optimal group sequential designs for simultaneous testing of superiority and non inferiority confirmatory clinical trials comparing the efficacy of a new treatment with an active control typically aim at demonstrating either superiority or non inferiority in the latter case the objective is to show that the experimental treatment is not worse than the active control by more than a pre specified non inferiority margin we consider two classes of group sequential designs that combine the superiority and non inferiority objectives non adaptive designs with fixed group sizes and adaptive designs where future group sizes may be based on the observed treatment effect for both classes we derive group sequential designs meeting error probability constraints that have the lowest possible expected sample size averaged over a set of values of the treatment effect these optimized designs provide an efficient means of reducing expected sample size under a range of treatment effects even when the separate objectives of proving superiority and non inferiority would require quite different fixed sample sizes we also present error spending versions of group sequential designs that are easily implementable and can handle unpredictable group sizes or information levels we find the adaptive choice of group sizes to yield some modest efficiency gains alternatively expected sample size may be reduced by adding another interim analysis to a non adaptive group sequential design

a second wronskian formulation of the boussinesq equation a wronskian formulation leading to rational solutions is presented for the boussinesq equation it involves third order linear partial differential equations whose representative systems are systematically solved the resulting solutions formulas provide a direct but powerful approach for constructing rational solutions positon solutions and complexiton solutions to the boussinesq equation various examples of exact solutions of those three kinds are computed the newly presented wronskian formulation is different from the one previously presented by li et al which does not yield rational solutions

symmetry aware graph matching visual symmetry encodes middle to high level geometric information and plays an important role in many computer vision applications not much effort however has been devoted to utilize symmetry information for graph matching in this paper we propose a new framework for symmetry aware graph matching in the context of image matching in the framework we first define symmetry matrices to characterize the geometric symmetry relation among image features and then develop two methods to discover such symmetry after that we design general strategies to boost graph matching algorithms with symmetry constraints and apply these strategies to several state of the art algorithms for evaluation the proposed symmetry aware graph matching algorithms are first applied to two datasets involving clear symmetry patterns a recently proposed architecture image set and a dental panoramic radiograph collection the results clearly demonstrate the benefits of using symmetry information an experiment is also conducted on a dataset where symmetry is less obvious the results show that our strategies still achieve better of similar performance compared with state of the arts highlightsit is the first time symmetry constraints that are introduced into graph matching the symmetry aware graph matching improves the matching performance a new dataset with annotation for evaluating graph matching is constructed

recursive combination tests we present a method that extends the flexibility of adaptive designs to the number of interim analyses and to the choice of decision boundaries at each stage of the trial the design of the next stage can be determined using all of the information gathered so far additionally one can specify the next stage as the final stage or can plan a further interim analysis the method is based on a recursive application of the two stage combination tests for p values the crucial point is the appropriate definition of a p value function that combines p values from two separate stages to a single p value formally we start with a two stage combination test however the p value of the second stage can be replaced by the p value of a further combination test this applies if the experimenter decides in the first interim analysis to perform another interim analysis thereby extending the design to at least three stages obviously this can be also done in a recursive way in the following interim analyses the test

on adaptive extensions of group sequential trials for clinical investigations in group sequential trials it is important to obtain adequate data to assess overall benefits and risks of an experimental treatment for patients to achieve this goal we provide a general formal framework for adaptively extending a group sequential trial to stop at any interim analysis time often after a significance boundary for a clinical endpoint is crossed for statistical inference we propose to order the sample space by a class of well ordered group sequential tests on this basis we develop a unified sequential statistical inference approach that is applicable to both interim monitoring and final analysis we also show that the new ordering provides the foundation for the repeated confidence intervals procedure of jennison and turnbull

definition and extraction of stable points from fingerprint images this paper introduces a new idea to define and extract singular points sps including cores and deltas from fingerprint images by a zone could be in theorem that describes harmonic relationships of a sp and its neighbors according to the theorem we can view sps as stable points attractors and rejectors by their rotations estimate core s direction and restore sp offset the proposed method is validated in the following two hierarchical aspects one is to test the reliability and accuracy of coarse sp detection by means of two indices ri and ac and the other is the accuracy of core s location and the stability of core s direction in terms of improved fingercode matching experiments on partial fvc2004 data sets show that it works well and outperforms three other methods

integrability and bright soliton solutions to the coupled nonlinear schrodinger equation with higher order effects in this paper we study the integrability and exact bright soliton solutions to the coupled nonlinear schrodinger equation with higher order effects arising from nonlinear fiber medium firstly the lax integrability of this equation is investigated by prolongation technique and an integrable generalized coupled higher order nonlinear schrodinger equation is proposed then the general n bright bright soliton solutions of this integrable equation are obtained by riemann hilbert formulation and the collision dynamics between two solitons is analyzed finally an integrable generalized n coupled higher order nonlinear schrodinger equation together with its linear spectral problem are given

special solutions from the variable separation approach the davey stewartson equation a variable separation procedure for the davey stewartson ds equation is proposed by using a prior ansatz to its bilinear form the reduced equations for two variable separated fields have the same trilinear form although they possess different independent variables the trilinear equation can be changed to a spacetime symmetric form and can be solved by means of a boussinesq type equation system whenever a pair of solutions of the reduced fields are obtained a corresponding solution of the ds equation can be obtained algebraically the single dromion solution and some kinds of positon solutions are obtained explicitly

