fast and exact simulation of stationary gaussian processes through circulant embedding of the covariance matrix geostatistical simulations often require the generation of numerous realizations of a stationary gaussian process over a regularly meshed sample grid omega this paper shows that for many important correlation functions in geostatistics realizations of the associated process over m 1 equispaced points on a line can be produced at the cost of an initial fft of length 2m with each new realization requiring an additional fft of the same length in particular the paper first notes that if an m 1 times m 1 toeplitz correlation matrix r can be embedded in a nonnegative definite 2m times2m circulant matrix s exact realizations of the normal multivariate y sim cal n 0 r can be generated via ffts of length 2m theoretical results are then presented to demonstrate that for many commonly used correlation structures the minimal embedding in which m m is nonnegative definite extensions to simulations of stationary fields in higher dimensions are also provided and illustrated

the expectation hypothesis of interest rates and network theory the case of brazil abstract this paper investigates the topological properties of the brazilian term structure of interest rates network we build the minimum spanning tree mst which is based on the concept of ultrametricity using the correlation matrix for interest rates of different maturities we show that the short term interest rate is the most important within the interest rates network which is in line with the expectation hypothesis of interest rates furthermore we find that the brazilian interest rates network forms clusters by maturity

generalizations of the clustering coefficient to weighted complex networks the recent high level of interest in weighted complex networks gives rise to a need to develop new measures and to generalize existing ones to take the weights of links into account here we focus on various generalizations of the clustering coefficient which is one of the central characteristics in the complex network theory we present a comparative study of the several suggestions introduced in the literature and point out their advantages and limitations the concepts are illustrated by simple examples as well as by empirical data of the world trade and weighted coauthorship networks

exponential input to state stabilization of a class of diagonal boundary control systems with delay boundary control abstract this paper deals with the exponential input to state stabilization with respect to boundary disturbances of a class of diagonal infinite dimensional systems via delay boundary control the considered input delays are uncertain and time varying the proposed control strategy consists of a constant delay predictor feedback controller designed on a truncated finite dimensional model capturing the unstable modes of the original infinite dimensional system we show that the resulting closed loop system is exponentially input to state stable with fading memory of both additive boundary input perturbations and disturbances in the computation of the predictor feedback

funnel control in the presence of infinite dimensional internal dynamics abstract we consider output trajectory tracking for a class of uncertain nonlinear systems whose internal dynamics may be modelled by infinite dimensional systems which are bounded input bounded output stable we describe under which conditions these systems belong to an abstract class for which funnel control is known to be feasible as an illustrative example we show that for a system whose internal dynamics are modelled by a transport equation which is not exponentially stable we obtain prescribed performance of the tracking error

topological properties of hierarchical networks hierarchical networks are attracting a renewal interest for modeling the organization of a number of biological systems and for tackling the complexity of statistical mechanical models beyond mean field limitations here we consider the dyson hierarchical construction for ferromagnets neural networks and spin glasses recently analyzed from a statistical mechanics perspective and we focus on the topological properties of the underlying structures in particular we find that such structures are weighted graphs that exhibit a high degree of clustering and of modularity with a small spectral gap the robustness of such features with respect to the presence of thermal noise is also studied these outcomes are then discussed and related to the statistical mechanics scenario in full consistency last we look at these weighted graphs as markov chains and we show that in the limit of infinite size the emergence of ergodicity breakdown for the stochastic process mirrors the emergence of metastabilities in the corresponding statistical mechanical analysis

iss like estimates for nonlinear parabolic pdes with variable coefficients on higher dimensional domains abstract this paper presents a maximum principle based approach in the establishment of iss like estimates for a class of nonlinear parabolic partial differential equations pdes with variable coefficients and different types of nonlinear boundary conditions on higher dimensional domains comparing with the existing literature the iss like estimates established in this paper are independent of the nonlinear terms of the pdes technical development on iss analysis of the considered systems is detailed and an example of establishing iss like estimates for a nonlinear parabolic equation with respectively a nonlinear robin boundary condition and a nonlinear dirichlet boundary condition is provided to illustrate the application of the developed method

