finite dimensional backward shift invariant subspaces of arveson spaces a description is given of finite dimensional backward shift invariant subspaces of arveson spaces which are certain multivariable analogues of the hardy space of the unit disk

the complexity of divisibility we address two sets of long standing open questions in linear algebra and probability theory from a computational complexity perspective stochastic matrix divisibility and divisibility and decomposability of probability distributions we prove that finite divisibility of stochastic matrices is an np complete problem and extend this result to nonnegative matrices and completely positive trace preserving maps i e the quantum analogue of stochastic matrices we further prove a complexity hierarchy for the divisibility and decomposability of probability distributions showing that finite distribution divisibility is in p but decomposability is np hard for the former we give an explicit polynomial time algorithm all results on distributions extend to weak membership formulations proving that the complexity of these problems is robust to perturbations

the complexity of relating quantum channels to master equations completely positive trace preserving cpt maps and lindblad master equations are both widely used to describe the dynamics of open quantum systems the connection between these two descriptions is a classic topic in mathematical physics one direction was solved by the now famous result due to lindblad kossakowski gorini and sudarshan who gave a complete characterisation of the master equations that generate completely positive semi groups however the other direction has remained open given a cpt map is there a lindblad master equation that generates it and if so can we find its form this is sometimes known as the markovianity problem physically it is asking how one can deduce underlying physical processes from experimental observations

on the dynamics of molecular conformation understanding the mechanism of fast transitions between conformed states of large biomolecules is central to reconciling the dichotomy between the relatively high speed of metabolic processes and slow random walk based estimates on the speed of biomolecular processes here we use the dynamical systems approach to suggest that the reduced time of transition between different conformations is due to features of the dynamics of molecules that are a consequence of their structural features long range and local effects both play a role long range molecular forces account for the robustness of final states and nonlinear processes that channel localized bounded disturbances into collective modal motions local interconnections provide fast transition dynamics these properties are shared by a class of networked systems with strong local interconnections and long range nonlinear forces that thus exhibit flexibility and robustness at the same time

identification of market trends with string and d2 brane maps abstract the multidimensional string objects are introduced as a new alternative for an application of string models for time series forecasting in trading on financial markets the objects are represented by open string with 2 endpoints and d2 brane which are continuous enhancement of 1 endpoint open string model we show how new object properties can change the statistics of the predictors which makes them the candidates for modeling a wide range of time series systems string angular momentum is proposed as another tool to analyze the stability of currency rates except the historical volatility to show the reliability of our approach with application of string models for time series forecasting we present the results of real demo simulations for four currency exchange pairs

riemannian geometry and matrix geometric means the geometric mean of two positive definite matrices has been defined in several ways and studied by several authors including pusz and woronowicz and ando the characterizations by these authors do not readily extend to three matrices and it has been a long standing problem to define a natural geometric mean of three positive definite matrices in some recent papers new understanding of the geometric mean of two positive definite matrices has been achieved by identifying the geometric mean of a and b as the midpoint of the geodesic with respect to a natural riemannian metric joining a and b this suggests some natural definitions for a geometric mean of three positive definite matrices we explain the necessary geometric background and explore the properties of some of these candidates

subgraph centrality in complex networks we introduce a new centrality measure that characterizes the participation of each node in all subgraphs in a network smaller subgraphs are given more weight than larger ones which makes this measure appropriate for characterizing network motifs we show that the subgraph centrality c s i can be obtained mathematically from the spectra of the adjacency matrix of the network this measure is better able to discriminate the nodes of a network than alternate measures such as degree closeness betweenness and eigenvector centralities we study eight real world networks for which c s i displays useful and desirable properties such as clear ranking of nodes and scale free characteristics compared with the number of links per node the ranking introduced by c s i for the nodes in the protein interaction network of s cereviciae is more highly correlated with the lethality of individual proteins removed from the proteome

scaling and memory in the return intervals of realized volatility abstract we perform return interval analysis of 1 min realized volatility defined by the sum of absolute high frequency intraday returns for the shanghai stock exchange composite index ssec and 22 constituent stocks of ssec the scaling behavior and memory effect of the return intervals between successive realized volatilities above a certain threshold q are carefully investigated in comparison with the volatility defined by the closest tick prices to the minute marks the return interval distribution for the realized volatility shows a better scaling behavior since 20 stocks out of 22 stocks and the ssec pass the kolmogorov smirnov ks test and exhibit scaling behaviors among which the scaling function for 8 stocks could be approximated well by a stretched exponential distribution revealed by the ks goodness of fit test under the significance level of 5 the improved scaling behavior is further confirmed by the relation between the fitted exponent and the threshold q in addition the similarity of the return interval distributions for different stocks is also observed for the realized volatility the investigation of the conditional probability distribution and the detrended fluctuation analysis dfa show that both short term and long term memory exists in the return intervals of realized volatility

