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Journal articles on the topic 'Double Branched Covers'

Author: Grafiati

Published: 19 October 2024

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1

Barbensi, Agnese, Dorothy Buck, Heather A. Harrington, and Marc Lackenby. "Double branched covers of knotoids." Communications in Analysis and Geometry 30, no. 5 (2022): 1007–57. http://dx.doi.org/10.4310/cag.2022.v30.n5.a3.

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2

Calcut, Jack S., and Jules R. Metcalf-Burton. "Double branched covers of theta-curves." Journal of Knot Theory and Its Ramifications 25, no. 08 (July 2016): 1650046. http://dx.doi.org/10.1142/s0218216516500462.

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We prove a folklore theorem of Thurston, which provides necessary and sufficient conditions for primality of a certain class of theta-curves. Namely, a theta-curve in the 3-sphere with an unknotted constituent knot [Formula: see text] is prime, if and only if lifting the third arc of the theta-curve to the double branched cover over [Formula: see text] produces a prime knot. We apply this result to Kinoshita’s theta-curve.

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3

Sato, Kouki. "On eigenvalues of double branched covers." Proceedings of the American Mathematical Society 147, no. 6 (March 1, 2019): 2707–22. http://dx.doi.org/10.1090/proc/14378.

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4

Kuznetsov, Alexander, and Alexander Perry. "Homological projective duality for quadrics." Journal of Algebraic Geometry 30, no. 3 (January 15, 2021): 457–76. http://dx.doi.org/10.1090/jag/767.

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We show that over an algebraically closed field of characteristic not equal to 2, homological projective duality for smooth quadric hypersurfaces and for double covers of projective spaces branched over smooth quadric hypersurfaces is a combination of two operations: one interchanges a quadric hypersurface with its classical projective dual and the other interchanges a quadric hypersurface with the double cover branched along it.

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5

Lee, Ronnie, and Steven H. Weintraub. "On the homology of double branched covers." Proceedings of the American Mathematical Society 123, no. 4 (April 1, 1995): 1263. http://dx.doi.org/10.1090/s0002-9939-1995-1224618-x.

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6

DOUROUDIAN, FATEMEH. "COMBINATORIAL KNOT FLOER HOMOLOGY AND DOUBLE BRANCHED COVERS." Journal of Knot Theory and Its Ramifications 22, no. 06 (May 2013): 1350014. http://dx.doi.org/10.1142/s0218216513500144.

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7

Roberts, Lawrence. "On knot Floer homology in double branched covers." Geometry & Topology 17, no. 1 (March 12, 2013): 413–67. http://dx.doi.org/10.2140/gt.2013.17.413.

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8

Przytycki, Józef H., and Witold Rosicki. "The Topological Interpretation of the Core Group of a Surface in S4." Canadian Mathematical Bulletin 45, no. 1 (March 1, 2002): 131–37. http://dx.doi.org/10.4153/cmb-2002-016-0.

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AbstractWe give a topological interpretation of the core group invariant of a surface embedded in S4 [F-R], [Ro]. We show that the group is isomorphic to the free product of the fundamental group of the double branch cover of S4 with the surface as a branched set, and the infinite cyclic group. We present a generalization for unoriented surfaces, for other cyclic branched covers, and other codimension two embeddings of manifolds in spheres.

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9

DOUROUDIAN, FATEMEH. "ERRATUM: "COMBINATORIAL KNOT FLOER HOMOLOGY AND DOUBLE BRANCHED COVERS"." Journal of Knot Theory and Its Ramifications 22, no. 07 (June 2013): 1392004. http://dx.doi.org/10.1142/s0218216513920041.

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10

Addington, Nicolas M., Edward P. Segal, and Eric R. Sharpe. "D-brane probes, branched double covers, and noncommutative resolutions." Advances in Theoretical and Mathematical Physics 18, no. 6 (2014): 1369–436. http://dx.doi.org/10.4310/atmp.2014.v18.n6.a5.

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11

Ozsváth, Peter, and Zoltán Szabó. "On the Heegaard Floer homology of branched double-covers." Advances in Mathematics 194, no. 1 (June 2005): 1–33. http://dx.doi.org/10.1016/j.aim.2004.05.008.

