebraic structure r cycle can be considered as the origin of the community to be a priori estimation for the community structure of the algorithm the community separability is introduced to indicate whether a network has distinct community structure by executing the algorithm on several typical networks and the lfr benchmark it shows that this gas algorithm can detect communities accurately and effectively in high clustered networks furthermore we compare the gas algorithm and the clique percolation algorithm on the lfr benchmark it is shown that the gas algorithm is more accurate at detecting non overlapping communities in clustered networks it is suggested that algebraic techniques can uncover fresh light on detecting communities in complex networks

community detection in networks based on minimum spanning tree and modularity abstract in this paper we propose a novel splitting and merging method for community detection in which a minimum spanning tree mst of dissimilarity between nodes in graph is employed in the splitting process edges with high dissimilarity in the mst are removed to construct small disconnected subgroups of nodes from the same community in the merging process subgroup pairs are iteratively merged to identify the final community structure maximizing the modularity the proposed method requires no parameter we provide a general framework for implementing such a method experimental results obtained by applying the method on computer generated networks and different real world networks show the effectiveness of the proposed method

design and analysis of mmse pilot aided cyclic prefixed block transmissions for doubly selective channels this paper considers affine cyclic prefixed block based pilot aided transmission pat over the single antenna doubly selective channel where the channel is assumed to obey a complex exponential basis expansion model first a tight lower bound on the mean squared error mse of pilot aided channel estimates is derived along with necessary and sufficient conditions on the pilot data pattern that achieves this bound from these conditions novel minimum mse mmse pat schemes are proposed and upper lower bounds on their ergodic achievable rates are derived a pilot data power allocation technique is also developed a high snr asymptotic analysis of the ergodic achievable rate of affine mmse pat is then performed which suggests that the channel s spreading parameters should be taken into account when choosing among affine mmse pat schemes specifically we establish that multicarrier mmse pat achieves higher rates than single carrier mmse pat when the channel s delay spread dominates its doppler spread and vice versa

community detection by fuzzy clustering abstract how to measure the similarity between nodes is of great importance for fuzzy clustering when we use the approach to uncover communities in complex networks in this paper we first measure the similarity between nodes in a network based on edge centralities and model the network as a fuzzy relation then two fuzzy transitive rules rule i and rule ii are applied on the relation respectively by which the similarity information can be transferred from one node to another in the network until the relation reaches a stable state by choosing different thresholds our method finally can partition the network into several non overlapping subgroups we compare our method with some state of the art methods on the lfr benchmark and real world networks we find that our method based on rule i can correctly identify communities when the similarity between nodes of same groups is greater than that of different groups while it is just opposite to rule ii our method achieves better results than the state of the art methods when the pre planted communities of the random networks are vaguer

constellation design for the noncoherent mimo rayleigh fading channel at general snr constellation design for the noncoherent multiple input multiple output mimo block rayleigh fading channel is considered for general signal to noise ratios snrs starting from a given base unitary constellation of finite cardinality and using the cutoff rate expression as the design criterion input probabilities and per antenna amplitudes for the constellation points are obtained via a difference of convex programming formulation using the mutual information as a performance metric it is shown that the optimized constellations significantly outperform the base unitary designs from which they are obtained in the low medium snr regime and indeed they also similarly outperform the mutual information achieved by isotropically distributed unitary inputs for the continuous input channel i e the so called unitary space time capacity ustc at sufficiently high snrs the resulting mutual information coincides with that of the base unitary designs thus the optimum constellation design technique works over the entire range of snrs the bit energy spectral efficiency tradeoff of the optimized constellations are also obtained and these provide valuable insights on modulation and coding which are especially useful for wideband channels where the snr per degree of freedom is low

a deep stochastic model for detecting community in complex networks discovering community structures is an important step to understanding the structure and dynamics of real world networks in social science biology and technology in this paper we develop a deep stochastic model based on non negative matrix factorization to identify communities in which there are two sets of parameters one is the community membership matrix of which the elements in a row correspond to the probabilities of the given node belongs to each of the given number of communities in our model another is the community community connection matrix of which the element in the i th row and j th column represents the probability of there being an edge between a randomly chosen node from the i th community and a randomly chosen node from the j th community the parameters can be evaluated by an efficient updating rule and its convergence can be guaranteed the community community connection matrix in our model is more precise than the community community connection matrix in traditional non negative matrix factorization methods furthermore the method called symmetric nonnegative matrix factorization is a special case of our model finally based on the experiments on both synthetic and real world networks data it can be demonstrated that our algorithm is highly effective in detecting communities

