ridge regression biased estimation for nonorthogonal problems in multiple regression it is shown that parameter estimates based on minimum residual sum of squares have a high probability of being unsatisfactory if not incorrect if the prediction vectors are not orthogonal proposed is an estimation procedure based on adding small positive quantities to the diagonal of x x introduced is the ridge trace a method for showing in two dimensions the effects of nonorthogonality it is then shown how to augment x x to obtain biased estimates with smaller mean square error

the entire regularization path for the support vector machine the support vector machine svm is a widely used tool for classification many efficient implementations exist for fitting a two class svm model the user has to supply values for the tuning parameters the regularization cost parameter and the kernel parameters it seems a common practice is to use a default value for the cost parameter often leading to the least restrictive model in this paper we argue that the choice of the cost parameter can be critical we then derive an algorithm that can fit the entire path of svm solutions for every value of the cost parameter with essentially the same computational cost as fitting one svm model we illustrate our algorithm on some examples and use our representation to give further insight into the range of svm solutions

the lack of a priori distinctions between learning algorithms this is the first of two papers that use off training set ots error to investigate the assumption free relationship between learning algorithms this first paper discusses the senses in which there are no a priori distinctions between learning algorithms the second paper discusses the senses in which there are such distinctions in this first paper it is shown loosely speaking that for any two algorithms a and b there are as many targets or priors over targets for which a has lower expected ots error than b as vice versa for loss functions like zero one loss in particular this is true if a is cross validation and b is anti cross validation choose the learning algorithm with largest cross validation error this paper ends with a discussion of the implications of these results for computational learning theory it is shown that one cannot say if empirical misclassification rate is low the vapnik chervonenkis dimension of your generalizer is small and the training set is large then with high probability your ots error is small other implications for membership queries algorithms and punting algorithms are also discussed

logarithmic integrals interpolation bounds and performance limitations in mimo feedback systems we study performance limitation issues found in linear multivariable feedback systems our main contributions include bode and poisson type integral inequalities and performance limits for the sensitivity and complementary sensitivity functions these results characterize and quantify explicitly how open loop unstable poles and nonminimum phase zeros may impose inherent limitations on feedback design and fundamental limits on the best achievable performance the role of time delay is also studied in this context most notably we show that the performance and design limitations in multivariable systems intrinsically depend on the locations as well as directions of unstable poles and nonminimum phase zeros and in particular on how pole and zero directions are aligned the latter is characterized by angles measuring the mutual orientation between zero and pole directions and it is shown to play a crucial role in multivariable system design

comparing classification methods for longitudinal fmri studies we compare 10 methods of classifying fmri volumes by applying them to data from a longitudinal study of stroke recovery adaptive fisher s linear and quadratic discriminant gaussian naive bayes support vector machines with linear quadratic and radial basis function rbf kernels logistic regression two novel methods based on pairs of restricted boltzmann machines rbm and k nearest neighbors all methods were tested on three binary classification tasks and their out of sample classification accuracies are compared the relative performance of the methods varies considerably across subjects and classification tasks the best overall performers were adaptive quadratic discriminant support vector machines with rbf kernels and generatively trained pairs of rbms

regularized discriminant analysis abstract linear and quadratic discriminant analysis are considered in the small sample high dimensional setting alternatives to the usual maximum likelihood plug in estimates for the covariance matrices are proposed these alternatives are characterized by two parameters the values of which are customized to individual situations by jointly minimizing a sample based estimate of future misclassification risk computationally fast implementations are presented and the efficacy of the approach is examined through simulation studies and application to data these studies indicate that in many circumstances dramatic gains in classification accuracy can be achieved

penalized least squares regression methods and applications to neuroimaging the goals of this paper are to review the most popular methods of predictor selection in regression models to explain why some fail when the number p of explanatory variables exceeds the number n of participants and to discuss alternative statistical methods that can be employed in this case we focus on penalized least squares methods in regression models and discuss in detail two such methods that are well established in the statistical literature the lasso and elastic net we introduce bootstrap enhancements of these methods the be lasso and be enet that allow the user to attach a measure of uncertainty to each variable selected our work is motivated by a multimodal neuroimaging dataset that consists of morphometric measures volumes at several anatomical regions of interest white matter integrity measures from diffusion weighted data fractional anisotropy mean diffusivity axial diffusivity and radial diffusivity and clinical and demographic variables age education alcohol and drug history in this dataset the number p of explanatory variables exceeds the number n of participants we use the be lasso and be enet to provide the first statistical analysis that allows the assessment of neurocognitive performance from high dimensional neuroimaging and clinical predictors including their interactions the major novelty of this analysis is that biomarker selection and dimension reduction are accomplished with a view towards obtaining good predictions for the outcome of interest i e the neurocognitive indices unlike principal component analysis that are performed only on the predictors space independently of the outcome of interest

