a vertex formalism for local ruled surfaces we develop a vertex formalism for topological string amplitudes on ruled surfaces with an arbitrary number of reducible fibers embedded in a calabi yau threefold our construction is based on large n duality and localization with respect to a degenerate torus action we also discuss potential generalizations of our formalism to a broader class of calabi yau threefolds using the same underlying principles

discrepancy between subcritical and fast rupture roughness a cumulant analysis rough crack fronts in a sheet of paper obtained during a creep experiment do not follow true scaling laws local roughness exponents are estimated using the first order cumulant a quantity recently introduced in the turbulence literature j delour j f muzy and a arneodo eur phys j b 23 243 2001 using a large data set 102 fronts we find a significant difference in local roughness between the slow subcritical and the fast growth regime

on the instanton r matrix a torus action on a symplectic variety allows one to construct solutions to the quantum yang baxter equations r matrices for a torus action on cotangent bundles over flag varieties the resulting r matrices are the standard rational solutions of the yang baxter equation well known in the theory of quantum integrable systems the torus action on the instanton moduli space leads to more complicated r matrices depending additionally on two equivariant parameters t1 and t2 in this paper we derive an explicit expression for the r matrix associated with the instanton moduli space we study its matrix elements and its taylor expansion in the powers of the spectral parameter certain matrix elements of this r matrix give a generating function for the characteristic classes of tautological bundles over the hilbert schemes in terms of the bosonic cut and join operators in particular we rederive from the r matrix the well known lehn s formula for the first chern class we explicitly compute the first several coefficients for the power series expansion of the r matrix in the spectral parameter these coefficients are represented by simple contour integrals of some symmetrized bosonic fields

counting bps states on the enriques calabi yau we study topological string amplitudes for the fhsv model using various techniques this model has a type ii realization involving a calabi yau threefold with enriques fibres which we call the enriques calabi yau by applying heterotic type iia duality we compute the topological amplitudes in the fibre to all genera it turns out that there are two different ways to do the computation that lead to topological couplings with different bps content one of them gives the standard d0 d2 counting amplitudes and from the other one we obtain information about bound states of d0 d4 d2 branes on the enriques fibre we also study the model using mirror symmetry and the holomorphic anomaly equations we verify in this way the heterotic results for the d0 d2 generating functional for low genera and find closed expressions for the topological amplitudes on the total space in terms of modular forms and up to genus three this model turns out to be much simpler than the generic b model and might be exactly solvable

effective superpotentials for compact d5 brane calabi yau geometries for compact calabi yau geometries with d5 branes we study n 1 effective superpotentials depending on both open and closed string fields we develop methods to derive the open closed picard fuchs differential equations which control d5 brane deformations as well as complex structure deformations of the compact calabi yau space their solutions encode the flat open closed coordinates and the effective superpotential for two explicit examples of compact d5 brane calabi yau hypersurface geometries we apply our techniques and express the calculated superpotentials in terms of flat open closed coordinates by evaluating these superpotentials at their critical points we reproduce the domain wall tensions that have recently appeared in the literature finally we extract orbifold disk invariants from the superpotentials which up to overall numerical normalizations correspond to orbifold disk gromov witten invariants in the mirror geometry

credal classification rule for uncertain data based on belief functions abstract in this paper we present a new credal classification rule ccr based on belief functions to deal with the uncertain data ccr allows the objects to belong with different masses of belief not only to the specific classes but also to the sets of classes called meta classes which correspond to the disjunction of several specific classes each specific class is characterized by a class center i e prototype and consists of all the objects that are sufficiently close to the center the belief of the assignment of a given object to classify with a specific class is determined from the mahalanobis distance between the object and the center of the corresponding class the meta classes are used to capture the imprecision in the classification of the objects when they are difficult to correctly classify because of the poor quality of available attributes the selection of meta classes depends on the application and the context and a measure of the degree of indistinguishability between classes is introduced in this new ccr approach the objects assigned to a meta class should be close to the center of this meta class having similar distances to all the involved specific classes centers and the objects too far from the others will be considered as outliers noise ccr provides robust credal classification results with a relatively low computational burden several experiments using both artificial and real data sets are presented at the end of this paper to evaluate and compare the performances of this ccr method with respect to other classification methods

top down approach to 6d scfts six dimensional 6d superconformal field theories scfts occupy a central place in the study of quantum field theories encountered in high energy theory this article reviews the top down construction and study of this rich class of quantum field theories in particular how they are realized by suitable backgrounds in string m f theory we review the recent f theoretic classification of 6d scfts explain how to calculate physical quantities of interest such as the anomaly polynomial of 6d scfts and also explain recent progress in understanding renormalization group flows for deformations of such theories additional topics covered by this review include some discussion on the weighted and signed counting of states in these theories via superconformal indices we also include several previously unpublished results as well as a new variant on the swampland conjecture for general quantum field theories decoupled from gravity the aim of the article is to provide a point of entry into this growing literature rather than an exhaustive overview