benchmark graphs for testing community detection algorithms community structure is one of the most important features of real networks and reveals the internal organization of the nodes many algorithms have been proposed but the crucial issue of testing i e the question of how good an algorithm is with respect to others is still open standard tests include the analysis of simple artificial graphs with a built in community structure that the algorithm has to recover however the special graphs adopted in actual tests have a structure that does not reflect the real properties of nodes and communities found in real networks here we introduce a class of benchmark graphs that account for the heterogeneity in the distributions of node degrees and of community sizes we use this benchmark to test two popular methods of community detection modularity optimization and potts model clustering the results show that the benchmark poses a much more severe test to algorithms than standard benchmarks revealing limits that may not be apparent at a first analysis

detection of community overlap according to belief propagation and conflict abstract most existing methods for detection of community overlap cannot balance efficiency and accuracy for large and densely overlapping networks to quickly identify overlapping communities for such networks we propose a new method that uses belief propagation and conflict pcb to occupy communities we first identify triangles with maximal clustering coefficients as seed nodes and sow a new type of belief to the seed nodes then the beliefs explore their territory by occupying nodes with high assent ability the beliefs propagate their strength along the graph to consolidate their territory and conflict with each other when they encounter the same node simultaneously finally the node membership is judged from the belief vectors the pcb time complexity is nearly linear and its space complexity is linear the algorithm was tested in extensive experiments on three real world social networks and three computer generated artificial graphs the experimental results show that pcb is very fast and highly reliable tests on real and artificial networks give excellent results compared with three newly proposed overlapping community detection algorithms

the linear model under mixed gaussian inputs designing the transfer matrix suppose a linear model y hx n where inputs x n are independent gaussian mixtures the problem is to design the transfer matrix h so as to minimize the mean square error mse when estimating x from y this problem has important applications but faces at least three hurdles firstly even for a fixed h the minimum mse mmse has no analytical form secondly the mmse is generally not convex in h thirdly derivatives of the mmse w r t h are hard to obtain this paper casts the problem as a stochastic program and invokes gradient methods the study is motivated by two applications in signal processing one concerns the choice of error reducing precoders the other deals with selection of pilot matrices for channel estimation in either setting our numerical results indicate improved estimation accuracy markedly better than those obtained by optimal design based on standard linear estimators some implications of the non convexities of the mmse are noteworthy yet to our knowledge not well known for example there are cases in which more pilot power is detrimental for channel estimation this paper explains why

inferring overlapping community structure with degree corrected block model abstract recent research has shown great interest in statistical inference methods for community detection not only in models and algorithms but also in the detectability in this paper we propose a fast community detection algorithm based on the degree corrected block model by introducing a parameter to select the candidate solutions our algorithm is able to detect overlapping communities experiments on a range of networks have achieved state of the art results moreover we show that the algorithm based on the degree corrected block model also suffers the detectability limitation which is in accord with the most recent research on the detectability threshold

a parameter free community detection method based on centrality and dispersion of nodes in complex networks abstract k means is a simple and efficient clustering algorithm to detect communities in networks however it may suffer from a bad choice of initial seeds also called centers that seriously affect the clustering accuracy and the convergence rate additionally in k means the number of communities should be specified in advance till now it is still an open problem on how to select initial seeds and how to determine the number of communities in this study a new parameter free community detection method named k rank d was proposed first based on the fact that good initial seeds usually have high importance and are dispersedly located in a network we proposed a modified pagerank centrality to evaluate the importance of a node and drew a decision graph to depict the importance and the dispersion of nodes then the initial seeds and the number of communities were selected from the decision graph actively and intuitively as the start parameter of k means experimental results on synthetic and real world networks demonstrate the superior performance of our approach over competing methods for community detection

adaptive multi resolution modularity for detecting communities in networks abstract community structure is a common topological property of complex networks which attracted much attention from various fields optimizing quality functions for community structures is a kind of popular strategy for community detection such as modularity optimization here we introduce a general definition of modularity by which several classical multi resolution modularity can be derived and then propose a kind of adaptive multi resolution modularity that can combine the advantages of different modularity by applying the modularity to various synthetic and real world networks we study the behaviors of the methods showing the validity and advantages of the multi resolution modularity in community detection the adaptive modularity as a kind of multi resolution method can naturally solve the first type limit of modularity and detect communities at different scales it can quicken the disconnecting of communities and delay the breakup of communities in heterogeneous networks and thus it is expected to generate the stable community structures in networks more effectively and have stronger tolerance against the second type limit of modularity

