standard monomial theory for g2 let g be a semi simple algebraic group and b a borel subgroup let x be a schubert variety in g b let l be an ample line bundle on g b as well as its restriction to x a standard monomial theory for schubert varieties in g b is developed in 9 11 8 10 as a generalization of the classical hodge young theory cf 3 4 this theory consists in the construction of a characteristic free basis for h0 x l this theory is extended to schubert varieties in the infinite dimensional flag variety ln b in 13 see also 12 in this paper we extend the theory to schubert varieties in the infinite dimensional flag variety p2n b

meaningful design and contrast estimability in fmri optimising the efficiency of an experimental design is known to be of great importance however existing methods for calculating design rank deficiency and contrast estimability an important aspect of experimental design relate to computational precision rather than image noise and are therefore not very meaningful for example a contrast between two experimental conditions may be mathematically estimable while requiring a huge differential bold response for statistical significance to be reached in this paper we formulate standard efficiency equations in terms of required bold effect and use this to generate measures of rank estimability which are meaningful this takes into account the strength and smoothness of the timeseries noise and is applicable to complex contrasts we show how to re express several regressors and an associated contrast vector as a single equivalent regressor so that we can calculate the contrast s effective peak peak height unambiguously we also present some example results on typical designs and characterise noise results from a range of typical fmri acquisitions in order to allow experimenters to apply efficiency estimation in advance of acquiring data

temporal autocorrelation in univariate linear modeling of fmri data in functional magnetic resonance imaging statistical analysis there are problems with accounting for temporal autocorrelations when assessing change within voxels techniques to date have utilized temporal filtering strategies to either shape these autocorrelations or remove them shaping or coloring attempts to negate the effects of not accurately knowing the intrinsic autocorrelations by imposing known autocorrelation via temporal filtering removing the autocorrelation or prewhitening gives the best linear unbiased estimator assuming that the autocorrelation is accurately known for single event designs the efficiency of the estimator is considerably higher for prewhitening compared with coloring however it has been suggested that sufficiently accurate estimates of the autocorrelation are currently not available to give prewhitening acceptable bias to overcome this we consider different ways to estimate the autocorrelation for use in prewhitening after high pass filtering is performed a tukey taper set to smooth the spectral density more than would normally be used in spectral density estimation performs best importantly estimation is further improved by using nonlinear spatial filtering to smooth the estimated autocorrelation but only within tissue type using this approach when prewhitening reduced bias to close to zero at probability levels as low as 1 x 10 5

on resolving the multiplicity of the branching rule gl 2k 1 c down arrow so 2k 1 c we consider the multiplicity problem of the branching rule gl 2k 1 c down arrow so 2k 1 c finite dimensional irreducible representations of gl 2k 1 c are realized as right translations on subspaces of the holomorphic hilbert bargmann spaces of q 2k 1 complex variables maps are exhibited which carry an irreducible representation of so 2k 1 c into these subspaces an algebra of commuting operators is constructed eigenvalues and eigenvectors of certain of these operators can then be used to resolve the multiplicity in the branching rule

the edge weighted clique problem valid inequalities facets and polyhedral computations abstract let kn v e be the complete undirected graph with weights ce associated to the edges in e we consider the problem of finding the subclique c u f of kn such that the sum of the weights of the edges in f is maximized and u b for some b 1 n this problem is called the maximum edge weighted clique problem mewcp and is np hard in this paper we investigate the facial structure of the polytope associated to the mewcp introducing new classes of facet defining inequalities computational experiments with a branch and cut algorithm are reported confirming the strength of these inequalities all instances with up to 48 nodes could be solved without entering into the branching phase moreover we show that some of these new inequalities also define facets of the boolean quadric polytope and generalize many of the previously known inequalities for this well studied polytope

detection power estimation efficiency and predictability in event related fmri experimental designs for event related functional magnetic resonance imaging can be characterized by both their detection power a measure of the ability to detect an activation and their estimation efficiency a measure of the ability to estimate the shape of the hemodynamic response randomized designs offer maximum estimation efficiency but poor detection power while block designs offer good detection power at the cost of minimum estimation efficiency periodic single trial designs are poor by both criteria we present here a theoretical model of the relation between estimation efficiency and detection power and show that the observed trade off between efficiency and power is fundamental using the model we explore the properties of semirandom designs that offer intermediate trade offs between efficiency and power these designs can simultaneously achieve the estimation efficiency of randomized designs and the detection power of block designs at the cost of increasing the length of an experiment by less than a factor of 2 experimental designs can also be characterized by their predictability a measure of the ability to circumvent confounds such as habituation and anticipation we examine the relation between detection power estimation efficiency and predictability and show that small increases in predictability can offer significant gains in detection power with only a minor decrease in estimation efficiency

roc analysis of statistical methods used in functional mri individual subjects the complicated structure of fmri signals and associated noise sources make it difficult to assess the validity of various steps involved in the statistical analysis of brain activation most methods used for fmri analysis assume that observations are independent and that the noise can be treated as white gaussian noise these assumptions are usually not true but it is difficult to assess how severely these assumptions are violated and what are their practical consequences in this study a direct comparison is made between the power of various analytical methods used to detect activations without reference to estimates of statistical significance the statistics used in fmri are treated as metrics designed to detect activations and are not interpreted probabilistically the receiver operator characteristic roc method is used to compare the efficacy of various steps in calculating an activation map in the study of a single subject based on optimizing the ratio of the number of detected activations to the number of false positive findings the main findings are as follows preprocessing the removal of intensity drifts and high pass filtering applied on the voxel time course level is beneficial to the efficacy of analysis temporal normalization of the global image intensity smoothing in the temporal domain and low pass filtering do not improve power of analysis choices of statistics the cross correlation coefficient and t statistic as well as nonparametric mann whitney statistics prove to be the most effective and are similar in performance by our criterion task design the proper design of task protocols is shown to be crucial in an alternating block design the optimal block length is be approximately 18 s spatial clustering an initial spatial smoothing of images is more efficient than cluster filtering of the statistical parametric activation maps

