identification of a single factor model using graphical gaussian rules we state a sufficient condition for the global identification of a single factor model when some conditional associations among residuals are allowed the condition relies on the structure of the conditional independence graph of the observed variable given the latent factor and can be derived using graphical rules

correlated wishart ensembles and chaotic time series we study the correlated wishart ensembles in the context of time series analysis we are interested in the statistics of eigenlevels viz variables associated with independent eigenmodes in the system the motivation of this work is to study the effect of time series correlations on the wishart ensembles in this connection we derive the level density and the two point function for the correlated wishart ensembles by using the binary correlation method using our analytic results we analyze spectra of autocovariance matrices derived from single variable stationary time series we consider the stochastic time series of gaussian variables with exponentially decaying correlations and time series of chaotic maps viz the arnold map the standard map and the stadium billiard map in both cases correlated time series are encountered and analyzed under the framework of random matrix theory it is shown that the eigenlevel statistics for the chaotic maps follow closely those of correlated wishart ensembles it is indicated that the presence of collective modes in the spectra of autocovariance matrices is related to the integrability of the system

efficient estimation for semiparametric structural equation models with censored data abstractstructural equation modeling is commonly used to capture complex structures of relationships among multiple variables both latent and observed we propose a general class of structural equation models with a semiparametric component for potentially censored survival times we consider nonparametric maximum likelihood estimation and devise a combined expectation maximization and newton raphson algorithm for its implementation we establish conditions for model identifiability and prove the consistency asymptotic normality and semiparametric efficiency of the estimators finally we demonstrate the satisfactory performance of the proposed methods through simulation studies and provide an application to a motivating cancer study that contains a variety of genomic variables supplementary materials for this article are available online

noise dressing of financial correlation matrices we show that results from the theory of random matrices are potentially of great interest to understand the statistical structure of the empirical correlation matrices appearing in the study of multivariate time series the central result of the present study which focuses on the case of financial price fluctuations is the remarkable agreement between the theoretical prediction based on the assumption that the correlation matrix is random and empirical data concerning the density of eigenvalues associated to the time series of the different stocks of the s 500 or other major markets in particular the present study raises serious doubts on the blind use of empirical correlation matrices for risk management

bayesian inference for graphical factor analysis models we generalize factor analysis models by allowing the concentration matrix of the residuals to have nonzero off diagonal elements the resulting model is named graphical factor analysis model allowing a structure of associations gives information about the correlation left unexplained by the unobserved variables which can be used both in the confirmatory and exploratory context we first present a sufficient condition for global identifiability of this class of models with a generic number of factors thereby extending the results in stanghellini 1997 and vicard 2000 we then consider the issue of model comparison and show that fast local computations are possible for this purpose if the conditional independence graphs on the residuals are restricted to be decomposable and a bayesian approach is adopted to achieve this aim we propose a new reversible jump mcmc method to approximate the posterior probabilities of the considered models we then study the evolution of political democracy in 75 developing countries based on eight measures of democracy in two different years

on the identification of a single factor model with correlated residuals summary a necessary and sufficient condition for the identification of a single factor model with correlated residuals is derived by studying the zero elements of their concentration matrix in particular the new condition is expressed in terms of the complementary graph of the residuals this graphical condition can be simply checked by means of an efficient algorithm an example is also given showing that sometimes the single factor model with correlated residuals can be used to overcome the problem of non identification of a larger factor model

graphical identifiability criteria for causal effects in studies with an unobserved treatment response variable summary we consider the problem of using data in studies with an unobserved treatment response variable in order to evaluate average causal effects when cause effect relationships between variables can be described by a directed acyclic graph and the corresponding recursive factorization of a joint distribution the paper proposes graphical criteria to test whether average causal effects are identifiable even if a treatment response variable is unobserved if the answer is affirmative we provide further formulations for average causal effects from the observed data the graphical criteria enable us to evaluate average causal effects when it is difficult to observe a treatment response variable

