separation of variables and exact solution to the dirac equation in curvilinear orthogonal coordinates with cylindrical symmetry in the present article a complete separation of variables in the dirac equation for a free particle is achieved in parabolic cylinder and elliptical coordinates the resulting system of ordinary differential equations is solved and the asymptotic behavior of the spinor solution is discussed

random walks on graphs ideas techniques and results random walks on graphs are widely used in all sciences to describe a great variety of phenomena where dynamical random processes are affected by topology in recent years relevant mathematical results have been obtained in this field and new ideas have been introduced which can be fruitfully extended to different areas and disciplines here we aim at giving a brief but comprehensive perspective of these progresses with a particular emphasis on physical aspects

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

multifractal detrended cross correlation analysis for two nonstationary signals we propose a method called multifractal detrended cross correlation analysis to investigate the multifractal behaviors in the power law cross correlations between two time series or higher dimensional quantities recorded simultaneously which can be applied to diverse complex systems such as turbulence finance ecology physiology geophysics and so on the method is validated with cross correlated one and two dimensional binomial measures and multifractal random walks as an example we illustrate the method by analyzing two financial time series

linear systems subject to input saturation and time delay global asymptotic stabilization this note deals with the problem of global asymptotic stabilization of linear systems by bounded static feedbacks subject to time delay under standard necessary conditions we provide two constructions of controllers of nested saturation type which extends to the general case partial results of previous papers for arbitrary small bound on the control and large constant delay to validate the approach a third order integrator and oscillator with multiplicity two example is presented

multifractal characterization of protein contact networks abstract the multifractal detrended fluctuation analysis of time series is able to reveal the presence of long range correlations and at the same time to characterize the self similarity of the series the rich information derivable from the characteristic exponents and the multifractal spectrum can be further analyzed to discover important insights into the underlying dynamical process in this paper we employ multifractal analysis techniques in the study of protein contact networks to this end initially a network is mapped to three different time series each of which is generated by a stationary unbiased random walk to capture the peculiarities of the networks at different levels we accordingly consider three observables at each vertex the degree the clustering coefficient and the closeness centrality to compare the results with suitable references we consider also instances of three well known network models and two typical time series with pure monofractal and multifractal properties the first result of notable interest is that time series associated to protein contact networks exhibit long range correlations strong persistence which are consistent with signals in between the typical monofractal and multifractal behavior successively a suitable embedding of the multifractal spectra allows to focus on ensemble properties which in turn gives us the possibility to make further observations regarding the considered networks in particular we highlight the different role that small and large fluctuations of the considered observables play in the characterization of the network topology

detrended cross correlation analysis consistently extended to multifractality we propose an algorithm multifractal cross correlation analysis mfcca which constitutes a consistent extension of the detrended cross correlation analysis and is able to properly identify and quantify subtle characteristics of multifractal cross correlations between two time series our motivation for introducing this algorithm is that the already existing methods like multifractal extension have at best serious limitations for most of the signals describing complex natural processes and often indicate multifractal cross correlations when there are none the principal component of the present extension is proper incorporation of the sign of fluctuations to their generalized moments furthermore we present a broad analysis of the model fractal stochastic processes as well as of the real world signals and show that mfcca is a robust and selective tool at the same time and therefore allows for a reliable quantification of the cross correlative structure of analyzed processes in particular it allows one to identify the boundaries of the multifractal scaling and to analyze a relation between the generalized hurst exponent and the multifractal scaling parameter ensuremath lambda q this relation provides information about the character of potential multifractality in cross correlations and thus enables a deeper insight into dynamics of the analyzed processes than allowed by any other related method available so far by using examples of time series from the stock market we show that financial fluctuations typically cross correlate multifractally only for relatively large fluctuations whereas small fluctuations remain mutually independent even at maximum of such cross correlations finally we indicate possible utility of mfcca to study effects of the time lagged cross correlations

