fdtd discrete planewave fdtd dpw formulation for a perfectly matched source in tfsf simulations a technique is proposed for the generation of planewaves in the total field scattered field tfsf formulation of the fdtd method the method is developed using the 1d properties of a planewave and optimized projection of the 3d finite difference operators to the 1d domain the result is an efficient and accurate planewave source that can be propagated on six 1d grids concurrent with the main simulation and that is perfectly matched to the main 2d 3d fdtd domain for any source function numerical simulations show that the technique is valid for any angle of propagation and for any gridcell aspect ratio with non physical reflections in the scattered field domain on the order of machine precision 300 db

high dimensional classification via nonparametric empirical bayes and maximum likelihood inference we propose new nonparametric empirical bayes methods for high dimensional classification our classifiers are designed to approximate the bayes classifier in a hypothesized hierarchical model where the prior distributions for the model parameters are estimated nonparametrically from the training data as is common with nonparametric empirical bayes the proposed classifiers are effective in high dimensional settings even when the underlying model parameters are in fact nonrandom we use nonparametric maximum likelihood estimates of the prior distributions following the elegant approach studied by kiefer wolfowitz in the 1950s however our implementation is based on a recent convex optimization framework for approximating these estimates that is well suited for large scale problems we derive new theoretical results on the accuracy of the approximate estimator which help control the misclassification rate of one of our classifiers we show that our methods outperform several existing methods in simulations and perform well when gene expression microarray data is used to classify cancer patients

parabolic orbifolds and the dimension of the maximal measure for rational maps let f g g be a rational map of the riemann sphere d e g f 2 a natural invariant measure m the measure of maximal entropy was constructed by ljubich lju and independently by freire lopes and mafi6 flm the aim of this paper is to compare this measure with some hausdorff measures first recall the following definition for a probabili ty measure v on or more generally on a smooth manifold the hausdorff dimension of v is defined by a formula hd v inf hd y y v y l

introduction of oblique incidence plane wave to stratified lossy dispersive media for fdtd analysis in the application of finite difference time domain fdtd method to the wideband plane wave scattering analysis of objects embedded in stratified lossy dispersive media it is a challenge to solve the obliquely incident wave in this work a novel configuration of auxiliary one dimensional 1 d fdtd grids is proposed to provide the obliquely incident plane wave at the total field scattered field tfsf boundary in stratified lossy dispersive media thus a closed tfsf boundary is formed where the incident waves are directly obtained from the auxiliary simulations without any interpolation the formulations of the auxiliary simulations are presented by the modified 1 d maxwell s equations given the dispersion characteristic perfectly matched layer pml is implemented to the 1 d simulations examples demonstrate the effectiveness of the proposed technique of obliquely incident wave introduction

estimation of error variance via ridge regression summarywe propose a novel estimator of error variance and establish its asymptotic properties based on ridge regression and random matrix theory the proposed estimator is valid under both low and high dimensional models and performs well not only in nonsparse cases but also in sparse ones the finite sample performance of the proposed method is assessed through an intensive numerical study which indicates that the method is promising compared with its competitors in many interesting scenarios

operator norm consistent estimation of large dimensional sparse covariance matrices estimating covariance matrices is a problem of fundamental importance in multivariate statistics in practice it is increasingly frequent to work with data matrices x of dimension n x p where p and n are both large results from random matrix theory show very clearly that in this setting standard estimators like the sample covariance matrix perform in general very poorly in this large n large p setting it is sometimes the case that practitioners are willing to assume that many elements of the population covariance matrix are equal to 0 and hence this matrix is sparse we develop an estimator to handle this situation the estimator is shown to be consistent in operator norm when for instance we have p n as n oo in other words the largest singular value of the difference between the estimator and the population covariance matrix goes to zero this implies consistency of all the eigenvalues and consistency of eigenspaces associated to isolated eigenvalues we also propose a notion of sparsity for matrices that is compatible with spectral analysis and is independent of the ordering of the variables

plane waves in fdtd simulations and a nearly perfect total field scattered field boundary the total field scattered field tfsf boundary has been successfully used for a number of years to introduce energy into finite difference time domain fdtd grids if the propagation of the incident field is grid aligned a perfect tfsf implementation can be realized by using an auxiliary one dimensional fdtd simulation which models propagation of the incident field here perfect implies the incident field propagation exactly matches the way in which the field propagates in the fdtd grid however for propagation which is not grid aligned no similarly perfect implementation has previously been presented this work provides a framework for a perfect tfsf boundary for pulsed plane waves which do not propagate in a grid aligned fashion to achieve this homogeneous plane wave propagation is rigorously quantified using this knowledge and a specification of the desired incident field the dispersion relation is used to ascertain the incident field at any point in the grid it is required to account for unlike in the continuous world the electric field the magnetic field and the wavenumber vector not forming a mutually orthogonal set group velocity is also considered because of its relevance to the implementation

