a note on a paper of hicks and rhoades abstract our aim is to point out an error in the proof of lemma 2 in the paper fixed point theory in symmetric spaces with applications to probabilistic spaces by t l hicks b e rhoades nonlinear analysis 36 1999 331 344 and to indicate a way to repair it

symmetric spaces approach to some fixed point results abstract in this paper we present a simple and unified approach to the fixed point results on cone symmetric spaces and metric type spaces based on symmetric spaces fixed point theory we also give a new characterization of semi metric spaces with open balls

nonstationary cluster size inference with random field and permutation methods because of their increased sensitivity to spatially extended signals cluster size tests are widely used to detect changes and activations in brain images however when images are nonstationary the cluster size distribution varies depending on local smoothness clusters tend to be large in smooth regions resulting in increased false positives while in rough regions clusters tend to be small resulting in decreased sensitivity worsley et al proposed a random field theory rft method that adjusts cluster sizes according to local roughness of images worsley k j 2002 nonstationary fwhm and its effect on statistical inference of fmri data presented at the 8th international conference on functional mapping of the human brain june 2 6 2002 sendai japan available on cd rom in neuroimage 16 2 779 780 hum brain mapp 8 1999 98 in this paper we implement this method in a permutation test framework which requires very few assumptions is known to be exact j cereb blood flow metab 16 1996 7 and is robust neuroimage 20 2003 2343 we compared our method to stationary permutation stationary rft and nonstationary rft methods using simulated data we found that our permutation test performs well under any setting examined whereas the nonstationary rft test performs well only for smooth images under high df we also found that the stationary rft test becomes anticonservative under nonstationarity while both nonstationary rft and permutation tests remain valid under nonstationarity on a real pet data set we found that though the nonstationary tests have reduced sensitivity due to smoothness estimation variability these tests have better sensitivity for clusters in rough regions compared to stationary cluster size tests we include a detailed and consolidated description of worsley nonstationary rft cluster size test

construction of fuzzy systems using least squares method and genetic algorithm the fuzzy basis function network which was proposed in wang and mendel ieee trans neural networks 3 5 1992b 807 provides a way of representing fuzzy inference systems in a simple structure similar to those of radial basis function networks in this paper two new algorithms based on the least squares method and genetic algorithm are proposed for autonomous learning and construction of fuzzy basis function networks when training data are available the proposed algorithms add a significant fuzzy basis function node at each iteration during training based on error reduction measures the first a least squares algorithm provides a way of sequentially constructing meaningful fuzzy systems which are not possible to achieve with the orthogonal least squares algorithm while the second an adaptive least squares algorithm based on the combined least squares and genetic algorithm realizes hybrid structure parameter learning without human intervention simulation studies are performed with numerical examples for comparison of its performance against the orthogonal least squares algorithm backpropagation algorithm and conventional genetic algorithm the adaptive least squares algorithm is also applied to a real world problem to construct a fuzzy basis function network model for surface roughness in a grinding process using experimental data

interaction analysis for mimo nonlinear systems based on a fuzzy basis function network model this paper describes an interaction analysis method for a general multi input multi output mimo nonlinear system based on its fuzzy rule based model most real world multivariable systems are nonlinear complex and time varying the multiple system input output variables interact and sometime even fight against each other causing significant challenges for system control and optimization especially in many practical applications the accurate quantitative system model is not available or difficult to obtain which subsequently makes it impossible to analyze the system multivariable interaction characteristics in this paper the nonlinear mimo system is first modeled by fuzzy basis function networks fbfn based on a set of linguistic if then rules or data the multivariable interaction property is analyzed locally around the operating point based on the relative gain array rga which is systematically formulated using the system steady state gain values two simulation examples of chemical distillation columns illustrate the system interaction degree obtained by the proposed method is in a sufficient accuracy compared with the result calculated from the system explicit mathematical model which indicates the applicability of the proposed method as an alternative way to derive the system multivariable interaction when the system mathematical model is not available

