multinomial regression models based on continuation ratios this paper concerns continuation ratio models for multinomial responses these are conditional probabilities used in logit models to define the dependence of the multinomial proportions on explanatory variables and unknown parameters a distinctive feature of these models is that if one models the various continuation ratios separately then the resulting estimates and test statistics are asymptotically independent this allows the partitioning of likelihood ratio statistics and the search for effects in specific categories of an ordinal response variable models that use the same parameters for different continuation ratios are suitable for estimating more global differences the fitting of these models to actual data is illustrated including an example from a pharmaceutical study the results show that different models are suitable for modelling complementary sorts of differences between multinomial response distributions

on the projective normality of double coverings over a rational surface abstract we study the projective normality of a minimal surface x which is a ramified double covering over a rational surface s with dim k s 1 in particular horikawa surfaces the minimal surfaces of general type with k x 2 2 p g x 4 are of this type up to resolution of singularities let be the covering map from x to s we show that the z 2 invariant adjoint divisors k x r a are normally generated where the integer r 3 and a is an ample divisor on s

location scale cumulative odds models for ordinal data a generalized non linear model approach proportional odds regression models for multinomial probabilities based on ordered categories have been generalized in two somewhat different directions models having scale as well as location parameters for adjustment of boundaries on an unobservable underlying continuum between categories have been employed in the context of roc analysis partial proportional odds models having different regression adjustments for different multinomial categories have also been proposed this paper considers a synthesis and further generalization of these two families with use of a number of examples i discuss and illustrate properties of this extended family of models emphasis is on the computation of maximum likelihood estimates of parameters asymptotic standard deviations and goodness of fit statistics with use of non linear regression programs in standard statistical software such as sas

association models and canonical correlation in the analysis of cross classifications having ordered categories abstract the association models considered in goodman 1979a for the analysis of cross classifications having ordered categories are presented in a somewhat different form in the present article to facilitate comparison of the results obtained using these models with those obtained using the earlier canonical correlation approach both the association models and the canonical correlation approach can provide meaningful scores for the row and column categories and these scores can be used to partition into relevant components the usual chi squared statistic for testing the null hypothesis of statistical independence between the row classification and column classification however while the usual procedure for testing the statistical significance of chi squared components is invalid when these components are based on the canonical correlations a corresponding procedure is valid when these components are obtained with the association models the components of association obtained with the association mo

a comparison of chi square partitioning and two logit analyses of ordinal pain data from a pharmaceutical study we study three approaches for the analysis of ordinal pain data the first is essentially non parametric based on partitioning the goodness of fit statistic for testing the homogeneity model the other two involve the modelling of quite different logit functions of the multinomial probabilities we discuss and compare the characteristics of these three approaches using actual data from an analgesic trial

blind multivariable arma subspace identification in this paper we study the deterministic blind identification of multiple channel state space models having a common unknown input using measured output signals that are perturbed by additive white noise sequences different from traditional blind identification problems the considered system is an autoregressive system rather than an fir system hence the concerned identification problem is more challenging but possibly having a wider scope of application two blind identification methods are presented for multi channel autoregressive systems a cross relation identification method is developed by exploiting the mutual references among different channels it requires at least three channel systems with square and stably invertible transfer matrices moreover a general subspace identification method is developed for which two channel systems are sufficient for the blind identification however it requires the additive noises to have identical variances and the transfer matrices having no transmission zeros finally numerical simulations are carried out to demonstrate the performance of the proposed identification algorithms

abelian surfaces of type 1 4 pair dl d2 is called the type of l according to riemann r o c h h did2 and l induces a rational map cpl a pn d2 t we want to study this map in the special case dl d2 1 4 let us first recollect what is known in the other cases for d 1 3 tp l is an embedding by a classical theorem of lefschetz see m for da 2 cpl is an embedding if and only if d2 2 and a l is not of the form el x e2 p li with elliptic curves e 1 and e 2 and line bundles l on e i see l n suppose now dl 1 the complete linear system ill has base components if and only if a l et x e2 p li as above we assume that a l is not a product of euiptic curves since it is easy to work out the map q l in the exceptional case for d2 2 ill has exactly 4 base points blowing up we get a morphism pt with general fibre a smooth curve of genus 3 see b if d2 3 ill is base point free and we get a morphism pz a p 1if d2 3 pl a p2 is a 6 1 covering ramified in a curve of degree 18 if de 4 there is a cyclic covering

