design of capacity approaching irregular low density parity check codes we design low density parity check ldpc codes that perform at rates extremely close to the shannon capacity the codes are built from highly irregular bipartite graphs with carefully chosen degree patterns on both sides our theoretical analysis of the codes is based on the work of richardson and urbanke see ibid vol 47 no 2 p 599 618 2000 assuming that the underlying communication channel is symmetric we prove that the probability densities at the message nodes of the graph possess a certain symmetry using this symmetry property we then show that under the assumption of no cycles the message densities always converge as the number of iterations tends to infinity furthermore we prove a stability condition which implies an upper bound on the fraction of errors that a belief propagation decoder can correct when applied to a code induced from a bipartite graph with a given degree distribution our codes are found by optimizing the degree structure of the underlying graphs we develop several strategies to perform this optimization we also present some simulation results for the codes found which show that the performance of the codes is very close to the asymptotic theoretical bounds

on the limiting zeros of sampled multivariable systems for time invariant linear systems with single input single output it has been shown 3 that as the sampling period goes to 0 the zeros of the corresponding discrete time system obtained by sampling converge to some specific constant values determined only be the degrees of the finite and the infinite zeros of the original continuous time system it is natural to inquire the extent to which this result may be carried over to the case of multivariable systems in this note it is shown that the result is true also for multivariable systems if the difference among the degrees of infinite elementary divisors of the pencil corresponding to the original continuous system is less than two when the last condition is not satisfied the limiting values of the zeros of the discrete system depend in general not only on the integers cited above but also on system parameters

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

the numerical analysis of ordinary differential equations runge kutta and general linear methods mathematical and computational introduction the euler method and its generalizations analysis of runge kutta methods general linear methods bibliography

average path length in random networks analytic solution for the average path length in a large class of uncorrelated random networks with hidden variables is found we apply the approach to classical random graphs of erdos and renyi er evolving networks introduced by barabasi and albert as well as random networks with asymptotic scale free connectivity distributions characterized by an arbitrary scaling exponent alpha 2 our result for 2 infinity there is a saturation effect for the average path length

algebraic construction of sparse matrices with large girth in this correspondence we present a method for constructing sparse matrices that have a compact description and whose associated bipartite graphs have large girth based on an arbitrary seed matrix of nonnegative integers a new matrix is constructed which replaces each entry of the seed matrix with a sum of permutation matrices algebraic conditions that lead to short cycles in the associated bipartite graph are analyzed and methods to achieve large girth in two special cases are presented in one all the permutation matrices are circulants in the other they are all affine permutation matrices when used to define a low density parity check ldpc code the compact description should lead to efficient implementation and the large girth to good error correction performance the method is adaptable to a variety of rates and a variety of row and column degrees

minimal positive realizations of transfer functions with nonnegative multiple poles this note concerns a particular case of the minimality problem in positive system theory a standard result in linear system theory states that any nth order rational transfer function of a discrete time invariant linear single input single output siso system admits a realization of order n in some applications however one is restricted to realizations with nonnegative entries i e a positive system and it is known that this restriction may force the order n of realizations to be strictly larger than n a general solution to the minimality problem i e determining the smallest possible value of n is not known in this note we consider the case of transfer functions with nonnegative multiple poles and give sufficient conditions for the existence of positive realizations of order n n with the help of our results we also give an improvement of an existing result in positive system theory

modified euler frobenius polynomials with application to sampled data modelling the broad class of polynomials generally known as eulerian or euler frobenius polynomials has a rich history in mathematics and engineering they have been generalised in several directions and find application in diverse areas ranging from sampled data modelling and polynomial interpolation to wavelets here we describe a modified class of euler frobenius polynomials which are functions of two independent variables we show that the sampling zero dynamics of general linear and nonlinear systems can be described using this new class of polynomials when considering several non standard sampled data modelling problems including when generalised hold functions are used to generate the input and when the continuous system has a time delay

paper zeros of sampled systems the zeros of the discrete time system obtained when sampling a continuous time system are explored theorems for the limiting zeros for large and small sampling periods are given conditions which guarantee that the sampled system has stable zeros are also presented

edge deletion problems if pi is a property on graphs or digraphs the edge deletion problem can be stated as follows find the minimum number of edges whose deletion results in a subgraph or subdigraph satisfying property pi several well studied graph problems can be formulated as edge deletion problems in this paper we show that the edge deletion problem is np complete for the following properties 1 without cycles of specified length l or of any length leqq l 2 connected and degree constrained 3 outerplanar 4 transitive digraph 5 line invertible 6 bipartite 7 transitively orientable for problems 5 6 7 we determine the best possible bounds on the node degrees for which the problems remain np complete

finding community structure in networks using the eigenvectors of matrices we consider the problem of detecting communities or modules in networks groups of vertices with a higher than average density of edges connecting them previous work indicates that a robust approach to this problem is the maximization of the benefit function known as modularity over possible divisions of a network here we show that this maximization process can be written in terms of the eigenspectrum of a matrix we call the modularity matrix which plays a role in community detection similar to that played by the graph laplacian in graph partitioning calculations this result leads us to a number of possible algorithms for detecting community structure as well as several other results including a spectral measure of bipartite structure in networks and a centrality measure that identifies vertices that occupy central positions within the communities to which they belong the algorithms and measures proposed are illustrated with applications to a variety of real world complex networks