quasiconformal homeomorphisms and dynamics i solution of the fatou julia problem on wandering domains on demontre un resultat dynamique sur l iteration d une application analytique complexe sur la sphere de riemann

fluctuations of eigenvalues and second order poincare inequalities linear statistics of eigenvalues in many familiar classes of random matrices are known to obey gaussian central limit theorems the proofs of such results are usually rather difficult involving hard computations specific to the model in question in this article we attempt to formulate a unified technique for deriving such results via relatively soft arguments in the process we introduce a notion of second order poincare inequalities just as ordinary poincare inequalities give variance bounds second order poincare inequalities give central limit theorems the proof of the main result employs stein s method of normal approximation a number of examples are worked out some of which are new one of the new results is a clt for the spectrum of gaussian toeplitz matrices

analytical expression for the time domain green s function of a discrete plane wave propagating in a 3 d fdtd grid in this paper a closed form expression for the time domain dyadic green s function of a discrete plane wave dpw propagating in a 3 d finite difference time domain fdtd grid is derived in order to verify our findings the time domain implementation of the dpw injection technique is developed with the use of the derived expression for 3 d total field scattered field tfsf fdtd simulations this implementation requires computations of the time domain green s function of dpw with the use of multiple precision arithmetic then excitations at the tfsf interface can be computed as a time domain convolution of a source function with green s function of dpw the developed time domain implementation of the dpw injection technique demonstrates the leakage error across the tfsf interface around the numerical noise level that verifies the correctness of the derivation

regularized estimation of large covariance matrices this paper considers estimating a covariance matrix of p variables from n observations by either banding the sample covariance matrix or estimating a banded version of the inverse of the covariance we show that these estimates are consistent in the operator norm as long as logp 2 n 0 and obtain explicit rates the results are uniform over some fairly natural well conditioned families of covariance matrices we also introduce an analogue of the gaussian white noise model and show that if the population covariance is embeddable in that model and well conditioned then the banded approximations produce consistent estimates of the eigenvalues and associated eigenvectors of the covariance matrix the results can be extended to smooth versions of banding and to non gaussian distributions with su ciently short tails a resampling approach is proposed for choosing the banding parameter in practice this approach is illustrated numerically on both simulated and real data

a transcendental julia set of dimension 1 we construct a non polynomial entire function whose julia set has finite 1 dimensional spherical measure and hence hausdorff dimension 1 in 1975 baker proved the dimension of such a julia set must be at least 1 but whether this minimum could be attained has remained open until now our example also has packing dimension 1 and is the first transcendental julia set known to have packing dimension strictly less than 2 it is also the first example with a multiply connected wandering domain where the dynamics can be completely described

analytic field propagation tfsf boundary for fdtd problems involving planar interfaces pecs te and tm a total field scattered field tfsf boundary can be used to introduce incident plane waves into finite difference time domain fdtd simulations for fields which are traveling obliquely to the grid axes there is no simple way to account fully for the effects of the inherent numerical artifacts associated with plane wave propagation in the fdtd grid failure to account for these artifacts causes erroneous fields to leak across the tfsf boundary recent publications have proposed ways to use the dispersion relation to describe precisely plane wave propagation in the fdtd grid thus permitting the realization of a nearly perfect tfsf boundary however these publications did not cover certain implementations details such as the type of fourier transform which is needed or their scope was so broad as to mask the relative simplicity with which the approach can be applied to problems involving planar interfaces this work considers the fourier transforms needed in order for the implementation to be exact reflection and transmission coefficients for a planar interface are derived implementation for planar perfect electric conductors is also presented

exponential error terms for growth functions on negatively curved surfaces in this paper we consider two counting problems associated with compact negatively curved surfaces and improve classical asymptotic estimates due to margulis in the first we show that the number of closed geodesies of length at most t has an exponential error term in the second we show that the number of geodesic arcs between two fixed points x and y of length at most t has an exponential error term the proof is based on a detailed study of the zeta function and poincar series and benefits from recent work of dolgopiat 0 introduction let v be a compact surface with negative curvature and let v be its universal cover with the lifted metric d the fundamental group n v can be realized as a group of isometries t acting on v with v t v given a point x g v9 we can introduce the orbital counting function n t defined