efficient design of event related fmri experiments using m sequences rapid event related fmri erfmri allows estimation of the shape of hemodynamic responses hdr associated with transient brain activation evoked by various sensory motor and cognitive events choosing a sequence of events that maximizes efficiency of estimating the hdr is essential for conducting event related brain imaging experiments since increasing efficiency is essentially equivalent to reducing scanning time or increasing the strength of the principal magnetic field the efficiency of an erfmri design depends critically on the temporal arrangement of the sequence of events and the noise in the fmri signal we introduce to erfmri a simple method for generating efficient event sequences based on maximum length shift register sequences or m sequences we show that under the assumption of white uncorrelated mri noise efficiency of erfmri experimental designs that employ m sequences exceeds efficiency of the best randomly generated sequences this is true for single and multiple event type experiments which allow either parallel events overlapping events design or designs in which only one event occurs at a time nonoverlapping events design hdr estimation efficiency afforded by m sequences grows with the number of event types and is greatest when event sequences are relatively short albeit within commonly used scan times i e 63 255 total events per scan the improvement in efficiency however comes at a cost of constraints imposed by m sequence generation rules such as predetermined sequence lengths for nonoverlapping events design m sequence based designs are not available for all possible numbers of event types nevertheless designs that are available with m sequences cover a large subset of commonly used erfmri experimental designs under conditions of characteristic time correlated fmri noise randomly generated sequences may yield efficiencies that exceed those afforded by m sequences for single event type designs since in this case one can generate random sequences that partially decorrelate mri noise by chance our simulations suggest that for designs of realistic sequence lengths that use more than one event type m sequence based designs tend to outperform random designs thus making the knowledge of noise inessential finally within an r th order m sequence generated by a shift register of length r all possible combinations of subsequences of length r occur and thus these subsequences are exactly counterbalanced this property is essential for minimizing effects of psychological and neuronal adaptation and expectation

on resolving the multiplicity of tensor products of irreducible representations of symplectic groups the multiplicity problem of r fold tensor products of irreducible representations of sp 2k c are considered the arbitrary r fold tensor product is shown to be isomorphic to a subspace of the holomorphic hilbert bargmann space of n 2k complex variables maps are constructed which carry an irreducible representation of sp 2k c into this subspace an algebra of commuting operators is constructed and it is shown how eigenvalues and eigenvectors of certain of these operators can be used to resolve the multiplicity

the equitable dispersion problem most optimization problems focus on efficiency based objectives given the increasing awareness of system inequity resulting from solely pursuing efficiency we conceptualize a number of new element based equity oriented measures in the dispersion context we propose the equitable dispersion problem that maximizes the equity among elements based on the introduced measures in a system defined by inter element distances given the proposed optimization framework we develop corresponding mathematical programming formulations as well as their mixed integer linear reformulations we also discuss computational complexity issues related graph theoretic interpretations and provide some preliminary computational results

optimal design of multi subject blocked fmri experiments the design of a multi subject fmri experiment needs specification of the number of subjects and scanning time per subject for example for a blocked design with conditions a or b fixed block length and block order abn where n denotes a null block the optimal number of cycles of abn and the optimal number of subjects have to be determined this paper presents a method to determine the optimal number of subjects and optimal number of cycles for a blocked design based on the a optimality criterion and a linear cost function by which the number of cycles and the number of subjects are restricted estimation of individual stimulus effects and estimation of contrasts between stimulus effects are both considered the mixed effects model is applied and analytical results for the a optimal number of subjects and a optimal number of cycles are obtained under the assumption of uncorrelated errors for correlated errors with a first order autoregressive ar1 error structure numerical results are presented our results show how the optimal number of cycles and subjects depend on the within to between subject variance ratio our method is a new approach to determine the optimal scanning time and optimal number of subjects for a multi subject fmri experiment in contrast to previous results based on power analyses the optimal number of cycles and subjects can be described analytically and costs are considered

induction and restriction of kazhdan lusztig cells abstract barbasch and vogan gave a beautiful rule for restricting and inducing kazhdan lusztig representations of weyl groups in this paper we show that this rule implies and generalizes the littlewood richardson rule for decomposing outer products of representations of the symmetric groups a new recursive rule for computing characters of arbitrary coxeter groups follows another application is a generalization of garsia remmel s algorithm for decomposing certain tensor products of symmetric groups representations

optimal spatial regularisation of autocorrelation estimates in fmri analysis in the general linear model glm framework for the statistical analysis of fmri data the problem of temporal autocorrelations in the residual signal after regression has been frequently addressed in the open literature there exist various methods for correcting the ensuing bias in the statistical testing among which the prewhitening strategy which uses a prewhitening matrix for rendering the residual signal white i e without temporal autocorrelations this correction is only exact when the autocorrelation structure of the noise generating process is accurately known and the estimates derived from the fmri data are too noisy to be used for correction recently worsley and co workers proposed to spatially smooth the noisy autocorrelation estimates effectively reducing their variance and allowing for a better correction in this article a systematic study into the effect of the smoothing kernel width is performed and a method is introduced for choosing this bandwidth in an optimal manner several aspects of the prewhitening strategy are investigated namely the choice of the autocorrelation estimate biased or unbiased the accuracy of the estimates the degree of spatial regularisation and the order of the autoregressive model used for characterising the noise the proposed method is extensively evaluated on both synthetic and real fmri data

