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Articles 181 - 210 of 294
Full-Text Articles in Mathematics
Common Edge-Unzippings For Tetrahedra, Joseph O'Rourke
Common Edge-Unzippings For Tetrahedra, Joseph O'Rourke
Computer Science: Faculty Publications
It is shown that there are examples of distinct polyhedra, each with a Hamiltonian path of edges, which when cut, unfolds the surfaces to a common net. In particular, it is established for infinite classes of triples of tetrahedra.
On Homotopy Poisson Actions And Reduction Of Symplectic Q-Manifolds, Rajan Amit Mehta
On Homotopy Poisson Actions And Reduction Of Symplectic Q-Manifolds, Rajan Amit Mehta
Mathematics Sciences: Faculty Publications
We present a general framework for reduction of symplectic Q-manifolds via graded group actions. In this framework, the homological structure on the acting group is a multiplicative multivector field.
Symmetric Factorization Of The Conformation Tensor In Viscoelastic Fluid Models, Nusret Balci, Becca Thomases, Michael Renardy, Charles R. Doering
Symmetric Factorization Of The Conformation Tensor In Viscoelastic Fluid Models, Nusret Balci, Becca Thomases, Michael Renardy, Charles R. Doering
Mathematics Sciences: Faculty Publications
The positive-definite symmetric polymer conformation tensor possesses a unique symmetric square root that satisfies a closed evolution equation in the Oldroyd-B and FENE-P models of viscoelastic fluid flow. When expressed in terms of the velocity field and the symmetric square root of the conformation tensor, these models' equations of motion formally constitute an evolution in a Hilbert space with a total energy functional that defines a norm. Moreover, this formulation is easily implemented in direct numerical simulations resulting in significant practical advantages in terms of both accuracy and stability.
Stability And Change In Self-Reported Sexual Orientation Identity In Young People: Application Of Mobility Metrics, Miles Q. Ott, Heather L. Corliss, David Wypij, Margaret Rosario, S. Bryn Austin
Stability And Change In Self-Reported Sexual Orientation Identity In Young People: Application Of Mobility Metrics, Miles Q. Ott, Heather L. Corliss, David Wypij, Margaret Rosario, S. Bryn Austin
Statistical and Data Sciences: Faculty Publications
This study investigated stability and change in self-reported sexual orientation identity over time in youth. We describe gender- and age-related changes in sexual orientation identity from early adolescence through emerging adulthood in 13,840 youth ages 12–25 employing mobility measure M, a measure we modified from its original application for econometrics. Using prospective data from a large, ongoing cohort of U.S. adolescents, we examined mobility in sexual orientation identity in youth with up to four waves of data. Ten percent of males and 20% of females at some point described themselves as a sexual minority, while 2% of both males and …
Continuous Blooming Of Convex Polyhedra, Erik D. Demaine, Martin L. Demaine, Vi Hart, Joan Iacono, Stefan Langerman, Joseph O'Rourke
Continuous Blooming Of Convex Polyhedra, Erik D. Demaine, Martin L. Demaine, Vi Hart, Joan Iacono, Stefan Langerman, Joseph O'Rourke
Computer Science: Faculty Publications
We construct the first two continuous bloomings of all convex polyhedra. First, the source unfolding can be continuously bloomed. Second, any unfolding of a convex polyhedron can be refined (further cut, by a linear number of cuts) to have a continuous blooming.
Age-Gaps In Sexual Partnerships: Seeing Beyond ‘Sugar Daddies’, Miles Q. Ott, Till Bärnighausen, Frank Tanser, Mark N. Lurie, Marie-Louise Newell
Age-Gaps In Sexual Partnerships: Seeing Beyond ‘Sugar Daddies’, Miles Q. Ott, Till Bärnighausen, Frank Tanser, Mark N. Lurie, Marie-Louise Newell
Statistical and Data Sciences: Faculty Publications
We examine for the first time age-mixing in sexual relationships in a population with very high HIV incidence and prevalence in rural South Africa. The highest levels of age assortativity (the pairing of like with like) were casual partnerships reported by men, the lowest levels were spousal relationships reported by women. Given the age–sex distribution of HIV prevalence in this population, interventions to decrease age-gaps in spousal relationships may be effective in reducing HIV incidence.