integral φ type contractions and existence of continuous solutions for nonlinear integral inclusions abstract in this paper we discuss a general common fixed point theorem of integral type for two pairs of weakly compatible mappings satisfying certain integral type implicit relations in symmetric spaces by using the notion of a pair of mappings satisfying property e a our main result improves and extends the recent results of aliouche a aliouche a common fixed point theorem for weakly compatible mappings in symmetric spaces satisfying a contractive condition of integral type j math anal appl 322 2006 796 802 pathak tiwari and khan h k pathak rakesh tiwari m s khan a common fixed point theorem satisfying implicit relation appl math e notes 7 2007 222 228 and several other known results subsequently a multi valued version of krasnoselski fixed point theorem in a cone is used to discuss the existence of c 0 t and l p 0 t solutions to nonlinear integral inclusion y t 0 t k t s a s g s y s f s y s y s ds which improves the recent result of agarwal meehan and o regan r p agarwal m meehan d o regan positive l p and continuous solutions for fredholm integral inclusions in set valued mappings with applications in nonlinear analysis gordon breach amsterdam simaa 4 2002 1 9

equivalence of kernel machine regression and kernel distance covariance for multidimensional phenotype association studies summary associating genetic markers with a multidimensional phenotype is an important yet challenging problem in this work we establish the equivalence between two popular methods kernel machine regression kmr and kernel distance covariance kdc kmr is a semiparametric regression framework that models covariate effects parametrically and genetic markers non parametrically while kdc represents a class of methods that include distance covariance dc and hilbert schmidt independence criterion hsic which are nonparametric tests of independence we show that the equivalence between the score test of kmr and the kdc statistic under certain conditions can lead to a novel generalization of the kdc test that incorporates covariates our contributions are 3 fold 1 establishing the equivalence between kmr and kdc 2 showing that the principles of kmr can be applied to the interpretation of kdc 3 the development of a broader class of kdc statistics where the class members are statistics corresponding to different kernel combinations finally we perform simulation studies and an analysis of real data from the alzheimer s disease neuroimaging initiative adni study the adni study suggest that snps of flj16124 exhibit pairwise interaction effects that are strongly correlated to the changes of brain region volumes

genetic evolution of radial basis function coverage using orthogonal niches a well performing set of radial basis functions rbfs can emerge from genetic competition among individual rbfs genetic selection of the individual rbfs is based on credit sharing which localizes competition within orthogonal niches these orthogonal niches are derived using singular value decomposition and are used to apportion credit for the overall performance of the rbf network among individual nonorthogonal rbfs niche based credit apportionment facilitates competition to fill each niche and hence to cover the training data the resulting genetic algorithm yields rbf networks with better prediction performance on the mackey glass chaotic time series than rbf networks produced by the orthogonal least squares method and by k means clustering

equivalent contractive conditions in symmetric spaces in this paper we introduce 22 contractive conditions in symmetric spaces we prove that all these contractive conditions are equivalent then we use these conditions to get some common fixed point theorems for noncompatible maps

common fixed points under contractive conditions in cone metric spaces the aim of this paper is to present coincidence point result for two mappings in cone metric space which satisfy new contractive conditions our results generalize fixed point theorems of jungck g jungck commuting maps and fixed points amer math monthly 83 1976 261 263 abbas jungck m abbas g jungck common fixed point results for noncommuting mappings without continuity in cone metric spaces j math anal appl 341 2008 416 420 and fisher b fisher four mappings with a common fixed point arabic summary j univ kuwait sci 8 1981 131 139 in cone metric spaces to symmetric spaces

semiparametric regression of multidimensional genetic pathway data least squares kernel machines and linear mixed models we consider a semiparametric regression model that relates a normal outcome to covariates and a genetic pathway where the covariate effects are modeled parametrically and the pathway effect of multiple gene expressions is modeled parametrically or nonparametrically using least squares kernel machines lskms this unified framework allows a flexible function for the joint effect of multiple genes within a pathway by specifying a kernel function and allows for the possibility that each gene expression effect might be nonlinear and the genes within the same pathway are likely to interact with each other in a complicated way this semiparametric model also makes it possible to test for the overall genetic pathway effect we show that the lskm semiparametric regression can be formulated using a linear mixed model estimation and inference hence can proceed within the linear mixed model framework using standard mixed model software both the regression coefficients of the covariate effects and the lskm estimator of the genetic pathway effect can be obtained using the best linear unbiased predictor in the corresponding linear mixed model formulation the smoothing parameter and the kernel parameter can be estimated as variance components using restricted maximum likelihood a score test is developed to test for the genetic pathway effect model variable selection within the lskm framework is discussed the methods are illustrated using a prostate cancer data set and evaluated using simulations