belief functions on distributive lattices the dempster shafer theory of belief functions is an important approach to deal with uncertainty in ai in the theory belief functions are defined on boolean algebras of events in many applications of belief functions in real world problems however the objects that we manipulate is no more a boolean algebra but a distributive lattice in this paper we employ birkhoff s representation theorem for finite distributive lattices to extend the dempster shafer theory to the setting of distributive lattices which has a mathematical theory as attractive as in that of boolean algebras moreover we use this more general theory to provide a framework for reasoning about belief functions in a deductive approach on non classical formalisms which assume a setting of distributive lattices as an illustration of this approach we investigate the theory of belief functions for a simple epistemic logic the first degree entailment fragment of relevance logic r by providing an axiomatization for reasoning about belief functions for this logic and by showing that the complexity of the satisfiability problem of a belief formula with respect to the class of the corresponding dempster shafer structures is np complete

handling possibilistic labels in pattern classification using evidential reasoning abstract a category of learning problems in which the class membership of training patterns is assessed by an expert and encoded in the form of a possibility distribution is considered each example i thus consists in a feature vector x i and a possibilistic label u 1 i u c i where u k i denotes the possibility of that example belonging to class k this problem is tackled in the framework of evidence theory the evidential distance based classifier previously introduced by one of the authors is extended to handle possibilistic labeling of training data two approaches are proposed based either on the transformation of each possibility distribution into a consonant belief function or on the use of generalized belief structures with fuzzy focal elements in each case a belief function modeling the expert s beliefs concerning the class membership of each new pattern is obtained this information may then be either interpreted by a human operator to support decision making or automatically processed to yield a final class assignment through the computation of pignistic probabilities experiments with synthetic and real data demonstrate the ability of both classification schemes to make effective use of possibilistic labels as training information

motivic donaldson thomas invariants of the conifold and the refined topological vertex abstract we compute the motivic donaldson thomas theory of the resolved conifold in all chambers of the space of stability conditions of the corresponding quiver the answer is a product formula whose terms depend on the position of the stability vector generalizing known results for the corresponding numerical invariants our formulae imply in particular a motivic form of the dt pt correspondence for the resolved conifold the answer for the motivic pt series is in full agreement with the prediction of the refined topological vertex formalism

kodaira spencer theory of gravity and exact results for quantum string amplitudes we develop techniques to compute higher loop string amplitudes for twistedn 2 theories with 3 i e the critical case an important ingredient is the discovery of an anomaly at every genus in decoupling of brst trivial states captured to all orders by a master anomaly equation in a particular realization of then 2 theories the resulting string field theory is equivalent to a topological theory in six dimensions the kodaira spencer theory which may be viewed as the closed string analog of the chern simons theory using the mirror map this leads to computation of the number of holomorphic curves of higher genus curves in calabi yau manifolds it is shown that topological amplitudes can also be reinterpreted as computing corrections to superpotential terms appearing in the effective 4d theory resulting from compactification of standard 10d superstrings on the correspondingn 2 theory relations withc 1 strings are also pointed out

generalized ablowitz ladik hierarchy in topological string theory this paper addresses the issue of integrable structures in topological string theory on generalized conifolds open string amplitudes of this theory can be expressed as the matrix elements of an operator on the fock space of 2d charged free fermion fields the generating function of these amplitudes with respect to the product of two independent schur functions becomes a tau function of the 2d toda hierarchy the associated lax operators turn out to have a particular factorized form this factorized form of the lax operators characterizes a generalization of the ablowitz ladik hierarchy embedded in the 2d toda hierarchy the generalized ablowitz ladik hierarchy is thus identified as a fundamental integrable structure of topological string theory on the generalized conifolds

affine manifolds syz geometry and the y vertex we study the real monge ampere equation in two and three dimensions both from the point of view of the syz conjecture where solutions give rise to semi flat calabi yau s and in affine differential geometry where solutions yield parabolic affine sphere hypersurfaces we find explicit examples connect the holomorphic function representation to hitchin s description of special lagrangian moduli space and construct the developing map explicitly for a singularity corresponding to the type in elliptic fiber after hyper kahler rotation following baues and cortes we show that various types of metric cones over two dimensional elliptic affine spheres generate solutions of the monge ampere equation in three dimensions we then prove a local and global existence theorem for an elliptic affine two sphere metric with prescribed singularities the metric cone over the two sphere minus three points yields a parabolic affine sphere with singularities along a y shaped locus this gives a semi flat calabi yau metric in a neighborhood of the y vertex

fuzzy hypothesis testing for a population proportion based on set valued information abstract in this paper we propose fuzzy hypothesis testing for a proportion with crisp data as the exact generalized one tailed hypergeometric test with fuzzy non complementary hypotheses and incorporate the conventional hypergeometric test with crisp hypotheses into its framework in particular we formulate hypotheses as ontic or epistemic fuzzy sets since we assume that presumptions regarding the true population proportion can be expressed in the conjunctive or disjunctive reading further we suggest modeling of membership functions in terms of cost or frequency due to considerations of user s priorities or incomplete knowledge in relation to hypotheses formulation considering a hypothesis as union of its crisp and fuzzy areas we illustrate via real life examples that in contrast to classical test theory fuzzy hypothesis testing provides an additional partial and gradual consideration of the indifference zone for both complementary and non complementary hypotheses the test concept is introduced for both test methods a test of significance and an alternative test and leads to a crisp test decision considering further cost aspects like the sample size the generalized error criteria are derived and interpreted in relation to both hypotheses additionally a corresponding sensitivity analysis is presented for one of the most promising test types

