scaling concepts in periodically modulated noisy systems abstract we show that scaling arguments are very useful to analyze the dynamics of periodically modulated noisy systems information about the behavior of the relevant quantities such as the signal to noise ratio upon variations of the noise level can be obtained by analyzing the symmetries and invariances of the system in this way it is possible to predict diverse physical manifestations of the cooperative behavior between noise and input signal as for instance stochastic resonance spatiotemporal stochastic resonance and stochastic multiresonance

an approach to time series analysis and arma spectral estimation this paper presents an approach to time series analysis and arma spectral estimation from only the output data corrupted by noise it is shown that the generalized not well known modified yule walker myw equations hold when the residual is some correlated noise to solve such equations a new version of the generalized least squares gls method is proposed yielding ar parameter estimates with higher accuracy this gls method can also be used to enhance the estimation accuracy of ar parameters for short and noisy data in case of the myw equation holding theoretically furthermore a simple procedure for improving ma parameter estimates is studied our approach as cadzow s singular value decomposition svd method has provided significantly higher performance spectral estimates for a low order arma model than those obtained via usual techniques which are based upon direct solution of the myw equations and which use a high order model without considering an additive noise

a trust region spectral bundle method for nonconvex eigenvalue optimization we present a nonsmooth optimization technique for nonconvex maximum eigenvalue functions and for nonsmooth functions which are infinite maxima of eigenvalue functions we prove global convergence of our method in the sense that for an arbitrary starting point every accumulation point of the sequence of iterates is critical the method is tested on several problems in feedback control synthesis

scaling in currency exchange we study the scaling behavior in currency exchange rates our results suggest that they satisfy scaling with an exponent close to 0 5 but that it differs qualitatively from that of a simple random walk indeed price variations cannot be considered as independent variables and subtle correlations are present furthermore we introduce a novel statistical analysis for economic data which makes the physical properties of a signal more evident and eliminates the systematic effects of time periodicity

brief papers linear identification of arma processes a new method for estimating the parameters of an arma process is presented the method consists of three linear least squares estimations in the first an autoregressive model is fitted to the observation sequence yielding an estimate of the values of the driving white noise sequence linear least squares is then used to fit an arma model to the observation and estimated white noise sequences this model is used to filter the observation and estimated white noise sequences finally an arma model is fitted to the filtered sequences it is shown that the resultant estimator is p consistent the asymptotic bias tends to zero as the degree p of the autoregressive model tends to infinity and is p efficient the asymptotic efficiency approaches the theoretical maximum as p tends to infinity

estimating continuous time processes subject to time deformation an application to postwar u s gnp abstract a class of time series models is presented in which variables evolve on a data based rather than calendar time scale the discrete calendar time model thus obtained exhibits time varying parameters and conditional heteroscedasticity using a procedure based on the kalman filter univariate models are estimated for postwar u s real gross national product gnp and short and long term interest rates the results indicate significant time scale nonlinearities

large deviations and portfolio optimization abstract risk control and optimal diversification constitute a major focus in the finance and insurance industries as well as more or less consciously in our everyday life we present a discussion of the characterization of risks and of the optimization of portfolios that starts from a simple illustrative model and ends by a general functional integral formulation a major item is that risk usually thought of as one dimensional in the conventional mean variance approach has to be addressed by the full distribution of losses furthermore the time horizon of the investment is shown to play a major role we show the importance of accounting for large fluctuations and use the theory of cramer for large deviations in this context we first treat a simple model with a single risky asset that exemplifies the distinction between the average return and the typical return and the role of large deviations in multiplicative processes and the different optimal strategies for the investors depending on their size we then analyze the case of assets whose price variations are distributed according to exponential laws a situation that is found to describe daily price variations reasonably well several portfolio optimization strategies are presented that aim at controlling large risks we end by extending the standard mean variance portfolio optimization theory first within the quasi gaussian approximation and then using a general formulation for non gaussian correlated assets in terms of the formalism of functional integrals developed in the field theory of critical phenomena

controller design for linear multivariable feedback systems with stable plants using optimization with inequality constraints this paper proposes a two part design method for unity feed back linear multivariable systems with stable plants first a known algebraic technique yields a matrix q with the property that the family of exponentially stable and proper q globally parametrizes the family of exponentially stable closed loop systems with proper controllers second having obtained such a family of qs a non linear programming problem is formulated which when solved will yield the best feasible q with respect to designer specified objective and constraint functions the method developed makes possible the systematic formulation and solution of a class of design problems which represent practical design considerations as inequality constraints in non linear programming problems several new design problem formulations are given and then solved for some specific plants these formulations include for example constraints to avoid plant saturation and the mixing of time and frequency domain objectives and constraints