characterization of event related designs using bold and iron fmri abstract despite many desirable characteristics event related er stimulus designs for bold and iron suffer from low detection power relative to block designs because the hemodynamic impulse response function irf acts as a low pass filter on neural activation to attenuate the size of differential responses to alternate stimuli while the use of exogenous contrast agent iron technique provides an alternative fmri method in animal models to improve sensitivity and spatial localization the inherently slower hemodynamic irf causes iron detection efficiency to decrease faster than bold efficiency as the interstimulus interval isi is shortened using simulations based upon assumptions of stimulus response linearity and experimental data obtained in awake non human primates this study compared detection efficiencies for fixed random and semi random isi distributions for bold and iron techniques a larger relative gain in detection efficiency at short isi was obtained by randomized designs using iron contrast relative to bold contrast due to the slower irf of the iron method to quantify tradeoffs between detection efficiency and the predictability of stimulus presentation the shannon entropy was introduced as an objective measure of predictability small amounts of entropy can be traded for large gains in efficiency particularly for the iron method

efficiency power and entropy in event related fmri with multiple trial types part i theory experimental designs for functional magnetic resonance imaging fmri experiments can be characterized by their estimation efficiency which is a measure of the variance in the estimate of the hemodynamic response function hrf and their detection power which is a measure of the variance in the estimate of the amplitude of functional activity previous studies have shown that there exists a fundamental trade off between efficiency and power for experiments with a single trial type of interest this paper extends the prior work by presenting a theoretical model for the relation between detection power and estimation efficiency in experiments with multiple trial types it is shown that the trade off between efficiency and power present in multiple trial type experiments is identical in form to that observed for single trial type experiments departures from the predicted trade off due to the inclusion of basis function expansions and the assumption of correlated noise are examined finally conditional entropy is introduced as measure for the randomness of a design and an empirical relation between entropy and estimation efficiency is presented

young diagrammatic methods for the representation theory of the classical groups of type bn cn dn since the appearance of the celebrated article the classical groups of weyl 7 numerous influences have occurred in the representation theory of the classical groups especially it has become folklore that the facts in this field should be expressed only in terms of young diagrams the aim of this paper is one of the realizations of this principle a classical model of our approach is the results for gl n which are known as littlewood richardson coefficients and the kostka coefficients these two coefficients can be stated in the combinatorial manner using only young diagrams independently of the rank n of gl n we generalize these results to the other classical groups over c namely we give explicit formulas to decompose the tensor product of two irreducible representations into irreducible constituents also we have obtained an interesting relationship linking the irreducible characters of sp and so which we call duality relation between the representations of sp and so as for explicit formulas for the multiplicities of weights in the form of polynomials in the rank n we refer to 3

tabu search and grasp for the maximum diversity problem in this paper we develop new heuristic procedures for the maximum diversity problem mdp this np hard problem has a significant number of practical applications such as environmental balance telecommunication services or genetic engineering the proposed algorithm is based on the tabu search methodology and incorporates memory structures for both construction and improvement although proposed in seminal tabu search papers memory based constructions have often been implemented in naive ways that disregard important elements of the fundamental tabu search proposals we will compare our tabu search construction with a memory less design and with previous algorithms recently developed for this problem the constructive method can be coupled with a local search procedure or a short term tabu search for improved outcomes extensive computational experiments with medium and large instances show that the proposed procedure outperforms the best heuristics reported in the literature within short computational times

improved detection of event related functional mri signals using probability functions selecting an optimal event distribution for experimental use in event related fmri studies can require the generation of large numbers of event sequences with characteristics hard to control the use of known probability distributions offers the possibility to control event timing and constrain the search space for finding optimal event sequences we investigated different probability distributions in terms of response estimation estimation efficiency detectability detection power parameter estimation efficiency sensitivity to true positives and false positive activation numerous simulated event sequences were generated selecting interevent intervals iei from the uniform uniform permuted latin square exponential binomial poisson chi 2 geometric and bimodal probability distributions and fixed iei event sequences from the bimodal distribution like block designs had the best performance for detection and the poorest for estimation while high estimation and detectability occurred for the long decay exponential distribution the uniform distribution also yielded high estimation efficiency but probability functions with a long tail toward higher iei such as the geometric and the chi 2 distributions had superior detectability the distributions with the best detection performance also had a relatively high incidence of false positives in contrast to the ordered distributions latin square and uniform permuted the predictions of improved sensitivities for distributions with long tails were confirmed with empirical data moreover the latin square design yielded detection of activated voxels similar to the chi 2 distribution these results indicate that high detection and suitable behavioral designs have compatibility for application of functional mri methods to experiments requiring complex designs

efficiency power and entropy in event related fmri with multiple trial types part ii design of experiments the performance of an experimental design for functional magnetic resonance imaging fmri can be characterized by its estimation efficiency which is the ability to make an estimate of the hemodynamic response its detection power which is the ability to detect an activation and its conditional entropy which is a measure of the randomness of the design in liu and frank neuroimage 21 2004 387 400 it is shown that there is a fundamental theoretical trade off between estimation efficiency and detection power for experiments with multiple trial types and that there is an empirical relation between estimation efficiency and conditional entropy this paper provides an intuitive interpretation of the theoretical results and examines the practical implications of these results for the optimal design of fmri experiments with multiple trial types the properties of block designs permuted block designs m sequence designs clustered m sequence designs and mixed designs are explored it is shown that these designs nearly achieve the theoretically predicted performance and can be used in practice to obtain advantageous trade offs among efficiency power and entropy

erratum to efficiency power and entropy in event related fmri with multiple trial types part i theory neuroimage 21 2004 387 400

medical image noise reduction using the sylvester lyapunov equation multiplicative noise is often present in medical and biological imaging such as magnetic resonance imaging mri ultrasound positron emission tomography pet single photon emission computed tomography spect and fluorescence microscopy noise reduction in medical images is a difficult task in which linear filtering algorithms usually fail bayesian algorithms have been used with success but they are time consuming and computationally demanding in addition the increasing importance of the 3 d and 4 d medical image analysis in medical diagnosis procedures increases the amount of data that must be efficiently processed this paper presents a bayesian denoising algorithm which copes with additive white gaussian and multiplicative noise described by poisson and rayleigh distributions the algorithm is based on the maximum a posteriori map criterion and edge preserving priors which avoid the distortion of relevant anatomical details the main contribution of the paper is the unification of a set of bayesian denoising algorithms for additive and multiplicative noise using a well known mathematical framework the sylvester lyapunov equation developed in the context of the control theory

