on stability of fuzzy systems expressed by fuzzy rules with singleton consequents addresses the issue of stability of a fuzzy system described by fuzzy rules with singleton consequents it first presents two canonical forms of a fuzzy system a parametric expression and a state space expression a fuzzy system with singleton consequents is found to be a piecewise polytopic affine system then the paper gives stability theorems for a discrete time system as well as for a continuous time system it also gives a brief survey on the stability issues of fuzzy control systems

work by robert kalaba on automated sensitivity analysis this paper reviews work by robert kalaba on the development of a program nasa for the automated sensitivity analysis of parametrized nonlinear systems over parameter intervals nasa incorporates a fast and efficient algorithm feed for higher order partial derivative evaluation as well as an adaptive homotopy continuation procedure for obtaining all required initial conditions applications are envisioned for fields such as economics and the biological sciences where models tend to be complex and closed form solutions are difficult to obtain

empirical scaling laws and the aggregation of non stationary data abstract widely cited evidence for scaling self similarity of the returns of stocks and other securities is inconsistent with virtually all currently used models for price movements in particular state of the art models provide for ubiquitous irregular and oftentimes high frequency fluctuations in volatility stochastic volatility both intraday and across the days weeks and years over which data is aggregated in demonstrations of self similarity of returns stochastic volatility renders these models which are based on variants and generalizations of random walks incompatible with self similarity we show here that empirical evidence for self similarity does not actually contradict the analytic lack of self similarity in these models the resolution of the mismatch between models and data can be traced to a statistical consequence of aggregating large amounts of non stationary data

the design methodology of radial basis function neural networks based on fuzzy k nearest neighbors approach various approaches to partitioning of high dimensional input space have been studied with the intent of developing homogeneous clusters formed over input and output spaces of variables encountered in system modeling in this study we propose a new design methodology of a fuzzy model where the input space is partitioned by making use of some classification algorithm especially fuzzy k nearest neighbors k nn classifier being guided by some auxiliary information granules formed in the output space this classifier being regarded in the context of this design as a supervision mechanism is used to capture the distribution of data over the output space this type of supervision is beneficial when developing the structure in the input space it is demonstrated that data involved in a partition constructed by the fuzzy k nn method realized in the input space show a high level of homogeneity with regard to the data present in the output space this enhances the performance of the fuzzy rule based model whose premises in the rules involve partitions formed by the fuzzy k nn the design is illustrated with the aid of numeric examples that also provide a detailed insight into the performance of the fuzzy models and quantify several crucial design issues

automatic differentiation of functions of derivatives in a recent paper an algorithm feed was introduced for the systematic exact evaluation of higher order partial derivatives of functions of many variables the present paper demonstrates that feed can be applied to a much broader class of functions than envisioned previously specifically feed can be used to evaluate the higher order partial derivatives of functions which are defined in terms of the derivatives of other functions a task required in many applications

an efficient immune based symbiotic particle swarm optimization learning algorithm for tsk type neuro fuzzy networks design in this paper we propose a new learning algorithm that can be used to design tsk type neuro fuzzy networks though there has been a great deal of interest in the use of immune algorithms ias for computer science and engineering in terms of fundamental methodologies they are not dramatically different from other algorithms in order to enhance the ia performance we propose the immune based symbiotic particle swarm optimization ispso for use in tsk type neuro fuzzy networks for solving the prediction and skin color detection problems the proposed ispso embeds the symbiotic evolution scheme in an ia and utilizes particle swarm optimization pso to improve the mutation mechanism in order to avoid trapping in a local optimal solution and to ensure the search capability of a near global optimal solution mutation plays an important role therefore we employed the advantages of pso to improve the mutation mechanism and used a method that introduces chaotic mapping with certainty ergodicity and the stochastic property into pso to improve global convergence unlike the ia that uses each individual in a population as a full solution to a problem symbiotic evolution assumes that each individual in a population represents only a partial solution to a problem complex solutions combine several individuals in the population

