principal component analysis based on l1 norm maximization a method of principal component analysis pca based on a new l1 norm optimization technique is proposed unlike conventional pca which is based on l2 norm the proposed method is robust to outliers because it utilizes l1 norm which is less sensitive to outliers it is invariant to rotations as well the proposed l1 norm optimization technique is intuitive simple and easy to implement it is also proven to find a locally maximal solution the proposed method is applied to several datasets and the performances are compared with those of other conventional methods

max min solutions for fuzzy multiobjective matrix games abstract in this paper we consider two person zero sum games with fuzzy multiple payoff matrices we assume that each player has a fuzzy goal for each of the payoffs a degree of attainment of the fuzzy goal is defined and the max min strategy with respect to the degree of attainment of the fuzzy goal is examined if all of the membership functions both for the fuzzy payoffs and for the fuzzy goals are linear the formulated mathematical programming problem which yields the max min strategy can be reduced to the linear programming problem by making use of sakawa s method the variable transformations and the relaxation procedure

a multiobjective fuzzy stopping in a stochastic and fuzzy environment abstract in a stochastic and fuzzy environment a multiobjective fuzzy stopping problem is discussed the randomness and fuzziness are evaluated by probabilistic expectations and linear ranking functions respectively pareto optimal fuzzy stopping times are given under the assumption of regularity for stopping rules by using optimal stopping times

interactive determination of a utility function represented as a fuzzy integral abstract in this paper we propose an alternative method for interactive assessment of a utility function when this function is represented by a fuzzy integral it is generally agreed that the fuzzy integral provides a good representation of the human subjective structure however this type of integral may not be convenient because the assessment of the underlying fuzzy measure requires a lot of data in this paper we adopt an alternative point of view for determining the values of the fuzzy measure from few data by interactively changing equation constraints our method will contribute to increasing the applicability of the fuzzy measure and of the fuzzy integral in the field of decision support systems

fuzzy real numbers abstract the paper gives a contribution to the study of fuzzy real numbers continuing that in eklund and gahler 1988 gahler and gahler 1992 and gahler 1992 we start with investigating algebraic properties using two types of decompositions of fuzzy numbers and the notions of fuzzy norm of symmetric difference and of supplements of fuzzy numbers by means of these notions two special fuzzy metrics on the fuzzy real line are given the fuzzy distance function d and the extended fuzzy distance function d the main interest concerns fuzzy topological properties of the fuzzy real line in particular there are studied the fuzzy topologies t t d and t d t is closely related to the fuzzy topology of hutton s fuzzy unit interval and t d and t d are canonically generated by the fuzzy metrics d and d respectively

least squares shadowing sensitivity analysis of chaotic limit cycle oscillations abstract the adjoint method among other sensitivity analysis methods can fail in chaotic dynamical systems the result from these methods can be too large often by orders of magnitude when the result is the derivative of a long time averaged quantity this failure is known to be caused by ill conditioned initial value problems this paper overcomes this failure by replacing the initial value problem with the well conditioned least squares shadowing lss problem the lss problem is then linearized in our sensitivity analysis algorithm which computes a derivative that converges to the derivative of the infinitely long time average we demonstrate our algorithm in several dynamical systems exhibiting both periodic and chaotic oscillations

sensitivity analysis of limit cycle oscillations many unsteady problems equilibrate to periodic behavior for these problems the sensitivity of periodic outputs to system parameters are often desired and must be estimated from a finite time span or frequency domain calculation sensitivities computed in the time domain over a finite time span can take excessive time to converge or fail altogether to converge to the periodic value additionally finite span outputs can exhibit local extrema in parameter space which the periodic outputs they approximate do not hindering their use in optimization we derive a theoretical basis for this error and demonstrate it using two examples a van der pol oscillator and vortex shedding from a low reynolds number airfoil we show that output windowing enables the accurate computation of periodic output sensitivities and may allow for decreased simulation time to compute both time averaged outputs and sensitivities we classify two distinct window types long time over a large not necessarily integer number of periods and short time over a small integer number of periods finally from these two classes we investigate several examples of window shape and demonstrate their convergence with window size and error in the period approximation respectively