a pseudospectral mapping theorem the pseudospectrum has become an important quantity for analyzing stability of nonnormal systems in this paper we prove a mapping theorem for pseudospectra extending an earlier result of trefethen our result consists of two relations that are sharp and contains the spectral mapping theorem as a special case necessary and sufficient conditions for these relations to collapse to an equality are demonstrated the theory is valid for bounded linear operators on banach spaces for normal matrices a special version of the pseudospectral mapping theorem is also shown to be sharp some numerical examples illustrate the theory

an effective matrix geometric mean satisfying the ando li mathias properties we propose a new matrix geometric mean satisfying the ten properties given by ando li and mathias linear alg appl 2004 this mean is the limit of a sequence which converges superlinearly with convergence of order 3 whereas the mean introduced by ando li and mathias is the limit of a sequence having order of convergence 1 this makes this new mean very easily computable we provide a geometric interpretation and a generalization which includes as special cases our mean and the ando li mathias mean

multifactor analysis of multiscaling in volatility return intervals we study the volatility time series of 1137 most traded stocks in the u s stock markets for the two year period 2001 2002 and analyze their return intervals which are time intervals between volatilities above a given threshold q we explore the probability density function of pq assuming a stretched exponential function pqe we find that the exponent depends on the threshold in the range between q 1 and 6 standard deviations of the volatility this finding supports the multiscaling nature of the return interval distribution to better understand the multiscaling origin we study how depends on four essential factors capitalization risk number of trades and return we show that depends on the capitalization risk and return but almost does not depend on the number of trades this suggests that relates to the portfolio selection but not on the market activity to further characterize the multiscaling of individual stocks we fit the moments of m s m 1 m in the range of 10 100 by a power law m the exponent is found also to depend on the capitalization risk and return but not on the number of trades and its tendency is opposite to that of moreover we show that decreases with increasing approximately by a linear relation the return intervals demonstrate the temporal structure of volatilities and our findings suggest that their multiscaling features may be helpful for portfolio optimization

dynamics of the n link pendulum a fractional perspective abstractthis paper addresses the dynamics of an n link planar pendulum in the perspective of fractional calculus the proposed methodology leads to a novel point of view for signal propagation as a time space wave within the system mechanical structure numerical simulations show the effectiveness of the approach both for signal visualisation and limit cycle detection

diffusion and consensus on weakly connected directed graphs abstract let g be a weakly connected directed graph with asymmetric graph laplacian l consensus and diffusion are dual dynamical processes defined on g by x l x for consensus and p p l for diffusion in this survey we consider both these processes as well their discrete time analogues we define a basis of row vectors i i 1 k of the left null space of l and a basis of column vectors i i 1 k of the right null space of l in terms of the partition of g into strongly connected components this allows for complete characterization of the asymptotic behavior of both diffusion and consensus discrete and continuous in terms of these eigenvectors as an application of these ideas we present a treatment of the pagerank algorithm that is dual to the usual one we further show that the teleporting see below feature usually included in the algorithm is not strictly necessary together with 1 this is a complete and self contained overview of the asymptotics of consensus and diffusion on digraphs many of the ideas presented here can be found scattered in the literature though mostly outside mainstream mathematics and not always with complete proofs this paper seeks to remedy this by providing a compact and accessible survey

fractional dynamics and mds visualization of earthquake phenomena this paper analyses earthquake data in the perspective of dynamical systems and fractional calculus fc this new standpoint uses multidimensional scaling mds as a powerful clustering and visualization tool fc extends the concepts of integrals and derivatives to non integer and complex orders mds is a technique that produces spatial or geometric representations of complex objects such that those objects that are perceived to be similar in some sense are placed on the mds maps forming clusters in this study over three million seismic occurrences covering the period from january 1 1904 up to march 14 2012 are analysed the events are characterized by their magnitude and spatiotemporal distributions and are divided into fifty groups according to the flinn engdahl f e seismic regions of earth several correlation indices are proposed to quantify the similarities among regions mds maps are proven as an intuitive and useful visual representation of the complex relationships that are present among seismic events which may not be perceived on traditional geographic maps therefore mds constitutes a valid alternative to classic visualization tools for understanding the global behaviour of earthquakes

