equidistribution of saddle periodic points for henon type automorphisms of mathbb c k in this paper we prove the equidistribution of saddle periodic points for henon type automorphisms of mathbb c k with respect to its equilibrium measure a general strategy to obtain equidistribution properties in any dimension is presented it is based on our recent theory of densities for positive closed currents several fine properties of dynamical currents are also proved

improving the speed of parallel decimal multiplication hardware support for decimal computer arithmetic is regaining popularity one reason is the recent growth of decimal computations in commercial scientific financial and internet based computer applications newly commercialized decimal arithmetic hardware units use radix 10 sequential multipliers that are rather slow for multiplication intensive applications therefore the future relevant processors are likely to host fast parallel decimal multiplication circuits the corresponding hardware algorithms are normally composed of three steps partial product generation ppg partial product reduction ppr and final carry propagating addition the state of the art is represented by two recent full solutions with alternative designs for all the three aforementioned steps in addition ppr by itself has been the focus of other recent studies in this paper we examine both of the full solutions and the impact of a ppr only design on the appropriate one in order to improve the speed of parallel decimal multiplication we present a new ppg method fine tune the ppr method of one of the full solutions and the final addition scheme of the other thus assembling a new full solution logical effort analysis and 0 13 mum synthesis show at least 13 percent speed advantage but at a cost of at most 36 percent additional area consumption

low power divider the general objective of our work is to develop methods to reduce the energy consumption of arithmetic modules while maintaining the delay unchanged and keeping the increase in the area to a minimum here we illustrate some techniques for dividers realized in cmos technology the energy dissipation reduction is carried out at different levels of abstraction from the algorithm level down to the implementation or gate level we describe the use of techniques such as switching off not active blocks retiming dual voltage and equalizing the paths to reduce glitches also we describe modifications in the on the fly conversion and rounding algorithm and in the redundant representation of the residual in order to reduce the energy dissipation the techniques and modifications mentioned above are applied to a radix 4 divider realized with static cmos standard cells for which a reduction of 40 percent is obtained with respect to the standard implementation this reduction is expected to be about 60 percent if low voltage gates for dual voltage implementation are available the techniques used here should be applicable to a variety of arithmetic modules which have similar characteristics

a sharper bonferroni procedure for multiple tests of significance summary a simple procedure for multiple tests of significance based on individual p values is derived this simple procedure is sharper than holm s 1979 sequentially rejective procedure both procedures contrast the ordered p values with the same set of critical values holm s procedure rejects an hypothesis only if its p value and each of the smaller p values are less than their corresponding critical values the new procedure rejects all hypotheses with smaller or equal p values to that of any one found less than its critical value

total positivity properties of absolute value multinormal variables with applications to confidence interval estimates and related probabilistic inequalities total positivity properties of multivariate densities are useful in deducing positive dependence of random vector components and related probability inequalities in this paper we determine necessary and sufficient conditions for total positivity of absolute value multinormal variables the results are applied to obtain positive dependence and associated inequalities for the multinormal and related distributions e g the multivariate t and wishart distributions inequalities of this type yield bounds for multivariate confidence set probabilities

high speed multioperand decimal adders there is increasing interest in hardware support for decimal arithmetic as a result of recent growth in commercial financial and internet based applications consequently new specifications for decimal floating point arithmetic have been added to the draft revision of the ieee 754 standard for floating point arithmetic this paper introduces and analyzes three techniques for performing fast decimal addition on multiple binary coded decimal bcd operands two of the techniques speculate bcd correction values and correct intermediate results while adding the input operands the first speculates over one addition the second speculates over two additions the third technique uses a binary carry save adder tree and produces a binary sum combinational logic is then used to correct the sum and determine the carry into the next more significant digit multioperand adder designs are constructed and synthesized for four to 16 input operands analyses are performed on the synthesis results and the merits of each technique are discussed finally these techniques are compared to several previous techniques for high speed decimal addition

sur les groupes de transformations birationnelles des surfaces ni agissant par transformations bi rationnelles sur les surfaces complexes compactes kahl eriennes nous mon trons a que le groupe des transformations birationnelles d une surface satisfait l alternative de tits b que les actions birationnelles de groupes de kazhdan sur les surfaces sont toutes birationnellement conjugu eesa des actions homographiques sur le plan projectif et c que si f et g sont deux transformations birationnelles de surfaces qui commutent alors ou bien f pr eserve un pinceau de courbes ou bien l un des it er es g m de g m 0 concide avec un it er e f n de f n 2 z let s be any compact complex kahler surface and bir s the group of birational transformations of s we study the structure of nitely genera ted subgroups of bir s and prove three main results a bir s satises the tits alternative b if a group with kazhdan property t acts on a compact kahler surface by birational transformations then the action is conjugate to an action by linear projective transformations on the projec tive plane and c if f is an element of bir s which does not preserve any pencil of curves and if g commutes with f then a positive iterate of g coincides with an iterate of f the second statement provides a positive answer to zimmer s conjecture for birational actions on surfaces