probably correct k nearest neighbor search in high dimensions a novel approach for k nearest neighbor k nn searching with euclidean metric is described it is well known that many sophisticated algorithms cannot beat the brute force algorithm when the dimensionality is high in this study a probably correct approach in which the correct set of k nearest neighbors is obtained in high probability is proposed for greatly reducing the searching time we exploit the marginal distribution of the k th nearest neighbors in low dimensions which is estimated from the stored data an empirical percentile approach we analyze the basic nature of the marginal distribution and show the advantage of the implemented algorithm which is a probabilistic variant of the partial distance searching its query time is sublinear in data size n that is o email protected with d o 1 in n and email protected 1 for any fixed dimension m

an optimal algorithm for approximate nearest neighbor searching fixed dimensions consider a set of s of n data points in real d dimensional space r d where distances are measured using any minkowski metric in nearest neighbor searching we preprocess s into a data structure so that given any query point q r d is the closest point of s to q can be reported quickly given any positive real e data point p is a 1 e approximate nearest neighbor of q if its distance from q is within a factor of 1 e of the distance to the true nearest neighbor we show that it is possible to preprocess a set of n points in r d in o dn log n time and o dn space so that given a query point q r d and e 0 a 1 e approximate nearest neighbor of q can be computed in o c d e log n time where c d e d 1 6d e d is a factor depending only on dimension and e in general we show that given an integer k 1 1 e approximations to the k nearest neighbors of q can be computed in additional o kd log n time

forward and adjoint sensitivity computation of chaotic dynamical systems this paper describes a forward algorithm and an adjoint algorithm for computing sensitivity derivatives in chaotic dynamical systems such as the lorenz attractor the algorithms compute the derivative of long time averaged statistical quantities to infinitesimal perturbations of the system parameters the algorithms are demonstrated on the lorenz attractor we show that sensitivity derivatives of statistical quantities can be accurately estimated using a single short trajectory over a time interval of 20 on the lorenz attractor

a framework for simultaneous aerodynamic design optimization in the presence of chaos abstract integrating existing solvers for unsteady partial differential equations into a simultaneous optimization method is challenging due to the forward in time information propagation of classical time stepping methods this paper applies the simultaneous single step one shot optimization method to a reformulated unsteady constraint that allows for both forward and backward in time information propagation especially in the presence of chaotic and turbulent flow solving the initial value problem simultaneously with the optimization problem often scales poorly with the time domain length the new formulation relaxes the initial condition and instead solves a least squares problem for the discrete partial differential equations this enables efficient one shot optimization that is independent of the time domain length even in the presence of chaos

a limit theorem in some dynamic fuzzy systems abstract in this paper using a fuzzy relation we define a dynamic fuzzy system with a compact state space by introducing a contraction property we study the limit of a sequence of fuzzy states and obtain a theorem for the existence and uniqueness of the solution of a fuzzy relational equation as an application we deal with a dynamic fuzzy system with a terminal fuzzy gain and give some characterizations for the fuzzy expected gain a numerical example is given to comprehend our idea in this paper

markov chains with a transition possibility measure and fuzzy dynamic programming abstract this paper constructs a markoov fuzzy process which represents transitions of grades of fuzzy sets with a transition possibility measure and a general state space we analyse snell s optimal stopping problem for the process and we apply the results to solve fuzzy dynamic programming with optimal stopping times and with general state spaces and action spaces under fuzzy transitions

a potential of fuzzy relations with a linear structure the unbounded case this paper is a sequel to yoshida et al 1993 in which the potential theory for linear fuzzy relations on the positive orthant r n is considered in the class of fuzzy sets with a compact support under the contractive assumption in this paper potential treatment for unbounded fuzzy sets is developed without the assumption of contraction and compactness the objective of this paper is to give the existence and the characterization of potentials for linear fuzzy relations under some reasonable conditions also introducing a partial order in fuzzy sets we prove riesz decomposition theorem in the fuzzy potential theory the proofs are shown by using only the linear structure and the monotonicity of fuzzy relations in the one dimensional case the potential and its cuts are explicitly calculated numerical examples are given to comprehend further discussions

convergence of the least squares shadowing method for computing derivative of ergodic averages for a parameterized hyperbolic system u i 1 f u i s the derivative of an ergodic average langle j rangle lim n rightarrow infty frac1n sum 1 n j u i s to the parameter s can be computed via the least squares shadowing method this method solves a constrained least squares problem and computes an approximation to the desired derivative frac d langle j rangle ds from the solution this paper proves that as the size of the least squares problem approaches infinity the computed approximation converges to the true derivative

