representations of the quantum group suq 2 and the little q jacobi polynomials abstract in this paper we study the finite dimensional unitary representations of the quantum group suq 2 then we obtain the peter weyl theorem for suq 2 and the matrix elements of these unitary representations are explicitly expressed in terms of the little q jacobi polynomials which are known as q analogues of orthogonal polynomials using these expressions the orthogonality relations of these polynomials are obtained in terms of the haar measure on the quantum group suq 2

strong connections and chern connes pairing in the hopf galois theory we reformulate the concept of connection on a hopf galois extension b p in order to apply it in computing the chern connes pairing between the cyclic cohomology hc 2 n b and k 0 b this reformulation allows us to show that a hopf galois extension admitting a strong connection is projective and left faithfully flat it also enables us to conclude that a strong connection is a cuntz quillen type bimodule connection to exemplify the theory we construct a strong connection super dirac monopole to find out the chern connes pairing for the super line bundles associated to a super hopf fibration

on maximally selected chi square statistics two samples can be compared by selecting a cutpoint and then forming a 2 x 2 table of the numbers of observations above and below the cutpoint in each sample miller and siegmund 1982 biometrics 38 1011 1016 investigated asymptotic theory relating to the distribution of the standard chisquare statistic when the cutpoint is selected to maximize its value in a companion article halpern 1982 biometrics 38 1017 1023 studied the finite sample distribution of this maximally selected chi square statistic via simulation exact finite sample distribution theory derived from durbin s 1971 journal of applied probability 8 431 453 1973 distribution theory for tests based on the sample distribution function philadelphia siam combinatorial approach is presented here

assessment of diagnostic markers by goodness of fit tests receiver operating characteristic roc curves are useful statistical tools used to assess the precision of diagnostic markers or to compare new diagnostic markers with old ones the most common index employed for these purposes is the area under the roc curve theta and several statistical tests exist that test the null hypotheses h 0 theta 0 5 or h 0 theta1 theta2 in the case of two marker comparisons against alternatives of interest in this paper we show that goodness of fit of uniformity of the distribution of the false positive true positive rates can be used instead of tests based on the area index a semi parametric approach is based on a completely specified distribution of marker measurements for either the healthy f or diseased g subjects and this is extended to the two marker case we then extend to the one and two marker case when neither distribution is specified the non parametric case in general roc based tests are more powerful than goodness of fit tests for location differences between the distributions of healthy and diseased subjects however roc based tests are less powerful when location scale differences exist producing roc curves that cross the diagonal and are incapable of discriminating between healthy and diseased samples when theta 0 5 but f not equal g in these cases goodness of fit tests have a distinct advantage over roc based tests in conclusion roc methodology should be used with recognition of its potential limitations and should be replaced by goodness of fit tests when appropriate the latter are a viable alternative and can be used as a black box or as an exploratory first step in the evaluation of novel diagnostic markers

asymptotic distributions of maximum likelihood tests for change in the mean summary for the maximum likelihood tests for a change in the mean of independent random variables it is proved that the limit distribution is a double exponential i e gumbel distribution our results also explain why the maximum likelihood methods are very powerful on the tails the time intervals between explosions in british coal mines between 1851 and 1950 in which more than ten people were killed were analysed by maguire pearson wynn 1952 who concluded that the data had an exponential distribution with constant mean over time cox lewis 1966 ch 3 jarrett 1979 and worsley 1986 have reanalysed the data and found strong evidence that the mean did not remain constant hsu 1979 found a significant change in stock market returns by analysing the weekly closing values of the dow jones industrial average from july 1 1971 to august 2 1974 cobb 1978 examined measurements of the annual volume of discharge from the nile river at aswan for the years 1871 to 1970 and found a decrease in annual volume after 1898

minimally selected p and other tests for a single abrupt changepoint in a binary sequence summary a novel changepoint statistic based on the minimum value over possible changepoint locations of fisher s exact test is introduced specific points in the exact distribution of the minimally selected fisher s value may be rapidly calculated as a lattice path counting problem via known recurrence methods the test is compared to the kolmogorov smirnov two sample test the maximally selected chi square and a likelihood ratio test the tests are applied to assessing recombination in genetic sequences of hiv

discrete aggregation operators with annihilator abstract mas et al have investigated a special kind of commutative and associative aggregation operators with annihilator on the unit interval 0 1 which includes s uninorms s nullnorms t uninorms t nullnorms bi uninorms and bi nullnorms this paper is devoted to extending this kind of operators from the unit interval 0 1 to a finite chain a characterization of this kind of operators on a finite chain is given including some examples this class of operators can be viewed as a generalization of both uninorms and nullnorms on a finite chain