experimental versus numerical eigenvalues of a bunimovich stadium billiard a comparison we compare the statistical properties of eigenvalue sequences for a gamma 1 bunimovich stadium billiard the eigenvalues have been obtained in two ways one set results from a measurement of the eigenfrequencies of a superconducting microwave resonator real system and the other set is calculated numerically ideal system we show influence of mechanical imperfections of the real system in the analysis of the spectral fluctuations and in the length spectra compared to the exact data of the ideal system we also discuss the influence of a family of marginally stable orbits the bouncing ball orbits in two microwave stadium billiards with different geometrical dimensions

saturation of number variance in embedded random matrix ensembles we study fluctuation properties of embedded random matrix ensembles of noninteracting particles for ensemble of two noninteracting particle systems we find that unlike the spectra of classical random matrices correlation functions are nonstationary in the locally stationary region of spectra we study the number variance and the spacing distributions the spacing distributions follow the poisson statistics which is a key behavior of uncorrelated spectra the number variance varies linearly as in the poisson case for short correlation lengths but a kind of regularization occurs for large correlation lengths and the number variance approaches saturation values these results are known in the study of integrable systems but are being demonstrated for the first time in random matrix theory we conjecture that the interacting particle cases which exhibit the characteristics of classical random matrices for short correlation lengths will also show saturation effects for large correlation lengths

non generic spectral statistics in the quantized stadium billiard we consider the effect of a continuous family of neutral bouncing ball orbits on the energy spectrum of the quantized stadium billiard using a semiclassical approximation we derive analytic expressions for standard two point spectral measures the corrections due to the bouncing ball orbits account for some of the non generic features observed in the analysis of the spectrum of a stadium cavity which was recently measured once the bouncing ball contributions are subtracted the spectrum is shown to be well reproduced by the semi classical trace formula based on unstable periodic orbits we also study special patterns in the spectrum which are due to other non generic features such as edge effects and whispering gallery trajectories

minimization of the makespan in a two machine problem under given resource constraints in the paper the classical two machine flow shop problem was generalized to the case when job processing times may be reduced linearly by the application of a limited continuously divisible resource e g financial outlay energy fuel catalyzer etc it is proved that the decision form of this problem is np complete even for the fixed job processing times on one of the machines and identical job reduction rates on another some polynomially solvable cases of the problem are identified four simple and modified approximate algorithms are presented together with their worst case and experimental analysis also a fast exact algorithm of the branch and bound type based on the shown elimination properties of the problem considered is presented some computational results and generalizations e g bicriterial approach are included as well

scheduling two agents with controllable processing times abstract we consider several two agent scheduling problems with controllable job processing times where agents a and b have to share either a single machine or two identical machines in parallel while processing their jobs the processing times of the jobs of agent a are compressible at additional cost the objective function for agent b is always the same namely a regular function f max several different objective functions are considered for agent a including the total completion time plus compression cost the maximum tardiness plus compression cost the maximum lateness plus compression cost and the total compression cost subject to deadline constraints the imprecise computation model all problems are to minimize the objective function of agent a subject to a given upper bound on the objective function of agent b these problems have various applications in computer systems as well as in operations management we provide np hardness proofs for the more general problems and polynomial time algorithms for several special cases of the problems

job shop scheduling with resource time models of operations abstract the job shop problems with allocation of continuously divisible nonrenewable resource is considered the mathematical models of operations are linear decreasing functions with respect to an amount of resource the objective is sequencing operations and allocation of constrained resource such that the project duration is minimized thus the problem considered is a generalization of the classical job shop problem some properties of the optimal solution are presented the algorithm of solving this problem is based on the disjunctive graphs theory and branch and bound technique the theory of the algorithm is based on the critical path concept using the segment system approach the special feature of the algorithm is that it gives a complete solution which is associated with each node of the enumeration tree possible generalizations of the results presented are indicated