exact solutions of the bogoyavlenskii equation using the multiple g g expansion method in this work exact traveling wave solutions of the bogoyavlenskii equation are studied by the g g expansion method and its variants the solutions obtained are general solutions which are in the form of hyperbolic trigonometric and rational functions and a variety of special solutions like kink shaped antikink shaped bell type soliton solutions etc can easily be derived from the general results under certain domain these methods are more effective and simple than other methods and a number of solutions can be obtained at the same time in order to visualize the underlying dynamics of the obtained solutions two and three dimensional plots are drawn

confidence intervals for a binomial parameter following a multistage test with application to mil std 105d and medical trials this paper describes a method for constructing confidence intervals for a binomial parameter upon termination of a sequential or multistage test tables are presented for use with the mil std 105d multiple sampling plans for acceptance sampling also given are tables for use with some three stage schemes that have been proposed in connection with biomedical trials the results are compared with confidence intervals calculated as if the sampling plan had been one with a fixed sample size

on the inefficiency of the adaptive design for monitoring clinical trials summary adaptive designs which allow the sample size to be modified based on sequentially computed observed treatment differences have been advocated recently for monitoring clinical trials although such methods have a great deal of appeal on the surface we show that such methods are inefficient and that one can improve uniformly on such adaptive designs using standard group sequential tests based on the sequentially computed likelihood ratio test statistic

fingerprint classification by directional image partitioning in this work we introduce a new approach to automatic fingerprint classification the directional image is partitioned into homogeneous connected regions according to the fingerprint topology thus giving a synthetic representation which can be exploited as a basis for the classification a set of dynamic masks together with an optimization criterion are used to guide the partitioning the adaptation of the masks produces a numerical vector representing each fingerprint as a multidimensional point which can be conceived as a continuous classification different search strategies are discussed to efficiently retrieve fingerprints both with continuous and exclusive classification experimental results have been given for the most commonly used fingerprint databases and the new method has been compared with other approaches known in the literature as to fingerprint retrieval based on continuous classification our method gives the best performance and exhibits a very high robustness

designed extension of studies based on conditional power we propose a flexible method of extending a study based on conditional power the possibility for extension when the p value at the planned end is small but not statistically significant is built in to the design of the study the significance of the treatment difference at the planned end is used to determine the number of additional observations needed and the critical value necessary for use after accruing those additional observations it may therefore be thought of as a two stage procedure even though the observed treatment difference at stage 1 is used to make decisions the type i error rate is protected

recognition by symmetry derivatives and the generalized structure tensor we suggest a set of complex differential operators that can be used to produce and filter dense orientation tensor fields for feature extraction matching and pattern recognition we present results on the invariance properties of these operators that we call symmetry derivatives these show that in contrast to ordinary derivatives all orders of symmetry derivatives of gaussians yield a remarkable invariance they are obtained by replacing the original differential polynomial with the same polynomial but using ordinary coordinates x and y corresponding to partial derivatives moreover the symmetry derivatives of gaussians are closed under the convolution operator and they are invariant to the fourier transform the equivalent of the structure tensor representing and extracting orientations of curve patterns had previously been shown to hold in harmonic coordinates in a nearly identical manner as a result positions orientations and certainties of intricate patterns e g spirals crosses parabolic shapes can be modeled by use of symmetry derivatives of gaussians with greater analytical precision as well as computational efficiency since gaussians and their derivatives are utilized extensively in image processing the revealed properties have practical consequences for local orientation based feature extraction the usefulness of these results is demonstrated by two applications 1 tracking cross markers in long image sequences from vehicle crash tests and 2 alignment of noisy fingerprints

optimal asymmetric one sided group sequential tests summary we extend the optimal symmetric group sequential tests of eales jennison 1992 to the broader class of asymmetric designs two forms of asymmetry are considered involving unequal type i and type ii error rates and different emphases on expected sample sizes at the null and alternative hypotheses we discuss the properties of our optimal designs and use them to assess the efficiency of the family of tests proposed by pampallona tsiatis 1994 and two families of one sided tests defined through error spending functions we show that the error spending designs are highly efficient while the easily implemented tests of pampallona tsiatis are a little less efficient but still not far from optimal our results demonstrate that asymmetric designs can decrease the expected sample size under one hypothesis but only at the expense of a significantly larger expected sample size under the other hypothesis

enhanced gradient based algorithm for the estimation of fingerprint orientation fields an accurate estimation of fingerprint orientation fields is an essential step in the overall fingerprint recognition process conventional gradient based approaches are popular but very sensitive to noise in this paper we propose a novel implementation to improve the performance of gradient based methods the enhanced algorithm chooses the best orientation estimate from four overlapping neighborhoods of every image block where the voting scheme is based on the reliability measures we test our algorithm on real fingerprint images the experiment results suggest that our enhanced algorithm achieves visibly better noise resistance with modest computation time in comparison with other gradient based methods

the extended tanh method for abundant solitary wave solutions of nonlinear wave equations the extended tanh method is used to establish abundant solitary wave solutions of nonlinear wave equations the obtained solutions include solitons kinks and plane periodic solutions the study is an extension to the remarkable development by malfliet 1 the extended tanh method presents a wider applicability for handling nonlinear wave equations