a further result on global stabilization of oscillators with bounded delayed input this note revisits the problem of globally stabilizing an oscillator with a bounded delayed input it establishes that an oscillator with input saturation can be globally asymptotically stabilized by a linear state feedback even in the presence of an arbitrarily large delay in the input this result strengthens a recent result in the literature which shows that such an oscillator can be globally asymptotically stabilized with a sufficiently small control input and the magnitude of the control input goes to zero as the delay increases to infinity the controller constructed in this note thus improves the efficiency of the closed loop system by fully utilizing the actuator capacity

regulator problem for linear continuous time delay systems with nonsymmetrical constrained control the regulator problem is studied for linear continuous time delay systems with nonsymmetrical constrained control necessary and sufficient conditions allowing the autors to obtain the largest nonsymmetrical polyhedral positively invariant with respect to w r t the system in the closed loop are given the case of symmetrical constrained control is obtained as a particular case

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

robust exponential convergence of a class of linear delayed systems with bounded controllers and disturbances this brief paper deals with the problem of robust exponential stabilization of a class of dynamic systems subject to time varying delays external disturbances and control saturation a linear memoryless state feedback controller is synthesized to guarantee that there is a domain of admissible initial conditions from which all solutions of the class of systems considered converge exponentially to a ball with a prespecified convergence rate the problem is formulated as a two step optimization problem with matrix inequality constraints to enlarge the size of the ball of admissible initial conditions

semiglobal stabilization and output regulation of singular linear systems with input saturation the semi global stabilization problem and output regulation problem of singular linear systems subject to input saturation are addressed a reduced order normal system is obtained by a standard coordinate transformation it is further shown that the controller that solves the stabilization output regulation problem of the reduced order normal systems also solves the stabilization output regulation problem of the original singular systems

statistical test for δρdcca cross correlation coefficient abstract in this paper we propose a new statistical test for d c c a detrended cross correlation coefficient difference a tool to measure contagion interdependence effect in time series of size n at different time scale n for this proposition we analyzed simulated and real time series the results showed that the statistical significance of d c c a depends on the size n and the time scale n and we can define a critical value for this dependency in 90 95 and 99 of confidence level as will be shown in this paper

toward a multilevel representation of protein molecules computational intelligence methods are typically designed according to the assumption that the input space is essentially a vector space when departing from vector based pattern representations many theoretical and practical problems arise which are mostly due to the absence of an intuitive geometric interpretation of the data however since such representations could offer additional insights when used in real world applications of data driven inference systems their exploitation is also a practical and convenient choice here we apply several state of the art classification methods for non geometric data with the aim to compare different representations of the proteins gathered from niwa et al 2009 35 such representations include sequences of objects and labeled contact graphs enriched with chemico physical attributes the experiment performed by niwa et al provides the unique possibility to analyze the relative aggregation folding propensity of the elements of the entire escherichia coli e coli proteome in a cell free standardized microenvironment by this comparison we are able to identify also some interesting general properties of proteins notably i we suggest a threshold around 250 residues discriminating easily foldable from hardly foldable molecules consistent with other independent experiments and ii we highlight the relevance of contact graph spectra for folding behavior discrimination and characterization of the e coli solubility data the soundness of the experimental results presented in this paper is proved by the statistically relevant relationships discovered among the chemico physical description of proteins and the developed cost matrix of substitution that we used in the various discrimination systems

separation of variables and exact solution of the dirac equation in nonstatic minkowski spacetimes using a second order formalism a complete separation of variables in the dirac equation for a free particle in nonstatic orthogonal curvilinear coordinates of the form t f u v x g u v y z is presented it is shown that the dirac equation is separable in eight nonequivalent coordinate systems where the klein gordon equation separates exact solutions of the dirac equation in the systems of coordinates obtained are presented