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12

Lamm, Tobias, and Reiner M. Schätzle. "Conformal Willmore tori in ℝ4." Journal für die reine und angewandte Mathematik (Crelles Journal) 2018, no. 742 (September 1, 2018): 281–301. http://dx.doi.org/10.1515/crelle-2015-0101.

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Abstract For every two-dimensional torus {T^{2}} and every k \in \mathbb{N} , {k\geq 3} , we construct a conformal Willmore immersion f : T^{2} \to \mathbb{R}^{4} with exactly one point of density k and Willmore energy 4πk. Moreover, we show that the energy value {8\pi} cannot be attained by such an immersion. Additionally, we characterize the branched double covers T^{2} \to S^{2} \times \{ 0 \} as the only branched conformal immersions, up to Möbius transformations of {\mathbb{R}^{4}} , from a torus into {\mathbb{R}^{4}} with at least one branch point and Willmore energy {8\pi} . Using a perturbation argument in order to regularize a branched double cover, we finally show that the infimum of the Willmore energy in every conformal class of tori is less than or equal to {8\pi} .

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13

Doria Medina, Fabian, Michael Jackson, Joaquín Ruales, and Hadas Zeilberger. "On left-orderability and double branched covers of Kanenobu’s knots." Journal of Knot Theory and Its Ramifications 24, no. 14 (December 2015): 1550071. http://dx.doi.org/10.1142/s0218216515500716.

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We show that the fundamental group of the double branched cover of an infinite family of homologically thin, non-quasi-alternating knots is not left-orderable, giving further support for a conjecture of Boyer, Gordon, and Watson that an irreducible rational homology 3-sphere is an L-space if and only if its fundamental group is not left-orderable.

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14

McCoy, Duncan. "Non-integer surgery and branched double covers of alternating knots." Journal of the London Mathematical Society 92, no. 2 (July 24, 2015): 311–37. http://dx.doi.org/10.1112/jlms/jdv030.

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15

Plamenevskaya, Olga. "Transverse knots, branched double covers and Heegaard Floer contact invariants." Journal of Symplectic Geometry 4, no. 2 (2006): 149–70. http://dx.doi.org/10.4310/jsg.2006.v4.n2.a2.

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16

Hendricks, Kristen. "A rank inequality for the knot Floer homology of double branched covers." Algebraic & Geometric Topology 12, no. 4 (December 26, 2012): 2127–78. http://dx.doi.org/10.2140/agt.2012.12.2127.

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17

Yamaguchi, Yoshikazu. "Twisted Alexander polynomials, character varieties and Reidemeister torsions of double branched covers." Topology and its Applications 204 (May 2016): 278–305. http://dx.doi.org/10.1016/j.topol.2016.03.021.

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18

Litherland, R. A. "The Homology of Abelian Covers of Knotted Graphs." Canadian Journal of Mathematics 51, no. 5 (October 1, 1999): 1035–72. http://dx.doi.org/10.4153/cjm-1999-046-7.

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AbstractLet be a regular branched cover of a homology 3-sphere M with deck group and branch set a trivalent graph Γ; such a cover is determined by a coloring of the edges of Γ with elements of G. For each index-2 subgroup H of G, MH = /H is a double branched cover of M. Sakuma has proved that H1() is isomorphic, modulo 2-torsion, to ⊕HH1(MH), and has shown that H1() is determined up to isomorphism by ⊕HH1(MH) in certain cases; specifically, when d = 2 and the coloring is such that the branch set of each cover MH → M is connected, and when d = 3 and Γ is the complete graph K4. We prove this for a larger class of coverings: when d = 2, for any coloring of a connected graph; when d = 3 or 4, for an infinite class of colored graphs; and when d = 5, for a single coloring of the Petersen graph.

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19

Motegi, Kimihiko. "A note on L-spaces which are double branched covers of non-quasi-alternating links." Topology and its Applications 230 (October 2017): 172–80. http://dx.doi.org/10.1016/j.topol.2017.08.043.

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20

Hirose, Susumu, and Eiko Kin. "On hyperbolic surface bundles over the circle as branched double covers of the $3$-sphere." Proceedings of the American Mathematical Society 148, no. 4 (January 15, 2020): 1805–14. http://dx.doi.org/10.1090/proc/14825.