stabilization of discrete system zeros an improved design stabilization of discrete system zeros has been previously achieved by providing a fixed pattern of inter sampling time input which deviates from zero order hold however a fixed non zoh input creates several problems indefinite fluctuation of the system output which causes a deterioration in performance highly fluctuating input which accelerates actuator fatigue and counter acting control which increases demand for input energy in this work zero placement is achieved with a temporary non zoh input this temporary input pattern which converges asymptotically toward a zoh input pattern removes the problems associated with a fixed non zoh input design

brief paper inversion of sampled data system approximates the continuous time counterpart in a noncausal framework although correspondence between the poles of a continuous time and sampled data system with a piecewise constant input is simple and desirable from the stability viewpoint the relationship between zeros is intricate inversion of a sampled data system is mostly unstable irrespective of the stability of the continuous time counterpart this makes it difficult to apply inversion based control techniques such as perfect tracking transient response shaping or iterative learning control to sampled data systems although recently developed noncausal inversion techniques help us to circumvent unboundedness of the inversion caused by unstable zeros whether the inversion of sampled data systems approximates the continuous time counterpart or not as the sample period is shortened is still to be determined this article gives a positive conclusion to this problem

detection of topological patterns in complex networks correlation profile of the internet abstract a general scheme for detecting and analyzing topological patterns in large complex networks is presented in this scheme the network in question is compared with its properly randomized version that preserves some of its low level topological properties statistically significant deviation of any topological property of a network from this null model likely reflects its design principles and or evolutionary history we illustrate this basic scheme using the example of the correlation profile of the internet quantifying correlations between degrees of its neighboring nodes this profile distinguishes the internet from previously studied molecular networks with a similar scale free degree distribution we finally demonstrate that the clustering in a network is very sensitive to both the degree distribution and its correlation profile and compare the clustering in the internet to the appropriate null model

general formalism for inhomogeneous random graphs we present and investigate an extension of the classical random graph to a general class of inhomogeneous random graph models where vertices come in different types and the probability of realizing an edge depends on the types of its terminal vertices this approach provides a general framework for the analysis of a large class of models the generic phase structure is derived using generating function techniques and relations to other classes of models are pointed out

properties of zeros in digital control systems with computational time delay abstract a digital control system with computational time delay is considered in which the controlled plant is a continuous time linear system and the control input is calculated by a digital computer based on the data of the output measured before a certain time not greater than the sampling period some qualitative properties of the zeros such as the characteristics of the limiting zeros the parity relation between real poles and zeros and the behaviour of the zeros with respect to the computational time delay are investigated and the parity interlacing property and its dual are derived a method of stabilization by a stable digital compensator using the inter sample data is also proposed finally the first order hold case is discussed

the relationship between real poles and real zeros in siso sampled data systems a relationship between real poles and real zeros of siso single input single output sampled data systems is presented which is independent of the sampling period the relation is stated in terms of a parity property involving the number of real zeros between any two real poles this property allows the investigation of conditions for the preservation of stable or unstable zeros under sampling a sufficient condition for stability of a sampled system with a continuous time plant having all real zeros and a sufficient condition for instability of a two sampled system with an unstable plant is developed

statistics of the number of minima in a random energy landscape dated february 6 2008 we consider random energy landscapes constructed from d dimensional lattices or trees thedistribution of the number of local minima in such landscapes follows a large deviation principleand we derive the associated law exactly for dimension 1 also of interest is the probability of themaximum possible number of minima this probability scales exponentially with the number of sites we calculate analytically the corresponding exponent for the cayley tree and the two leg ladder for 2 to 5 dimensional hypercubic lattices we compute the exponent numerically and compare tothe cayley tree case

random removal of edges from scale free graphs abstract it has been discovered that many naturally occurring networks the internet the power grid of the western us various biological networks etc satisfy a power law degree distribution such scale free networks have many interesting properties one of which is robustness to random damage this problem has been analyzed from the point of view of node deletion and connectedness recently it has also been considered from the point of view of node deletion and scale preservation in this paper we consider the problem from the point of view of edge deletion and scale preservation in agreement with the work on node deletion and scale preservation we show that a scale free graph should not be expected to remain scale free when edges are removed at random

efficient encoding of low density parity check codes low density parity check ldpc codes can be considered serious competitors to turbo codes in terms of performance and complexity and they are based on a similar philosophy constrained random code ensembles and iterative decoding algorithms we consider the encoding problem for ldpc codes more generally we consider the encoding problem for codes specified by sparse parity check matrices we show how to exploit the sparseness of the parity check matrix to obtain efficient encoders for the 3 6 regular ldpc code for example the complexity of encoding is essentially quadratic in the block length however we show that the associated coefficient can be made quite small so that encoding codes even of length n spl sime 100000 is still quite practical more importantly we show that optimized codes actually admit linear time encoding

