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Full-Text Articles in Physical Sciences and Mathematics
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.
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 …
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 …
Biwave Maps Into Manifolds, Yuan-Jen Chiang
Biwave Maps Into Manifolds, Yuan-Jen Chiang
Mathematics
We generalize wave maps to biwave maps. We prove that the composition of a biwave map and a totally geodesic map is a biwave map. We give examples of biwave nonwave maps. We show that if f is a biwave map into a Riemannian manifold under certain circumstance, then f is a wave map. We verify that if f is a stable biwave map into a Riemannian manifold with positive constant sectional curvature satisfying the conservation law, then f is a wave map. We finally obtain a theorem involving an unstable biwave map.
On The Number Of K-Gons In Finite Projective Planes, Felix Lazebnik, Keith Mellinger, Oscar Vega
On The Number Of K-Gons In Finite Projective Planes, Felix Lazebnik, Keith Mellinger, Oscar Vega
Mathematics
Let π = πq denote a finite projective plane of order q, and let G = Levi(π) be the bipartite point-line incidence graph of π. For k ≥ 3, let c2k(π) denote the number of cycles of length 2k in G. Are the numbers c2k(π) the same for all πq? We prove that this is the case for k = 3, 4, 5, 6 by computing these numbers.