discrete velocity models for mixtures without nonphysical collision invariants an important aspect of constructing discrete velocity models dvms for the boltzmann equation is to obtain the right number of collision invariants it is a well known fact that dvms can also have extra collision invariants so called spurious collision invariants in plus to the physical ones a dvm with only physical collision invariants and so without spurious ones is called normal for binary mixtures also the concept of supernormal dvms was introduced meaning that in addition to the dvm being normal the restriction of the dvm to any single species also is normal here we introduce generalizations of this concept to dvms for multicomponent mixtures we also present some general algorithms for constructing such models and give some concrete examples of such constructions one of our main results is that for any given number of species and any given rational mass ratios we can construct a supernormal dvm the dvms are constructed in such a way that for half space problems as the milne and kramers problems but also nonlinear ones we obtain similar structures as for the classical discrete boltzmann equation for one species and therefore we can apply obtained results for the classical boltzmann equation

community structure and scale free collections of erdős renyi graphs community structure plays a significant role in the analysis of social networks and similar graphs yet this structure is little understood and not well captured by most models we formally define a community to be a subgraph that is internally highly connected and has no deeper substructure we use tools of combinatorics to show that any such community must contain a dense erd ifmmode mbox h o else h o fi s r enyi er subgraph based on mathematical arguments we hypothesize that any graph with a heavy tailed degree distribution and community structure must contain a scale free collection of dense er subgraphs these theoretical observations corroborate well with empirical evidence from this we propose the block two level erd ifmmode mbox h o else h o fi s r enyi bter model and demonstrate that it accurately captures the observable properties of many real world social networks

weighting links based on edge centrality for community detection abstract link weights have the equally important position as links in complex networks and they are closely associated with each other for the emergence of communities how to assign link weights to make a clear distinction between internal links of communities and external links connecting communities is of vital importance for community detection edge centralities provide a powerful approach for distinguishing internal links from external ones here we first use edge centralities such as betweenness information centrality and edge clustering coefficient to weight links of networks respectively to transform unweighted networks into weighted ones and then a weighted function that both considers links and link weights is adopted on the weighted networks for community detection we evaluate the performance of our approach on random networks as well as real world networks better results are achieved on weighted networks with stronger weights of internal links of communities and the results on unweighted networks outperform that of weighted networks with weaker weights of internal links of communities the availability of our findings is also well supported by the study of granovetter that the weak links maintain the global integrity of the network while the strong links maintain the communities especially in the karate club network all the nodes are correctly classified when we weight links by edge betweenness the results also give us a more comprehensive understanding on the correlation between links and link weights for community detection

two stage beamformer design for massive mimo downlink by trace quotient formulation in this paper the problem of outer beamformer design based only on channel statistic information is considered for two stage beamforming for multi user massive mimo downlink and the problem is approached based on signal to leakage plus noise ratio slnr to eliminate the dependence on the instantaneous channel state information a lower bound on the average slnr is derived by assuming zero forcing zf inner beamforming and an outer beamformer design method that maximizes the lower bound on the average slnr is proposed it is shown that the proposed slnr based outer beamformer design problem reduces to a trace quotient problem tqp which is often encountered in the field of machine learning an iterative algorithm is presented to obtain an optimal solution to the proposed tqp the proposed method has the capability of optimally controlling the weighting factor between the signal power to the desired user and the interference leakage power to undesired users according to different channel statistics numerical results show that the proposed outer beamformer design method yields significant performance gain over existing methods

training sequence optimization in mimo systems with colored interference we address the problems of channel estimation and optimal training sequence design for multiple input multiple output systems over flat fading channels in the presence of colored interference in practice knowledge of the unknown channel is often obtained by sending known training symbols to the receiver during the training period we obtain the best linear unbiased estimates of the channel parameters based on the received training block we determine the optimal training sequence set that minimizes the mean square error of the channel estimator under a total transmit power constraint in order to obtain the advantage of the optimal training sequence design long term statistics of the interference correlation are needed at the transmitter hence this information needs to be estimated at the receiver and fed back to the transmitter obviously it is desirable that only a minimal amount of information needs to be fed back from the receiver to gain the advantage in reducing the estimation error of the short term channel fading parameters we develop such a feedback strategy in this paper