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

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

search in power law networks many communication and social networks have power law link distributions containing a few nodes that have a very high degree and many with low degree the high connectivity nodes play the important role of hubs in communication and networking a fact that can be exploited when designing efficient search algorithms we introduce a number of local search strategies that utilize high degree nodes in power law graphs and that have costs scaling sublinearly with the size of the graph we also demonstrate the utility of these strategies on the gnutella peer to peer network

preservation of reachability and observability under sampling with a first order hold this paper gives the necessary and sufficient condition for the reachability of the sampled data system s sub 1 obtained by the discretization of a linear time invariant continuous time system with a first order hold equivalence of the reachability and controllability of s sub 1 is also shown similar results are given also for observability and reconstructibility it turns out that s sub 1 is reachable only if s sub 0 is reachable while s sub 1 is observable if and only if s sub 4 l0 is observable where s sub 0 is the sampled data system obtained by the discretization with a zero order hold of the same sampling period

log concavity property of the error probability with application to local bounds for wireless communications a clear understanding of the behavior of error probability ep as a function of signal to noise ratio snr and other system parameters is fundamental for assessing the design of digital wireless communication systems we propose an analytical framework based on the log concavity property of the ep which we prove for a wide family of multidimensional modulation formats in the presence of gaussian disturbances and fading based on this property we construct a class of local bounds for the ep that improve known generic bounds in a given region of the snr and are invertible as well as easily tractable for further analysis this concept is motivated by the fact that communication systems often operate with performance in a certain region of interest roi and thus it may be advantageous to have tighter bounds within this region instead of generic bounds valid for all snrs we present a possible application of these local bounds but their relevance is beyond the example made in this paper

percolation in hierarchical scale free nets we study the percolation phase transition in hierarchical scale free nets depending on the method of construction the nets can be fractal or small world the diameter grows either algebraically or logarithmically with the net size assortative or disassortative a measure of the tendency of like degree nodes to be connected to one another or possess various degrees of clustering the percolation phase transition can be analyzed exactly in all these cases due to the self similar structure of the hierarchical nets we find different types of criticality illustrating the crucial effect of other structural properties aside from the scale free degree distribution of the nets

scale free brain functional networks functional magnetic resonance imaging is used to extract functional networks connecting correlated human brain sites analysis of the resulting networks in different tasks shows that a the distribution of functional connections and the probability of finding a link versus distance are both scale free b the characteristic path length is small and comparable with those of equivalent random networks and c the clustering coefficient is orders of magnitude larger than those of equivalent random networks all these properties typical of scale free small world networks reflect important functional information about brain states

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

on the relationship between spline interpolation sampling zeros and numerical integration in sampled data models abstract real systems are usually modeled in continuous time by differential equations in practice however we have to deal with them using discretized models and sampled data these models however have more zeros than the continuous time model in this paper we show that there is a specific relation between these sampling zeros and the smoothness of the continuous time input to the plant generated by a hold device using spline interpolation on the other hand in numerical analysis ordinary differential equations are solved using numerical integration methods such as runge kutta in this paper we also characterize the asymptotic sampling zeros of approximate sampled data models when using a runge kutta method of a given order under uniform sampling and the input signal is obtained by spline interpolation these results show the strong connections between the presence and characterization of sampling zeros spline interpolation and numerical integration techniques moreover the results presented in the paper provide additional insights about the impact of the details of the sampling process on the resulting discrete time model

a stability condition of zeros of sampled multivariable systems this note derives a new condition for zeros of sampled multivariable systems to be stable for sufficiently small sampling periods it is a natural extension of hagiwara s result for single input single output systems 1993 to multivariable systems

zero dynamics of sampled data models for nonlinear multivariable systems in fractional order hold case the paper is concerned with the properties of approximate sampled data models and their zero dynamics as the sampling period tends to zero composed of a fractional order hold froh a continuous time multivariable plant and a sampler in cascade the emphasis of this paper is the stability of discrete zero dynamics with the generalized gain of the froh where we also present a condition to assure the stability of the sampling zero dynamics which they have no counterpart in the underlying continuous time system of the resulting model similar to the linear case the parameter is the only factor in affecting the stability of discrete zero dynamics and the appropriate is determined to obtain the froh that provides zero dynamics as stable as possible or with improved stability properties even when unstable for a given continuous time multivariable plant the study is also shown that the stability of the sampling zero dynamics is improved compared with a zero order hold zoh

quasi cyclic generalized ldpc codes with low error floors in this paper a novel methodology for designing structured generalized low density parity check g ldpc codes is presented the proposed design results in quasi cyclic g ldpc codes for which efficient encoding is feasible through shift register based circuits the structure imposed on the bipartite graphs together with the choice of simple component codes leads to a class of codes suitable for fast iterative decoding a pragmatic approach to the construction of g ldpc codes is proposed the approach is based on the substitution of check nodes in the protograph of a low density parity check code with stronger nodes based for instance on hamming codes such a design approach which we call low density parity check ldpc code doping leads to low rate quasi cyclic g ldpc codes with excellent performance in both the error floor and waterfall regions on the additive white gaussian noise channel

