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Articles 61 - 90 of 188
Full-Text Articles in Mathematics
Augmented Measurement System Assessment, Nathaniel Stevens, R Browne, S H. Steiner, R J. Mackay
Augmented Measurement System Assessment, Nathaniel Stevens, R Browne, S H. Steiner, R J. Mackay
Mathematics
The standard plan for the assessment of the variation due to a measurement system involves a number of operators repeatedly measuring a number of parts in a balanced design. In this article, we consider the performance of two types of (unbalanced) assessment plans. In each type, we use a standard plan augmented with a second component. In type A augmentation, each operator measures a different set of parts once each. In type B augmentation, each operator measures the same set of parts once each. The goal of the paper is to identify good augmented plans for estimating the gauge repeatability …
The Ro(G)-Graded Serre Spectral Sequence, William C. Kronholm
The Ro(G)-Graded Serre Spectral Sequence, William C. Kronholm
Mathematics
In this paper the Serre spectral sequence of Moerdijk and Svensson is extended from Bredon cohomology to RO(G)RO(G)-graded cohomology for finite groups GG. Special attention is paid to the case G=Z/2G=Z/2 where the spectral sequence is used to compute the cohomology of certain projective bundles and loop spaces.
U-Singularity And T-Topos Theoretic Entropy, Goro C. Kato
U-Singularity And T-Topos Theoretic Entropy, Goro C. Kato
Mathematics
We will give descriptions of u-singularities as we introduce the notion of t-topos theoretic entropies. The unifying methodology for a u-singularity is the universal mapping property of an inverse or direct limit. The qualitative, conceptual, and structural analyses of u-singularities are given in terms of inverse and direct limits of micro decompositions of a presheaf and coverings of an object in t-site in the theory of temporal topos.
Urcohomologies And Cohomologies Of N -Complexes, Naoya Hiramatsu, Goro Kato
Urcohomologies And Cohomologies Of N -Complexes, Naoya Hiramatsu, Goro Kato
Mathematics
For a general sequence of objects and morphisms, we construct two N-complexes. Then we can define cohomologies (i, k)-type of the N-complexes not only on a diagonal region but also in the triangular region. We obtain an invariant defined on a general sequence of objects and morphisms. For a short exact sequence of N-complexes, we get the associated long exact sequence generalizing the classical long exact sequence. Lastly, several properties of the vanishing cohomologies of N-complexes are given.
Reverse Mathematics, Computability, And Partitions Of Trees, Jennifer Chubb, Jeffry L. Hirst, Timothy H. Mcnicholl
Reverse Mathematics, Computability, And Partitions Of Trees, Jennifer Chubb, Jeffry L. Hirst, Timothy H. Mcnicholl
Mathematics
We examine the reverse mathematics and computability theory of a form of Ramsey’s theorem in which the linear n-tuples of a binary tree are colored.
Degree Spectra Of The Successor Relation Of Computable Linear Orderings, Jennifer Chubb, Andrey Frolov, Valentina Harizanov
Degree Spectra Of The Successor Relation Of Computable Linear Orderings, Jennifer Chubb, Andrey Frolov, Valentina Harizanov
Mathematics
We establish that for every computably enumerable (c.e.) Turing degree b, the upper cone of c.e. Turing degrees determined by b is the degree spectrum of the successor relation of some computable linear ordering. This follows from our main result, that for a large class of linear orderings, the degree spectrum of the successor relation is closed upward in the c.e. Turing degrees.