link between solitary waves and projective riccati equations many solitary wave solutions of nonlinear partial differential equations can be written as a polynomial in two elementary functions which satisfy a projective hence linearizable riccati system from that property the authors deduce a method for building these solutions by determining only a finite number of coefficients this method is much shorter and obtains more solutions than the one which consists of summing a perturbation series built from exponential solutions of the linearized equation they handle several examples for the henon heiles hamiltonian system they obtain several exact solutions one of them defines a new solitary wave solution for a coupled system of boussinesq and nonlinear schrodinger equations for a third order dispersive equation with two monomial nonlinearities they isolate all cases where the general solution is single valued

singular point detection by shape analysis of directional fields in fingerprints this paper presents a new fingerprint singular point detection method that is type distinguishable and applicable to various fingerprint images regardless of their resolutions the proposed method detects singular points by analyzing the shapes of the local directional fields of a fingerprint image using the predefined rules all types of singular points upper core lower core and delta points can be extracted accurately and delineated in terms of the type of singular points in case of arch type fingerprints there exists no singular point but reference points for arch type fingerprints are required to be detected for registration therefore we propose a new reference point detection method for arch type fingerprints as well the result of the experiments on the two public databases fvc2000 2a fvc2002 2a with different resolutions demonstrates that the proposed method has high accuracy in locating each types of singular points and detecting the reference points of arch type fingerprints without regard to their image resolutions

unsharp masking using quadratic filter for the enhancement of fingerprints in noisy background the paper summarizes the design and implementation of a quadratic edge detection filter based on volterra series the filter is employed in an unsharp masking scheme for enhancing fingerprints in a dark and noisy background the proposed filter can account for much of the polynomial nonlinearities inherent in the input image and can replace the conventional edge detectors like laplacian log etc the application of the new filter is in forensic investigation where enhancement and identification of latent fingerprints are key issues the enhancement of images by the proposed method is superior to that with unsharp masking scheme employing conventional filters in terms of the visual quality the noise performance and the computational complexity making it an ideal candidate for latent fingerprint enhancement

direct search for exact solutions to the nonlinear schrodinger equation a five dimensional symmetry algebra consisting of lie point symmetries is firstly computed for the nonlinear schrodinger equation which together with a reflection invariance generates two five parameter solution groups three ansatze of transformations are secondly analyzed and used to construct exact solutions to the nonlinear schrodinger equation various examples of exact solutions with constant trigonometric function type exponential function type and rational function amplitude are given upon careful analysis a bifurcation phenomenon in the nonlinear schrodinger equation is clearly exhibited during the solution process

modified method of simplest equation and its applications to the bogoyavlenskii equation in this paper we construct the exact traveling wave solutions of the bogoyavlenskii equation using modified method of simplest equation the simplest equation herewith is a special riccati equation in the meantime the proposed method in this work is proved to be a powerful mathematical tool for obtaining exact solutions of other nonlinear partial differential equations in mathematical physics and other research fields

constructing nonlinear discrete integrable hamiltonian couplings beginning with lax pairs from special non semisimple matrix lie algebras we establish a scheme for constructing nonlinear discrete integrable couplings discrete variational identities over the associated loop algebras are used to build hamiltonian structures for the resulting integrable couplings we illustrate the application of the scheme by means of an enlarged volterra spectral problem and present an example of nonlinear discrete integrable hamiltonian couplings for the volterra lattice equations

pixel level singular point detection from multi scale gaussian filtered orientation field singular point as a global feature plays an important role in fingerprint recognition inconsistent detection of singular points apparently gives an affect to fingerprint alignment classification and verification accuracy this paper proposes a novel approach to pixel level singular point detection from the orientation field obtained by multi scale gaussian filters initially a robust pixel level orientation field is estimated by a multi scale averaging framework then candidate singular points in pixel level are extracted from the complex angular gradient plane derived directly from the pixel level orientation field the candidate singular points are finally validated via a cascade framework comprised of nested poincare indices and local feature based classification experimental results over the fvc 2000 db2 confirm that the proposed method achieves robust and accurate orientation field estimation and consistent pixel level singular point detection the experimental results exhibit a low computational cost with better performance thus the proposed method can be employed in real time fingerprint recognition

increasing the sample size when the unblinded interim result is promising increasing the sample size based on unblinded interim result may inflate the type i error rate and appropriate statistical adjustments may be needed to control the type i error rate at the nominal level we briefly review the existing approaches which allow early stopping due to futility or change the test statistic by using different weights or adjust the critical value for final test or enforce rules for sample size recalculation the implication of early stopping due to futility and a simple modification to the weighted z statistic approach are discussed in this paper we show that increasing the sample size when the unblinded interim result is promising will not inflate the type i error rate and therefore no statistical adjustment is necessary the unblinded interim result is considered promising if the conditional power is greater than 50 per cent or equivalently the sample size increment needed to achieve a desired power does not exceed an upper bound the actual sample size increment may be determined by important factors such as budget size of the eligible patient population and competition in the market the 50 per cent conditional power approach is extended to a group sequential trial with one interim analysis where a decision may be made at the interim analysis to stop the trial early due to a convincing treatment benefit or to increase the sample size if the interim result is not as good as expected the type i error rate will not be inflated if the sample size may be increased only when the conditional power is greater than 50 per cent if there are two or more interim analyses in a group sequential trial our simulation study shows that the type i error rate is also well controlled