a limiting property of the inverse of sampled data systems on a finite time interval if one considers a sampled data system derived from a continuous time system with a relative degree of one or two on a finite time interval it is not simple to predict the behavior of the output of the inverse of the sampled data system as the sampling period goes to zero this is because the number of sample points increases while the zeros of the pulse transfer function tend to the boundary between the stable and unstable areas the paper shows that the output of the sampled data inverse systems converges to the output of the continuous time inverse systems independently of the stability of zeros

a framework for stabilization of nonlinear sampled data systems based on their approximate discrete time models a unified framework for design of stabilizing controllers for sampled data differential inclusions via their approximate discrete time models is presented both fixed and fast sampling are considered in each case sufficient conditions are presented which guarantee that the controller that stabilizes a family of approximate discrete time plant models also stabilizes the exact discrete time plant model for sufficiently small integration and or sampling periods previous results in the literature are extended to cover 1 continuous time plants modeled as differential inclusions 2 general approximate discrete time plant models 3 dynamical discontinuous controllers modeled as difference inclusions and 4 stability with respect to closed arbitrary not necessarily compact sets

stability of the limiting zeros of sampled data systems with zero and first order holds this paper is concerned with the zeros of sampled data systems resulting from continuous time systems preceded by a hold and followed by a sampler the holds we shall consider are a zero order hold and a first order hold for sufficiently small or large sampling periods such zeros are called limiting zeros for sufficiently small sampling periods they are known to consist of two different types of zeros the zeros of the first type correspond to the zeros of the original continuous time system while those of the second type have no continuous time counterparts we first show basic properties of the zeros of sample data systems for sufficiently small sampling periods next we clarify in more detail the correspondence between the former type zeros of the sampled data systems and the zeros of the original continuous time system including the stability property of these zeros we also study stability properties of the latter type zeros in addition we study limiting zeros for sufficiently large sampli

non normal amplification in random balanced neuronal networks in dynamical models of cortical networks the recurrent connectivity can amplify the input given to the network in two distinct ways one is induced by the presence of near critical eigenvalues in the connectivity matrix w producing large but slow activity fluctuations along the corresponding eigenvectors dynamical slowing the other relies on w not being normal which allows the network activity to make large but fast excursions along specific directions here we investigate the trade off between non normal amplification and dynamical slowing in the spontaneous activity of large random neuronal networks composed of excitatory and inhibitory neurons we use a schur decomposition of w to separate the two amplification mechanisms assuming linear stochastic dynamics we derive an exact expression for the expected amount of purely non normal amplification we find that amplification is very limited if dynamical slowing must be kept weak we conclude that to achieve strong transient amplification with little slowing the connectivity must be structured we show that unidirectional connections between neurons of the same type together with reciprocal connections between neurons of different types allow for amplification already in the fast dynamical regime finally our results also shed light on the differences between balanced networks in which inhibition exactly cancels excitation and those where inhibition dominates

taylor series expansion for zeros of sampled data systems this paper introduces key properties that are useful for the computation of a taylor expansion of discretization zeros or single intrinsic zeros of sampled data systems furthermore regularity is shown to exist in the suffixes of the coefficients of the expansion expressions which implies that the sampling zeros or every coefficient in the numerator of the transfer function of the sampled data systems is dominated by the coefficients of higher order terms in the numerator and denominator of the continuous time counterpart moreover it is shown that the regularity can reduce the calculation effort for expansions of higher order systems

organization of growing random networks the organizational development of growing random networks is investigated these growing networks are built by adding nodes successively and linking each to an earlier node of degree k with an attachment probability a k when a k grows more slowly than linearly with k the number of nodes with k links n k t decays faster than a power law in k while for a k growing faster than linearly in k a single node emerges which connects to nearly all other nodes when a k is asymptotically linear n k t ensuremath sim mathrm tk ensuremath ensuremath nu with ensuremath nu dependent on details of the attachment probability but in the range 2l ensuremath nu l ensuremath infty the combined age and degree distribution of nodes shows that old nodes typically have a large degree there is also a significant correlation in the degrees of neighboring nodes so that nodes of similar degree are more likely to be connected the size distributions of the in and out components of the network with respect to a given node namely its descendants and ancestors are also determined the in component exhibits a robust s ensuremath 2 power law tail where s is the component size the out component has a typical size of order mathrm ln t and it provides basic insights into the genealogy of the network

hub synchronization in scale free networks heterogeneity in the degree distribution is known to suppress global synchronization in complex networks of symmetrically coupled oscillators scale free networks display a great deal of heterogeneity containing a few nodes termed hubs that are highly connected while most nodes receive only a few connections here we show that a group of synchronized nodes may appear in scale free networks hubs undergo a transition to synchronization while the other nodes remain unsynchronized this general phenomenon can occur even in the absence of global synchronization our results suggest that scale free networks may have evolved to complement various levels of synchronization