Generalized Helmholtz-Kirchhoff Model For Two-Dimensional Distributed Vortex Motion, Raymond J. Nagem, Guido Sandri, David Uminsky, C. Eugene Wayne
Generalized Helmholtz-Kirchhoff Model For Two-Dimensional Distributed Vortex Motion, Raymond J. Nagem, Guido Sandri, David Uminsky, C. Eugene Wayne
Mathematics
The two-dimensional Navier-Stokes equations are rewritten as a system of coupled nonlinear ordinary differential equations. These equations describe the evolution of the moments of an expansion of the vorticity with respect to Hermite functions and of the centers of vorticity concentrations. We prove the convergence of this expansion and show that in the zero viscosity and zero core size limit we formally recover the Helmholtz-Kirchhoff model for the evolution of point vortices. The present expansion systematically incorporates the effects of both viscosity and finite vortex core size. We also show that a low-order truncation of our expansion leads to the …
Cooperation In An Evolutionary Prisoner's Dilemma On Networks With Degree-Degree Correlations, Stephen Devlin, T Treloar
Cooperation In An Evolutionary Prisoner's Dilemma On Networks With Degree-Degree Correlations, Stephen Devlin, T Treloar
Mathematics
We study the effects of degree-degree correlations on the success of cooperation in an evolutionary prisoner's dilemma played on a random network. When degree-degree correlations are not present, the standardized variance of the network's degree distribution has been shown to be an accurate analytical measure of network heterogeneity that can be used to predict the success of cooperation. In this paper, we use a local-mechanism interpretation of standardized variance to give a generalization to graphs with degree-degree correlations. Two distinct mechanisms are shown to influence cooperation levels on these types of networks. The first is an intrinsic measurement of base-line …
Evolution Of Cooperation Through The Heterogeneity Of Random Networks, Stephen Devlin, T Treloar
Evolution Of Cooperation Through The Heterogeneity Of Random Networks, Stephen Devlin, T Treloar
Mathematics
We use the standardized variance (nu_{st}) of the degree distribution of a random network as an analytic measure of its heterogeneity. We show that nu_{st} accurately predicts, quantitatively, the success of cooperators in an evolutionary prisoner's dilemma. Moreover, we show how the generating functional expression for nu_{st} suggests an intrinsic interpretation for the heterogeneity of the network that helps explain local mechanisms through which cooperators thrive in heterogeneous populations. Finally, we give a simple relationship between nu_{st} , the cooperation level, and the epidemic threshold of a random network that reveals an appealing connection between epidemic disease models and the …
Multiscale Registration Of Planning Ct And Daily Cone Beam Ct Images For Adaptive Radiation Therapy, Dana C. Paquin, Doron Levy, Lei Xing
Multiscale Registration Of Planning Ct And Daily Cone Beam Ct Images For Adaptive Radiation Therapy, Dana C. Paquin, Doron Levy, Lei Xing
Mathematics
Adaptive radiation therapy (ART) is the incorporation of daily images in the radiotherapy treatment process so that the treatment plan can be evaluated and modified to maximize the amount of radiation dose to the tumor while minimizing the amount of radiation delivered to healthy tissue. Registration of planning images with daily images is thus an important component of ART. In this article, the authors report their research on multiscale registration of planning computed tomography (CT) images with daily cone beam CT (CBCT) images. The multiscale algorithm is based on the hierarchical multiscale image decomposition of E. Tadmor, S. Nezzar, and …
Partial Automorphism Semigroups, Jennifer Chubb, Valentina Harizanov, Andrei Morozov, Sarah Pingrey, Eric Ufferman
Partial Automorphism Semigroups, Jennifer Chubb, Valentina Harizanov, Andrei Morozov, Sarah Pingrey, Eric Ufferman
Mathematics
We study the relationship between algebraic structures and their inverse semigroups of partial automorphisms. We consider a variety of classes of natural structures including equivalence structures, orderings, Boolean algebras, and relatively complemented distributive lattices. For certain subsemigroups of these inverse semigroups, isomorphism (elementary equivalence) of the subsemigroups yields isomorphism (elementary equivalence) of the underlying structures. We also prove that for some classes of computable structures, we can reconstruct a computable structure, up to computable isomorphism, from the isomorphism type of its inverse semigroup of computable partial automorphisms.