large n duality lagrangian cycles and algebraic knots we consider knot invariants in the context of large n transitions of topological strings in particular we consider aspects of lagrangian cycles associated to knots in the conifold geometry we show how these can be explicitly constructed in the case of algebraic knots we use this explicit construction to explain a recent conjecture relating study of stable pairs on algebraic curves with homfly polynomials furthermore for torus knots using the explicit construction of the lagrangian cycle we also give a direct a model computation and recover the homfly polynomial for this case

refining the shifted topological vertex we study aspects of the refining and shifting properties of the 3d macmahon function c3 q used in topological string theory and bkp hierarchy we derive the explicit expressions of the shifted topological vertex s q and its refined version t q t these vertices complete results in literature

on the axiomatic requirement of range to measure uncertainty abstract how to measure uncertainty is still an open issue probability theory is a primary tool to express the aleatoric uncertainty the shannon s information entropy is an effective measure for the uncertainty in probability theory dempster shafer theory an extension of probability theory has the ability to express the aleatoric and epistemic uncertainty simultaneously with respect to such uncertainties in dempster shafer theory a justifiable uncertainty measure is required to satisfy five axiomatic requirements based on previous studies in this paper we show that one of the axiomatic requirements the requirement of range is questionable the correct range of uncertainty should be 0 log 2 2 x rather than 0 log 2 x according to the concept of entropy

object association with belief functions an application with vehicles the problem tackled in this article consists in associating perceived objects detected at a certain time with known objects previously detected knowing uncertain and imprecise information regarding the association of each perceived objects with each known objects for instance this problem can occur during the association step of an obstacle tracking process especially in the context of vehicle driving aid a contribution in the modeling of this association problem in the belief function framework is introduced by interpreting belief functions as weighted opinions according to the transferable belief model semantics pieces of information regarding the association of known objects and perceived objects can be expressed in a common global space of association to be combined by the conjunctive rule of combination and a decision making process using the pignistic transformation can be made this approach is validated on real data

computation of open gromov witten invariants for toric calabi yau 3 folds by topological recursion a proof of the bkmp conjecture the bkmp conjecture 2006 2008 proposed a new method to compute closed and open gromov witten invariants for every toric calabi yau 3 folds through a topological recursion based on mirror symmetry so far this conjecture has been verified to low genus for several toric cy3folds and proved to all genus only for mathbb c 3 in this article we prove the general case our proof is based on the fact that both sides of the conjecture can be naturally written in terms of combinatorial sums of weighted graphs on the a model side this is the localization formula and on the b model side the graphs encode the recursive algorithm of the topological recursion

curve counting via stable pairs in the derived category for a nonsingular projective 3 fold x we define integer invariants virtually enumerating pairs c d where c x is an embedded curve and d c is a divisor a virtual class is constructed on the associated moduli space by viewing a pair as an object in the derived category of x the resulting invariants are conjecturally equivalent after universal transformations to both the gromov witten and dt theories of x for calabi yau 3 folds the latter equivalence should be viewed as a wall crossing formula in the derived category

all loop topological string amplitudes from chern simons theory we demonstrate the equivalence of all loop closed topological string amplitudes on toric local calabi yau threefolds with computations of certain knot invariants for chern simons theory we use this equivalence to compute the topological string amplitudes in certain cases to very high degree and to all genera in particular we explicitly compute the topological string amplitudes for open image in new window 2 up to degree 12 and open image in new window 1 open image in new window 1 up to total degree 10 to all genera this also leads to certain novel large n dualities in the context of ordinary superstrings involving duals of type ii superstrings on local calabi yau three folds without any fluxes

set based representations of conjunctive and disjunctive knowledge abstract we look at the use of sets as a method of representing information we study the use of different set operators to implement different semantic operations careful distinction is made between conjunctive and disjunctive type information

crystal melting and toric calabi yau manifolds we construct a statistical model of crystal melting to count bps bound states of d0 and d2 branes on a single d6 brane wrapping an arbitrary toric calabi yau threefold the three dimensional crystalline structure is determined by the quiver diagram and the brane tiling which characterize the low energy effective theory of d branes the crystal is composed of atoms of different colors each of which corresponds to a node of the quiver diagram and the chemical bond is dictated by the arrows of the quiver diagram bps states are constructed by removing atoms from the crystal this generalizes the earlier results on the bps state counting to an arbitrary non compact toric calabi yau manifold we point out that a proper understanding of the relation between the topological string theory and the crystal melting involves the wall crossing in the donaldson thomas theory

random skew plane partitions and the pearcey process we study random skew 3d partitions weighted by qvol and specifically the q 1 asymptotics of local correlations near various points of the limit shape we obtain sine kernel asymptotics for correlations in the bulk of the disordered region airy kernel asymptotics near a general point of the frozen boundary and a pearcey kernel asymptotics near a cusp of the frozen boundary

representing uncertainty on set valued variables using belief functions a formalism is proposed for representing uncertain information on set valued variables using the formalism of belief functions a set valued variable x on a domain w is a variable taking zero one or several values in w while defining mass functions on the frame 2 2 w is usually not feasible because of the double exponential complexity involved we propose an approach based on a definition of a restricted family of subsets of 2 w that is closed under intersection and has a lattice structure using recent results about belief functions on lattices we show that most notions from dempster shafer theory can be transposed to that particular lattice making it possible to express rich knowledge about x with only limited additional complexity as compared to the single valued case an application to multi label classification in which each learning instance can belong to several classes simultaneously is demonstrated