sequential adaptive fuzzy inference system safis for nonlinear system identification and prediction in this paper a sequential adaptive fuzzy inference system called safis is developed based on the functional equivalence between a radial basis function network and a fuzzy inference system fis in safis the concept of influence of a fuzzy rule is introduced and using this the fuzzy rules are added or removed based on the input data received so far if the input data do not warrant adding of fuzzy rules then only the parameters of the closest in a euclidean sense rule are updated using an extended kalman filter ekf scheme the performance of safis is compared with several existing algorithms on two nonlinear system identification benchmark problems and a chaotic time series prediction problem results indicate that safis produces similar or better accuracies with less number of rules compared to other algorithms

solving the banach fixed point principle for nonlinear contractions in probabilistic metric spaces abstract the probabilistic version of the classical banach contraction principle was proved in 1972 by sehgal and bharucha reid v m sehgal a t bharucha reid fixed points of contraction mappings on pm spaces math syst theory 6 97 102 their fixed point theorem is further generalized by many authors in the intervening years many others have proved the probabilistic versions of the other known metric fixed point theorems however the problem to prove the probabilistic versions of the very important generalization of the banach contraction principle obtained in 1969 by boyd and wong d w boyd j s w wong on nonlinear contractions proc am math soc 20 1969 458 464 who proved the fixed point theorem for a self mapping of a metric space satisfying the very general nonlinear contractive condition is unsolved in these days similarly as in the metric space case to prove a fixed point theorem for a mapping satisfying the general probabilistic nonlinear contractive condition it was necessary to find a new approach substantially different from the previous technique for cases where a mapping satisfies the probabilistic linear contraction condition introduced by sehgal and bharucha reid and further used by many authors so the problem to obtain a truthful probabilistic version of the banach fixed point principle for general nonlinear contractions existed unsolved for over 35 years we have solved this problem in this paper

learning control using fuzzified self organizing radial basis function network this note describes an approach to integrating fuzzy reasoning systems with radial basis function rbf networks and shows how the integrated network can be employed as a multivariable self organizing and self learning fuzzy controller in particular by drawing some equivalence between a simplified fuzzy control algorithm sfca and a rbf network we conclude that the rbf network can be interpreted in the context of fuzzy systems and can be naturally fuzzified into a class of more general networks referred to as fbfn with a variety of basis functions not necessarily globally radial synthesized from each dimension by fuzzy logical operators on the other hand as a result of natural generalization from rbf to sfca we claim that the fuzzy system like rbf is capable of universal approximation next the fbfn is used as a multivariable rule based controller but with an assumption that no rule base exists leading to a challenging problem of how to construct such a rule base directly from the control environment we propose a simple and systematic approach to performing this task by using a fuzzified competitive self organizing scheme and incorporating an iterative learning control algorithm into the system we have applied the approach to a problem of multivariable blood pressure control with a fbfn based controller having six inputs and two outputs representing a complicated control structure

fixed point theorems for non self mappings in symmetric spaces under φ weak contractive conditions and an application to functional equations in dynamic programming in this paper we prove some common fixed point theorems for two pairs of non self weakly compatible mappings enjoying common limit range property besides satisfying a generalized f weak contractive condition in symmetric spaces we furnish some illustrative examples to highlight the realized improvements in our results over the corresponding relevant results of the existing literature we extend our main result to four finite families of mappings in symmetric spaces using the notion of pairwise commuting mappings finally we utilize our results to discuss the existence and uniqueness of solutions of certain system of functional equations arising in dynamic programming

fixed point theorems in symmetric spaces and applications to probabilistic spaces abstract several fixed point theorems for symmetric spaces are proved then these theorems are used in symmetric ppm space to prove and generalize theorem 6 of t l hicks b e rhoades fixed point theory in symmetric spaces with applications to probabilistic spaces nonlinear anal 36 1999 331 344

