complete divisibility problems for slowly utilized oracles abstract the concept of np completeness relative to a slowly utilized oracle is introduced and shown to be useful for providing evidence of intractability of some problems that are not known to be np complete one such problem is to decide if a sparse polynomial has a root in the integers mod p for prime p relationships between unrelativized complexity relative to a slowly utilized oracle are also given

on the complexity of familiar functions and numbers this paper examines low complexity approximations to familiar functions and numbers the intent is to suggest that it is possible to base a taxonomy of such functions and numbers on their computational complexity a central theme is that traditional methods of approximation are often very far from optimal while good or optimal methods are often very far from obvious for most functions provably optimal methods are not known however the gap between what is known and what is possible is often small a considerable number of open problems are posed and a number of related examples are presented

a preparation theorem for weierstrass systems it is shown that lion and rolin s preparation theorem for globally subanalytic functions holds for the collection of definable functions in any expansion of the real ordered field by a weierstrass system

cartan decomposition subgroups of 2 for g sl 3 r and g so 2 n we give explicit practical conditions that determine whether or not a closed connected subgroup h of g has the property that there exists a compact subset c of g with chc g to do this we fix a cartan decomposition g ka k of g and then carry out an approximate calculation of khk n a for each closed connected subgroup h of g

modelling dependence within joint tail regions standard approaches for modelling dependence within joint tail regions are based on extreme value methods which assume max stability a particular form of joint tail dependence we develop joint tail models based on a broader class of dependence structure which provides a natural link between max stable models and weaker forms of dependence including independence and negative association this approach overcomes many of the problems that are encountered with standard methods and is the basis for a poisson process representation that generalizes existing bivariate results we apply the new techniques to simulated and environmental data and demonstrate the marked advantage that the new approach offers for joint tail extrapolation

sublinear root detection and new hardness results for sparse polynomials over finite fields we present a deterministic 2 o t q frac t 2 t 1 o 1 algorithm to decide whether a univariate polynomial f with t monomial terms and degree q has a root in the finite field math

approximate generalizations and computational experiments in this paper i demonstrate how one can generalize finitely many examples to statements about infinite classes of economic models if there exist upper bounds on the number of connected components of one dimensional linear subsets of the set of parameters for which a conjecture is true one can conclude that it is correct for all parameter values in the class considered except for a small residual set once one has verified the conjecture for a predetermined finite set of points i show how to apply this insight to computational experiments and spell out assumptions on the economic fundamentals that ensure that the necessary bounds on the number of connected components exist

direct estimation of the fiber orientation density function from diffusion weighted mri data using spherical deconvolution diffusion weighted magnetic resonance imaging can provide information related to the arrangement of white matter fibers the diffusion tensor is the model most commonly used to derive the orientation of the fibers within a voxel however this model has been shown to fail in regions containing several fiber populations with distinct orientations a number of alternative models have been suggested such as multiple tensor fitting q space and q ball imaging however each of these has inherent limitations in this study we propose a novel method for estimating the fiber orientation distribution directly from high angular resolution diffusion weighted mr data without the need for prior assumptions regarding the number of fiber populations present we assume that all white matter fiber bundles in the brain share identical diffusion characteristics thus implicitly assigning any differences in diffusion anisotropy to partial volume effects the diffusion weighted signal attenuation measured over the surface of a sphere can then be expressed as the convolution over the sphere of a response function the diffusion weighted attenuation profile for a typical fiber bundle with the fiber orientation density function odf the fiber odf the distribution of fiber orientations within the voxel can therefore be obtained using spherical deconvolution the properties of the technique are demonstrated using simulations and on data acquired from a volunteer using a standard 1 5 t clinical scanner the technique can recover the fiber odf in regions of multiple fiber crossing and holds promise for applications such as tractography

entropy and asymptotic geometry of non symmetric convex bodies abstract we extend to the general not necessarily centrally symmetric setting a number of basic results of local theory which were known before for centrally symmetric bodies and were using very essentially the symmetry in their proofs some of these extensions look surprising the main additional tool is a study of volume behavior around the centroid of the body