convex combinations in terms of triangular norms a characterization of idempotent bisymmetrical and self dual compensatory operators it is observed that most of the well known compensatory operators are defined in terms of convex transformations of the values of triangular norms and conorms or other operators in this paper the characterization and the applicability of parametrized operators constructed again in terms of triangular norms and conorms but as transformations of their arguments are studied it turns out that these operators are closely related to the ordinary convex combination moreover when idempotency is required these operators can be characterized algebraically as bisymmetrical and self dual operators that satisfy the cancellation law

accuracy and cut off point selection in three class classification problems using a generalization of the youden index we study properties of the index j 3 defined as the accuracy or the maximum correct classification for a given three class classification problem specifically using j 3 one can assess the discrimination between the three distributions and obtain an optimal pair of cut off points c 1 c 2 in the sense that the sum of the correct classification proportions will be maximized it also serves as the generalization of the youden index in three class problems parametric and non parametric approaches for estimation and testing are considered and methods are applied to data from an mrs study on human immunodeficiency virus hiv patients

a nonparametric likelihood test for detecting discordance between two measurements with application to censored viral load determinations patient management frequently involves quantitative evaluation of a patient s attributes for example in hiv studies a high viral load can be a trigger to initiate or modify an antiretroviral therapy at times a new method of evaluation may substitute for an established one provided that the new method does not result in different clinical decisions compared with the old method traditional measures of agreement between the two methods are inadequate for deciding if a new method can replace the old especially when the data are censored by a detection limit estimates of agreement can be biased unless the distribution for the censored data is correctly specified this is usually not feasible in practice we propose a nonparametric likelihood test that seamlessly handles censored data we further show that the proposed test is a generalization of the test on nominal measurement concordance to continuous measurement an exact permutation procedure is proposed for implementing the test our application is an hiv study to determine whether one method of processing plasma samples can safely substitute for the other the plasma samples are used to determine viral load and a large portion of data are left censored due to a lower detection limit

noncommutative circle bundles and new dirac operators we study spectral triples over noncommutative principal u 1 bundles basing on the classical situation and the abstract algebraic approach we propose an operatorial definition for a connection and compatibility between the connection and the dirac operator on the total space and on the base space of the bundle we analyze in details the example of the noncommutative three torus viewed as a u 1 bundle over the noncommutative two torus and find all connections compatible with an admissible dirac operator conversely we find a family of new dirac operators on the noncommutative tori which arise from the base space dirac operator and a suitable connection

noncommutative instantons on the 4 sphere from quantum groups we describe an approach to the noncommutative instantons on the 4 sphere based on quantum group theory we quantize the hopf bundle 7 4 making use of the concept of quantum coisotropic subgroups the analysis of the semiclassical poisson lie structure of u 4 shows that the diagonal su 2 must be conjugated to be properly quantized the quantum coisotropic subgroup we obtain is the standard su q 2 it determines a new deformation of the 4 sphere 4 q as the algebra of coinvariants in q 7 we show that the quantum vector bundle associated to the fundamental corepresentation of su q 2 is finitely generated and projective and we compute the explicit projector we give the unitary representations of 4 q we define two 0 summable fredholm modules and we compute the chern connes pairing between the projector and their characters it comes out that even the zero class in cyclic homology is non trivial

multiple changepoint testing for an alternating segments model of a binary sequence summary a binary sequence may give the appearance of being composed of alternating segments with relatively high and relatively low probability of success determining whether such an alternating pattern is significant is a multiple changepoint problem where the number of segments and their success probabilities are unknown with the added constraint of segment alternation a dynamic programming method for determining the optimal segmentation into a given number of segments is provided given this a variation on the simulation method of venter and steel 1996 computational statistics and data analysis22 481 504 may be employed t o test the null hypothesis of a homogeneous sequence as well as to estimate the number and location of changepoints a sample application the assessment of the possibility of genetic recombination in hiv sequences is presented

inflation of the type i error rate when a continuous confounding variable is categorized in logistic regression analyses this paper demonstrates an inflation of the type i error rate that occurs when testing the statistical significance of a continuous risk factor after adjusting for a correlated continuous confounding variable that has been divided into a categorical variable we used monte carlo simulation methods to assess the inflation of the type i error rate when testing the statistical significance of a risk factor after adjusting for a continuous confounding variable that has been divided into categories we found that the inflation of the type i error rate increases with increasing sample size as the correlation between the risk factor and the confounding variable increases and with a decrease in the number of categories into which the confounder is divided even when the confounder is divided in a five level categorical variable the inflation of the type i error rate remained high when both the sample size and the correlation between the risk factor and the confounder were high

