estimation and control of systems with unknown covariance and multiplicative noise the problem of estimation and control for systems with multiplicative noise and unknown second order statistics is considered conditions are found for the existence of a solution based on game theoretic ideas the conditions for the existence of a saddle point for the time invariant filtering problem are necessary and sufficient whereas for all other cases only necessary the central idea of the solution is to convert the stochastic problem to a deterministic optimal control problem whose minimax point is sought with respect to the control filter and unknown statistics parameters the results that are derived show that the problem of estimation for systems with unknown covariances depends on the costate matrix which in turn is a function of the performance measure thus the filter loses one of its best known properties that of independence of the performance functional this property holds not only for the classical kalman filter but also for multiplicative systems

brief robust h filtering for uncertain impulsive stochastic systems under sampled measurements this paper is concerned with the problem of robust h filtering for uncertain impulsive stochastic systems under sampled measurements the parameter uncertainties are assumed to be time varying norm bounded the aim is to design a stochastically stable filter using the locally sampled measurements which ensures both the robust stochastic stability and a prescribed level of h performance for the filtering error dynamics for all admissible uncertainties a sufficient condition for the existence of such a filter is proposed in terms of certain linear matrix inequalities lmis when these lmis are feasible an explicit expression of a desired filter is given an example is provided to demonstrate the effectiveness of the proposed approach

how community structure influences epidemic spread in social networks abstract two key features of social networks are the community structure and the high clustering coefficient for understanding their influences on dynamical processes we present a model with both an adjustable clustering coefficient and an adjustable degree of community this model has an invariant degree distribution when its clustering coefficient is being adjusted we find that the efficiency of epidemic spreading in this model depends mainly on the degree of community and decreases with increase of the degree of community for a fixed degree of community the efficiency will decrease with increase of the clustering coefficient numerical simulations have confirmed the theoretic analysis

models of social networks based on social distance attachment we propose a class of models of social network formation based on a mathematical abstraction of the concept of social distance social distance attachment is represented by the tendency of peers to establish acquaintances via a decreasing function of the relative distance in a representative social space we derive analytical results corroborated by extensive numerical simulations showing that the model reproduces the main statistical characteristics of real social networks large clustering coefficient positive degree correlations and the emergence of a hierarchy of communities the model is confronted with the social network formed by people that shares confidential information using the pretty good privacy pgp encryption algorithm the so called web of trust of pgp

robust l_ infty induced filtering and control of stochastic systems with state multiplicative noise linear continuous time systems with stochastic uncertainties in their state space model are considered the problems of induced l state feedback control and filtering are solved for the stationary case in both problems the cost function is defined to be the expected value of the standard induced l performance index with respect to the uncertain parameters an example that demonstrates the applicability of the theory is given

a stochastic model for internal hiv dynamics in this paper we analyse a stochastic model representing hiv internal virus dynamics the stochasticity in the model is introduced by parameter perturbation which is a standard technique in stochastic population modelling we show that the model established in this paper possesses non negative solutions as this is essential in any population dynamics model we also carry out analysis on the asymptotic behaviour of the model we approximate one of the variables by a mean reverting process and find out the mean and variance of this process numerical simulations conclude the paper

a stabilization algorithm for a class of uncertain linear systems abstract this paper presents an algorithm for the stabilization of a class of uncertain linear systems the uncertain systems under consideration are described by state equations which depend on time varying unknown but bounded uncertain parameters the construction of the stabilizing controller involves solving a certain algebraic riccati equation furthermore the solution to this riccati equation defines a quadratic lyapunov function which is used to establish the stability of the closed loop system this leads to a notion of quadratic stabilizability it is shown that the stabilization procedure will succeed if and only if the given uncertain linear system is quadratically stabilizable the paper also deals with a notion of overbounding for uncertain linear systems this procedure enables the stabilization algorithm to be applied to a larger class of uncertain linear systems also included in the paper are results which indicate the degree of conservativeness introduced by this overbounding process