analysis of fmri time series revisited again friston et al 1995 neuroimage 2 45 53 presented a method for detecting activations in fmr1 time series based on the general linear model and a heuristic analysis of the effective degrees of freedom in this communication we present corrected results that replace those of the previous paper and solve the same problem without recourse to heuristic arguments specifically we introduce a proper and unbiased estimator for the error terms and provide a more generally correct expression for the effective degrees of freedom the previous estimates of error variance were biased and in some instances could have led to a 10 20 overestimate of z values although the previous results are almost correct for the random regressors chosen for validation the present theoretical results are exact for any covariate or waveform we comment on some aspects of experimental design and data analysis in the light of the theoretical framework discussed here

selc sequential elimination of level combinations by means of modified genetic algorithms to search for an optimum in a large search space wu mao and ma suggested the sequential elimination of levels sels method to find an optimal setting genetic algorithms gas can be used to improve on this method to make the search procedure more efficient new ideas of forbidden array and weighted mutation are introduced relaxing the condition of orthogonality gas are able to accommodate a variety of design points which allows more flexibility and enhances the likelihood of getting the best setting in fewer runs particularly in the presence of interactions the search procedure is enriched by a bayesian method for identifying the important main effects and two factor interactions illustration is given with the optimization of three functions one of which is from shekel s family a real example on compound optimization is also given

optimal designs in three level cluster randomized trials with a binary outcome cluster randomized trials crts were originally proposed for use when randomization at the subject level is practically infeasible or may lead to a severe estimation bias of the treatment effect however recruiting an additional cluster costs more than enrolling an additional subject in an individually randomized trial under budget constraints researchers have proposed the optimal sample sizes in two level crts crts may have a three level structure in which two levels of clustering should be considered in this paper we propose optimal designs in three level crts with a binary outcome assuming a nested exchangeable correlation structure in generalized estimating equation models we provide the variance of estimators of three commonly used measures risk difference risk ratio and odds ratio for a given sampling budget we discuss how many clusters and how many subjects per cluster are necessary to minimize the variance of each measure estimator for known association parameters the locally optimal design is proposed when association parameters are unknown but within predetermined ranges the maximin design is proposed to maximize the minimum of relative efficiency over the possible ranges that is to minimize the risk of the worst scenario

a reciprocity law and the skew pieri rule for the symplectic group we use the theory of skew duality to show that decomposing the tensor product of k irreducible representations of the symplectic group sp2m sp2m is equivalent to branching from sp2n to sp2n1 sp2nk where n n1 nk are positive integers such that n n1 nk and the njs depend on m as well as the representations in the tensor product using this result and a work of lepowsky we obtain a skew pieri rule for sp2m i e a description of the irreducible decomposition of the tensor product of an irreducible representation of the symplectic group sp2m with a fundamental representation

demazure characters and wzw fusion rules the demazure character formula is applied to the verlinde formula for the fusion rules of wess zumino witten wzw models we follow littelmann s derivation of a generalized littlewood richardson rule that computes tensor products for simple lie algebras a combinatorial rule for wzw fusions does not result however only a modified version of the littlewood richardson rule is obtained that computes an old upper bound on the fusion coefficients of ar wzw models we argue that this is because the characters of simple lie algebras appear in this treatment instead of the corresponding affine characters the bruhat order on the affine weyl group must be implicated in any combinatorial rule for wzw fusions the bruhat order on subgroups of this group such as the finite weyl group does not suffice

a branch and bound algorithm for the maximum diversity problem this article begins with a review of previously proposed integer formulations for the maximum diversity problem mdp this problem consists of selecting a subset of elements from a larger set in such a way that the sum of the distances between the chosen elements is maximized we propose a branch and bound algorithm and develop several upper bounds on the objective function values of partial solutions to the mdp empirical results with a collection of previously reported instances indicate that the proposed algorithm is able to solve all the medium sized instances with 50 elements as well as some large sized instances with 100 elements we compare our method with the best previous linear integer formulation solved with the well known software cplex the comparison favors the proposed procedure

sections of homogeneous vector bundles abstract in this work we give a method for computing sections of homogeneous vector bundles on any rational homogeneous variety g p of type ade our main tool is the equivalence of categories between homogeneous vector bundles on g p and finite dimensional representations of a given quiver with relations our result generalizes the work of ottaviani and rubei 2006 or06

a hybrid metaheuristic approach to solving the ubqp problem this paper presents a hybrid metaheuristic approach hma for solving the unconstrained binary quadratic programming ubqp problem by incorporating a tabu search procedure into the framework of evolutionary algorithms the proposed approach exhibits several distinguishing features including a diversification based combination operator and a distance and quality based replacement criterion for pool updating the proposed algorithm is able to easily obtain the best known solutions for 31 large random instances up to 7000 variables which no previous algorithm has done and find new best solutions for three of nine instances derived from the set partitioning problem demonstrating the efficacy of our proposed algorithm in terms of both solution quality and computational efficiency furthermore some key elements and properties of the hma algorithm are also analyzed

construction and improvement algorithms for dispersion problems abstract given a set n a pairwise distance function d and an integer number m the dispersion problems dps require to extract from n a subset m of cardinality m so as to optimize a suitable function of the distances between the elements in m different functions give rise to a whole family of combinatorial optimization problems in particular the max sum dp and the max min dp have received strong attention in the literature other problems e g the max minsum dp and the min diffsum dp have been recently proposed with the aim to model the optimization of equity requirements as opposed to that of more classical efficiency requirements building on the main ideas which underly some state of the art methods for the max sum dp and the max min dp this work proposes some constructive procedures and a tabu search algorithm for the new problems in particular we investigate the extension to the new context of key features such as initialization tenure management and diversification mechanisms the computational experiments show that the algorithms applying these ideas perform effectively on the publicly available benchmarks but also that there are some interesting differences with respect to the dps more studied in the literature as a result of this investigation we also provide optimal results and bounds as a useful reference for further studies