adaptive and nonadaptive group sequential tests summary methods have been proposed for redesigning a clinical trial at an interim stage in order to increase power in order to preserve the type i error rate methods for unplanned design change have to be defined in terms of nonsufficient statistics and this calls into question their efficiency and the credibility of conclusions reached we evaluate schemes for adaptive redesign extending the theoretical arguments for use of sufficient statistics of tsiatis mehta 2003 and assessing the possible benefits of preplanned adaptive designs by numerical computation of optimal tests these optimal adaptive designs are concrete examples of optimal sequentially planned sequential tests proposed by schmitz 1993 we conclude that the flexibility of unplanned adaptive designs comes at a price and we recommend that the appropriate power for a study should be determined as thoroughly as possible at the outset then standard error spending tests possibly with unevenly spaced analyses provide efficient designs but it is still possible to fall back on flexible methods for redesign should study objective change unexpectedly once the trial is under way

systematic methods for the computation of the directional fields and singular points of fingerprints the first subject of the paper is the estimation of a high resolution directional field of fingerprints traditional methods are discussed and a method based on principal component analysis is proposed the method not only computes the direction in any pixel location but its coherence as well it is proven that this method provides exactly the same results as the averaged square gradient method that is known from literature undoubtedly the existence of a completely different equivalent solution increases the insight into the problem s nature the second subject of the paper is singular point detection a very efficient algorithm is proposed that extracts singular points from the high resolution directional field the algorithm is based on the poincare index and provides a consistent binary decision that is not based on postprocessing steps like applying a threshold on a continuous resemblance measure for singular points furthermore a method is presented to estimate the orientation of the extracted singular points the accuracy of the methods is illustrated by experiments on a live scanned fingerprint database

fingerprint classification based on extraction and analysis of singularities and pseudo ridges in this paper we introduce a new approach to fingerprint classification based on extraction and analysis of both singularities and traced pseudo ridges relating to singular points because of the image quality it is difficult to get the correct number and position of the singularities that are widely used in current structural classification methods with the help of pseudo ridge tracing and analysis of the traced curves our method does not rely on the extraction of the exact number and positions of the true singular point s thus improving the classification accuracy this method has been tested on the nist special fingerprint database 4 for the 4000 images in this database the classification accuracy reaches 92 7 for the 4 class problem

discrete sequential boundaries for clinical trials summary pocock 1977 o brien fleming 1979 and slud wei 1982 have proposed different methods to construct discrete sequential boundaries for clinical trials these methods require that the total number of decision times be specified in advance in the present paper we propose a more flexible way to construct discrete sequential boundaries the method is based on the choice of a function a t which characterizes the rate at which the error level ac is spent the boundary at a decision time is determined by a t and by past and current decision times but does not depend on the future decision times or the total number of decision times

adaptive group sequential designs for clinical trials combining the advantages of adaptive and of classical group sequential approaches a general method is presented integrating the concept of adaptive interim analyses into classical group sequential testing this allows the researcher to represent every group sequential plan as an adaptive trial design and to make design changes during the course of the trial after every interim analysis in the same way as with adaptive designs the concept of adaptive trial designing is thereby generalized to a large variety of possible sequential plans

evaluation of experiments with adaptive interim analyses summary a general method for statistical testing in experiments with an adaptive interim analysis is proposed the method is based on the observed error probabilities from the disjoint subsamples before and after the interim analysis formally an intersection of individual null hypotheses is tested by combining the twop values into a global test statistic stopping rules for fisher s product criterion in terms of critical limits for the p value in the first subsample are introduced including early stopping in the case of missing effects the control of qualitative treatment stage interactions is considered a generalization to three stages is outlined the loss of power when using the product criterion instead of the optimal classical test on the whole sample is calculated for the test of the mean of a normal distribution depending on increasing proportions of the first subsample in relation to the total sample size an upper bound on the loss of power due to early stopping is derived a general example is presented and rules for assessing the sample size in the second stage of the trial are given the problems of interpretation and precautions to be taken for applications are discussed finally the sources of bias for estimation in such designs are described

group sequential tests for delayed responses with discussion summary group sequential methods are used routinely to monitor clinical trials and to provide early stopping when there is evidence of a treatment effect a lack of an effect or concerns about patient safety in many studies the response of clinical interest is measured some time after the start of treatment and there are subjects at each interim analysis who have been treated but are yet to respond we formulate a new form of group sequential test which gives a proper treatment of these pipeline subjects these tests can be applied even when the continued accrual of data after the decision to stop the trial is unexpected we illustrate our methods through a series of examples we define error spending versions of these new designs which handle unpredictable group sizes and provide an information monitoring framework that can accommodate nuisance parameters such as an unknown response variance by studying optimal versions of our new designs we show how the benefits of lower expected sample size that are normally achieved by a group sequential test are reduced when there is a delay in response the loss of efficiency for larger delays can be ameliorated by incorporating data on a correlated short term end point fitting a joint model for the two end points but still making inferences on the original longer term end point we derive p values and confidence intervals on termination of our new tests

application of the kudryashov method for finding exact solutions of the high order nonlinear evolution equations abstract the application of the kudryashov method for finding exact solutions of the high order nonlinear evolution equations is considered some classes of solitary wave solutions for the families of nonlinear evolution equations of fifth sixth and seventh order are obtained the efficiency of the kudryashov method for finding exact solutions of the high order nonlinear evolution equations is demonstrated