personalized pagerank clustering a graph clustering algorithm based on random walks abstract graph clustering has been an essential part in many methods and thus its accuracy has a significant effect on many applications in addition exponential growth of real world graphs such as social networks biological networks and electrical circuits demands clustering algorithms with nearly linear time and space complexity in this paper we propose personalized pagerank clustering ppc that employs the inherent cluster exploratory property of random walks to reveal the clusters of a given graph we combine random walks and modularity to precisely and efficiently reveal the clusters of a graph ppc is a top down algorithm so it can reveal inherent clusters of a graph more accurately than other nearly linear approaches that are mainly bottom up it also gives a hierarchy of clusters that is useful in many applications ppc has a linear time and space complexity and has been superior to most of the available clustering algorithms on many datasets furthermore its top down approach makes it a flexible solution for clustering problems with different requirements

i o efficient calculation of h group closeness centrality over disk resident graphs we introduce h group closeness centrality in this work h group closeness centrality of a group of nodes measures how close this node group is to other nodes in a graph and can be used in numerous applications such as measuring the importance and influence of a group of users in a social network when a large graph contains billions of edges that cannot reside entirely in a computers main memory computing and maximizing h group closeness centrality both become challenging in this work we present a systematic solution for efficiently computing and maximizing h group closeness centrality in large disk resident graphs only using a common pc our solution leverages a probabilistic counting method to efficiently estimate h group closeness with high accuracy rather than exhaustively computing it in an exact fashion furthermore we design an i o efficient greedy algorithm to find a node group that approximately maximizes h group closeness centrality in a graph our algorithm exploits several appealing properties of the defined h group closeness measure to reduce the computational cost of handling a disk resident graph extensive evaluation on large real world and synthetic graphs demonstrates the efficiency of our proposed method for example our proposed i o efficient greedy algorithm is about 300 times faster than a simple multi pass method on the twitter graph with 1 4 billion edges this reduces the running time of identifying one group member from nearly an hour to less than 20s on average

optimal time decay of the boltzmann system for gas mixtures abstract in this paper we are concerned with the boltzmann equation for the mixture of vapors of two gases in the whole space given the initial data of one gas near vacuum and the other near a global maxwellian state we obtain the global existence and optimal large time behaviors of the boltzmann system for such binary mixture the proof is based on kawashima s compensating function technique and a refined energy method

on training optimization for estimation of correlated mimo channels in the presence of multiuser interference in this paper the problem of estimating multiple input multiple output mimo channels in a realistic environment involving correlated channel fading and multiuser interference is considered four estimation schemes are studied including the linear minimum mean squared error lmmse least squares ls and gauss markov gm estimators as well as a novel scheme which is derived here as an alternative to lmmse estimation the mse optimal training sequences for each of them are provided and their requirements for side information feedback are assessed the new scheme is shown to exhibit a performance comparable to or even better than lmmse at a significantly lower feedback and computational cost the analytical comparison of the estimation schemes is supported by numerous simulation results that cover a wide range of antenna configurations relative interference power and channel correlation strengths the results of this paper provide a complete picture for a palette of estimation schemes with their relative performance and costs of training

on the amount of downlink training in correlated massive mimo channels in this paper we study the effect of downlink dl training on the achievable sum rate of multiuser massive mimo channels with spatial correlations and derive sufficient conditions of the dl channel estimation error covariance matrices that maintain the full multiplexing gain at high data signal to noise ratios snrs given the derived conditions a simple asymptotic upper bound on the average sum rate loss due to channel estimation is obtained we derive in closed form training sequences of limited duration that satisfy these conditions the training duration is variable and increases with the data snr while the sequences lie in a subspace spanned by a variable number of user spatial covariance matrices eigenvectors we additionally study the problem of sequence codebook design and find solutions to this problem for uniform linear and rectangular arrays using asymptotic results for the aforementioned training structure the designed codebooks are observed numerically to be near optimal for a moderate number of base station antennas due to their ability to identify a sufficient limited number of channel directions to train the proposed solutions can substantially reduce dl training overheads while providing achievable rates that are comparable with the rates achieved with perfect channel state information