taylor s theorem for matrix functions with applications to condition number estimation we derive an explicit formula for the remainder term of a taylor polynomial of a matrix function this formula generalizes a known result for the remainder of the taylor polynomial for an analytic function of a complex scalar we investigate some consequences of this result which culminate in new upper bounds for the level 1 and level 2 condition numbers of a matrix function in terms of the pseudospectrum of the matrix numerical experiments show that although the bounds can be pessimistic they can be computed much faster than the standard methods this makes the upper bounds ideal for a quick estimation of the condition number whilst a more accurate and expensive method can be used if further accuracy is required they are also easily applicable to more complicated matrix functions for which no specialized condition number estimators are currently available

the schur algorithm and reproducing kernel hilbert spaces in the ball abstract using reproducing kernel hilbert spaces methods we develop a schur type algorithm for a subclass of the functions analytic and contractive in the ball we also consider the nevanlinna pick interpolation problem in that class

computing short interval transition matrices of a discrete time markov chain from partially observed data markov chains constitute a common way of modelling the progression of a chronic disease through various severity states for these models a transition matrix with the probabilities of moving from one state to another for a specific time interval is usually estimated from cohort data quite often however the cohort is observed at specific times with intervals that may be greater than the interval of interest the transition matrix computed then needs to be decomposed in order to estimate the desired interval transition matrix suited to the model although simple to implement this method of matrix decomposition can yet result in an invalid short interval transition matrix with negative or complex entries in this paper we present a method for computing short interval transition matrices that is based on regularization techniques our method operates separately on each row of the invalid short interval transition matrix aiming to minimize an appropriate distance measure we test our method on various matrix structures and sizes and evaluate its performance on a real life transition model for hiv infected individuals

backward shift operator and finite dimensional de branges rovnyak spaces in the ball recently bolotnikov and rodman characterized finite dimensional backward shift invariant subspaces of the arveson space in this note we study finite dimensional backward shift invariant hilbert spaces contractively included in the arveson space to that purpose we redefine in an appropriate way the backward shift operators in terms of power series expansions

information mobility in complex networks the concept of information mobility in complex networks is introduced on the basis of a stochastic process taking place in the network the transition matrix for this process represents the probability that the information arising at a given node is transferred to a target one we use the fractional powers of this transition matrix to investigate the stochastic process at fractional time intervals the mobility coefficient is then introduced on the basis of the trace of these fractional powers of the stochastic matrix the fractional time at which a network diffuses 50 of the information contained in its nodes 1 k50 is also introduced we then show that the scale free random networks display better spread of information than the non scale free ones we study 38 real world networks and analyze their performance in spreading information from their nodes we find that some real world networks perform even better than the scale free networks with the same average degree and we point out some of the structural parameters that make this possible

a top bottom price approach to understanding financial fluctuations abstract the presence of sequences of top and bottom tb events in financial series is investigated for the purpose of characterizing such switching points they clearly mark a change in the trend of rising or falling prices of assets to the opposite tendency are of crucial importance for the players decision and also for the market stability previous attempts to characterize switching points have been based on the behavior of the volatility and on the definition of microtrends the approach used herein is based on the smoothing of the original data with a gaussian kernel the events are identified by the magnitude of the difference of the extreme prices by the time lag between the corresponding events waiting time and by the time interval between events with a minimal magnitude return time results from the analysis of the inter day dow jones industrial average index djia from 1928 to 2011 are discussed q gaussian functions with power law tails are found to provide a very accurate description of a class of measures obtained from the series statistics

scaling properties and universality of first passage time probabilities in financial markets financial markets provide an ideal frame for the study of crossing or first passage time events of non gaussian correlated dynamics mainly because large data sets are available tick by tick data of six futures markets are herein considered resulting in fat tailed first passage time probabilities the scaling of the return with its standard deviation collapses the probabilities of all markets examined and also for different time horizons into single curves suggesting that first passage statistics is market independent at least for high frequency data on the other hand a very closely related quantity the survival probability shows away from the center and tails of the distribution a hyperbolic t ensuremath 1 2 decay typical of a markovian dynamics albeit the existence of memory in markets modifications of the weibull and student distributions are good candidates for the phenomenological description of first passage time properties under certain regimes the scaling strategies shown may be useful for risk control and algorithmic trading

boundary interpolation in the ball we solve a boundary interpolation problem in the reproducing kernel hilbert space of functions analytic in the unit ball of cn with reproducing kernel 1 1 1nzkwk we introduce the notion of brune factor or blaschke potapov factor of the third kind in this setting

communicability in complex networks we propose a new measure of the communicability of a complex network which is a broad generalization of the concept of the shortest path according to the new measure most of the real world networks display the largest communicability between the most connected popular nodes of the network assortative communicability there are also several networks with the disassortative communicability where the most popular nodes communicate very poorly to each other using this information we classify a diverse set of real world complex systems into a small number of universality classes based on their structure dynamic correlation in addition the new communicability measure is able to distinguish finer structures of networks such as communities into which a network is divided a community is unambiguously defined here as a set of nodes displaying larger communicability among them than to the rest of the nodes in the network