robustness of optimal design of fmri experiments with application of a genetic algorithm in this paper we apply the genetic algorithm developed by kao et al 2009 to find designs which are robust against misspecification of the error autocorrelation two common optimality criteria the a optimality criterion and the d optimality criterion based upon a general linear model are employed to obtain locally optimal designs for a given value of the autocorrelation the maximin criterion is then used to obtain designs which are robust against misspecification of the autocorrelation furthermore robustness depending on the choice of optimality criterion is evaluated we show analytically and empirically that the a and d optimality criterion will result in different optimal designs e g with different stimulus frequencies optimal stimulus frequency for the a optimality criterion has been derived by liu et al 2004 whereas we derive here the optimal stimulus frequency for the d optimality criterion conclusions about the robustness of an optimal design against misspecification of model parameters and choice of optimality criterion are drawn based upon our results

to smooth or not to smooth bias and efficiency in fmri time series analysis this paper concerns temporal filtering in fmri time series analysis whitening serially correlated data is the most efficient approach to parameter estimation however if there is a discrepancy between the assumed and the actual correlations whitening can render the analysis exquisitely sensitive to bias when estimating the standard error of the ensuing parameter estimates this bias although not expressed in terms of the estimated responses has profound effects on any statistic used for inference the special constraints of fmri analysis ensure that there will always be a misspecification of the assumed serial correlations one resolution of this problem is to filter the data to minimize bias while maintaining a reasonable degree of efficiency in this paper we present expressions for efficiency of parameter estimation and bias in estimating standard error in terms of assumed and actual correlation structures in the context of the general linear model we show that i whitening strategies can result in profound bias and are therefore probably precluded in parametric fmri data analyses ii band pass filtering and implicitly smoothing has an important role in protecting against inferential bias

the impact of study design on pattern estimation for single trial multivariate pattern analysis a prerequisite for a pattern analysis using functional magnetic resonance imaging fmri data is estimating the patterns from time series data which then are input into the pattern analysis here we focus on how the combination of study design order and spacing of trials with pattern estimator impacts the type i error rate of the subsequent pattern analysis when type i errors are inflated the results are no longer valid so this work serves as a guide for designing and analyzing mvpa studies with controlled false positive rates the mvpa strategies examined are pattern classification and similarity utilizing single trial activation patterns from the same functional run primarily focusing on the least squares single and least square all pattern estimators we show that collinearities in the models along with temporal autocorrelation can cause false positive correlations between activation pattern estimates that adversely impact the false positive rates of pattern similarity and classification analyses it may seem intuitive that increasing the interstimulus interval isi would alleviate this issue but remaining weak correlations between activation patterns persist and have a strong influence in pattern similarity analyses pattern similarity analyses using only activation patterns estimated from the same functional run of data are susceptible to inflated false positives unless trials are randomly ordered with a different randomization for each subject in other cases where there is any structure to trial order valid pattern similarity analysis results can only be obtained if similarity computations are restricted to pairs of activation patterns from independent runs likewise for pattern classification false positives are minimized when the testing and training sets in cross validation do not contain patterns estimated from the same run

a generalization of the littlewood richardson rule for the general linear group gz the littlewood richardson rule see 18 193 gives a method to calculate the decomposition of a tensor product of two irreducible g representations the aim of this article is to give a generalization of this rule for all simple simply connected algebraic groups of type a b c d g2 and e we obtain also partial results for g of type f4 e and es the restrictions in the last three cases come from the fact that for the formulation of the decomposition rules we need the notion of a standard young tableau such a notion has been developed by seshadri lakshmibai musili and rajeswari in a series of articles see ll 13 14 16 but not yet for all representations of the last three exceptional groups the advantage of the notion of a young tableau developed by seshadri et al is that it is independent of the type of the group for the convenience of the reader not used to this notion we give first a seperate proof for g sz using the classical notion of a standard young tableau of course for applications the classical notion is much more appropriate in the appendix we give a translation of the notion of a standard young tableau in the sense of seshadri et al into the classical notion of a young tableau for g sp2 and spin in 3 8 we give also such a translation for g g for the other exceptional groups such a translation is not known to the author let p be a dominant weight for g and denote by i the corresponding simple g module we assume that the character of vp is given by ct eycr where the sum has to be taken over all standard young tableaux f of shape p p and v 5 is the weight of the tableau y now by the

matched subspace detectors we formulate a general class of problems for detecting subspace signals in subspace interference and broadband noise we derive the generalized likelihood ratio glr for each problem in the class we then establish the invariances for the glr and argue that these are the natural invariances for the problem in each case the glr is a maximal invariant statistic and the distribution of the maximal invariant statistic is monotone this means that the glr test glrt is the uniformly most powerful invariant detector we illustrate the utility of this finding by solving a number of problems for detecting subspace signals in subspace interference and broadband noise in each case we give the distribution for the detector and compute performance curves

a hybrid metaheuristic method for the maximum diversity problem abstract the maximum diversity problem mdp consists in selecting a subset of m elements from a given set of n elements n m in such a way that the sum of the pairwise distances between the m chosen elements is maximized we present a hybrid metaheuristic algorithm denoted by mamdp for mdp the algorithm uses a dedicated crossover operator to generate new solutions and a constrained neighborhood tabu search procedure for local optimization mamdp applies also a distance and quality based replacement strategy to maintain population diversity extensive evaluations on a large set of 120 benchmark instances show that the proposed approach competes very favorably with the current state of art methods for mdp in particular it consistently and easily attains all the best known lower bounds and yields improved lower bounds for 6 large mdp instances the key components of mamdp are analyzed to shed light on their influence on the performance of the algorithm