stepup procedures controlling generalized fwer and generalized fdr in many applications of multiple hypothesis testing where more than one false rejection can be tolerated procedures controlling error rates measuring at least k false rejections instead of at least one for some fixed k 1 can potentially increase the ability of a procedure to detect false null hypotheses the k fwer a generalized version of the usual familywise error rate fwer is such an error rate that has recently been introduced in the literature and procedures controlling it have been proposed a further generalization of a result on the k fwer is provided in this article in addition an alternative and less conservative notion of error rate the k fdr is introduced in the same spirit as the k fwer by generalizing the usual false discovery rate fdr a k fwer procedure is constructed given any set of increasing constants by utilizing the kth order joint null distributions of the p values without assuming any specific form of dependence among all the p values procedures controlling the k fdr are also developed by using the kth order joint null distributions of the p values first assuming that the sets of null and nonnull p values are mutually independent or they are jointly positively dependent in the sense of being multivariate totally positive of order two mtp2 and then discarding that assumption about the overall dependence among the p values

an improved bonferroni procedure for multiple tests of significance summary a modification of the bonferroni procedure for testing multiple hypotheses is presented the method based on the ordered p values of the individual tests is less conservative than the classical bonferroni procedure but is still simple to apply a simulation study shows that the probability of a type i error of the procedure does not exceed the nominal significance level a for a variety of multivariate normal and multivariate gamma test statistics for independent tests the procedure has type i error probability equal to a the method appears particularly advantageous over the classical bonferroni procedure when several highly correlated test statistics are involved

correlations and anticorrelations in resting state functional connectivity mri a quantitative comparison of preprocessing strategies resting state data sets contain coherent fluctuations unrelated to neural processes originating from residual motion artefacts respiration and cardiac action such confounding effects may introduce correlations and cause an overestimation of functional connectivity strengths in this study we applied several multidimensional linear regression approaches to remove artificial coherencies and examined the impact of preprocessing on sensitivity and specificity of functional connectivity results in simulated data and resting state data sets from 40 subjects furthermore we aimed at clarifying possible causes of anticorrelations and test the hypothesis that anticorrelations are introduced via certain preprocessing approaches with particular focus on the effects of regression against the global signal our results show that preprocessing in general greatly increased connection specificity in particular correction for global signal fluctuations almost doubled connection specificity however widespread anticorrelated networks were only found when regression against the global signal was applied results in simulated data sets compared with result of human data strongly suggest that anticorrelations are indeed introduced by global signal regression and should therefore be interpreted very carefully in addition global signal regression may also reduce the sensitivity for detecting true correlations i e increase the number of false negatives concluding from our results we suggest that is highly recommended to apply correction against realignment parameters white matter and ventricular time courses as well as the global signal to maximize the specificity of positive resting state correlations

polynomial diffeomorphisms of ii stable manifolds and recurrence f x y y y ax c the diffeomorphisms in this class have complicated dynamics in particular they have periodic points of infinitely many periods and positive topological entropy see fm s we can distinguish between these classes by considering the growth of the degrees of iterates of the diffeomorphism define deg f to be the maximum of the degrees of the coordinate functions this quantity is not a conjugacy invariant of f hence not a dynamical invariant we can construct a conjugacy invariant which we call the dynamical degree as follows

the simes method for multiple hypothesis testing with positively dependent test statistics abstract the simes method for testing intersection of more than two hypotheses is known to control the probability of type i error only when the underlying test statistics are independent although this method is more powerful than the classical bonferroni method it is not known whether it is conservative when the test statistics are dependent this article proves that for multivariate distributions exhibiting a type of positive dependence that arise in many multiple hypothesis testing situations the simes method indeed controls the probability of type i error this extends some results established very recently in the special case of two hypotheses