world trade web topological properties dynamics and evolution this paper studies the statistical properties of the web of import export relationships among world countries using a weighted network approach we analyze how the distributions of the most important network statistics measuring connectivity assortativity clustering and centrality have coevolved over time we show that all node statistic distributions and their correlation structure have remained surprisingly stable in the last 20 years and are likely to do so in the future conversely the distribution of positive link weights is slowly moving from a log normal density towards a power law we also characterize the autoregressive properties of network statistics dynamics we find that network statistics growth rates are well proxied by fat tailed densities like the laplace or the asymmetric exponential power finally we find that all our results are reasonably robust to a few alternative economically meaningful weighting schemes

lyapunov characterization of input to state stability for semilinear control systems over banach spaces abstract we prove that input to state stability iss of nonlinear systems over banach spaces is equivalent to existence of a coercive lipschitz continuous iss lyapunov function for this system for linear infinite dimensional systems we show that iss is equivalent to existence of a non coercive iss lyapunov function and provide two simpler constructions of coercive and non coercive iss lyapunov functions for input to state stable linear systems

input to state stability of nonlinear impulsive systems we prove that impulsive systems which possess an input to state stable iss lyapunov function are iss for time sequences satisfying the fixed dwell time condition if an iss lyapunov function is the exponential one we provide a stronger result which guarantees uniform iss of the whole system over sequences satisfying the generalized average dwell time condition then we prove two small gain theorems that provide a construction of an iss lyapunov function for an interconnection of impulsive systems if the iss lyapunov functions for subsystems are known the construction of local iss lyapunov functions via the linearization method is provided relations between small gain and dwell time conditions as well as between different types of dwell time conditions are also investigated although our results are novel already in the context of finite dimensional systems we prove them for systems based on differential equations in banach spaces that makes obtained results considerably more general

a characterization of integral input to state stability the notion of input to state stability iss is now recognized as a central concept in nonlinear systems analysis it provides a nonlinear generalization of finite gains with respect to supremum norms and also of finite l sup 2 gains it plays a central role in recursive design coprime factorizations controllers for nonminimum phase systems and many other areas in this paper a newer notion that of integral input to state stability iiss is studied the notion of iiss generalizes the concept of finite gain when using an integral norm on inputs but supremum norms of states in that sense generalizing the linear h sup 2 theory it allows one to quantify sensitivity even in the presence of certain forms of nonlinear resonance we obtain several necessary and sufficient characterizations of the iiss property expressed in terms of dissipation inequalities and other alternative and nontrivial characterizations

construction of lyapunov functions for interconnected parabolic systems an iiss approach this paper is devoted to two issues the first one is to provide lyapunov based tools to establish integral input to state stability iiss and input to state stability iss for some classes of nonlinear parabolic equations the other one is to provide a stability criterion for interconnections of iiss parabolic systems the results addressing the former problem allow us to overcome obstacles arising in tackling the latter one the results for the latter problem are a small gain condition and a formula of lyapunov functions which can be constructed for interconnections whenever the small gain condition holds it is demonstrated that for interconnections of partial differential equations the choice of a right state and input spaces is crucial in particular for iiss subsystems which are not iss as illustrative examples stability of two highly nonlinear reaction diffusion systems is established by the proposed small gain criterion

a de giorgi iteration based approach for the establishment of iss properties for burgers equation with boundary and in domain disturbances this note addresses input to state stability iss properties with respect to w r t boundary and in domain disturbances for burgers equation the developed approach is a combination of the method of de giorgi iteration and the technique of lyapunov functionals by adequately splitting the original problem into two subsystems the iss properties in l 2 norm for burgers equation have been established using this method moreover as an application of de giorgi iteration iss in l infty norm w r t in domain disturbances and actuation errors in boundary feedback control for a one dimensional linear unstable reaction diffusion equation have also been established it is the first time that the method of de giorgi iteration is introduced in the iss theory for infinite dimensional systems and the developed method can be generalized for tackling some problems on multidimensional spatial domains and to a wider class of nonlinear partial differential equations