hodge gue correspondence and the discrete kdv equation we prove the conjectural relationship recently proposed in dubrovin and yang commun number theory phys 11 311 336 2017 between certain special cubic hodge integrals of the gopakumar marino vafa type gopakumar and vafa in adv theor math phys 5 1415 1443 1999 marino and vafa in contemp math 310 185 204 2002 and gue correlators and the conjecture proposed in dubrovin et al adv math 293 382 435 2016 that the partition function of these hodge integrals is a tau function of the discrete kdv hierarchy

remodeling the b model we propose a complete new formalism to compute unambiguously b model open and closed amplitudes in local calabi yau geometries including the mirrors of toric manifolds the formalism is based on the recursive solution of matrix models recently proposed by eynard and orantin the resulting amplitudes are non perturbative in both the closed and the open moduli the formalism can then be used to study stringy phase transitions in the open closed moduli space at large radius this formalism may be seen as a mirror formalism to the topological vertex but it is also valid in other phases in the moduli space we develop the formalism in general and provide an extensive number of checks including a test at the orbifold point of ap fibrations where the amplitudes compute the t hooft expansion of vevs of wilson loops in chern simons theory on lens spaces we also use our formalism to predict the disk amplitude for the orbifold mathbb c 3 mathbb z 3

curve counting and dt pt correspondence for calabi yau 4 folds abstract recently cao maulik toda defined stable pair invariants of a compact calabi yau 4 fold x their invariants are conjecturally related to the gopakumar vafa type invariants of x defined using gromov witten theory by klemm pandharipande in this paper we consider curve counting invariants of x using hilbert schemes of curves and conjecture a dt pt correspondence which relates these to stable pair invariants of x after providing evidence in the compact case we define analogous invariants for toric calabi yau 4 folds we formulate a vertex formalism for both theories and conjecture a relation between the fully equivariant dt pt vertex which we check in several cases this relation implies a dt pt correspondence for toric calabi yau 4 folds with primary insertions

superroughening versus intrinsic anomalous scaling of surfaces we study kinetically rough surfaces which display anomalous scaling in local properties such as the roughness or the height difference correlation function by studying the power spectrum of the surface and its relation to the height difference correlation we distinguish two independent causes for anomalous scaling one is superroughening global roughness exponent larger than or equal to 1 even if the spectrum behaves nonanomalously another cause is what we term an intrinsically anomalous spectrum in whose scaling an independent exponent exists which induces different scaling properties for small and large length scales we show that in this case the surface does not need to be superrough in order to display anomalous scaling the scaling relations we propose for the structure factor and height difference correlation for intrinsically anomalous surfaces are shown to hold for a random diffusion equation independently of the value of the global roughness exponent below or above one

topological open strings on orbifolds we use the remodeling approach to the b model topological string in terms of recursion relations to study open string amplitudes at orbifold points to this end we clarify modular properties of the open amplitudes and rewrite them in a form that makes their transformation properties under the modular group manifest we exemplify this procedure for the mathbb c 3 mathbb z 3 orbifold point of local mathbb p 2 where we present results for topological string amplitudes for genus zero and up to three holes and for the one holed torus these amplitudes can be understood as generating functions for either open orbifold gromov witten invariants of mathbb c 3 mathbb z 3 or correlation functions in the orbifold cft involving insertions of both bulk and boundary operators

on the gromov witten donaldson thomas correspondence and ruan s conjecture for calabi yau 3 orbifolds for any toric calabi yau 3 orbifold with transverse a singularities we prove the gromov witten donaldson thomas correspondence and ruan s crepant resolution conjecture in all genera

reasoning with conjunctive knowledge abstract we carefully distinguish between variables whose value is the disjunction of a set of elements and those whose values are the conjunction of a set of elements we extend the theory of approximate reasoning from its initial setting of reasoning with disjunctive variables to include conjunctive type variables

the weil petersson geometry of the moduli space of su n 3 calabi yau manifolds i the weil petersson metric is defined on the moduli space of calabi yau manifolds the curvature of this weil petersson metrics is computed and its potential is explicitely defined it is proved that the moduli space of calabi yau manifolds is unobstructed see tian

topological strings and almost modular forms the b model topological string theory on a calabi yau threefold x has a symmetry group generated by monodromies of the periods of x this acts on the topological string wave function in a natural way governed by the quantum mechanics of the phase space h3 x we show that depending on the choice of polarization the genus g topological string amplitude is either a holomorphic quasi modular form or an almost holomorphic modular form of weight 0 under moreover at each genus certain combinations of genus g amplitudes are both modular and holomorphic we illustrate this for the local calabi yau manifolds giving rise to seiberg witten gauge theories in four dimensions and local ip2 and ip1 ip1 as a byproduct we also obtain a simple way of relating the topological string amplitudes near different points in the moduli space which we use to give predictions for gromov witten invariants of the orbifold mathbb c 3 mathbb z 3

the topological vertex we construct a cubic field theory which provides all genus amplitudes of the topological a model for all non compact toric calabi yau threefolds the topology of a given feynman diagram encodes the topology of a fixed calabi yau with schwinger parameters playing the role of kahler classes of the threefold we interpret this result as an operatorial computation of the amplitudes in the b model mirror which is the quantum kodaira spencer theory the only degree of freedom of this theory is an unconventional chiral scalar on a riemann surface in this setup we identify the b branes on the mirror riemann surface as fermions related to the chiral boson by bosonization