invariance in the recurrence of large returns and the validation of models of price dynamics starting from a robust nonparametric definition of large returns excursions we study the statistics of their occurrences focusing on the recurrence process the empirical waiting time distribution between excursions is remarkably invariant to year stock and scale return interval this invariance is related to self similarity of the marginal distributions of returns but the excursion waiting time distribution is a function of the entire return process and not just its univariate probabilities generalized autoregressive conditional heteroskedasticity garch models market time transformations based on volume or trades and generalized l evy random walk models all fail to fit the statistical structure of excursions

a self adaptive neural fuzzy network with group based symbiotic evolution and its prediction applications in this paper we propose a self adaptive neural fuzzy network with group based symbiotic evolution sanfn gse method a self adaptive learning algorithm consists of two major components first a self clustering algorithm sca identifies a parsimonious internal structure an internal structure is said to be parsimonious in the sense that the number of clusters fuzzy rules is equal to the true number of clusters in a given training data set the proposed sca is an online method and is a distance based connectionist clustering method unlike the traditional cluster techniques that only consider the total variation to updates the only one mean and deviation the proposed sca method considers the variation of each dimension for the input data second a group based symbiotic evolution learning gse method is used to adjust the parameters for the desired outputs the gse method is different from traditional gas genetic algorithms with each chromosome in the gse method representing a fuzzy system moreover in the gse method there are several groups in the population each group represents a set of the chromosomes that belong to a cluster computing by the sca in this paper we used numerical time series examples one step ahead prediction mackey glass chaotic time series and sunspot number forecasting to evaluate the proposed sanfn gse model the performance of the sanfn gse model compares excellently with other existing models in our time series simulations

scaling self similarity and multifractality in fx markets abstract this paper presents an empirical investigation of scaling and multifractal properties of us dollar deutschemark usd dem returns the data set is ten years of 5 min returns the cumulative return distributions of positive and negative tails at different time intervals are linear in the double logarithmic space this presents strong evidence that the usd dem returns exhibit power law scaling in the tails to test the multifractal properties of usd dem returns the mean moment of the absolute returns as a function of time intervals is plotted for different powers of absolute returns these moments show different slopes for these powers of absolute returns the nonlinearity of the scaling exponent indicates that the returns are multifractal

gensofnn a generic self organizing fuzzy neural network existing neural fuzzy neuro fuzzy networks proposed in the literature can be broadly classified into two groups the first group is essentially fuzzy systems with self tuning capabilities and requires an initial rule base to be specified prior to training the second group of neural fuzzy networks on the other hand is able to automatically formulate the fuzzy rules from the numerical training data no initial rule base needs to be specified prior to training a cluster analysis is first performed on the training data and the fuzzy rules are subsequently derived through the proper connections of these computed clusters however most existing neural fuzzy systems whether they belong to the first or second group encountered one or more of the following major problems they are 1 inconsistent rule base 2 heuristically defined node operations 3 susceptibility to noisy training data and the stability plasticity dilemma and 4 needs for prior knowledge such as the number of clusters to be computed hence a novel neural fuzzy system that is immune to the above mentioned deficiencies is proposed in this paper this new neural fuzzy system is named the generic self organizing fuzzy neural network gensofnn the gensofnn network has strong noise tolerance capability by employing a new clustering technique known as discrete incremental clustering dic the fuzzy rule base of the gensofnn network is consistent and compact as gensofnn has built in mechanisms to identify and prune redundant and or obsolete rules extensive simulations were conducted using the proposed gensofnn network and its performance is encouraging when benchmarked against other neural and neural fuzzy systems