necessary conditions for the exact observability of systems on hilbert spaces abstract in this paper we introduce the zero class of admissible observation operators for which the norm of the output map tends to zero as the time tends to zero we show that for such an observation operator exact observability implies that the semigroup of the system is bounded from below in addition if the semigroup generator has no residual spectrum then the semigroup can be extended to a c 0 group

quasi monte carlo methods for elliptic pdes with random coefficients and applications we devise and implement quasi monte carlo methods for computing the expectations of nonlinear functionals of solutions of a class of elliptic partial differential equations with random coefficients our motivation comes from fluid flow in random porous media where relevant functionals include the fluid pressure velocity at any point in space or the breakthrough time of a pollution plume being transported by the velocity field our emphasis is on situations where a very large number of random variables is needed to model the coefficient field as an alternative to classical monte carlo we here employ quasi monte carlo methods which use deterministically chosen sample points in an appropriate usually high dimensional parameter space each realization of the pde solution requires a finite element fe approximation in space and this is done using a realization of the coefficient field restricted to a suitable regular spatial grid not necessarily the same as the fe grid in the statistically homogeneous case the corresponding covariance matrix can be diagonalized and the required coefficient realizations can be computed efficiently using fft in this way we avoid the use of a truncated karhunen loeve expansion but introduce high nominal dimension in parameter space numerical experiments with 2 dimensional rough random fields high variance and small length scale are reported showing that the quasi monte carlo method consistently outperforms the monte carlo method with a smaller error and a noticeably better than o n 1 2 convergence rate where n is the number of samples moreover the rate of convergence of the quasi monte carlo method does not appear to degrade as the nominal dimension increases examples with dimension as high as 10 6 are reported

zero class admissibility of observation operators abstract an admissible observation operator is zero class admissible if the norm of the output map tends to zero as the time tends to zero sufficient and necessary conditions for zero class admissibility of observation operators are developed and a modified weiss condition is studied it is shown that the modified weiss condition is in general necessary but not sufficient for zero class admissibility for several important classes of c 0 semigroups it is proved that the modified weiss condition is indeed equivalent to zero class admissibility the methods are illustrated by certain pde examples

iss property with respect to boundary disturbances for a class of riesz spectral boundary control systems abstract this paper deals with the establishment of input to state stability iss estimates for infinite dimensional systems with respect to both boundary and distributed disturbances first a new approach is developed for the establishment of iss estimates for a class of riesz spectral boundary control systems satisfying certain eigenvalue constraints second a concept of weak solutions is introduced in order to relax the disturbances regularity assumptions required to ensure the existence of classical solutions the proposed concept of weak solutions that applies to a large class of boundary control systems which is not limited to the riesz spectral ones provides a natural extension of the concept of both classical and mild solutions assuming that an iss estimate holds true for classical solutions we show the existence the uniqueness and the iss property of the weak solutions

on continuity of solutions for parabolic control systems and input to state stability abstract we study minimal conditions under which mild solutions of linear evolutionary control systems are continuous for arbitrary bounded input functions this question naturally appears when working with boundary controlled linear partial differential equations here we focus on parabolic equations which allow for operator theoretic methods such as the holomorphic functional calculus moreover we investigate stronger conditions than continuity leading to input to state stability with respect to orlicz spaces this also implies that the notions of input to state stability and integral input to state stability coincide if additionally the uncontrolled equation is dissipative and the input space is finite dimensional

dynamics of cluster structures in a financial market network abstract in the course of recent fifteen years the network analysis has become a powerful tool for studying financial markets in this work we analyze stock markets of the usa and sweden we study cluster structures of a market network constructed from a correlation matrix of returns of the stocks traded in each of these markets such cluster structures are obtained by means of the p median problem pmp whose objective is to maximize the total correlation between a set of stocks called medians of size p and other stocks every cluster structure is an undirected disconnected weighted graph in which every connected component cluster is a star or a tree with one central node called a median and several leaf nodes connected with the median by weighted edges our main observation is that in non crisis periods of time cluster structures change more chaotically while during crises they show more stable behavior and fewer changes thus an increasing stability of a market graph cluster structure obtained via the pmp could be used as an indicator of a coming crisis