unsupervised self normalized change point testing for time series abstractwe propose a new self normalized method for testing change points in the time series setting self normalization has been celebrated for its ability to avoid direct estimation of the nuisance asymptotic variance and its flexibility of being generalized to handle quantities other than the mean however it was developed and mainly studied for constructing confidence intervals for quantities associated with a stationary time series and its adaptation to change point testing can be nontrivial as direct implementation can lead to tests with nonmonotonic power compared with existing results on using self normalization in this direction the current article proposes a new self normalized change point test that does not require prespecifying the number of total change points and is thus unsupervised in addition we propose a new contrast based approach in generalizing self normalized statistics to handle quantities other than the mean which is specifically tailored for change point testing monte car

integrability of oscillatory functions on local fields transfer principles for oscillatory functions on local fields coming from motivic exponential functions we show that integrability over q n p implies integrability over f p t n for large p and vice versa more generally the integrability only depends on the isomorphism class of the residue field of the local field once the characteristic of the residue field is large enough this principle yields general local integrability results for harish chandra characters in positive characteristic as we show in other work transfer principles for related conditions such as boundedness and local integrability are also obtained the proofs rely on a thorough study of loci of integrability to which we give a geometric meaning by relating them to zero loci of functions of a specific kind

relational queries over interpreted structures we rework parts of the classical relational theory when the underlying domain is a structure with some interpreted operations that can be used in queries we identify parts of the classical theory that go through as before when interpreted structure is present parts that go through only for classes of nicely behaved structures and parts that only arise in the interpreted case the first category include a number of results on language equivalence and expressive power characterizations for the active domain semantics for a variety of logics under this semantics quantifiers range over elements of a relational database the main kind of results we prove here are generic collapse results for generic queries adding operations beyond order does not give us extra power the second category includes results on the natural semantics under which quantifiers range over the entire interpreted structure we prove for a variety of structures natural active collapse results showing that using unrestricted quantification does not give us any extra power moreover for a variety of structures including the real field we give a set of algorithms for eliminating unbounded quantifications in favor of bounded ones furthermore we extend these collapse results to a new class of higher order logics that mix unbounded and bounded quantification we give a set of normal forms for these logics under special conditions on the interpreted structures as a by product we obtain an elementary proof of the fact that parity test is not definable in the relational calculus with polynomial inequality constraints we also give examples of structures with nice model theoretic properties over which the natural active collapse fails

definable sets in ordered structures i this paper introduces and begins the study of a well behaved class of linearly ordered structures the minimal structures the definition of this class and the corresponding class of theories the strongly dlminlmal theories is made in analogy with the notions from stability theory of minimal structures and strongly minimal theories theorems 2 1 and 2 3 respectively provide characterizations of 41 minimal ordered groups and rings several other simple results are collected in 3 the primary tool in the analysis of minimal structures is a strong analogue of ii forking symmetry given by theorem 4 2 this result states that any parametri cally definable unary function in an yminimal structure is piecewise either constant or an ore er preserving or reversing bijection of intervals the results that follow include the existence and uniqueness of prime models over sets theorem 5 1 and a characterization of all bto categorical aminimal structures theorem 6 1 1 introduction the class of linearly ordered structures has long been an im portant subject of concern to model theorists impressive results have been obtained in the study of models of several particular theories that extend the theory of linear order among those theories that have been approached successfully are peano arithmetic the theory of ordered abelian groups that of real closed fields and that of linear order itself yet very little has been done in the way of developing a general model theory for ordered structures in this paper we develop the model theory for a class of linearly ordered structures that we isolate by demanding that a structure in this class satisfy a condition whose effect is that the linear ordering and the algebraic part of the structure behave quite well with respect to one another let l be a finitary first order language and w an l structure a set of n tuples a c x is said to be parametrically definable if there is some l formula

stochastic completion fields a neural model of illusory contour shape and salience we describe an algorithm and representation level theory of illusory contour shape and salience unlike previous theories our model is derived from a single assumption that the prior probability distribution of boundary completion shape can be modeled by a random walk in a lattice whose points are positions and orientations in the image plane i e the space that one can reasonably assume is represented by neurons of the mammalian visual cortex our model does not employ numerical relaxation or other explicit minimization but instead relies on the fact that the probability that a particle following a random walk will pass through a given position and orientation on a path joining two boundary fragments can be computed directly as the product of two vector field convolutions we show that for the random walk we define the maximum likelihood paths are curves of least energy that is on average random walks follow paths commonly assumed to model the shape of illusory contours a computer model is demonstrated on numerous illusory contour stimuli from the literature