on the minority game analytical and numerical studies abstract we investigate further several properties of the minority game we have recently introduced we explain the origin of the phase transition and give an analytical expression of 2 n in the n 2 m region the ability of the players to learn a given payoff is also analyzed and we show that the darwinian evolution process tends to a self organized state in particular the lifetime distribution is a power law with exponent 2 furthermore we study the influence of identical players on their gain and on the systems performance finally we show that large brains always take advantage of small brains

statistical properties of deterministic threshold elements the case of market price abstract we analyze statistical properties of a set of deterministic threshold elements which is introduced as a model for the stock market the macroscopic variable of the stock market price shows seemingly stochastic fluctuation with a f 2 power spectrum consistent with real economic fluctuations the maximum lyapunov exponent is estimated to be zero indicating that the system is at the edge of chaos

fast algorithms for l p deconvolution this paper discusses two algorithms for l p 1 leq p leq 2 deconvolution one iterative reweighted least squares irls is discussed with an eye toward improving its computational efficiency while the other residual steepest descent rsd is considered in an attempt to improve its convergence properties in the first case fast fourier transforms are used to reduce the number of computations in the second a new rescaling procedure which enhances rsd convergence is introduced the lack of stability of l 1 filters and its implications are discussed simple examples are used to illustrate pertinent concepts

on the estimation of two dimensional moving average parameters the authors address the estimation problem of moving average ma parameters of a 2d autoregressive moving average arma model the problem is equivalent to solving a set of overdetermined 2d transcendental equations based on some extensions of the newton raphson method an iterative algorithm is proposed for estimating 2d ma parameters the performance of the algorithm is demonstrated by a numerical example for 2d sinusoids in white noise spatial series some interesting features of 2d arma modeling are observed

hydrodynamics from kinetic models of conservative economies in this paper we introduce and discuss the passage to hydrodynamic equations for kinetic models of conservative economies in which the density of wealth depends on additional parameters like the propensity to invest as in kinetic theory of rarefied gases the closure depends on the knowledge of the homogeneous steady wealth distribution the maxwellian of the underlying kinetic model the collision operator used here is the fokker planck operator introduced by j p bouchaud and m mezard wealth condensation in a simple model of economy physica a 282 2000 536 545 which has been recently obtained in a suitable asymptotic of a boltzmann like model involving both exchanges between agents and speculative trading by s cordier l pareschi and one of the authors s cordier l pareschi g toscani on a kinetic model for a simple market economy j stat phys 120 2005 253 277 numerical simulations on the fluid equations are then proposed and analyzed for various laws of variation of the propensity

determination of the ma order of an arma process using sample correlations it is shown that autoregressive information and moving average information are implicitly contained in two different correlation matrices an algorithm for ma order determination which adopts only autocorrelations and the ar order without requiring ar coefficients is proposed numerical simulations are presented to show the practical value of the proposed singular value decomposition svd based algorithm

stock market dynamics and turbulence parallel analysis of fluctuation phenomena abstract we report analogies and differences between the fluctuations in an economic index and the fluctuations in velocity of a fluid in a fully turbulent state specifically we systematically compare i the statistical properties of the s p 500 cash index recorded during the period january 84 december 89 with ii the statistical properties of the velocity of turbulent air measured in the atmospheric surface layer about 6 m above a wheat canopy in the connecticut agricultural research station we find non gaussian statistics and intermittency for both processes i and ii but the deviation from a gaussian probability density function are different for stock market dynamics and turbulence

two dimensional harmonic retrieval and its time domain analysis technique the two dimensional harmonic retrieval is examined in theory by confirming that the 2 d sinusoids in white noise are modeled as a special 2 d autoregressive moving average arma process whose ar parameters are identical to the ma ones a new analysis technique for resolving 2 d sinusoids in white noise is proposed

a hierarchical model of financial crashes abstract we follow up our previous conjecture that large stock market crashes are analogous to critical points in statistical physics the term critical refers to regimes of cooperative behavior such as magnetism at the curie temperature and liquid gas transitions and is characterized by the singular mathematical behavior of relevant observables to illustrate the concept of criticality we present a simple hierarchical model of traders exhibiting crowd behavior and show that it has a well defined critical point whose mathematical signature is a power law dependence of the price modulated by log periodic structures as recently found in market data by several independent groups