linear filtering for bilinear stochastic differential systems with unknown inputs investigates the problem of state estimation for bilinear stochastic multivariable differential systems in the presence of an additional disturbance whose statistics are completely unknown a linear filter is proposed based on a suitable decomposition of the state of the bilinear system into two components the first one is a computable function of the observations while the second component is estimated via a suitable linear filtering algorithm no a priori information on the disturbance is required for the filter implementation the proposed filter is robust with respect to the unknown input in that the covariance of the estimation error is not affected by such input numerical simulations show the effectiveness of the proposed filter

extinction time for stochastic population models the analysis of interacting population models is the subject of much interest in mathematical ecology moreover the persistence and extinction of these models is one of the most interesting and important topics because it provides insight into their behavior the mean extinction time for stochastic population models considered in this paper depends on the initial population size and satisfies a stationary partial differential equation related to the backward kolmogorov differential equation a linear second order partial differential equation with variable coefficients in this communication we review several papers where we have proposed some numerical techniques in order to estimate the mean extinction time for stochastic population models besides we will compare the theoretical predictions and numerical simulations for stochastic differential equations sdes this work can be viewed as a unified review of the contributions de la hoz and vadillo 2012 de la hoz et al 2014 and doubova and vadillo 2014

an evolving model of online bipartite networks abstract understanding the structure and evolution of online bipartite networks is a significant task since they play a crucial role in various e commerce services nowadays recently various attempts have been tried to propose different models resulting in either power law or exponential degree distributions however many empirical results show that the user degree distribution actually follows a shifted power law distribution the so called mandelbrot s law which cannot be fully described by previous models in this paper we propose an evolving model considering two different user behaviors random and preferential attachment extensive empirical results on two real bipartite networks delicious and citeulike show that the theoretical model can well characterize the structure of real networks for both user and object degree distributions in addition we introduce a structural parameter p to demonstrate that the hybrid user behavior leads to the shifted power law degree distribution and the region of power law tail will increase with the increment of p the proposed model might shed some lights in understanding the underlying laws governing the structure of real online bipartite networks

robust h sub spl infin filtering of stationary continuous time linear systems with stochastic uncertainties the problem of applying h sub spl infin filters on stationary continuous time linear systems with stochastic uncertainties in the state space signal model is addressed these uncertainties are modeled via white noise processes the relevant cost function is the expected value of the standard h sub spl infin performance index with respect to the uncertain parameters the solution is obtained via a stochastic bounded real lemma that results in a modified riccati inequality this inequality is expressed in the form of a linear matrix inequality whose solution provides the filter parameters the method proposed is also applied to the case where in addition to the stochastic uncertainty other deterministic parameters of the system are not perfectly known and are assumed to lie in a given polytope the problem of mixed h sub 2 h sub spl infin filtering for the above system is also treated the theory developed is demonstrated by a practical example

on uniform observation of nonuniformly observable systems abstract in 4 7 9 12 classes of nonlinear systems are considered for which observers can be designed although observability of nonlinear systems is known to be dependent on the input the proposed observers have the property that the estimation error decays to zero irrespective of the input in the first part of this paper it is shown that this phenomenon follows from a common property of these systems for all of them the unobservable states with respect to some input are in some sense stable in the linear case these systems are called detectable and for this reason a reduced order observer can be designed in the second part is given a more general class of nonlinear systems for which such an observer can be designed

the observer follower filter a new approach to nonlinear suboptimal filtering this paper investigates the state estimation problem for a class of stochastic nonlinear differential systems a novel algorithm is proposed denoted as observer follower filter off based on a two steps mixed approach the first step makes use of a high gain observer based estimator for nonlinear systems applied to the system equations in order to provide the trajectory around which a n degree carleman approximation of the stochastic differential system is achieved second step in principle any other high gain estimator can be used but in this note we prove that the one here proposed provides a bounded mean square error numerical simulations show the effectiveness of the proposed methodology and the improvements of the off with respect to the standard extended kalman bucy filter ekbf obtained by increasing the order of the carleman approximation

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

an existence theorem for observers of bilinear systems under suitable uniformity assumptions the existence of nonlinear state observers with exponentially decaying error for bilinear systems is proved to be equivalent to that of observers whose corresponding error dynamics is linear with respect to the error