a new class of models for bivariate joint tails summary a fundamental issue in applied multivariate extreme value analysis is modelling dependence within joint tail regions the primary focus of this work is to extend the classical pseudopolar treatment of multivariate extremes to develop an asymptotically motivated representation of extremal dependence that also encompasses asymptotic independence starting with the usual mild bivariate regular variation assumptions that underpin the coefficient of tail dependence as a measure of extremal dependence our main result is a characterization of the limiting structure of the joint survivor function in terms of an essentially arbitrary non negative measure that must satisfy some mild constraints we then construct parametric models from this new class and study in detail one example that accommodates asymptotic dependence asymptotic independence and asymmetry within a straightforward parsimonious parameterization we provide a fast simulation algorithm for this example and detail likelihood based inference including tests for asymptotic dependence and symmetry which are useful for submodel selection we illustrate this model by application to both simulated and real data in contrast with the classical multivariate extreme value approach which concentrates on the limiting distribution of normalized componentwise maxima our framework focuses directly on the structure of the limiting joint survivor function and provides significant extensions of both the theoretical and the practical tools that are available for joint tail modelling

trace inference curvature consistency and curve detection an approach is described for curve inference that is based on curvature information the inference procedure is divided into two stages a trace inference stage which is the subject of the present work and a curve synthesis stage it is shown that recovery of the trace of a curve requires estimating local models for the curve at the same time and that tangent and curvature information are sufficient these make it possible to specify powerful constraints between estimated tangents to a curve in terms of a neighborhood relationship called cocircularity and between curvature estimates in terms of a curvature consistency relation because all curve information is quantized special care must be taken to obtain accurate estimates of trace points tangents and curvatures this issue is addressed specifically to the introduction of a smoothness constraint and a maximum curvature constraint the procedure is applied to two types of images artificial images designed to evaluate curvature and noise sensitivity and natural images

flow based fiber tracking with diffusion tensor and q ball data validation and comparison to principal diffusion direction techniques in this study we evaluate the performance of a flow based surface evolution fiber tracking algorithm by means of a physical anisotropic diffusion phantom with known connectivity we introduce a novel speed function for surface evolution that is derived from either diffusion tensor dt data high angular resolution diffusion hard data or a combined dt hard hybrid approach we use the model free q ball imaging qbi approach for hard reconstruction the anisotropic diffusion phantom allows us to compare and evaluate the performance of different fiber tracking approaches in the presence of real imaging artifacts noise and subvoxel partial volume averaging of fiber directions the surface evolution approach using the full diffusion tensor as opposed to the principal diffusion direction pdd only is compared to pdd based line propagation fiber tracking additionally dt reconstruction is compared to hard reconstruction for fiber tracking both using surface evolution we show the potential for surface evolution using the full diffusion tensor to map connections in regions of subvoxel partial volume averaging of fiber directions which can be difficult to map with pdd based methods we then show that the fiber tracking results can be improved by using high angular resolution reconstruction of the diffusion orientation distribution function in cases where the diffusion tensor model fits the data poorly

the field of reals with multisummable series and the exponential function we show that the field of real numbers with multisummable real power series is model complete o minimal and polynomially bounded further expansion by the exponential function yields again a model complete and o minimal structure which is exponentially bounded and in which the gamma function on the positive real line is definable 2000 mathematics subject classification primary 03c10 32b05 32b20 secondary 26e05

a diffusion tensor imaging tractography algorithm based on navier stokes fluid mechanics we introduce a fluid mechanics based tractography method for estimating the most likely connection paths between points in diffusion tensor imaging dti volumes we customize the navier stokes equations to include information from the diffusion tensor and simulate an artificial fluid flow through the dti image volume we then estimate the most likely connection paths between points in the dti volume using a metric derived from the fluid velocity vector field we validate our algorithm using digital dti phantoms based on a helical shape our method segmented the structure of the phantom with less distortion than was produced using implementations of heat based partial differential equation pde and streamline based methods in addition our method was able to successfully segment divergent and crossing fiber geometries closely following the ideal path through a digital helical phantom in the presence of multiple crossing tracts to assess the performance of our algorithm on anatomical data we applied our method to dti volumes from normal human subjects our method produced paths that were consistent with both known anatomy and directionally encoded color images of the dti dataset