geometrical finiteness for hyperbolic groups abstract in this paper we give an account of the notion of geometrical finiteness as applied to discrete groups acting on hyperbolic space of any dimension we prove the equivalence of various definitions of geometrical finiteness and describe the geometry of fundamental domains we give a complete account of when dirichiet domains are finite sided

on the degrees of freedom of the lasso we study the effective degrees of freedom of the lasso in the framework of stein s unbiased risk estimation sure we show that the number of nonzero coefficients is an unbiased estimate forthe degrees of freedom of the lasso a conclusion that requires no special assumption on the predictors in addition the unbiased estimator is shown to be asymptotically consistent with these results on hand various model selection criteria cp aic and bic are available which along with the lars algorithm provide a principled and efficient approach to obtaining the optimal lasso fit with the computational effort of a single ordinary least squares fit

the risk inflation criterion for multiple regression a new criterion is proposed for the evaluation of variable selection procedures in multiple regression this criterion which we call the risk inflation is based on an adjustment to the risk essentially the risk inflation is the maximum increase in risk due to selecting rather than knowing the correct predictors a new variable selection procedure is obtained which in the case of orthogonal predictors substantially improves on aic c p and bic and is close to optimal in contrast to aic c p and bic which use dimensionality penalties of 2 2 and log n respectively this new procedure uses a penalty 2 log p where p is the number of available predictors for the case of nonorthogonal predictors bounds for the optimal penalty are obtained

eigenprism inference for high dimensional signal to noise ratios consider the following three important problems in statistical inference namely constructing confidence intervals for 1 the error of a high dimensional p n regression estimator 2 the linear regression noise level and 3 the genetic signal to noise ratio of a continuous valued trait related to the heritability all three problems turn out to be closely related to the little studied problem of performing inference on the formula see text norm of the signal in high dimensional linear regression we derive a novel procedure for this which is asymptotically correct when the covariates are multivariate gaussian and produces valid confidence intervals in finite samples as well the procedure called eigenprism is computationally fast and makes no assumptions on coefficient sparsity or knowledge of the noise level we investigate the width of the eigenprism confidence intervals including a comparison with a bayesian setting in which our interval is just 5 wider than the bayes credible interval we are then able to unify the three aforementioned problems by showing that the eigenprism procedure with only minor modifications is able to make important contributions to all three we also investigate the robustness of coverage and find that the method applies in practice and in finite samples much more widely than just the case of multivariate gaussian covariates finally we apply eigenprism to a genetic dataset to estimate the genetic signal to noise ratio for a number of continuous phenotypes

analytic fields with higher order compensations for 3 d fdtd tf sf formulation with application to beam excitations the total field scattered field tf sf formulation is widely used to initiate incident waves for scattering problems in finite difference time domain fdtd simulations an important aspect of the tf sf formulation is the calculation of incident fields at the tf sf boundary by methods that account for the numerical nature of the incident wave in the fdtd grid failure to do so can lead to high levels of field leakage errors across the tf sf boundary this paper presents an improved analytic time domain method for accurately computing incident fields in the tf sf formulation using analytic field expressions with higher order dispersion and polarization compensations the proposed method compensates for 1 the fdtd numerical dispersion and 2 the lack of orthogonality between the frequency dependent field polarizations and the wavevector which was not accounted for in existing analytic time domain methods the higher order compensations result in further suppression of field leakage errors in the sf region in addition to exciting a plane wave the proposed method can be employed to excite an incident beam to demonstrate this numerical experiments that source both 3 d plane wave and focused beam into a free space fdtd grid are presented and compared with existing methods

rational maps with real multipliers let f be a rational function such that the multipliers of all repelling periodic points are real we prove that the julia set of such a function belongs to a circle combining this with a result of fatou we conclude that whenever j f belongs to a smooth curve it also belongs to a circle then we discuss rational functions whose julia sets belong to a circle