on the identification of path analysis models with one hidden variable summary we study criteria for identifiability of path analysis models with one hidden variable we first derive sufficient criteria for identification of models in which marginalisation is carried out over the hidden variable the sufficient criteria are based on the structure of the directed acyclic graph associated with the path analysis model and can be derived from the graph we treat further the identification of models when the hidden variable is conditioned on and establish connections with the extended skew normal distribution finally it is shown that the derived conditions extend the existing graphical criteria for identification

universal and nonuniversal properties of cross correlations in financial time series we use methods of random matrix theory to analyze the cross correlation matrix c of stock price changes of the largest 1000 u s companies for the 2 year period 1994 1995 we find that the statistics of most of the eigenvalues in the spectrum of c agree with the predictions of random matrix theory but there are deviations for a few of the largest eigenvalues we find that c has the universal properties of the gaussian orthogonal ensemble of random matrices furthermore we analyze the eigenvectors of c through their inverse participation ratio and find eigenvectors with large ratios at both edges of the eigenvalue spectrum a situation reminiscent of localization theory results

spectral fluctuation properties of hamiltonian systems the transition region between order and chaos the authors study numerically the classical dynamical behaviour and the spectral fluctuation properties of a class of hamiltonian systems with two degrees of freedom the quantum mechanical properties of these systems are monotonic but non universal functions of the fraction of classical phase space filled by chaotic trajectories it is found that the observed spectral fluctuation measures can be reproduced by a random matrix model which depends on one parameter only

on recovering a population covariance matrix in the presence of selection bias this paper considers the problem of using observational data in the presence of selection bias to identify causal effects in the framework of linear structural equation models we propose a criterion for testing whether or not observed statistical dependencies among variables are generated by conditioning on a common response variable when the answer is affirmative we further provide formulations for recovering the covariance matrix of the whole population from that of the selected population the results of this paper provide guidance for reliable causal inference based on the recovered covariance matrix obtained from the statistical information with selection bias

spectral form factor in a random matrix theory in the theory of disordered systems the spectral form factor s ensuremath tau the fourier transform of the two level correlation function with respect to the difference of energies is linear for ensuremath tau mathrm ensuremath tau mathrm c and constant for ensuremath tau g mathrm ensuremath tau mathrm c near zero and near mathrm ensuremath tau mathrm c it exhibits oscillations which have been discussed in several recent papers in problems of mesoscopic fluctuations and quantum chaos a comparison is often made with a random matrix theory it turns out that even in the simplest gaussian unitary ensemble these oscillations have not yet been studied there for random matrices the two level correlation function ensuremath rho ensuremath lambda 1 ensuremath lambda 2 exhibits several well known universal properties in the large n limit its fourier transform is linear as a consequence of the short distance universality of ensuremath rho ensuremath lambda 1 ensuremath lambda 2 however the crossover near zero and mathrm ensuremath tau mathrm c requires one to study these correlations for finite n for this purpose we use an exact contour integral representation of the two level correlation function which allows us to characterize these crossover oscillatory properties this representation is then extended to the case in which the hamiltonian is the sum of a deterministic part mathrm h 0 and of a gaussian random potential v finally we consider the extension to the time dependent case

the riemann zeros and eigenvalue asymptotics comparison between formulae for the counting functions of the heights tn of the riemann zeros and of semiclassical quantum eigenvalues en suggests that the tn are eigenvalues of an unknown hermitean operator h obtained by quantizing a classical dynamical system with hamiltonian hcl many features of hcl are provided by the analogy for example the riemann dynamics should be chaotic and have periodic orbits whose periods are multiples of logarithms of prime numbers statistics of the tn have a similar structure to those of the semiclassical en in particular they display random matrix universality at short range and nonuniversal behaviour over longer ranges very refined features of the statistics of the tn can be computed accurately from formulae with quantum analogues the riemann siegel formula for the zeta function is described in detail its interpretation as a relation between long and short periodic orbits gives further insights into the quantum spectral fluctuations we speculate that the riemann dynamics is related to the trajectories generated by the classical hamiltonian hcl xp

