spectral statistics for unitary transfer matrices of binary graphs quantum graphs have recently been introduced as model systems to study the spectral statistics of linear wave problems with chaotic classical limits it is proposed here to generalize this approach by considering arbitrary directed graphs with unitary transfer matrices an exponentially increasing contribution to the form factor is identified when performing a diagonal summation over periodic orbit degeneracy classes a special class of graphs so called binary graphs is studied in more detail for these the conditions for periodic orbit pairs to be correlated including correlations due to the unitarity of the transfer matrix can be given explicitly using combinatorial techniques it is possible to perform the summation over correlated periodic orbit pair contributions to the form factor for some low dimensional cases gradual convergence towards random matrix results is observed when increasing the number of vertices of the binary graphs

fine structure of spectral properties for random correlation matrices an application to financial markets we study some properties of eigenvalue spectra of financial correlation matrices in particular we investigate the nature of the large eigenvalue bulks which are observed empirically and which have often been regarded as a consequence of the supposedly large amount of noise contained in financial data we challenge this common knowledge by acting on the empirical correlation matrices of two data sets with a filtering procedure which highlights some of the cluster structure they contain and we analyze the consequences of such filtering on eigenvalue spectra we show that empirically observed eigenvalue bulks emerge as superpositions of smaller structures which in turn emerge as a consequence of cross correlations between stocks we interpret and corroborate these findings in terms of factor models and we compare empirical spectra to those predicted by random matrix theory for such models

bayesian single and double variable sampling plans for the weibull distribution with censoring the sampling inspection problem is one of the main research topics in quality control in this paper we employ bayesian decision theory to study single and double variable sampling plans for the weibull distribution with type ii censoring a general loss function which includes the sampling cost the time consuming cost the salvage value and the after sales cost is proposed to determine the bayes risk and the corresponding optimal sampling plan explicit expressions for the bayes risks for both single and double sampling plans are derived respectively numerical examples are given to illustrate the effectiveness of the proposed method comparisons between single and double sampling plans are made and sensitivity analysis is performed

eigenvalue significance testing for genetic association genotype eigenvectors are widely used as covariates for control of spurious stratification in genetic association significance testing for the accompanying eigenvalues has typically been based on a standard tracy widom limiting distribution for the largest eigenvalue derived under white noise assumptions it is known that even modest local correlation among markers inflates the largest eigenvalues even in the absence of true stratification in addition a few sample eigenvalues may be extreme creating further complications in accurate testing we explore several methods to identify appropriate null eigenvalue thresholds while remaining sensitive to eigenvalues corresponding to population stratification we introduce a novel block permutation approach designed to produce an appropriate null eigenvalue distribution by eliminating long range genomic correlation while preserving local correlation we also propose a fast approach based on eigenvalue distribution modeling using a simple fit criterion and the general marcenko pastur equation under a simple discrete eigenvalue model block permutation and the model based approach work well for pure simulations and for data resampled from the 1000 genomes project in contrast we find that the standard approach of computing an effective number of markers does not perform well the performance of the methods is also demonstrated for a motivating example from the international cystic fibrosis consortium

augmented implicitly restarted lanczos bidiagonalization methods new restarted lanczos bidiagonalization methods for the computation of a few of the largest or smallest singular values of a large matrix are presented restarting is carried out by augmentation of krylov subspaces that arise naturally in the standard lanczos bidiagonalization method the augmenting vectors are associated with certain ritz or harmonic ritz vectors computed examples show the new methods to be competitive with available schemes

random matrix theory and fund of funds portfolio optimisation abstract the proprietary nature of hedge fund investing means that it is common practise for managers to release minimal information about their returns the construction of a fund of hedge funds portfolio requires a correlation matrix which often has to be estimated using a relatively small sample of monthly returns data which induces noise in this paper random matrix theory rmt is applied to a cross correlation matrix c constructed using hedge fund returns data the analysis reveals a number of eigenvalues that deviate from the spectrum suggested by rmt the components of the deviating eigenvectors are found to correspond to distinct groups of strategies that are applied by hedge fund managers the inverse participation ratio is used to quantify the number of components that participate in each eigenvector finally the correlation matrix is cleaned by separating the noisy part from the non noisy part of c this technique is found to greatly reduce the difference between the predicted and realised risk of a portfolio leading to an improved risk profile for a fund of hedge funds

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

the bulk of the stock market correlation matrix is not pure noise abstract we analyse the structure of the distribution of eigenvalues of the stock market correlation matrix with increasing length of the time series representing the price changes we use 100 highly capitalized stocks from the american market and relate the result to the corresponding ensemble of wishart random matrices it turns out that systematically more eigenvalues remain beyond the borders prescribed by this variant of the random matrix theory rmt this may indicate that even the bulk of the spectrum of the stock market correlation matrix carries some sort of correlations that are masked by a measurement noise when the time series used to construct the matrix are short we also study some other characteristics of the noisy eigensignals like their return distributions temporal correlations or their multifractal spectra and the results support the above conclusions

beyond the heisenberg time semiclassical treatment of spectral correlations in chaotic systems with spin 1 2 the two point correlation function of chaotic systems with spin 1 2 is evaluated using periodic orbits the spectral form factor for all times thus becomes accessible equivalence with the predictions of random matrix theory for the gaussian symplectic ensemble is demonstrated a duality between the underlying generating functions of the orthogonal and symplectic symmetry classes is semiclassically established