issues in designing flexible trials we outline the general framework of adaptive combination tests and discuss their relationship to flexible group sequential designs an important field of applications is sample size reassessment we discuss reassessment rules based on conditional power arguments using either the observed or the prefixed effect size these rules tend to lead to large expected sample sizes for small actual effects however the application of a maximal bound for the second stage sample size leads to more favourable properties additionally we consider an optimized reassessment rule in terms of expected sample sizes since the adaptive design does not use the classical test statistics for some types of sample size reassessments the adaptive test may reject the null hypothesis while the classical one sample test does not we characterize sample size reassessment rules where such inconsistencies are avoided finally the extension of flexibility to the number of stages is explored in the first interim analysis a second interim analysis is only planned if the chance to achieve a decision there is high this leads to savings in the average number of interim analysis performed without paying a noticeable price in terms of expected sample size

modification of sample size in group sequential clinical trials in group sequential clinical trials sample size reestimation can be a complicated issue when it allows for change of sample size to be influenced by an observed sample path our simulation studies show that increasing sample size based on an interim estimate of the treatment difference can substantially inflate the probability of type i error in most practical situations a new group sequential test procedure is developed by modifying the weights used in the traditional repeated significance two sample mean test the new test has the type i error probability preserved at the target level and can provide a substantial gain in power with the increase of sample size generalization of the new procedure is discussed

1 soliton solution of the generalized zakharov equation in plasmas by he s variational principle this paper obtains the 1 soliton solution to zakharov equation with power law and dual power law nonlinearities the he s variational principle is used to carry out the integration of this equation

solitary wave solutions for nonlinear partial differential equations that contain monomials of odd and even grades with respect to participating derivatives the method of simplest equation is applied to nonlinear pdes the pdes contain monomials of odd and even order with respect to derivatives solitary wave solutions are studied numerous examples of the methodology are presented we apply the method of simplest equation for obtaining exact solitary traveling wave solutions of nonlinear partial differential equations that contain monomials of odd and even grade with respect to participating derivatives we consider first the general case of presence of monomials of the both odd and even grades and then turn to the two particular cases of nonlinear equations that contain only monomials of odd grade or only monomials of even grade the methodology is illustrated by numerous examples

combining weighted linear project analysis with orientation diffusion for fingerprint orientation field reconstruction this paper presents a novel algorithm for reconstructing the fingerprint orientation field fof the basic idea of the algorithm is to reconstruct the fof by combining weighted linear project analysis with orientation diffusion we first compute the weight values of point gradients according to the similarity of point orientations in the second procedure the qualities of blocks are assessed by the coherence of point orientations and then the block orientation with high quality are estimated by the weighted linear projection analysis based on the vector set of point gradients the fingerprint blocks that will be reconstructed is selected by the priority of them in the third procedure in the end the fof is reconstructed by orientation diffusion based on the reconstruction priorities of blocks to validate the performance the proposed method has been applied to fingerprint enhancement fingerprint singularity detection fingerprint minutiae extraction and fingerprint matching using the fvc2000 and fvc2004 databases the experiments show that the proposed method is more accurate and more reliable and it is more robust against noise

semiparametric efficiency and its implication on the design and analysis of group sequential studies abstract authors have shown that the time sequential joint distributions of many statistics used to analyze data arising from group sequential time to event and longitudinal studies are multivariate normal with an independent increments covariance structure in theorem 1 of this article we demonstrate that this limiting distribution arises naturally when one uses an efficient test statistic to test a single parameter in a semiparametric or parametric model because we are able to think of many of the statistics in the literature in this fashion the limiting distribution under investigation is just a special case of theorem 1 using this general structure we then develop an information based design and monitoring procedure that can be applied to any type of model for any type of group sequential study provided that there is a unique parameter of interest that can be efficiently tested

adaptive sample size modification in clinical trials start small then ask for more we consider sample size re estimation in a clinical trial in particular when there is a significant delay before the measurement of patient response mehta and pocock have proposed methods in which sample size is increased when interim results fall in a promising zone where it is deemed worthwhile to increase conditional power by adding more subjects our analysis reveals potential pitfalls in applying this approach mehta and pocock use results of chen demets and lan to identify when increasing sample size but applying a conventional level significance test at the end of the trial does not inflate the type i error rate we have found the greatest gains in power per additional observation are liable to lie outside the region defined by this method mehta and pocock increase sample size to achieve a particular conditional power calculated under the current estimate of treatment effect this leads to high increases in sample size for a small range of interim outcomes whereas we have found it more efficient to make moderate increases in sample size over a wider range of cases if the aforementioned pitfalls are avoided we believe the broad framework proposed by mehta and pocock is valuable for clinical trial design working in this framework we propose sample size rules that apply explicitly the principle of adding observations when they are most beneficial the resulting trial designs are closely related to efficient group sequential tests for a delayed response proposed by hampson and jennison copyright 2015 john wiley sons ltd

exact confidence intervals following a group sequential trial a comparison of methods summary with interest in designing group sequential clinical trials increasing methodology for analysing the data arising in such trials is needed we discuss several approaches to constructing confidence intervals for the parameter of interest in a group sequential trial after the trial has ended we compare these met1fods to one already in the literature and point out interesting differences