two layer approximate boundary conditions for large eddy simulations a new method to model the effect of the solid boundaries on the rest of the flowfield in large eddy simulations is proposed the filtered navier stokes equations are solved up to the first computational point from there to the wall a simplified set of equations is solved and an estimate of the instantaneous wall shear stress required to impose boundary conditions is obtained computations performed for the plane channel square duct and the rotating channel flow cases gave improved results compared with existing models the additional computing time required by the model is on the order of 10 15 of the overall computing time the mean flow quantities and low order statistics which are of primary interest in engineering calculations are in very good agreement with the reference data available in the literature

model sparsity and brain pattern interpretation of classification models in neuroimaging interest is increasing in applying discriminative multivariate analysis techniques to the analysis of functional neuroimaging data model interpretation is of great importance in the neuroimaging context and is conventionally based on a brain map derived from the classification model in this study we focus on the relative influence of model regularization parameter choices on both the model generalization the reliability of the spatial patterns extracted from the classification model and the ability of the resulting model to identify relevant brain networks defining the underlying neural encoding of the experiment for a support vector machine logistic regression and fisher s discriminant analysis we demonstrate that selection of model regularization parameters has a strong but consistent impact on the generalizability and both the reproducibility and interpretable sparsity of the models for both 2 and 1 regularization importantly we illustrate a trade off between model spatial reproducibility and prediction accuracy we show that known parts of brain networks can be overlooked in pursuing maximization of classification accuracy alone with either 2 and or 1 regularization this supports the view that the quality of spatial patterns extracted from models cannot be assessed purely by focusing on prediction accuracy our results instead suggest that model regularization parameters must be carefully selected so that the model and its visualization enhance our ability to interpret the brain

statistical inference and multiple testing correction in classification based multi voxel pattern analysis mvpa random permutations and cluster size control an ever increasing number of functional magnetic resonance imaging fmri studies are now using information based multi voxel pattern analysis mvpa techniques to decode mental states in doing so they achieve a significantly greater sensitivity compared to when they use univariate frameworks however the new brain decoding methods have also posed new challenges for analysis and statistical inference on the group level we discuss why the usual procedure of performing t tests on accuracy maps across subjects in order to produce a group statistic is inappropriate we propose a solution to this problem for local mvpa approaches which achieves higher sensitivity than other procedures our method uses random permutation tests on the single subject level and then combines the results on the group level with a bootstrap method to preserve the spatial dependency induced by local mvpa methods we generate a random permutation set and keep it fixed across all locations this enables us to later apply a cluster size control for the multiple testing problem more specifically we explicitly compute the distribution of cluster sizes and use this to determine the p values for each cluster using a volumetric searchlight decoding procedure we demonstrate the validity and sensitivity of our approach using both simulated and real fmri data sets in comparison to the standard t test procedure implemented in spm8 our results showed a higher sensitivity we discuss the theoretical applicability and the practical advantages of our approach and outline its generalization to other local mvpa methods such as surface decoding techniques

principal gains and principal phases in the analysis of linear multivariable feedback systems the concepts of principal gain and principal phase are introduced for linear multivariable systems and their use in the analysis of feedback behavior is demonstrated a sufficient nyquist type stability criterion is presented in terms of these quantities and is used to characterize the robustness of the closed loop stability property when the system model is subjected to a linear perturbation either multiplicative or additive at any point in the feedback configuration the results presented are less conservative than those obtained via the small gain theorem

paper sensitivity integrals for multivariable discrete time systems the purpose of this paper is to develop integral formulae for singular values of the sensitivity function to express design constraints in multivariable discrete time systems we present extensions to both the classical poisson integral and bode s sensitivity integral formulae the main utility of these results is that they can be used to quantify design limitations that arise in multivariable discrete time systems due to such system characteristics as open loop unstable poles and nonminimum phase zeros and to such design requirements as stability and bandwidth constraints these formulae are similar to those for multivariable continuous time systems obtained elsewhere and they reveal that feedback design limitations depend on directionality properties of the sensitivity function and on those of unstable poles and nonminimum phase zeros in the open loop transfer function