a review on algorithms for maximum clique problems the maximum clique problem mcp is to determine in a graph a clique i e a complete subgraph of maximum cardinality the mcp is notable for its capability of modeling other combinatorial problems and real world applications as one of the most studied np hard problems many algorithms are available in the literature and new methods are continually being proposed given that the two existing surveys on the mcp date back to 1994 and 1999 respectively one primary goal of this paper is to provide an updated and comprehensive review on both exact and heuristic mcp algorithms with a special focus on recent developments to be informative we identify the general framework followed by these algorithms and pinpoint the key ingredients that make them successful by classifying the main search strategies and putting forward the critical elements of the most relevant clique methods this review intends to encourage future development of more powerful methods and motivate new applications of the clique approaches

analysis of fmri time series revisited abstract this paper presents a general approach to the analysis of functional mri time series from one or more subjects the approach is predicated on an extension of the general linear model that allows for correlations between error terms due to physiological noise or correlations that ensue after temporal smoothing this extension uses the effective degrees of freedom associated with the error term the effective degrees of freedom are a simple function of the number of scans and the temporal autocorrelation function a specific form for the latter can be assumed if the data are smoothed in time to accentuate hemodynamic responses with a neural basis this assumption leads to an expedient implementation of a flexible statistical framework the importance of this small extension is that in contradistinction to our previous approach any parametric statistical analysis can be implemented we demonstrate this point using a multiple regression analysis that tests for effects of interest activations due to word generation while taking explicit account of some obvious confounds

multi objective optimal experimental designs for event related fmri studies in this article we propose an efficient approach to find optimal experimental designs for event related functional magnetic resonance imaging er fmri we consider multiple objectives including estimating the hemodynamic response function hrf detecting activation circumventing psychological confounds and fulfilling customized requirements taking into account these goals we formulate a family of multi objective design criteria and develop a genetic algorithm based technique to search for optimal designs our proposed technique incorporates existing knowledge about the performance of fmri designs and its usefulness is shown through simulations although our approach also works for other linear combinations of parameters we primarily focus on the case when the interest lies either in the individual stimulus effects or in pairwise contrasts between stimulus types under either of these popular cases our algorithm outperforms the previous approaches we also find designs yielding higher estimation efficiencies than m sequences when the underlying model is with white noise and a constant nuisance parameter the stimulus frequencies of the designs we obtained are in good agreement with the optimal stimulus frequencies derived by liu and frank 2004 neuroimage 21 387 400 in addition our approach is built upon a rigorous model formulation

iterated greedy for the maximum diversity problem abstract the problem of choosing a subset of elements with maximum diversity from a given set is known as the maximum diversity problem many algorithms and methods have been proposed for this hard combinatorial problem including several highly sophisticated procedures by contrast in this paper we present a simple iterated greedy metaheuristic that generates a sequence of solutions by iterating over a greedy construction heuristic using destruction and construction phases extensive computational experiments reveal that the proposed algorithm is highly effective as compared to the best so far metaheuristics for the problem under consideration

a new young diagrammatic method for kronecker products of and a new simple young diagrammatic method for kronecker products of o n and sp 2m is proposed based on the representation theory of brauer algebras a general procedure for the decomposition of the tensor products of representations for o n and sp 2m is outlined which is similar to that for u n known as the littlewood rules together with trace contractions from a brauer algebra and some modification rules given by king

solving the maximum edge weight clique problem via unconstrained quadratic programming the unconstrained quadratic binary program uqp is proving to be a successful modeling and solution framework for a variety of combinatorial optimization problems experience reported in the literature with several problem classes has demonstrated that this approach works surprisingly well in terms of solution quality and computational times often rivaling and sometimes surpassing more traditional methods in this paper we report on the application of uqp to the maximum edge weighted clique problem computational experience is reported illustrating the attractiveness of the approach

on bias in the estimation of autocorrelations for fmri voxel time series analysis for fmri time series analysis to be statistically valid it is important to deal correctly with temporal autocorrelation in the noise most of the approaches in the literature adopt a two stage approach in which the autocorrelation structure is estimated using the residuals of an initial model fit this estimate is then used to prewhiten the data and the model before the model is refit to obtain final activation parameter estimates an assumption implicit in this scheme is that the residuals from the initial model fit represent a realization of the true noise process in general this assumption will not be correct as certain components of the noise will be removed by the model fit in this paper we examine i the form of the bias induced by the initial model fit ii methods of correcting for the bias and iii the impact of bias correction on the model parameter estimates we find that while bias correction does result in more accurate estimates of the correlation structure this does not translate into improved estimates of the model parameters in fact estimates of the model parameters and their standard errors are seen to be so accurate that we conclude that bias correction is unnecessary

quivers and the cohomology of homogeneous vector bundles we describe the cohomology groups of a homogeneous vector bundle e on any hermitian symmetric variety x g p of ade type as the cohomology of a complex explicitly described the main tool is the equivalence introduced by bondal kapranov and hille between the category of homogeneous bundles and the category of representations of a certain quiver qx with relations we prove that the relations are the commutative ones on projective spaces but they involve additional scalars on general grassmannians in addition we introduce moduli spaces of homogeneous

a recursive rule for kazhdan lusztig characters abstract a formula for computing kazhdan lusztig characters in hecke algebras of coxeter groups is given this formula holds for products of coxeter elements of parabolic subgroups in an arbitrary coxeter group where the parabolic subgroups are of type a and the kazhdan lusztig representations are of finite dimension the formula yields new combinatorial interpretations of murnaghan nakayama type to these characters and to other related characters

estimating the global order of the fmri noise model one of the major issues in glm based fmri analysis techniques is the presence of temporal autocorrelations in the residual signal after regression a possible correction method is that of prewhitening which fits an autoregressive or other model to the residual and uses the expected temporal autocorrelations of the model to transform the data and design matrix such that the residual becomes white noise in this article a method is introduced to estimate the global autoregressive model order of a data set based on the residuals after regression the proposed global standardized partial autocorrelation spac method tests whether the spatial profile of partial autocorrelations at a certain lag is random and uses random field theory to account for the spatial correlations typical for fmri data it is tested both on synthetic and fmri data and is compared to two traditional techniques for model order estimation