semiclassical theory of spectral rigidity the spectral rigidity l of a set of quantal energy levels is the mean square deviation of the spectral staircase from the straight line that best fits it over a range of l mean level spacings in the semiclassical limit 0 formulae are obtained giving l as a sum over classical periodic orbits when l l max where l max n 1 for a system of n freedoms l is shown to display the following universal behaviour as a result of properties of very long classical orbits if the system is classically integrable all periodic orbits filling tori l 1 5 l as in an uncorrelated poisson eigenvalue sequence if the system is classically chaotic all periodic orbits isolated and unstable and has no symmetry l in l 2 2 d if 1 l l max as in the gaussian unitary ensemble of random matrix theory if the system is chaotic and has time reversal symmetry l in l 2 e if 1 l l max as in the gaussian orthogonal ensemble when l l max l saturates non universally at a value determined by short classical orbits of order n 1 for integrable systems and in 1 for chaotic systems these results are obtained by using the periodic orbit expansion for the spectral density together with classical sum rules for the intensities of long orbits and a semiclassical sum rule restricting the manner in which their contributions interfere for two examples l is studied in detail the rectangular billiard integrable and the riemann zeta function assuming its zeros to be the eigenvalues of an unknown quantum system whose unknown classical limit is chaotic

measurement bias and effect restoration in causal inference summary this paper highlights several areas where graphical techniques can be harnessed to address the problem of measurement errors in causal inference in particular it discusses the control of unmeasured confounders in parametric and nonparametric models and the computational problem of obtaining bias free effect estimates in such models we derive new conditions under which causal effects can be restored by observing proxy variables of unmeasured confounders with without external studies

spectral properties of directed random networks with modular structure we study spectra of directed networks with inhibitory and excitatory couplings we investigate in particular eigenvector localization properties of various model networks for different values of correlation among their entries spectra of random networks with completely uncorrelated entries show a circular distribution with delocalized eigenvectors whereas networks with correlated entries have localized eigenvectors in order to understand the origin of localization we track the spectra as a function of connection probability and directionality as connections are made directed eigenstates start occurring in complex conjugate pairs and the eigenvalue distribution combined with the localization measure shows a rich pattern moreover for a very well distinguished community structure the whole spectrum is localized except few eigenstates at the boundary of the circular distribution as the network deviates from the community structure there is a sudden change in the localization property for a very small value of deformation from the perfect community structure we search for this effect for the whole range of correlation strengths and for different community configurations furthermore we investigate spectral properties of a metabolic network of zebrafish and compare them with those of the model networks

gaussian markov distributions over finite graphs on s interesse aux modeles de selection de covariance introduites par dempster 1972 et etudies par wermuth 1976

spectral statistics in the quantized cardioid billiard the spectral statistics of the strongly chaotic cardioid billiard is studied the analysis is based on the first 11 000 quantal energy levels for both odd and even symmetry it is found that the level spacing distribution is in good agreement with the gaussian orthogonal ensemble distribution of random matrix theory in the cases of the number variance and rigidity we observe agreement with the random matrix model for short range correlations only whereas for long range correlations both statistics saturate in agreement with semiclassical expectations furthermore the conjecture that for classically chaotic systems the normalized mode fluctuations have a universal gaussian distribution with unit variance is tested and found to be in very good agreement for both symmetry classes by means of the gutzwiller trace formula the trace of the cosine modulated heat kernel is studied since the billiard boundary is focusing there are conjugate points that give rise to zeros instead of exclusively at gaussian peaks at the locations of the periodic orbits

random matrix ensembles involving gaussian wigner and wishart matrices and biorthogonal structure we consider four nontrivial ensembles involving gaussian wigner and wishart matrices these are relevant to problems ranging from multiantenna communication to random supergravity we derive the matrix probability density as well as the eigenvalue densities for these ensembles in all cases the joint eigenvalue density exhibits a biorthogonal structure a determinantal representation based on a generalization of andreief s integration formula is used to compactly express the r point correlation function of eigenvalues this representation circumvents the complications encountered in the usual approaches and the answer is obtained immediately by examining the joint density of eigenvalues we validate our analytical results using monte carlo simulations