solving nonlinear equations by adaptive homotopy continuation standard homotopy continuation methods for solving systems of nonlinear equations require the continuation parameter to move from 0 to 1 along the real line difficulties can occur however if a point of singularity is encountered during the course of the integration to ameliorate these difficulties this paper proposes extending the continuation parameter to complex values and adaptively computing a continuation path in the complex plane that avoids points giving rise to singularities specifically it is proposed that the continuation parameter move from 0 0i to 1 0i along a spider web grid centered at 1 0i in the complex plane the actual path through the grid is determined step by step in accordance with two objectives short path length and avoidance of singular points a two phase homotopy continuation is used to study the implementation of this idea numerical examples are presented which indicate the effectiveness of the approach

complete comparative static differential equations equations having form 1 arise as first order conditions in microeconomic constrained optimization models as defining characterizations for general equilibrium and macroeconomic models and as steady state solution characterizations for descriptive and optimal growth models see silberberg 12 hansen 7 cass and shell 3 and brock l if y r r is continuously differentiable over a neighborhood of a point x0 a in r n l for which y xo lx 0 and iy x0 or 0 then the implicit function theorem guarantees the existence of a continuously differentiable function x n cr r over some open neighborhood n cro of cx in r such that dx z ix yx x x a lyjx a x g e n cp 2

an ada library for automatic evaluation of derivatives requirements for the evaluation of high order partial derivatives arise in many applications including optimal control system identification and the numerical solution of nonlinear algebraic equations two point boundary value problems and integral equations these evaluations have long been shunned by numerical analysts because of the difficulty in forming symbolic expressions for the derivatives this paper describes in detail an implementation in ada of a set of simple procedures for evaluating derivatives exactly without the requirement to form their symbolic expressions and without resorting to finite difference methods an expression whose derivatives are desired is written in the usual way using standard mathematical operators and intrinsic functions and values of all desired derivatives are returned automatically two examples of parameter identification are shown one from economics and one from guidance and control a complete listing of all ada code is included

a finite algorithm for the exact evaluation of higher order partial derivatives of functions of many variables abstract a formal algorithm is given for the systematic exact evaluation of higher order partial derivatives of functions of many variables the algorithm improves upon wengert s method in two key respects applications are envisioned wherever gradients jacobians hessians and power series expansions could be employed

generalized autoregressive conditional heteroskedasticity a natural generalization of the arch autoregressive conditional heteroskedastic process introduced in engle 1982 to allow for past conditional variances in the current conditional variance equation is proposed stationarity conditions and autocorrelation structure for this new class of parametric models are derived maximum likelihood estimation and testing are also considered finally an empirical example relating to the uncertainty of the inflation rate is presented

nonlocal automated sensitivity analysis previously a complete ordinary differential equation ode system was developed for tracking the solution x of a parameterized system of nonlinear equations 0 x over an interval 0 this paper develops a two phase complex homotopy continuation method for obtaining the required initial conditions at t an initial short artificial continuation is followed by a continuation which essentially proceeds through the physically meaningful function which can ameliorate the problem of artificially induced singularities also the path in the complex plane followed by the continuation parameter in each phase evolves sequentially in an attempt to keep the path both short minimal number of integration steps and numerically stable avoidance of singular points a fortran program nasa has been developed for solving the complete ode system starting with a two phase initialization the program incorporates a fast and efficient procedure for the automatic evaluation of partial derivatives numerical experiments are reported which illustrate the program s effectiveness in ref 1 an analytically complete system of ordinary differential equations odes was developed for finding a solution vector x for a parameterized system of nonlinear equations 0 p x the well known ode dx d x was supplemented with odes for the adjoint a and the determinant 6 of the jacobian matrix vx x this differential system in principle permits nonlocal sensitivity analysis i e the tracking of the solution vector x and the sensitivity vector dx d together with the adjoint a and the determinant i over any closed interval 0 where the determinant i remains nonzero a fortran program was used successfully in ref 1 to solve this differential system for several illustrative examples subsequently the program was modified to incorporate a fast and efficient algorithm feed for the automatic evaluation of higher order partial derivatives 2 nevertheless to make the program a truly practical tool a simple and reliable procedure was still needed for obtaining the initial conditions x a and c required by the differential system at the initial parameter point ct this paper develops a simple but effective homotopy continuation method for obtaining these initial conditions which differs in two principal respects from standard homotopy continuation methods first the proposed continuation essentially proceeds through the function rather than through an artificial construct letting f x d x t a standard continuation method for finding a solu tion vector x x to the system of equations 0 f x would generally involve solving a system of equations of the form

