resolutions of fat point ideals involving eight general points of p2 abstract the main result theorem 1 provides an algorithm for determining the minimal free resolution of fat point subschemes of p 2 involving up to eight general points of arbitrary multiplicities the resolutions obtained hold for any algebraically closed field independent of the characteristic the algorithm works by giving a formula in nice cases and a reduction to the nice cases otherwise the algorithm which does not involve grobner bases is very fast partial information is also obtained in certain cases with n 8

conditions imposed by tacnodes and cusps the study of linear systems of algebraic plane curves with fixed imposed singularities is a classical subject which has recently experienced important progress the horace method introduced by a hirschowitz has been successfully exploited to prove many h1 vanishing theorems even in higher dimension other specialization techniques which include degenerations of the plane are due to z ran and c ciliberto and r miranda g m greuel c lossen and e shustin use a local specialization procedure together with the horace method to give the first asymptotically proper general existence criterion for singular curves of low degree in this paper we develop a specialization method which allows us to compute the dimension of several linear systems as well as to substantially improve the bounds given by greuel lossen and shustin for curves with tacnodes and cusps

on bounding the number of generators for fat point ideals on the projective plane abstract let x be the surface obtained by blowing up general points p1 pn of the projective plane over an algebraically closed ground field k and let l be the pullback to x of a line on the plane if c is a rational curve on x with c l d then for every t there is a natural map c o c t x o x l c o c t d given by multiplication on simple tensors the ranks of such maps are determined as a function of t d and m where m is the largest multiplicity of c at any of the points pi if i is the ideal defining the fat point subscheme z m1p1 mnpn p2 and is the least degree in which i has generators then the ranks of the maps c o c t x o x l c o c t d can be used for bounding the number of generators of i in degrees t 1

minimization of a class of matrix trace functions by means of refined majorization a procedure is described for minimizing a class of matrix trace functions the procedure is a refinement of an earlier procedure for minimizing the class of matrix trace functions using majorization it contains a recently proposed algorithm by koschat and swayne for weighted procrustes rotation as a special case a number of trial analyses demonstrate that the refined majorization procedure is more efficient than the earlier majorization based procedure

weighted least squares fitting using ordinary least squares algorithms a general approach for fitting a model to a data matrix by weighted least squares wls is studied this approach consists of iteratively performing steps of existing algorithms for ordinary least squares ols fitting of the same model the approach is based on minimizing a function that majorizes the wls loss function the generality of the approach implies that for every model for which an ols fitting algorithm is available the present approach yields a wls fitting algorithm in the special case where the wls weight matrix is binary the approach reduces to missing data imputation

linear systems of plane curves through fixed fat points of p2 abstract given any s points p1 ps in p 2 and s positive integers m1 ms let sn be the linear system of plane curves of degree n through pi with multiplicity at least mi 1 i s we give numerical bounds for the regularity of sn in the following cases a the points pi are non singular points of an integral curve of degree d b the pi s are in general position c the pi s are in uniform position d the pi s are generic points of p 2 we also study the sharpness of such bounds

fitting longitudinal reduced rank regression models by alternating least squares an alternating least squares method for iteratively fitting the longitudinal reduced rank regression model is proposed the method uses ordinary least squares and majorization substeps to estimate the unknown parameters in the system and measurement equations of the model in an example with cross sectional data it is shown how the results conform closely to results from eigenanalysis optimal scaling of nominal and ordinal variables is added in a third substep and illustrated with two examples involving cross sectional and longitudinal data

positivity of divisors on blown up projective spaces ii we construct log resolutions of pairs on the blow up of the projective space in an arbitrary number of general points and we discuss the semi ampleness of the strict transforms as an application we give an explicit proof that the abundance conjecture holds for an infinite family of such pairs for n 2 points these strict transforms are f nef divisors on the moduli space m0 n 3 in a kapranov s model we show that all of them are nef

degeneration of linear systems through fat points on k3 surfaces in this paper we introduce a technique to degenerate k3 surfaces and linear systems through fat points in general position on k3 surfaces using this degeneration we show that on generic k3 surfaces it is enough to prove that linear systems with one fat point are non special in order to obtain the non speciality of homogeneous linear systems through n 4 u 9 w fat points in general position moreover we use this degeneration to obtain a result for homogeneous linear systems through n 4 u 9 w fat points in general position on a general quartic surface in p 3

regularity of linear systems of plane curves the subject of this paper is the study of linear systems of plane curves which are given by assigning a set of fixed multiple points this study not only has an interest per se but is connected to other subjects for example results on rational surfaces and curves on them can be found in ro a and gil a linear system of plane curves of projective dimension r is a subvector space i s