context dependent fuzzy systems with application to time series prediction in this paper we introduce an implementation of a fuzzy system whose parameters are mutable according to the context the construction of the system is done via two steps first we build a based type 1 takagi sugeno kang tsk fuzzy system whose membership functions will be later adjusted to the situation by means of contextual transformation to reflect the influence of context in the interpretation of fuzzy sets second an iterative algorithm is performed to identify the transformation matrix which is used to scale the membership functions of the reference based fuzzy sets in each of the contexts the identification of the premise part of the based fuzzy system is performed via a combination of an island model parallel genetic algorithm and a space search memetic algorithm while the identification of the consequent parameters of the system is done via an improved qr householder least squares method the proposed system is evaluated using the well known mackey glass time series prediction benchmark dataset and has shown better accuracy than any other previous works concerning the same problem

validating cluster size inference random field and permutation methods cluster size tests used in analyses of brain images can have more sensitivity compared to intensity based tests the random field rf theory has been widely used in implementation of such tests however the behavior of such tests is not well understood especially when the rf assumptions are in doubt in this paper we carried out a simulation study of cluster size tests under varying smoothness thresholds and degrees of freedom comparing rf performance to that of the permutation test which is known to be exact for gaussian images we find that the rf methods are generally conservative especially for low smoothness and low threshold for t images the rf tests are found to be conservative at lower thresholds and do not perform well unless the threshold is high and images are sufficiently smooth the permutation test performs well for any settings though the discreteness in cluster size must be accounted for we make specific recommendations on when permutation tests are to be preferred to rf tests

robust smoothness estimation in statistical parametric maps using standardized residuals from the general linear model the assessment of significant activations in functional imaging using voxel based methods often relies on results derived from the theory of gaussian random fields these results solve the multiple comparison problem and assume that the spatial correlation or smoothness of the data is known or can be estimated end results i e p values associated with local maxima clusters or sets of clusters critically depend on this assessment which should be as exact and as reliable as possible in some earlier implementations of statistical parametric mapping spm spm94 spm95 the smoothness was assessed on gaussianized t fields gt f that are not generally free of physiological signal this technique has two limitations first the estimation is not stable the variance of the estimator being far from negligible and second physiological signal in the gt f will bias the estimation in this paper we describe an estimation method that overcomes these drawbacks the new approach involves estimating the smoothness of standardized residual fields which approximates the smoothness of the component fields of the associated t field knowing the smoothness of these component fields is important because it allows one to compute corrected p values for statistical fields other than the t field or the gt f e g the f map and eschews bias due to deviation from the null hypothesis we validate the method on simulated data and demonstrate it using data from a functional mri study

combining spatial extent and peak intensity to test for activations in functional imaging within the framework of statistical mapping there are up to now only two tests used to assess the regional significance in functional images one is based on the magnitude of the foci and tends to detect high intensity signals while the second is based on the spatial extent of regions defined by a simple thresholding of the statistical map a test that is more sensitive to extended signals the aim of this paper is to combine the two tests into a single test that is more sensitive to a wider range of signals this combined test is based on an analytical approximation of the distribution of these two parameters size and height and is applied in the context of statistical maps the risk of error in noise only 2d or 3d volumes is assessed under a wide range of experimental conditions obtained by varying both the resolution of the map and the threshold at which clusters are defined in addition we have investigated this new test on simulated signals and applied it to an experimental pet dataset the experimental risk of error is close to the predicted one and the overall sensitivity increases when analyzing a volume containing different types of signals

statistical properties of jacobian maps and the realization of unbiased large deformation nonlinear image registration maps of local tissue compression or expansion are often computed by comparing magnetic resonance imaging mri scans using nonlinear image registration the resulting changes are commonly analyzed using tensor based morphometry to make inferences about anatomical differences often based on the jacobian map which estimates local tissue gain or loss here we provide rigorous mathematical analyses of the jacobian maps and use them to motivate a new numerical method to construct unbiased nonlinear image registration first we argue that logarithmic transformation is crucial for analyzing jacobian values representing morphometric differences we then examine the statistical distributions of log jacobian maps by defining the kullback leibler kl distance on material density functions arising in continuum mechanical models with this framework unbiased image registration can be constructed by quantifying the symmetric kl distance between the identity map and the resulting deformation implementation details addressing the proposed unbiased registration as well as the minimization of symmetric image matching functionals are then discussed and shown to be applicable to other registration methods such as inverse consistent registration in the results section we test the proposed framework as well as present an illustrative application mapping detailed 3 d brain changes in sequential magnetic resonance imaging scans of a patient diagnosed with semantic dementia using permutation tests we show that the symmetrization of image registration statistically reduces skewness in the log jacobian map