estimating the error variance in a high dimensional linear model the lasso has been studied extensively as a tool for estimating the coefficient vector in the high dimensional linear model however considerably less is known about estimating the error variance in this context in this paper we propose the natural lasso estimator for the error variance which maximizes a penalized likelihood objective a key aspect of the natural lasso is that the likelihood is expressed in terms of the natural parameterization of the multiparameter exponential family of a gaussian with unknown mean and variance the result is a remarkably simple estimator of the error variance with provably good performance in terms of mean squared error these theoretical results do not require placing any assumptions on the design matrix or the true regression coefficients we also propose a companion estimator called the organic lasso which theoretically does not require tuning of the regularization parameter both estimators do well empirically compared to preexisting methods especially in settings where successful recovery of the true support of the coefficient vector is hard finally we show that existing methods can do well under fewer assumptions than previously known thus providing a fuller story about the problem of estimating the error variance in high dimensional linear models

dimension rigidity in conformal structures abstract let be the limit set of a conformal dynamical system i e a kleinian group acting on either finite or infinite dimensional real hilbert space a conformal iterated function system or a rational function we give an easily expressible sufficient condition requiring that the limit set is not too much bigger than the radial limit set for the following dichotomy is either a real analytic manifold or a fractal in the sense of mandelbrot i e its hausdorff dimension is strictly greater than its topological dimension our primary focus is on the infinite dimensional case an important component of the strategy of our proof comes from the rectifiability techniques of mayer and urbanski 03 who obtained a dimension rigidity result for conformal iterated function systems including those with infinite alphabets in order to handle the infinite dimensional case both for kleinian groups and for iterated function systems we introduce the notion of pseudorectifiability a variant of rectifiability and develop a theory around this notion similar to the theory of rectifiable sets our approach also extends existing results in the finite dimensional case where it unifies the realms of kleinian groups conformal iterated function systems and rational functions for kleinian groups we improve on the rigidity result of kapovich 09 by substantially weakening its hypothesis of geometrical finiteness moreover our proof based on rectifiability is entirely different than that of kapovich which depends on homological algebra another advantage of our approach is that it allows us to use the demension of stan ko 69 as a substitute for topological dimension for example we prove that any dynamically defined version of antoine s necklace must have hausdorff dimension strictly greater than 1 i e the demension of antoine s necklace

optimal rates of convergence for covariance matrix estimation covariance matrix plays a central role in multivariate statistical analysis significant advances have been made recently on developing both theory and methodology for estimating large covariance matrices however a minimax theory has yet been developed in this paper we establish the optimal rates of convergence for estimating the covariance matrix under both the operator norm and frobenius norm it is shown that optimal procedures under the two norms are different and consequently matrix estimation under the operator norm is fundamentally different from vector estimation the minimax upper bound is obtained by constructing a special class of tapering estimators and by studying their risk properties a key step in obtaining the optimal rate of convergence is the derivation of the minimax lower bound the technical analysis requires new ideas that are quite different from those used in the more conventional function sequence estimation problems

hausdorff dimension of wild fractals we show that for every s n 2 n there exists a homogeneously embedded wild cantor set c s in r n n 3 of local hausdorff dimension s also it is shown that for every s n 2 n and for any integer k n such that 1 k s there exist everywhere wild k spheres and k cells in r n n 3 of local hausdorff dimension s

optimized analytic field propagator o afp for plane wave injection in fdtd simulations optimizations are proposed for the original frequency domain analytic field propagator afp to source plane waves in a 1d 2d 3d total field scattered field tf sf fdtd formulation the proposed technique essentially produces no field leakage error limited by 300 db machine precision error with finite sampling points dictated by temporal aliasing constraints by taking advantage of the inherent 1d nature of a plane wave the memory requirements for the original afp are reduced significantly the proposed optimized solution o afp greatly reduces the computational complexity by calculating a number of spatial fields of o n rather than o n 2 which then makes the technique practical enough to include fully 3d simulations

prime number theorems and holonomies for hyperbolic rational maps for a hyperbolic rational map f of degree at least two on the riemann sphere we obtain estimates for the number of primitive periodic orbits of f ordered by their multiplier and establish equidistribution of the associated holonomies both with power saving error terms

a flexible framework for hypothesis testing in high dimensions hypothesis testing in the linear regression model is a fundamental statistical problem we consider linear regression in the high dimensional regime where the number of parameters exceeds the number of samples p n to make informative inference we assume that the model is approximately sparse i e the effect of covariates on the response can be well approximated by conditioning on a relatively small number of covariates whose identities are unknown we develop a framework for testing very general hypotheses regarding the model parameters our framework encompasses testing whether the parameter lies in a convex cone testing the signal strength and testing arbitrary functionals of the parameter we show that the procedure proposed controls the type i error and we also analyse the power of the procedure our numerical experiments confirm our theoretical findings and demonstrate that we control the false positive rate type i error near the nominal level and have high power by duality between hypotheses testing and confidence intervals the framework proposed can be used to obtain valid confidence intervals for various functionals of the model parameters for linear functionals the length of confidence intervals is shown to be minimax rate optimal