state space size considerations for disease progression models markov models of disease progression are widely used to model transitions in patients health state over time usually patients health status may be classified according to a set of ordered health states modelers lump together similar health states into a finite and usually small number of health states that form the basis of a markov chain disease progression model this increases the number of observations used to estimate each parameter in the transition probability matrix however lumping together observably distinct health states also obscures distinctions among them and may reduce the predictive power of the model moreover as we demonstrate precision in estimating the model parameters does not necessarily improve as the number of states in the model declines this paper explores the tradeoff between lumping error introduced by grouping distinct health states and sampling error that arises when there are insufficient patient data to precisely estimate the transition probability matrix copyright 2013 john wiley sons ltd

multifractals embedded in short time series an unbiased estimation of probability moment an exact estimation of probability moments is the base for several essential concepts such as the multifractals the tsallis entropy and the transfer entropy by means of approximation theory we propose a new method called factorial moment based estimation of probability moments theoretical prediction and computational results show that it can provide us an unbiased estimation of the probability moments of continuous order calculations on probability redistribution model verify that it can extract exactly multifractal behaviors from several hundred recordings its powerfulness in monitoring evolution of scaling behaviors is exemplified by two empirical cases i e the gait time series for fast normal and slow trials of a healthy volunteer and the closing price series for shanghai stock market by using short time series with several hundred lengths a comparison with the well established tools displays significant advantages of its performance over the other methods the factorial moment based estimation can evaluate correctly the scaling behaviors in a scale range about three generations wider than the multifractal detrended fluctuation analysis and the basic estimation the estimation of partition function given by the wavelet transform modulus maxima has unacceptable fluctuations besides the scaling invariance focused in the present paper the proposed factorial moment of continuous order can find its various uses such as finding nonextensive behaviors of a complex system and reconstructing the causality relationship network between elements of a complex system

statistical analysis of the overnight and daytime return we investigate the two components of the total daily return close to close the overnight return close to open and the daytime return open to close as well as the corresponding volatilities of the 2215 new york stock exchange stocks for the 20 year period from 1988 to 2007 the tail distribution of the volatility the long term memory in the sequence and the cross correlation between different returns are analyzed our results suggest that i the two component returns and volatilities have features similar to that of the total return and volatility the tail distribution follows a power law for all volatilities and long term correlations exist in the volatility sequences but not in the return sequences ii the daytime return contributes more to the total return both the tail distribution and the long term memory of the daytime volatility are more similar to that of the total volatility compared to the overnight records in addition the cross correlation between the daytime return and the total return is also stronger iii the two component returns tend to be anticorrelated moreover we find that the cross correlations between the three different returns total overnight and daytime are quite stable over the entire 20 year period

on the exponential metric increasing property a short and simple proof is given for the inequality that shows that positive definite matrices constitute a riemannian manifold of negative curvature the idea of the proof leads to generalisations to non riemannian metrics and to connections with some well known inequalities of mathematical physics

pseudospectra of the orr sommerfeld operator this paper investigates the pseudospectra and the numerical range of the orr sommerfeld operator for plane poiseuille flow a number z in bf c is in the epsilon pseudospectrum of a matrix or operator a if zi a 1 geq epsilon 1 or equivalently if z is in the spectrum of a e for some perturbation e satisfying e leq epsilon the numerical range of a is the set of numbers of the form au u where cdot cdot is the inner product and u is a vector or function with huh u 1 the spectrum of the orr sommerfeld operator consists of three branches it is shown that the eigenvalues at the intersection of the branches are highly sensitive to perturbations and that the sensitivity increases dramatically with the reynolds number the associated eigenfunctions are nearly linearly dependent even though they form a complete set to understand the high sensitivity of the eigenvalues a model operator is considered related to the airy equation tha