fuzzy basis functions universal approximation and orthogonal least squares learning fuzzy systems are represented as series expansions of fuzzy basis functions which are algebraic superpositions of fuzzy membership functions using the stone weierstrass theorem it is proved that linear combinations of the fuzzy basis functions are capable of uniformly approximating any real continuous function on a compact set to arbitrary accuracy based on the fuzzy basis function representations an orthogonal least squares ols learning algorithm is developed for designing fuzzy systems based on given input output pairs then the ols algorithm is used to select significant fuzzy basis functions which are used to construct the final fuzzy system the fuzzy basis function expansion is used to approximate a controller for the nonlinear ball and beam system and the simulation results show that the control performance is improved by incorporating some common sense fuzzy control rules

a fixed point theorem in probabilistic metric spaces and an application abstract the notion of a c contraction type multivalued mapping is introduced this notion is a generalization of the notion of c contraction introduced by t l hicks univ u novom sadu zb rad prirod mat fak ser mat 13 1983 63 72 a fixed point theorem for c contraction is proved an application on the existence of a random fixed point for random operator f m m where m d is a separable metric space and a m a measure space with a decomposable measure of nsa type is given

abstract metric spaces and sehgal guseman type theorems recently raja and vaezpour p raja and s m vaezpour some extensions of banach s contraction principle in complete cone metric spaces fixed point theory appl 2008 11 pages doi 10 1155 2008 768294 article id 768294 proved some results for sehgal guseman type theorems in the framework of abstract cone metric spaces over a normal solid cone the purpose of this paper is to present this in the framework of symmetric spaces which are associated with abstract cone metric spaces introduced by radenovic and kadelburg s radenovic z kadelburg quasi contractions on symmetric and cone symmetric spaces isi j bjma electronic in press our results extend and generalize sehgal guseman type theorems from metric and abstract metric spaces to some symmetric spaces examples are given to illustrate the results

increasing power for voxel wise genome wide association studies the random field theory least square kernel machines and fast permutation procedures imaging traits are thought to have more direct links to genetic variation than diagnostic measures based on cognitive or clinical assessments and provide a powerful substrate to examine the influence of genetics on human brains although imaging genetics has attracted growing attention and interest most brain wide genome wide association studies focus on voxel wise single locus approaches without taking advantage of the spatial information in images or combining the effect of multiple genetic variants in this paper we present a fast implementation of voxel and cluster wise inferences based on the random field theory to fully use the spatial information in images the approach is combined with a multi locus model based on least square kernel machines to associate the joint effect of several single nucleotide polymorphisms snp with imaging traits a fast permutation procedure is also proposed which significantly reduces the number of permutations needed relative to the standard empirical method and provides accurate small p value estimates based on parametric tail approximation we explored the relation between 448 294 single nucleotide polymorphisms and 18 043 genes in 31 662 voxels of the entire brain across 740 elderly subjects from the alzheimer s disease neuroimaging initiative adni structural mri scans were analyzed using tensor based morphometry tbm to compute 3d maps of regional brain volume differences compared to an average template image based on healthy elderly subjects we find method to be more sensitive compared with voxel wise single locus approaches a number of genes were identified as having significant associations with volumetric changes the most associated gene was grin2b which encodes the n methyl d aspartate nmda glutamate receptor nr2b subunit and affects both the parietal and temporal lobes in human brains its role in alzheimer s disease has been widely acknowledged and studied suggesting the validity of the approach the various advantages over existing approaches indicate a great potential offered by this novel framework to detect genetic influences on human brains