clustering coefficients of large networks abstract let g be a network with n nodes and eigenvalues 1 2 n then g is called an n d network if it is d regular and max 2 3 n it is shown that if g is an n d network and o d the average clustering coefficient c g of g satisfies c g d n for large d we show that this description also holds for strongly regular graphs and erd s renyi graphs although most real world networks are not constructed theoretically we find that many of them have c g close to d n and many close to 1 2 n d 1 d d 1 where d is the average degree of g and 2 is the average of the numbers of common neighbors over all non adjacent pairs of nodes

infinite dimensional input to state stability and orlicz spaces in this work the relation between input to state stability and integral input to state stability is studied for linear infinite dimensional systems with an unbounded control operator although a special focus is laid on the case l infty general function spaces are considered for the inputs we show that integral input to state stability can be characterized in terms of input to state stability with respect to orlicz spaces since we consider linear systems the results can also be formulated in terms of admissibility for parabolic diagonal systems with scalar inputs both stability notions with respect to l infty are equivalent

stability and convergence properties of forced infinite dimensional discrete time lur e systems incremental stability and convergence properties for forced infinite dimensional discrete time lur e systems are addressed lur e systems have a linear and nonlinear component and arise as the fe

unified analysis of periodization based sampling methods for matern covariances the periodization of a stationary gaussian random field on a sufficiently large torus comprising the spatial domain of interest is the basis of various efficient computational methods such as the

comparison of different generalizations of clustering coefficient and local efficiency for weighted undirected graphs binary undirected graphs are well established but when these graphs are constructed often a threshold is applied to a parameter describing the connection between two nodes therefore the use of weighted graphs is more appropriate in this work we focus on weighted undirected graphs this implies that we have to incorporate edge weights in the graph measures which require generalizations of common graph metrics after reviewing existing generalizations of the clustering coefficient and the local efficiency we proposed new generalizations for these graph measures to be able to compare different generalizations a number of essential and useful properties were defined that ideally should be satisfied we applied the generalizations to two real world networks of different sizes as a result we found that not all existing generalizations satisfy all essential properties furthermore we determined the best generalization for the clustering coefficient and local efficiency based on their properties and the performance when applied to two networks we found that the best generalization of the clustering coefficient is defined in miyajima and sakuragawa 2014 while the best generalization of the local efficiency is proposed in this letter depending on the application and the relative importance of sensitivity and robustness to noise other generalizations may be selected on the basis of the properties investigated in this letter

local input to state stability characterizations and counterexamples abstract we show that a nonlinear locally uniformly asymptotically stable infinite dimensional system is automatically locally input to state stable liss provided the nonlinearity possesses some sort of uniform continuity with respect to external inputs also we prove that liss is equivalent to existence of a liss lyapunov function we show by means of a counterexample that if this uniformity is not present then the equivalence of local asymptotic stability and local iss does not hold anymore using a modification of this counterexample we show that in infinite dimensions a uniformly globally asymptotically stable at zero globally stable and locally iss system possessing an asymptotic gain property does not have to be iss in contrast to finite dimensional case

applications of laplace carleson embeddings to admissibility and controllability it is shown how results on carleson embeddings induced by the laplace transform can be used to derive new and more general results concerning the weighted infinite time admissibility of control and observation operators for linear semigroup systems with q riesz bases of eigenvectors as an example the heat equation is considered next a new carleson embedding result is proved which gives further results on weighted admissibility for analytic semigroups finally controllability by smoother inputs is characterized by means of a new result about weighted interpolation

input to state stability with respect to boundary disturbances for a class of semi linear parabolic equations abstract this paper studies the input to state stability iss properties for a class of semi linear parabolic partial differential equations pdes with respect to boundary disturbances in order to avoid the appearance of time derivatives of the disturbances in iss estimates some technical inequalities are first developed which allow directly dealing with the boundary conditions and establishing the iss based on the method of lyapunov functionals the well posedness analysis of the considered problem is carried out and the conditions for iss are derived two examples are used to illustrate the application of the developed method