likelihood ratio tests for a changepoint with survival data summary we consider the likelihood ratio test for a changepoint or lag of the effect of some covariates e g treatment in regression modelling of survival data subject to right censoring asymptotic distributions under null hypotheses are derived numerical examples are used to illustrate the implementation of the procedure finally we apply the theory to data from a large randomised cancer prevention trial

discrete supergroups and super riemann surfaces the properties of discrete supergroups that represent the homotopy groups of super riemann surfaces are emphasized after the study of the superforms invariant with respect to these supergroups the set of superconformal differentials are defined and an example is given of those by defining poincare s super theta functions some remarks on a possible definition of the jacobi variety of a super riemann surface are given

survival trees by goodness of split abstract a tree based method for censored survival data is developed based on maximizing the difference in survival between groups of patients represented by nodes in a binary tree the method includes a pruning algorithm with optimal properties analogous to the classification and regression tree cart pruning algorithm uniform convergence of the estimates of the conditional cumulative hazard and survival functions is discussed and an example is given to show the utility of the algorithm for developing prognostic classifications for patients

the power of likelihood ratio and cumulative sum tests for a change in a binomial probability summary a simple iterative procedure is found for the exact null and alternative distributions of likelihood ratio cumulative sum and related statistics for testing for a change in probability of a sequence of independent binomial random variables it is concluded that the likelihood ratio test is slightly less powerful than the cumulative sum test near the middle of the sequence but that the likelihood ratio test is much more powerful near the ends an example from epidemiology is used to illustrate the results under certain conditions the cumulative sum test is identical to a two sample kolmogorov smirnov test and so the iterative procedure can be used to find the null distribution of kolmogorov smirnov and related statistics

likelihood ratio tests for a change in the multivariate normal mean abstract a sequence of independent multivariate normal vectors with equal but possibly unknown variance matrices are hypothesized to have equal mean vectors and we wish to test that the mean vectors have changed after an unknown point in the sequence the likelihood ratio test is based on the maximum hotelling t 2 for the sequences before and after the change point the main result is a conservative approximation for its null distribution based on an improved bonferroni inequality if the change is judged significant then further changes are estimated by splitting the two subsequences formed by the first change point the methods can also be used to test for a change in row probabilities of a contingency table allowing for extramultinomial variation the results are used to find changes in a set of geological data previously analyzed by chernoff 1973 by the faces method and to find changes in the frequencies of pronouns in the plays of shakespeare

approximating the distribution of maximally selected mcnemar s statistics summary it is common in epidemiologic analyses to summarize continuous outcomes as falling above or below a threshold with paired data and with a threshold chosen without reference to the outcomes mcnemar s test of marginal homogeneity may be applied to the resulting dichotomous pairs when testing for equality of the marginal distributions of the underlying continuous outcomes if the threshold is chosen to maximize the test statistic however referring the resulting test statistic to the nominal x2 distribution is incorrect instead the p value must be adjusted for the multiple comparisons here the distribution of a maximally selected mcnemar s statistic is derived and it is shown that an approximation due to durbin 1985 journal of applied probability22 99 122 may be used to estimate approximate p values the methodology is illustrated by an application to measurements of insulin like growth factor i igf i in matched prostate cancer cases and controls from the physicians health study the results of simulation experiments that assess the accuracy of the approximation in moderate sample sizes are reported

maximally selected chi square statistics two samples can be compared by selecting a cut point and then forming a 2 x 2 table of the numbers of observations above and below the cut point in each sample when the cut point is selected so as to maximize the standard chi square statistic the chi square percentile points are inappropriate actual significance levels are computed for large samples and correct percentile poillts are tabulated

braided affine geometry and q analogs of wave operators the main goal of this review is to compare different approaches to constructing the geometry associated with a hecke type braiding in particular with that related to the quantum group uq sl n we place emphasis on the affine braided geometry related to the so called reflection equation algebra rea all objects of such a type of geometry are defined in the spirit of affine algebraic geometry via polynomial relations on generators we begin by comparing the poisson counterparts of quantum varieties and describe different approaches to their quantization also we exhibit two approaches to introducing q analogs of vector bundles and defining the chern connes index for them on quantum spheres in accordance with the serre swan approach the q vector bundles are treated as finitely generated projective modules over the corresponding quantum algebras besides we describe the basic properties of the rea used in this construction and compare different ways of defining q analogs of partial derivatives and differentials on the rea and algebras close to them in particular we present a way of introducing a q differential calculus via koszul type complexes the elements of the q calculus are applied to defining q analogs of some relativistic wave operators