characterizing dynamics with covariant lyapunov vectors a general method to determine covariant lyapunov vectors in both discrete and continuous time dynamical systems is introduced this allows us to address fundamental questions such as the degree of hyperbolicity which can be quantified in terms of the transversality of these intrinsic vectors for spatially extended systems the covariant lyapunov vectors have localization properties and spatial fourier spectra qualitatively different from those composing the orthonormalized basis obtained in the standard procedure used to calculate the lyapunov exponents

an optimal stopping problem in dynamic fuzzy systems with fuzzy rewards abstract this paper deals with an optimal stopping problem in dynamic fuzzy systems with fuzzy rewards and shows that the optimal discounted fuzzy reward is characterized by a unique solution of a fuzzy relational equation we define a fuzzy expectation with a density given by fuzzy goals and we estimate discounted fuzzy rewards by the fuzzy expectation this paper characterizes the optimal fuzzy expected value and gives an optimal stopping time

a fast nearest neighbor algorithm based on a principal axis search tree a new fast nearest neighbor algorithm is described that uses principal component analysis to build an efficient search tree at each node in the tree the data set is partitioned along the direction of maximum variance the search algorithm efficiently uses a depth first search and a new elimination criterion the new algorithm was compared to 16 other fast nearest neighbor algorithms on three types of common benchmark data sets including problems from time series prediction and image vector quantization this comparative study illustrates the strengths and weaknesses of all of the leading algorithms the new algorithm performed very well on all of the data sets and was consistently ranked among the top three algorithms

discrete second order adjoints in atmospheric chemical transport modeling atmospheric chemical transport models ctms are essential tools for the study of air pollution for environmental policy decisions for the interpretation of observational data and for producing air quality forecasts many air quality studies require sensitivity analyses i e the computation of derivatives of the model output with respect to model parameters the derivatives of a cost functional defined on the model output with respect to a large number of model parameters can be calculated efficiently through adjoint sensitivity analysis while the traditional first order adjoint models give the gradient of the cost functional with respect to parameters second order adjoint models give second derivative information in the form of products between the hessian of the cost functional and a vector representing a perturbation in sensitivity analysis a search direction in optimization an eigenvector etc in this paper we discuss the mathematical foundations of the discrete second order adjoint sensitivity method and present a complete set of computational tools for performing second order sensitivity studies in three dimensional atmospheric ctms the tools include discrete second order adjoints of runge kutta and of rosenbrock time stepping methods for stiff equations together with efficient implementation strategies numerical examples illustrate the use of these computational tools in important applications like sensitivity analysis optimization uncertainty quantification and the calculation of directions of maximal error growth in three dimensional atmospheric ctms

optimal stopping problems in a stochastic and fuzzy system in a stochastic and fuzzy environment two kinds of stopping models are discussed and compared the optimal fuzzy stopping times are given under the assumptions of monotonicity and regularity for stopping rules also we find that fuzzy stopping times are favored in a comparison between fuzzy and classical stopping models

a geometric levy model for n fold compound option pricing in a fuzzy framework in this paper we study the problem of n fold compound option valuation using the martingale method and the theory of fuzzy sets we adopt a geometric levy process for modeling the underlying asset price dynamics the log price is the sum of a brownian motion with drift and a poisson process describing jumps in the price to obtain the pricing formula for n fold compound option we use the esscher transformed martingale measure as the equivalent martingale measure the major challenge in deriving the closed form analytic expression for n fold compound options is to calculate complex multivariate normal integrals the complexity is due to the sophisticated structure of the options in order to overcome this difficulty we prove a mathematical expectation related to multivariate normal variables to the best of our knowledge this report describes the first time that such an approach has been adopted and it is highly useful in the pricing of n fold compound options and many other financial derivatives because the uncertainty in financial markets simultaneously involves randomness and fuzziness we assume that the underlying asset price follows a fuzzy stochastic process under this assumption the cut of the fuzzy price of n fold compound call options is derived considering a decision maker s subjective judgment the permissible range of the expected prices of n fold compound call options with uncertainty is given finally numerical examples are presented to illustrate and analyze the theoretical results