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

generating multi scaling networks with two types of vertices abstract a variety of scale free networks have been created since the pioneer work by barabasi and albert science 286 1999 509 most of these models are homogeneous since they are composed of the same kind of nodes in the realistic world however elements nodes or vertices in the network may play different roles or have different functions in this work we develop an alternative way of vertex classification other than the ordinary modularity method by introducing two types of vertices the interaction between two neighbor vertices is dependent on their types it is found that the vertex degree exhibits a multi scaling law distribution with the scaling exponent of each types of vertex adjustable this network model may exhibit some interesting properties concerning the dynamical processes on it

organization of modular networks we examine the global organization of heterogeneous equilibrium networks consisting of a number of well distinguished interconnected parts char22 communities or modules we develop an analytical approach allowing us to obtain the statistics of connected components and the intervertex distance distribution in these modular networks and to describe their global organization and structure in particular we study the evolution of the intervertex distance distribution with an increasing number of interlinks connecting two infinitely large uncorrelated networks we demonstrate that even a relatively small number of shortcuts unite the networks into one in more precise terms if the number of interlinks is any finite fraction of the total number of connections then the intervertex distance distribution approaches a ensuremath delta function peaked form and so the network is united

transitivity and degree assortativity explained the bipartite structure of social networks dynamical processes such as the diffusion of knowledge opinions pathogens fake news innovation and others are highly dependent on the structure of the social network in which they occur however questions on why most social networks present some particular structural features namely high levels of transitivity and degree assortativity when compared to other types of networks remain open first we argue that every one mode network can be regarded as a projection of a bipartite network and we show that this is the case using two simple examples solved with the generating functions formalism second using synthetic and empirical data we reveal how the combination of the degree distribution of both sets of nodes of the bipartite network together with the presence of cycles of lengths four and six explain the observed values of transitivity and degree assortativity coefficients in the one mode projected network bipartite networks with top node degrees that display a more right skewed distribution than the bottom nodes result in highly transitive and degree assortative projections especially if a large number of small cycles are present in the bipartite structure

interpersonal interactions and human dynamics in a large social network we study a large social network consisting of over 10 6 individuals who form an internet community and organize themselves in groups of different sizes on the basis of the users list of friends and other data registered in the database we investigate the structure and time development of the network the structure of this friendship network is very similar to the structure of different social networks however here a degree distribution exhibiting two scaling regimes power law for low connectivity and exponential for large connectivity was found the groups size distribution and distribution of number of groups of an individual have power law form we found very interesting scaling laws concerning human dynamics our research has shown how long people are interested in a single task

exploring the assortativity clustering space of a network s degree sequence nowadays there is a multitude of measures designed to capture different aspects of network structure to be able to say if a measured value is expected or not one needs to compare it with a refere

efficient sampling of complex network with modified random walk strategies abstract we present two novel random walk strategies choosing seed node csn random walk and no retracing nr random walk different from the classical random walk sampling the csn and nr strategies focus on the influences of the seed node choice and path overlap respectively three random walk samplings are applied in the erdos renyi er barabasi albert ba watts strogatz ws and the weighted usair networks respectively then the major properties of sampled subnets such as sampling efficiency degree distributions average degree and average clustering coefficient are studied the similar conclusions can be reached with these three random walk strategies firstly the networks with small scales and simple structures are conducive to the sampling secondly the average degree and the average clustering coefficient of the sampled subnet tend to the corresponding values of original networks with limited steps and thirdly all the degree distributions of the subnets are slightly biased to the high degree side however the nr strategy performs better for the average clustering coefficient of the subnet in the real weighted usair networks some obvious characters like the larger clustering coefficient and the fluctuation of degree distribution are reproduced well by these random walk strategies

what is the dimension of citation space abstract citation networks represent the flow of information between agents they are constrained in time and so form directed acyclic graphs which have a causal structure here we provide novel quantitative methods to characterise that structure by adapting methods used in the causal set approach to quantum gravity by considering the networks to be embedded in a minkowski spacetime and measuring its dimension using myrheim meyer and midpoint scaling estimates we illustrate these methods on citation networks from the arxiv supreme court judgements from the usa and patents and find that otherwise similar citation networks have measurably different dimensions we suggest that these differences can be interpreted in terms of the level of diversity or narrowness in citation behaviour