nonparametric tests for constant tail dependence with an application to energy and finance the present paper proposes new tests for detecting structural breaks in the tail dependence of multivariate time series using the concept of tail copulas to obtain asymptotic properties we derive a new limit result for the sequential empirical tail copula process moreover consistency of both the tests and a change point estimator are proven we analyze the finite sample behavior of the tests by monte carlo simulations finally and crucial from a risk management perspective we apply the new findings to datasets from energy and financial markets

hardy type derivations on generalised series fields abstract we consider the valued field k r of generalised series with real coefficients and monomials in a totally ordered multiplicative group we investigate how to endow k with a series derivation that is a derivation that satisfies some natural properties such as commuting with infinite sums strong linearity and an infinite version of leibniz rule we characterise when such a derivation is of hardy type that is when it behaves like differentiation of germs of real valued functions in a hardy field we provide a necessary and sufficient condition for a series derivation of hardy type to be surjective

limit theorems for empirical processes of cluster functionals let x n i 1 i n m is an element of n be a triangular array of row wise stationary r d valued random variables we use a blocks method to define clusters of extreme values the rows of x n i are divided into m n blocks y n j and if a block contains at least one extreme value the block is considered to contain a cluster the cluster starts at the first extreme value in the block and ends at the last one the main results are uniform central limit theorems for empirical processes z n f 1 root nv n sigma mn j 1 f y n y j ef y n y j for v n p x n x i not equal 0 and f belonging to classes of cluster functionals that is functions of the blocks y n y j which only depend on the cluster values and which are equal to 0 if y n y j does not contain a cluster conditions for finite dimensional convergence include beta mixing suitable lindeberg conditions and convergence of covariances to obtain full uniform convergence we use either bracketing entropy or bounds on covering numbers with respect to a random semi metric the latter makes it possible to bring the powerful vapnik cervonenkis theory to bear applications include multivariate tail empirical processes and empirical processes of cluster values and of order statistics in clusters although our main field of applications is the analysis of extreme values the theory can be applied more generally to rare events occurring for example in nonparametric curve estimation

definable sets in ordered structures on introduit la notion de theorie o minimale des structures ordonnees une telle theorie etant telle que les sous ensembles definissables de ses modeles soient particulierement simples

statistics for near independence in multivariate extreme values we propose a multivariate extreme value threshold model for joint tail estimation which overcomes the problems encountered with existing techniques when the variables are near independence we examine inference under the model and develop tests for independence of extremes of the marginal variables both when the thresholds are fixed and when they increase with the sample size motivated by results obtained from this model we give a new and widely applicable characterisation of dependence in the joint tail which includes existing models as special cases a new parameter which governs the form of dependence is of fundamental importance to this characterisation by estimating this parameter we develop a diagnostic test which assesses the applicability of bivariate extreme value joint tail models the methods are demonstrated through simulation and by analysing two previously published data sets

o minimal hauptvermutung for polyhedra i milnor discovered two compact polyhedra which are homeomorphic but not pl homeomorphic a counterexample to the hauptvermutung he constructed the homeomorphism by a finite procedure repeated infinitely often informally we call a procedure constructive if it consists of an explicit procedure that is repeated only finitely many times in this sense milnor did not give a constructive procedure to define the homeomorphism between the two polyhedra in the case where the homeomorphism is semialgebraic the author and yokoi proved that the polyhedra in r n are pl homeomorphic in that article the required pl homeomorphism was not constructively defined from the given homeomorphism in the present paper we obtain the pl homeomorphism by a constructive procedure starting from the homeomorphism we prove in fact that for any ordered field r equipped with any o minimal structure two definably homeomorphic compact polyhedra in r n are pl homeomorphic the o minimal hauptvermutung theorem 1 1 together with the fact that any compact definable set is definably homeomorphic to a compact polyhedron we can say that o minimal topology is tame