repeated confidence intervals for the median survival time summary we describe methods for the construction of a confidence interval for median survival time based on right censored data these methods are extended to the construction of repeated confidence intervals for the median based on accumulating data here the overall probability that all intervals contain the true median is guaranteed at a fixed level the use of repeated confidence intervals for median survival time in post marketing surveillance is discussed a confidence interval for median survival time provides a useful summary of the survival experience of a group of patients if confidence intervals are calculated repeatedly as data accumulates the probability that at least one interval fails to contain the median may be much higher than the error rate for a single interval and if these confidence intervals are used in a decision making process the probability of an incorrect decision increases accordingly jennison turnbull 1984 have proposed methods for calculating repeated confidence intervals appropriate to such situations similar ideas have also been discussed by lai 1984 in 2 we propose a new form of single sample nonparametric confidence interval this interval has asymptotically correct coverage probability and monte carlo simulations suggest it is superior to its competitors for small sample sizes repeated confidence intervals for the median are presented in 3 and their stnall sample size performance is assessed by monte carlo simulation an example of their use is given in 4 all the methods considered can easily be modified to give confidence intervals for other quantiles or for the survival probability at a fixed time

fingerprint reference point detection for image retrieval based on symmetry and variation reference point plays an important role in fingerprint identification systems the reference point is widely used for the fingerprint retrieval in large scale databases this paper proposes a novel algorithm for detecting a convex core point as a unique reference point consistently and accurately for all types of fingerprints in order to detect robust core point candidates a modified complex filter called semi radial symmetry filter is proposed to detect correctly rotational symmetries of core points moreover a vertical orientation variation feature called voriv feature is proposed to remove spurious core points and concave core points therefore the proposed technique computes the variation and symmetry combined energy vscome then the reference point is located by searching the global vscome maximum the experimental results on the public database fvc2004 db1 set a show that the proposed technique exhibits a very high robustness and gets the best performance in comparing with other approaches in literature

an improved method for deriving optimal one sided group sequential tests summary we derive one sided group sequential tests for normal responses which minimize expected sample size minimization is at a single value of the normal mean or integrated with respect to a normal density the methods employed are much faster and also numerically more stable than those of jennison 1987 they provide solutions for cases with as many as 200 groups and for small numbers of groups facilitate optimization over the choice of group sizes we present a new method for constructing near optimal tests when group sizes are unpredictable based on interpolating the error spending function of an optimal test with a large number of groups

fingerprint indexing based on minutiae pairs and convex core point an efficient fingerprint indexing which uses ellipse properties is proposed a new fingerprint indexing is proposed using minutiae pairs and convex core point our fingerprint representation is very robust to distortions and noise the proposed fingerprint features are invariant to rotation and translation fingerprint identification is an important issue for identifying fingerprints and plays a key role in the fingerprint recognition systems however performing a fingerprint identification over a large database can be an inefficient task due to the lack of scalability and high computing times of fingerprint matching algorithms fingerprint indexing is a key strategy in automatic fingerprint identification systems afiss which allows us to reduce the number of candidates the search space and the occurrences of false acceptance in large databases in this paper an efficient indexing algorithm is proposed using minutiae pairs and convex core point which employs k means clustering and candidate list reduction criteria to improve the identification performance our proposal can effectively reduce the search space and number of candidates for fingerprint matching and thus achieves higher efficiency and significantly improves the system retrieval performance experimental results over some of the fingerprint verification competition fvc and the national institute of standards and technology nist databases prove the superiority of the proposed approach against some of the well known indexing algorithms

combining singular points and orientation image information for fingerprint classification fingerprint classification is crucial to reduce the processing time in a large scale database two popular features used are the singularities and orientation information and they are complementary therefore an algorithm based on the interactive validation of singular points and the constrained nonlinear orientation model is proposed the final features used for classification comprises the coefficients of the orientation model and the singularity information this resulted in very compact feature vector which is used as input to an svm classifier to perform the classification the experiments conducted on the nist database 4 show the effectiveness of the proposed method in producing good classification result

efficient group sequential tests with unpredictable group sizes summary we derive group sequential tests to minimize expected sample size a parametric family of group sequential tests is proposed containing tests which are nearly optimal in terms of minimizing expected sample size amongst all group sequential tests these parametric tests can be implemented when group sizes are unequal and unpredictable they are shown to achieve error rates close to their nominal level in a wide range of situations and to be efficient when compared with other tests based on the same group sizes and achieving the same error rates we consider group sequential procedures for choosing between two hypotheses concerning the mean of a normal distribution with known variance the group sequential approach pocock 1977 offers a practicable alternative to fully sequential tests which require accumulating data to be examined as each new observation is recorded it is also desirable to ensure the maximum sample size needed in a long term experiment is not much greater than that of the corresponding fixed sample size test and we shall take the specification of the maximum allowable sample size and the number of groups of observations as our starting point in deriving sequential procedures in 2 we formulate the testing problem and discuss its relevance to clinical trials in 3 we describe the derivation of boundaries which are optimal in the sense of minimizing various expected sample sizes subject to a fixed number of equally sized groups and a fixed maximum sample size in 4 we introduce a parametric family of group sequential tests containing tests which are nearly optimal by the criteria of 3 these tests are easily adapted to allow unequal and unpredictable group sizes we show in 5 that they remain efficient when actual group sizes are quite different from those anticipated programs used for the calculations are available from the author