discriminative metric learning for multi view graph partitioning we propose discriminative metric learning for multi view graph partitioning we envision the multi view graph as an adaptive dynamic system the intra view connections and the inter view couplings are interplayed extensive experiments have been conducted to show the effectiveness in recent years multi view graph partitioning has attracted more and more attention but most efforts have been made to develop graph partitioning approaches directly in the original topological structure in many real world applications graph may contain noisy links and the distance metric may not be so discriminative for revealing cluster structure this paper addresses the problem of discriminative metric learning for multi view graph partitioning in particular we propose a novel method called multi view dml abbr of multi view discriminative metric learning to transform the metric space in the original graph into a more discriminative metric space in which better graph partitioning results will be obtained we envision the multi view graph as an adaptive dynamic system where both the intra view connections and the inter view couplings are interplayed to gradually update the relation metric among nodes on the one hand the inter view coupling will be influenced by the intra view connection between two nodes on the other hand the inter view coupling will also affect the intra view connection such interplay eventually makes the whole graph reach a steady state which has a stronger cluster structure than the original graph extensive experiments are conducted on both synthetic and real world graphs to confirm that the proposed method is able to learn more discriminative metric

detecting one mode communities in bipartite networks by bipartite clustering triangular abstract in this paper an algorithm is proposed to detect one mode community structures in bipartite networks and to deduce which one mode community structures are weighted after analyzing the topological properties in bipartite networks bipartite clustering triangular is introduced first bipartite networks are projected into two weighted one mode networks by bipartite clustering triangular then all the maximal sub graphs from two one mode weighted networks are extracted and the maximal sub graphs are merged together using a weighted clustering threshold in addition the proposed algorithm successfully finds overlapping vertices between one mode communities experimental results using some real world network data shows that the performance of the proposed algorithm is satisfactory

limits of modularity maximization in community detection modularity maximization is the most popular technique for the detection of community structure in graphs the resolution limit of the method is supposedly solvable with the introduction of modified versions of the measure with tunable resolution parameters we show that multiresolution modularity suffers from two opposite coexisting problems the tendency to merge small subgraphs which dominates when the resolution is low the tendency to split large subgraphs which dominates when the resolution is high in benchmark networks with heterogeneous distributions of cluster sizes the simultaneous elimination of both biases is not possible and multiresolution modularity is not capable to recover the planted community structure not even when it is pronounced and easily detectable by other methods for any value of the resolution parameter this holds for other multiresolution techniques and it is likely to be a general problem of methods based on global optimization

downlink training sequence design for fdd multiuser massive mimo systems we consider the problem of downlink training sequence design for frequency division duplex multiuser massive multiple input multiple output systems in the general case where users have distinct spatial correlations the training sequences leverage spatial correlations and are designed to minimize the channel estimation weighted sum mean square error mse under the assumption that users employ minimum mse estimators noting that the weighted sum mse function is invariant to unitary rotations of its argument a solution is obtained using a steepest descent method on the grassmannian manifold we extend the proposed design to scenarios with temporal correlations combined with kalman filters at the users and design sequences exploiting the multiuser spatio temporal channel structure finally we consider scenarios where only a limited number of bits b are available at the base station bs to inform the users of each chosen sequence e g sequences are chosen from a set of 2 b vectors known to the bs and users and develop a subspace version of matching pursuit techniques to choose the desired sequences simulation results using realistic channel models show that the proposed solutions improve user fairness with a proper choice of weights lead to accurate channel estimates with training durations that can be much smaller than the number of bs antennas and show substantial gains over randomly chosen sequences for even small values of b

fundamentals of statistical signal processing estimation theory minimum variance unbiased estimation cramer rao lower bound linear models general minimum variance unbiased estimation best linear unbiased estimators maximum likelihood estimation least squares method of moments the bayesian philosophy general bayesian estimators linear bayesian estimators kalman filters summary of estimators extension for complex data and parameters

adaptive modularity maximization via edge weighting scheme modularity maximization is one of the state of the art methods for community detection that has gained popularity in the last decade yet it suffers from the resolution limit problem by preferring under certain conditions large communities over small ones to solve this problem we propose to expand the meaning of the edges that are currently used to indicate propensity of nodes for sharing the same community in our approach this is the role of edges with positive weights while edges with negative weights indicate aversion for putting their end nodes into one community we also present a novel regression model which assigns weights to the edges of a graph according to their local topological features to enhance the accuracy of modularity maximization algorithms we construct artificial graphs based on the parameters sampled from a given unweighted network and train the regression model on ground truth communities of these artificial graphs in a supervised fashion the extraction of local topological edge features can be done in linear time making this process efficient experimental results on real and synthetic networks show that the state of the art community detection algorithms improve their performance significantly by finding communities in the weighted graphs produced by our model

