the wssus pulse design problem in multicarrier transmission optimal link adaption to the scattering function of wide sense stationary uncorrelated scattering wssus mobile communication channels is still an unsolved problem despite its importance for next generation system design in multicarrier transmission such link adaption is performed by pulse shaping i e by properly adjusting the transmit and receive filters for example pulse shaped offset quadrature amplitude modulation oqam systems have recently been shown to have superior performance over standard cyclic prefix orthogonal frequency division multiplexing ofdm while operating at higher spectral efficiency in this paper we establish a general mathematical framework for joint transmitter and receiver pulse shape optimization for so called weyl heisenberg or gabor signaling with respect to the scattering function of the wssus channel in our framework the pulse shape optimization problem is translated to an optimization problem over trace class operators which in turn is related to fidelity optimization in quantum information processing by convexity relaxation the problem is shown to be equivalent to a convex constraint quasi convex maximization problem thereby revealing the nonconvex nature of the overall wssus pulse design problem we present several iterative algorithms for optimization providing applicable results even for large scale problem constellations we show that with transmitter side knowledge of the channel statistics a gain of 3 6 db in signal to interference and noise ratio sinr can be expected

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

t 0 mean field population dynamics approach for the random 3 satisfiability problem during the past decade phase transition phenomena in the random 3 satisfiability 3 sat problem has been intensively studied by statistical physics methods in this work we study the random 3 sat problem by the mean field first step replica symmetry broken cavity theory at the limit of temperature t 0 the reweighting parameter y of the cavity theory is allowed to approach infinity together with the inverse temperature beta with fixed ratio r y beta focusing on the system s space of satisfiable configurations we carry out extensive population dynamics simulations using the technique of importance sampling and we obtain the entropy density s r and complexity sigma r of zero energy clusters at different r values we demonstrate that the population dynamics may reach different fixed points with different types of initial conditions by knowing the trends of s r and sigma r with r we can judge whether a certain type of initial condition is appropriate at a given r value this work complements and confirms the results of several other very recent theoretical studies

extended mlse diversity receiver for the time and frequency selective channel this paper develops a maximum likelihood sequence estimation mlse diversity receiver for the time and frequency selective channel corrupted by additive gaussian noise when linear constellations m ask m psk m qam are employed the paper extends ungerboeck s derivation of the extended mlse receiver for the purely frequency selective channel to the more general channel although the new receiver structure and metric assume ideal channel state information csi the receiver can be used wherever high quality csi is available such as a comb of pilot tones or time isolated symbols the major contributions of this paper are as follows 1 the derivation of a finite complexity diversity receiver that is maximum likelihood ml for all linear channel models and sources of diversity as long as ideal csi is available 2 a benchmark in that the new receiver s performance is a lower bound on the performance of practical systems which either lack ideal csi or are not ml 3 insight into matched filtering and ml diversity receiver processing for the time and frequency selective channels and 4 bounds on the new receiver s bit error rate ber for ideal csi and pilot tone csi in a fast rayleigh fading channel with multiple independently faded paths the new receiver can seamlessly tolerate square root nyquist pulses without a fading induced isi error floor

multiple travelling wave solutions of nonlinear evolution equations using a unified algebraic method a new direct and unified algebraic method for constructing multiple travelling wave solutions of general nonlinear evolution equations is presented and implemented in a computer algebraic system compared with most of the existing tanh methods the jacobi elliptic function method or other sophisticated methods the proposed method not only gives new and more general solutions but also provides a guideline to classify the various types of the travelling wave solutions according to the values of some parameters the solutions obtained in this paper include a kink shaped and bell shaped soliton solutions b rational solutions c triangular periodic solutions and d jacobi and weierstrass doubly periodic wave solutions among them the jacobi elliptic periodic wave solutions exactly degenerate to the soliton solutions at a certain limit condition the efficiency of the method can be demonstrated on a large variety of nonlinear evolution equations such as those considered in this paper kdv mkdv ito s fifth mkdv hirota nizhnik novikov veselov broer kaup generalized coupled hirota satsuma coupled schrodinger kdv 2 1 dimensional dispersive long wave 2 1 dimensional davey stewartson equations in addition as an illustrative sample the properties of the soliton solutions and jacobi doubly periodic solutions for the hirota equation are shown by some figures the links among our proposed method the tanh method extended tanh method and the jacobi elliptic function method are clarified generally

typical approximation performance for maximum coverage problem this study investigated the typical performance of approximation algorithms known as belief propagation the greedy algorithm and linear programming relaxation for maximum coverage problems in sparse biregular random graphs after we used the cavity method for a corresponding hard core lattice gas model results showed that two distinct thresholds of replica symmetry and its breaking exist in the typical performance threshold of belief propagation in the low density region the superiority of three algorithms in terms of a typical performance threshold is obtained by some theoretical analyses although the greedy algorithm and linear programming relaxation have the same approximation ratio in worst case performance their typical performance thresholds are mutually different indicating the importance of typical performance results of numerical simulations validate the theoretical analyses and imply further mutual relations of approximation algorithms