fgwas functional genome wide association analysis functional phenotypes e g subcortical surface representation which commonly arise in imaging genetic studies have been used to detect putative genes for complexly inherited neuropsychiatric and neurodegenerative disorders however existing statistical methods largely ignore the functional features e g functional smoothness and correlation the aim of this paper is to develop a functional genome wide association analysis fgwas framework to efficiently carry out whole genome analyses of functional phenotypes fgwas consists of three components a multivariate varying coefficient model a global sure independence screening procedure and a test procedure compared with the standard multivariate regression model the multivariate varying coefficient model explicitly models the functional features of functional phenotypes through the integration of smooth coefficient functions and functional principal component analysis statistically compared with existing methods for genome wide association studies gwas fgwas can substantially boost the detection power for discovering important genetic variants influencing brain structure and function simulation studies show that fgwas outperforms existing gwas methods for searching sparse signals in an extremely large search space while controlling for the family wise error rate we have successfully applied fgwas to large scale analysis of data from the alzheimer s disease neuroimaging initiative for 708 subjects 30 000 vertices on the left and right hippocampal surfaces and 501 584 snps

orthogonal least squares learning algorithm for radial basis function networks the radial basis function network offers a viable alternative to the two layer neural network in many applications of signal processing a common learning algorithm for radial basis function networks is based on first choosing randomly some data points as radial basis function centers and then using singular value decomposition to solve for the weights of the network such a procedure has several drawbacks and in particular an arbitrary selection of centers is clearly unsatisfactory the authors propose an alternative learning procedure based on the orthogonal least squares method the procedure chooses radial basis function centers one by one in a rational way until an adequate network has been constructed in the algorithm each selected center maximizes the increment to the explained variance or energy of the desired output and does not suffer numerical ill conditioning problems the orthogonal least squares learning strategy provides a simple and efficient means for fitting radial basis function networks this is illustrated using examples taken from two different signal processing applications

common fixed points for jℋ operators and occasionally weakly biased pairs under relaxed conditions abstract some common fixed point theorems due to bhatt et al a bhatt et al common fixed point theorems for occasionally weakly compatible mappings under relaxed conditions nonlinear anal 73 2010 176 182 jungck and rhoades g jungck and b e rhoades fixed point theorems for occasionally weakly compatible mappings fixed point theory 7 2 2006 287 296 fixed point theory 9 2008 383 384 erratum and imdad and soliman m imdad a h soliman some common fixed point theorems for a pair of tangential mappings in symmetric spaces appl math lett 23 2010 351 355 are extended to two new classes of non commuting selfmaps which contain the occasionally weakly compatible and weakly biased selfmaps as proper subclasses some illustrative examples are also provided to highlight the realized improvements

generalized reduced rank latent factor regression for high dimensional tensor fields and neuroimaging genetic applications we propose a generalized reduced rank latent factor regression model grrlf for the analysis of tensor field responses and high dimensional covariates the model is motivated by the need from imaging genetic studies to identify genetic variants that are associated with brain imaging phenotypes often in the form of high dimensional tensor fields grrlf identifies from the structure in the data the effective dimensionality of the data and then jointly performs dimension reduction of the covariates dynamic identification of latent factors and nonparametric estimation of both covariate and latent response fields after accounting for the latent and covariate effects grllf performs a nonparametric test on the remaining factor of interest grrlf provides a better factorization of the signals compared with common solutions and is less susceptible to overfitting because it exploits the effective dimensionality the generality and the flexibility of grrlf also allow various statistical models to be handled in a unified framework and solutions can be efficiently computed within the field of neuroimaging it improves the sensitivity for weak signals and is a promising alternative to existing approaches the operation of the framework is demonstrated with both synthetic datasets and a real world neuroimaging example in which the effects of a set of genes on the structure of the brain at the voxel level were measured and the results compared favorably with those from existing approaches

euler characteristics for gaussian fields on manifolds we are interested in the geometric properties of real valued gaussian random fields defined on manifolds our manifolds m are of class c3 and the random fields f are smooth our interest in these fields focuses on their excursion sets f 1 u and their geometric properties specifically we derive the expected euler characteristic ee f 1 u of an excursion set of a smooth gaussian random field part of the motivation for this comes from the fact that ee f 1 u relates global properties of m to a geometry related to the covariance structure of f of further interest is the relation between the expected euler characteristic of an excursion set above a level u and pp supp mf p u our proofs rely on results from random fields on rrn as well as differential and riemannian geometry