euler spiral for shape completion in this paper we address the curve completion problem e g the geometric continuation of boundaries of objects which are temporarily interrupted by occlusion also known as the gap completion or shape completion problem this problem is a significant element of perceptual grouping of edge elements and has been approached by using cubic splines or biarcs which minimize total curvature squared elastica as motivated by a physical analogy our approach is motivated by railroad design methods of the early 1900 s which connect two rail segments by transition curves and by the work of knuth on mathematical typography we propose that in using an energy minimizing solution completion curves should not penalize curvature as in elastica but curvature variation the minimization of total curvature variation leads to an euler spiral solution a curve whose curvature varies linearly with arclength the construction of this curve from a pair of points and tangents at these points is reduced to a nonlinear system of equations involving fresnel integrals whose solution relies on optimization from a suitable initial condition constrained to satisfy given boundary conditions since the choice of an appropriate initial curve is critical in this optimization we analytically derive an optimal solution in the class of biarc curves which is then used as the initial curve the resulting interpolations yield intuitive interpolation across gaps and occlusions and are extensible in contrast to scale invariant elastica in addition euler spiral segments can be used in other applications of curve completions e g modeling boundary segments between curvature extrema or skeletal branch geometry

tests for permutation polynomials if mathbb f q is a finite field and f in mathbb f q x then f is called a permutation polynomial if the mapping mathbb f q to mathbb f q induced by f is bijective this property can be tested by a probabilistic algorithm whose number of operations is polynomial in fact essentially linear in the input size i e in deg f cdot log q this is extended to almost permutation polynomials whose value set consists of almost all elements of mathbb f q

a game theoretic approach to fault diagnosis and identification of hybrid systems physical systems can fail for this reason the problem of identifying and reacting to faults has received a lot of attention in the control and computer science communities in this paper we study the fault diagnosis problem for hybrid systems from a game theoretical point of view a hybrid system is a system mixing continuous and discrete behaviours that cannot be faithfully modelled neither by using a formalism with continuous dynamics only nor by a formalism including only discrete dynamics we model hybrid systems as hybrid automata and add distinguished actions to describe faults we define a fault identification game on them using two players the environment and the identifier the environment controls the evolution of the system and chooses whether and when a fault occurs the identifier observes the external behaviour of the system and announces whether a fault has occurred or not existence of a winning strategy for the identifier implies that faults can be detected correctly while computing such a winning strategy corresponds to implementing an identifier for the system we will show how to determine the existence of a winning strategy and how to compute it for all decidable classes of hybrid automata that admit a finite bisimulation quotient

comparison theorems for o minimal singular co homology fct grant sfrh bpd 6015 2001 european research and training network hprn ct 2001 00271 raag

towards estimating extremal serial dependence via the bootstrapped extremogram abstract davis and mikosch 2009a introduced the extremogram as a flexible quantitative tool for measuring various types of extremal dependence in a stationary time series there we showed some standard statistical properties of the sample extremogram a major difficulty was the construction of credible confidence bands for the extremogram in this paper we employ the stationary bootstrap to overcome this problem the use of the stationary bootstrap for the extremogram and the resulting interpretations are illustrated with several financial time series

the real field with convergent generalized power series we construct a model complete and o minimal expansion of the field of real numbers in which each real function given on 0 1 by a series cnxn with 0 n and cn r n 1 is definable this expansion is polynomially bounded

amoebas monge ampere measures and triangulations of the newton polytope the amoeba of a holomorphic function f is by definition the image in mathbf r n of the zero locus of f under the simple mapping that takes each coordinate to the logarithm of its modulus the terminology was introduced in the 1990s by the famous biologist and mathematician israel gelfand and his coauthors kapranov and zelevinsky gkz in this paper we study a natural convex potential function n f with the property that its monge ampere mass is concentrated to the amoeba of f we obtain results of two kinds by approximating n f with a piecewise linear function we get striking combinatorial information regarding the amoeba and the newton polytope of f by computing the monge ampere measure we find sharp bounds for the area of amoebas in mathbf r n we also consider systems of functions f 1 dots f n and prove a local version of the classical bernstein theorem on the number of roots of systems of algebraic equations

the six grothendieck operations on o minimal sheaves in this paper we develop the formalism of the grothendieck six operations on o minimal sheaves the grothendieck formalism allows us to obtain o minimal versions of i derived projection formula ii universal coefficient formula iii derived base change formula iv kunneth formula v local and global verdier duality

filtered multitensor tractography we describe a technique that uses tractography to drive the local fiber model estimation existing techniques use independent estimation at each voxel so there is no running knowledge of confidence in the estimated model fit we formulate fiber tracking as recursive estimation at each step of tracing the fiber the current estimate is guided by those previous to do this we perform tractography within a filter framework and use a discrete mixture of gaussian tensors to model the signal starting from a seed point each fiber is traced to its termination using an unscented kalman filter to simultaneously fit the local model to the signal and propagate in the most consistent direction despite the presence of noise and uncertainty this provides a causal estimate of the local structure at each point along the fiber using two and three fiber models we demonstrate in synthetic experiments that this approach significantly improves the angular resolution at crossings and branchings in vivo experiments confirm the ability to trace through regions known to contain such crossing and branching while providing inherent path regularization