finding community structure in very large networks the discovery and analysis of community structure in networks is a topic of considerable recent interest within the physics community but most methods proposed so far are unsuitable for very large networks because of their computational cost here we present a hierarchical agglomeration algorithm for detecting community structure which is faster than many competing algorithms its running time on a network with n vertices and m edges is o md phantom rule 0 2em 0ex mathrm log phantom rule 0 2em 0ex n where d is the depth of the dendrogram describing the community structure many real world networks are sparse and hierarchical with m ensuremath sim n and d ensuremath sim mathrm log phantom rule 0 2em 0ex n in which case our algorithm runs in essentially linear time o n phantom rule 0 2em 0ex mathrm log 2 phantom rule 0 2em 0ex n as an example of the application of this algorithm we use it to analyze a network of items for sale on the web site of a large on line retailer items in the network being linked if they are frequently purchased by the same buyer the network has more than 400 000 vertices and 2 ifmmode times else texttimes fi 10 6 edges we show that our algorithm can extract meaningful communities from this network revealing large scale patterns present in the purchasing habits of customers

computational experience with approximation algorithms for the set covering problem the set covering problem scp is a well known combinatorial optimization problem which is np hard we conducted a comparative study of eight different approximation algorithms for the scp including several greedy variants fractional relaxations randomized algorithms and a neural network algorithm the algorithms were tested on a set of random generated problems with up to 500 rows and 5000 columns and on two sets of problems originating in combinatorial questions with up to 28160 rows and 11264 columns on the random problems and on one set of combinatorial problems the best algorithm among those we tested was the neural network algorithm with greedy variants very close in second and third place on the other set of combinatorial problems the best algorithm was a greedy variant and the neural network performed quite poorly the other algorithms we tested were always inferior to the ones mentioned above

asymptotic properties and stability criteria of zeros of sampled data models for decouplable mimo systems this note analyzes the zeros of the sampled data models corresponding to continuous time decouplable mimo systems with all relative degrees less than or equal to two and shows approximate expressions of the zeros as power series expansions with respect to a sampling period further stability criteria of the zeros for small sampling periods are given

networks with given two point correlations hidden correlations from degree correlations this paper orders certain important issues related to both uncorrelated and correlated networks with hidden variables in which hidden variables correspond to desired node degrees in particular we show that networks being uncorrelated at the hidden level are also lacking in correlations between node degrees the observation supported by the depoissonization idea allows us to extract a distribution of hidden variables from a given node degree distribution it completes the algorithm for generating uncorrelated networks that was suggested by other authors in this paper we also carefully analyze the interplay between hidden attributes and node degrees we show how to extract hidden correlations from degree correlations our derivations provide a mathematical background for the algorithm for generating correlated networks that was proposed by boguna and pastor satorras

regular and irregular progressive edge growth tanner graphs we propose a general method for constructing tanner graphs having a large girth by establishing edges or connections between symbol and check nodes in an edge by edge manner called progressive edge growth peg algorithm lower bounds on the girth of peg tanner graphs and on the minimum distance of the resulting low density parity check ldpc codes are derived in terms of parameters of the graphs simple variations of the peg algorithm can also be applied to generate linear time encodeable ldpc codes regular and irregular ldpc codes using peg tanner graphs and allowing symbol nodes to take values over gf q q 2 are investigated simulation results show that the peg algorithm is a powerful algorithm to generate good short block length ldpc codes

partition of networks into basins of attraction we study partition of networks into basins of attraction based on a steepest ascent search for the node of highest degree each node is associated with or attracted to its neighbor of maximal degree as long as the degree is increasing a node that has no neighbors of higher degree is a peak attracting all the nodes in its basin maximally random scale free networks exhibit different behavior based on their degree distribution exponent gamma for small gamma broad distribution networks are dominated by a giant basin whereas for large gamma narrow distribution there are numerous basins with peaks attracting mainly their nearest neighbors we derive expressions for the first two moments of the number of basins we also obtain the complete distribution of basin sizes for a class of hierarchical deterministic scale free networks that resemble random nets finally we generalize the problem to regular networks and lattices where all degrees are equal and thus the attractiveness of a node must be determined by an assigned weight rather than the degree we derive the complete distribution of basins of attraction resulting from randomly assigned weights in one dimensional chains

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

detecting communities in large networks we develop an algorithm to detect community structure in complex networks the algorithm is based on spectral methods and takes into account weights and link orientation since the method detects efficiently clustered nodes in large networks even when these are not sharply partitioned it turns to be specially suitable for the analysis of social and information networks we test the algorithm on a large scale data set from a psychological experiment of word association in this case it proves to be successful both in clustering words and in uncovering mental association patterns

effect of random edge failure on the average path length we study the effect of random removal of edges on the average path length apl in a large class of uncorrelated random networks in which vertices are characterized by hidden variables controlling the attachment of edges between pairs of vertices a formula for approximating the apl of networks suffering random edge removal is derived first then the formula is confirmed by simulations for classical er erdos and renyi random graphs ba barabasi and albert networks networks with exponential degree distributions as well as random networks with asymptotic power law degree distributions with exponent 2

network robustness and random processes abstract we introduce two new measures of network robustness and apply them to four different strategies the measures are independent from the number of nodes in the network and have the strong potential to cover a large portfolio of applications using the monte carlo methods we demonstrate how to approximate the measures the methods are based on random interruption of links with suitable constraints which represent the above mentioned strategies we introduce two networks with obvious varying robustness to demonstrate the measures we also demonstrate how to employ the measures in order to improve the robustness of the networks by adding one new link we further indicate that the measures are able to identify the infrequently connected parts of the network and suggest the most appropriate improvement we also discuss the consequences of the obtained results and the possible applications of the measures