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

gensvm a generalized multiclass support vector machine traditional extensions of the binary support vector machine svm to multiclass problems are either heuristics or require solving a large dual optimization problem here a generalized multiclass svm is proposed called gensvm in this method classification boundaries for a k class problem are constructed in a k 1 dimensional space using a simplex encoding additionally several different weightings of the misclassification errors are incorporated in the loss function such that it generalizes three existing multiclass svms through a single optimization problem an iterative majorization algorithm is derived that solves the optimization problem without the need of a dual formulation this algorithm has the advantage that it can use warm starts during cross validation and during a grid search which significantly speeds up the training phase rigorous numerical experiments compare linear gensvm with seven existing multiclass svms on both small and large data sets these comparisons show that the proposed method is competitive with existing methods in both predictive accuracy and training time and that it significantly outperforms several existing methods on these criteria

on the first infinitesimal neighborhood of a linear configuration of points in p2 abstract we consider the following open questions fix a hilbert function h that occurs for a reduced zero dimensional subscheme of p 2 among all subschemes x with hilbert function h what are the possible hilbert functions and graded betti numbers for the first infinitesimal neighborhood z of x i e the double point scheme supported on x is there a minimum h min and maximum h max such function the numerical information encoded in h translates to a type vector which allows us to find unions of points on lines called linear configurations with hilbert function h we give necessary and sufficient conditions for the hilbert function and graded betti numbers of the first infinitesimal neighborhoods of all such linear configurations to be the same even for those h for which the hilbert functions or graded betti numbers of the resulting double point schemes are not uniquely determined we give one depending only on h that does occur we prove the existence of h max in general and discuss h min our methods include liaison techniques

some results on rational surfaces and fano varieties this is the publisher s version also available electronically from http www degruyter com view j crll 2001 2001 issue 538 crll 2001 068 crll 2001 068 xml

resolutions of ideals of any six fat points in p2 the graded betti numbers of the minimal free resolution and also therefore the hilbert function of the ideal of a fat point subscheme z of p2 are determined whenever z is supported at any 6 or fewer distinct points all results hold over an algebraically closed field k of arbitrary characteristic

big rational surfaces we prove that the cox ring of a smooth rational surface with big anticanonical class is finitely generated we classify surfaces of this type that are blow ups of mathbb p 2 at distinct points lying on a possibly reducible cubic

configuration types and cubic surfaces this paper is a sequel to the paper e guardo b harbourne resolutions of ideals of six fat points in p2 j algebra 318 2 2007 619 640 we relate the matroid notion of a combinatorial geometry to a generalization which we call a configuration type configuration types arise when one classifies the hilbert functions and graded betti numbers for fat point subschemes supported at n 8 essentially distinct points of the projective plane each type gives rise to a surface x obtained by blowing up the points we classify those types such that n 6 and kx is nef the surfaces obtained are precisely the desingularizations of the normal cubic surfaces by classifying configuration types we recover in all characteristics the classification of normal cubic surfaces which is well known in characteristic 0 j w bruce c t c wall on the classification of cubic surfaces j london math soc 2 19 2 1979 245 256 as an application of our classification of configuration types we obtain a numerical procedure for determining the hilbert function and graded betti numbers for the ideal of any fat point subscheme z m1p1 m6p6 such that the points pi are essentially distinct and kx is nef given only the configuration type of the points p1 p6 and the coefficients mi

positivity of line bundles on general blow ups of p2 abstract let x be the blow up of p 2 at r general points p 1 p r p 2 we study line bundles on x given by plane curves of degree d passing through p i with multiplicity at least m i motivated by results in 39 we establish conditions for ampleness very ampleness and global generation of such line bundles

a multivariate reduced rank growth curve model with unbalanced data a multivariate reduced rank growth curve model is proposed that extends the univariate reducedrank growth curve model to the multivariate case in which several response variables are measured over multiple time points the proposed model allows us to investigate the relationships among a number of response variables in a more parsimonious way than the traditional growth curve model in addition the method is more flexible than the traditional growth curve model for example response variables do not have to be measured at the same time points nor the same number of time points it is also possible to apply various kinds of basis function matrices with different ranks across response variables it is not necessary to specify an entire set of basis functions in advance examples are given for illustration

cox rings of surfaces and the anticanonical iitaka dimension abstract in this paper we investigate the relation between the finite generation of the cox ring r x of a smooth projective surface x and its anticanonical iitaka dimension k x