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21

LOGAN, ADAM. "The Brauer–Manin obstruction on del Pezzo surfaces of degree 2 branched along a plane section of a Kummer surface." Mathematical Proceedings of the Cambridge Philosophical Society 144, no. 3 (May 2008): 603–22. http://dx.doi.org/10.1017/s0305004108001102.

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AbstractThis paper discusses the Brauer–Manin obstruction on double covers of the projective plane branched along a plane section of a Kummer surface from both the practical and the theoretical points of view. Theoretical highlights include the determination of a complete set of generators for the Brauer group; on the practical side, we give several surfaces with a Brauer–Manin obstruction and verify that the Brauer–Manin obstruction is the only one for a collection of several thousand surfaces of this type.

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22

Boninger, Joe. "On the cosmetic crossing conjecture for special alternating links." Proceedings of the American Mathematical Society, Series B 10, no. 26 (August 23, 2023): 288–95. http://dx.doi.org/10.1090/bproc/184.

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We prove that a family of links, which includes all special alternating knots, does not admit non-nugatory crossing changes which preserve the isotopy type of the link. Our proof incorporates a result of Lidman and Moore [Trans. Amer. Math. Soc. 369 (2017), pp. 3639–3654] on crossing changes to knots with L L -space branched double-covers, as well as tools from Scharlemann and Thompson’s [Comment. Math. Helv. 64 (1989), pp. 527–535] proof of the cosmetic crossing conjecture for the unknot.

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23

Aceto, Paolo. "Symmetric ribbon disks." Journal of Knot Theory and Its Ramifications 23, no. 09 (August 2014): 1450048. http://dx.doi.org/10.1142/s0218216514500485.

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We study the ribbon disks that arise from a symmetric union presentation of a ribbon knot. A natural notion of symmetric ribbon number rS(K) is introduced and compared with the classical ribbon number r(K). We show that the difference rS(K) - r(K) can be arbitrarily large by constructing an infinite family of ribbon knots Kn such that r(Kn) = 2 and rS(Kn) > n. The proof is based on a particularly simple description of symmetric unions in terms of certain band diagrams which leads to an upper bound for the Heegaard genus of their branched double covers.

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24

Marengon, Marco. "On d-invariants and generalized Kanenobu knots." Journal of Knot Theory and Its Ramifications 25, no. 08 (July 2016): 1650048. http://dx.doi.org/10.1142/s0218216516500486.

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We prove that for particular infinite families of [Formula: see text]-spaces, arising as branched double covers, the [Formula: see text]-invariants defined by Ozsváth and Szabó assume arbitrarily large positive and negative values. As a consequence, we generalize a result by Greene and Watson by proving, for every odd number [Formula: see text], the existence of infinitely many non-quasi-alternating homologically thin knots with determinant [Formula: see text], and a result by Hoffman and Walsh concerning the existence of hyperbolic weight [Formula: see text] manifolds, that are not surgery on a knot in [Formula: see text].

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25

LIDMAN, TYE, and STEVEN SIVEK. "Quasi-alternating links with small determinant." Mathematical Proceedings of the Cambridge Philosophical Society 162, no. 2 (July 14, 2016): 319–36. http://dx.doi.org/10.1017/s0305004116000578.

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AbstractQuasi-alternating links of determinant 1, 2, 3 and 5 were previously classified by Greene and Teragaito, who showed that the only such links are two-bridge. In this paper, we extend this result by showing that all quasi-alternating links of determinant at most 7 are connected sums of two-bridge links, which is optimal since there are quasi-alternating links not of this form for all larger determinants. We achieve this by studying their branched double covers and characterising distance-one surgeries between lens spaces of small order, leading to a classification of formal L-spaces with order at most 7.

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26

Pyataeva, S. V., and I. A. Kosevich. "Soft tissue organization in some sertulariid colonial hydroids (Hydrozoa: Sertulariidae)." Journal of the Marine Biological Association of the United Kingdom 88, no. 8 (November 26, 2008): 1703–13. http://dx.doi.org/10.1017/s002531540800204x.