disease prediction based on functional connectomes using a scalable and spatially informed support vector machine substantial evidence indicates that major psychiatric disorders are associated with distributed neural dysconnectivity leading to a strong interest in using neuroimaging methods to accurately predict disorder status in this work we are specifically interested in a multivariate approach that uses features derived from whole brain resting state functional connectomes however functional connectomes reside in a high dimensional space which complicates model interpretation and introduces numerous statistical and computational challenges traditional feature selection techniques are used to reduce data dimensionality but are blind to the spatial structure of the connectomes we propose a regularization framework where the 6 d structure of the functional connectome defined by pairs of points in 3 d space is explicitly taken into account via the fused lasso or the graphnet regularizer our method only restricts the loss function to be convex and margin based allowing non differentiable loss functions such as the hinge loss to be used using the fused lasso or graphnet regularizer with the hinge loss leads to a structured sparse support vector machine svm with embedded feature selection we introduce a novel efficient optimization algorithm based on the augmented lagrangian and the classical alternating direction method which can solve both fused lasso and graphnet regularized svm with very little modification we also demonstrate that the inner subproblems of the algorithm can be solved efficiently in analytic form by coupling the variable splitting strategy with a data augmentation scheme experiments on simulated data and resting state scans from a large schizophrenia dataset show that our proposed approach can identify predictive regions that are spatially contiguous in the 6 d connectome space offering an additional layer of interpretability that could provide new insights about various disease processes

regularized discriminant analysis ridge regression and beyond fisher linear discriminant analysis fda and its kernel extension kernel discriminant analysis kda are well known methods that consider dimensionality reduction and classification jointly while widely deployed in practical problems there are still unresolved issues surrounding their efficient implementation and their relationship with least mean squares procedures in this paper we address these issues within the framework of regularized estimation our approach leads to a flexible and efficient implementation of fda as well as kda we also uncover a general relationship between regularized discriminant analysis and ridge regression this relationship yields variations on conventional fda based on the pseudoinverse and a direct equivalence to an ordinary least squares estimator

nonlinear denoising and analysis of neuroimages with kernel principal component analysis and pre image estimation we investigate the use of kernel principal component analysis pca and the inverse problem known as pre image estimation in neuroimaging i we explore kernel pca and pre image estimation as a means for image denoising as part of the image preprocessing pipeline evaluation of the denoising procedure is performed within a data driven split half evaluation framework ii we introduce manifold navigation for exploration of a nonlinear data manifold and illustrate how pre image estimation can be used to generate brain maps in the continuum between experimentally defined brain states classes we base these illustrations on two fmri bold data sets one from a simple finger tapping experiment and the other from an experiment on object recognition in the ventral temporal lobe

tradeoffs in linear time varying systems an analogue of bode s sensitivity integral bode s integral characterizes some of the tradeoffs imposed by the open loop dynamics of a linear time invariant system here we present an analogous time domain characterization applicable to time varying systems

sparse regularization techniques provide novel insights into outcome integration processes abstract by exploiting information that is contained in the spatial arrangement of neural activations multivariate pattern analysis mvpa can detect distributed brain activations which are not accessible by standard univariate analysis recent methodological advances in mvpa regularization techniques have made it feasible to produce sparse discriminative whole brain maps with highly specific patterns furthermore the most recent refinement the graph net explicitly takes the 3d structure of fmri data into account here these advanced classification methods were applied to a large fmri sample n 70 in order to gain novel insights into the functional localization of outcome integration processes while the beneficial effect of differential outcomes is well studied in trial and error learning outcome integration in the context of instruction based learning has remained largely unexplored in order to examine neural processes associated with outcome integration in the context of instruction based learning two groups of subjects underwent functional imaging while being presented with either differential or ambiguous outcomes following the execution of varying stimulus response instructions while no significant univariate group differences were found in the resulting fmri dataset l1 regularized sparse classifiers performed significantly above chance and also clearly outperformed the standard l2 regularized dense support vector machine on this whole brain between subject classification task moreover additional l2 regularization via the elastic net and spatial regularization by the graph net improved interpretability of discriminative weight maps but were accompanied by reduced classification accuracies most importantly classification based on sparse regularization facilitated the identification of highly specific regions differentially engaged under ambiguous and differential outcome conditions comprising several prefrontal regions previously associated with probabilistic learning rule integration and reward processing additionally a detailed post hoc analysis of these regions revealed that distinct activation dynamics underlay the processing of ambiguous relative to differential outcomes together these results show that l1 regularization can improve classification performance while simultaneously providing highly specific and interpretable discriminative activation patterns