dynamical optimization theory of a diversified portfolio abstract we propose and study a simple model of dynamical redistribution of capital in a diversified portfolio we consider a hypothetical situation of a portfolio composed of n uncorrelated stocks each stock price follows a multiplicative random walk with identical drift and dispersion the rules of our model naturally give rise to power law tails in the distribution of capital fractions invested in different stocks the exponent of this scale free distribution is calculated in both discrete and continuous time formalism it is demonstrated that the dynamical redistribution strategy results in a larger typical growth rate of the capital than a static buy and hold strategy in the large n limit the typical growth rate is shown to asymptotically approach that of the expectation value of the stock price the finite dimensional variant of the model is shown to describe the partition function of directed polymers in random media

model space of economic events abstract a method for constructing the model or virtual space of economic events when economic objects can be considered as material ones is suggested we describe change of share rates in time at stock markets as the potential difference of attracted bodies in time in this virtual space each share of each enterprise is displayed by a single particle with a unit charge it is shown that the random value of potential difference at the origin of coordinates measured at a definite time interval has the probability density coinciding with the known distribution of levy flights or levy walks a distribution of alteration in time of the standard and poor index value obtained by mantegna and stanley they shown that it is the levy walks distribution too mantegna and stanley nature 376 1995 46 is used for determination of the introduced potential dependence on coordinates in the model space a simple phenomenological model of interaction potential is introduced the potential law of each particle turns out to be closed to r 2 14 in the minimum possible three dimensional model space this model permits calculation of time of random potential correlations at a certain point of the model space these correlations could characterize the time period of making a decision by an investor at stock exchange it is shown that this time is notably shorter in unstable periods 1987 a microscopical model of interaction in the virtual space is also discussed

prediction and entropy of nonlinear dynamical systems and symbolic sequences with lro abstract following shannon we introduce higher order entropies and derive dynamic entropies the nth order dynamic entropy conditional entropy is a measure of the uncertainty of the next state which follows after the observation of n foregoing states the asymptotic behaviour of the dynamic entropies at large n is studied for several nonlinear model systems and for symbolic sequences with long range order lro for example we investigate 1d maps texts dna strings and time series it is shown that the existence of long correlations improves the possibility of predictions characteristic scaling laws for the higher order shannon entropies and the conditional entropies are derived and a new interpolation formula is tested finally instead of the dynamic entropies which yield mean values of the uncertainty predictability we investigate the local values of the uncertainty predictability

a modified sqp algorithm for minimax problems in this paper a modified nonmonotone line search sqp algorithm for nonlinear minimax problems is presented during each iteration of the proposed algorithm a main search direction is obtained by solving a reduced quadratic program qp in order to avoid the maratos effect a correction direction is generated by solving the reduced system of linear equations under mild conditions the global and superlinear convergence can be achieved finally some preliminary numerical results are reported

analytical representation of stock and stock indexes returns non gaussian random walks with various jump laws abstract empirical data for stock and stock indexes returns that is available for international markets as well as for the russian stock market is introduced and discussed random walk process with a specific law of an elementary independent increment jump in some random walk space is proposed for a proper basic description an analytical representation of a random walk distribution law is derived from a general conception of stochastic elementary jumps this representation covers classic s chandrasekhar s results for gauss random walks with limited jumps and jumps having distributions with all moments as well as p levy flights with jump distributions without moments starting from the second one finally it describes truncated levy random walks for jumps having distributions with at least the second moment the natural generalization of truncated levy walks is done the random walk process is compared with known empirical data for the above discussed return fluctuations of international assets and stock indexes there is a very good agreement of the elaborated theory with empirical data

statistical properties of the volatility of price fluctuations we study the statistical properties of volatility measured by locally averaging over a time window t the absolute value of price changes over a short time interval ensuremath delta t we analyze the s 500 stock index for the 13 year period jan 1984 to dec 1996 we find that the cumulative distribution of the volatility is consistent with a power law asymptotic behavior characterized by an exponent ensuremath mu ensuremath approx 3 similar to what is found for the distribution of price changes the volatility distribution retains the same functional form for a range of values of t further we study the volatility correlations by using the power spectrum analysis both methods support a power law decay of the correlation function and give consistent estimates of the relevant scaling exponents also both methods show the presence of a crossover at approximately 1 5 days in addition we extend these results to the volatility of individual companies by analyzing a data base comprising all trades for the largest 500 u s companies over the two year period jan 1994 to dec 1995