a reductive approach to hypergraph clustering an application to image segmentation in the last few years hypergraph based methods have gained considerable attention in the resolution of real world clustering problems since such a mode of representation can handle higher order relationships between elements compared to the standard graph theory the most popular and promising approach to hypergraph clustering arises from concepts in spectral hypergraph theory 53 and clustering is configured as a hypergraph cut problem where an appropriate objective function has to be optimized the spectral relaxation of this optimization problem allows to get a clustering that is close to the optimum but this approach generally suffers from its high computational demands especially in real world problems where the size of the data involved in their resolution becomes too large a natural way to overcome this limitation is to operate a reduction of the hypergraph where spectral clustering should be applied over a hypergraph of smaller size in this paper we introduce two novel hypergraph reduction algorithms that are able to maintain the hypergraph structure as accurate as possible these algorithms allowed us to design a new approach devoted to hypergraph clustering based on the multilevel paradigm that operates in three steps i hypergraph reduction ii initial spectral clustering of the reduced hypergraph and iii clustering refinement the accuracy of our hypergraph clustering framework has been demonstrated by extensive experiments with comparison to other hypergraph clustering algorithms and have been successfully applied to image segmentation for which an appropriate hypergraph based model have been designed the low running times displayed by our algorithm also demonstrates that the latter unlike the standard spectral clustering approach can handle datasets of considerable size

ldpc coded mimo systems with unknown block fading channels soft mimo detector design channel estimation and code optimization this paper considers the design of a practical low density parity check ldpc coded multiple input multiple output mimo system composed of m transmit and n receive antennas operating in a flat fading environment where channel state information csi is assumed to be unavailable both to the transmitter and the receiver a soft iterative receiver structure is developed which consists of three main blocks a soft mimo detector and two ldpc component soft decoders we first propose at the component level several soft input soft output mimo detectors whose performances are much better than the conventional minimal mean square error mmse based detectors in particular one optimal soft mimo detector and two simplified suboptimal detectors are developed that do not require an explicit channel estimate and offer an effective tradeoff between complexity and performance in addition a modified expectation maximization em based mimo detector is developed that completely removes positive feedback between input and output extrinsic information and provides much better performance compared with the direct em based detector that has strong correlations especially in fast fading channels at the structural level the ldpc coded mimo receiver is constructed in an unconventional manner where the soft mimo detector and ldpc variable node decoder form one super soft decoding unit and the ldpc check node decoder forms the other component of the iterative decoding scheme by exploiting the proposed receiver structure tractable extrinsic information transfer functions of the component soft decoders are obtained which further lead to a simple and efficient ldpc code degree profile optimization algorithm with proven global optimality and guaranteed convergence from any initialization finally numerical and simulation results are provided to confirm the advantages of the proposed design approach for the coded mimo system

capacity scaling and spectral efficiency in wide band correlated mimo channels the dramatic linear increase in ergodic capacity with the number of antennas promised by multiple input multiple output mimo wireless communication systems is based on idealized channel models representing a rich scattering environment is such scaling sustainable in realistic scattering scenarios existing physical models although realistic are intractable for addressing this problem analytically due to their complicated nonlinear dependence on propagation path parameters such as the angles of arrival and delays in this paper we leverage a recently introduced virtual representation of physical models that is essentially a fourier series representation of wide band mimo channels in terms of fixed virtual angles and delays motivated by physical considerations we propose a d connected model for correlated channels defined by a virtual spatial channel matrix consisting of d nonvanishing diagonals with independent and identically distributed i i d gaussian entries the parameter d provides a meaningful and tractable measure of the richness of scattering we derive general bounds for the coherent ergodic capacity and investigate capacity scaling with the number of antennas and bandwidth in the large antenna regime we show that linear capacity scaling is possible if d scales linearly with the number of antennas this in turn is possible if the number of resolvable paths grows quadratically with the number of antennas the capacity saturates for linear growth in the number of paths fixed d the ergodic capacity does not depend on frequency selectivity of the channel in the wide band case increasing bandwidth tightens the bounds and hastens the convergence of scaling behavior for large bandwidth the capacity scales linearly with the signal to noise ratio snr as well we also provide an explicit characterization of the wide band slope recently proposed by verdu numerical results are presented to illustrate the key theoretical results

semi supervised community detection based on discrete potential theory abstract in recent studies of the complex network most of the community detection methods only consider the network topological structure without background information this leads to a relatively low accuracy in this paper a novel semi supervised community detection algorithm is proposed based on the discrete potential theory it effectively incorporates individual labels the labels of corresponding communities to guide the community detection process for achieving better accuracy specifically a number of vertices with user defined labels are first identified to act as unit elementary charges which can generate different electrostatic fields then community detection can be translated into a potential transmission problem by formulating the problem using combinational dirichlet labels of those unlabeled vertices can be determined by the labels for which the greatest potential is calculated finally a better community partition can be obtained our extensive numerical experiments in both artificial and real networks lead to two key observations first individual labels play an important role in community detection and second our proposed semi supervised community detection algorithm outperforms existing counterparts in both accuracy and time complexity especially for obscure networks