efficient bayesian multivariate fmri analysis using a sparsifying spatio temporal prior bayesian logistic regression with a multivariate laplace prior is introduced as a multivariate approach to the analysis of neuroimaging data it is shown that by rewriting the multivariate laplace distribution as a scale mixture we can incorporate spatio temporal constraints which lead to smooth importance maps that facilitate subsequent interpretation the posterior of interest is computed using an approximate inference method called expectation propagation and becomes feasible due to fast inversion of a sparse precision matrix we illustrate the performance of the method on an fmri dataset acquired while subjects were shown handwritten digits the obtained models perform competitively in terms of predictive performance and give rise to interpretable importance maps estimation of the posterior of interest is shown to be feasible even for very large models with thousands of variables

crossover frequency limitations in mimo nonminimum phase feedback systems this paper investigates limitations and design tradeoffs of the closed loop sensitivity performance of linear time invariant nonminimum phase uncertain multiple input multiple output plants with i inputs and m outputs where m spl les l it is shown that if rows i sub 1 i sub k of the plant transfer function form a k spl times l nonminimum phase transfer matrix and if the design is such that the sensitivity gain of k 1 rows among the rows i sub 1 i sub k of the closed loop transfer function is low then by necessity the sensitivity gain of the remaining row is high this sensitivity constraint is quantified with the help of the crossover frequency restriction of a specially constructed single input single output transfer function that includes the right half plane zeros and poles of the k spl times l transfer matrix

multivariable gain phase and sensitivity integral relations and design trade offs we present several extensions of the classical bode integral relations to multivariable systems the main contributions are an extended gain phase integral formula and an extended sensitivity integral relation these results are useful for analyzing fundamental design limitations that arise in linear multivariable feedback systems in particular they provide important insights into feedback properties which are unique to multivariable systems and which cannot be inferred from the previously known integral relations applicable to single input single output systems both results show that design limitations in multivariable systems depend strongly upon certain directionality properties

inherent design limitations for linear sampled data feedback systems there is a well developed theory describing inherent design limitations for linear time invariant feedback systems consisting of an analogue plant and analogue controller this theory describes limitations on achievable performance present when the plant has non minimum phase zeros unstable poles and or time delays the parallel theory for linear time invariant discrete time systems is less interesting because it describes system behaviour only at sampling instants this paper develops a theory of design limitations for sampled data feedback systems wherein the response of the analogue system output is considered this is done using the fact that the steady state response of a hybrid feedback system to a sinusoidal input consists of a fundamental component at the frequency of the input together with infinitely many harmonics at frequencies spaced integer multiples of the sampling frequency away from the fundamental this fact allows fundamental sensitivity and complementary sensitivity functions that re

analysis and design for ill conditioned plants part 1 lower bounds on the structured singular value abstract a study is made of a special case of the robust performance problem given by freudenberg 1989 when the weightings used to describe the uncertainty and performance specifications vary only with frequency then it is possible to strengthen the results in the above mentioned work by deriving both upper and lower bounds upon the structured singular value both sets of bounds are stated in terms of the coupling coefficients introduced by freudenberg 1989 and essentially yield necessary and sufficient conditions for the structured singular value to be small this information is used to suggest a strategy for compensator design to achieve robust performance despite plant ill conditioning applying this strategy to an example it can be seen how the design trade offs quantified by the bode gain phase relation manifest themselves in the robust performance problem finally the design is compared with one obtained using the synthesis approach

integral constraints and performance limits on complementary sensitivity discrete time systems abstract we study performance limitation issues for multivariable discrete time feedback systems the complementary sensitivity function is employed as a performance measure and bode and poisson type integral inequalities and h type performance limits are derived the results exhibit frequency dependent constraints as well as best achievable limits on the complementary sensitivity function which are shown to be determined by nonminimum phase zeros unstable poles and time delays in particular the directions of such zeros and poles are seen to play a central role to this effect