inverse stable sampled low pass systems it is shown that for low pass systems the fractional order hold and the pulse amplitude modulation signal reconstruction methods produce an inverse stable sampled transfer function h z in some cases when zero order hold fails to do so therefore they may be desirable alternatives to the zero order hold reconstruction in certain control problems the problem of how well h z models the continuous g s is also discussed

dynamics of two van der pol oscillators coupled via a bath abstract in this work we study a system of two van der pol oscillators x and y coupled via a bath z x 1 x 2 x x k z x y 1 y 2 y y k z y z k x z k y z we investigate the existence and stability of the in phase and out of phase modes for parameters 0 and k 0 to this end we use floquet theory and numerical integration surprisingly our results show that the out of phase mode exists and is stable for a wider range of parameters than the in phase mode this behavior is compared to that of two directly coupled van der pol oscillators and it is shown that the effect of the bath is to reduce the stability of the in phase mode we also investigate the occurrence of other periodic motions by using bifurcation theory and the auto bifurcation and continuation software package our motivation for studying this system comes from the presence of circadian rhythms in the chemistry of the eyes we present a simplified model of a circadian oscillator which shows that it can be modeled as a van der pol oscillator in our model although there is no direct connection between the two eyes they can influence each other by affecting the concentration of melatonin in the bloodstream which is represented by the bath

enhancing neural network performance via assortativity the performance of attractor neural networks has been shown to depend crucially on the heterogeneity of the underlying topology we take this analysis a step further by examining the effect of degree degree correlations assortativity on neural network behavior we make use of a method recently put forward for studying correlated networks and dynamics thereon both analytically and computationally which is independent of how the topology may have evolved we show how the robustness to noise is greatly enhanced in assortative positively correlated neural networks especially if it is the hub neurons that store the information

brief paper generalized sampled data hold functions with asymptotic zero order hold behavior and polynomic reconstruction we present a generalized sampled data hold function that combines arbitrary z domain zero placement ability with zero order hold behavior under constant input thus exhibiting minimal intersample ripple by design our hold can be regarded as a generalization of the fractional order hold with a polynomial instead of a simple linear pattern and therefore with as many tuning parameters as desired moreover the polynomial approach turns out to provide a simple mechanism of control energy minimization among other benefits all these features help to achieve qualitatively better perfect model referencing because problematic sampling z zeros or the intersample issues of the conventional generalized holds need no longer be endured

limiting zeros of decouplable mimo systems for sufficiently rapid zero order hold zoh sampling it is known that the zeros of single input single output discrete time systems expressed in the forward shift operator converge to values determined only by the degrees of the finite and infinite zeros of the underlying continuous time system in this paper it is shown how this result can be generalized to multi input multi output mimo systems decouplable by static state feedback equivalently having a diagonal interactor matrix in the fast sampling limit the authors show how invariant and infinite zero structure is mapped under zoh sampling for discrete time systems expressed in either the delta forward difference or forward shift operators

on girth conditioning for low density parity check codes low density parity check ldpc codes are gaining interest for high data rate applications in both terrestrial and spatial communications they can be designed and studied through a bipartite graph whose characteristics affect the performance this paper proposes a low complexity method to improve the performance of ldpc codes by selectively removing some cycles from the associated bipartite graph the method is based on a modified version of the breadth first search bfs algorithm that we call modified bfs mbfs which is applied to find cycles and a greedy procedure to eliminate them throughout the paper we will give a detailed description of the algorithm proposed and analytically study its complexity simulation results show that this girth conditioning method applied to some classes of codes whose structure allows further optimization can lead to a significative complexity reduction and a performance improvements with respect to other methods

on sampled data models for nonlinear systems models for deterministic continuous time nonlinear systems typically take the form of ordinary differential equations to utilize these models in practice invariably requires discretization in this paper we show how an approximate sampled data model can be obtained for deterministic nonlinear systems such that the local truncation error between the output of this model and the true system is of order spl delta sup r 1 where spl delta is the sampling period and r is the system relative degree the resulting model includes extra zero dynamics which have no counterpart in the underlying continuous time system the ideas presented here generalize well known results for the linear case we also explore the implications of these results in nonlinear system identification

quasicyclic low density parity check codes from circulant permutation matrices in this correspondence the construction of low density parity check ldpc codes from circulant permutation matrices is investigated it is shown that such codes cannot have a tanner graph representation with girth larger than 12 and a relatively mild necessary and sufficient condition for the code to have a girth of 6 8 10 or 12 is derived these results suggest that families of ldpc codes with such girth values are relatively easy to obtain and consequently additional parameters such as the minimum distance or the number of redundant check sums should be considered to this end a necessary condition for the codes investigated to reach their maximum possible minimum hamming distance is proposed

scale free networks from varying vertex intrinsic fitness a new mechanism leading to scale free networks is proposed in this letter it is shown that in many cases of interest the connectivity power law behavior is neither related to dynamical properties nor to preferential attachment assigning a quenched fitness value x i to every vertex and drawing links among vertices with a probability depending on the fitnesses of the two involved sites gives rise to what we call a good get richer mechanism in which sites with larger fitness are more likely to become hubs i e to be highly connected