Full Algebra Of Generalized Functions And Non-Standard Asymptotic Analysis, Todor D. Todorov, Hans Vernaeve
Full Algebra Of Generalized Functions And Non-Standard Asymptotic Analysis, Todor D. Todorov, Hans Vernaeve
Mathematics
We construct an algebra of generalized functions endowed with a canonical embedding of the space of Schwartz distributions. We offer a solution to the problem of multiplication of Schwartz distributions similar to but different from Colombeau’s solution. We show that the set of scalars of our algebra is an algebraically closed field unlike its counterpart in Colombeau theory, which is a ring with zero divisors. We prove a Hahn–Banach extension principle which does not hold in Colombeau theory. We establish a connection between our theory with non-standard analysis and thus answer, although indirectly, a question raised by Colombeau. This article …
On Powers Associated With Sierpiński Numbers, Riesel Numbers And Polignac's Conjecture, Mark Kozek, Michael Filaseta, Carrie Finch
On Powers Associated With Sierpiński Numbers, Riesel Numbers And Polignac's Conjecture, Mark Kozek, Michael Filaseta, Carrie Finch
Mathematics
We address conjectures of P. Erdős and conjectures of Y.-G. Chen concerning the numbers in the title. We obtain a variety of related results, including a new smallest positive integer that is simultaneously a Sierpiński number and a Riesel number and a proof that for every positive integer r, there is an integer k such that the numbers k,k2, k3,...,kr are simultaneously Sierpiński numbers.
Local Geometry Of Zero Sets Of Holomorphic Functions Nears The Torus, Jim Agler, John E. Mccarthy, Mark Stankus
Local Geometry Of Zero Sets Of Holomorphic Functions Nears The Torus, Jim Agler, John E. Mccarthy, Mark Stankus
Mathematics
We call a holomorphic function f on a domain in Cn locally toral at the point P in the n-torus if the intersection of the zero set of f with the n-torus has dimension n−1 at P. We study the interplay between the structure of locally toral functions and the geometry of their zero sets.
Sheaf Theoretic Formulation Of Entanglement, Goro C. Kato
Sheaf Theoretic Formulation Of Entanglement, Goro C. Kato
Mathematics
A formulation in terms of sheaf theoretic (or categorical) notions for quantum entanglement is given with direct experimental consequences. The notions from sheaf theory and category theory give structural theory, i.e., qualitative theory, as a candidate for quantum gravity. Its advantage is the following: it provides not only space-time background independent, but also scale independent.This theory is called the theory of temporal topos (or simply t-topos theory).
A Positive Mass Theorem On Asymptotically Hyperbolic Manifolds With Corners Along A Hypersurface, Vincent Bonini, Jie Qing
A Positive Mass Theorem On Asymptotically Hyperbolic Manifolds With Corners Along A Hypersurface, Vincent Bonini, Jie Qing
Mathematics
In this paper we take an approach similar to that in [13] to establish a positive mass theorem for spin asymptotically hyperbolic manifolds admitting corners along a hypersurface. The main analysis uses an integral representation of a solution to a perturbed eigenfunction equation to obtain an asymptotic expansion of the solution in the right order. This allows us to understand the change of the mass aspect of a conformal change of asymptotically hyperbolic metrics.
A Lost Theorem: Definite Integrals In An Asymptotic Setting, Ray Cavalcante, Todor D. Todorov
A Lost Theorem: Definite Integrals In An Asymptotic Setting, Ray Cavalcante, Todor D. Todorov
Mathematics
No abstract provided.