penalized discriminant analysis of sup 15 o water pet brain images with prediction error selection of smoothness and regularization hyperparameters the authors propose a flexible comprehensive approach for analysis of sup 15 o water positron emission tomography pet brain images using a penalized version of linear discriminant analysis pda they applied it to scans from 20 subjects eight scans subject performing a finger movement task and analyzed 1 two classes to obtain a covariance normalized baseline activation image and 2 eight classes for the mean within subject temporal structure which contained baseline activation and time dependent changes in a two dimensional canonical subspace the authors imposed spatial smoothness on the resulting image s by expanding it in five tensor product b spline tps bases of varying smoothness and further regularized with a ridge type penalty on the noise covariance matrix the discrimination approach of pda provides a probabilistic framework within which prediction error pe estimates are derived the authors used these to optimize over tps bases and a ridge hyperparameter expressed as equivalent degrees of freedom edf they obtained unbiased low variance pe estimates using modern resampling tools 632 bootstrap and cross validation and compared pda of 1 tps projected mean normalized and unnormalized scans and 2 mean normalized scans with and without additional presmoothing by examining the tradeoffs between pe and edf as a function of basis selection and image smoothing the authors demonstrate the utility of pda the pe framework and the relationship between singular value decomposition and smooth tps bases in the analysis of functional neuroimages

logarithmic integrals and system dynamics an analogue of bode s sensitivity integral for continuous time time varying systems a new time domain interpretation of bode s integral is presented this allows for a generalization to the class of time varying systems which possess an exponential dichotomy it is shown that the sensitivity function is constrained on average by the spectral values in the dichotomy spectrum of the antistable component of the open loop dynamics

right half plane poles and zeros and design tradeoffs in feedback systems this paper expresses limitations imposed by right half plane poles and zeros of the open loop system directly in terms of the sensitivity and complementary sensitivity functions of the closed loop system the limitations are determined by integral relationships which must be satisfied by these functions the integral relationships are interpreted in the context of feedback design

gain phase relationships for discrete time systems the classical gain phase relations obtained by bode for minimum phase continuous time systems can be used to establish bounds on the performance of feedback systems it is shown that completely analogous relations can be obtained for discrete time systems and can be used for the same purpose in particular the limitations imposed by plant zeros and poles which lie outside the unit circle are investigated for both genuine discrete time systems namely those defined by difference equations and for sampled data systems one of the results shows that sampled data systems may practically be unstabilizable if their unstable poles lie outside a particular circular region the intended application of these results is to allow preliminary screening of proposed specifications for feasibility in a cad system before embarking on a detailed design

dimensionality estimation for optimal detection of functional networks in bold fmri data estimation of the intrinsic dimensionality of fmri data is an important part of data analysis that helps to separate the signal of interest from noise we have studied multiple methods of dimensionality estimation proposed in the literature and used these estimates to select a subset of principal components that was subsequently processed by linear discriminant analysis lda using simulated multivariate gaussian data we show that the dimensionality that optimizes signal detection in terms of the receiver operating characteristic roc metric goes through a transition from many dimensions to a single dimension as a function of the signal to noise ratio this transition happens when the loci of activation are organized into a spatial network and the variance of the networked task related signals is high enough for the signal to be easily detected in the data we show that reproducibility of activation maps is a metric that captures this switch in intrinsic dimensionality except for reproducibility all of the methods of dimensionality estimation we considered failed to capture this transition optimization of bayesian evidence minimum description length supervised and unsupervised lda prediction and stein s unbiased risk estimator this failure results in sub optimal roc performance of lda in the presence of a spatially distributed network and may have caused lda to underperform in many of the reported comparisons in the literature using real fmri data sets including multi subject group and within subject longitudinal analysis we demonstrate the existence of these dimensionality transitions in real data

analytic properties of the singular values of a rational matrix abstract it is shown that the singular values of a rational matrix g s where s x jy are locally a set of real analytic functions of x and y a brief discussion is given of their global properties

flux reconstruction implementation of an algebraic wall model for large eddy simulation in the present study an algebraic equilibrium wall model is implemented and tested for a large eddy simulation les solver based on the flux reconstruction fr method one of the objectives of t

penalized discriminant analysis fisher s linear discriminant analysis lda is a popular data analytic tool for studying the relationship between a set of predictors and a categorical response in this paper we describe a penalized version of lda it is designed for situations in which there are many highly correlated predictors such as those obtained by discretizing a function or the grey scale values of the pixels in a series of images in cases such as these it is natural efficient and sometimes essential to impose a spatial smoothness constraint on the coefficients both for improved prediction performance and interpretability we cast the classification problem into a regression framework via optimal scoring using this our proposal facilitates the use of any penalized regression technique in the classification setting the technique is illustrated with examples in speech recognition and handwritten character recognition