entropy of network ensembles in this paper we generalize the concept of random networks to describe network ensembles with nontrivial features by a statistical mechanics approach this framework is able to describe undirected and directed network ensembles as well as weighted network ensembles these networks might have nontrivial community structure or in the case of networks embedded in a given space they might have a link probability with a nontrivial dependence on the distance between the nodes these ensembles are characterized by their entropy which evaluates the cardinality of networks in the ensemble in particular in this paper we define and evaluate the structural entropy i e the entropy of the ensembles of undirected uncorrelated simple networks with given degree sequence we stress the apparent paradox that scale free degree distributions are characterized by having small structural entropy while they are so widely encountered in natural social and technological complex systems we propose a solution to the paradox by proving that scale free degree distributions are the most likely degree distribution with the corresponding value of the structural entropy finally the general framework we present in this paper is able to describe microcanonical ensembles of networks as well as canonical or hidden variable network ensembles with significant implications for the formulation of network constructing algorithms

technical communique nyquist stability criterion of intrinsic zeros for continuous time pure imaginary zeros this note treats a stability condition of the zeros of sampled systems corresponding to continuous time pure imaginary zeros with multiplicity one for systems with the relative degree one it is shown that the nyquist plot can be used to check the stability condition

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

design of a stable state feedback controller based on the multirate sampling of the plant output a new type of controller is proposed which detects the ith plant output n sub i times during a period of t sub 0 and changes the plant inputs once during t sub 0 it is shown that an arbitrary state feedback can be realized by such controllers if the plant is observable this implies for instance that arbitrary symmetric pole assignment is possible if the plant is controllable it is also shown that if the plant has no zeros at the origin the state transition matrix of the controller itself can be set arbitrarily without changing the state feedback to be realized that is to say inversely expressed any state feedback can be equivalently realized by a controller with any prescribed degree of stability

entropic origin of disassortativity in complex networks why are most empirical networks with the prominent exception of social ones generically degree degree anticorrelated to answer this long standing question we define the ensemble of correlated networks and obtain the associated shannon entropy maximum entropy can correspond to either assortative correlated or disassortative anticorrelated configurations but in the case of highly heterogeneous scale free networks a certain disassortativity is predicted offering a parsimonious explanation for the question above our approach provides a neutral model from which in the absence of further knowledge regarding network evolution one can obtain the expected value of correlations when empirical observations deviate from the neutral predictions as happens for social networks one can then infer that there are specific correlating mechanisms at work

class of correlated random networks with hidden variables we study a class of models of correlated random networks in which vertices are characterized by hidden variables controlling the establishment of edges between pairs of vertices we find analytical expressions for the main topological properties of these models as a function of the distribution of hidden variables and the probability of connecting vertices the expressions obtained are checked by means of numerical simulations in a particular example the general model is extended to describe a practical algorithm to generate random networks with an a priori specified correlation structure we also present an extension of the class to map nonequilibrium growing networks to networks with hidden variables that represent the time at which each vertex was introduced in the system

improvement of stability of zeros in discrete time multivariable systems using fractional order hold this paper is concerned with the stability of zeros of the discrete time multivariable systems composed of a fractional order hold froh a continuous time plant and a sampler in cascade the properties of the limiting zeros are studied and a condition for obtaining stable zeros for sufficiently small sampling periods is derived an approximate fractional order hold afroh is proposed as an implementation of froh it is shown that the afroh as well as the froh can locate the zeros of discrete time multivariable systems inside the stable region and improve stability properties when the zero order hold zoh cannot experimental results of adaptive control with afroh demonstrate a significant improvement of control performance compared with the use of a zoh

on the stabilization of discrete system zeros the stabilization of discrete system zeros is commonly achieved by allowing the input pattern to deviate from zero order hold zoh in this paper we show that this design technique may not be practical at small sampling times when the continuous system has unstable zero s deviation of the input pattern from zoh may also cause undesirable fluctuation in the inter sampling time output in order to reduce this effect we present a method which uses linear quadratic optimization for the determination of suitable zero locations

network growth by copying we introduce a growing network model in which a new node attaches to a randomly selected node as well as to all ancestors of the target node this mechanism produces a sparse ultrasmall network where the average node degree grows logarithmically with network size while the network diameter equals 2 we determine basic geometrical network properties such as the size dependence of the number of links and the in and out degree distributions we also compare our predictions with real networks where the node degree also grows slowly with time the internet and the citation network of all physical review papers

covariance correlation matrix and the multiscale community structure of networks empirical studies show that real world networks often exhibit multiple scales of topological descriptions however it is still an open problem how to identify the intrinsic multiple scales of networks in this paper we consider detecting the multiscale community structure of network from the perspective of dimension reduction according to this perspective a covariance matrix of network is defined to uncover the multiscale community structure through the translation and rotation transformations it is proved that the covariance matrix is the unbiased version of the well known modularity matrix we then point out that the translation and rotation transformations fail to deal with the heterogeneous network which is very common in nature and society to address this problem a correlation matrix is proposed through introducing the rescaling transformation into the covariance matrix extensive tests on real world and artificial networks demonstrate that the correlation matrix significantly outperforms the covariance matrix identically the modularity matrix as regards identifying the multiscale community structure of network this work provides a novel perspective to the identification of community structure and thus various dimension reduction methods might be used for the identification of community structure through introducing the correlation matrix we further conclude that the rescaling transformation is crucial to identify the multiscale community structure of network as well as the translation and rotation transformations