origin of degree correlations in the internet and other networks it has been argued that the observed anticorrelation between the degrees of adjacent vertices in the network representation of the internet has its origin in the restriction that no two vertices have more than one edge connecting them here we propose a formalism for modeling ensembles of graphs with single edges only and derive values for the exponents and correlation coefficients characterizing them our results confirm that the conjectured mechanism does indeed give rise to correlations of the kind seen in the internet although only a part of the measured correlation can be accounted for in this way

small world properties emerge in highly compartmentalized networks with intermediate group sizes and numbers many recent studies have focused on two statistical properties observed in diverse real world networks the small world property and compartmentalization d j watts and s h strogatz nature 393 440 1998 m girvan and m e j newman proc natl acad sci 99 7821 2002 models that include group affiliations have been shown to produce networks with high clustering coefficients a necessary condition for small world properties m e j newman phys rev e 68 026121 2003 m e j newman and j park phys rev e 68 036122 2003 however the consequences of varying the number and size of groups in a network are not well understood in order to investigate the consequences of group organization we examined sets of networks that varied simultaneously in the size and number of groups while maintaining the same overall size and average degree here we show that the small world property arises in maximally compartmentalized and clustered networks that occur in the intermediate region between few very large groups and many very small groups

two walks degree assortativity in graphs and networks degree assortativity is the tendency for nodes of high degree resp low degree in a graph to be connected to high degree nodes resp to low degree ones it is usually quantified by the pearson correlation coefficient of the degreedegree correlation here we extend this concept to account for the effect of second neighbours to a given node in a graph that is we consider the two walks degree of a node as the sum of all the degrees of its adjacent nodes the two walks degree assortativity of a graph is then the pearson correlation coefficient of the two walks degreedegree correlation we found here analytical expression for this two walks degree assortativity index as a function of contributing subgraphs we then study all the 261 000 connected graphs with 9 nodes and observe the existence of assortativeassortative and disassortativedisassortative graphs according to degree and two walks degree respectively more surprisingly we observe a class of graphs which are degree disassortative and two walks degree assortative we explain the existence of some of these graphs due to the presence of certain topological features such as a node of low degree connected to high degree ones more importantly we study a series of 49 real world networks where we observe the existence of the disassortativeassortative class in several of them in particular all biological networks studied here were in this class we also conclude that no graphs networks are possible with assortativedisassortative structure

highly clustered scale free networks we propose a model for growing networks based on a finite memory of the nodes the model shows stylized features of real world networks power law distribution of degree linear preferential attachment of new links and a negative correlation between the age of a node and its link attachment rate notably the degree distribution is conserved even though only the most recently grown part of the network is considered as the network grows the clustering reaches an asymptotic value larger than that for regular lattices of the same average connectivity and similar to the one observed in the networks of movie actors coauthorship in science and word synonyms these highly clustered scale free networks indicate that memory effects are crucial for a correct description of the dynamics of growing networks

stochastic stabilization and destabilization it is shown in this paper that any nonlinear systems dot x t f x t t in rd can be stabilized by brownian motion provided f hook x t k x for some k 0 on the other hand this system can also be destabilized by brownian motion if the dimension d 2 similar results are also obtained for any given stochastic differential equation dx t f hook x t t g x t t dw t

network formation determined by the diffusion process of random walkers we studied the diffusion process of random walkers in networks formed by their traces this model considers the rise and fall of links determined by the frequency of transports of random walkers in order to examine the relation between the formed network and the diffusion process a situation in which multiple random walkers start from the same vertex is investigated the difference in diffusion rate of random walkers according to the difference in dimension of the initial lattice is very important for determining the time evolution of the networks for example complete subgraphs can be formed on a one dimensional lattice while a graph with a power law vertex degree distribution is formed on a two dimensional lattice we derived some formulae for predicting network changes for the 1d case such as the time evolution of the size of nearly complete subgraphs and conditions for their collapse the networks formed on the 2d lattice are characterized by the existence of clusters of highly connected vertices and their life time as the life time of such clusters tends to be small the exponent of the power law distribution changes from 1 2 to 3