scaling theory of transport in complex biological networks transport is an important function in many network systems and understanding its behavior on biological social and technological networks is crucial for a wide range of applications however it is a property that is not well understood in these systems probably because of the lack of a general theoretical framework here based on the finding that renormalization can be applied to bionetworks we develop a scaling theory of transport in self similar networks we demonstrate the networks invariance under length scale renormalization and we show that the problem of transport can be characterized in terms of a set of critical exponents the scaling theory allows us to determine the influence of the modular structure on transport in metabolic and protein interaction networks we also generalize our theory by presenting and verifying scaling arguments for the dependence of transport on microscopic features such as the degree of the nodes and the distance between them using transport concepts such as diffusion and resistance we exploit this invariance and we are able to explain based on the topology of the network recent experimental results on the broad flow distribution in metabolic networks

topological properties of the limited penetrable horizontal visibility graph family the limited penetrable horizontal visibility graph algorithm was recently introduced to map time series in complex networks in this work we extend this algorithm to create a directed limited penetrable horizontal visibility graph and an image limited penetrable horizontal visibility graph we define two algorithms and provide theoretical results on the topological properties of these graphs associated with different types of real value series we perform several numerical simulations to check the accuracy of our theoretical results finally we present an application of the directed limited penetrable horizontal visibility graph to measure real value time series irreversibility and an application of the image limited penetrable horizontal visibility graph that discriminates noise from chaos we also propose a method to measure the systematic risk using the image limited penetrable horizontal visibility graph and the empirical results show the effectiveness of our proposed algorithms

a history of graph entropy measures this survey seeks to describe methods for measuring the entropy of graphs and to demonstrate the wide applicability of entropy measures setting the scene with a review of classical measures for determining the structural information content of graphs we discuss graph entropy measures which play an important role in a variety of problem areas including biology chemistry and sociology in addition we examine relationships between selected entropy measures illustrating differences quantitatively with concrete examples

signatures of chaotic and stochastic dynamics uncovered with recurrence networks an old and important problem in the field of nonlinear time series analysis entails the distinction between chaotic and stochastic dynamics recently recurrence networks have been proposed as a t

wavelet versus detrended fluctuation analysis of multifractal structures we perform a comparative study of applicability of the multifractal detrended fluctuation analysis mfdfa and the wavelet transform modulus maxima wtmm method in proper detecting of monofractal and multifractal character of data we quantify the performance of both methods by using different sorts of artificial signals generated according to a few well known exactly soluble mathematical models monofractal fractional brownian motion bifractal levy flights and different sorts of multifractal binomial cascades our results show that in the majority of situations in which one does not know a priori the fractal properties of a process choosing mfdfa should be recommended in particular wtmm gives biased outcomes for the fractional brownian motion with different values of hurst exponent indicating spurious multifractality in some cases wtmm can also give different results if one applies different wavelets we do not exclude using wtmm in real data analysis but it occurs that while one may apply mfdfa in a more automatic fashion wtmm must be applied with care in the second part of our work we perform an analogous analysis on empirical data coming from the american and from the german stock market for this data both methods detect rich multifractality in terms of broad f alpha but mfdfa suggests that this multifractality is poorer than in the case of wtmm

on separable solutions of dirac s equation for the electron the properties of coordinate systems that admit separation of the laplacian and hamilton jacobi operators have been thoroughly explored so that the nature of solutions in separable form of laplace s equation the wave equation schrodinger s equation and the hamilton jacobi equation are well understood the corresponding problems for the dirac operator in flat space time have been less completely examined and this paper contains studies intended to produce a more systematic account of possible solutions of dirac s equation because the dirac operator differs from the laplacian in being a first degree differential operator and in having matrix coefficients it is not possible to discuss possible solutions in as general a way and the separable solutions are far less rich than for equations with the laplacian in particular the forms of the potentials for which separable solutions are possible are not for the most part of physical interest although the discussion is confined to coordinates in flat space time some of the procedures are derived from those developed to solve dirac s equation in coordinates with a kerr metric