semiclassical form factor for chaotic systems with spin we study the properties of the two point spectral form factor for classically chaotic systems with spin in the semiclassical limit with a suitable semiclassical trace formula as our principal tool to this end we introduce a regularized form factor and discuss the limit in which the so called diagonal approximation can be recovered the incorporation of the spin contribution to the trace formula requires an appropriate variant of the equidistribution principle of long periodic orbits as well as the notion of a skew product of the classical translational and spin dynamics provided this skew product is mixing we show that generically the diagonal approximation of the form factor coincides with the respective predictions from random matrix theory

universal spectral form factor for chaotic dynamics we consider the semiclassical limit of the spectral form factor k of fully chaotic dynamics starting from the gutzwiller type double sum over classical periodic orbits we set out to recover the universal behaviour predicted by random matrix theory both for dynamics with and without time reversal invariance for times smaller than half the heisenberg time th f 1 we extend the previously known expansion to include the cubic term beyond confirming the random matrix behaviour of individual spectra the virtue of that extension is that the diagrammatic rules come in sight which determine the families of orbit pairs responsible for all orders of the expansion

quantum scars of classical closed orbits in phase space the way in which quantum eigenstates are influenced by the closed orbits of a chaotic classical system is analysed in phase space x q p through the spectral wigner function w x e this is a sum over wigner functions of eigenstates within a range of energy e in the classical limit w is concentrated on the energy surface and smoothly distributed over it closed orbits provide oscillatory corrections scars for which explicit semiclassical formulae are calculated each scar is a fringe pattern decorating the orbit as x moves off the energy surface the fringes form an airy pattern with spacing of order h as x moves off the closed orbit the fringes form a complex gaussian with spacing h

random effects weibull regression model for occupational lifetime abstract with great interest we read the recent publication of sohn et al sohn s y chang i s moon t h 2007 random effects weibull regression model for occupational lifetime european journal of operational research 179 124 131 on a weibull regression model with random effects for modelling occupational lifetime we congratulate sohn and colleagues on their comprehensive and clearly written paper nevertheless we would like to comment on two points the first regarding the moments of the underlying weibull distribution the second regarding the relations of sohn s model to the class of frailty models

semiclassical theory for parametric correlation of energy levels parametric energy level correlation describes the response of the energy level statistics to an external parameter such as the magnetic field using semiclassical periodic orbit theory for a chaotic system we evaluate the parametric energy level correlation depending on the magnetic field difference the small time expansion of the spectral form factor k is shown to be in agreement with the prediction of parameter dependent random matrix theory to all orders in

random matrix approach to cross correlations in financial data we analyze cross correlations between price fluctuations of different stocks using methods of random matrix theory rmt using two large databases we calculate cross correlation matrices c of returns constructed from i 30 min returns of 1000 us stocks for the 2 yr period 1994 1995 ii 30 min returns of 881 us stocks for the 2 yr period 1996 1997 and iii 1 day returns of 422 us stocks for the 35 yr period 1962 1996 we test the statistics of the eigenvalues lambda i of c against a null hypothesis a random correlation matrix constructed from mutually uncorrelated time series we find that a majority of the eigenvalues of c fall within the rmt bounds lambda lambda for the eigenvalues of random correlation matrices we test the eigenvalues of c within the rmt bound for universal properties of random matrices and find good agreement with the results for the gaussian orthogonal ensemble of random matrices implying a large degree of randomness in the measured cross correlation coefficients further we find that the distribution of eigenvector components for the eigenvectors corresponding to the eigenvalues outside the rmt bound display systematic deviations from the rmt prediction in addition we find that these deviating eigenvectors are stable in time we analyze the components of the deviating eigenvectors and find that the largest eigenvalue corresponds to an influence common to all stocks our analysis of the remaining deviating eigenvectors shows distinct groups whose identities correspond to conventionally identified business sectors finally we discuss applications to the construction of portfolios of stocks that have a stable ratio of risk to return less

cluster structure in the correlation coefficient matrix can be characterized by abnormal eigenvalues abstract in a large number of previous studies the researchers found that some of the eigenvalues of the financial correlation matrix were greater than the predicted values of the random matrix theory r m t here we call these eigenvalues as abnormal eigenvalues in order to reveal the hidden meaning of these abnormal eigenvalues we study the toy model with cluster structure and find that these eigenvalues are related to the cluster structure of the correlation coefficient matrix in this paper model based experiments show that in most cases the number of abnormal eigenvalues of the correlation matrix is equal to the number of clusters in addition empirical studies show that the sum of the abnormal eigenvalues is related to the clarity of the cluster structure and is negatively correlated with the correlation dimension

on the distribution of the largest eigenvalue in principal components analysis let x 1 denote the square of the largest singular value of an n p matrix x all of whose entries are independent standard gaussian variates equivalently x 1 is the largest principal component variance of the covariance matrix x x or the largest eigenvalue of a p variate wishart distribution on n degrees of freedom with identity covariance consider the limit of large p and n with n p gamma ge 1 when centered by mu p sqrt n 1 sqrt p 2 and scaled by sigma p sqrt n 1 sqrt p 1 sqrt n 1 1 sqrt p 1 3 the distribution of x 1 approaches the tracey widom law of order 1 which is defined in terms of the painleve ii differential equation and can be numerically evaluated and tabulated in software simulations show the approximation to be informative for n and p as small as 5 the limit is derived via a corresponding result for complex wishart matrices using methods from random matrix theory the result suggests that some aspects of large p multivariate distribution theory may be easier to apply in practice than their fixed p counterparts