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

a new general algebraic method and its applications to the 2 1 dimensional broer kaup kupershmidt equations abstract using a computerized symbolic computation technique a new method named the repeated general algebraic method rgam is established in this study in order to find exact solutions of nonlinear partial differential equations nlpdes the new method is validated based on the 2 1 dimensional broer kaup kupershmidt bkk equations by using the rgam in various conditions a number of exact solutions of nlpdes have been obtained showing potential importance in future physical applications also it is anticipated that the rgam can be applied to other nonlinear evolution equations in mathematical physics to produce some interesting outcomes

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

generalized method and new exact wave solutions for 2 1 dimensional broer kaup kupershmidt system in this paper a new algebra method i e generalized elliptic equation rational expansion method is devised to uniformly construct a series of exact solutions for nonlinear partial differential equations compared with most existing tanh methods the proposed method not only recover some known solutions but also find some new and general solutions the efficiency of the method can be demonstrated on the 2 1 dimensional broer kaup kupershmidt system as a result we obtain many new types of solutions include rational formal solitary wave solutions rational formal triangular periodic wave solutions rational formal jacobi and weierstrass double period solutions and rational wave solutions

minimal vertex covers on finite connectivity random graphs a hard sphere lattice gas picture the minimal vertex cover or maximal independent set problem is studied on random graphs of finite connectivity analytical results are obtained by a mapping to a lattice gas of hard spheres of chemical radius 1 and they are found to be in excellent agreement with numerical simulations we give a detailed description of the replica symmetric phase including the size and entropy of the minimal vertex covers and the structure of the unfrozen component which is found to percolate at a connectivity c approximately 1 43 the replica symmetric solution breaks down at c e approximately 2 72 we give a simple one step replica symmetry broken solution and discuss the problems in the interpretation and generalization of this solution

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

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

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

viterbi decoding of differentially encoded psk signals transmitted over rayleigh frequency flat fading channels maximum likelihood bit detection of differentially encoded m psk signals on rayleigh fading channels is investigated it is shown that the solution to this problem can be related to previous results vitetta and taylor 1994 and leads to the implementation of a receiver structure based on the viterbi algorithm and employing per survivor processing the error rate performance of this receiver is evaluated by means of computer simulations for both trellis coded and uncoded systems

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

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

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

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

maximum likelihood synchronization equalization and sequence estimation for unknown time varying frequency selective rician channels this paper develops a receiver structure to perform jointly maximum likelihood ml synchronization equalization and detection of a linearly modulated signal transmitted over a time varying frequency selective rician faded channel corrupted by additive white gaussian noise awgn the receiver is particularly suited to a fast fading channel where other receivers that rely on estimating the channel cannot track it quickly enough the signal mean and autocovariance are needed and a scheme is proposed for estimating these quantities adaptively the receiver processes the specular and diffuse components corresponding to the signal mean and autocovariance separately processing the known specular component is the classical detection problem the unknown diffuse component is processed by predictors we show that the predictors can achieve synchronization in a novel manner if synchronization is required a union bound on the receiver s bit error rate ber is derived and it tightly bounds simulated bers in fast fading at high signal to noise ratios snrs