coble rational surfaces dedicated to professor m miyanishi on the occasion of his sixtieth birthday abstract a coble surface is a smooth rational projective surface such that its anti canonical linear system is empty while the anti bicanonical linear system is nonempty in this paper we shall classify coble surfaces and consider the finiteness problem of the number of negative rational curves on it modulo automorphisms

birational morphisms of rational surfaces abstract a fairly complete characterization on anticanonical rational surfaces of the divisor classes whose sections define birational morphisms is given most results are proven over an algebraically closed field of arbitrary characteristic

fuzzy quantification a state of the art abstract quantified sentences are a very powerful notion for modelling statements in natural language nl but in practice they have been used to solve several problems this paper is intended to offer a global view of the development on this branch until now focusing in the different approaches dealing with quantification specially those involving imprecision called fuzzy quantification we put attention to the different mechanisms for defining them the evaluation methods for measuring their fulfilment as well as the properties they should satisfy

multivariate analysis with linearizable regressions we study the class of multivariate distributions in which all bivariate regressions can be linearized by separate transformation of each of the variables this class seems more realistic than the multivariate normal or the elliptical distributions and at the same time its study allows us to combine the results from multivariate analysis with optimal scaling and classical multivariate analysis in particular a two stage procedure which first scales the variables optimally and then fits a simultaneous equations model is studied in detail and is shown to have some desirable properties

estimating linear statistical relationships this paper on estimating linear statistical relationships includes three lectures on linear functional and structural relationships factor analysis and simultaneous equations models the emphasis is on relating the several models by a general approach and on the similarity of maximum likelihood estimators under normality in the different models in the first two lectures the observable vector is decomposed into a systematic part and a random error the systematic part satisfies the linear relationships estimators are derived for several cases and some of their properties given estimation of the coefficients of a single equation in a simultaneous equations model is shown to be equivalent to estimation of linear functional relationships

rational surfaces having only a finite number of exceptional curves we characterize the rational surfaces x which have a finite number of 1 curves under the assumption that kx is nef and having self intersection zero

on the resolution of a curve lying on a smooth cubic surface in ℙ 3 let c be any reduced and irreducible curve lying on a smooth cubic surface in p 3 in this paper we determine the graded betti numbers of the ideal sheaf j c

a framework for fuzzy quantification models analysis a framework for description of fuzzy quantification models is presented within this framework the fuzzy quantified statements evaluation problem is described as the compatibility between the fuzzy quantifier and a fuzzy cardinality or a fuzzy aggregation measure a list of desirable properties for quantification models is presented and those models that fit the framework are confronted with it

asymptotically log fano varieties abstract motivated by the study of fano type varieties we define a new class of log pairs that we call asymptotically log fano varieties and strongly asymptotically log fano varieties we study their properties in dimension two under an additional assumption of log smoothness and give a complete classification of two dimensional strongly asymptotically log smooth log fano varieties based on this classification we formulate an asymptotic logarithmic version of calabi s conjecture for del pezzo surfaces for the existence of kahler einstein edge metrics in this regime we make some initial progress towards its proof by demonstrating some existence and non existence results among them a generalization of matsushima s result on the reductivity of the automorphism group of the pair and results on log canonical thresholds of pairs one by product of this study is a new conjectural picture for the small angle regime and limit which reveals a rich structure in the asymptotic regime of which a folklore conjecture concerning the case of a fano manifold with an anticanonical divisor is a special case

representation by levels an alternative to fuzzy sets for fuzzy data mining abstract in this paper we describe and discuss the main contributions of the representation by levels approach to fuzzy data mining representation by levels is an alternative representation of fuzziness in information and data which is complementary to fuzzy sets in the sense that it provides tools and algebraic structures beyond the capabilities of fuzzy set theories based on t norms t conorms and fuzzy negations our approach allows to extend any crisp mining technique to the fuzzy case in a simple way keeping all the properties of the crisp technique we illustrate our discussion with examples and existing approaches based on representation by levels to fuzzy association rules and the related issues of mining exception anomalous rules and mining fuzzy bag databases

a mass assignment theory of the probability of fuzzy events abstract mass assignment theory techniques for processing uncertainty in fril are reviewed the notion of the probability of a fuzzy event is introduced together with the t norm definition of conditional probabilities the latter is then shown to be probability possibility inconsistent an alternative theory of conditional probabilities based on mass assignments is presented together with a number of results illustrating some intuitive properties in particular the mass assignment theory of conditional probabilities is shown to be probability possibility consistent