string theory and the kauffman polynomial we propose a new precise integrality conjecture for the colored kauffman polynomial of knots and links inspired by large n dualities and the structure of topological string theory on orientifolds according to this conjecture the natural knot invariant in an unoriented theory involves both the colored kauffman polynomial and the colored homfly polynomial for composite representations i e it involves the full homfly skein of the annulus the conjecture sheds new light on the relationship between the kauffman and the homfly polynomials and it implies for example rudolph s theorem we provide various non trivial tests of the conjecture and we sketch the string theory arguments that lead to it

polynomial invariants for torus knots and topological strings we make a precision test of a recently proposed conjecture relating chern simons gauge theory to topological string theory on the resolution of the conifold first we develop a systematic procedure to extract string amplitudes from vacuum expectation values vevs of wilson loops in chern simons gauge theory and then we evaluate these vevs in arbitrary irreducible representations of su n for torus knots we find complete agreement with the predictions derived from the target space interpretation of the string amplitudes we also show that the structure of the free energy of topological open string theory gives further constraints on the chern simons vevs our work provides strong evidence towards an interpretation of knot polynomial invariants as generating functions associated to enumerative problems

macdonald operators and homological invariants of the colored hopf link using a power sum boson realization for the macdonald operators we investigate the gukov iqbal kozcaz and vafa gikv proposal for the homological invariants of the colored hopf link which include khovanov rozansky homology as a special case we prove the polynomiality of the invariants obtained by gikv s proposal for arbitrary representations we derive a closed formula of the invariants of the colored hopf link for antisymmetric representations we argue that a little amendment of gikv s proposal is required to make all the coefficients of the polynomial non negative integers

the topological open string wavefunction we show that in local calabi yau manifolds the topological open string partition function transforms as a wavefunction under modular transformations our derivation is based on the topological recursion for matrix models and it generalizes in a natural way the known result for the closed topological string sector as an application we derive results for vacuum expectation values of 1 2 bps wilson loops in abjm theory at all genera in a strong coupling expansion for various representations

matrix models and stochastic growth in donaldson thomas theory we show that the partition functions which enumerate donaldson thomas invariants of local toric calabi yau threefolds without compact divisors can be expressed in terms of specializations of the schur measure we also discuss the relevance of the hall littlewood and jack measures in the context of bps state counting and study the partition functions at arbitrary points of the kahler moduli space this rewriting in terms of symmetric functions leads to a unitary one matrix model representation for donaldson thomas theory we describe explicitly how this result is related to the unitary matrix model description of chern simons gauge theory this representation is used to show that the generating functions for donaldson thomas invariants are related to tau functions of the integrable toda and toeplitz lattice hierarchies the matrix model also leads to an interpretation of donaldson thomas theory in terms of non intersecting paths in the lock step model of vicious walkers we further show that these generati

a simple proof of gopakumar vafa conjecture for local toric calabi yau manifolds we prove gopakumar vafa conjecture for local toric calabi yau manifolds it is also proven that the local gopakumar vafa invariants of a given class vanish at large genera

gopakumar vafa bps invariants hilbert schemes and quasimodular forms i we prove a closed formula for leading gopakumar vafa bps invariants of local calabi yau geometries given by the canonical line bundles of toric fano surfaces it shares some sim ilar features with gottsche yau zaslow formula connection with hilbert schemes connection with quasimodular forms and qua dratic property after suitable transformation in part i of this paper we will present the case of projective plane more general cases will be presented in part ii the problem of counting curves in algebraic varieties dates back to the nineteenth century classical examples include the famous 27 lines on a cubic surface and the 2875 lines on a quintic 3 fold through the interaction with string theory spectacular progresses in this classi cal branch of algebraic geometry have been made over the years since 1990 s first of all gromov witten theory and its various variants have laid the foundation for the modern treatment of many classical enumerative problems and greatly expanded the range of enumerative problems being considered see pt for an introduction to some of the exciting developments the study of the problems of counting curves in surfaces and calabi yau 3 folds have served both as motivations and applications of gromov witten theory we will recall some results in these directions in 2 and 3 to serve as motivations for this work we emphasize on the following three salient features for the curving counting problems for algebraic surfaces connection with hilbert schemes connection with quasimod ular forms and quadratic properties of the node polynomials after suit able transformation our main results will show that these features are also shared in the curve counting problems of some noncompact calabi yau 3 folds arising as the the total space of the canonical line bundles of toric fano surfaces 1

determination of the hurst exponent by use of wavelet transforms we propose a method for global hurst exponent determination based on wavelets using this method we analyze synthetic data with predefined hurst exponents fracture surfaces and data from economy the results are compared to those obtained with fourier spectral analysis when many samples are available the wavelet and fourier methods are comparable in accuracy however when one or only a few samples are available the wavelet method outperforms the fourier method by a large margin

reliability of self affine measurements reliability and accuracy of the determination of self affine exponents are studied and quantified from the analysis of synthetic self affine profiles and surfaces the self affine exponent is measured using different methods either relying on the determination of a fractal dimension i e box counting and divider methods or directly analyzing the self affine exponent the second group of methods includes the variable bandwidth the first return and the multireturn probability distribution and the power spectrum the accuracy of all these methods is assessed in terms of the difference between an input self affine exponent used for the synthetic construction and the output exponent measured by those different methods the statistical results of this study provide a quantitative estimate of the dependence of the accuracy with the system size and the value of the self affine exponent artifacts in the measurement of self affine profiles or surfaces misorientation signal amplification and local geometric filtering which lead to biased estimates of the self affine exponent are also discussed