scaling of the distribution of fluctuations of financial market indices up to more than one month we find that the distributions for dt 4d 1560 min are consistent with a power law asymptotic behavior characterized by an exponent a 3 well outside the stable levy regime 0 a 2 to test the robustness of the s p result we perform a parallel analysis on two other financial market indices database iv contains 3560 daily records of the nikkei index for the 14 year period 1984 1997 and database v contains 4649 daily records of the hang seng index for the 18 year period 1980 1997 we find estimates ofa consistent with those describing the distribution of s p 500 daily returns one possible reason for the scaling of these distributions is the long persistence of the autocorrelation function of the volatility for time scales longer than dt 3 4 d our results are consistent with a slow convergence to gaussian behavior s1063 651x 99 11211 x pacs number s 05 40 fb 05 45 tp 89 90 1n

simultaneous design of membership functions and rule sets for fuzzy controllers using genetic algorithms this paper examines the applicability of genetic algorithms ga s in the simultaneous design of membership functions and rule sets for fuzzy logic controllers previous work using genetic algorithms has focused on the development of rule sets or high performance membership functions however the interdependence between these two components suggests a simultaneous design procedure would be a more appropriate methodology when ga s have been used to develop both it has been done serially e g design the membership functions and then use them in the design of the rule set this however means that the membership functions were optimized for the initial rule set and not the rule set designed subsequently ga s are fully capable of creating complete fuzzy controllers given the equations of motion of the system eliminating the need for human input in the design loop this new method has been applied to two problems a cart controller and a truck controller beyond the development of these controllers we also examine the design of a robust controller for the cart problem and its ability to overcome faulty rules

scaling and memory of intraday volatility return intervals in stock markets we study the return interval tau between price volatilities that are above a certain threshold q for 31 intraday data sets including the standard and poor s 500 index and the 30 stocks that form the dow jones industrial index for different threshold q the probability density function pq tau scales with the mean interval tau as formula see text similar to that found in daily volatilities since the intraday records have significantly more data points compared to the daily records we could probe for much higher thresholds and still obtain good statistics we find that the scaling function f x is consistent for all 31 intraday data sets in various time resolutions and the function is well approximated by the stretched exponential f x similar to e ax gamma with gamma 0 38 0 05 and a 3 9 0 5 which indicates the existence of correlations we analyze the conditional probability distribution pq tau tau0 for tau following a certain interval tau0 and find pq tau tau0 depends on tau0 which demonstrates memory in intraday return intervals also we find that the mean conditional interval tau tau0 increases with tau0 consistent with the memory found for pq tau tau0 moreover we find that return interval records in addition to having short term correlations as demonstrated by pq tau tau0 have long term correlations with correlation exponents similar to that of volatility records

a new kernel based fuzzy clustering approach support vector clustering with cell growing in this paper the support vector clustering is extended to an adaptive cell growing model which maps data points to a high dimensional feature space through a desired kernel function this generalized model is called multiple spheres support vector clustering which essentially identifies dense regions in the original space by finding their corresponding spheres with minimal radius in the feature space a multisphere clustering algorithm based on adaptive cluster cell growing method is developed whereby it is possible to obtain the grade of memberships as well as cluster prototypes in partition the effectiveness of the proposed algorithm is demonstrated for the problem of arbitrary cluster shapes and for prototype identification in an actual application to a handwritten digit data set