revealing the efficiency of information diffusion in online social networks of microblog abstract online social networks osns such as microblogs enable people to simultaneously share information with a large number of peers and revealing the properties of the formed network structure and the corresponding impacts on information diffusion are important in this article we empirically study 10 millions user profiles from the largest chinese mircoblog sina weibo and 41 7 millions profiles from twitter by studying followers topology we find an invariant characteristic that the followers count of users obeys a power law distribution with exponent near 2 we then investigate the reason from the theoretical view and find this network structure achieves the optimal information diffusion in terms of inducing a minimal propagation times our study thus reveals the efficiency of information diffusion in osns of microblogs which is validated by experimental examination theoretical analysis and numerical simulation

epidemic outbreaks in growing scale free networks with local structure abstract the class of generative models has already attracted considerable interest from researchers in recent years and much expanded the original ideas described in ba model most of these models assume that only one node per time step joins the network in this paper we grow the network by adding n interconnected nodes as a local structure into the network at each time step with each new node emanating m new edges linking the node to the preexisting network by preferential attachment this successfully generates key features observed in social networks these include power law degree distribution p k k 3 where n 1 m is a tuning parameter defined as the modularity strength of the network nontrivial clustering assortative mixing and modular structure moreover all these features are dependent in a similar way on the parameter we then study the susceptible infected epidemics on this network with identical infectivity and find that the initial epidemic behavior is governed by both of the infection scheme and the network structure especially the modularity strength the modularity of the network makes the spreading velocity much lower than that of the ba model on the other hand increasing the modularity strength will accelerate the propagation velocity

evolving networks with distance preferences we study evolving networks where new nodes when attached to the network form links with other nodes of preferred distances a particular case is where always the shortest distances are selected make friends with the friends of your present friends we present simulation results for network parameters like the first eigenvalue of the graph laplacian synchronizability clustering coefficients average distances and degree distributions for different distance preferences and compare them with the parameter values for random and scale free networks we find that for the shortest distance rule we obtain a power law degree distribution as in scale free networks while the other parameters are significantly different especially the clustering coefficient

diversity of graphs with highly variable connectivity a popular approach for describing the structure of many complex networks focuses on graph theoretic properties that characterize their large scale connectivity while it is generally recognized that such descriptions based on aggregate statistics do not uniquely characterize a particular graph and also that many such statistical features are interdependent the relationship between competing descriptions is not entirely understood this paper lends perspective on this problem by showing how the degree sequence and other constraints e g connectedness no self loops or parallel edges on a particular graph play a primary role in dictating many features including its correlation structure building on recent work we show how a simple structural metric characterizes key differences between graphs having the same degree sequence more broadly we show how the often implicit choice of a background set against which to measure graph features has serious implications for the interpretation and comparability of graph theoretic descriptions

filtering of nonlinear stochastic feedback systems this paper concerns the filtering problem for a class of stochastic nonlinear systems where the drift term may depend either on some external function open loop system or on the system output closed loop system through a controller such systems are denoted feedback systems the following result is proven for feedback systems the optimal filter in the open loop case remains optimal when the feedback is closed the proof is obtained by showing equivalence of suitable expressions for the estimators of the open loop and closed loop systems obtained using the kallianpur striebel formula g kallianpur and c striebel ann math statist 39 1968 pp 785 801

a decoupled approach to filter design for stochastic systems abstractthis paper presents a new theorem to guarantee the almost sure exponential stability for a class of stochastic triangular systems by studying only the stability of each diagonal subsystems this result allows to solve the filtering problem of the stochastic systems with multiplicative noises by using the almost sure exponential stability concept two kinds of observers are treated the full order and reduced order cases

survey paper a partial history of the early development of continuous time nonlinear stochastic systems theory this article is a survey of the early development of selected areas in nonlinear continuous time stochastic control key developments in optimal control and the dynamic programming principle existence of optimal controls under complete and partial observations nonlinear filtering stochastic stability the stochastic maximum principle and ergodic control are discussed issues concerning wide bandwidth noise for stability modeling filtering and ergodic control are dealt with the focus is on the earlier work but many important topics are omitted for lack of space