design of efficiently encodable moderate length high rate irregular ldpc codes this paper presents a new class of irregular low density parity check ldpc codes of moderate length 10 sup 3 spl les n spl les 10 sup 4 and high rate r spl ges 3 4 codes in this class admit low complexity encoding and have lower error rate floors than other irregular ldpc code design approaches it is also shown that this class of ldpc codes is equivalent to a class of systematic serial turbo codes and is an extension of irregular repeat accumulate codes a code design algorithm based on the combination of density evolution and differential evolution optimization with a modified cost function is presented moderate length high rate codes with no error rate floors down to a bit error rate of 10 sup 9 are presented although our focus is on moderate length high rate codes the proposed coding scheme is applicable to irregular ldpc codes with other lengths and rates

a novel approach to stable zero dynamics of sampled data models for nonlinear systems in backward triangle sample and hold case abstract it is well known that a good approximate sampled data model is very important in sampled data controller design of nonlinear continuous time system because the exact sampled data model of nonlinear continuous time system is often unavailable it is also a truth that unstable zero dynamics of sampled data model greatly limit the control performance of the system this paper investigates the properties of approximate sampled data model and its zero dynamics which generated during the process of discretization with backward triangle sample and hold btsh further a more accurate sampled data model is obtained for nonlinear systems in btsh case the zero dynamics form and stable conditions are also derived finally numerical examples are provided to better show the results developed in this paper

zero pearson coefficient for strongly correlated growing trees we obtained pearson s coefficient of strongly correlated recursive networks growing by preferential attachment of every new vertex by m edges we found that the pearson coefficient is exactly zero in the infinite network limit for the recursive trees m 1 if the number of connections of new vertices exceeds one mg1 then the pearson coefficient in the infinite networks equals zero only when the degree distribution exponent ensuremath gamma does not exceed 4 we calculated the pearson coefficient for finite networks and observed a slow power law like approach to an infinite network limit our findings indicate that pearson s coefficient strongly depends on size and details of networks which makes this characteristic virtually useless for quantitative comparison of different networks

on approximate pulse transfer functions a systematic approach to a class of approximations to the pulse transfer function of a system consisting of a zero order hold and a linear continuous time plant is presented it is based on the asymptotic result of astrom hagander and sternby 1984 on zeros of sampled systems at high sampling rates and on the bilinear transformation since the number of intrinsic parameters does not change in the discretization process model matching control robust control and identification are suggested as possible areas of application superiority of the approximations considered over a spl delta operator based truncated approximation is shown the results are illustrated by an example

zero dynamics of sampled nonlinear systems abstract the behaviour of the zero dynamics of a discrete time system obtained when sampling a continuous time nonlinear system is studied we give a result which generalizes the known behaviour of the zeros of a sampled linear system for small time intervals

mean field diffusive dynamics on weighted networks diffusion is a key element of a large set of phenomena occurring on natural and social systems modeled in terms of complex weighted networks here we introduce a general formalism that allows to easily write down mean field equations for any diffusive dynamics on weighted networks we also propose the concept of annealed weighted networks in which such equations become exact we show the validity of our approach addressing the problem of the random walk process pointing out a strong departure of the behavior observed in quenched real scale free networks from the mean field predictions additionally we show how to employ our formalism for more complex dynamics our work sheds light on mean field theory on weighted networks and on its range of validity and warns about the reliability of mean field results for complex dynamics

on the distribution of surface extrema in several one and two dimensional random landscapes we study here a standard next nearest neighbor nnn model of ballistic growth on one and two dimensional substrates focusing our analysis on the probability distribution function p m l of the number m of maximal points i e local peaks of growing surfaces our analysis is based on two central results i the proof presented here of the fact that uniform one dimensional ballistic growth process in the steady state can be mapped onto rise and descent sequences in the ensemble of random permutation matrices and ii the fact established in ref g oshanin and r voituriez j phys a math gen 37 6221 2004 that different characteristics of rise and descent patterns in random permutations can be interpreted in terms of a certain continuous space hammersley type process for one dimensional system we compute p m l exactly and also present explicit results for the correlation function characterizing the enveloping surface for surfaces grown on 2d substrates we pursue similar approach considering the ensemble of permutation matrices with long ranged correlations determining exactly the first three cumulants of the corresponding distribution function we define it in the scaling limit using an expansion in the edgeworth series and show that it converges to a gaussian function as l

technical communique comparing digital implementation via the bilinear and step invariant transformations from an analog system k digital systems k d and k b t are often obtained via the step invariant and bilinear transformations respectively for the case when k is stable it is shown that under certain conditions k b t converges to k d in p induced norms as the sampling period tends to zero for 1