modified method of simplest equation for obtaining exact analytical solutions of nonlinear partial differential equations we discuss the application of a variant of the method of simplest equation for obtaining exact traveling wave solutions of a class of nonlinear partial differential equations containing polynomial nonlinearities as simplest equation we use differential equation for a special function that contains as particular cases trigonometric and hyperbolic functions as well as the elliptic function of weierstrass and jacobi we show that for this case the studied class of nonlinear partial differential equations can be reduced to a system of two equations containing polynomials of the unknown functions this system may be further reduced to a system of nonlinear algebraic equations for the parameters of the solved equation and parameters of the solution any nontrivial solution of the last system leads to a traveling wave solution of the solved nonlinear partial differential equation the methodology is illustrated by obtaining solitary wave solutions for the generalized korteweg devries equation and by obtaining solutions of the higher order korteweg devries equation

exp function method for riccati equation and new exact solutions with two arbitrary functions of 2 1 dimensional konopelchenko dubrovsky equations in this paper new exact solutions with two arbitrary functions of the 2 1 dimensional konopelchenko dubrovsky equations are obtained by means of the riccati equation and its generalized solitary wave solutions constructed by the exp function method it is shown that the exp function method provides us with a straightforward and important mathematical tool for solving nonlinear evolution equations in mathematical physics

a comparison of adaptive allocation rules for group sequential binary response clinical trials in clinical trials to compare two or more treatments with dichotomous responses group sequential designs may reduce the total number of patients involved in the trial and response adaptive designs may result in fewer patients being assigned to the inferior treatments in this paper we combine group sequential and response adaptive designs extending recent work on sample size re estimation in trials to compare two treatments with normally distributed responses to analogous binary response trials we consider the use of two parameters of interest in the group sequential design the log odds ratio and the simple difference between the probabilities of success in terms of the adaptive sampling rules we study two urn models the drop the loser rule and the randomized polya urn rule and compare their properties with those of two sequential maximum likelihood estimation rules which minimize the expected number of treatment failures we investigate two ways in which adaptive urn designs can be used in conjunction with group sequential designs the first method updates the urn at each interim analysis and the second method continually updates the urn after each patient response assuming immediate patient responses our simulation results show that the group sequential design which uses the drop the loser rule applied fully sequentially is the most effective method for reducing the expected number of treatment failures and the average sample number whilst still maintaining the nominal error rates over a range of success probabilities

exact confidence intervals following a group sequential test a numerical method is used to compute confidence intervals which have exact coverage probabilities for the mean of a normal distribution following a group sequential test this method which uses an ordering of the sample space similar to that employed by siegmund 1978 biometrika 65 341 349 is contrasted with the usual confidence interval for the mean

p values for tests using a repeated significance test design summary repeated significance testing can be used as a multistage testing procedure which has advantages over single sample tests and purely sequential tests repeated significance tests having a constant nominal level of significance have designs which are more easily understood by researchers and still have good power relative to designs using varying nominal levels of significance in this paper we present a method for defining an overall p value for repeated significance tests with constant significance levels which can aid researchers in interpreting the observed results of such tests a table of p values for various designs is given

a combination model for orientation field of fingerprints orientation field is a global feature of fingerprints that is very important in automatic fingerprint identification systems afis establishing an accurate and concise model for orientation fields will not only improve the performance of orientation estimation but also make it feasible to apply orientation information in the matching process in this paper a novel model for the orientation field of fingerprints is proposed we use a polynomial model to approximate the orientation field globally and a point charge model at each singular point to improve the approximation locally these two models are combined together by a weight function experimental results are provided to illustrate the fact that this combination model is more accurate and robust with respect to noise compared with the previous works the application of the model is discussed at the end

a jacobi gauss lobatto collocation method for solving generalized fitzhugh nagumo equation with time dependent coefficients in this paper we propose a new jacobi gauss lobatto collocation method for solving the generalized fitzhugh nagumo equation the jacobi gauss lobatto points are used as collocation nodes for spatial derivatives the proposed method has the advantage of obtaining the solution in terms of the jacobi parameters a and b in addition the problem is reduced to a system of ordinary differential equations in time this system can be solved by any standard numerical techniques numerical solutions obtained by this method when compared with the exact solution reveal that the obtained solution produces high accurate results numerical results show that the proposed method is of high accuracy and is efficient for solving the generalized fitzhugh nagumo equation also the results demonstrate that the proposed method is powerful algorithm for solving the nonlinear partial differential equations

efficient group sequential designs when there are several effect sizes under consideration we consider the construction of efficient group sequential designs where the goal is a low expected sample size not only at the null hypothesis and the alternative taken to be the minimal clinically meaningful effect size but also at more optimistic anticipated effect sizes pre specified type i error rate and power requirements can be achieved both by standard group sequential tests and by more recently proposed adaptive procedures we investigate four nested classes of designs a group sequential tests with equal group sizes and stopping boundaries determined by a monomial error spending function the rho family b as a but the initial group size is allowed to be different from the others c group sequential tests with arbitrary group sizes and arbitrary boundaries fixed in advance d adaptive tests as c but at each analysis future group sizes and critical values are updated depending on the current value of the test statistic by examining the performance of optimal procedures within each class we conclude that class b provides simple and efficient designs with efficiency close to that of the more complex designs of classes c and d we provide tables and figures illustrating the performances of optimal designs within each class and defining the optimal procedures of classes a and b

are flexible designs sound flexible designs allow large modifications of a design during an experiment in particular the sample size can be modified in response to interim data or external information a standard flexible methodology combines such design modifications with a weighted test which guarantees the type i error level however this inference violates basic inference principles in an example with independent n mu 1 observations the test rejects the null hypothesis of mu or 0 while the average of the observations is negative we conclude that flexible design in its most general form with the corresponding weighted test is not valid several possible modifications of the flexible design methodology are discussed with a focus on alternative hypothesis tests