constraints on sensitivity characteristics in linear multivariable discrete time control systems abstract this paper is concerned with the limitations on the sensitivity characteristics for linear multivariable discrete time control systems some integral type constraints and the lower bounds of the weighted h norm imposed by the unstable poles the unstable zeros and their directions of the open loop system or the given plant are developed by a factorization approach these constraints and bounds which are tighter than those in the previous work are also characterized by the state space representations the descriptions are closely related to a special type of the algebraic riccati equation and the relation between the sampling period and the sensitivity performance is discussed for digital control systems the constraints on the more general function mixed sensitivity function are investigated in a similar way

controlling the false discovery rate a practical and powerful approach to multiple testing summary the common approach to the multiplicity problem calls for controlling the familywise error rate fwer this approach though has faults and we point out a few a different approach to problems of multiple significance testing is presented it calls for controlling the expected proportion of falsely rejected hypotheses the false discovery rate this error rate is equivalent to the fwer when all hypotheses are true but is smaller otherwise therefore in problems where the control of the false discovery rate rather than that of the fwer is desired there is potential for a gain in power a simple sequential bonferronitype procedure is proved to control the false discovery rate for independent test statistics and a simulation study shows that the gain in power is substantial the use of the new procedure and the appropriateness of the criterion are illustrated with examples

deep neural network predicts emotional responses of the human brain from functional magnetic resonance imaging abstract an artificial neural network with multiple hidden layers known as a deep neural network or dnn was employed as a predictive model dnnp for the first time to predict emotional responses using whole brain functional magnetic resonance imaging fmri data from individual subjects during fmri data acquisition 10 healthy participants listened to 80 international affective digital sound stimuli and rated their own emotions generated by each sound stimulus in terms of the arousal dominance and valence dimensions the whole brain spatial patterns from a general linear model i e beta valued maps for each sound stimulus and the emotional response ratings were used as the input and output for the dnnp respectively based on a nested five fold cross validation scheme the paired input and output data were divided into training three fold validation one fold and test one fold data the dnnp was trained and optimized using the training and validation data and was tested using the test data the pearson s correlation coefficients between the rated and predicted emotional responses from our dnnp model with weight sparsity optimization mean standard error 0 52 0 02 for arousal 0 51 0 03 for dominance and 0 51 0 03 for valence with an input denoising level of 0 3 and a mini batch size of 1 were significantly greater than those of dnn models with conventional regularization schemes including elastic net regularization 0 15 0 05 0 15 0 06 and 0 21 0 04 for arousal dominance and valence respectively those of shallow models including logistic regression 0 11 0 04 0 10 0 05 and 0 17 0 04 for arousal dominance and valence respectively average of logistic regression and sparse logistic regression and those of support vector machine based predictive models svmps 0 12 0 06 0 06 0 06 and 0 10 0 06 for arousal dominance and valence respectively average of linear and non linear svmps this difference was confirmed to be significant with a bonferroni corrected p value of less than 0 001 from a one way analysis of variance anova and subsequent paired t test the weights of the trained dnnps were interpreted and input patterns that maximized or minimized the output of the dnnps i e the emotional responses were estimated based on a binary classification of each emotion category e g high arousal vs low arousal the error rates for the dnnp 31 2 1 3 for arousal 29 0 1 7 for dominance and 28 6 3 0 for valence were significantly lower than those for the linear svmp 44 7 2 0 50 7 1 7 and 47 4 1 9 for arousal dominance and valence respectively and the non linear svmp 48 8 2 3 52 2 1 9 and 46 4 1 3 for arousal dominance and valence respectively as confirmed by the bonferroni corrected p

generalizable patterns in neuroimaging how many principal components generalization can be defined quantitatively and can be used to assess the performance of principal component analysis pca the generalizability of pca depends on the number of principal components retained in the analysis we provide analytic and test set estimates of generalization we show how the generalization error can be used to select the number of principal components in two analyses of functional magnetic resonance imaging activation sets

an ode based wall model for turbulent flow simulations this paper presents a new wall model to compute turbulent boundary layers using the reynolds averaged navier stokes equations in high reynolds number flows the model solves a two point boundary va

finite time behavior of inner systems in this paper we investigate how nonminimum phase characteristics of a dynamical system affect its controllability and tracking properties for the class of linear time invariant dynamical systems these characteristics are determined by transmission zeros of the inner factor of the system transfer function the relation between nonminimum phase zeros and hankel singular values of inner systems is studied and it is shown how the singular value structure of a suitably defined operator provides relevant insight about system invertibility and achievable tracking performance the results are used to solve various tracking problems both on finite as well as on infinite time horizons a typical receding horizon control scheme is considered and new conditions are derived to guarantee stabilizability of a receding horizon controller