differentiation of srb states abstract let f be a diffeomorphism of a manifold m and f a generalized srb state for f if supp f is a hyperbolic compact set we show that the map is differentiable in a suitable functional setup and we compute the derivative when supp f is an attractor the derivative is given by where x is the vector field this formula can be extended to time dependent situations and also at least formally to nonuniformly hyperbolic situations the above results will find their use in the study of the onsager reciprocity relations and the fluctuation dissipation formula of nonequilibrium statistical mechanics

a potential of fuzzy relations with a linear structure the contractive case abstract in this paper we develop a potential theory of fuzzy relations on the positive orthant in a euclidean space by introducing a linear structure for fuzzy relations the existence of a potential and its characterization by fuzzy relational equation are derived under the assumption of contraction and compactness in the one dimensional unimodal case a potential is given explicity also a numerical example is shown to illustrate our approaches

dynamic programming for fuzzy systems with fuzzy environment abstract a dynamic programming functional equation for a multi stage decision problem with fuzzy dynamics and environment is formulated and solved by a process of fuzzy interpolation this is an extension of the bellman zadeh model

a simple algorithm for nearest neighbor search in high dimensions the problem of finding the closest point in high dimensional spaces is common in pattern recognition unfortunately the complexity of most existing search algorithms such as k d tree and r tree grows exponentially with dimension making them impractical for dimensionality above 15 in nearly all applications the closest point is of interest only if it lies within a user specified distance spl epsiv we present a simple and practical algorithm to efficiently search for the nearest neighbor within euclidean distance spl epsiv the use of projection search combined with a novel data structure dramatically improves performance in high dimensions a complexity analysis is presented which helps to automatically determine spl epsiv in structured problems a comprehensive set of benchmarks clearly shows the superiority of the proposed algorithm for a variety of structured and unstructured search problems object recognition is demonstrated as an example application the simplicity of the algorithm makes it possible to construct an inexpensive hardware search engine which can be 100 times faster than its software equivalent a c implementation of our algorithm is available

minimal repetition dynamic checkpointing algorithm for unsteady adjoint calculation adjoint equations of differential equations have seen widespread applications in optimization inverse problems and uncertainty quantification a major challenge in solving adjoint equations for time dependent systems has been the need to use the solution of the original system in the adjoint calculation and the associated memory requirement in applications where storing the entire solution history is impractical checkpointing methods have frequently been used however traditional checkpointing algorithms such as revolve require a priori knowledge of the number of time steps making these methods incompatible with adaptive time stepping we propose a dynamic checkpointing algorithm applicable when the number of time steps is a priori unknown our algorithm maintains a specified number of checkpoints on the fly as time integration proceeds for an arbitrary number of time steps the resulting checkpoints at any snapshot during the time integration have the optimal repetition number the efficiency of our algorithm is demonstrated both analytically and experimentally in solving adjoint equations this algorithm also has significant advantage in automatic differentiation when the length of execution is variable

fuzzy stopping in continuous time dynamic fuzzy systems in a continuous time dynamic fuzzy system a stopping problem regarding fuzzy rewards is discussed using fuzzy stopping times the fuzzy rewards are evaluated by an expectation generated from a linear ranking function the optimality equations for the optimal fuzzy rewards are given by variational inequalities and an optimal fuzzy stopping time is constructed under assumptions of monotonicity and regularity for stopping rules a numerical example is given to discuss that fuzzy stopping times are better than non fuzzy ones in comparison between the fuzzy stopping models and the non fuzzy ones

markov type fuzzy decision processes with a discounted reward on a closed interval abstract we formulate a new multi stage decision process with markov type fuzzy transition which is termed markov type fuzzy decision process in the general framework of the decision process both of state and action are assumed to be fuzzy itself the transition of states is defined using the fuzzy relation with markov property and the discounted total reward is described as a fuzzy number on a closed bounded interval to discuss the optimization problem a partial order of convex fuzzy numbers is introduced in this paper the discounted total reward associated with an admissible stationary policy is characterized by a unique fixed point of the contractive mapping moreover the optimality equation for the fuzzy decision model is derived under some continuity conditions also an illustrated example is given to explain the theoretical results and the computation in the paper