Microcosm To Macrocosm Via The Notion Of A Sheaf (Observers In Terms Of T-Topos), Goro Kato
Microcosm To Macrocosm Via The Notion Of A Sheaf (Observers In Terms Of T-Topos), Goro Kato
Mathematics
The fundamental approach toward matter, space and time is that particles (either objects of macrocosm or microcosm), space and time are all presheafified. Namely, the concept of a presheaf is most fundamental for matter, space and time. An observation of a particle is represented by a morphism from the observed particle (its associated presheaf) to the observer (its associated presheaf) over a specified object (called a generalized time period) of a t-site (i.e. a category with a Grothendieck topology). This formulation provides a scale independent and background space-time free theory (since, for the t-topos theoretic formulation, space and time are …
Multiscale Deformable Registration Of Noisy Medical Images, Dana C. Paquin, Doron Levy, Lei Xing
Multiscale Deformable Registration Of Noisy Medical Images, Dana C. Paquin, Doron Levy, Lei Xing
Mathematics
Multiscale image registration techniques are presented for the registration of medical images using deformable registration models. The techniques are particularly effective for registration problems in which one or both of the images to be registered contains significant levels of noise. A brief overview of existing deformable registration techniques is presented, and experiments using B-spline free-form deformation registration models demonstrate that ordinary deformable registration techniques fail to produce accurate results in the presence of significant levels of noise. The hierarchical multiscale image decomposition described in E. Tadmor, S. Nezzar, and L. Vese’s, ”A multiscale image representation using hierarchical (BV, L2 …
A Manifold Structure For The Group Of Orbifold Diffeomorphisms Of A Smooth Orbifold, Joseph E. Borzellino, Victor Brunsden
A Manifold Structure For The Group Of Orbifold Diffeomorphisms Of A Smooth Orbifold, Joseph E. Borzellino, Victor Brunsden
Mathematics
For a compact, smooth Cr orbifold (without boundary), we show that the topological structure of the orbifold diffeomorphism group is a Banach manifold for 1 ≤ r < ∞ and a Fréchet manifold if r = ∞. In each case, the local model is the separable Banach (Fréchet) space of Cr (C ∞, resp.) orbisections of the tangent orbibundle.
Deformable Image Registration With Inclusion Of Auto-Detected Homologous Tissue Features, Y. Xie, Lei Xing, Dana C. Paquin, Doron Levy, T. Yang
Deformable Image Registration With Inclusion Of Auto-Detected Homologous Tissue Features, Y. Xie, Lei Xing, Dana C. Paquin, Doron Levy, T. Yang
Mathematics
No abstract provided.
Hybrid Multiscale Landmark And Deformable Image Registration, Dana C. Paquin, Doron Levy, Lei Xing
Hybrid Multiscale Landmark And Deformable Image Registration, Dana C. Paquin, Doron Levy, Lei Xing
Mathematics
An image registration technique is presented for the registration of medical images using a hybrid combination of coarse-scale landmark and B-splines deformable registration techniques. The technique is particularly effective for registration problems in which the images to be registered contain large localized deformations. A brief overview of landmark and deformable registration techniques is presented. The hierarchical multiscale image decomposition of E. Tadmor, S. Nezzar, and L. Vese, A multiscale image representation using hierarchical (BV,L2) decompositions, Multiscale Modeling and Simulations, vol. 2, no. 4, pp. 554-579, 2004, is reviewed, and an image registration algorithm is developed based on …
Vorticity Dynamics And Sound Generation In Two-Dimensional Fluid Flow, Raymond J. Nagem, Guido Sandri, David Uminsky
Vorticity Dynamics And Sound Generation In Two-Dimensional Fluid Flow, Raymond J. Nagem, Guido Sandri, David Uminsky
Mathematics
An approximate solution to the two-dimensional incompressible fluid equations is constructed by expanding the vorticity field in a series of derivatives of a Gaussian vortex. The expansion is used to analyze the motion of a corotating Gaussian vortex pair, and the spatial rotation frequency of the vortex pair is derived directly from the fluid vorticity equation. The resulting rotation frequency includes the effects of finite vortex core size and viscosity and reduces, in the appropriate limit, to the rotation frequency of the Kirchhoff point vortex theory. The expansion is then used in the low Mach number Lighthill equation to derive …
Relationships Between Braid Length And The Number Of Braid Strands, Cornelia A. Van Cott
Relationships Between Braid Length And The Number Of Braid Strands, Cornelia A. Van Cott
Mathematics
For a knot K, let ℓ(K,n) be the minimum length of an n–stranded braid representative of K. Fixing a knot K, ℓ(K,n) can be viewed as a function of n, which we denote by ℓK(n). Examples of knots exist for which ℓK(n) is a nonincreasing function. We investigate the behavior of ℓK(n), developing bounds on the function in terms of the genus of K. The bounds lead to the conclusion that for any knot K the function ℓK(n) is eventually stable. We study the stable behavior of ℓK(n), with stronger results for homogeneous knots. For knots of nine or fewer …
Π01 Classes And Strong Degree Spectra Of Relations, John Chisholm, Jennifer Chubb, Valentina S. Harizanov, Denise R. Hirschfeldt, Carl G. Jockusch, Timothy H. Mcnicholl, Sarah Pingrey
Π01 Classes And Strong Degree Spectra Of Relations, John Chisholm, Jennifer Chubb, Valentina S. Harizanov, Denise R. Hirschfeldt, Carl G. Jockusch, Timothy H. Mcnicholl, Sarah Pingrey
Mathematics
We study the weak truth-table and truth-table degrees of the images of subsets of computable structures under isomorphisms between computable structures. In particular, we show that there is a low c.e. set that is not weak truth-table reducible to any initial segment of any scattered computable linear order. Countable Π01 subsets of 2w and Kolmogorov complexity play a major role in the proof.