ising model and n 2 supersymmetric theories we establish a direct link between massive ising model and arbitrary massiven 2 supersymmetric qft s in two dimensions this explains why the equations which appear in the computation of spin correlations in the non critical ising model are the same as those describing the geometry of vacua inn 2 theories the tau function appearing in the ising model i e the spin correlation function is reinterpreted in then 2 context as a new index in special cases this new index is related to the ray singer analytic torsion and can be viewed as a generalization of that to the loop space of kahler manifolds

gromov witten pairs correspondence for the quintic 3 fold we use the gromov witten pairs descendent correspondence for toric 3 folds and degeneration arguments to establish the gw p correspondence for several compact calabi yau 3 folds including all cy complete intersections in products of projective spaces a crucial aspect of the proof is the study of the gw p correspondence for descendents in relative geometries projective bundles over surfaces relative to a section play a special role the gw p correspondence for calabi yau complete intersections provides a structure result for the gromov witten invariants in a fixed curve class after change of variables the gromov witten series is a rational function in the variable q eiu invariant under q q 1

the analysis of elliptic families i metrics and connections on determinant bundles in this paper we construct the quillen metric on the determinant bundle associated with a family of elliptic first order differential operators we also introduce a unitary connection on and calculate its curvature our results will be applied to the case of dirac operators in a forthcoming paper

the orbifold topological vertex abstract we develop a topological vertex formalism for computing the donaldson thomas invariants of calabi yau orbifolds the basic combinatorial object is the orbifold vertex v g a generating function for the number of 3d partitions asymptotic to 2d partitions and colored by representations of a finite abelian group g acting on c 3 in the case where g z n acting on c 3 with transverse a n 1 quotient singularities we give an explicit formula for v g in terms of schur functions we discuss applications of our formalism to the donaldson thomas crepant resolution conjecture and to the orbifold donaldson thomas gromov witten correspondence we also explicitly compute the donaldson thomas partition function for some simple orbifold geometries the local football p a b 1 and the local b z 2 gerbe

stable quotients and the holomorphic anomaly equation abstract we study the fundamental relationship between stable quotient invariants and the b model for local p 2 in all genera our main result is a direct geometric proof of the holomorphic anomaly equation in the precise form predicted by b model physics the method yields new holomorphic anomaly equations for an infinite class of twisted theories on projective spaces an example of such a twisted theory is the formal quintic defined by a hyperplane section of p 4 in all genera via the euler class of a complex the formal quintic theory is found to satisfy the holomorphic anomaly equations conjectured for the true quintic theory therefore the formal quintic theory and the true quintic theory should be related by transformations which respect the holomorphic anomaly equations

the quantum mckay correspondence for polyhedral singularities let g be a polyhedral group namely a finite subgroup of so 3 nakamura s g hilbert scheme provides a preferred calabi yau resolution y of the polyhedral singularity 3 g the classical mckay correspondence describes the classical geometry of y in terms of the representation theory of g in this paper we describe the quantum geometry of y in terms of r an ade root system associated to g namely we give an explicit formula for the gromov witten partition function of y as a product over the positive roots of r in terms of counts of bps states gopakumar vafa invariants our result can be stated as a correspondence each positive root of r corresponds to one half of a genus zero bps state as an application we use the crepant resolution conjecture to provide a full prediction for the orbifold gromov witten invariants of 3 g

conjunctive and disjunctive combination of belief functions induced by nondistinct bodies of evidence dempster s rule plays a central role in the theory of belief functions however it assumes the combined bodies of evidence to be distinct an assumption which is not always verified in practice in this paper a new operator the cautious rule of combination is introduced this operator is commutative associative and idempotent this latter property makes it suitable to combine belief functions induced by reliable but possibly overlapping bodies of evidence a dual operator the bold disjunctive rule is also introduced this operator is also commutative associative and idempotent and can be used to combine belief functions issues from possibly overlapping and unreliable sources finally the cautious and bold rules are shown to be particular members of infinite families of conjunctive and disjunctive combination rules based on triangular norms and conorms

stable pairs and the homfly polynomial given a planar curve singularity we prove a conjecture of oblomkov shende relating the geometry of its hilbert scheme of points to the homfly polynomial of the associated algebraic link more generally we prove an extension of this conjecture due to diaconescu hua soibelman relating stable pair invariants on the conifold to the colored homfly polynomial of the algebraic link our proof uses wall crossing techniques to prove a blowup identity on the algebro geometric side we prove a matching identity for the colored homfly polynomials of a link using skein theoretic techniques