absolute stabilization and minimax optimal control of uncertain systems with stochastic uncertainty this paper is concerned with existence and optimality properties of so called guaranteed cost controllers for an uncertain system subject to structured uncertainty the uncertainty in the system is assumed to have a stochastic character and to satisfy certain stochastic integral constraints it is shown that a minimax optimal guaranteed cost state feedback controller for a stochastic system can be synthesized as a state feedback controller absolutely stabilizing this system for each initial state of the system this controller can be found by parametric optimization of solutions of a parameter dependent generalized matrix riccati equation arising in stochastic h infty theory

linearized reduced order filtering a reduced order version of extended kalman filtering is presented in which both the filtering equation and the associated riccati equation have been reduced in dimension to allow for real time processing the procedure for designing the reduced order filter is similar to that for designing the extended kalman filter the same approximations being applied one technique useful for limiting the computational burden in a linearized filter design problems is presented and illustrated by an example the primary limitation of the result is that the nonlinearity must be in terms of the vector to be estimated

brief paper h functional filtering for stochastic bilinear systems with multiplicative noises this paper deals with the design of a reduced order h filter for a stochastic bilinear system with a prescribed h norm criterion the considered system is bilinear in control and with multiplicative noises in the dynamics and in the measurement equations the problem is transformed into the search of a unique gain matrix by using sylvester like constraints the approach is based on the resolution of lmi and is then easily implementable

voter model dynamics in complex networks role of dimensionality disorder and degree distribution we analyze the ordering dynamics of the voter model in different classes of complex networks we observe that whether the voter dynamics orders the system depends on the effective dimensionality of the interaction networks we also find that when there is no ordering in the system the average survival time of metastable states in finite networks decreases with network disorder and degree heterogeneity the existence of hubs i e highly connected nodes in the network modifies the linear system size scaling law of the survival time the size of an ordered domain is sensitive to the network disorder and the average degree decreasing with both however it seems not to depend on network size and on the heterogeneity of the degree distribution

properties of highly clustered networks we propose and solve exactly a model of a network that has both a tunable degree distribution and a tunable clustering coefficient among other things our results indicate that increased clustering leads to a decrease in the size of the giant component of the network we also study susceptible infective recovered type epidemic processes within the model and find that clustering decreases the size of epidemics but also decreases the epidemic threshold making it easier for diseases to spread in addition clustering causes epidemics to saturate sooner meaning that they infect a near maximal fraction of the network for quite low transmission rates

a new b spline collocation method for singular integro differential equations of higher orders abstract two numerical schemes based on b spline collocation method are presented for approximate solution of the systems of singular integro differential equations of higher orders appearing in fracture problems with steigmann ogden surface energy it is shown that the resulting systems of linear equations are well conditioned and the numerical examples are in good agreement with known solutions although this paper is concerned with the numerical solution to the specific equations the proposed method can be easily generalized to a large class of singular integro differential equations

counting triangles in massive graphs with mapreduce graphs and networks are used to model interactions in a variety of contexts there is a growing need to quickly assess the characteristics of a graph in order to understand its underlying structure some of the most useful metrics are triangle based and give a measure of the connectedness of mutual friends this is often summarized in terms of clustering coefficients which measure the likelihood that two neighbors of a node are themselves connected computing these measures exactly for large scale networks is prohibitively expensive in both memory and time however a recent wedge sampling algorithm has proved successful in efficiently and accurately estimating clustering coefficients in this paper we describe how to implement this approach in mapreduce to deal with massive graphs we show results on publicly available networks the largest of which is 132m nodes and 4 7b edges as well as artificially generated networks using the graph500 benchmark the largest of which has 240m nodes and 8 5b edges