a classification of well posed kinetic layer problems in the first part of this paper we study the half space boundary value problem for the boltzmann equation with an incoming distribution obtained when considering the boundary layer arising in the kinetic theory of gases as the mean free path tends to zero we linearize it about a drifting maxwellian and prove that as conjectured by cercignani 4 the problem is well posed when the drift velocity u exceeds the sound speed c but that one respectively four five additional conditions must be imposed when 0 u c respectively c u 0 and u c in the second part we show that the well posedness and the asymptotic behavior results for kinetic layers equations with prescribed incoming flux can be extended to more general and realistic boundary conditions

optimal constellations for the low snr noncoherent mimo block rayleigh fading channel reliable communication over the discrete input continuous output noncoherent multiple input multiple output mimo rayleigh block fading channel is considered when the signal to noise ratio snr per degree of freedom is low two key problems are posed and solved to obtain the optimum discrete input in both problems the average and peak power per space time slot of the input constellation are constrained in the first one the peak power to average power ratio ppapr of the input constellation is held fixed while in the second problem the peak power is fixed independently of the average power in the first ppapr constrained problem the mutual information which grows as o snr2 is maximized up to second order in snr in the second peak constrained problem where the mutual information behaves as o snr the structure of constellations that are optimal up to first order or equivalently that minimize energy per bit are explicitly characterized furthermore among constellations that are first order optimal those that maximize the mutual information up to second order or equivalently the wideband slope are characterized in both ppapr constrained and peak constrained problems the optimal constellations are obtained in closed form as solutions to nonconvex optimizations and interestingly they are found to be identical due to its special structure the common solution is referred to as space time orthogonal rank one modulation or storm in both problems it is seen that storm provides a sharp characterization of the behavior of noncoherent mimo capacity

correlated mimo wireless channels capacity optimal signaling and asymptotics the capacity of the multiple input multiple output mimo wireless channel with uniform linear arrays ulas of antennas at the transmitter and receiver is investigated it is assumed that the receiver knows the channel perfectly but that the transmitter knows only the channel statistics the analysis is carried out using an equivalent virtual representation of the channel that is obtained via a spatial discrete fourier transform a key property of the virtual representation that is exploited is that the components of virtual channel matrix are approximately independent with this approximation the virtual representation allows for a general capacity analysis without the common simplifying assumptions of gaussian statistics and product form correlation kronecker model for the channel matrix elements a deterministic line of sight los component in the channel is also easily incorporated in much of the analysis it is shown that in the virtual domain the capacity achieving input vector consists of independent zero mean proper complex gaussian entries whose variances can be computed numerically using standard convex programming algorithms based on the channel statistics furthermore in the asymptotic regime of low signal to noise ratio snr it is shown that beamforming along one virtual transmit angle is asymptotically optimal necessary and sufficient conditions for the optimality of beamforming and the value of the corresponding optimal virtual angle are also derived based on only the second moments of the virtual channel coefficients numerical results indicate that beamforming may be close to optimum even at moderate values of snr for sparse scattering environments finally the capacity is investigated in the asymptotic regime where the numbers of receive and transmit antennas go to infinity with their ratio being kept constant using a result of girko an expression for the asymptotic capacity scaling with the number of antennas is obtained in terms

why does the kronecker model result in misleading capacity estimates many recent works that study the performance of multiple input multiple output mimo systems in practice assume a kronecker model where the variances of the channel entries upon decomposition on to the transmit and the receive eigenbases admit a separable form measurement campaigns however show that the kronecker model results in poor estimates for capacity motivated by these observations a channel model that does not impose a separable structure has been recently proposed and shown to fit the capacity of measured channels better in this paper we show that this recently proposed modeling framework can be viewed as a natural consequence of channel decomposition on to its canonical coordinates the transmit and or the receive eigenbases using tools from random matrix theory we then establish the theoretical basis behind the kronecker mismatch at the low and the high snr extremes 1 sparsity of the dominant statistical degrees of freedom dof in the true channel at the low snr extreme and 2 nonregularity of the sparsity structure disparities in the distribution of the dof across the rows and the columns at the high snr extreme