path integrals diffusion on su 2 and the fully frustrated antiferromagnetic spin cluster we study the path integral treatment of the quantum mechanics of a fully frustrated cluster of spins a cluster in which every pair of spins is coupled equally by antiferromagnetic heisenberg interactions such clusters are interesting partly because they are the building blocks of geometrically frustrated spin systems using a hubbard stratonovich transformation to decouple the interactions the boltzmann factor for the spin cluster is written in terms of the time evolution operator for a single spin in a stochastically varying magnetic field the time evolution operator follows a random walk in su 2 by switching from a langevin to a fokker planck description of this walk and computing the probability distribution of its end point we arrive at an expression for the partition function as a finite sum of single integrals the calculation provides an analytically tractable illustration of the auxiliary field approach as used in quantum monte carlo calculations and may potentially be extended to treat more complex frustrated spin systems

computation of ancestry scores with mixed families and unrelated individuals the issue of robustness to family relationships in computing genotype ancestry scores such as eigenvector projections has received increased attention in genetic association and is particularly challenging when sets of both unrelated individuals and closely related family members are included the current standard is to compute loadings left singular vectors using unrelated individuals and to compute projected scores for remaining family members however projected ancestry scores from this approach suffer from shrinkage toward zero we consider two main novel strategies i matrix substitution based on decomposition of a target family orthogonalized covariance matrix and ii using family averaged data to obtain loadings we illustrate the performance via simulations including resampling from 1000 genomes project data and analysis of a cystic fibrosis dataset the matrix substitution approach has similar performance to the current standard but is simple and uses only a genotype covariance matrix while the family average method shows superior performance our approaches are accompanied by novel ancillary approaches that provide considerable insight including individual specific eigenvalue scree plots

universality for the largest eigenvalue of sample covariance matrices with general population this paper is aimed at deriving the universality of the largest eigenvalue of a class of high dimensional real or complex sample covariance matrices of the form mathcal w n sigma 1 2 xx sigma 1 2 here x x ij m n is an m times n random matrix with independent entries x ij 1 leq i leq m 1 leq j leq n such that mathbb e x ij 0 mathbb e x ij 2 1 n on dimensionality we assume that m m n and n m rightarrow d in 0 infty as n rightarrow infty for a class of general deterministic positive definite m times m matrices sigma under some additional assumptions on the distribution of x ij s we show that the limiting behavior of the largest eigenvalue of mathcal w n is universal via pursuing a green function comparison strategy raised in probab theory related fields154 2012 341 407 adv math 229 2012 1435 1515 by erd s yau and yin for wigner matrices and extended by pillai and yin ann appl probab 24 2014 935 1001 to sample covariance matrices in the null case sigma i consequently in the standard complex case mathbb e x ij 2 0 combing this universality property and the results known for gaussian matrices obtained by el karoui in ann probab 35 2007 663 714 nonsingular case and onatski in ann appl probab 18 2008 470 490 singular case we show that after an appropriate normalization the largest eigenvalue of mathcal w n converges weakly to the type 2 tracy widom distribution mathrm tw 2 moreover in the real case we show that when sigma is spiked with a fixed number of subcritical spikes the type 1 tracy widom limit mathrm tw 1 holds for the normalized largest eigenvalue of mathcal w n which extends a result of feral and peche in j math phys 50 2009 073302 to the scenario of nondiagonal sigma and more generally distributed x in summary we establish the tracy widom type universality for the largest eigenvalue of generally distributed sample covariance matrices under quite light assumptions on sigma applications of these limiting results to statistical signal detection and structure recognition of separable covariance matrices are also discussed

shape fluctuations and random matrices we study a certain random growth model in two dimensions closely related to the one dimensional totally asymmetric exclusion process the results show that the shape fluctuations appropriately scaled converges in distribution to the tracy widom largest eigenvalue distribution for the gaussian unitary ensemble gue

the bakerian lecture 1987 quantum chaology bounded or driven classical systems often exhibit chaos exponential instability that persists but their quantum counterparts do not nevertheless there are new regimes of quantum behaviour that emerge in the semiclassical limit and depend on whether the classical orbits are regular or chaotic and this motivates the following definition definition quantum chaology is the study of semiclassical but nonclassical behaviour characteristic of systems whose classical motion exhibits chaos this is illustrated by the statistics of energy levels on scales comparable with the mean level spacing of order h n for n freedoms these fall into universality classes for classically chaotic systems the statistics are those of random matrices real symmetric or complex hermitian depending on the presence or absence of time reversal symmetry for classically regular ones the statistics are poisson on larger scales of order h i e classically small but semiclassically large universality breaks down these phenomena are being explained by representing spectra in terms of classical closed orbits universal spectral behaviour has its origin in very long orbits non universal behaviour depends only on short ones