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

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

identifying optimal targets of network attack by belief propagation for a network formed by nodes and undirected links between pairs of nodes the network optimal attack problem aims at deleting a minimum number of target nodes to break the network down into many small components this problem is intrinsically related to the feedback vertex set problem that was successfully tackled by spin glass theory and an associated belief propagation guided decimation bpd algorithm zhou eur phys j b 86 455 2013 in the present work we apply the bpd algorithm which has approximately linear time complexity to the network optimal attack problem and demonstrate that it has much better performance than a recently proposed collective information algorithm morone and makse nature 524 65 2015 for different types of random networks and real world network instances the bpd guided attack scheme often induces an abrupt collapse of the whole network which may make it very difficult to defend

further improved extended fan sub equation method and new exact solutions of the 2 1 dimensional broer kaup kupershmidt equations abstract in this paper a further improved extended fan sub equation method is proposed by taking a more general transformation to seek more types of exact solutions of non linear partial differential equations with the aid of symbolic computation we choose the 2 1 dimensional broer kaup kupershmidt equations to illustrate the validity and advantages of this method as a result many new and more general non travelling wave and coefficient function solutions are obtained including soliton like solutions triangular like solutions single and combined non degenerate jacobi elliptic wave function like solutions weierstrass elliptic doubly like periodic solutions

maximum likelihood sequence estimation of cpm signals transmitted over rayleigh flat fading channels a method for the sequential updating of log likelihood functions for maximum likelihood sequence estimation is presented it is shown that in a general case this method can be implemented using kalman filtering techniques for the special case of rayleigh flat fading and continuous phase modulation cpm signaling this approach is shown to lead to an attractive receiver structure this type of receiver called the linear predictive receiver can be implemented in the form of the viterbi algorithm with the trellis updates being computed using a bank of finite pulse response fir filter and square operations simulation results are presented that demonstrate the superiority of the linear predictive receiver over receivers employing differential detection in the presence of fast fading it is shown that the optimal linear predictive receiver does not possess an irreducible error rate for a class of rayleigh fading channels used to model terrestrial mobile channels

network dismantling abstract we study the network dismantling problem which consists of determining a minimal set of vertices in which removal leaves the network broken into connected components of subextensive size for a large class of random graphs this problem is tightly connected to the decycling problem the removal of vertices leaving the graph acyclic exploiting this connection and recent works on epidemic spreading we present precise predictions for the minimal size of a dismantling set in a large random graph with a prescribed light tailed degree distribution building on the statistical mechanics perspective we propose a three stage min sum algorithm for efficiently dismantling networks including heavy tailed ones for which the dismantling and decycling problems are not equivalent we also provide additional insights into the dismantling problem concluding that it is an intrinsically collective problem and that optimal dismantling sets cannot be viewed as a collection of individually well performing nodes

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

decision feedback differential detection of mdpsk for flat rayleigh fading channels in this paper decision feedback differential detection df dd of m ary differential phase shift keying mdpsk signals which has been introduced previously for the additive white gaussian noise awgn channel by leib et al 1988 and edbauer 1992 is extended to flat rayleigh fading channels the corresponding df dd metric is derived from the multiple symbol detection msd metric and for genie aided df dd an exact expression for the bit error rate ber of qdpsk m 4 is calculated furthermore the dependence of ber on the power spectrum of the fading process is investigated for feedback filters of infinite order it is shown that in this case for ideally bandlimited fading processes the error floor of conventional differential detection dd can be removed entirely simulation results confirm that both msd and df dd with feedback filters of finite order can reduce the error floor of conventional dd significantly df dd thereby causes considerably less computational load

an algebraic method for finding a series of exact solutions to integrable and nonintegrable nonlinear evolution equations an algebraic method is devised to uniformly construct a series of exact solutions for general integrable and nonintegrable nonlinear evolution equations compared with most existing tanh methods the jacobi function expansion method or other sophisticated methods the proposed method not only gives new and more general solutions but also provides a guideline to classify the various types of the solutions according to the values of some parameters the solutions obtained in this paper include a polynomial solutions b exponential solutions c rational solutions d triangular periodic wave solutions e hyperbolic and solitary wave solutions and f jacobi and weierstrass doubly periodic wave solutions the efficiency of the method can be demonstrated on a large variety of nonlinear equations such as those considered in this paper new 2 1 dimensional calogero kdv equation 3 1 dimensional jimbo miwa equation symmetric regular long wave equation drinfel d sokolov wilson equation 2 1 dimensional generalized dispersive long wave equation double sine gordon equation calogero degasperis fokas equation and coupled schrodinger boussinesq equation in addition the links among our proposed method the tanh method the extended method and the jacobi function expansion method are also clarified generally

exact solutions for some coupled nonlinear equations ii for pt i see ibid vol 23 p 3923 1990 the authors use the method previously presented to obtain the exact solutions for some coupled nonlinear equations