the level crossing and inverse statistic analysis of german stock market index dax and daily oil price time series a b s t r a c t the level crossing and inverse statistics analysis of dax and oil price time series are given we determine the average frequency of positive slope crossings where t 1 is the average waiting time for observing the level again we estimate the probability p k which provides us the probability of observing k times of the level with positive slope in time scale t for analyzed time series we found that maximum k is about 6 we show that by using the level crossing analysis one can estimate how the dax and oil time series will develop we carry out the same analysis for the increments of dax and oil price log returns which is known as inverse statistics and provide the distribution of waiting times to observe some level for the increments 2011 elsevier b v all rights reserved stochastic processes occur in many natural and man made phenomena ranging from various indicators of economic activities in the stock market velocity fluctuations in turbulent flows and heartbeat dynamics etc 1 the level crossing analysis of stochastic processes has been introduced by rice 1944 1945 2 26 and used to describe the turbulence 16 rough surfaces 27 stock markets 28 burgers turbulence and kardar parisi zhang equation 29 30 the level crossing analysis of the data set has the advantage that it gives important global properties of the time series and do not need the scaling feature the almost of the methods in time series analysis are using the scaling features of time series and their applications are restricted to the time series with scaling properties our goal with the level crossing analysis is to characterize the statistical properties of the data set with the hope to better understand the underlying stochastic dynamics and provide a possible tool to estimate its dynamics the level crossing and inverse statistics analysis can be viewed as the complementary method to the other well known methods such as detrended fluctuation analysis dfa 31 detrended moving average dma 32 wavelet transform modulus maxima wtmm 33 rescaled range analysis r s 34 scaled windowed variance swv 35 langevin dynamics 36 detrended cross correlation analysis 37 multifactor analysis of

the resolvent average for positive semidefinite matrices we define a new average termed the resolvent average for positive semidefinite matrices for positive definite matrices the resolvent average enjoys self duality and it interpolates between the harmonic and the arithmetic averages which it approaches when taking appropriate limits we compare the resolvent average to the geometric mean some applications to matrix functions are also given

fingerprinting networks correlations of local and global network properties in complex networks a common task is to identify the most important or central nodes there are several definitions often called centrality measures which often lead to different results here we introduce fingerprints of networks which we define as correlation plots of local and global network properties we show that these fingerprints are suitable tools for characterizing networks beyond single quantity distributions in particular we study the correlations between four local and global measures namely the degree the shortest path betweenness the random walk betweenness and the subgraph centrality on different random network models like erd s renyi small world and barabasi albert as well as on different real networks like metabolic pathways social collaborations and computer networks and compare those fingerprints to determine the quality of those basic models the correlation fingerprints are quite different between the real networks and the model networks questioning whether the models really reflect all important properties of the real world

computing real square roots of a real matrix bjorck and hammarling 1 describe a fast stable schur method for computing a square root x of a matrix a x2 a we present an extension of their method which enables real arithmetic to be used throughout when computing a real square root of a real matrix for a nonsingular real matrix a conditions are given for the existence of a real square root and for the existence of a real square root which is a polynomial in a the number of square roots of the latter type is determined the conditioning of matrix square roots is investigated and an algorithm is given for the computation of a well conditioned square root

monotonic properties of the least squares mean we settle an open problem of several years standing by showing that the least squares mean for positive definite matrices is monotone for the usual loewner order indeed we show this is a special case of its appropriate generalization to partially ordered complete metric spaces of nonpositive curvature our techniques extend to establish other basic properties of the least squares mean such as continuity and joint concavity moreover we introduce a weighted least squares mean and derive our results in this more general setting

dividing quantum channels we investigate the possibility of dividing quantum channels into concatenations of other channels thereby studying the semigroup structure of the set of completely positive trace preserving maps we show the existence of indivisible channels which can not be written as non trivial products of other channels and study the set of infinitesimal divisible channels which are elements of continuous completely positive evolutions for qubit channels we obtain a complete characterization of the sets of indivisible and infinitesimal divisible channels moreover we identify those channels which are solutions of time dependent master equations for both positive and completely positive evolutions for arbitrary finite dimension we prove a representation theorem for elements of continuous completely positive evolutions based on new results on determinants of quantum channels and markovian approximations

caratheodory fejer interpolation in the ball with mixed derivatives we use reproducing kernel hilbert space methods to solve a caratheodory fejer type interpolation problem with mixed derivatives corresponding to a so called lower inclusive set in the class of schur multipliers

stochastic nature of series of waiting times although fluctuations in the waiting time series have been studied for a long time some important issues such as its long range memory and its stochastic features in the presence of nonstationarity have so far remained unstudied here we find that the waiting times series for a given increment level have long range correlations with hurst exponents belonging to the interval 1 2lhl1 we also study positive negative level asymmetry of the waiting time distribution we find that the logarithmic difference of waiting times series has a short range correlation and then we study its stochastic nature using the markovian method and determine the corresponding kramers moyal coefficients as an example we analyze the velocity fluctuations in high reynolds number turbulence and determine the level dependence of markov time scales as well as the drift and diffusion coefficients we show that the waiting time distributions exhibit power law tails and we were able to model the distribution with a continuous time random walk