maximally selected chi square statistics for small samples two samples can be compared by selecting a cut point and forming a 2 x 2 table of the numbers of observations above and below the cut point in each sample different cut points correspond to the maximum chi square statistic the maximum squared log odds ratio and the generalized kolmogorov smirnov statistic we simulated the small sample null distribution of these statistics the distributions of the maximally selected chi square statistic and the squared log odds ratio statistic are compared to each other and to the large sample results of miller and siegmund 1982 biometrics 38 1011 1016 the distributions of and agreement among the three cut points are also considered

chern simons forms on principal superfiber bundles a graded weil homomorphism is defined for principal superfiber bundles and the related transgression or chern simons forms are introduced as an example of the application of these concepts a superextension of the dirac monopole is discussed

quantum group gauge theory on quantum spaces we construct quantum group valued canonical connections on quantum homogeneous spaces including aq deformed dirac monopole on the quantum sphere of podles with quantum differential structure coming from the 3d calculus of woronowicz onsu q 2 the construction is presented within the setting of a general theory of quantum principal bundles with quantum group hopf algebra fibre associated quantum vector bundles and connection one forms both the base space spacetime and the total space are non commutative algebras quantum spaces

on modules associated to coalgebra galois extensions abstract for a given entwining structure a c involving an algebraa a coalgebrac and an entwining map c a a c a categorymca of right a c modules is defined and its structure analysed in particular the notion of a measuring of a c to a c is introduced and certain functors betweenmca andmca induced by such a measuring are defined it is shown that these functors are inverse equivalences iff they are exact or one of them faithfully exact and the measuring satisfies a certain galois type condition next left moduleseand right modules associated to ac galois extensionaofbare defined these can be thought of as objects dual to fibre bundles with coalgebracin the place of a structure group and a fibrev cross sections of such associated modules are defined as module mapse bor b it is shown that they can be identified with suitably equivariant maps from the fibre toa also it is shown that ac galois extension is cleft if and only ifa b cas leftb modules and rightc comodules the relationship between the moduleseand is studied in the case whenvis finite dimensional and in the case when the canonical entwining map is bijective

deformation quantization of surjective submersions and principal fibre bundles in this paper we establish a notion of deformation quantization of a surjective submersion which is specialized further to the case of a principal fibre bundle the functions on the total space are deformed into a right module for the star product algebra of the functions on the base manifold in case of a principal fibre bundle we require in addition invariance under the principal action we prove existence and uniqueness of such deformations the commutant within all differential operators on the total space is computed and gives a deformation of the algebra of vertical differential operators applications to noncommutative gauge field theories and phase space reduction of star products are discussed

topologically nontrivial field configurations in noncommutative geometry in the framework of noncommutative geometry we describe spinor fields with nonvanishing winding number on a truncated fuzzy sphere the corresponding field theory actions conserve all basic symmetries of the standard commutative version space isometries and global chiral symmetry but due to the noncommutativity of the space the fields are regularized and they contain only a finite number of modes

strong connections on quantum principal bundles a gauge invariant notion of a strong connection is presented and characterized it is then used to justify the way in which a global curvature form is defined strong connections are interpreted as those that are induced from the base space of a quantum bundle examples of both strong and non strong connections are provided in particular such connections are constructed on a quantum deformation of the two sphere fibrations2 rp2 a certain class of stronguq 2 connections on a trivial quantum principal bundle is shown to be equivalent to the class of connections on a free module that are compatible with theq dependent hermitian metric a particular form of the yang mills action on a trivialuq 2 bundle is investigated it is proved to coincide with the yang mills action constructed by a connes and m rieffel furthermore it is shown that the moduli space of critical points of this action functional is independent ofq

a characterization of discrete uninorms having smooth underlying operators in this paper discrete uninorms u such that their underlying t norm t and t conorm s are smooth are characterized the different cases combining when t is the minimum or the ukasiewicz t norm and s is the maximum or the ukasiewicz t conorm are given separately and the number of discrete uninorms with these underlying operators is given the same is done for the general case when t and or s are smooth but ordinal sums