The Geometric And Dynamic Essence Of Phyllotaxis, Pau Atela
The Geometric And Dynamic Essence Of Phyllotaxis, Pau Atela
Mathematics Sciences: Faculty Publications
We present a dynamic geometric model of phyllotaxis based on two postulates, primordia formation and meristem expansion. We find that Fibonacci, Lucas, bijugate and multijugate are all variations of the same unifying phenomenon and that the difference lies on small changes in the position of initial primordia. We explore the set of all initial positions and color-code its points depending on the phyllotactic type of the pattern that arises.
Conical Existence Of Closed Curves On Convex Polyhedra, Joseph O'Rourke, Costin Vîlcu
Conical Existence Of Closed Curves On Convex Polyhedra, Joseph O'Rourke, Costin Vîlcu
Computer Science: Faculty Publications
Let C be a simple, closed, directed curve on the surface of a convex polyhedron P. We identify several classes of curves C that "live on a cone," in the sense that C and a neighborhood to one side may be isometrically embedded on the surface of a cone Lambda, with the apex a of Lambda enclosed inside (the image of) C; we also prove that each point of C is "visible to" a. In particular, we obtain that these curves have non-self-intersecting developments in the plane. Moreover, the curves we identify that live on cones to both sides support …
Convex Polyhedra Realizing Given Face Areas, Joseph O'Rourke
Convex Polyhedra Realizing Given Face Areas, Joseph O'Rourke
Computer Science: Faculty Publications
Given n ≥ 4 positive real numbers, we prove in this note that they are the face areas of a convex polyhedron if and only if the largest number is not more than the sum of the others.
Orbifold Singularities, Lie Algebras Of The Third Kind (Latkes), And Pure Yang-Mills With Matter, Tamar Friedmann
Orbifold Singularities, Lie Algebras Of The Third Kind (Latkes), And Pure Yang-Mills With Matter, Tamar Friedmann
Mathematics Sciences: Faculty Publications
We discover the unique, simple Lie Algebra of the Third Kind, or LATKe, that stems from codimension 6 orbifold singularities and gives rise to a new kind of YangMills theory which simultaneously is pure and contains matter. The root space of the LATKe is 1-dimensional and its Dynkin diagram consists of one point. The uniqueness of the LATKe is a vacuum selection mechanism.
A Note On Solid Coloring Of Pure Simplicial Complexes, Joseph O'Rourke
A Note On Solid Coloring Of Pure Simplicial Complexes, Joseph O'Rourke
Computer Science: Faculty Publications
We establish a simple generalization of a known result in the plane. The simplices in any pure simplicial complex in Rd may be colored with d+1 colors so that no two simplices that share a (d-1)-facet have the same color. In R2 this says that any planar map all of whose faces are triangles may be 3-colored, and in R3 it says that tetrahedra in a collection may be "solid 4-colored" so that no two glued face-to-face receive the same color.
Slider-Pinning Rigidity: A Maxwell-Laman-Type Theorem, Ileana Streinu, Louis Theran
Slider-Pinning Rigidity: A Maxwell-Laman-Type Theorem, Ileana Streinu, Louis Theran
Computer Science: Faculty Publications
We define and study slider-pinning rigidity, giving a complete combinatorial characterization. This is done via direction-slider networks, which are a generalization of Whiteley’s direction networks.
Smoothness Of Lipschitz Minimal Intrinsic Graphs In Heisenberg Groups ℍN, N > 1, Luca Capogna, Giovanna Citti, Maria Manfredini
Smoothness Of Lipschitz Minimal Intrinsic Graphs In Heisenberg Groups ℍN, N > 1, Luca Capogna, Giovanna Citti, Maria Manfredini
Mathematics Sciences: Faculty Publications
We prove that Lipschitz intrinsic graphs in the Heisenberg groups ℍn, with n > 1, which are vanishing viscosity solutions of the minimal surface equation, are smooth and satisfy the PDE in a strong sense.