an economic production lot size model with deteriorating items stock dependent demand inflation and partial backlogging in this paper we present an optimization framework to derive optimal production over a fixed planning horizon for items with a stock dependent demand rate and under inflationary conditions we consider a perishable item that follows a two parameter weibull distribution shortage is allowed and partially backlogged at a fixed rate a numerical example is taken up to illustrate the solution procedure and sensitivity analysis of the optimal solution with respect to the parameters of the system is carried out

distribution of the ratio of consecutive level spacings in random matrix ensembles we derive expressions for the probability distribution of the ratio of two consecutive level spacings for the classical ensembles of random matrices this ratio distribution was recently introduced to study spectral properties of many body problems as contrary to the standard level spacing distributions it does not depend on the local density of states our wigner like surmises are shown to be very accurate when compared to numerics and exact calculations in the large matrix size limit quantitative improvements are found through a polynomial expansion examples from a quantum many body lattice model and from zeros of the riemann zeta function are presented

finding optimal s s policies is about as simple as evaluating a single policy in this paper a new algorithm for computing optimal s s policies is derived based upon a number of new properties of the infinite horizon cost function c s s as well as a new upper bound for optimal order up to levels s and a new lower bound for optimal reorder levels s the algorithm is simple and easy to understand its computational complexity is only 2 4 times that required to evaluate a specific single s s policy the algorithm applies to both periodic review and continuous review inventory systems

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

random matrix analysis of human eeg data we use random matrix theory to demonstrate the existence of generic and subject independent features of the ensemble of correlation matrices extracted from human eeg data in particular the spectral density as well as the level spacings was analyzed and shown to be generic and subject independent we also investigate number variance distributions in this case we show that when the measured subject is visually stimulated the number variance displays deviations from the random matrix prediction

topological properties of stock networks based on minimal spanning tree and random matrix theory in financial time series abstract we investigated the topological properties of stock networks constructed by a minimal spanning tree we compared the original stock network with the estimated network the original network is obtained by the actual stock returns while the estimated network is the correlation matrix created by random matrix theory we found that the consistency between the two networks increases as more eigenvalues are considered in addition we suggested that the largest eigenvalue has a significant influence on the formation of stock networks

an efficient algorithm for computing optimal s s policies this paper presents an algorithm to compute an optimal s s policy under standard assumptions stationary data well behaved one period costs discrete demand full backlogging and the average cost criterion the method is iterative starting with an arbitrary given s s policy and converging to an optimal policy in a finite number of iterations any of the available approximations can thus be used as an initial solution each iteration requires only modest computations also a lower bound on the true optimal cost can be computed and used in a termination test empirical testing suggests very fast convergence

action correlations and random matrix theory the correlations in the spectra of quantum systems are intimately related to correlations which are of genuine classical origin and which appear in the spectra of actions of the classical periodic orbits of the corresponding classical systems we review this duality and the semiclassical theory which brings it about the conjecture that the quantum spectral statistics are described in terms of random matrix theory leads to the proposition that the classical two point correlation function is also given in terms of a universal function we study in detail the spectrum of actions of the baker map and use it to illustrate the steps needed to reveal the classical correlations their origin and their relation to symbolic dynamics

semiclassical universality of parametric spectral correlations we consider quantum systems with a chaotic classical limit that depends on an external parameter and study correlations between the spectra at different parameter values in particular we consider the parametric spectral form factor k x which depends on a scaled parameter difference x for parameter variations that do not change the symmetry of the system we show by using semiclassical periodic orbit expansions that the small expansion of the form factor agrees with random matrix theory for systems with and without time reversal symmetry

an epq model with partial backorders considering two backordering costs abstract we propose an epq model with partial backorders considering linear and fixed backordering costs time intervals rather than ordering size and backordering level are used as decision variables to derive the closed form optimal solution our approach analyzes different optimal inventory policies and decides whether shortage period should be scheduled in addition a critical backordering rate is derived to determine the feasible optimal solution the numerical example is provided to illustrate the solution procedure

matrix models for beta ensembles this paper constructs tridiagonal random matrix models for general 0 hermite gaussian and laguerre wishart ensembles these generalize the well known gaussian and wishart models for 1 2 4 furthermore in the cases of the laguerre ensembles we eliminate the exponent quantization present in the previously known models we further discuss applications for the new matrix models and present some open problems

an epq model with inflation in an imperfect production system in this paper a production inventory model is considered for stochastic demand with the effect of inflation generally every manufacturing system wants to produce perfect quality items however due to real life problems labor problems machine breakdown etc a certain percentage of products are of imperfect quality the imperfect items are reworked at a cost the lifetime of a defective item follows a weibull distribution due to the production of imperfect quality items a product shortage occurs the profit function is derived by using both a general distribution of demand and the uniform rectangular distribution of demand computational experiments along with graphical illustrations are presented to discuss the optimality of the probability functions

the spin contribution to the form factor of quantum graphs following the quantization of a graph with the dirac operator spin 1 2 we explain how additional weights in the spectral form factor k due to spin propagation around orbits produce higher order terms in the small asymptotics in agreement with symplectic random matrix ensembles we determine conditions on the group of spin rotations sufficient to generate cse statistics