visual characterization of associative quasitrivial nondecreasing operations on finite chains abstract in this paper we provide visual characterization of associative quasitrivial nondecreasing operations on finite chains we also provide a characterization of bisymmetric quasitrivial nondecreasing binary operations on finite chains finally we estimate the number of operations belonging to the previous classes

on some classes of discrete additive generators this work is developed in the field of the additive generation of discrete aggregation operators specifically this article deals with the study and applicability of disjunctions that are additively generated by concave convex and symmetric generators

goodness of fit tests in models for life history data based on cumulative hazard rates to check the validity of an assumed parametric model for survival data one may compare t the nonparametric nelson aalen plot of the cumulative hazard rate with a t the estimated parametric cumulative hazard rate being for example the maximum likelihood estimator convergence in distribution of n t a t and more general processes is studied employing the general framework of counting processes which allows for quite general models for life history data and for quite general censoring schemes the results are applied to the construction of 2 type statistics for goodness of fit cramer von mises and kolmogorov smirnov type tests are presented in the case where the unknown parameter is one dimensional

a maximally selected test of symmetry about zero the problem of testing symmetry about zero has a long and rich history in the statistical literature we introduce a new test that sequentially discards observations whose absolute value is below increasing thresholds defined by the data mcnemar s statistic is obtained at each threshold and the largest is used as the test statistic we obtain the exact distribution of this maximally selected mcnemar and provide tables of critical values and a program for computing p values power is compared with the t test the wilcoxon signed rank test and the sign test the new test mm is slightly less powerful than the t test and wilcoxon signed rank test for symmetric normal distributions with nonzero medians and substantially more powerful than all three tests for asymmetric mixtures of normal random variables with or without zero medians the motivation for this test derives from the need to appraise the safety profile of new medications if pre and post safety measures are obtained then under the null hypothesis the variables are exchangeable and the distribution of their difference is symmetric about a zero median large pre post differences are the major concern of a safety assessment the discarded small observations are not particularly relevant to safety and can reduce power to detect important asymmetry the new test was utilized on data from an on road driving study performed to determine if a hypnotic a drug used to promote sleep has next day residual effects

prediction in censored survival data a comparison of the proportional hazards and linear regression models although the analysis of censored survival data using the proportional hazards and linear regression models is common there has been little work examining the ability of these estimators to predict time to failure this is unfortunate since a predictive plot illustrating the relationship between time to failure and a continuous covariate can be far more informative regarding the risk associated with the covariate than a kaplan meier plot obtained by discretizing the variable in this paper the predictive power of the cox 1972 journal of the royal statistical society series b 34 187 202 proportional hazards estimator and the buckley james 1979 biometrika 66 429 436 censored regression estimator are compared using computer simulations and heuristic arguments it is shown that the choice of method depends on the censoring proportion strength of the regression the form of the censoring distribution and the form of the failure distribution several examples are provided to illustrate the usefulness of the methods

smooth t subnorms on finite scales in this work smooth t subnorms and boundary weak t norms bwt norms defined on a finite chain are studied in the smooth case it is proved that smooth bwt norms reduces to smooth t norms whereas a classification of smooth t subnorms as ordinal sums of a smooth t norm and an archimedean smooth t subnorm is proved in a similar way as in the case of 0 1 with respect to archimedean smooth t subnorms some cases depending on their zero region are considered classifying all of them in some cases and some specific families in others

a schneider type theorem for hopf algebroids abstract comodule algebras of a hopf algebroid h with a bijective antipode i e algebra extensions b a by h are studied assuming that a lifted canonical map is a split epimorphism of modules of the non commutative base algebra of h relative injectivity of the h comodule algebra a is related to the galois property of the extension b a and also to the equivalence of the category of relative hopf modules to the category of b modules this extends a classical theorem by h j schneider on galois extensions by a hopf algebra our main tool is an observation that relative injectivity of a comodule algebra is equivalent to relative separability of a forgetful functor a notion introduced and analysed hereby