the local gromov witten theory of mathbb c mathbb p 1 and integrable hierarchies in this paper we begin the study of the relationship between the local gromov witten theory of calabi yau rank two bundles over the projective line and the theory of integrable hierarchies we first of all construct explicitly in a large number of cases the hamiltonian dispersionless hierarchies that govern the full descendent genus zero theory our main tool is the application of dubrovin s formalism based on associativity equations to the known results on the genus zero theory from local mirror symmetry and localization the hierarchies we find are apparently new with the exception of the resolved conifold mathcal o mathbb p 1 1 bigoplus mathcal o mathbb p 1 1 in the equivariantly calabi yau case for this example the relevant dispersionless system turns out to be related to the long wave limit of the ablowitz ladik lattice this identification provides us with a complete procedure to reconstruct the dispersive hierarchy which should conjecturally be related to the higher genus theory of the resolved conifold we give a complete proof of this conjecture for genus g 1 our methods are based on establishing analogously to the case of kdv a quasi triviality property for the ablowitz ladik hierarchy at the leading order of the dispersive expansion we furthermore provide compelling evidence in favour of the resolved conifold ablowitz ladik correspondence at higher genus by testing it successfully in the primary sector for g 2

the transferable belief model abstract we describe the transferable belief model a model for representing quantified beliefs based on belief functions beliefs can be held at two levels 1 a credal level where beliefs are entertained and quantified by belief functions 2 a pignistic level where beliefs can be used to make decisions and are quantified by probability functions the relation between the belief function and the probability function when decisions must be made is derived and justified four paradigms are analyzed in order to compare bayesian upper and lower probability and the transferable belief approaches

evidential reasoning rule for evidence combination this paper aims to establish a unique evidential reasoning er rule to combine multiple pieces of independent evidence conjunctively with weights and reliabilities the novel concept of weighted belief distribution wbd is proposed and extended to wbd with reliability wbdr to characterise evidence in complement of belief distribution bd introduced in dempster shafer d s theory of evidence the implementation of the orthogonal sum operation on wbds and wbdrs leads to the establishment of the new er rule the most important property of the new er rule is that it constitutes a generic conjunctive probabilistic reasoning process or a generalised bayesian inference process it is shown that the original er algorithm is a special case of the er rule when the reliability of evidence is equal to its weight and the weights of all pieces of evidence are normalised it is proven that email protected s rule is also a special case of the er rule when each piece of evidence is fully reliable the er rule completes and enhances email protected s rule by identifying how to combine pieces of fully reliable evidence that are highly or completely conflicting through a new reliability perturbation analysis the main properties of the er rule are explored to facilitate its applications several existing rules are discussed and compared with the er rule numerical and simulation studies are conducted to show the features of the er rule

three partition hodge integrals and the topological vertex we give a new proof of the equivalence between the cubic hodge integrals and the topological vertex in topological string theory a central role is played by the notion of generalized shift symmetries in a fermionic realization of the two dimensional quantum torus algebra these algebraic relations of operators in the fermionic fock space are used to convert generating functions of the cubic hodge integrals and the topological vertex to each other as a byproduct the generating function of the cubic hodge integrals at special values of the parameters overrightarrow w therein is shown to be a tau function of the generalized kdv aka gelfand dickey hierarchies

chern simons perturbation theory ii we study the perturbation theory for three dimensional chern simons quantum field theory on a general compact three manifold without boundary we show that after a simple change of variables the action obtained by brs gauge fixing in the lorentz gauge has a superspace formulation the basic properties of the propagator and the feynman rules are written in a precise manner in the language of differential forms using the explicit description of the propagator singularities we prove that the theory is finite finally the anomalous metric dependence of the 2 loop partition function on the riemannian metric which was introduced to define the gauge fixing can be cancelled by a local counterterm as in the 1 loop case in fact the counterterm is equal to the chern simons action of the metric connection normalized precisely as one would expect based on the framing dependence of witten s exact solution invited talk at the xxth conference on differential geometric methods in physics new york june 1991

self affine nature of the stress strain behavior of thin fiber networks the stress strain behavior of toilet paper is studied we find that the damaged parts of stress strain curves possess a self affine scaling invariance moreover we find that the stress strain behavior and the rupture line roughness are characterized by the same scaling hurst exponent h which is not universal rather it changes from sample to sample the variations on h are mainly due to fluctuations in the paper structure which are larger than statistical errors within a sample furthermore the same exponent governs the changes in the stress strain curve as the strain rate increases the fractal damage model is employed to explain experimental observations

wall crossing as seen by matrix models the number of bps bound states of d branes on a calabi yau manifold depends on two sets of data the bps charges and the stability conditions for d0 and d2 branes bound to a single d6 brane wrapping a calabi yau 3 fold x both are naturally related to the kahler moduli space mathcal m x we construct unitary one matrix models which count such bps states for a class of toric calabi yau manifolds at infinite t hooft coupling the matrix model for the bps counting on x turns out to give the topological string partition function for another calabi yau manifold y whose kahler moduli space mathcal m y contains two copies of mathcal m x one related to the bps charges and another to the stability conditions the two sets of data are unified in mathcal m y the matrix models have a number of other interesting features they compute spectral curves and mirror maps relevant to the remodeling conjecture for finite t hooft coupling they give rise to yet more general geometry widetilde y containing y

gromov witten donaldson thomas correspondence for toric 3 folds we prove the equivariant gromov witten theory of a nonsingular toric 3 fold x with primary insertions is equivalent to the equivariant donaldson thomas theory of x as a corollary the topological vertex calculations by agangic klemm marino and vafa of the gromov witten theory of local calabi yau toric 3 folds are proven to be correct in the full 3 leg setting