on decay of correlations in anosov flows there is some disagreement about the meaning of the phrase chaotic flow however there is no doubt that mixing anosov flows provides an example of such systems anosov systems were introduced and extensively studied in his classical memoir a among other things he proved the following fact known now as anosov alternative for flows either every strong stable and strong unstable manifold is everywhere dense or the flow gt is a suspension over an anosov diffeomorphism by a constant roof function if the first alternative holds gt is mixing with respect to every gibbs measure see pp2 now the natural question is what is the estimated rate of mixing this is certainly one of the simplest questions concerning correlation decay in continuous time systems nevertheless the only results obtained until recently dealt with the case when the system discussed had an additional algebraic structure the easier case of anosov diffeomorphisms can be treated by the methods of thermodynamic formalism of sinai ruelle and bowen b2 namely one uses markov partitions to construct an isomorphism between the diffeomorphism and a subshift of finite type and then proves that all such subshifts are exponentially mixing this method would succeed also for flows if any suspension over a subshift of finite type had exponentially decaying correlations however the simplest example suspensions with locally constant roof functions never have such a property ri one can use the above observation to produce examples of axiom a flows with arbitrary slow correlation decay it became clear therefore that some additional geometric properties should be taken into account in recent work chernov chl ch2 has employed a uniform nonintegrability condition to get a subexponential estimate for correlation functions for geodesic flows on surfaces of variable negative curvature his method relies on the technique of markov approximation developed in chl the aim of this paper is to combine geometric considerations of chernov with the thermodynamic formalism approach the later method seems to be more appropriate than markov approximations since it gives simpler

the thermodynamic formalism for expanding maps letf x x be an expanding map of a compact space small distances are increased by a factor 1 a generating function z is defined which countsf periodic points with a weight one can express in terms of nonstandard fredholm determinants of certain transfer operators which can be studied by methods borrowed from statistical mechanics in this paper we review the spectral properties of the transfer operators and the corresponding analytic properties of z gibbs distributions and applications to julia sets are also discussed some new results are proved and some natural conjectures are proposed

a direct approach to false discovery rates summary multiple hypothesis testing involves guarding against much more complicated errors than single hypothesis testing whereas we typically control the type i error rate for a single hypothesis test a compound error rate is controlled for multiple hypothesis tests for example controlling the false discovery rate fdr traditionally involves intricate sequential p value rejection methods based on the observed data whereas a sequential p value method fixes the error rate and estimates its corresponding rejection region we propose the opposite approach we fix the rejection region and then estimate its corresponding error rate this new approach offers increased applicability accuracy and power we apply the methodology to both the positive false discovery rate pfdr and fdr and provide evidence for its benefits it is shown that pfdr is probably the quantity of interest over fdr also discussed is the calculation of the q value the pfdr analogue of the p value which eliminates the need to set the error rate beforehand as is traditionally done some simple numerical examples are presented that show that this new approach can yield an increase of over eight times in power compared with the benjamini hochberg fdr method

statistical inference of genetic pathway analysis in high dimensions genetic pathway analysis has become an important tool for investigating the association between a group of genetic variants and traits with dense genotyping and extensive imputation the number of genetic variants in biological pathways has increased considerably and sometimes exceeds the sample size formula see text conducting genetic pathway analysis and statistical inference in such settings is challenging we introduce an approach that can handle pathways whose dimension formula see text could be greater than formula see text our method can be used to detect pathways that have nonsparse weak signals as well as pathways that have sparse but stronger signals we establish the asymptotic distribution for the proposed statistic and conduct theoretical analysis on its power simulation studies show that our test has correct type i error control and is more powerful than existing approaches an application to a genome wide association study of high density lipoproteins demonstrates the proposed approach

optimal estimation of genetic relatedness in high dimensional linear models estimating the genetic relatedness between two traits based on the genome wide association data is an important problem in genetics research in the framework of high dimensional linear models we