characteristic cycles of constructible sheaves in his paper k kashiwara introduced the notion of characteristic cycle for complexes of constructible sheaves on manifolds let x be a real analytic manifold and f a complex of sheaves of c vector spaces on x whose cohomology is constructible with respect to a subanalytic strati cation the characteristic cycle cc f is a subanalytic lagrangian cycle with in nite support and with values in the orientation sheaf of x in the cotangent bundle t x the de nition of cc f is morse theoretic heuristically cc f encodes the in nitesimal change of the euler characteristic of the stalks of f along the various directions in x it tends to be di cult in practice to calculate cc f explicitly for all but the simplest complexes f on the other hand the characteristic cycle construction has good functorial properties the behavior of cc f with respect to the operations of proper direct image verdier duality and non characteristic inverse image of f is well understood ks in this paper we describe the e ect of the operation of direct image by an open embedding combining our result with those that were previously known we obtain descriptions of cc rf f and cc f f analogous to those in ks for arbitrary morphisms f x y in the semi algebraic category and complexes f with semi algebraically constructible cohomology in e ect this provides an axiomatic characterization of the functor cc at least in the semi algebraic context our arguments do apply more generally in the subanalytic case but because statements become quite convoluted we shall not strive for the greatest degree of generality as a concrete application we consider the case of the ag manifold x of a complex semisimple lie algebra g here the weyl group w of g operates

ax lindemann for mathcal a _g we prove the ax lindemann theorem for the coarse moduli space a g of principally polarized abelian varieties of dimension g 1 we affirm the andre oort conjecture unconditionally for a g for g 6 and under grh for all g

isomorphism theorem for bss recursively enumerable sets over real closed fields the main result of this paper lies in the framework of bss computability it shows roughly that any recursively enumerable set s in rn n where r is a real closed field is isomorphic to rdims by a bijection which is decidable over s moreover the map s is computable some related matters are also considered like characterization of the real closed fields with a r e set of infinitesimals and the dimension of r e sets

radial projection an efficient update rule for relaxation labeling relaxation labeling uses contextual information for finding consistent labelings of graphs although relaxation labeling is parallel and iterative the complexity of updating with standard rules is too costly for practical implementation a description is given of a computationally more efficient updating rule that utilizes radial projection instead of normal projection to avoid the complexities incurred by previous update rules when boundaries to the labeling space are encountered this reduction in complexity is achieved by first restricting support vectors to the positive quadrant and then using radial projection onto the constraint instead of normal projection crucial order information is conserved through smooth convergence towards the optimum and a rate of convergence proportional to the magnitudes of the support functions

sources of nonmonotonic power when testing for a shift in mean of a dynamic time series sources of nonmonotonic power are uncovered for a wide variety of tests for a shift in the mean of a dynamic time series two main sources of nonmonotonic power are found the first source is the behavior of the estimate of error variance under the alternative hypothesis of a shift in mean in particular if the error variance is estimated under the null hypothesis nonmonotonic power can result the second source is the presence of a lagged dependent variable in the estimated regression

the rational points of a definable set let x r n be a set that is definable in an o minimal structure over r this article shows that in a suitable sense there are very few rational points of x which do not lie on some connected semialgebraic subset of x of positive dimension

inferring global perceptual contours from local features we address the problem of contour inference from partial data as obtained from state of the art edge detectors we argue that in order to obtain more pereeptually salient contours it is necessary to impose generic constraints such as continuity and co curvilinearity the implementation is in the form of a convolution with a mask which encodes both the orientation and the strength of the possible continuations we first show how the mask called the extension field is derived then how the contributions from different sites are collected to produce a saliency map we show that the scheme can handle a variety of input data from dot patterns to oriented edgels in a unified manner and demonstrate results on a variety of input stimuli we also present a similar approach to the problem of inferring contours formed by end points in both cases the scheme is non linear non iterative and unified in the sense that all types of input tokens are handled in the same manner