optimization of blocked designs in fmri studies blocked designs in functional magnetic resonance imaging fmri are useful to localize functional brain areas a blocked design consists of different blocks of trials of the same stimulus type and is characterized by three factors the length of blocks i e number of trials per blocks the ordering of task and rest blocks and the time between trials within one block optimal design theory was applied to find the optimal combination of these three design factors furthermore different error structures were used within a general linear model for the analysis of fmri data and the maximin criterion was applied to find designs which are robust against misspecification of model parameters

on character generators for simple lie algebras we study character generating functions character generators of simple lie algebras the expression due to patera and sharp derived from the weyl character formula is first reviewed a new general formula is then found it makes clear the distinct roles of outside and inside elements of the integrity basis and helps determine their quadratic incompatibilities we review analyse and extend the results obtained by gaskell using the demazure character formulae we find that the fundamental generalized poset graphs underlying the character generators can be deduced from such calculations these graphs introduced by baclawski and towber can be simplified for the purposes of constructing the character generator the generating functions can be written easily using the simplified graphs and associated demazure expressions the rank two algebras are treated in detail but we believe our results are indicative of those for general simple lie algebras

characterizing the hemodynamic response effects of presentation rate sampling procedure and the possibility of ordering brain activity based on relative timing rapid presentation event related functional mri er fmri allows neuroimaging methods based on hemodynamics to employ behavioral task paradigms typical of cognitive settings however the sluggishness of the hemodynamic response and its variance provide constraints on how er fmri can be applied in a series of two studies estimates of the hemodynamic response in or near the primary visual and motor cortices were compared across various paradigms and sampling procedures to determine the limits of er fmri procedures and more generally to describe the behavior of the hemodynamic response the temporal profile of the hemodynamic response was estimated across overlapping events by solving a set of linear equations within the general linear model no assumptions about the shape were made in solving the equations following estimation of the temporal profile the amplitude and timing were modeled using a gamma function results indicated that 1 within a region for a given subject estimation of the hemodynamic response is extremely stable for both amplitude r 2 0 98 and time to peak r 2 0 95 from one series of measurements to the next and slightly less stable for estimation of time to onset r 2 0 60 2 as the trial presentation rate changed from those spaced 20 s apart to temporally overlapping trials the hemodynamic response amplitude showed a small but significant decrease trial onsets spaced on average 5 s apart showed a 17 25 reduction in amplitude compared to those spaced 20 s apart power analysis indicated that the increased number of trials at fast rates outweighs this decrease in amplitude if statistically reliable response detection is the goal 3 knowledge of the amplitude and timing of the hemodynamic response in one region failed to predict those properties in another region even for within subject comparisons 4 across subjects the amplitude of the response showed no significant correlation with timing of the response for either time to onset or time to peak estimates 5 the within region stability of the response was sufficient to allow offsets in the timing of the response to be detected that were under a second placing event related fmri methods in a position to answer questions about the change in relative timing between regions

a general statistical analysis for fmri data we propose a method for the statistical analysis of fmri data that seeks a compromise between efficiency generality validity simplicity and execution speed the main differences between this analysis and previous ones are a simple bias reduction and regularization for voxel wise autoregressive model parameters the combination of effects and their estimated standard deviations across different runs sessions subjects via a hierarchical random effects analysis using the em algorithm overcoming the problem of a small number of runs session subjects using a regularized variance ratio to increase the degrees of freedom

heuristic and special case algorithms for dispersion problems the dispersion problem arises in selecting facilities to maximize some function of the distances between the facilities the problem also arises in selecting nondominated solutions for multiobjective decision making it is known to be np hard under two objectives maximizing the minimum distance max min between any pair of facilities and maximizing the average distance max avg we consider the question of obtaining near optimal solutions for max min we show that if the distances do not satisfy the triangle inequality there is no polynomial time relative approximation algorithm unless p np when the distances satisfy the triangle inequality we analyze an efficient heuristic and show that it provides a performance guarantee of two we also prove that obtaining a performance guarantee of less than two is np hard for max avg we analyze an efficient heuristic and show that it provides a performance guarantee of four when the distances satisfy the triangle inequality we also present a polynomial ti

separating processes within a trial in event related functional mri many cognitive processes occur on time scales that can significantly affect the shape of the blood oxygenation level dependent bold response in eventrelated functional mri this shape can be estimated from event related designs even if these processes occur in a fixed temporal sequence j m ollinger g l shulman and m corbetta 2001 neuroimage 13 210 217 several important considerations come into play when interpreting these time courses first in single subjects correlations among neighboring time points give the noise a smooth appearance that can be confused with changes in the bold response second the variance and degree of correlation among estimated time courses are strongly influenced by the timing of the experimental design simulations show that optimal results are obtained if the intertrial intervals are as short as possible if they follow an exponential distribution with at least three distinct values and if 40 of the trials are partial trials these results are not particularly sensitive to the fraction of partial trials so accurate estimation of time courses can be obtained with lower percentages of partial trials 20 25 third statistical maps can be formed from f statistics computed with the extra sum of square principle or by t statistics computed from the cross correlation of the time courses with a model for the hemodynamic response the latter method relies on an accurate model for the hemodynamic response the most robust model among those tested was a single gamma function finally the power spectrum of the measured bold signal in rapid event related paradigms is similar to that of the noise nevertheless highpass filtering is desirable if the appropriate model for the hemodynamic response is used 2001 academic press

iterated tabu search for the maximum diversity problem in this paper we deal with the maximum diversity problem mdp which asks to select a specified number of elements from a given set so that the sum of distances between the selected elements is as large as possible we develop an iterated tabu search its algorithm for solving this problem we also present a steepest ascent algorithm which is well suited in application settings where solutions of satisfactory quality are required to be provided very quickly computational results for problem instances involving up to 5000 elements show that the its algorithm is a very attractive alternative to the existing approaches in particular we demonstrate the outstanding performance of its on the mdp instances taken from the literature for 69 such instances new best solutions were found