the curvature of a hilbert module over ℂ z1 zd a notion of curvature is introduced in multivariable operator theory the curvature invariant of a hilbert module over z1 zd is a nonnegative real number which has significant extremal properties which tends to be an integer and which is hard to compute directly it is shown that for graded hilbert modules the curvature agrees with the euler characteristic of a certain finitely generated algebraic module over the appropriate polynomial ring this result is a higher dimensional operator theoretic counterpart of the gauss bonnet formula which expresses the average gaussian curvature of a compact oriented riemann surface as the alternating sum of the betti numbers of the surface and it solves the problem of calculating the curvature of graded hilbert modules the proof of that result is based on an asymptotic formula which expresses the curvature of a hilbert module in terms that allow its comparison to a corresponding asymptotic expression for the euler characteristic

modelling volatility recurrence intervals in the chinese commodity futures market abstract the law of extreme event occurrence attracts much research the volatility recurrence intervals of chinese commodity futures market prices are studied the results show that the probability distributions of the scaled volatility recurrence intervals have a uniform scaling curve for different thresholds q so we can deduce the probability distribution of extreme events from normal events the tail of a scaling curve can be well fitted by a weibull form which is significance tested by ks measures both short term and long term memories are present in the recurrence intervals with different thresholds q which denotes that the recurrence intervals can be predicted in addition similar to volatility volatility recurrence intervals also have clustering features through monte carlo simulation we artificially synthesise arma garch class sequences similar to the original data and find out the reason behind the clustering the larger the parameter d of the figarch model the stronger the clustering effect is finally we use the fractionally integrated autoregressive conditional duration model fiacd to analyse the recurrence interval characteristics the results indicated that the fiacd model may provide a method to analyse volatility recurrence intervals

the nonnegative inverse eigenvalue problem abstract let 1 n be a list of complex numbers the nonnegative inverse eigenvalue problem niep is the problem of determining necessary and sufficient conditions in order that be the spectrum of an entrywise nonnegative n n matrix our purpose is to give an overview of the niep its history modern results and subproblems with particular emphasis on symmetric realizing matrices a substantial bibliography is included

cycles and clustering in bipartite networks we investigate the clustering coefficient in bipartite networks where cycles of size three are absent and therefore the standard definition of clustering coefficient cannot be used instead we use another coefficient given by the fraction of cycles with size four showing that both coefficients yield the same clustering properties the new coefficient is computed for two networks of sexual contacts one bipartite and another where no distinction between the nodes is made monopartite in both cases the clustering coefficient is similar furthermore combining both clustering coefficients we deduce an expression for estimating cycles of larger size which improves previous estimations and is suitable for either monopartite and multipartite networks and discuss the applicability of such analytical estimations

on pth roots of stochastic matrices in markov chain models in finance and healthcare a transition matrix over a certain time interval is needed but only a transition matrix over a longer time interval may be available the problem arises of determining a stochastic pth root of a stochastic matrix the given transition matrix by exploiting the theory of functions of matrices we develop results on the existence and characterization of matrix pth roots and in particular on the existence of stochastic pth roots of stochastic matrices our contributions include characterization of when a real matrix has a real pth root a classification of pth roots of a possibly singular matrix a sufficient condition for a pth root of a stochastic matrix to have unit row sums and the identification of two classes of stochastic matrices that have stochastic pth roots for all p we also delineate a wide variety of possible configurations as regards existence nature primary or nonprimary and number of stochastic roots and develop a necessary condition for existence of a stochastic root in terms of the spectrum of the given matrix

how to transform one convex function continuously into another the proximal average operator provides a parametric family of convex functions that continuously transform one convex function into another even when the domains of the two functions do not intersect we prove that the proximal average operator is a homotopy with respect to the epi topology study its properties and present several explicit formulas for specific classes of functions the parametric family inherits desirable properties such as differentiability and strict convexity from the given functions the results illustrate the powerful tools available in convex and variational analysis from both a theoretical and a computational point of view

multi variable weighted geometric means of positive definite matrices abstract we define a family of weighted geometric means g t a t 0 1 n where and a vary over all positive probability vectors in r n and n tuples of positive definite matrices resp each of these weighted geometric means interpolates between the weighted alm t 0 n and bmp t 1 n geometric means alm and bmp geometric means have been defined by ando li mathias and bini meini poloni respectively we show that the weighted geometric means satisfy multidimensional versions of all properties that one would expect for a two variable weighted geometric mean

structure preserving matrix means on the marcus minc stochastic matrices abstract in this paper we show that the set ps m of all m m positive definite stochastic matrices with diagonal entries bounded above by 1 m 1 is stable under the weighted geometric mean operation it is further shown that ps m is stable for some well known multivariable matrix means the least squares means for the riemannian trace metric and the kullback leibler divergence on the convex cone of m m positive definite matrices and alm ando li mathias and bmp bini meini poloni geometric means