Flat Zipper-Unfolding Pairs For Platonic Solids, Joseph O'Rourke
Flat Zipper-Unfolding Pairs For Platonic Solids, Joseph O'Rourke
Computer Science: Faculty Publications
We show that four of the five Platonic solids' surfaces may be cut open with a Hamiltonian path along edges and unfolded to a polygonal net each of which can "zipper-refold" to a flat doubly covered parallelogram, forming a rather compact representation of the surface. Thus these regular polyhedra have particular flat "zipper pairs." No such zipper pair exists for a dodecahedron, whose Hamiltonian unfoldings are "zip-rigid." This report is primarily an inventory of the possibilities, and raises more questions than it answers.
Curvedland: An Applet For Illustrating Curved Geometry Without Embedding, Gary Felder, Stephanie Erickson
Curvedland: An Applet For Illustrating Curved Geometry Without Embedding, Gary Felder, Stephanie Erickson
Physics: Faculty Publications
We have written a Java applet to illustrate the meaning of curved geometry. The applet provides a mapping interface similar to MapQuest or Google Maps; features include the ability to navigate through a space and place permanent point objects and/or shapes at arbitrary positions. The underlying two-dimensional space has a constant, positive curvature, which causes the apparent paths and shapes of the objects in the map to appear distorted in ways that change as you view them from different relative angles and distances.
Convexity And Horizontal Second Fundamental Forms For Hypersurfaces In Carnot Groups, Luca Capogna, Scott D. Pauls, Jeremy T. Tyson
Convexity And Horizontal Second Fundamental Forms For Hypersurfaces In Carnot Groups, Luca Capogna, Scott D. Pauls, Jeremy T. Tyson
Mathematics Sciences: Faculty Publications
We use a Riemannian approximation scheme to give a characterization for smooth convex functions on a Carnot group (in the sense of Danielli-Garofalo- Nhieu or Lu-Manfredi-Stroffolini) in terms of the positive semidefiniteness of the horizontal second fundamental form of their graph.
On Folding A Polygon To A Polyhedron, Joseph O'Rourke
On Folding A Polygon To A Polyhedron, Joseph O'Rourke
Computer Science: Faculty Publications
We show that the open problem presented in "Geometric Folding Algorithms: Linkages, Origami, Polyhedra" [DO07] is solved by a theorem of Burago and Zalgaller [BZ96] from more than a decade earlier.
Poset Pinball, Gkm-Compatible Subspaces, And Hessenberg Varieties, Megumi Harada, Julianna Tymoczko
Poset Pinball, Gkm-Compatible Subspaces, And Hessenberg Varieties, Megumi Harada, Julianna Tymoczko
Mathematics Sciences: Faculty Publications
This paper has three main goals. First, we set up a general framework to address the problem of constructing module bases for the equivariant cohomology of certain subspaces of GKM spaces. To this end we introduce the notion of a GKM-compatible subspace of an ambient GKM space. We also discuss poset-upper-triangularity, a key combinatorial notion in both GKM theory and more generally in localization theory in equivariant cohomology. With a view toward other applications, we present parts of our setup in a general algebraic and combinatorial framework. Second, motivated by our central problem of building module bases, we introduce a …
On Flat Polyhedra Deriving From Alexandrov's Theorem, Joseph O'Rourke
On Flat Polyhedra Deriving From Alexandrov's Theorem, Joseph O'Rourke
Computer Science: Faculty Publications
We show that there is a straightforward algorithm to determine if the polyhedron guaranteed to exist by Alexandrov's gluing theorem is a degenerate flat polyhedron, and to reconstruct it from the gluing instructions. The algorithm runs in O(n3) time for polygons whose gluings are specified by n labels.