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

the circulation of money and holding time distribution we have studied the statistical mechanics of money circulation in a closed economic system an explicit statistical formulation of the circulation velocity of money is presented for the first time by introducing the concept of holding time of money the result indicates that the velocity is governed by behavior patterns of economic agents computer simulations have been carried out in order to demonstrate the shape of the holding time distribution we find that money circulation is a poisson process in which the holding time probability distribution follows a type of gamma distribution and the velocity of money depends on the share for exchange and the number of agents

time intervals distribution of stock transactions and time correlation of stock indices in the model space abstract the formerly introduced model physica a 265 1999 264 physica a 287 2000 450 of stock market where bodies in the virtual space represent companies and enterprises is used for calculation of time transaction intervals as well as the time correlation of stock indices a single transaction is treated as an act of transient radiation while a body in a model space passes the boundary between two areas of different potentials existed due to potential fluctuations the first approximation gives the transaction time intervals t distribution t tr 2 1 2 instead of t 3 4 obtained by stanley s group physica a 287 2000 362 time correlations of stock indices are inversely proportional to the square root of the number of companies listed at the corresponding stock exchange the first approximation of ratio of djia stock index time correlation to sp500 one is 500 30 4 082

truncated levy distribution of sp500 stock index fluctuations distribution of one share fluctuations in a model space abstract truncated levy distributions of sp500 stock index fluctuations mantegna stanley nature 376 1995 46 are obtained in the formerly introduced model romanovsky physica a 265 1999 264 for stock market a one body random kinematics in this space corresponds to the one shares fluctuations on stock exchange the statistics of such kinematics is investigated and the asymptotic distribution of one share fluctuations was obtained all results are compared with the known experimental data mantegna stanley nature 376 1995 46 plerou et al phys rev e 60 1999 6519 and 5306 gopikrishnan et al eur j phys b 1998 138

volatility distribution in the s p500 stock index abstract we study the volatility of the s p500 stock index from 1984 to 1996 and find that the volatility distribution can be very well described by a log normal function further using detrended fluctuation analysis we show that the volatility is power law correlated with hurst exponent 0 9

varieties of long memory models long memory is defined as a series having a slowly declining correlogram or equivalently an infinite spectrum at zero frequency fractional integrated processes have such properties but here it is pointed out that a number of other processes can also be long memory including generalized fractionally integrated models arising from aggregation time changing coefficient models and possibly nonlinear models it seems that there are many classes of processes that deserve further study the relevance of long memory is illustrated using absolute returns from a daily stock market index

design of multivariable feedback systems with simple unstable plant this paper proposes a design methodology for distributed linear multivariable feedback systems with simple unstable plants a simple unstable plant has either first or second order unstable poles the methodology developed provides a global characterization of all realizable compensators which stabilize a given simple unstable plant a design example is given to show that this methodology can be used to generate in an appropriate computer aided design environment controllers which are optimal with respect to designer specified criteria additionally it is shown that the nature of the design methodology gives geometric insight into the dynamics of the process whereby an unstable plant is stabilized

levy walks and enhanced diffusion in milan stock exchange abstract we perform statistical analyses of the general and sectorial historical m i b indices of the milan stock exchange our analyses show that the price indices have statistical properties which are compatible with a levy random walk the time evolution of the daily variations of indices is intermittent on a time scale of years and the variance of almost all indices displays a superdiffusive behavior by using the theory of enhanced diffusion in levy walks as theoretical framework we ascribe the superdiffusive behavior to a nonlocal memory coupling price and time

scaling and correlation in financial time series we discuss the results of three recent phenomenological studies focussed on understanding the distinctive statistical properties of nancial time series i the probability distribution of stock price uctuations stock price uctuations occur in all magnitudes in analogy to earthquakes from tiny uctuations to very drastic events such as the crash of 19 october 1987 sometimes referred to as black monday the distribution of price uctuations decays with a power law tail well outside the levy stable regime and describes uctuations that dier by as much as 8 orders of magnitude in addition this distribution preserves its functional form for uctuations on time scales that dier by 3 orders of magnitude from 1 min up to approximately 10 days ii correlations in nancial time series while price uctuations themselves have rapidly decaying correlations the magnitude of uctuations measured by either the absolute value or the square of the price uctuations has correlations that decay as a power law persisting for several months iii volatility and trading activity we quantify the relation between trading activity measured by the number of transactions nt and the price change gt for a given stock over a time interval t t t we nd that nt displays long range power law correlations in time which leads to the interpretation that the long range correlations previously found for jgtj are connected to those of nt c 2000 elsevier science b v all rights reserved

