the motivic nearby fiber and degeneration of stable rationality we prove that stable rationality specializes in regular families whose fibers are integral and have at most ordinary double points as singularities our proof is based on motivic specialization techniques and the criterion of larsen and lunts for stable rationality in the grothendieck ring of varieties

on compositions of lattice matrices in this paper we give some properties of compositions of matrices whose elements belong to a distributive lattice we also construct an idempotent matrix from a given matrix and factor a matrix into a product of a square matrix and a rectangular matrix of the same dimension this square matrix has reflexivity and transitivity the main results obtained in this paper are generalizations of previous results on fuzzy matrices by ragab emam and hashimato

the transitive closure convergence of powers and adjoint of generalized fuzzy matrices generalized fuzzy matrices are considered as matrices over a special type of semiring which is called an incline and their transitive closure powers determinant and adjoint matrices are studied an expression for the transitive closure of a matrix a as a sum of its powers and some su2cient conditions for powers of a matrix to converge are given if the incline is commutative a su2cient condition for nilpotency of a matrix is obtained namely the determinants of the principal submatrices of the matrix are all equal to zero element in addition it is proved that a n 1 is equal to the adjoint matrix of a if the matrix a satis5es a in

algorithms for computing the min transitive closure and associated partition tree of a symmetric fuzzy relation abstract based on a previously derived weight driven algorithm for the computation of the t transitive closure of an arbitrary binary fuzzy relation on a finite universe with t a triangular norm we establish three algorithms for the computation of the min transitive closure of a symmetric matrix with elements in 0 1 as a by product these algorithms enable to generate the partition tree associated with the min transitive closure of the given matrix in descending order of the cutting parameter

unirational threefolds with no universal codimension 2 cycle we prove that the general quartic double solid with k le 7 nodes does not admit a chow theoretic decomposition of the diagonal or equivalently has a nontrivial universal mathrm ch 0 group and the same holds if we replace in this statement chow theoretic by cohomological in particular it is not stably rational we also deduce that the general quartic double solid with seven nodes does not admit a universal codimension 2 cycle parameterized by its intermediate jacobian and even does not admit a parametrization with rationally connected fibers of its jacobian by a family of 1 cycles this finally implies that its third unramified cohomology group is not universally trivial

on the existence and construction of t transitive closures in this paper it is shown that any fuzzy relation r on an arbitrary universe x has a t transitive closure the triangular norm t involved is not subject to any conditions this existential result can be turned into an explicit expression in the case of a left continuous triangular norm t furthermore this continuity restriction vanishes in the case of a finite universe x in that case the explicit expression can also be operationalized

factoring fuzzy transitivity transitivity of a precise weak preference relation implies that its asymmetric component strict preference and its symmetric component indifference are transitive and conversely the transitivity of strict preference and indifference implies that the underlying weak preference relation is transitive this paper examines to what extent analogous results may be obtained for the different transitivity conditions and different methods for deriving strict preference and indifference being used in the literature of choice with fuzzy preferences

unramified cohomology of degree 3 and noether s problem let g be a finite group and w be a faithful representation of g over c the group g acts on the field of rational functions c w the question whether the field of invariant functions c w g is purely transcendental over c goes back to emmy noether using the unramified cohomology group of degree 2 of this field as an invariant saltman gave the first examples for which c w g is not rational over c around 1986 bogomolov gave a formula which expresses this cohomology group in terms of the cohomology of the group g

regression aware decompositions abstract linear least squares regression with a design matrix a approximates a given matrix b via minimization of the spectral or frobenius norm discrepancy a x b over every conformingly sized matrix x also popular is low rank approximation to b through the interpolative decomposition which traditionally has no supervision from any auxiliary matrix a the traditional interpolative decomposition selects certain columns of b and constructs numerically stable multi linear interpolation from those columns to all columns of b thus approximating all of b via the chosen columns accounting for regression with an auxiliary matrix a leads to a regression aware interpolative decomposition which selects certain columns of b and constructs numerically stable multi linear interpolation from the corresponding least squares solutions to the least squares solutions x minimizing a x b for all columns of b the regression aware decompositions reveal the structure inherent in b that is relevant to regression against a they effectively enable supervision to inform classical dimensionality reduction which classically has been restricted to strictly unsupervised learning