algebra extensions and nonsingularity this paper is concerned with a notion of nonsingularity for noncommutative algebras which arises naturally in connection with cyclic homology let us consider associative unital algebras over the complex numbers we call an algebra a quasi free when it behaves like a free algebra with respect to nilpotent extensions in the sense that any homomorphism a r i where i is a nilpotent ideal in r can be lifted to a homomorphism a r if we restrict to the category of finitely generated commutative algebras then this lifting property characterizes smooth algebras the ones corresponding to nonsingular affine varieties in this way quasi free algebras appear as noncommutative analogues of smooth algebras stretching the analogy we can even regard quasi free algebras as analogues of manifolds one of the aims of this paper is to develop the analogy further by showing that quasi free algebras provide a natural setting for noncommutative versions of certain aspects of manifolds to give an example let us consider the analogue of an embedding an extension a r i where a and r are quasi free algebras playing the role of the submanifold and ambient manifold respectively in the manifold situation i i2 is the module of linear functions on the nor2 mal bundle and the symmetric algebra sa iii is the algebra of polynomial functions now in passing from commutative to noncommutative algebras the symmetric algebra of a module is replaced by the tensor algebra of a bimodule

copula like operations on finite settings this paper deals with discrete copulas considered as a class of binary aggregation operators on a finite chain a representation theorem by means of permutation matrices is given from this characterization we study the structure of associative discrete copulas and a theorem of decomposition of any discrete copula in terms of associative discrete copulas is obtained finally some aspects concerning their extension to copulas are dealt with

a simulation study of cross validation for selecting an optimal cutpoint in univariate survival analysis continuous measurements are often dichotomized for classification of subjects this paper evaluates two procedures for determining a best cutpoint for a continuous prognostic factor with right censored outcome data one procedure selects the cutpoint that minimizes the significance level of a logrank test with comparison of the two groups defined by the cutpoint this procedure adjusts the significance level for maximal selection the other procedure uses a cross validation approach the latter easily extends to accommodate multiple other prognostic factors we compare the methods in terms of statistical power and bias in estimation of the true relative risk associated with the prognostic factor both procedures produce approximately the correct type i error rate use of a maximally selected cutpoint without adjustment of the significance level however results in a substantially elevated type i error rate the cross validation procedure unbiasedly estimated the relative risk under the null hypothesis while the procedure based on the maximally selected test resulted in an upward bias when the relative risk for the two groups defined by the covariate and true changepoint was small the cross validation procedure provided greater power than the maximally selected test the cross validation based estimate of relative risk was unbiased while the procedure based on the maximally selected test produced a biased estimate as the true relative risk increased the power of the maximally selected test was about 10 per cent greater than the power obtained using cross validation the maximally selected test overestimated the relative risk by about 10 per cent the cross validation procedure produced at most 5 per cent underestimation of the true relative risk finally we report the effect of dichotomizing a continuous non linear relationship between covariate and risk we compare using a linear proportional hazard model to using models based on optimally selected cutpoints our simulation study indicates that we can have a substantial loss of statistical power when we use cutpoint models in cases where there is a continuous relationship between covariate and risk

boundary crossing probabilities and statistical applications abstract this paper surveys recent results involving boundary crossing probabilities and related statistical applications the first part is concerned with problems of sequential analysis especially repeated significance tests and their application to sequential clinical trials involving survival data the second part develops the probability theory motivated by the problems of part 1 a method for computing first passage distributions of brownian motion to linear boundaries is introduced and then modified to handle problems in discrete time and those involving nonlinear boundaries the third part is concerned with fixed sample statistical problems especially change point problems which involve boundary crossing probabilities examples are given of problems for which methods of part 2 appear adequate and of problems which require new methods

additive generators of discrete conjunctive aggregation operations this paper deals with a class of conjunction like binary operations defined on a finite totally ordered set the concept of additive generator of a discrete conjunctive aggregation operation is introduced and we obtain a description of those operations having an additive generator by means of nonstrict archimedean t norms the main goal is to give a procedure for deciding whether a conjunctive aggregation operation is additively generated or not the problem of the existence of additive generators for discrete t norms is also discussed

quantum geometry of algebra factorisations and coalgebra bundles we develop the noncommutative geometry bundles connections etc associated to algebras that factorise into two subalgebras an example is the factorisation of matrices m2 2 2 we also further extend the coalgebra version of theory introduced previously to include frame resolutions and corresponding covariant derivatives and torsions as an example we construct q monopoles on all the podle quantum spheres s2q s

characterizations of idempotent discrete uninorms in this paper we provide an axiomatic characterization of the idempotent discrete uninorms by means of three conditions only conservativeness symmetry and nondecreasing monotonicity we also provide an alternative characterization involving the bisymmetry property finally we provide a graphical characterization of these operations in terms of their contour plots and we mention a few open questions for further research