conditional probability on mv algebras an appropriate definition of a conditional probability on an mv algebra was an open problem mentioned in riecan and mundici handbook of measure theory north holland amsterdam 2002 we propose some concept of conditional probability state on a complete mv algebra with product its basic properties will be proven and it will also be demonstrated that the conditional probability in classical probability theory is a special case of this definition moreover the paper contains also a discussion of the interpretation of fuzzy sets and conditioning in fuzzy probability theory

towards mirror symmetry for varieties of general type abstract the goal of this paper is to propose a theory of mirror symmetry for varieties of general type using landau ginzburg mirrors as motivation we describe the mirror of a hypersurface of general type and more generally varieties of non negative kodaira dimension as the critical locus of the zero fibre of a certain landau ginzburg potential the critical locus carries a perverse sheaf of vanishing cycles our main result shows that one obtains the interchange of hodge numbers expected in mirror symmetry this exchange is between the hodge numbers of the hypersurface and certain hodge numbers defined using a mixed hodge structure on the hypercohomology of the perverse sheaf

link homologies and the refined topological vertex we establish a direct map between refined topological vertex and sl n homological invariants of the of hopf link which include khovanov rozansky homol ogy as a special case this relation provides an exact answer for homological invariants of the hopf link whose components are colored by arbitrary representations of sl n at present the mathematical formulation of such homological invariants is available only for the fundamental representation the khovanov rozansky theory and the rela tion with the refined topological vertex should be useful for categorizing quantum group invariants associated with other representations r1 r2 our result is a first direct veri fication of a series of conjectures which identifies link homologies with the hilbert space of bps states in the presence of branes where the physical interpretation of gradings is in terms of charges of the branes ending on lagrangian branes

topological strings and integrable hierarchies we consider the topological b model on local calabi yau geometries we show how one can solve for the amplitudes by using w algebra symmetries which encodes the symmetries of holomorphic diffeomorphisms of the calabi yau in the highly effective fermionic brane formulation this leads to a free fermion description of the amplitudes furthermore we argue that topological strings on calabi yau geometries provide a unifying picture connecting non critical super strings integrable hierarchies and various matrix models in particular we show how the ordinary matrix model the double scaling limit of matrix models and kontsevich like matrix model are all related and arise from studying branes in specific local calabi yau three folds we also show how a model topological string on p 1 and local toric threefolds and in particular the topological vertex can be realized and solved as b model topological string amplitudes on a calabi yau manifold

mirror symmetry for orbifold hurwitz numbers we study mirror symmetry for orbifold hurwitz numbers we show that the laplace transform of orbifold hurwitz numbers satisfy a dierential recursion which is then proved to be equivalent to the integral recursion of eynard and orantin with spectral curve given by the r lambert curve we argue that the r lambert curve also arises in the innite framing limit of orbifold gromov witten theory of c 3 z rz finally we prove that the mirror model to orbifold hurwitz numbers admits a quantum curve

incomplete conjunctive information abstract many information systems capable of handling incomplete or fuzzy information manipulate objects with single valued attributes information is then said to be disjunctive information is said to be conjunctive when pertaining to many valued attributes while a piece of incomplete disjunctive information is easily represented by means of a set of mutually exclusive possible values modeling incomplete conjunctive information theoretically leads to consider families of sets since attributes are then set valued under complete information some proposals are made in order to efficiently and rigorously represent incomplete conjunctive information and deal with query evaluation especially in the case where only upper and or lower bounds of the set of values of a many valued attribute are known applications of this approach can be expected for the processing of time intervals as well as spatial reasoning among other topics in knowledge base management

a formula of two partition hodge integrals jmg n where tpi ci l is the first chern class of l and xj cj e is the j th chern class of the hodge bundle the study of hodge integrals is an important part of intersection theory on mg n hodge integrals also naturally arise when one computes gromov witten invariants by localization techniques for example the following generating series of hodge integrals arises when one computes local invariants of a toric fano surface in a calabi yau 3 fold by virtual localization 33

a note on computations of the d brane superpotential we develop some computational methods for the integrals over the 3 chains on the compact calabi yau 3 folds that play a prominent role in the analysis of the topological b model in the context of the open mirror symmetry we discuss such 3 chain integrals in two approaches in the first approach we provide an algorithm to obtain the inhomogeneous picard fuchs equations in the second approach we discuss the analytic continuation of the period integral to compute the 3 chain integral directly the latter direct integration method is applicable for both on shell and off shell formalisms

canonical decomposition of belief functions based on teugels representation of the multivariate bernoulli distribution abstract a canonical decomposition of belief functions is a unique decomposition of belief functions into elementary pieces of evidence smets found an equivalent representation of belief functions which he interpreted as a canonical decomposition however his proposal is not entirely satisfactory as it involves elementary pieces of evidence corresponding to a generalisation of belief function axioms whose semantics lacks formal justifications in this paper a new canonical decomposition relying only on well defined concepts is proposed in particular it is based on a means to induce belief functions from the multivariate bernoulli distribution and on teugels representation of this distribution which consists of the means and the central moments of the underlying bernoulli random variables according to our decomposition a belief function results from as many crisp pieces of information as there are elements in its domain and from simple probabilistic knowledge concerning their marginal reliability and the dependencies between their reliability in addition we show that instead of interpreting with some difficulty smets representation of belief functions as a canonical decomposition it is possible to give it a different and well defined semantics in terms of measures of information associated with the reliability of the pieces of information in our decomposition