The Q-Exponential Generating Function For Permutations By Consecutive Patterns And Inversions, Don Rawlings
The Q-Exponential Generating Function For Permutations By Consecutive Patterns And Inversions, Don Rawlings
Mathematics
The inverse of Fedou's insertion-shift bijection is used to deduce a general form for the q-exponential generating function for permutations by consecutive patterns (overlaps allowed) and inversion number from a result due to Jackson and Goulden for enumerating words by distinguished factors. Explicit q-exponential generating functions are then derived for permutations by the consecutive patterns 12…m, 12…(m−2)m(m−1), 1m(m−1)…2, and by the pair of consecutive patterns (123,132).
Unbounded Regions Of Infinitely Logconcave Sequences, David Uminsky, Karen Yeats
Unbounded Regions Of Infinitely Logconcave Sequences, David Uminsky, Karen Yeats
Mathematics
We study the properties of a logconcavity operator on a symmetric, unimodal subset of finite sequences. In doing so we are able to prove that there is a large unbounded region in this subset that is ∞-logconcave. This problem was motivated by the conjecture of Boros and Moll in [1] that the binomial coefficients are ∞-logconcave.
Closed Geodesics On Orbifolds Of Revolution, Joseph E. Borzellino, Christopher R. Jordan-Squire, Gregory C. Petrics, D. Mark Sullivan
Closed Geodesics On Orbifolds Of Revolution, Joseph E. Borzellino, Christopher R. Jordan-Squire, Gregory C. Petrics, D. Mark Sullivan
Mathematics
Using the theory of geodesics on surfaces of revolution, we show that any two-dimensional orbifold of revolution homeomorphic to S2 must contain an infinite number of geometrically distinct closed geodesics. Since any such orbifold of revolution can be regarded as a topological two-sphere with metric singularities, we will have extended Bangert's theorem on the existence of infinitely many closed geodesics on any smooth Riemannian two-sphere. In addition, we give an example of a two-sphere cone-manifold of revolution which possesses a single closed geodesic, thus showing that Bangert's result does not hold in the wider class of closed surfaces with …
Toral Algebraic Sets And Function Theory On Polydisks, Jim Agler, John E. Mccarthy, Mark Stankus
Toral Algebraic Sets And Function Theory On Polydisks, Jim Agler, John E. Mccarthy, Mark Stankus
Mathematics
A toral algebraic set A is an algebraic set in Cn whose intersection with Tn is sufficiently large to determine the holomorphic functions on A. We develop the theory of these sets, and give a number of applications to function theory in several variables and operator theoretic model theory. In particular, we show that the uniqueness set for an extremal Pick problem on the bidisk is a toral algebraic set, that rational inner functions have zero sets whose irreducible components are not toral, and that the model theory for a commuting pair of contractions with finite defect …
Multiscale Image Registration, Dana C. Paquin, Doron Levy, Lei Xing
Multiscale Image Registration, Dana C. Paquin, Doron Levy, Lei Xing
Mathematics
Abstract of paper presented at the 48th Annual Meeting of the American Society for Therapeutic Radiology and Oncology.