principal fibrations from noncommutative spheres we construct noncommutative principal fibrations s 7 s 4 which are deformations of the classical su 2 hopf fibration over the four sphere we realize the noncommutative vector bundles associated to the irreducible representations of su 2 as modules of coequivariant maps and construct corresponding projections the index of dirac operators with coefficients in the associated bundles is computed with the connes moscovici local index formula the algebra inclusion is an example of a not trivial quantum principal bundle

characterizing autodistributive aggregation operations defined on finite linearly ordered scales abstract observe that for continuous strictly increasing binary means defined on a unit interval autodistributivity and bisymmetry are equivalent bisymmetric aggregation operations defined on finite linearly ordered scales have been studied in the past and their behavior is unlike that of corresponding operations defined on the unit interval 0 1 this paper investigates two families of autodistributive aggregation operations defined on finite linearly ordered scales one with a neutral element and the other under some partial smoothness related conditions the former is fully described as the family of idempotent uninorms and the latter is completely characterized as the family of idempotent t operators through these results we can deduce that compared with bisymmetry autodistributivity is much stronger and the behavior of autodistributive aggregation operations defined on finite linearly ordered scales is significantly different from that of corresponding operations defined on 0 1

a hopf bundle over a quantum four sphere from the symplectic group we construct a quantum version of the su 2 hopf bundle s7 s4 the quantum sphere s7q arises from the symplectic group spq 2 and a quantum 4 sphere s4q is obtained via a suitable self adjoint idempotent p whose entries generate the algebra a s4q of polynomial functions over it this projection determines a deformation of an anti instanton bundle over the classical sphere s4 we compute the fundamental k homology class of s4q and pair it with the class of p in the k theory getting the value 1 for the topological charge there is a right coaction of suq 2 on s7q such that the algebra a s7q is a non trivial quantum principal bundle over a s4q with structure quantum group a suq 2

comparing two samples extensions of the t rank sum and log rank tests abstract i consider the problem of testing that two populations are identical with respect to the distribution of a continuous variable against the alternative that values tend to be larger in one population i observe that the t rank sum and log rank tests are insensitive for a large class of alternatives that may be expected to occur commonly in practice propose a criterion for identifying this problem in a particular data set and propose corresponding extensions of the conventional methods the proposed methods should be useful for both identifying and interpreting group differences

assessing the relative power of structural break tests using a framework based on the approximate bahadur slope abstract we compare the asymptotic relative efficiency of the exp mean and sup functionals of the wald lm and lr tests for structural change analyzed by andrews andrews d w k 1993 tests for parameter instability and structural change with unknown change point econometrica 61 821 856 and andrews and ploberger andrews d w k ploberger w 1994 optimal tests when a nuisance parameter is present only under the alternative econometrica 62 1383 1414 we derive the approximate bahadur slopes of these tests using large deviations techniques these show that tests based on the mean functional are inferior to those based on the sup and exp when using the same base statistic also for a given functional the wald based test dominates the lr based test which dominates the lm based one we show that the sup and mean type tests satisfy wieand s wieand h s 1976 a condition under which the pitman and bahadur approaches to efficiency coincide annals of statistics 4 1003 1011 condition so that their slopes yield the limiting as the size tends to zero asymptotic relative pitman efficiency whether this holds for the exp type tests still remains a conjecture using this measure of efficiency the mean type tests are also inferior to the sup we also compare tests based on the wald and lm statistics modified with a hac estimator in this case the inferiority of the lm based tests is especially pronounced the relevance of our theoretical results in finite samples is assessed via simulations our results are in contrast to those obtained by the authors in the second reference cited above based on a local asymptotic framework and our analysis thereby reveals its potential weaknesses in the context of structural change problems

noncommutative principal bundles through twist deformation we construct noncommutative principal bundles deforming principal bundles with a drinfeld twist 2 cocycle if the twist is associated with the structure group then we have a deformation of the fibers if the twist is associated with the automorphism group of the principal bundle then we obtain noncommutative deformations of the base space as well combining the two twist deformations we obtain noncommutative principal bundles with both noncommutative fibers and base space more in general the natural isomorphisms proving the equivalence of a closed monoidal category of modules and its twist related one are used to obtain new hopf galois extensions as twists of hopf galois extensions a sheaf approach is also considered and examples presented