rational hyperholomorphic functions in r4 we introduce the notion of rationality for hyperholomorphic functions functions in the kernel of the cauchy fueter operator following the case of one complex variable we give three equivalent definitions the first in terms of cauchy kovalevskaya quotients of polynomials the second in terms of realizations and the third in terms of backward shift invariance also introduced and studied are the counterparts of the arveson space and blaschke factors

the matrix geometric mean of parameterized weighted arithmetic and harmonic means we define a new family of matrix means l a r where and a vary over all positive probability vectors in rm and m tuples of positive definite matrices resp each of these means interpolates between the weighted harmonic mean and the arithmetic mean of the same weight with l l for each has a variational characterization as the unique minimizer of the weighted sum for the symmetrized parameterized kullback leibler divergence furthermore each can be realized as the common limit of the mean iteration by arithmetic and harmonic means in the unparameterized case or more generally the arithmetic and resolvent means other basic typical properties for a multivariable mean are derived

estimating and interpolating a markov chain from aggregate data given aggregated longitudinal data generated by a markov chain which may be nonhomogeneous the problem considered is that of modelling estimating and interpolating the logarithms of partial odds and hence the transition probabilities by partial odds is meant the probability of a transition to another state divided by the probability of no transition a result establishing asymptotic normality leads to vector weighted least squares estimation of parameterised partial odds using standard regression methods it is shown how to obtain estimates of one step transition probabilities from widely or irregularly spaced data the methods are illustrated on an example concerning competing causes of death

roots of completely positive maps abstract we introduce the concept of completely positive roots of completely positive maps on operator algebras we do this in different forms as asymptotic roots proper discrete roots and as continuous one parameter semigroups of roots we present structural and general existence and non existence results some special examples in settings where we understand the situation better and several challenging open problems our study is closely related to elfving s embedding problem in classical probability and the divisibility problem of quantum channels

analysis of non linear dynamics and bifurcations of a double pendulum abstract in this paper the dynamic behaviour of a double pendulum system in the vicinity of several compound critical points is explored through both analytical and numerical approaches four types of critical points are considered which are characterized by a double zero eigenvalue a simple zero and a pair of pure imaginary eigenvalues and two pairs of pure imaginary eigenvalues including resonant and non resonant cases with the aid of normal form theory the explicit expressions for the critical bifurcation lines leading to incipient and secondary bifurcations are obtained possible bifurcations leading to 2 d and 3 d tori are also investigated closed form stability conditions of the bifurcation solutions are presented a time integration scheme is used to find the numerical solutions for these bifurcation cases which agree with the analytical results finally numerical simulation is also applied to obtain double period cascading bifurcations leading to chaos

topological structural classes of complex networks we use theoretical principles to study how complex networks are topologically organized at large scale using spectral graph theory we predict the existence of four different topological structural classes of networks these classes correspond respectively to highly homogenous networks lacking structural bottlenecks networks organized into highly interconnected modules with low inter community connectivity networks with a highly connected central core surrounded by a sparser periphery and networks displaying a combination of highly connected groups quasicliques and groups of nodes partitioned into disjoint subsets quasibipartites here we show by means of the spectral scaling method that these classes really exist in real world ecological biological informational technological and social networks we show that neither of three network growth mechanisms random with uniform distribution preferential attachment and random with the same degree sequence as real network is able to reproduce the four structural classes of complex networks these models reproduce two of the network classes as a function of the average degree but completely fail in reproducing the other two classes of networks

aggregation and disaggregation techniques and methodology in optimization a fundamental issue in the use of optimization models is the tradeoff between the level of detail and the ease of using and solving the model aggregation and disaggregation techniques have proven to be valuable tools for manipulating data and determining the appropriate policies to employ for this tradeoff furthermore aggregation and disaggregation techniques offer promise for solving large scale optimization models supply a set of promising methodologies for studying the underlying structure of both univariate and multivariate data sets and provide a set of tools for manipulating data for different levels of decision makers in this paper we develop a general framework for aggregation and disaggregation methodology survey previous work regarding aggregation and disaggregation techniques for optimization problems illuminate the appropriate role of aggregation and disaggregation methodology for optimization applications and propose future research directions