Star Unfolding Convex Polyhedra Via Quasigeodesic Loops, Jin-Ichi Itoh, Joseph O'Rourke, Costin Vîlcu
Star Unfolding Convex Polyhedra Via Quasigeodesic Loops, Jin-Ichi Itoh, Joseph O'Rourke, Costin Vîlcu
Computer Science: Faculty Publications
We extend the notion of star unfolding to be based on a quasigeodesic loop Q rather than on a point. This gives a new general method to unfold the surface of any convex polyhedron ℘ to a simple (nonoverlapping) planar polygon: cut along one shortest path from each vertex of ℘ toQ, and cut all but one segment of Q.
The Yao Graph Y6 Is A Spanner, Joseph O'Rourke
The Yao Graph Y6 Is A Spanner, Joseph O'Rourke
Computer Science: Faculty Publications
We prove that Y6 is a spanner. Y6 is the Yao graph on a set of planar points, which has an edge from each point x to a closest point y within each of the six angular cones of 60◦ surrounding x .
Schubert Polynomials And Classes Of Hessenberg Varieties, Dave Anderson, Julianna Tymoczko
Schubert Polynomials And Classes Of Hessenberg Varieties, Dave Anderson, Julianna Tymoczko
Mathematics Sciences: Faculty Publications
Regular semisimple Hessenberg varieties are a family of subvarieties of the flag variety that arise in number theory, numerical analysis, representation theory, algebraic geometry, and combinatorics. We give a " Giambelli formula" expressing the classes of regular semisimple Hessenberg varieties in terms of Chern classes. In fact, we show that the cohomology class of each regular semisimple Hessenberg variety is the specialization of a certain double Schubert polynomial, giving a natural geometric interpretation to such specializations. We also decompose such classes in terms of the Schubert basis for the cohomology ring of the flag variety. The coefficients obtained are nonnegative, …
A Sharp Diameter Bound For Unipotent Groups Of Classical Type Overℤ /Pℤ, Jordan S. Ellenberg, Julianna Tymoczko
A Sharp Diameter Bound For Unipotent Groups Of Classical Type Overℤ /Pℤ, Jordan S. Ellenberg, Julianna Tymoczko
Mathematics Sciences: Faculty Publications
The unipotent subgroup of a finite group of Lie type over a prime field Fp comes equipped with a natural set of generators; the properties of the Cayley graph associated to this set of generators have been much studied. In the present paper, we show that the diameter of this Cayley graph is bounded above and below by constant multiples of np + n2 log p, where n is the rank of the associated Lie group. This generalizes the result of Ellenberg, A sharp diameter bound for an upper triangular matrix group, Harvard University, 1993, which treated the case of …
Lie Algebroid Structures On Double Vector Bundles And Representation Theory Of Lie Algebroids, Alfonso Gracia-Saz, Rajan Amit Mehta
Lie Algebroid Structures On Double Vector Bundles And Representation Theory Of Lie Algebroids, Alfonso Gracia-Saz, Rajan Amit Mehta
Mathematics Sciences: Faculty Publications
A VB-algebroid is essentially defined as a Lie algebroid object in the category of vector bundles. There is a one-to-one correspondence between VB-algebroids and certain flat Lie algebroid superconnections, up to a natural notion of equivalence. In this setting, we are able to construct characteristic classes, which in special cases reproduce characteristic classes constructed by Crainic and Fernandes. We give a complete classification of regular VB-algebroids, and in the process we obtain another characteristic class of Lie algebroids that does not appear in the ordinary representation theory of Lie algebroids.
Highway Hull Revisited, Greg Aloupis, Jean Cardinal, Sébastien Collette, Ferran Hurtado, Stefan Langerman, Joseph O'Rourke, Belén Palop
Highway Hull Revisited, Greg Aloupis, Jean Cardinal, Sébastien Collette, Ferran Hurtado, Stefan Langerman, Joseph O'Rourke, Belén Palop
Computer Science: Faculty Publications
A highway H is a line in the plane on which one can travel at a greater speed than in the remaining plane. One can choose to enter and exit H at any point. The highway time distance between a pair of points is the minimum time required to move from one point to the other, with optional use of H. The highway hull H(S,H) of a point set S is the minimal set containing S as well as the shortest paths between all pairs of points in H(S,H), using the highway time distance. We provide a Θ(nlogn) worst-case …
On Baryon Number Non-Conservation In Two-Dimensional O(2n+1) Qcd, Tamar Friedmann
On Baryon Number Non-Conservation In Two-Dimensional O(2n+1) Qcd, Tamar Friedmann
Mathematics Sciences: Faculty Publications
We construct a classical dynamical system whose phase space is a certain infinite dimensional Grassmannian manifold, and propose that it is equivalent to the large N limit of two-dimensional QCD with an O(2N + 1) gauge group. In this theory, we find that baryon number is a topological quantity that is conserved only modulo 2. We also relate this theory to the master field approach to matrix models.