quantification of the impact of a confounding variable on functional connectivity confirms anti correlated networks in the resting state the effect of regressing out the global average signal gas in resting state fmri data has become a concern for interpreting functional connectivity analyses it is not clear whether the reported anti correlations between the default mode and the dorsal attention networks are intrinsic to the brain or are artificially created by regressing out the gas here we introduce a concept impact of the global average on functional connectivity igafc for quantifying the sensitivity of seed based correlation analyses to the regression of the gas this voxel wise igafc index is defined as the product of two correlation coefficients the correlation between the gas and the fmri time course of a voxel times the correlation between the gas and the seed time course this definition enables the calculation of a threshold at which the impact of regressing out the gas would be large enough to introduce spurious negative correlations it also yields a post hoc impact correction procedure via thresholding which eliminates spurious correlations introduced by regressing out the gas in addition we introduce an artificial negative correlation index anci defined as the absolute difference between the igafc index and the impact threshold the anci allows a graded confidence scale for ranking voxels according to their likelihood of showing artificial correlations by applying this method we observed regions in the default mode and dorsal attention networks that were anti correlated these findings confirm that the previously reported negative correlations between the dorsal attention and default mode networks are intrinsic to the brain and not the result of statistical manipulations our proposed quantification of the impact that a confound may have on functional connectivity can be generalized to global effect estimators other than the gas it can be readily applied to other confounds such as systemic physiological or head movement interferences in order to quantify their impact on functional connectivity in the resting state

a stagewise rejective multiple test procedure based on a modified bonferroni test summary simes 1986 has proposed a modified bonferroni procedure for the test of an overall hypothesis which is the combination of n individual hypotheses in contrast to the classical bonferroni procedure it is not obvious how statements about individual hypotheses are to be made for this procedure in the present paper a multiple test procedure allowing statements on individual hypotheses is proposed it is based on the principle of closed test procedures marcus peritz gabriel 1976 and controls the multiple level a

henon like mappings in c we study the dynamics of a class of nonalgebraic holomorphic diffeomorphisms topo logical analogues in the unit bidisk of complex h6non mappings in c2 in particular a dynamical degree is defined which is related to topological entropy and we construct stable unstable invariant currents and prove there is a unique mixing measure of maximal entropy with product structure 1 introduction one of the most famous 2 dimensional dynamical systems is smale s horseshoe it is a basic example of a simple map with complicated dynamics and has served as a guideline for the whole modern development of discrete time dynamical systems a very natural problem in this context is to understand the dynamical phenomena occuring when uniform hyperbolicity of the horseshoe degenerates this was a motivation for the study of the so called henon map

stability and bifurcations for dissipative polynomial automorphisms of mathbb c 2 we study stability and bifurcations in holomorphic families of polynomial automorphisms of mathbb c 2 we say that such a family is weakly stable over some parameter domain if periodic orbits do not bifurcate there we first show that this defines a meaningful notion of stability which parallels in many ways the classical notion of j stability in one dimensional dynamics define the bifurcation locus to be the complement of the weak stability locus in the second part of the paper we prove that under an assumption of moderate dissipativity the parameters displaying homoclinic tangencies are dense in the bifurcation locus this confirms one of palis conjectures in the complex setting the proof relies on the formalism of semi parabolic bifurcation and the construction of critical points in semi parabolic basins which makes use of the classical denjoy carleman ahlfors and wiman theorems

some probability inequalities for ordered rm mtp sb 2 random variables a proof of the simes conjecture some new probability inequalities involving the ordered components of an mtp 2 random vector are derived which provide an analytical proof of an important conjecture in the field of multiple hypothesis testing this conjecture has been mostly validated so far using simulation

dependency and false discovery rate asymptotics some effort has been undertaken over the last decade to provide conditions for the control of the false discovery rate by the linear step up procedure lsu for testing n hypotheses when test statistics are dependent in this paper we investigate the expected error rate eer and the false discovery rate fdr in some extreme parameter configurations when n tends to infinity for test statistics being exchangeable under null hypotheses all results are derived in terms of p values in a general setup we present a series of results concerning the interrelation of simes rejection curve and the limiting empirical distribution function of the p values main objects under investigation are largest limiting crossing points between these functions which play a key role in deriving explicit formulas for eer and fdr as specific examples we investigate equi correlated normal and t variables in more detail and compute the limiting eer and fdr theoretically and numerically a surprising limit behavior occurs if these models tend to independence