the impact of temporal regularization on estimates of the bold hemodynamic response function a comparative analysis in fmri data analysis it has been shown that for a wide range of situations the hemodynamic response function hrf can be reasonably characterized as the impulse response function of a linear and time invariant system an accurate and robust extraction of the hrf is essential to infer quantitative information about the relative timing of the neuronal events in different brain regions when no assumptions are made about the hrf shape it is most commonly estimated using time windowed averaging or a least squares estimated general linear model based on either fourier or delta basis functions recently regularization methods have been employed to increase the estimation efficiency of the hrf typically these methods produce more accurate hrf estimates than the least squares approach goutte c nielsen f a hansen l k 2000 modeling the haemodynamic response in fmri using smooth fir filters ieee trans med imag 19 12 1188 1201 here we use simulations to clarify the relative merit of temporal regularization based methods compared to the least squares methods with respect to the accuracy of estimating certain characteristics of the hrf such as time to peak ttp height hr and width w of the response we implemented a bayesian approach proposed by marrelec et al marrelec g benali h ciuciu p pelegrini issac m poline j b 2003 robust estimation of the hemodynamic response function in event related bold fmri using basic physiological information hum brain mapp 19 1 17 marrelec g benali h ciuciu p poline j b bayesian estimation of the hemodynamic of the hemodynamic response function in functional mri in r f editor 2001 melville p 229 247 and its deterministic counterpart based on a combination of tikhonov regularization tikhonov a n arsenin v y 1977 solution of ill posed problems washington dc w h winston and generalized cross validation gcv wahba g 1990 spline models for observational data philadelphia siam for selecting the regularization parameter the performance of both methods is compared with least square estimates as a function of temporal resolution color and strength of the noise and the type of stimulus sequences used in almost all situations under the considered assumptions e g linearity time invariance and smooth hrf the regularization based techniques more accurately characterize the hrf compared to the least squares method our results clarify the effects of temporal resolution noise color and experimental design on the accuracy of hrf estimation

identities for classical group characters of nearly rectangular shape abstract we derive several identities that feature irreducible characters of the general linear the symplectic the orthogonal and the special orthogonal groups all of the identities feature characters that are indexed by shapes that are nearly rectangular by which we mean that the shapes are rectangles except for one row or column that might be shorter than the others as applications we prove new results in plane partitions and tableaux enumeration including new refinements of the bender knuth and macmahon ex conjectures

generalized theta functions strange duality and odd orthogonal bundles on curves this paper studies spaces of generalized theta functions for odd orthogonal bundles with nontrivial stiefel whitney class and the associated space of twisted spin bundles in particular we prove a verlinde type formula and a dimension equality that was conjectured by oxbury wilson modifying hitchin s argument we also show that the bundle of generalized theta functions for twisted spin bundles over the moduli space of curves admits a flat projective connection we furthermore address the issue of strange duality for odd orthogonal bundles and we demonstrate that the naive conjecture fails in general a consequence of this is the reducibility of the projective representations of spin mapping class groups arising from the hitchin connection for these moduli spaces finally we answer a question of nakanishi tsuchiya about rank level duality for conformal blocks on the pointed projective line with spin weights

a comparison of methods for characterizing the event related bold timeseries in rapid fmri abstract information about the shape and temporal duration of the blood oxygenation level dependent bold response can inform both functional neuroanatomy and psychological theory however the bold response evolves over 20 s or more making it difficult to distinguish the unique characteristics of the response evoked by temporally adjacent stimuli fortunately event related bold signals can be extracted given that there is adequate variance in the distribution of inter stimulus intervals isi unfortunately the isi distribution that yields the highest statistical efficiency is not always optimal from a psychological perspective variability in the stimulus timing may complicate the interpretation of neuroimaging data in terms of underlying cognitive operations in the present paper monte carlo simulations are used to evaluate two techniques for estimating the event related bold timeseries event related averaging and deconvolution using the ordinary least squares estimate with respect to maintaining acceptable levels of statistical power and experimental validity while the unbiased deconvolution technique more robustly estimates the shape of the bold response functions both methods succeed in accurately re producing known differences between evoked bold responses when the stimulus ordering is randomized however the deconvolution method is more effective at preserving differences when there are sequential dependencies in the stimulus presentation order and restricted isi distributions are used particularly if the second of two sequentially dependent stimuli is omitted on some portion of the trials importantly the successful re production of the evoked bold response using restricted isi distributions often maximizes the ability to make psychologically valid experimental conclusions

a dictionary learning approach for poisson image deblurring the restoration of images corrupted by blur and poisson noise is a key issue in medical and biological image processing while most existing methods are based on variational models generally derived from a maximum a posteriori map formulation recently sparse representations of images have shown to be efficient approaches for image recovery following this idea we propose in this paper a model containing three terms a patch based sparse representation prior over a learned dictionary the pixel based total variation regularization term and a data fidelity term capturing the statistics of poisson noise the resulting optimization problem can be solved by an alternating minimization technique combined with variable splitting extensive experimental results suggest that in terms of visual quality peak signal to noise ratio value and the method noise the proposed algorithm outperforms state of the art methods

tensor products of representations if g is a reductive group in characteristic zero with two irreducible representations v1 and v2 we may form the tensor product representation v1 0 v2 where g acts diagonally the problem is to decompose v1 0 v2 into its irreducible components with their multiplicities of course this may be done using weyl s character formula but this is a very difficult calculation this paper presents a general method for doing this calculation in a more efficient way for the general linear group the method was explained in 2 with a minimum of group theoretic language for the other classical groups this paper will give explicit formulas the method of this paper may be used for exceptional groups but for combinatorial reasons it does not seem worthwhile at this point to write an explicit formula perhaps it would be more useful to have a computer program for the calculation as an after thought i have included an appendix on how to decompose an irreducible representation of g when restricted to a large reductive subgroup the case of the general linear group is well known