a top down algorithm for generating the hasse tree of a fuzzy preorder closure this paper describes a new top down algorithm for the stepwise generation of the different levels or hasse diagrams of the hasse tree associated to the fuzzy preorder closure min transitive closure of a given reflexive binary fuzzy relation the algorithm is based upon a recently established weight driven method for computing the min transitive closure of a reflexive binary fuzzy relation the way in which this method gradually establishes the fuzzy preorder closure implies that for the generation of a specific level of the hasse tree the newly proposed algorithm does not require the complete computation of this closure

transitive closure and betweenness relations indistinguishability operators fuzzify the concept of equivalence relation and have been proved a useful tool in theoretical studies as well as in different applications such as fuzzy control or approximate reasoning one interesting problem is their construction there are different ways depending on how the data are given and on their future use in this paper the length of an indistinguishability operator is defined and it is used to relate its generation via max t product and via the representation theorem when t is an archimedean t norm the link is obtained taking into account that indistinguishability operators generate betweenness relations the study is also extended to decomposable operators

on motivic cohomology with z l coefficients in this paper we prove the conjecture of bloch and kato which relates milnor s k theory of a field with its galois cohomology as well as the related comparisons results for motivic cohomology with finite coefficients in the nisnevich and etale topologies

stably irrational hypersurfaces of small slopes we show that over any uncountable field of characteristic different from two a very general hypersurface of dimension n 2 and degree at least log 2 n 2 is not stably rational this significantly improves earlier results of kollar and totaro as a byproduct of our proof we obtain new counterexamples to the integral hodge conjecture answering a question of voisin and colliot thelene voisin

finding rough and fuzzy rough set reducts with sat feature selection refers to the problem of selecting those input features that are most predictive of a given outcome a problem encountered in many areas such as machine learning pattern recognition and signal processing in particular solution to this has found successful application in tasks that involve datasets containing huge numbers of features in the order of tens of thousands which would otherwise be impossible to process further recent examples include text processing and web content classification rough set theory has been used as such a dataset pre processor with much success but current methods are inadequate at finding globally minimal reductions the smallest sets of features possible this paper proposes a technique that considers this problem from a propositional satisfiability perspective in this framework globally minimal subsets can be located and verified

varietes unirationnelles non rationnelles au dela de l exemple d artin et mumford keywords non rational but unirational variety grothendieck invariants rationality brauer invariants reference cma article 1989 001doi 10 1007 bf01850658 record created on 2008 12 16 modified on 2016 08 08

a pencil of enriques surfaces with non algebraic integral hodge classes we prove that there exists a pencil of enriques surfaces defined over mathbb q with non algebraic integral hodge classes of non torsion type this gives the first example of a threefold with the trivial chow group of zero cycles on which the integral hodge conjecture fails as an application we construct a fourfold which gives the negative answer to a classical question of murre on the universality of the abel jacobi maps in codimension three

an optimal algorithm for computing the max min transitive closure of a fuzzy similarity matrix abstract many algorithms have been proposed for computing the max min transitive closure of fuzzy similarity matrices in this paper a new algorithm is proposed to compute the max min transitive closure of a fuzzy similarity matrix which runs in o n 2 time for n by n matrices

on the rationality problem for quadric bundles we classify all positive integers n and r such that stably nonrational complex r fold quadric bundles over rational n folds exist we show in particular that for any n and r a wide class of smooth r fold quadric bundles over pcn are not stably rational if r 2n 1 1 2n 2 in our proofs we introduce a generalization of the specialization method of voisin and of colliot thelene and pirutka which avoids universally ch0 trivial resolutions of singularities

numerical representation of transitive fuzzy relations we show that there exists a continuous fuzzy quasi order r on the set of real numbers r such that for any fuzzy quasiorder r on a finite set x there is a mapping f x r such that r x y r f x f y for all x y x