optimization models and a ga based algorithm for stochastic time cost trade off problem in real life projects both the trade off between the project cost and the project completion time and the uncertainty of the environment are considerable aspects for decision makers however the research on the time cost trade off problem seldom concerns stochastic environments besides optimizing the expected value of the objective is the exclusive decision making criterion in the existing models for the stochastic time cost trade off problem in this paper two newly developed alternative stochastic time cost trade off models are proposed in which the philosophies of chance constrained programming and dependent chance programming are adopted for decision making in addition a hybrid intelligent algorithm integrating stochastic simulations and genetic algorithm is designed to search the quasi optimal schedules under different decision making criteria the goal of the paper is to reveal how to obtain the optimal balance of the project completion time and the project cost in stochastic environments

random matrix approach to categorical data analysis correlation and similarity measures are widely used in all the areas of sciences and social sciences often the variables are not numbers but are instead qualitative descriptors called categorical data we define and study similarity matrix as a measure of similarity for the case of categorical data this is of interest due to a deluge of categorical data such as movie ratings top 10 rankings and data from social media in the public domain that require analysis we show that the statistical properties of the spectra of similarity matrices constructed from categorical data follow random matrix predictions with the dominant eigenvalue being an exception we demonstrate this approach by applying it to the data for indian general elections and sea level pressures in the north atlantic ocean

scaling in the eigenvalue fluctuations of correlation matrices the spectra of empirical correlation matrices constructed from multivariate data are widely used in many areas of sciences engineering and social sciences as a tool to understand the information contained in typically large datasets in the last two decades random matrix theory based tools such as the nearest neighbour eigenvalue spacing and eigenvector distributions have been employed to extract the significant modes of variability present in such empirical correlations in this work we present an alternative analysis in terms of the recently introduced spacing ratios which does not require the cumbersome unfolding process it is shown that the higher order spacing ratio distributions for the wishart ensemble of random matrices characterized by the dyson index beta is related to the first order spacing ratio distribution with a modified value of co dimension beta this scaling is demonstrated for wishart ensemble and also for the spectra of empirical correlation matrices drawn from the observed stock market and atmospheric pressure data using a combination of analytical and numerics such scalings in spacing distributions are also discussed

two storage inventory problem with dynamic demand and interval valued lead time over finite time horizon under inflation and time value of money a finite time horizon inventory problem for a deteriorating item having two separate warehouses one is a own warehouse ow of finite dimension and other a rented warehouse rw is developed with interval valued lead time under inflation and time value of money due to different preserving facilities and storage environment inventory holding cost is considered to be different in different warehouses the demand rate of item is increasing with time at a decreasing rate shortages are allowed in each cycle and backlogged them partially shortages may or may not be allowed in the last cycle and under this circumstance there may be three different types of model here it is assumed that the replenishment cycle lengths are of equal length and the stocks of rw are transported to ow in continuous release pattern for each model different scenarios are depicted depending upon the re order point for the next lot representing the lead time by an interval number and using the interval arithmetic the single objective function for profit is changed to corresponding multi objective functions these functions are maximized and solved by fast and elitist multi objective genetic algorithm femga the models are illustrated numerically and the results are presented in tabular form

continuous review inventory model in mixed fuzzy and stochastic environment in this paper we consider a continuous review inventory system where fuzziness and randomness appear simultaneously into an optimization setting since demand plays an important role in such type of inventory systems we develop a model in a mixed environment by incorporating fuzzy random variable as customer demand after fuzzifying the random lead time demand we consider the annual average demand as a fuzzy random variable we provide an elegant methodology to determine the optimal order quantity and reorder point such that the total expected annual cost in the fuzzy sense has a minimum value since the expected value of a fuzzy random variable is a fuzzy quantity a method of ranking fuzzy numbers using their possibilistic mean values is adopted to achieve the optimal solution a numerical example is presented to illustrate the proposed model

spectral statistics in chaotic systems with a point interaction we consider quantum systems with a chaotic classical limit that are perturbed by a point like scatterer the spectral form factor k for these systems is evaluated semiclassically in terms of periodic and diffractive orbits it is shown for order 2 and 3 that off diagonal contributions to the form factor which involve diffractive orbits cancel exactly the diagonal contributions from diffractive orbits implying that the perturbation by the scatterer does not change the spectral statistic we further show that parametric spectral statistics for these systems are universal for small changes of the strength of the scatterer

periodic orbits and spectral statistics of pseudointegrable billiards we demonstrate for a generic pseudointegrable billiard that the number of periodic orbit families with length less than l increases as frac ensuremath pi b 0 l 2 a l where b 0 is a constant and a l is the average area occupied by these families we also find that a l increases with l before saturating finally we show that periodic orbits provide a good estimate of spectral correlations in the corresponding quantum spectrum and thus conclude that diffraction effects are not as significant in such studies

characterization of strange attractors a new measure of strange attractors is introduced which offers a practical algorithm to determine their character from the time series of a single observable the relation of this new measure to fractal dimension and information theoretic entropy is discussed

the liouville arnold nekhoroshev theorem for non compact invariant manifolds under certain conditions generalized action angle coordinates can be introduced near non compact invariant manifolds of completely and partially integrable hamiltonian systems

multi item imperfect production lot size model with hybrid number cost parameters in this study we have developed a multi item finite production lot size model with reworking of imperfect quality items when production stops defected items are assumed to rework at a constant rate the cost parameters in this model are taken here as hybrid numbers i e some of the costs are fuzzy numbers as well as random variables then the model is converted into a multi objective geometric programming gp problem a numerical example is given to support the problem a sensitivity analysis has given to study the nature of the objective functions