probabilistic streamline q ball tractography using the residual bootstrap q ball imaging has the ability to discriminate multiple intravoxel fiber populations within regions of complex white matter architecture this information can be used for fiber tracking however diffusion mr is susceptible to noise and multiple other sources of uncertainty affecting the measured orientation of fiber bundles the proposed residual bootstrap method utilizes a spherical harmonic representation for high angular resolution diffusion imaging hardi data in order to estimate the uncertainty in multimodal q ball reconstructions the accuracy of the q ball residual bootstrap technique was examined through simulation the residual bootstrap method was then used in combination with q ball imaging to construct a probabilistic streamline fiber tracking algorithm the residual bootstrap q ball fiber tracking algorithm is capable of following the corticospinal tract and corpus callosum through regions of crossing white matter tracts in the centrum semiovale this fiber tracking algorithm is an improvement upon prior diffusion tensor methods and the q ball data can be acquired in a clinically feasible time frame

a note on divisible points of curves let c be an irreducible algebraic curve defined over a number field and inside an algebraic torus of dimension at least 3 we partially answer a question posed by levin on points on c for which a non trivial power lies again on c our results have connections to zilber s conjecture on intersections with tori and yield to methods arising in transcendence theory and the theory of o minimal structures

diagnostics for dependence within time series extremes summary the analysis of extreme values within a stationary time series entails various assumptions concerning its long and short range dependence we present a range of new diagnostic tools for assessing whether these assumptions are appropriate and for identifying structure within extreme events these tools are based on tail characteristics of joint survivor functions but can be implemented by using existing estimation methods for extremes of univariate independent and identically distributed variables our diagnostic aids are illustrated through theoretical examples simulation studies and by application to rainfall and exchange rate data on the basis of these diagnostics we can explain characteristics that are found in the observed extreme events of these series and also gain insight into the properties of events that are more extreme than those observed

tropical varieties for exponential sums we study the complexity of approximating complex zero sets of certain n variate exponential sums we show that the real part r of such a zero set can be approximated by the n 1 dimensional skeleton t of a polyhedral subdivision of mathbb r n in particular we give an explicit upper bound on the hausdorff distance delta r t o left t 3 5 delta right where t and delta are respectively the number of terms and the minimal spacing of the frequencies of g on the side of computational complexity we show that even the n 2 case of the membership problem for r is undecidable in the blum shub smale model over mathbb r whereas membership and distance queries for our polyhedral approximation t can be decided in polynomial time for any fixed n

3d stochastic completion fields for mapping connectivity in diffusion mri the 2d stochastic completion field algorithm introduced by williams and jacobs 1 2 uses a directional random walk to model the prior probability of completion curves in the plane this construct has had a powerful impact in computer vision where it has been used to compute the shapes of likely completion curves between edge fragments in visual imagery motivated by these developments we extend the algorithm to 3d using a spherical harmonics basis to achieve a rotation invariant computational solution to the fokker planck equation describing the evolution of the probability density function underlying the model this provides a principled way to compute 3d completion patterns and to derive connectivity measures for orientation data in 3d as arises in 3d tracking motion capture and medical imaging we demonstrate the utility of the approach for the particular case of diffusion magnetic resonance imaging where we derive connectivity maps for synthetic data on a physical phantom and on an in vivo high angular resolution diffusion image of a human brain

counting special points logic diophantine geometry and transcendence theory we expose a theorem of pila and wilkie on counting rational points in sets definable in o minimal structures and some applications of this theorem to problems in diophantine geometry due to masser peterzil pila starchenko and

relational expressive power of constraint query languages the expressive power of first order query languages with several classes of equality and inequality constraints is studied in this paper we settle the conjecture that recursive queries such as parity test and transitive closure cannot be expressed in the relational calculus augmented with polynomial inequality constraints over the reals furthermore noting that relational queries exhibit several forms of genericity we establish a number of collapse results of the following form the class of generic boolean queries expressible in the relational calculus augmented with a given class of constraints coincides with the class of queries expressible in the relational calculus with or without an order relation we prove such results for both the natural and active domain semantics as a consequence the relational calculus augmented with polynomial inequalities expresses the same classes of generic boolean queries under both the natural and active domain semantics in the course of proving these results for the active domin semantics we establish ramsey type theorems saying that any query involving certain kinds of constraints coincides with a constraint free query on databases whose elements come from a certain infinite subset of the domain to prove the collapse results for the natural semantics we make use of techniques from nonstandard analysis and from the model theory of ordered structures