detect local communities in networks with an outside rate coefficient abstract in this paper we present a local method for detecting communities in networks we define an outside rate coefficient o u t in our method o u t has a very simple form and is easy to calculate the local community enclosing a starting node can be detected by agglomerating the node with the smallest o u t at each time step when there are two or more nodes having the same smallest outside rate coefficient o u t we agglomerate the node with the largest k i n this operation is remarkably beneficial to the accuracy of our method and simulations on benchmark networks and real networks demonstrate that our local method is efficient to detect communities in networks

surveying network community structure in the hidden metric space abstract most real world networks from various fields share a universal topological property as community structure in this paper we propose a node similarity based mechanism to explore the formation of modular networks by applying the concept of hidden metric spaces of complex networks it is demonstrated that network community structure could be formed according to node similarity in the underlying hidden metric space to clarify this we generate a set of observed networks using a typical kind of hidden metric space model by detecting and analyzing corresponding communities both in the observed network and the hidden space we show that the values of the fitness are rather close and the assignments of nodes for these two kinds of community structures detected based on the fitness parameter are extremely matching ones furthermore our research also shows that networks with strong clustering tend to display prominent community structures with large values of network modularity and fitness

training signal design for estimation of correlated mimo channels with colored interference in this paper we study the problem of estimating correlated multiple input multiple output mimo channels in the presence of colored interference the linear minimum mean square error mmse channel estimator is derived and the optimal training sequences are designed based on the mse of channel estimation we propose an algorithm to estimate the long term channel statistics needed for the construction of the optimal training sequences we also design an efficient scheme to feed back the required information to the transmitter where we can approximately construct the optimal sequences numerical results show that the optimal training sequences provide substantial performance gain for channel estimation when compared with other training sequences

a central limit theorem for the sinr at the lmmse estimator output for large dimensional signals this paper is devoted to the performance study of the linear minimum mean squared error lmmse estimator for multidimensional signals in the large dimension regime such an estimator is frequently encountered in wireless communications and in array processing and the signal to interference plus noise ratio sinr at its output is a popular performance index the sinr can be modeled as a random quadratic form which can be studied with the help of large random matrix theory if one assumes that the dimension of the received and transmitted signals go to infinity at the same pace this paper considers the asymptotic behavior of the sinr for a wide class of multidimensional signal models that includes general multiple antenna as well as spread spectrum transmission models the expression of the deterministic approximation of the sinr in the large dimension regime is recalled and the sinr fluctuations around this deterministic approximation are studied these fluctuations are shown to converge in distribution to the gaussian law in the large dimension regime and their variance is shown to decrease as the inverse of the signal dimension

robust training sequence design for correlated mimo channel estimation we study how to design a worst case robust training sequence for multiple input multiple output mimo channel estimation we consider mean squared error of channel estimates as the figure of merit which is a function of second order statistics of the mimo channel i e channel covariance matrix in order to optimize training sequences under a total power constraint in practical applications the channel covariance matrix is not known perfectly thus the main aspect of our design is to improve robustness of the training sequences against possible uncertainties in the available channel covariance matrix using a deterministic uncertainty model we formulate a robust training sequence design as a minimax optimization problem where we take such imperfections into account we investigate the robust design problem assuming the general case of an arbitrarily correlated mimo channel and a non empty compact convex uncertainty set we prove that such a problem admits a globally optimal solution by exploiting the convex concave structure of the objective function and propose numerical algorithms to address the robust training design problem we proceed the analysis by considering multiple input single output miso channels and kronecker structured mimo channels along with unitarily invariant uncertainty sets for these scenarios we show that the problem is diagonalized by the eigenvectors of the nominal covariance matrices so that the robust design is significantly simplified from a complex matrix variable problem to a real vector variable power allocation problem for the miso channel we provide closed form solutions for the robust training sequences with the uncertainty sets defined by the spectral norm and nuclear norm

estimating statistical properties of mimo fading channels we propose maximum likelihood ml and restricted maximum likelihood reml methods for estimating the mean and covariance parameters of multi input multi output mimo ricean and rayleigh block fading channels using measurements from multiple coherent intervals containing both amplitudes and phases of the received signal correlated and independent fading scenarios with structured and unstructured line of sight los array response models are considered computationally efficient ml and approximate ml aml estimators are proposed for unitary space time modulation schemes and orthogonal designs in correlated fading we also derive crame spl acute r rao bounds crbs for the unknown parameters discuss initialization of the proposed algorithms and evaluate their performance via numerical simulations under the block and continuous fading scenarios