research on the co movement between high end talent and economic growth a complex network approach abstract the major goal of this paper is to focus on the co movement between high end talent and economic growth by a complex network approach firstly the national high end talent development efficiency from 1990 to 2015 is taken as the quantitative index to measure the development of high end talent the added values of the primary industry secondary industry tertiary industry are selected as economic growth indexes and all the selected sample data are standardized by the mean value processing method secondly let seven months as the length of the sliding window and one month as the sliding step then the grey correlation degrees between systems are measured using the slope correlation degrees and the grey correlation degree sequence is mapped into the symbol series composed by three symbols y o n based on the coarse graining method let three characters as a mode the nodes are obtained by the modes according to the time sequence let the transformation between the modal be the edge and the times of the transformation be weight then the co movement networks between national high end talent development efficiency and the added values of the primary industry secondary industry tertiary industry are built respectively finally the dynamic characteristics of the networks are analysed by the node strength strength distribution weighted clustering coefficient conversion cycle of the modes and the transition between the co movement modes the results indicate that there are mutual influence and promotion relations between the national high end talent development efficiency and the added values of the primary secondary and tertiary industry

robust controller design of uncertain discrete time delay systems with input saturation and disturbances this technical note deals with the problem of robust controller design of uncertain discrete time delay systems subject to control input saturation and bounded external disturbances a sufficient condition is obtained which guarantees the existence of state feedback controllers and an admissible initial condition domain such that the resulting closed loop system is uniformly exponentially convergent to a ball with certain exponential decay rate for every initial condition emanating from the admissible domain an iterative linear matrix inequality relaxation scheme can be used to construct desired state feedback controllers a simulation example is provided to demonstrate the effectiveness of the proposed method

multifractality tests using bootstrapped wavelet leaders multifractal analysis which mostly consists of measuring scaling exponents is becoming a standard technique available in most empirical data analysis toolboxes making use of the most recent theoretical results it is based here on the estimation of the cumulants of the log of the wavelet leaders an elaboration on the wavelet coefficients these log cumulants theoretically enable discrimination between mono and multifractal processes as well as between simple log normal multifractal models and more advanced ones the goal of the present contribution is to design nonparametric bootstrap hypothesis tests aiming at testing the nature of the multifractal properties of stochastic processes and empirical data bootstrap issues together with six declinations of test designs are analyzed their statistical performance significances powers and p values are assessed and compared by means of monte carlo simulations performed on synthetic stochastic processes whose multifractal properties and log cumulants are known theoretically a priori we demonstrate that the joint use of wavelet leaders log cumulants and bootstrap procedures enable us to obtain a powerful tool for testing the multifractal properties of data this tool is practically effective and can be applied to a single observation of data with finite length

multifractal cross correlation effects in two variable time series of complex network vertex observables we investigate the scaling of the cross correlations calculated for two variable time series containing vertex properties in the context of complex networks time series of such observables are obtained by means of stationary unbiased random walks we consider three vertex properties that provide respectively short medium and long range information regarding the topological role of vertices in a given network in order to reveal the relation between these quantities we applied the multifractal cross correlation analysis technique which provides information about the nonlinear effects in coupling of time series we show that the considered network models are characterized by unique multifractal properties of the cross correlation in particular it is possible to distinguish between erdos renyi barabasi albert and watts strogatz networks on the basis of fractal cross correlation moreover the analysis of protein contact networks reveals characteristics shared with both scale free and small world models

semi global exponential stabilization of linear discrete time systems subject to input saturation via linear feedbacks abstract in this paper we show that a linear discrete time system subject to input saturation is semi globally exponentially stabilizable via linear state and or output feedback laws as long as the system in the absence of input saturation is stabilizable and detectable and has all its poles located inside or on the unit circle furthermore the semi globally stabilizing feedback laws are explicitly constructed the results presented here are parallel to our earlier results on the continuous time counterpart lin and saberi 1993

can the bivariate hurst exponent be higher than an average of the separate hurst exponents abstract in this note we investigate possible relationships between the bivariate hurst exponent h x y and an average of the separate hurst exponents 1 2 h x h y we show that two cases are well theoretically founded these are the cases when h x y 1 2 h x h y and h x y 1 2 h x h y however we show that the case of h x y 1 2 h x h y is not possible regardless of stationarity issues further discussion of the implications is provided as well together with a note on the finite sample effect