identification of physiological response functions to correct for fluctuations in resting state fmri related to heart rate and respiration abstract functional magnetic resonance imaging fmri is widely viewed as the gold standard for studying brain function due to its high spatial resolution and non invasive nature however it is well established that changes in breathing patterns and heart rate strongly influence the blood oxygen level dependent bold fmri signal and this in turn can have considerable effects on fmri studies particularly resting state studies the dynamic effects of physiological processes are often quantified by using convolution models along with simultaneously recorded physiological data in this context physiological response function p r f curves cardiac and respiratory response functions which are convolved with the corresponding physiological fluctuations are commonly employed while it has often been suggested that the p r f curves may be region or subject specific it is still an open question whether this is the case in the present study we propose a novel framework for the robust estimation of p r f curves and use this framework to rigorously examine the implications of using population subject session and scan specific p r f curves the proposed framework was tested on resting state fmri and physiological data from the human connectome project our results suggest that p r f curves vary significantly across subjects and to a lesser extent across sessions from the same subject these differences can be partly attributed to physiological variables such as the mean and variance of the heart rate during the scan the proposed methodological framework can be used to obtain robust scan specific p r f curves from data records with duration longer than 5 min exhibiting significantly improved performance compared to previously defined canonical cardiac and respiration response functions besides removing physiological confounds from the bold signal accurate modeling of subject or session scan specific p r f curves is of importance in studies that involve populations with altered vascular responses such as aging subjects

conditional association and unidimensionality in monotone latent variable models latent variable models represent the joint distribution of observable variables in terms of a simple structure involving unobserved or latent variables usually assuming the conditional independence of the observable variables given the latent variables these models play an important role in educational measurement and psychometrics in sociology and in population genetics and are implicit in some work on systems reliability we study a broad class of latent variable models namely the monotone unidimensional models in which the latent variable is a scalar the observable variables are conditionally independent given the latent variable and the conditional distribution of the observables given the latent variable is stochastically increasing in the latent variable all models in this class imply a new strong form of positive dependence among the observable variables namely conditional positive association this positive dependence condition may be used to test whether any model in this class can provide an adequate fit to observed data various applications generalizations and a numerical example are discussed

testing the conditional independence and monotonicity assumptions of item response theory when item characteristic curves are nondecreasing functions of a latent variable the conditional or local independence of item responses given the latent variable implies nonnegative conditional covariances between all monotone increasing functions of a set of item responses given any function of the remaining item responses this general result provides a basis for testing the conditional independence assumption without first specifying a parametric form for the nondecreasing item characteristic curves the proposed tests are simple have known asymptotic null distributions and possess certain optimal properties in an example the conditional independence hypothesis is rejected for all possible forms of monotone item characteristic curves

support vector machines for dyadic data we describe a new technique for the analysis of dyadic data where two sets of objects row and column objects are characterized by a matrix of numerical values that describe their mutual relationships the new technique called potential support vector machine p svm is a large margin method for the construction of classifiers and regression functions for the column objects contrary to standard support vector machine approaches the p svm minimizes a scale invariant capacity measure and requires a new set of constraints as a result the p svm method leads to a usually sparse expansion of the classification and regression functions in terms of the row rather than the column objects and can handle data and kernel matrices that are neither positive definite nor square we then describe two complementary regularization schemes the first scheme improves generalization performance for classification and regression tasks the second scheme leads to the selection of a small informative set of row support objects and can be applied to feature selection benchmarks for classification regression and feature selection tasks are performed with toy data as well as with several real world data sets the results show that the new method is at least competitive with but often performs better than the benchmarked standard methods for standard vectorial as well as true dyadic data sets in addition a theoretical justification is provided for the new approach

joint mean and covariance estimation with unreplicated matrix variate data abstractit has been proposed that complex populations such as those that arise in genomics studies may exhibit dependencies among observations as well as among variables this gives rise to the challenging problem of analyzing unreplicated high dimensional data with unknown mean and dependence structures matrix variate approaches that impose various forms of inverse covariance sparsity allow flexible dependence structures to be estimated but cannot directly be applied when the mean and covariance matrices are estimated jointly we present a practical method utilizing generalized least squares and penalized inverse covariance estimation to address this challenge we establish consistency and obtain rates of convergence for estimating the mean parameters and covariance matrices the advantages of our approaches are i dependence graphs and covariance structures can be estimated in the presence of unknown mean structure ii the mean structure becomes more efficiently estimated when accounting for

digit recurrence dividers with reduced logical depth in this paper we propose a class of division algorithms with the aim of reducing the delay of the selection of the quotient digit by introducing more concurrency and flexibility in its computation from the proposed class of algorithms we select one that moves part of the selection function out of the critical path with a corresponding reduction in the critical path compared with existing alternatives we present the algorithm and describe the architectures for radix 4 and for radix 16 for radix 16 we use the scheme of overlapping two radix 4 stages in both cases radix 4 and radix 16 we show that our algorithms allow the design of units with well balanced critical paths with consequent decreases of the cycle times moreover in the radix 16 case we include some additional speculation techniques to estimate the speedup we used a rough timing model based on logical effort for both radices we estimate a speedup of about 25 percent with respect to previous implementations in the radix 4 case this is achieved by using roughly the same area while in the radix 16 case the area is increased by about 30 percent we verified our estimations by performing a synthesis of the radix 4 units