scaling properties of foreign exchange volatility in this paper we investigate the scaling properties of foreign exchange volatility our methodology is based on a wavelet multi scaling approach which decomposes the variance of a time series and the covariance between two time series on a scale by scale basis through the application of a discrete wavelet transformation it is shown that foreign exchange rate volatilities follow different scaling laws at different horizons particularly there is a smaller degree of persistence in intra day volatility as compared to volatility at one day and higher scales therefore a common practice in the risk management industry to convert risk measures calculated at shorter horizons into longer horizons through a global scaling parameter may not be appropriate this paper also demonstrates that correlation between the foreign exchange volatilities is the lowest at the intra day scales but exhibits a gradual increase up to a daily scale the correlation coefficient stabilizes at scales one day and higher therefore the benefit of currency diversification is the greatest at the intra day scales and diminishes gradually at higher scales lower frequencies the wavelet cross correlation analysis also indicates that the association between two volatilities is stronger at lower frequencies

local and nonlocal comparative static analysis of economic systems a complete differential equation system has been developed for the local and nonlocal comparative static analysis of general parametrized economic systems j x a 0 the differential equations allow both qualitative and quantitative sensitivity studies at parameter points or over parameter intervals a fortran program comstat is now available for the numerical integration of the differential equations the only input requirements are j and initial conditions initialization is rendered routine by a two stage application of comstat derivatives are automatically evaluated via a generalized wengert method freeing the user from ever having to form analytical derivatives comstat is applied to a problem in optimal economic growth to show the sensitivity of the steady state capital labor ratio to changes in the time preference parameter

nonlinear least squares via automatic derivative evaluation this paper further develops the table algorithm kalaba et al 1981 for exact evaluation of higher order partial derivatives of functions of many variables we present and apply the table algorithm in the least squares estimation of the parameters of a ces production function the actual use of the algorithm proved to be easy and accurate

efficient self evolving evolutionary learning for neurofuzzy inference systems this study proposes an efficient self evolving evolutionary learning algorithm seela for neurofuzzy inference systems nfiss the major feature of the proposed seela is that it is based on evolutionary algorithms that can determine the number of fuzzy rules and adjust the nfis parameters the seela consists of structure learning and parameter learning the structure learning attempts to determine the number of fuzzy rules a subgroup symbiotic evolution is adopted to yield several variable fuzzy systems and an elite based structure strategy is adopted to find a suitable number of fuzzy rules for solving a problem the parameter learning is to adjust parameters of the nfis it is a hybrid evolutionary algorithm of cooperative particle swarm optimization cpso and cultural algorithm called cultural cpso ccpso the ccpso which uses cooperative behavior among multiple swarms can increase the global search capacity using the belief space experimental results demonstrate that the proposed method performs well in predicting time series and solving nonlinear control problems

long term learning for type 2 neural fuzzy systems abstract the development of a new long term learning framework for interval valued neural fuzzy systems is presented for the first time in this article the need for such a framework is twofold to address continuous batch learning of data sets and to take advantage the extra degree of freedom that type 2 fuzzy logic systems offer for better model predictive ability the presented long term learning framework uses principles of granular computing grc to capture information knowledge from raw data in the form of interval valued sets in order to build a computational mechanism that has the ability to adapt to new information in an additive and long term learning fashion the latter is to accommodate new input output mappings and new classes of data without significantly disturbing existing input output mappings therefore maintaining existing performance while creating and integrating new knowledge rules this is achieved via an iterative algorithmic process which involves a two step operation iterative rule base growth capturing new knowledge and iterative rule base pruning removing redundant knowledge for type 2 rules the two step operation helps create a growing but sustainable model structure the performance of the proposed system is demonstrated using a number of well known non linear benchmark functions as well as a highly nonlinear multivariate real industrial case study simulation results show that the performance of the original model structure is maintained and it is comparable to the updated model s performance following the incremental learning routine the study is concluded by evaluating the performance of the proposed framework in frequent and consecutive model updates where the balance between model accuracy and complexity is further assessed