Morphing Of Triangular Meshes In Shape Space, Stefanie Wuhrer, Prosenjit Bose, Chang Shu, Joseph O'Rourke, Alan Brunton
Morphing Of Triangular Meshes In Shape Space, Stefanie Wuhrer, Prosenjit Bose, Chang Shu, Joseph O'Rourke, Alan Brunton
Computer Science: Faculty Publications
We present a novel approach to morph between two isometric poses of the same non-rigid object given as triangular meshes. We model the morphs as linear interpolations in a suitable shape space S. For triangulated 3D polygons, we prove that interpolating linearly in this shape space corresponds to the most isometric morph in R3 . We then extend this shape space to arbitrary triangulations in 3D using a heuristic approach and show the practical use of the approach using experiments. Furthermore, we discuss a modified shape space that is useful for isometric skeleton morphing. All of the newly presented …
Regularity Of Non-Characteristic Minimal Graphs In The Heisenberg Group ℍ1, Luca Capogna, Giovanna Citti, Maria Manfredini
Regularity Of Non-Characteristic Minimal Graphs In The Heisenberg Group ℍ1, Luca Capogna, Giovanna Citti, Maria Manfredini
Mathematics Sciences: Faculty Publications
Minimal surfaces in the sub-Riemannian Heisenberg group can be constructed by means of a Riemannian approximation scheme, as limit of Riemannian minimal surfaces. We study the regularity of Lipschitz, non-characteristic minimal surfaces which arise as such limits. Our main results are apriori estimates on the solutions of the approximating Riemannian PDE and the ensuing C∞ regularity of the sub-Riemannian minimal surface along its Legendrian foliation.
Using Labeled Data To Evaluate Change Detectors In A Multivariate Streaming Environment, Albert Y. Kim, Caren Marzban, Donald B. Percival, Werner Stuetzle
Using Labeled Data To Evaluate Change Detectors In A Multivariate Streaming Environment, Albert Y. Kim, Caren Marzban, Donald B. Percival, Werner Stuetzle
Statistical and Data Sciences: Faculty Publications
We consider the problem of detecting changes in a multivariate data stream. A change detector is defined by a detection algorithm and an alarm threshold. A detection algorithm maps the stream of input vectors into a univariate detection stream. The detector signals a change when the detection stream exceeds the chosen alarm threshold. We consider two aspects of the problem: (1) setting the alarm threshold and (2) measuring/comparing the performance of detection algorithms. We assume we are given a segment of the stream where changes of interest are marked. We present evidence that, without such marked training data, it might …
Sparse Hypergraphs And Pebble Game Algorithms, Ileana Streinu, Louis Theran
Sparse Hypergraphs And Pebble Game Algorithms, Ileana Streinu, Louis Theran
Computer Science: Faculty Publications
A hypergraph G=(V,E) is (k,ℓ)-sparse if no subset V′⊂V spans more than k|V′|−ℓ hyperedges. We characterize (k,ℓ)-sparse hypergraphs in terms of graph theoretic, matroidal and algorithmic properties. We extend several well-known theorems of Haas, Lovász, Nash-Williams, Tutte, and White and Whiteley, linking arboricity of graphs to certain counts on the number of edges. We also address the problem of finding lower-dimensional representations of sparse hypergraphs, and identify a critical behavior in terms of the sparsity parameters k and ℓ. Our constructions extend the pebble games of Lee and Streinu [A. Lee, I. Streinu, Pebble game algorithms …