hyperelliptic curves on 1 4 polarised abelian surfaces we investigate the number and the geometry of smooth hyperelliptic curves on a general complex abelian surface we give a short proof for the known fact the only possibilities of genera of such curves are 2 3 4 and 5 then we focus on the genus five case we prove that up to translation there is a unique hyperelliptic curve in the linear system of a general 1 4 polarised abelian surface moreover the curve is invariant with respect to a subgroup of translations isomorphic to the klein group our proof of the existence of hyperelliptic curves on general 1 4 polarised abelian surfaces is different from that in the recent paper 10 we give the decomposition of the jacobian of such a curve into abelian subvarieties displaying jacobians of quotient curves and prym varieties motivated by the construction we prove the statement every etale klein covering of a hyperelliptic curve is a hyperelliptic curve provided that the group of 2 torsion points defining the covering is non isotropic with respect to the weil pairing and every element of this group can be written as a difference of two weierstrass points

a new model for ordinal pain data from a pharmaceutical study for the pain data analysed previously by cox and chuang this paper proposes a new model that assumes monotone scores for ordered response categories this proposed model possesses several attractive features and allows a stochastic ordering of the drugs under comparison such a model also provides insight regarding the ordinal scale used to classify response estimation of the parameters in the model is obtained by use of bmdp3r

are ordinal models useful for classification there is recent interest in classification procedures intended for use only when the response is ordinal ordinal response however is evident in the parameters estimated by either multinomial logistic or normal discriminant analyses both of which classify either ordinal or non ordinal responses further there may be harm in applying ordinal models inappropriately and ample opportunity to assume mistakenly ordinality in real data sets therefore it becomes important to ascertain whether there is benefit obtained in the appropriate application of ordinal models this paper presents the results of a simulation study designed to compare classification accuracy of various models we show that ordinal models classify less accurately than the multinomial logistic and normal discriminant procedures under a variety of circumstances until further studies become available we presently conclude that ordinal models confer no advantage when the main purpose of the analysis is classification

a new deterministic identification approach to hammerstein systems the deterministic identification of hammerstein systems is investigated in this paper based on the over sampling technique a new deterministic identification approach is presented which blindly identifies the linear dynamic part followed by the estimation of the nonlinear function the proposed method allows us to identify the hammerstein system using an over sampling rate smaller than the numerator polynomial s length of the linear dynamic part as required by other existing methods in addition it can obtain the true values of the system parameters in the noise free case and an asymptotically consistent estimate in the presence of noise the richness condition of the system input and the selection of the over sampling rate are studied for the identifiability of the hammerstein system simulation examples are given to show the performance of the proposed method

technical communique blind identifiability of iir systems it is shown that with no prior information a necessary and sufficient condition for an nth order iir system to be blindly identifiable is that the over sampling ratio p n 1

a sharp lower bound for the canonical volume of 3 folds of general type let v be a smooth projective 3 fold of general type denote by k 3 a rational number the self intersection of the canonical sheaf of any minimal model of v one defines k 3 as the canonical volume of v assume p g v 2 we show that k 3 ge frac 1 3 which is a sharp lower bound then we classify those v with small volume we also give some new examples with p g 2 which have maximal canonical stability index finally we give an application to 4 folds of general type

a blind approach to closed loop identification of hammerstein systems this paper is a continuing study of the blind approach for the hammerstein identification in sun et al 1999 and bai and fu 2002 in the framework of a closed loop sampled data system the output is sampled faster than the updating period of the input the parameters of the linear dynamics are consistently estimated from the information of the output only after which the unmeasurable inner signal is uniquely reconstructed the noise effect is explicitly considered in both the parameter and inner signal estimation the estimation of the system orders and time delay are studied on the basis of two groups of basic equations obtained by polyphase decomposition the proposed blind approach is validated and illustrated by a simulated numerical example

vector bundles of rank 2 and linear systems on algebraic surfaces let s be a smooth complex algebraic surface and let l be a divisor on s it is well known that the linear system il ksi where ks is the canonical divisor plays an important role in understanding the geometry of s several authors see for example 8 11 studied various properties of this system our paper treats the same subject but the point of view is different from the works mentioned above the philosophy underlying our approach is almost classical points on s more generally effective 0 cycles in special position with respect to il ksi see definition below contain information about the geometry of s this point of view was recently revived in 5 also 10 in fact this paper contains the technique of going from the effective 0 cycle z in special position with respect to il ksi to the geometry of s for the sake of completeness we give a definition and state a theorem which can be found in 5 10

identification of hammerstein systems without explicit parameterisation of non linearity this article proposes a new approach to identification of hammerstein systems where a non linearity precedes a linear dynamic system driven by piece wise constant inputs the proposed approach does not require an explicit parameterisation of the non linearity moreover the non linearity does not have to be static but could be the one with finite memories like backlash by exploiting input s piecewise constant property the denominator of the linear system described by an arx model is consistently identified from the information of the output only next a subspace direct equalisation method estimates the unmeasurable inner signal based on the resulted denominator estimate and output measurements contrary to the existing blind approaches the numerator of the linear system is not required which leads to a significant improvement of removing an error propagation on the basis of the estimated inner signal the measured input and output the non linearity and linear system are obtained separately the