variable diffusion in stock market fluctuations abstract we analyze intraday fluctuations in several stock indices to investigate the underlying stochastic processes using techniques appropriate for processes with nonstationary increments the five most actively traded stocks each contains two time intervals during the day where the variance of increments can be fit by power law scaling in time the fluctuations in return within these intervals follow asymptotic bi exponential distributions the autocorrelation function for increments vanishes rapidly but decays slowly for absolute and squared increments based on these results we propose an intraday stochastic model with linear variable diffusion coefficient as a lowest order approximation to the real dynamics of financial markets and to test the effects of time averaging techniques typically used for financial time series analysis we find that our model replicates major stylized facts associated with empirical financial time series we also find that ensemble averaging techniques can be used to identify the underlying dynamics correctly whereas time averages fail in this task our work indicates that ensemble average approaches will yield new insight into the study of financial markets dynamics our proposed model also provides new insight into the modeling of financial markets dynamics in microscopic time scales

operational characterization of divisibility of dynamical maps in this work we show the operational characterization to the divisibility of dynamical maps in terms of the distinguishability of quantum channels it is proven that the distinguishability of any pair of quantum channels does not increase under divisible maps in which the full hierarchy of divisibility is isomorphic to the structure of entanglement between system and environment this shows that i channel distinguishability is the operational quantity signifying detecting divisibility indivisibility of dynamical maps and ii the decision problem for the divisibility of maps is as hard as the separability problem in entanglement theory we also provide the information theoretic characterization to the divisibility of maps with conditional min entropy

invariant subspaces and nevanlinna pick kernels abstract a theorem of beurling lax halmos represents a subspace m of h2 c d the hardy space of analytic functions with values in the hilbert space e and square summable power series invariant for multiplication by z as h2 f where f is a subspace of e and is an inner function with values in l f e when the hardy space is replaced by the hilbert space h k determined by a nevanlinna pick kernel k such as the dirichlet kernel or the row contraction kernel on the ball in c d the blh theorem survives with f an auxiliary hilbert space and a l f e valued function which is inner in the sense that the operator m of multiplication by is a partial isometry under mild additional hypotheses when e c mz the operator of multiplication by z is cellularly indecomposable and has the codimension one property however if m is invariant for mz m mz m need not be a cyclic subspace for mz restricted to m

estimating the estrada index abstract let g be a graph on n vertices and let 1 2 n be its eigenvalues the estrada index of g is a recently introduced graph invariant defined as ee i 1 n e i we establish lower and upper bounds for ee in terms of the number of vertices and number of edges also some inequalities between ee and the energy of g are obtained

complementation in krein spaces a generalization of the concept of orthogonal complement is introduced in complete and decomposable complex vector spaces with scalar product complementation is a construction in the geometry of hilbert space which was applied to the invariant subspace theory of contractive transformations in hilbert space by james rovnyak and the author 6 the concept was later formalized by the author 3 continuous and contractive transformations in krein spaces appear in the estimation theory of riemann mapping functions 4 it is therefore of interest to know whether a generalization of complementation theory applies in krein spaces such a generalization is now obtained the results are also of interest in the invariant subspace theory of continuous and contractive transformations in krein spaces 5 the vector spaces considered are taken over the complex numbers a scalar product for a vector space 1 is a complex valued function a b of a and b in 1 which is linear symmetric and nondegenerate linearity means that the identity aa 3b c a a c 3 b c holds for all elements a b and c of 1 when a and are complex numbers symmetry means that the identity b a a b holds for all elements a and b of 1 nondegeneracy means that an element a of 1 is zero if the scalar product a b is zero for every element b of 1 every element b of 1 determines a linear functional bon 1 which is defined by b a a b for every element a of 1 the weak topology of 1 is the weakest topology with respect to which bis a continuous linear functional on 1 for every element b of 1 the weak topology of 1 is a locally convex topology having the property that every continuous linear functional on 1 is of the form bfor an element b of 1 the element b is then unique the antispace of a vector space with scalar product is the same vector space considered with the negative of the given scalar product a fundamental example of a vector space with scalar product is a hilbert space a krein space is a vector space with scalar product which is the orthogonal sum of a hilbert space and the antispace of a hilbert space received by the editors october 10 1986 and in revised form february 23 1987 the results of the paper were presented to the department of mathematics indiana and purdue university in indianapolis on march 27 1987 as the ernest j johnson colloquium 1980 mathematics subject classification 1985 revision primary 46d05 research supported by the national science foundation 1988 american mathematical society 0002 9947 88 1 00 25 per page

the proximal average basic theory the recently introduced proximal average of two convex functions is a convex function with many useful properties in this paper we introduce and systematically study the proximal average for finitely many convex functions the basic properties of the proximal average with respect to the standard convex analytical notions domain fenchel conjugate subdifferential proximal mapping epi continuity and others are provided and illustrated by several examples