reduced order h sub spl infin filtering for stochastic systems this paper deals with the reduced order h sub spl infin filtering problem for stochastic systems necessary and sufficient conditions are obtained for the existence of solutions to the continuous time and discrete time problems in terms of certain linear matrix inequalities lmis and a coupling nonconvex rank constraint condition furthermore when these conditions are feasible an explicit parametrization of all desired reduced order filters corresponding to a feasible solution is given in particular when the reduced order filter is restricted to be a static one then simple conditions expressed by lmis only without any rank constraints are derived and a parametrization of all solutions is also given finally an illustrative example is provided to show the effectiveness of the proposed approach

on almost sure sample stability of nonlinear stochastic dynamic systems in this note an extension of khasminskii s theorem on almost sure stability of linear stochastic differential equations to a class of nonlinear stochastic differential equations is presented the necessary and sufficient conditions for almost sure stability are proved it is shown that in the second order case the stable region can be exactly determined by studying the singular boundaries of one dimensional diffusion processes the authors present a modified form of feller s criteria for classification of singular boundaries the new criteria are equivalent to and much simpler for applications than feller s criteria two examples of nonlinear stochastic dynamic systems with stable regions illustrate the application procedures

a new suboptimal approach to the filtering problem for bilinear stochastic differential systems the aim of this paper is to present a new approach to the filtering problem for the class of bilinear stochastic multivariable systems consisting in searching for suboptimal state estimates instead of the conditional statistics as a first result a finite dimensional optimal linear filter for the considered class of systems is defined then the more general problem of designing polynomial finite dimensional filters is considered the equations of a finite dimensional filter are given producing a state estimate which is optimal in a class of polynomial transformations of the measurements with arbitrarily fixed degree numerical simulations show the effectiveness of the proposed filter

cost effective campaigning in social networks campaigners are increasingly using online social networking platforms for promoting products ideas and information a popular method of promoting a product or even an idea is incentivizing individuals to evangelize the idea vigorously by providing them with referral rewards in the form of discounts cash backs or social recognition due to budget constraints on scarce resources such as money and manpower it may not be possible to provide incentives for the entire population and hence incentives need to be allocated judiciously to appropriate individuals for ensuring the highest possible outreach size we aim to do the same by formulating and solving an optimization problem using percolation theory in particular we compute the set of individuals that are provided incentives for minimizing the expected cost while ensuring a given outreach size we also solve the problem of computing the set of individuals to be incentivized for maximizing the outreach size for given cost budget the optimization problem turns out to be non trivial it involves quantities that need to be computed by numerically solving a fixed point equation our primary contribution is that for a fairly general cost structure we show that the optimization problems can be solved by solving a simple linear program we believe that our approach of using percolation theory to formulate an optimization problem is the first of its kind c 2016 elsevier b v all rights reserved

scaling behavior in probabilistic neuronal cellular automata we study a neural network model of interacting stochastic discrete two state cellular automata on a regular lattice the system is externally tuned to a critical point which varies with the degree of stochasticity or the effective temperature there are avalanches of neuronal activity namely spatially and temporally contiguous sites of activity a detailed numerical study of these activity avalanches is presented and single joint and marginal probability distributions are computed at the critical point we find that the scaling exponents for the variables are in good agreement with a mean field theory

exponential stability of large scale stochastic differential equations abstract given a large scale stochastic system described by a number of subsystems we introduce the corresponding isolated subsystems it is shown that the exponential stability of the isolated systems implies the exponential stability of the large scale system under some hypotheses added on the interconnected terms we also study a slightly special case where the large scale system is described in a hierarchical form i e the system consists of several subsystems and each subsystem interacts only with lower subsystems but not with higher subsystems

optimal unbiased filtering via linear matrix inequalities abstract solutions to the optimal h and l2 l unbiased reduced order filtering problems are obtained in terms of linear matrix inequalities lmis the order of the optimal filter is equal to the number of measurements both continuous and discrete time results are presented an explicit parametrization of all optimal unbiased filters is provided in terms of a free contractive matrix