cramer rao bounds and maximum likelihood estimation for random amplitude phase modulated signals the problem of estimating the phase parameters of a phase modulated signal in the presence of colored multiplicative noise random amplitude modulation and additive white noise both gaussian is addressed closed form expressions for the exact and large sample cramer rao bounds crbs are derived it is shown that the crb is significantly affected by the color of the modulating process when the signal to noise ratio snr or the intrinsic snr is small maximum likelihood type estimators that ignore the noise color and optimize a criterion with respect to only the phase parameters are proposed these estimators are shown to be equivalent to the nonlinear least squares estimators which consist of matching the squared observations with a constant amplitude phase modulated signal when the mean of the multiplicative noise is forced to zero closed form expressions are derived for the efficiency of these estimators and are verified via simulations

adaptive mlse for dpsk in time and frequency selective channels an adaptive equalizer structure based on a state space formulation and maximum likelihood sequence estimation mlse is developed for a time varying frequency selective channel differential phase shift keying dpsk is assumed at the transmitter and effective differential decoding is performed at the receiver the standard models of a time varying linear channel and the karhunen loeve kl expansion underpin the receiver structure analytical and simulation results for the receiver are shown the resulting receiver is a per survivor structure

message passing for vertex covers constructing a minimal vertex cover of a graph can be seen as a prototype for a combinatorial optimization problem under hard constraints in this paper we develop and analyze message passing techniques namely warning and survey propagation which serve as efficient heuristic algorithms for solving these computational hard problems we show also how previously obtained results on the typical case behavior of vertex covers of random graphs can be recovered starting from the message passing equations and how they can be extended

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

spin glass phase transitions and minimum energy of the random feedback vertex set problem a feedback vertex set fvs of an undirected graph contains vertices from every cycle of this graph constructing a fvs of sufficiently small cardinality is very difficult in the worst cases but for random graphs this problem can be efficiently solved by converting it into an appropriate spin glass model h j zhou eur phys j b 86 455 2013 in the present work we study the spin glass phase transitions and the minimum energy density of the random fvs problem by the first step replica symmetry breaking 1rsb mean field theory for both regular random graphs and erdos renyi graphs we determine the inverse temperature beta 1 at which the replica symmetric mean field theory loses its local stability the inverse temperature beta d of the dynamical clustering phase transition and the inverse temperature beta s of the static condensation phase transition these critical inverse temperatures all change with the mean vertex degree in a nonmonotonic way and beta d is distinct from beta s for regular random graphs of vertex degrees k 60 while beta d are identical to beta s for erdos renyi graphs at least up to mean vertex degree c 512 we then derive the zero temperature limit of the 1rsb theory and use it to compute the minimum fvs cardinality

minimal contagious sets in random regular graphs the bootstrap percolation or threshold model is a dynamic process modelling the propagation of an epidemic on a graph where inactive vertices become active if their number of active neighbours reach some threshold we study an optimization problem related to it namely the determination of the minimal number of active sites in an initial configuration that leads to the activation of the whole graph under this dynamics with and without a constraint on the time needed for the complete activation this problem encompasses in special cases many extremal characteristics of graphs like their independence decycling or domination number and can also be seen as a packing problem of repulsive particles we use the cavity method including the effects of replica symmetry breaking an heuristic technique of statistical mechanics many predictions of which have been confirmed rigorously in the recent years we have obtained in this way several quantitative conjectures on the size of minimal contagious sets in large random regular graphs the most striking being that 5 regular random graph with a threshold of activation of 3 resp 6 regular with threshold 4 have contagious sets containing a fraction 1 6 resp 1 4 of the total number of vertices equivalently these numbers are the minimal fraction of vertices that have to be removed from a 5 regular resp 6 regular random graph to destroy its 3 core we also investigated survey propagation like algorithmic procedures for solving this optimization problem on single instances of random regular graphs

differentially coherent decorrelating detector for cdma single path time varying rayleigh fading channels this paper describes a differentially coherent decorrelating detector for a k user reverse link code division multiple access environment that exhibits time varying rayleigh fading the channel is modeled as providing only a single fading path for each user and with no additional means to achieve diversity the design of the detector is based on using fractionally sampled matched filter outputs to simultaneously achieve two goals 1 the novel realization of a one shot decorrelator with lower computational complexity and 2 the forming of the maximum likelihood decision rule on the decorrelated outputs which results in an effective increase of the correlation in the fading process analytical evaluation and simulation of the error probability of the detector demonstrates significant lowering of the error floor in comparison to the decorrelating detector that employs conventional differentially coherent detection