new approaches to fuzzy rough feature selection there has been great interest in developing methodologies that are capable of dealing with imprecision and uncertainty the large amount of research currently being carried out in fuzzy and rough sets is representative of this many deep relationships have been established and recent studies have concluded as to the complementary nature of the two methodologies therefore it is desirable to extend and hybridize the underlying concepts to deal with additional aspects of data imperfection such developments offer a high degree of flexibility and provide robust solutions and advanced tools for data analysis fuzzy rough set based feature fs selection has been shown to be highly useful at reducing data dimensionality but possesses several problems that render it ineffective for large datasets this paper proposes three new approaches to fuzzy rough fs based on fuzzy similarity relations in particular a fuzzy extension to crisp discernibility matrices is proposed and utilized initial experimentation shows that the methods greatly reduce dimensionality while preserving classification accuracy

computationally efficient sup t transitive closure for sparse fuzzy binary relations the property of transitivity is one of the most important for fuzzy binary relations especially in the cases when they are used for the representation of real life similarity or ordering information as far as the algorithmic part of the actual calculation of the transitive closure of such relations is concerned works in the literature mainly focus on crisp symmetric relations paying little attention to the case of general fuzzy binary relations most works that deal with the algorithmic part of the transitive closure of fuzzy relations focus only on the case of max min transitivity disregarding other types of transitivity in this paper after formalizing the notion of sparseness and providing a representation model for sparse relations that displays both computational and storage merits we propose an algorithm for the incremental update of fuzzy sup t transitive relations the incremental transitive update itu algorithm achieves the re establishment of transitivity when an already transitive relation is only locally disturbed based on this algorithm we propose an extension to handle the sup t transitive closure of any fuzzy binary relation through a novel incremental transitive closure itc algorithm the itu and itc algorithms can be applied on any fuzzy binary relation and t norm properties such as reflexivity symmetricity and idempotency are not a requirement under the specified assumptions for the average sparse relation both of the proposed algorithms have considerably smaller computational complexity than the conventional approach this is established both theoretically and verified via appropriate computing experiments

cohomologie non ramifiee et conjecture de hodge entiere en nous appuyant sur la conjecture de bloch kato en k theorie de milnor nous etablissons un lien general entre le defaut de la conjecture de hodge entiere pour la cohomologie de degre 4 et le troisieme groupe de cohomologie non ramifiee a coefficients q z ceci permet de montrer que sur un solide en anglais threefold uniregle le troisieme groupe de cohomologie non ramifiee a coefficients q z s annule ce que la k theorie algebrique ne permet d obtenir que dans certains cas ceci permet a l inverse de deduire d exemples ayant leur source en k theorie que la conjecture de hodge entiere pour la cohomologie de degre 4 peut etre en defaut pour les varietes rationnellement connexes pour certaines familles a un parametre de surfaces on etablit un lien entre la conjecture de hodge entiere et l indice de la fibre generique

computing a t transitive lower approximation or opening of a proximity relation since transitivity is quite often violated even by decision makers that accept transitivity in their preferences as a condition for consistency a standard approach to deal with intransitive preference elicitations is the search for a close enough transitive preference relation assuming that such a violation is mainly due to decision maker estimation errors in some way the more number of elicitations the more probable inconsistency is this is mostly the case within a fuzzy framework even when the number of alternatives or object to be classified is relatively small in this paper we propose a fast method to compute a t indistinguishability from a reflexive and symmetric fuzzy relation being t any left continuous t norm the computed approximation we propose will take o n 3 time complexity where n is the number of elements under consideration and is expected to produce a t transitive opening to the authors knowledge there are no other proposed algorithm that computes t transitive lower approximations or openings while preserving the reflexivity and symmetry properties

efficient algorithms for computing a strong rank revealing qr factorization given anm n matrixm withm n it is shown that there exists a permutation fi and an integer k such that the qr factorization myi q ak ckbk reveals the numerical rank of m the k k upper triangular matrix ak is well conditioned ilckll2 is small and bk is linearly dependent on ak with coefficients bounded by a low degree polynomial in n existing rank revealing qr rrqr algorithms are related to such factorizations and two algorithms are presented for computing them the new algorithms are nearly as efficient as qr with column pivoting for most problems and take o ran2 floating point operations in the worst case