a non linear programming approach to the computer aided design of regulators using a linear quadratic formulation a design technique is proposed for linear regulators in which a feedback controller of fixed structure is chosen to minimize an integral quadratic objective function subject to the satisfaction of integral quadratic constraint functions application of a non linear programming algorithm to this mathematically tractable formulation results in an efficient and useful computer aided design tool particular attention is paid to computational efficiency and various recommendations are made two design examples illustrate the flexibility of the approach and highlight the special insight afforded to the designer

singular value decomposition and improved frequency estimation using linear prediction linear prediction based lp methods for fitting multiple sinusoid signal models to observed data such as the forward backward fblp method of nuttall 5 and ulrych and clayton 6 are very ill conditioned the locations of estimated spectral peaks can be greatly affected by a small amount of noise because of the appearance of outliers lp estimation of frequencies can be greatly improved at low snr by singular value decomposition svd of the lp data matrix the improved performance at low snr is also better than that obtained by using the eigenvector corresponding to the minimum eigenvalue of the correlation matrix as is done in pisarenko s method and its variants

a new problem in control system design and circuit design an optimisation problem arising in the design of circuits and control systems is formulated and an outer approximation algorithm for solving it is presented the problem is characterized by constraints that must be satisfied for all functions in a given subset of a function space it is shown that an outer approximation type algorithm increases the number of variables and constraints at each iteration a practical algorithm will require a constraint dropping scheme

crossover in the cont bouchaud percolation model for market fluctuations abstract monte carlo simulations of the cont bouchaud herding model for stock market traders show power law distributions for short times and exponential truncation for longer time intervals if they are made at the percolation threshold in two to seven dimensions

interacting individuals leading to zipf s law institut de physique th eorique universit e de fribourg ch 1700 february 1 2008 we present a general approach to explain the zipf s law of city distribution if the simplestinteraction pairwise is assumed individuals tend to form cities in agreement with the well knownstatisticspacs numbers 89 50 r 05 20 y 05 40 j

covariance sequence approximation for parametric spectrum modeling parametric methods of spectrum analysis are founded on finite dimensional models for covariance sequences rational spectrum approximants for continuous spectra are based on autoregressive ar moving average ma or autoregressive moving average arma models for covariance sequences line spectrum approximants to discrete spectra are based on cosinusoidal models for covariance sequences in this paper we make the point that a wide variety of spectrum types admit to modal analysis wherein the modes are characterized by amplitudes frequencies and damping factors the associated modal decomposition is appropriate for both continuous and discrete components of the spectrum the domain of attraction for the decomposition includes arma sequences harmonically or nonharmonically related sinusoids damped sinusoids white noise and linear combinations of these the parametric spectrum analysis problem now becomes one of identifying mode parameters this we achieve by solving two modified least squares problems numerical results are presented to illustrate the identification of mode parameters and corresponding spectra from finite records of perfect and estimated covariance sequences the results for sinusoids and sinusoids in white noise are interpreted in terms of in phase and quadrature effects attributable to the finite record length

high resolution two dimensional arma spectral estimation the authors present a practical algorithm for estimating the power spectrum of a 2 d homogeneous random field based on 2 d autoregressive moving average arma modeling this algorithm is a two step approach first the ar parameters are estimated by solving a version of the 2 d modified yule walker equation for which some existing efficient algorithms are available then the ma spectrum parameters are obtained by simple computations the potential capability and the high resolution performance of the algorithm are demonstrated by using some numerical examples

parametric estimation of the cross power spectral density a new cross spectral analysis procedure is proposed for the parametric estimation of the relationship between two time sequences in the frequency domain in this method the two observable outputs are modeled as a pair of autoregressive moving average and moving average armama models under the assumption that the two outputs are driven by a common input and independent ones simultaneously cross and auto power spectral densities psds of a pair of armama models can be derived as forms of rational polynomial functions the coefficients of these functions can be estimated from the cross correlation function or the auto correlation functions of the two observed sequences by using the method presented in this paper the main advantage of the present procedure is that the physical parameters of an unknown system can be easily estimated from the coefficients of the cross and auto psd functions to illustrate the effectiveness of the proposed procedure numerical and practical examples of a mechanical vibration problem are analyzed the results show that the proposed procedure gives accurate cross and auto psd estimates moreover the physical properties of the unknown system can be well estimated from the obtained cross and auto psds