elliptic equation s new solutions and their applications to two nonlinear partial differential equations abstract in the present paper with the aid of symbolic computation families of new nontrivial solutions of first order elliptic equation 2 a 0 a 1 a 2 2 a 3 3 a 4 4 where d d x are obtained to our knowledge these nontrivial solutions can not be found in chaos solitons fract 26 2005 785 794 and phys lett a 336 2005 463 476 by yomba and other existent papers until now by using these nontrivial solutions a direct algebraic method is described to construct several kinds of exact non travelling wave solutions for the 2 1 dimensional breaking soliton equations and the 2 1 dimensional asymmetric nizhnik novikov vesselov equation by using this method many other physically important nonlinear partial differential equations nlpdes can be investigated and new non travelling wave solutions can be explicitly obtained with the aid of symbolic computation system maple

a new general algebraic method with symbolic computation to construct new travelling wave solution for the 1 1 dimensional dispersive long wave equation with the aid of symbolic computation a new algebraic method named riccati equation rational expansion rere method is devised for constructing multiple travelling wave solutions for nonlinear evolution equations nees compared with most existing tanh methods for finding travelling wave solutions the proposed method not only recover the results by most known algebraic methods but also provides new and more general solutions with the aid of symbolic computation we choose 1 1 dimensional dispersive long wave equation dlwe to illustrate our method as a result we obtain many types of solutions including rational form solitary wave solutions triangular periodic wave solutions and rational wave solutions the properties of the new solitary wave solutions are shown by some figures

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

cramer rao bounds in the parametric estimation of fading radiotransmission channels the context of this paper is parameter estimation for linearly modulated digital data signals observed on a frequency flat time selective fading channel affected by additive white gaussian noise the aim is the derivation of cramer rao lower bounds for the joint estimation of all those channel parameters that impact signal detection namely carrier phase carrier frequency offset doppler shift frequency rate of change doppler rate signal amplitude fading power and gaussian noise power time selective frequency flat fading is modeled as a low pass autoregressive multiplicative distortion process in particular the important case of slow fading with the multiplicative process remaining constant over the whole data burst is specifically discussed asymptotic expressions of the bounds valid for a large observed sample or for high signal to noise ratio snr are also derived in closed form a few charts with numerical results are finally reported to highlight the dependence of the bounds on channel status snr fading bandwidth etc

a generalized g g expansion method and its application to the 2 1 dimensional broer kaup equations abstract in this paper a generalized g g expansion method is used to seek more general exact solutions of the 2 1 dimensional broer kaup equations as a result non travelling wave solutions with three arbitrary functions are obtained including hyperbolic function solutions trigonometric function solutions and rational solutions the proposed method is more powerful than wang et al s method in m l wang x z li j l zhang the g g expansion method and travelling wave solutions of nonlinear evolution equations in mathematical physics phys lett a 372 2008 417 423 and it can be used for many other nonlinear evolution equations in mathematical physics

an adaptive maximum likelihood receiver for correlated rayleigh fading channels the paper develops a receiver structure for random gaussian signals in additive noise based on the classic maximum likelihood m l estimator correlator derivation of kailath 1960 and applies it to differential phase shift keying dpsk on the correlated rayleigh fading channel it is shown to lower the error floor found in the performance of conventional dpsk receivers by orders of magnitude in addition the maximum likelihood procedure is shown to make uncorrelated symbol decisions the performance of both conventional and optimal receivers which require knowledge of the channel statistics is examined analytically a recursive channel adaptive version of the optimal receiver utilizing decision feedback to estimate the channel statistics is developed its simulated performance shows no penalty compared to theoretical calculations which require explicit knowledge of the channel statistics

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

stability analysis on the finite temperature replica symmetric and first step replica symmetry broken cavity solutions of the random vertex cover problem the vertex cover problem is a prototypical hard combinatorial optimization problem it was studied in recent years by physicists using the cavity method of statistical mechanics in this paper the stability of the finite temperature replica symmetric rs and the first step replica symmetry broken 1rsb cavity solutions of the vertex cover problem on random regular graphs of finite vertex degree k are analyzed by population dynamics simulations we found that 1 the lowest temperature for the rs solution to be stable t rs k is not a monotonic function of k 2 at relatively large connectivity k and temperature t slightly below the dynamic transition temperature t d k the 1rsb solutions with small but non negative complexity values are stable and 3 the dynamical transition temperature t d and kauzmann temperature t k is equal to each other similar results are obtained on random poissonian graphs

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

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