on asymptotics of eigenvectors of large sample covariance matrix let x ij i j be a double array of i i d complex random variables with ex 11 0 e x 11 2 1 and e x 11 4 and let an 1 n t 1 2 n x n x n t 1 2 n where t 1 2 n is the square root of a nonnegative definite matrix t n and x n is the n x n matrix of the upper left comer of the double array the matrix an can be considered as a sample covariance matrix of an i i d sample from a population with mean zero and covariance matrix t n or as a multivariate f matrix if t n is the inverse of another sample covariance matrix to investigate the limiting behavior of the eigenvectors of an a new form of empirical spectral distribution is defined with weights defined by eigenvectors and it is then shown that this has the same limiting spectral distribution as the empirical spectral distribution defined by equal weights moreover if x ij and t n are either real or complex and some additional moment assumptions are made then linear spectral statistics defined by the eigenvectors of an are proved to have gaussian limits which suggests that the eigenvector matrix of an is nearly haar distributed when t n is a multiple of the identity matrix an easy consequence for a wishart matrix

single realization stochastic fdtd for weak scattering waves in biological random media this paper introduces an iterative scheme to overcome the unresolved issues presented in s fdtd stochastic finite difference time domain for obtaining ensemble average field values recently reported by smith and furse in an attempt to replace the brute force multiple realization also known as monte carlo approach with a single realization scheme our formulation is particularly useful for studying light interactions with biological cells and tissues having sub wavelength scale features numerical results demonstrate that such a small scale variation can be effectively modeled with a random medium problem which when simulated with the proposed s fdtd indeed produces a very accurate result

variance estimation in high dimensional linear models the residual variance and the proportion of explained variation are important quantities in many statistical models and model fitting procedures they play an important role in regression diagnostics and model selection procedures as well as in determining the performance limits in many problems in this paper we propose new method of moments based estimators for the residual variance the proportion of explained variation and other related quantities such as the l2 signal strength the proposed estimators are consistent and asymptotically normal in high dimensional linear models with gaussian predictors and errors where the number of predictors d is proportional to the number of observations n in fact consistency holds even in settings where d n existing results on residual variance estimation in high dimensional linear models depend on sparsity in the underlying signal our results require no sparsity assumptions and imply that the residual variance and the proportion of explained variation can be consistently estimated even when d n and the underlying signal itself is nonestimable numerical work suggests that some of our distributional assumptions may be relaxed a real data analysis involving gene expression data and single nucleotide polymorphism data illustrates the performance of the proposed methods

optimal rates of convergence for estimating toeplitz covariance matrices toeplitz covariance matrices are used in the analysis of stationary stochastic processes and a wide range of applications including radar imaging target detection speech recognition and communications systems in this paper we consider optimal estimation of large toeplitz covariance matrices and establish the minimax rate of convergence for two commonly used parameter spaces under the spectral norm the properties of the tapering and banding estimators are studied in detail and are used to obtain the minimax upper bound the results also reveal a fundamental difference between the tapering and banding estimators over certain parameter spaces the minimax lower bound is derived through a novel construction of a more informative experiment for which the minimax lower bound is obtained through an equivalent gaussian scale model and through a careful selection of a finite collection of least favorable parameters in addition optimal rate of convergence for estimating the inverse of a toeplitz covariance matrix is also established

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

dimensions and measures in infinite iterated function systems the hausdorff and packing measures and dimensions of the limit sets of iterated function systems generated by countable families of conformal contractions are investigated conformal measures for such systems reflecting geometric properties of the limit set are introduced proved to exist and to be unique the existence of a unique invariant probability equivalent to the conformal measure is derived our methods employ the concepts of the perron frobenius operator symbolic dynamics on a shift space with an infinite alphabet and the properties of the above mentioned ergodic invariant measure a formula for the hausdorff dimension of the limit set in terms of the pressure function is derived fractal phenomena not exhibited by finite systems are shown to appear in the infinite case in particular a variety of conditions are provided for hausdorff and packing measures to be positive or finite and a number of examples are described showing the appearance of various possible combinations for these quantities one example given special attention is the limit set associated to the complex continued fraction expansion in particular lower and upper estimates for its hausdorff dimension are given a large natural class of systems whose limit sets are dimensionless in the restricted sense is described

divergence groups have the bowen property we show that every deformation of a divergence type fuchsian group has a limit set which is either a circle or has dimension strictly larger than 1 this is known to be false for all convergence type groups and hence solves bowen s problem in the general case the proof uses a theorem of dennis sullivan s about convex hulls in hyperbolic 3 space and we give a new simpler proof of this result as well