a study of decimal left shifters for binary numbers the importance of decimal floating point dfp arithmetic has been growing in the last years and specifications for it are included in the revised ieee 754 standard for floating point arithmetic ieee 754 2008 ieee 754 2008 specifies a binary encoding for decimal significands in which the significands of dfp numbers are represented as unsigned binary integers for this representation which is commonly referred to as the binary integer decimal bid encoding fast decimal left shifting of a binary number is useful for operand alignment normalization overflow avoidance and quantize operations a decimal left shift of an unsigned binary integer i by s digit positions corresponds to multiplying i by 10 s this paper presents the theory and design of decimal left shifters for binary numbers the designs perform decimal left shifting using optimized constant multiplications by selected powers of ten we propose and analyze different combinational and sequential decimal left shifter architectures for binary numbers the designs are compared to one another in terms of area and delay using both theoretical estimates and synthesis results for 16 digit 54 bit binary inputs and 4 bit shift amounts the results indicate that an optimized radix 2 decimal shifter implementing partial shifters in carry save format has 80 less area and 68 less delay than a lookup table followed by a binary multiplier to compute ix10 s when both designs are optimized for delay when both designs are optimized for area the radix 2 decimal shifter has 89 less area and 31 less delay

the control of the false discovery rate in multiple testing under dependency benjamini and hochberg suggest that the false discovery rate may be the appropriate error rate to control in many applied multiple testing problems a simple procedure was given there as an fdr controlling procedure for independent test statistics and was shown to be much more powerful than comparable procedures which control the traditional familywise error rate we prove that this same procedure also controls the false discovery rate when the test statistics have positive regression dependency on each of the test statistics corresponding to the true null hypotheses this condition for positive dependency is general enough to cover many problems of practical interest including the comparisons of many treatments with a single control multivariate normal test statistics with positive correlation matrix and multivariate t furthermore the test statistics may be discrete and the tested hypotheses composite without posing special difficulties for all other forms of dependency a simple conservative modification of the procedure controls the false discovery rate thus the range of problems for which a procedure with proven fdr control can be offered is greatly increased 1 1 simultaneous hypotheses testing the control of the increased type i error when testing simultaneously a family of hypotheses is a central issue in the area of multiple comparisons rarely are we interested only in whether all hypotheses are jointly true or not which is the test of the intersection null hypothesis in most applications we infer about the individual hypotheses realizing that some of the tested hypotheses are usually true we hope not all and some are not we wish to decide which ones are not true indicating statistical discoveries an important such problem is that of multiple endpoints in a clinical trial a new treatment is compared with an existing one in terms of a large number of potential benefits endpoints

a radix 10 digit recurrence division unit algorithm and architecture in this work we present a radix 10 division unit that is based on the digit recurrence algorithm the previous decimal division designs do not include recent developments in the theory and practice of this type of algorithm which were developed for radix 2k dividers in addition to the adaptation of these features the radix 10 quotient digit is decomposed into a radix 2 digit and a radix 5 digit in such a way that only five and two times the divisor are required in the recurrence moreover the most significant slice of the recurrence which includes the selection function is implemented in radix 2 avoiding the additional delay introduced by the radix 10 carry save additions and allowing the balancing of the paths to reduce the cycle delay the results of the implementation of the proposed radix 10 division unit show that its latency is close to that of radix 16 division units comparable dynamic range of significant and it has a shorter latency than a radix 10 unit based on the newton raphson approximation

an ergodic study of painleve vi an ergodic study of painleve vi is developed the chaotic nature of its poincare return map is established for almost all loops the exponential growth of the numbers of periodic solutions is also shown principal ingredients of the arguments are a moduli theoretical formulation of painleve vi a riemann hilbert correspondence the dynamical system of a birational map on a cubic surface and the lefschetz fixed point formula

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

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

the equidistribution of small points for strongly regular pairs of polynomial maps in this paper we prove the equidistribution of periodic points of a regular polynomial automorphism f mathbb a n rightarrow mathbb a n defined over a number field k let f be a regular polynomial automorphism defined over a number field k and let v in m k then there exists an f invariant probability measure mu f v on mathrm berk bigl mathbb p n mathbb c v bigr such that the set of periodic points of f is equidistributed with respect to mu f v