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

brief paper almost sure exponential stabilisation of stochastic systems by state feedback control so far a major part of the literature on the stabilisation issues of stochastic systems has been dedicated to mean square stability this paper develops a new class of criteria for designing a controller to stabilise a stochastic system almost surely which is unable to be stabilised in mean square sense the results are expressed in terms of linear matrix inequalities lmis which are easy to be checked in practice by using matlab toolbox moreover the control structure in this paper appears not only in the drift part but also in the diffusion part of the underlying stochastic system

a note on observers for lipschitz nonlinear systems this note deals with the design of reduced order observers for lipschitz nonlinear systems it shows that the conditions under which a full order observer exists also guarantee the existence of a reduced order observer a design method of the reduced order observer that is dependent on the solution of the riccati equation is then presented and an example is given to illustrate effects of the design method

a family network model for wealth distribution in societies a model based on first degree family relations network is used to describe the wealth distribution in societies the network structure is not a priori introduced in the model it is generated in parallel with the wealth values through simple and realistic dynamical rules the model has two main parameters governing the wealth exchange in the network choosing their values realistically leads to wealth distributions in good agreement with measured data the cumulative wealth distribution function has an exponential behavior in the low and medium wealth limit and shows the pareto like power law tail for the upper 5 of the society the obtained pareto indexes are in good agreement with the measured ones the generated family networks also converge to a statistically stable topology with a simple poissonian degree distribution on this family network many interesting correlations are studied and the main factors leading to wealth diversification and the formation of the pareto law are identified

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

robust h reduced order filtering for uncertain bilinear systems this paper investigates both the h and robust h reduced order unbiased filtering problems for respectively a nominal bilinear system and a bilinear system affected by norm bounded structured uncertainties in all the system matrices first an algebraic framework is used to solve the unbiasedness condition and second a change of variable is introduced on the inputs of the system to reduce the conservatism inherent to the requirement of exponential convergence of the filter then the reduced order filtering solution is obtained through lmi with an equality constraint by transforming the problem into a robust state feedback in the nominal case and a robust static output feedback in the presence of uncertainties in the last case an additional bilinear matrix equality must also be solved

degree landscapes in scale free networks we generalize the degree organizational view of real world networks with broad degree distributions in a landscape analog with mountains high degree nodes and valleys low degree nodes for exam

why social networks are different from other types of networks we argue that social networks differ from most other types of networks including technological and biological networks in two important ways first they have nontrivial clustering or network transitivity and second they show positive correlations also called assortative mixing between the degrees of adjacent vertices social networks are often divided into groups or communities and it has recently been suggested that this division could account for the observed clustering we demonstrate that group structure in networks can also account for degree correlations we show using a simple model that we should expect assortative mixing in such networks whenever there is variation in the sizes of the groups and that the predicted level of assortative mixing compares well with that observed in real world networks

existence and design of functional observers for linear systems this paper presents straightforward derivations of the functional observers design for linear time invariant multivariable systems the order of these observers is equal to the dimension spl tau of the vector to be estimated necessary and sufficient conditions for the existence and stability of these observers are given illustrative examples are included

remarks on nonlinear adaptive observer design abstract a solution to the problem of state estimation for systems with unknown parameters is to use some on line adaptation of the observer parameters on the basis of various existing results for such adaptive observer designs a unifying adaptive observer form is proposed in this paper this form indeed emphasizes properties allowing some asymptotic state estimation in spite of unknown parameters as well as additional properties which further allow parameter estimation as an example it is shown how an adaptive observer can be designed for a class of state affine systems

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

robust h sub spl infin filtering for nonlinear stochastic systems this paper describes the robust h sub spl infin filtering analysis and synthesis of nonlinear stochastic systems with state and exogenous disturbance dependent noise we assume that the state and measurement are corrupted by stochastic uncertain exogenous disturbance and that the system dynamic is modeled by ito spl circ type stochastic differential equations for general nonlinear stochastic systems the h sub spl infin filter can be obtained by solving second order nonlinear hamilton jacobi inequalities when the worst case disturbance is considered in the design procedure a mixed h sub 2 h sub spl infin filtering problem is also solved by minimizing the total estimation error energy it is found that for a class of special nonlinear stochastic systems the h sub spl infin filtering design can be given via solving several linear matrix inequalities instead of hamilton jacobi inequalities a few examples show that the proposed methods are effective