application of the method of simplest equation for obtaining exact traveling wave solutions for the extended korteweg de vries equation and generalized camassa holm equation a version of the method of the simplest equation called modified method of simplest equation is applied to the extended korteweg de vries equation and to generalized camassa holm equation exact traveling wave solutions of these two nonlinear partial differential equations are obtained the equations of bernoulli riccati and the extended tanh equation are used as simplest equations some of the obtained solutions correspond to surface water waves

group sequential analysis incorporating covariate information abstract in this article we survey existing results concerning the joint distribution of the sequence of estimates of the parameter vector when a model is fitted to accumulating data and provide a unified theory that explains the independent increments structure commonly seen in group sequential test statistics our theory covers normal linear models including the case of correlated observations and asymptotic results extend to generalized linear models and the proportional hazards regression model for survival data the asymptotic results are derived using standard methods for the nonsequential case and they hold as long as these nonsequential techniques are applicable at each individual analysis in all cases the joint distribution of the sequence of parameter estimates has the same form exactly or asymptotically as that of the sequence of means of an increasing number of independent identically distributed normal variables thus our results provide the formal basis for extending the scope of s

explicit exact solutions of some nonlinear evolution equations with their geometric interpretations in this paper the simplest equation method is applied to obtain multiple explicit exact solutions of the combined dispersion equation the hirota satsuma korteweg de vries system and the generalized burgers huxley equation these solutions are constructed on the basis of solutions of bernoulli equation which is used as simplest equation it is shown that this method is very powerful tool for obtaining exact solutions of a large class of nonlinear partial differential equations the geometric interpretation for some of these solutions are introduced

modified method of simplest equation and its application to nonlinear pdes abstract we search for traveling wave solutions of the class of pdes p 1 n 1 a p q p q t p r 2 n 2 b r q q t r s 1 n 3 c s q s q x s u 2 n 4 d u q q x u f q 0 where a p q b r q c s q d u q and f q are polynomials of q the basis of the investigation is a modification of the method of simplest equation the equations of bernoulli riccati and the extended tanh function equation are used as simplest equations the obtained general results are illustrated by obtaining exact solutions of versions of the generalized kuramoto sivashinsky equation reaction diffusion equation with density dependent diffusion and the reaction telegraph equation

sequential tests and estimators after overrunning based on maximum likelihood ordering summary often in sequential trials some additional data become available after a stopping boundary has been reached a method for incorporating such information from overrunning is developed based on a maximum likelihood ordering of the sample space after overrunning this yields a p value for the primary test and a median unbiased estimator and confidence intervals for the parameter under test the context is that of observing a brownian motion with drift with either linear stopping boundaries in continuous time or discrete time group sequential boundaries the methods apply to many clinical trials and are exemplified with data from a survival analysis based sequential clinical trial

linear superposition principle of hyperbolic and trigonometric function solutions to generalized bilinear equations linear subspaces of hyperbolic and trigonometric function solutions to generalized bilinear equations are analyzed necessary and sufficient conditions are presented to apply the linear superposition principles applications of an algorithm using weights are made together with a few concrete examples

an efficient jacobi pseudospectral approximation for nonlinear complex generalized zakharov system in this paper we derive an efficient spectral collocation algorithm to solve numerically the nonlinear complex generalized zakharov system gzs subject to initial boundary conditions the jacobi pseudospectral approximation is investigated for spatial approximation of the gzs it possesses the spectral accuracy in space the jacobi gauss lobatto quadrature rule is established to treat the boundary conditions and then the problem with its boundary conditions is reduced to a system of ordinary differential equations in time variable this scheme has the advantage of allowing us to obtain the spectral solution in terms of the jacobi parameters and which therefore means that the algorithm holds a number of collocation methods as special cases finally two illustrative examples are implemented to assess the efficiency and high accuracy of the jacobi pseudo spectral scheme

a novel algorithm for detecting singular points from fingerprint images fingerprint analysis is typically based on the location and pattern of detected singular points in the images these singular points cores and deltas not only represent the characteristics of local ridge patterns but also determine the topological structure i e fingerprint type and largely influence the orientation field in this paper we propose a novel algorithm for singular points detection after an initial detection using the conventional poincare index method a so called doric feature is used to remove spurious singular points then the optimal combination of singular points is selected to minimize the difference between the original orientation field and the model based orientation field reconstructed using the singular points a core delta relation is used as a global constraint for the final selection of singular points experimental results show that our algorithm is accurate and robust giving better results than competing approaches the proposed detection algorithm can also be used for more general 2d oriented patterns such as fluid flow motion and so forth

internal pilot studies i type i error rate of the naive t test when sample size is recalculated using unblinded interim data use of the usual t test at the end of a study may lead to an elevated type i error rate this paper describes a numerical quadrature investigation to calculate the true probability of rejection as a function of the time of the recalculation the magnitude of the detectable treatment effect and the ratio of the guessed to the true variance we consider both restricted designs those that require final sample size at least as large as the originally calculated size and unrestricted designs those that permit smaller final sample sizes than originally calculated our results indicate that the bias in the type i error rate is often negligible especially in restricted designs some sets of parameters however induce non trivial bias in the unrestricted design