on the discrete bisymmetry it is known that bisymmetry generalizes the simultaneous commutativity and associativity in the framework of the unit interval in this work we will completely characterize two classes of bisymmetric aggregation operators one with a neutral element and the other with the vertical and horizontal sections of the idempotent elements being smooth on a finite chain but not necessarily smooth and commutative thus the previous results based on the smoothness that is known as a very restrictive condition are improved for example there is only one smooth archimedean t norm on a finite chain in this paper the discrete bisymmetric aggregation operators are explored without the limit of the smoothness as a by product it is deduced that for smooth aggregation operators on a finite chain the bisymmetry is equivalent to the commutativity and associativity which improves the conclusion obtained by mas et al that associativity and bisymmetry are equivalent for commutative smooth aggregation operators on a finite chain

quantum principal bundles and corresponding gauge theories a generalization of classical gauge theory is presented in which compact quantum groups play the role of the internal symmetry groups all considerations are performed in the framework of a noncommutative geometric formalism of locally trivial quantum principal bundles over classical smooth manifolds quantum counterparts of classical gauge bundles and classical gauge transformations are introduced and investigated a natural dierential calculus on quantum gauge bundles is constructed and analyzed kinematical and dynamical properties of corresponding gauge theories are discussed a particular attention is given to the purely quantum phenomenas appearing in the formalism and their physical interpretation an example with quantum su 2 group is considered

on bisymmetric operators on a finite chain the bisymmetry property is studied for operators defined on a finite chain in particular a characterization of all bisymmetric commutative and smooth binary operators is given it is deduced from this characterization that bisymmetry and associativity are equivalent for finite chains under these additional conditions

correction of the p value after multiple coding of an explanatory variable in logistic regression we propose a method and a program to determine a significance level for a series of codings of an explanatory variable in logistic regression dichotomous and box cox transformations are considered three methods of correcting the significance level are studied the bonferroni method efron s method which uses the correlation between successive tests and the exact calculation by numerical integration using all correlations a simulation study has led to a strategy for the choice and number of the different codings of the variable this method is illustrated using the data of a study of the relation between cholesterol and dementia

generalized maximally selected statistics maximally selected statistics for the estimation of simple cutpoint models are embedded into a generalized conceptual framework based on conditional inference procedures this powerful framework contains most of the published procedures in this area as special cases such as maximally selected chi squared and rank statistics but also allows for direct construction of new test procedures for less standard test problems as an application a novel maximally selected rank statistic is derived from this framework for a censored response partitioned with respect to two ordered categorical covariates and potential interactions this new test is employed to search for a high risk group of rectal cancer patients treated with a neo adjuvant chemoradiotherapy moreover a new efficient algorithm for the evaluation of the asymptotic distribution for a large class of maximally selected statistics is given enabling the fast evaluation of a large number of cutpoints

projective module description of the q monopole the dirac q monopole connection is used to compute projector matrices of quantum hopf line bundles for arbitrary winding number the chern connes pairing of cyclic cohomology and k theory is computed for the winding number 1 the non triviality of this pairing is used to conclude that the quantum principal hopf fibration is non cleft among general results we provide a left right symmetric characterization of the canonical strong connections on quantum principal homogeneous spaces with an injective antipode we also provide for arbitrary strong connections on algebraic quantum principal bundles hopf galois extensions their associated covariant derivatives on projective modules

on graphical tests for proportionality of hazards in two samples in this paper we present a class of graphical tests of the proportional hazards hypothesis for two sample censored survival data the proposed tests are improvements over some existing tests based on asymptotic confidence bands of certain functions of the estimated cumulative hazard functions the new methods are based on the comparison of unrestricted estimates of the said functions and their restricted versions under the hypothesis they combine the rigour of analytical tests with the descriptive value of plots monte carlo simulations suggest that the proposed asymptotic procedures have reasonable small sample properties the power is much higher than existing graphical tests and comparable with existing analytical tests the method is then illustrated through the analysis of a data set on bone marrow transplantation for leukemia patients

the area between curves abc measure in nutritional anthropometry this paper considers a statistic recently suggested by mora for the deviation of a sample distribution from a reference distribution which typically arises in anthropometry when using the nutritional indicators height age weight age or weight height the statistic measures the area between curves abc and stands for the mass of the sample distribution which is not covered by the reference distribution the paper provides a statistical framework for the abc and includes some minor corrections of mora s original paper for the normal distribution situation with common or different variances formulae are derived which include a partition of abc into parts corresponding to malnourished and well nourished groups however the main result is a non parametric generalization of the abc motivated by the fact that the nutritional indicators often have skewed distributions with heavier left tails non parametric statistical inference is provided by linking the abc to the kolmogorov smirnov statistic