tracy widom limit for the largest eigenvalue of a large class of complex sample covariance matrices we consider the asymptotic fluctuation behavior of the largest eigenvalue of certain sample covariance matrices in the asymptotic regime where both dimensions of the corresponding data matrix go to infinity more precisely let x be an n x p matrix and let its rows be i i d complex normal vectors with mean 0 and covariance p we show that for a large class of covariance matrices p the largest eigenvalue of x x is asymptotically distributed after recentering and rescaling as the tracy widom distribution that appears in the study of the gaussian unitary ensemble we give explicit formulas for the centering and scaling sequences that are easy to implement and involve only the spectral distribution of the population covariance n and p the main theorem applies to a number of covariance models found in applications for example well behaved toeplitz matrices as well as covariance matrices whose spectral distribution is a sum of atoms under some conditions on the mass of the atoms are among the models the theorem can handle generalizations of the theorem to certain spiked versions of our models and a s results about the largest eigenvalue are given we also discuss a simple corollary that does not require normality of the entries of the data matrix and some consequences for applications in multivariate statistics

correlation and network analysis of global financial indices random matrix theory rmt and network methods are applied to investigate the correlation and network properties of 20 financial indices the results are compared before and during the financial crisis of 2008 in the rmt method the components of eigenvectors corresponding to the second largest eigenvalue form two clusters of indices in the positive and negative directions the components of these two clusters switch in opposite directions during the crisis the network analysis uses the fruchterman reingold layout to find clusters in the network of indices at different thresholds at a threshold of 0 6 before the crisis financial indices corresponding to the americas europe and asia pacific form separate clusters on the other hand during the crisis at the same threshold the american and european indices combine together to form a strongly linked cluster while the asia pacific indices form a separate weakly linked cluster if the value of the threshold is further increased to 0 9 then the european indices france germany and the united kingdom are found to be the most tightly linked indices the structure of the minimum spanning tree of financial indices is more starlike before the crisis and it changes to become more chainlike during the crisis the average linkage hierarchical clustering algorithm is used to find a clearer cluster structure in the network of financial indices the cophenetic correlation coefficients are calculated and found to increase significantly which indicates that the hierarchy increases during the financial crisis these results show that there is substantial change in the structure of the organization of financial indices during a financial crisis

large scale cross correlations in internet traffic the internet is a complex network of interconnected routers and the existence of a collective behavior such as congestion suggests that the correlations between the different connections play a crucial role it is thus critical to measure and quantify these correlations we use methods of random matrix theory rmt to analyze the cross correlation matrix c of information flow changes of 650 connections between 26 routers of the french scientific network renater we find that c has the universal properties of the gaussian orthogonal ensemble of random matrices the distribution of eigenvalues up to a rescaling that exhibits a typical correlation time of the order of 10 min and the spacing distribution follow the predictions of rmt there are some deviations for large eigenvalues which contain network specific information and which identify genuine correlations between the connections the study of the most correlated connections reveals the existence of active centers that are exchanging information with a large number of routers thereby inducing correlations between the corresponding connections these strong correlations could be a reason for the observed self similarity in the world wide web traffic

semiclassical quantization of sawtooth map with inclusion of next leading order and its failure the semiclassical quantization of sawtooth maps is reconsidered from the viewpoint of the higher order terms in the asymptotic series we carry out the semiclassical quantization in the leading and next leading orders however we fail in both cases the reasons are discussed in detail

semiclassical approach to parametric spectral correlation with spin 1 2 the spectral correlation of a chaotic system with spin 1 2 is universally described by the gse gaussian symplectic ensemble of random matrices in the semiclassical limit in semiclassical theory the spectral form factor is expressed in terms of the periodic orbits and the spin state is simulated by the uniform distribution on a sphere in this paper instead of the uniform distribution we introduce brownian motion on a sphere to yield the parametric motion of the energy levels as a result the small time expansion of the form factor is obtained and found to be in agreement with the prediction of parametric random matrices in the transition within the gse universality class moreover by starting the brownian motion from a point distribution on the sphere we gradually increase the effect of the spin and calculate the form factor describing the transition from the gaussian orthogonal ensemble class to the gse class

an eoq model with delay in payments and stock dependent demand in the presence of imperfect production abstract in real life situation supplier generally offers a delay period to the retailer to buy more in this connection a mathematical model is considered to investigate the retailer s optimal replenishment policy under permissible delay in payment with stock dependent demand within the eoq economic order quantity framework most of the eoq models are considered with infinite replenishment rate in this article the model is considered with finite replenishment rate under progressive payment scheme with the production of defective items within the cycle time the mathematical models have been derived for obtaining the optimal cycle time so that the annual total relevant cost is minimized numerical examples along with graphical representation and sensitivity analysis are provided to illustrate the model