linear systems on the blow up of p1 n abstract in this note we study linear systems on the blow up of p 1 n at r points in very general position we prove that the fibers of the projections p 1 n p 1 s 1 s n 1 can give contribution to the speciality of the linear system this allows us to give a new definition of expected dimension of a linear system in p 1 n which we call fiber dimension finally we state a conjecture about linear systems on p 1 3

resolutions of ideals of quasiuniform fat point subschemes of the notion of a quasiuniform fat point subscheme z p 2 is introduced and conjectures for the hilbert function and minimal free resolution of the ideal i defining z are put forward in a large range of cases it is shown that the hilbert function conjecture implies the resolution conjecture in addition the main result gives the first determination of the resolution of the mth symbolic power i m n of an ideal defining n general points of p 2 when both m and n are large in particular for infinitely many m for each of infinitely many n and for infinitely many n for every m 2 resolutions in other cases such as fat points with tails are also given except where an explicit exception is made all results hold for an arbitrary algebraically closed field k as an incidental result a bound for the regularity of i m n is given which is often a significant improvement on previously known bounds

dynamic structural systems under indirect observation identifiability and estimation aspects from a system theoretic perspective in this partly expository paper the parameter identifiability and estimation of a general dynamic structural model under indirect observation will be considered from a system theoretic perspective the general dynamic model covers dynamic factor analytic models dynamic mimic models and joreskog s linear structural model as special cases its reduced form is under a slightly different specification known in system theory and econometrics as the stochastic stationary version of the state space model by using concepts and methods from system theory such as the observability and controllability concept the steady state kalman filter and a general nonlinear ml estimation procedure known as prediction error estimation the general dynamic model will be identified it will be shown that joreskog s lisrel procedure is a special case of the prediction error estimation procedure

a probabilistic quantifier fuzzification mechanism the model and its evaluation for information retrieval in this paper we propose a new quantifier fuzzification mechanism which is deeply rooted in the theory of probability this quantifier fuzzification mechanism skips the nested assumption which is inherent to other probabilistic quantification methods the new quantification approach complies with the properties required for determiner fuzzification schemes dfs with finite sets and hence its good behavior is assured moreover this new approach is suitable for some application domains in particular the use of fuzzy quantifiers for implementing query quantified statements for information retrieval exemplifies the adequacy of the new proposal the new quantifier fuzzification mechanism has been efficiently implemented and empirically tested for a retrieval task this practical evaluation followed the standard methodology in the field of information retrieval and was conducted against a popular benchmark consisting of a large collection of documents the retrieval performance evaluation made evident that 1 the new method can work in realistic scenarios and 2 it can overcome recent proposals for applying fuzzy quantifiers in information retrieval

betti numbers for fat point ideals in the plane a geometric approach we consider the open problem of determining the graded betti numbers for fat point subschemes z supported at general points of p 2 we relate this problem to the open geometric problem of determining the splitting type of the pullback of p2 to the normalization of certain rational plane curves we give a conjecture for the graded betti numbers which would determine them in all degrees but one for every fat point subscheme supported at general points of p 2 we also prove our betti number conjecture in a broad range of cases an appendix discusses many more cases in which our conjecture has been verified computationally and provides a new and more efficient computational approach for computing graded betti numbers in certain degrees it also demonstrates how to derive explicit conjectural values for the betti numbers and how to compute splitting types

a probabilistic framework for interval type 2 fuzzy linguistic summarization many studies on linguistic summarization have addressed the use of ordinary fuzzy set type 1 fuzzy set t1fs for modeling words however few of them have exploited interval type 2 fuzzy set it2fs although it2fs is better able to deal with the uncertainty associated with words the existing studies on linguistic summarization using it2fs have focused on scalar cardinality based degree of truth in this paper for the first time we propose a probabilistic framework based on the idea of interval mass assignment to evaluate interval type 2 fuzzy linguistic summaries based on the type ii quantified sentences and the semi fuzzy quantifiers as an alternative method to the scalar cardinality based methods we implement a real case study on linguistic summarization of time series data of europe brent spot price as well as a comparison of the results obtained with our approach and those of the existing approaches

infinitesimal deformations of rational surface automorphisms if x is a rational surface without nonzero holomorphic vector field and f is an automorphism of x we study in several examples the zariski tangent space of the local deformation space of the pair x f

seshadri constants and very ample divisors on algebraic surfaces a broadly applicable geometric approach for constructing nef divisors on blow ups of algebraic surfaces at n general points is given it works for all surfaces in all characteristics for any n this construction is used to obtain substantial improvements for currently known lower bounds for n point seshadri constants remarks are included about a range of applications to classical problems involving linear systems on p 2