break detection in the covariance structure of multivariate time series models in this paper we introduce an asymptotic test procedure to assess the stability of volatilities and cross volatilites of linear and nonlinear multivariate time series models the test is very flexible as it can be applied for example to many of the multivariate garch models established in the literature and also works well in the case of high dimensionality of the underlying data since it is nonparametric the procedure avoids the difficulties associated with parametric model selection model fitting and parameter estimation we provide the theoretical foundation for the test and demonstrate its applicability via a simulation study and an analysis of financial data extensions to multiple changes and the case of infinite fourth moments are also discussed

inclusion dynamics hybrid automata hybrid systems are dynamical systems with the ability to describe mixed discrete continuous evolution of a wide range of systems consequently at first glance hybrid systems appear powerful but recalcitrant neither yielding to analysis and reasoning through a purely continuous time modeling as with systems of differential equations nor open to inferential processes commonly used for discrete state transition systems such as finite state automata a convenient and popular model called hybrid automata was introduced to model them and has spurred much interest on its tractability as a tool for inference and model checking in a general setting intuitively a hybrid automaton is simply a finite state automaton with each state augmented by continuous variables which evolve according to a set of well defined continuous laws each specified separately for each state this article investigates both the notion of hybrid automaton and the model checking problem over such a structure in particular it relates first order theories and analysis results on multivalued maps and reduces the bounded reachability problem for hybrid automata whose continuous laws are expressed by inclusions x f x t to a decidability problem for first order formulaeover the reals furthermore the paper introduces a class of hybrid automata for which the reachability problem can be decided and shows that the problem of deciding whether a hybrid automaton belongs to this class can be again decided using first order formulaeover the reals despite the fact that the bisimulation quotient for this class of hybrid automata can be infinite we show that our techniques permit effective model checking for a nontrivial fragment of ctl

schubert calculus on the grassmannian of hermitian lagrangian spaces abstract with an eye towards index theoretic applications we describe a schubert like stratification on the grassmannian of hermitian lagrangian spaces in c n c n this is a natural compactification of the space of hermitian n n matrices the closures of the strata define integral cycles and we investigate their intersection theoretic properties we achieve this by blending morse theoretic ideas with techniques from o minimal or tame geometry and geometric integration theory

new np hard and np complete polynomial and integer divisibility problems abstract we show that some problems involving sparse polynomials are np hard for example it is np hard to determine if a sparse polynomial has a root of modulus 1 and it is np hard to decide if two sparse polynomials are not relatively prime also we show that a divisibility problem involving an unbounded number of sparse polynomials is np complete using a theorem of linnik concerning the distribution of primes in arithmetic sequences from these results it follows that certain problems involving inequalities recurrence relations differential equations and eigenvalues of sparse matrices are np hard problems involving divisibility properties of two sparse polynomials divisibility of sparse binary numbers and ring homomorphisms are also np hard

a structural break test for extremal dependence in β mixing random vectors summarywe derive a structural break test for extremal dependence in beta mixing possibly high dimensional random vectors with either asymptotically dependent or asymptotically independent components existing tests require serially independent observations with asymptotically dependent components to avoid estimating a long run variance we use self normalization which obviates the need to estimate the coefficient of tail dependence when components are asymptotically independent simulations show favourable empirical size and power of the test which we apply to s p 500 and dax log returns we find evidence for one break in the coefficient of tail dependence for the upper and lower joint tail at the beginning of the 2007 08 financial crisis leading to more extremal co movement

o minimality and the andre oort conjecture for mathbb c n we give an unconditional proof of the andre oort conjecture for arbitrary products of modular curves we establish two generalizations the first includes the manin mumford conjecture for arbitrary products of elliptic curves defined over q as well as lang s conjecture for torsion points in powers of the multiplicative group the second includes the manin mumford conjecture for abelian varieties defined over q our approach uses the theory of o minimal structures a part of model theory and follows a strategy proposed by zannier and implemented in three recent papers a new proof of the manin mumford conjecture by pila zannier a proof of a special but new case of pink s relative manin mumford conjecture by masser zannier and new proofs of certain known results of andre oort manin mumford type by pila 2010 mathematics subject classification 11g18 03c64