technical communique linear estimation of arma processes the method of estimating arma parameters first discussed by mayne and firoozan is investigated it is shown that if at the first stage the order of the fitted autoregression is allowed to depend on the number of time points in a reasonable manner then it will still be true that the final estimate of the parameter vector will converge almost surely to the true value this is to be compared to the result in the original paper where the order is fixed and it is shown that as the sample size increases the estimate converges to a value which if the order of the autoregression is high enough will be arbitrarily near to the true value some comments are made on other extensions on the law of the iterated logarithm on the central limit theorem and on the choice of the order of the fitted autoregression the innovation sequence need not be gaussian and for the convergence result only a natural condition relating to prediction needs be imposed

an order recursive generalized least squares algorithm for system identification in system identification an order recursive algorithm is of practical interest however such an algorithm for obtaining asymptotically unbiased and consistent parameter estimates in a noisy linear system is lacking an order recursive generalized least squares gls algorithm is presented this is based on a new recursive method for computing the least squares inverse developed in section ii and is an extension of hsia s gls algorithm 2

computer aided design via optimization many design problems including control design problems involve infinite dimensional constraints of the form f z a 0 for all a e a where a denotes time or frequency or a parameter vector in other design problems tuning or trimming of certain parameters after manufacture of the system is permitted the corresponding constraint is that for each a in a there exists a value t of the tuning parameter in a permissible set t such that f z a t 0 recent algorithms for solving design problems having such constraints are summarized

algebraic theory of linear multivariable feedback systems this paper presents an algebraic theory for analysis and design of linear multivariable feedback systems the theory is developed in an algebraic setting sufficiently general to include as special cases continuous and discrete time systems both lumped and distributed designs are implemented by construction of a controller with two vector inputs and one vector output use of controllers of this type is shown to generate convenient stability results and convenient global parametrizations of all i o maps and all disturbance to output maps achievable for a given plant by a stabilizing compensator these parametrizations are then used to show that any such i o map and any such disturbance to output map may be simultaneously realized by choice of an appropriate controller in the special case of lumped systems it is shown that the design theory can be reduced to manipulations involving polynomial matrices only the resulting design procedure is thus shown to be more efficient computationally finally the problem of asymptotically tracking a class of input signals is considered in the general algebraic setting it is shown that the classical results on asymptotic tracking can be generalized to this setting additionally sufficient conditions for robustness of asymptotic tracking and robustness of stability are developed

singular value decomposition based ma order determination of non gaussian arma models singular value decomposition svd based moving average ma order determination of non gaussian processes using higher order statistics is addressed it is shown that the ma order determination of autoregressive moving average arma models is equivalent to the rank determination of a certain error matrix and a svd approach is proposed its simplified form is applied to pure ma models to improve the robustness of the order selection a combination of the svd and the product of diagonal entries pode test is proposed some interesting applications of the two svd approaches are presented and simulations verify their performance

a finitely convergent algorithm for convex inequalities in engineering design problems it is often necessary to find a solution to a system of nonlinear inequalities in which the functions involved are not necessarily differentiable in this paper assuming convexity of the functions an algorithm is presented for solving such systems of inequalities in a finite number of iterations

correlations in economic time series a financial index of the new york stock exchange the sp here f is called the crossover frequency iii we confirm these results using the dfa detrended fluctuation analysis method see fig 2b which allows accurate estimates of exponents independent of local trends

universal features in the growth dynamics of complex organizations we analyze the fluctuations in the gross domestic product gdp of 152 countries for the period 1950 1992 we find that i the distribution of annual growth rates for countries of a given gdp decays with fatter tails than for a gaussian and ii the width of the distribution scales as a power law of gdp with a scaling exponent b 0 15 both findings are in surprising agreement with results on firm growth these results are consistent with the hypothesis that the evolution of organizations with complex structure is governed by similar growth mechanisms s0031 9007 98 07339 6 pacs numbers 02 50 ey 01 75 m 05 40 j 05 45 b in the study of physical systems the analysis of the scaling properties of the fluctuations has been shown to give important information regarding the underlying processes responsible for the observed macroscopic behavior in contrast most studies on the time evolution of economic time series have concentrated on average growth rates 1 18 here we investigate the possibility that the study of fluctuations in economics may also lead to a better understanding of the mechanisms responsible for the observed dynamics 19 23 we therefore analyze the fluctuations in the growth rate of the gross domestic product gdp of 152 countries during the period 1950 1992 24 we will show that i the distribution of annual growth rates for countries of a given gdp is consistent for a certain range with an exponential decay and ii the width of the distribution scales as a power law of gdp with a scaling exponent b 0 15 both findings are in surprising agreement with