distribution of the ratio of two consecutive level spacings in orthogonal to unitary crossover ensembles the ratio of two consecutive level spacings has emerged as a very useful metric in investigating universal features exhibited by complex spectra it does not require the knowledge of density of states and is therefore quite convenient to compute in analyzing the spectrum of a general system the wigner surmise like results for the ratio distribution are known for the invariant classes of gaussian random matrices however for the crossover ensembles which are useful in modeling systems with partially broken symmetries corresponding results have remained unavailable so far in this work we derive exact results for the distribution and average of the ratio of two consecutive level spacings in the gaussian orthogonal to unitary crossover ensemble using a 3 3 random matrix model this crossover is useful in modeling time reversal symmetry breaking in quantum chaotic systems although based on a 3 3 matrix model our results can also be applied in the study of large spectra provided the symmetry breaking parameter facilitating the crossover is suitably scaled we substantiate this claim by considering gaussian and laguerre crossover ensembles comprising large matrices moreover we apply our result to investigate the violation of time reversal invariance in the quantum kicked rotor system

correlation dimension of financial market abstract in this paper correlation dimension is applied to financial data analysis we calculate the correlation dimensions of some real market data and find that the dimensions are significantly smaller than those of the simulation data based on geometric brownian motion based on the analysis of the chinese and us stock market data the main results are as follows first by calculating three data sets for the chinese and us market we find that large market volatility leads to a significant decrease in the dimensions second based on 5 min stock price data we find that the chinese market dimension is significantly larger than the us market this shows a significant difference between the two markets for high frequency data third we randomly extract stocks from a stock set and calculate the correlation dimensions and find that the average value of these dimensions is close to the dimension of the original set in addition we analyse the intuitional meaning of the relevant dimensions used in this paper which are directly related to the average degree of the financial threshold network the dimension measures the speed of the average degree that varies with the threshold value a smaller dimension means that the rate of change is slower

an inventory model for imperfect items under inflationary conditions with considering inspection errors this paper represents a discounted cash flow approach for an inventory model for imperfect items under inflationary conditions with considering inspection errors the previous imperfect quality inventory studies however have mostly had the emphasis on developing cost minimizing models that do not consider imperfect inspection processes and related defect sales return issues despite their practical significance in this paper we assume that some produced items might not be perfect and the first stage inspector of product quality control might make some inspection errors during the separation of defective and perfect items thus this study proposes a profit maximizing inventory model with incorporating both imperfect production quality and two way imperfect inspection i e type one inspection error of falsely screening out a proportion of no defects and disposing of them like defects and type two inspection error of falsely not screening out a proportion of defects thereby passing them on to customers resulting in defect sales returns in addition this model includes one more stage of inspection that is after the rework process and there is no inspection error in this stage the purpose of this model is to determine the important factors of an inventory system to optimize the present value of the total profit in the finite time horizon finally a numerical example is provided to solve the presented inventory model using our proposed innovative approach which is further clarified through a sensitivity analysis

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

statistics of atmospheric correlations for a large class of quantum systems the statistical properties of their spectrum show remarkable agreement with random matrix predictions recent advances show that the scope of random matrix theory is much wider in this work we show that the random matrix approach can be beneficially applied to a completely different classical domain namely to the empirical correlation matrices obtained from the analysis of the basic atmospheric parameters that characterize the state of atmosphere we show that the spectrum of atmospheric correlation matrices satisfy the random matrix prescription in particular the eigenmodes of the atmospheric empirical correlation matrices that have physical significance are marked by deviations from the eigenvector distribution

spectral density of the correlation matrix of factor models a random matrix theory approach we studied the eigenvalue spectral density of the correlation matrix of factor models of multivariate time series by making use of the random matrix theory we analytically quantified the effect of statistical uncertainty on the spectral density due to the finiteness of the sample we considered a broad range of models ranging from one factor models to hierarchical multifactor models

moments of the wigner delay times the wigner time delay is a measure of the time spent by a particle inside the scattering region of an open system for chaotic systems the statistics of the individual delay times whose average is the wigner time delay are thought to be well described by random matrix theory here we present a semiclassical derivation showing the validity of random matrix results in order to simplify the semiclassical treatment we express the moments of the delay times in terms of correlation functions of scattering matrices at different energies in the semiclassical approximation the elements of the scattering matrix are given in terms of the classical scattering trajectories requiring one to study correlations between sets of such trajectories we describe the structure of correlated sets of trajectories and formulate the rules for their evaluation to the leading order in inverse channel number this allows us to derive a polynomial equation satisfied by the generating function of the moments along with showing the agreement of our semiclassical results with the moments predicted by random matrix theory we infer that the scattering matrix is unitary to all orders in the semiclassical approximation

wigner surmise for high order level spacing distributions of chaotic systems we suggest an extension of the wigner surmise for the nearest neighbor spacing distribution of energy levels of chaotic systems to include the nth order spacing distributions the main assumption is that the conditional probability density of occurrence of a level at a given distance from a fixed level provided that this distance contains n levels is expressed in terms of the n 1 th power of corresponding probability for a distance containing no levels at large spacings the nth order level distributions are assumed to have a gaussian shape as in the cases covered by the wigner surmise the expressions obtained are in good agreement with the results of numerical calculation by means of the random matrix theory for the three universal classes of symmetry

joint probability densities of level spacing ratios in random matrices we calculate analytically for finite size matrices joint probability densities of ratios of level spacings in ensembles of random matrices characterized by their associated confining potential we focus on the ratios of two spacings between three consecutive real eigenvalues as well as certain generalizations such as the overlapping ratios the resulting formulas are further analyzed in detail in two specific cases the hermite and the laguerre cases for which we offer explicit calculations for small n the analytical results are in excellent agreement with numerical simulations of usual random matrix ensembles and with the level statistics of a quantum many body lattice model and zeros of the riemann zeta function