families of rationally connected varieties recall that a proper variety x is said to be rationally connected if two general points p q x are contained in the image of a map g p x this is clearly a birationally invariant property when x is smooth this turns out to be equivalent to the a priori weaker condition that two general points can be joined by a chain of rational curves and also to the a priori stronger condition that for any finite subset x there is a map g p x whose image contains and such that gtx is an ample bundle

a novel hierarchical clustering combination scheme based on fuzzy similarity relations clustering combination methods have received considerable attentions in recent years and many ensemble based clustering methods have been introduced however clustering combination techniques have been limited to flat clustering combination and the combination of hierarchical clusterings has yet to be addressed in this paper we address and formalize the concept of hierarchical clustering combination and introduce an algorithmic framework in which multiple hierarchical clusterings could be easily combined in this framework the similarity based description matrices of input hierarchical clusterings are aggregated into a transitive consensus matrix in which the final hierarchy could be formed empirical evaluation by using popular available datasets confirms the superiority of combined hierarchical clustering introduced by our method over the standard single hierarchical clustering methods

on the compression of low rank matrices a procedure is reported for the compression of rank deficient matrices a matrix a of rank k is represented in the form a u circ b circ v where b is a k times k submatrix of a and u v are well conditioned matrices that each contain a k times k identity submatrix this property enables such compression schemes to be used in certain situations where the singular value decomposition svd cannot be used efficiently numerical examples are presented

fuzzy information retrieval based on multi relationship fuzzy concept networks abstract in this paper we present a new method for fuzzy information retrieval based on multi relationship fuzzy concept networks there are four kinds of fuzzy relationships in a multi relationship fuzzy concept network i e fuzzy positive association relationship fuzzy negative association relationship fuzzy generalization relationship and fuzzy specialization relationship by performing fuzzy inferences based on the multi relationship fuzzy concept network the fuzzy information retrieval system can retrieve documents containing concepts that are not directly specified by the user but are somehow related to the user s query in order to perform fuzzy inferences more efficiently we use concept matrices to represent the degrees of fuzzy relationships between concepts in a multi relationship fuzzy concept network by calculating the transitive closures of concept matrices the implicit degrees of fuzzy relationships between concepts are obtained multiple degrees of satisfaction that a document satisfies the user s query with respect to the fuzzy relationships between concepts are calculated these satisfaction degrees are aggregated according to the user s specification to find the most relevant documents with respect to the user s query the proposed fuzzy information retrieval method is more flexible and more intelligent than the one we presented in ieee trans systems man cybernet part b cybernet 29 1 1999 126

algorithms for the computation of t transitive closures we present two weight driven algorithms for the computation of the t transitive closure of a symmetric binary fuzzy relation on a finite universe x with cardinality n or equivalently of a symmetric n spl times n matrix with elements in 0 1 with t a triangular norm the first algorithm is proven to be valid for any triangular norm t whereas the second algorithm is shown to be valid when t is either the minimum operator or an archimedean triangular norm furthermore we investigate how these algorithms can be appropriately adapted to generate the t transitive closure of nonsymmetric binary fuzzy relations or matrices as well

hypersurfaces that are not stably rational a fundamental problem of algebraic geometry is to determine which varieties are rational that is isomorphic to projective space after removing lower dimensional subvarieties from both sides in particular we want to know which smooth hypersurfaces in projective space are rational an easy case is that smooth complex hypersurfaces of degree at least n 2 in p are not covered by rational curves and hence are not rational by far the most general result on rationality of hypersurfaces is kollar s theorem that for d at least 2d n 3 3e a very general complex hypersurface of degree d in p is not ruled and therefore not rational 13 theorem v 5 14 very little is known about rationality in lower degrees except for cubic 3 folds and quintic 4 folds 4 19 chapter 3 a rational variety is also stably rational meaning that some product of the variety with projective space is rational many techniques for proving non rationality give no information about stable rationality voisin made a breakthrough in 2013 by showing that a very general quartic double solid a double cover of p ramified over a quartic surface is not stably rational 23 these fano 3 folds were known to be non rational over the complex numbers but stable rationality was an open question voisin s method was to show that the chow group of zero cycles is not universally trivial that is the chow group becomes nontrivial over some extension of the base field by degenerating the variety to a nodal 3 fold which has a resolution of singularities x with nonzero torsion in h3 x z colliot thelene and pirutka simplified and generalized voisin s degeneration method they deduced that very general quartic 3 folds are not stably rational 6 this was striking in that non rationality of smooth quartic 3 folds was the original triumph of iskovskikh manin s work on birational rigidity while stable rationality of these varieties was unknown 11 beauville applied the method to prove that very general sextic double solids quartic double 4 folds and quartic double 5 folds are not stably rational 1 2 in this paper we show that a wide class of hypersurfaces in all dimensions are not stably rational namely for all d 2d n 2 3e and n 3 a very general complex hypersurface of degree d in p is not stably rational theorem 2 1 the theorem covers all the degrees in which kollar proved non rationality in fact we get a bit more since kollar assumed d 2d n 3 3e for example very general quartic 4 folds are not stably rational whereas it was not even known whether these varieties are rational the method applies to some smooth hypersurfaces over q in each even degree section 3 gives some examples over q which are not stably rational over c the idea is that the most powerful results are obtained by degenerating a smooth complex variety to a singular variety in positive characteristic rather than to a sin

a representation theorem for min transitive fuzzy relations abstract we provide an abstract representation theorem for an arbitrary min transitive fuzzy relation r x y on a set x in terms of a specific min transitive relation on the interval 0 1 the technique used here gives us a fuzzy lattice structure on f x the set of all fuzzy subsets of x the underlying partial ordering on f x which can be regarded as a fuzzy subset hood relation satisfies the min transitivity and is superior to kosko s notion of subset hood in the sense that the latter does not satisfy the min transitivity

boundedness of pluricanonical maps of varieties of general type using the techniques of 20 and 10 we prove that certain log forms may be lifted from a divisor to the ambient variety as a consequence of this result following 22 we show that for any positive integer n there exists an integer rn such that if x is a smooth projective variety of general type and dimension n then phi rk x colon x dasharrow mathbb p h 0 mathcal o x rk x is birational for all r rn

convergence of products of fuzzy matrices convergence of powers of a fuzzy matrix has been studied in the literature in this paper we shall extend the scope to the products of a finite number of fuzzy matrices we shall demonstrate that the outcomes of products of fuzzy matrices will be more complicated than the cases of powers of a fuzzy matrix two notions of convergence are established weak convergence and strong convergence the main results to guarantee the weak convergence of products of fuzzy matrices are due to the concepts of transitive and compact properties of fuzzy matrices which can be viewed as a generalization of the transitive and compact properties of a fuzzy matrix sufficient conditions similar to the pinching theorem in calculus are given as well for strong convergence

formal concept analysis based on fuzzy granularity base for different granulations this paper introduces granular computing grc into formal concept analysis fca it provides a unified model for concept lattice building and rule extraction on a fuzzy granularity base for different granulations one of the strengths of grc is that larger granulations help to hide some specific details whereas fca in a grc context can prevent losses due to concept lattice complexity however the number of superfluous rules increases exponentially with the scale of the decision context to overcome this we present some inference rules and maximal rules and prove that the set of all these maximal rules is complete and nonredundant thus users who want to obtain decision rules should generate maximal rules examples demonstrate that application of the method is valid and practicable in summary this approach utilizes fca in a grc context and provides a practical basis for data analysis and processing

fuzzy relational inequalities and equations fuzzy quasi orders closures and openings of fuzzy sets the paper deals with systems of fuzzy relation equations known in the literature as eigen fuzzy set equations as well as with systems of related fuzzy relation inequalities our main results are algorithms for computing the greatest and the smallest solutions to the considered systems of fuzzy relation inequalities and algorithms for computing the greatest solutions to the considered systems of fuzzy relation equations the systems are studied in the framework of complete residuated lattices as the structure of membership values by means of fuzzy quasi orders and closures and openings on a collection of fuzzy sets