random matrix theory for portfolio optimization a stability approach we apply random matrix theory rmt to an empirically measured financial correlation matrix c and show that this matrix contains a large amount of noise in order to determine the sensitivity of the spectral properties of a random matrix to noise we simulate a set of data and add different volumes of random noise having ascertained that the eigenspectrum is independent of the standard deviation of added noise we use rmt to determine the noise percentage in a correlation matrix based on real data from s p500 eigenvalue and eigenvector analyses are applied and the experimental results for each of them are presented to identify qualitatively and quantitatively different spectral properties of the empirical correlation matrix to a random counterpart finally we attempt to separate the noisy part from the non noisy part of c we apply an existing technique to cleaning c and then discuss its associated problems we propose a technique of filtering c that has many advantages from the stability point of view over the existing method of cleaning

deterministic parallel analysis an improved method for selecting factors and principal components factor analysis and principal component analysis are used in many application areas the first step choosing the number of components remains a serious challenge our work proposes improved methods for this important problem one of the most popular state of the art methods is parallel analysis pa which compares the observed factor strengths with simulated strengths under a noise only model the paper proposes improvements to pa we first derandomize it proposing deterministic pa which is faster and more reproducible than pa both pa and deterministic pa are prone to a shadowing phenomenon in which a strong factor makes it difficult to detect smaller but more interesting factors we propose deflation to counter shadowing we also propose to raise the decision threshold to improve estimation accuracy we prove several consistency results for our methods and test them in simulations we also illustrate our methods on data from the human genome diversity project where they significantly improve the accuracy

periodic orbits and a correlation function for the semiclassical density of states through the rule that there is one quantum state per planck cell in phase space classical mechanics supplies an average semiclassical density of states for a system with bound motion can it supply more refined averages such as the correlation function for the density of states i shall argue that for the two extreme cases of integrable classical motion and ergodic classical motion information can indeed be obtained on not quite this but a closely related correlation function the results for the two types of motion are markedly different

on the principal components of sample covariance matrices we introduce a class of m times m sample covariance matrices mathcal q which subsumes and generalizes several previous models the associated population covariance matrix sigma mathbb e mathcal q is assumed to differ from the identity by a matrix of bounded rank all quantities except the rank of sigma i m may depend on m in an arbitrary fashion we investigate the principal components i e the top eigenvalues and eigenvectors of mathcal q we derive precise large deviation estimates on the generalized components langle mathbf w varvec xi i rangle of the outlier and non outlier eigenvectors varvec xi i our results also hold near the so called bbp transition where outliers are created or annihilated and for degenerate or near degenerate outliers we believe the obtained rates of convergence to be optimal in addition we derive the asymptotic distribution of the generalized components of the non outlier eigenvectors a novel observation arising from our results is that unlike the eigenvalues the eigenvectors of the principal components contain information about the subcritical spikes of sigma the proofs use several results on the eigenvalues and eigenvectors of the uncorrelated matrix mathcal q satisfying mathbb e mathcal q i m as input the isotropic local marchenko pastur law established in bloemendal et al electron j probab 19 1 53 2014 level repulsion and quantum unique ergodicity of the eigenvectors the latter is a special case of a new universality result for the joint eigenvalue eigenvector distribution

a random matrix decimation procedure relating β 2 r 1 to β 2 r 1 classical random matrix ensembles with orthogonal symmetry have the property that the joint distribution of every second eigenvalue is equal to that of a classical random matrix ensemble with symplectic symmetry these results are shown to be the case r 1 of a family of inter relations between eigenvalue probability density functions for generalizations of the classical random matrix ensembles referred to as ensembles the inter relations give that the joint distribution of every r 1 st eigenvalue in certain ensembles with 2 r 1 is equal to that of another ensemble with 2 r 1 the proof requires generalizing a conditional probability density function due to dixon and anderson

optimal selling price and lotsize with time varying deterioration and partial backlogging the article deals with an eoq economic order quantity model over an infinite time horizon for perishable items where demand is price dependent and partial backorder is permitted the rate of deterioration is taken to be time proportional and it is assumed that shortage occurs at starting of the inventory cycle based on the partial backlogging and lost sale cases the author develops the criterion for the optimal solution for the replenishment schedule and proves the optimal ordering policy is unique moreover the article suggests to new functions regarding price dependent demand and time varying deterioration rate finally numerical examples are illustrated to test the model in various issues

semiclassical form factor for spectral and matrix element fluctuations of multidimensional chaotic systems we present a semiclassical calculation of the generalized form factor kab tau which characterizes the fluctuations of matrix elements of the operators a and b in the eigenbasis of the hamiltonian of a chaotic system our approach is based on some recently developed techniques for the spectral form factor of systems with hyperbolic and ergodic underlying classical dynamics and f 2 degrees of freedom that allow us to go beyond the diagonal approximation first we extend these techniques to systems with f 2 then we use these results to calculate kab tau we show that the dependence on the rescaled time tau time in units of the heisenberg time is universal for both the spectral and the generalized form factor furthermore we derive a relation between kab tau and the classical time correlation function of the weyl symbols of a and b