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The simplified text-book view holds that hydroids' soft body is composed of a branched double-layered tube, whose wall consists of two epithelial layers (the inner gastrodermis and the outer epidermis) separated by the mesoglea. Some hydroids are characterized by large, complex colonies and likely an even more complicated inner organization. By using three species from the thecate hydroids of the family Sertulariidae we investigated the soft body structure of such hydroids. The anatomical study revealed some new features of colonial hydroids. The double layered coenosarc fills the perisarc (outer skeleton) tube only at the endings of the branched colony. More proximally, the coenosarc tube becomes narrower and a thin epidermal lining covers the inner surface of the perisarc tube. In some species the soft tissues of the shoots form a network of anastomosing canals. The canals are formed by the gastrodermal epithelium and they are embedded in epidermal tissue. In the upper part of the shoot, these canals are located at the periphery, along the inner surface of the perisarc. In more proximal regions of the stem, the whole lumen of the perisarc tube can be occupied by gastrodermal canals; the canals are enclosed in a parenchyma-like epidermal tissue. The organization of the soft tissue in these thecate hydroids is a striking example of structural complexity that does not contravene the limits of the ground plan of the phylum.

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27

BUCK, DOROTHY, and MAURO MAURICIO. "Connect sum of lens spaces surgeries: application to Hin recombination." Mathematical Proceedings of the Cambridge Philosophical Society 150, no. 3 (March 9, 2011): 505–25. http://dx.doi.org/10.1017/s0305004111000090.

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AbstractWe extend the tangle model, originally developed by Ernst and Sumners [18], to include composite knots. We show that, for any prime tangle, there are no rational tangle attachments of distance greater than one that first yield a 4-plat and then a connected sum of 4-plats. This is done by studying the corresponding Dehn filling problem via double branched covers. In particular, we build on results on exceptional Dehn fillings at maximal distance to show that if Dehn filling on an irreducible manifold gives a lens space and then a connect sum of lens spaces, the distance between the slopes must be one. We then apply our results to the action of the Hin recombinase on mutated sites. In particular, after solving the tangle equations for processive recombination, we use our work to give a complete set of solutions to the tangle equations modelling distributive recombination.

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28

Ikeda, Atsushi. "The double cover of cubic surfaces branched along their Hessian." International Journal of Mathematics 25, no. 08 (July 2014): 1450075. http://dx.doi.org/10.1142/s0129167x1450075x.

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We establish a relation between the Hodge structure of the double cover of a nonsingular cubic surface branched along its Hessian and the Hodge structure of the triple cover of P3 branched along the cubic surface. Then we introduce a method to study the infinitesimal variations of Hodge structure of the double cover of the cubic surface. Using these results, we compute the Néron–Severi lattices for the double cover of a generic cubic surface and the Fermat cubic surface.

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29

Brunner, A. M. "The Double Cover of S3 Branched along a Link." Journal of Knot Theory and Its Ramifications 06, no. 05 (October 1997): 599–619. http://dx.doi.org/10.1142/s0218216597000339.

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Let L be an unsplittable link in S3 and let V denote the double cover of S3 branched along L. Starting with an arbitrary planar projection of L, it is shown how to construct a special presentation for the fundamental group π1V which encodes in a simple way geometric data from a (checkerboard) spanning surface obtained from the given projection, and which relates to the construction of Coxeter quotients of π1 (S3-L) previously studied by the author and Y. W. Lee.

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30

Choi, Doo Ho, and Ki Hyoung Ko. "Parameterizations of 1-Bridge Torus Knots." Journal of Knot Theory and Its Ramifications 12, no. 04 (June 2003): 463–91. http://dx.doi.org/10.1142/s0218216503002445.

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A 1-bridge torus knot in a 3-manifold of genus ≤ 1 is a knot drawn on a Heegaard torus with one bridge. We give two types of normal forms to parameterize the family of 1-bridge torus knots that are similar to the Schubert's normal form and the Conway's normal form for 2-bridge knots. For a given Schubert's normal form we give algorithms to determine the number of components and to compute the fundamental group of the complement when the normal form determines a knot. We also give a description of the double branched cover of an ambient 3-manifold branched along a 1-bridge torus knot by using its Conway's normal form and obtain an explicit formula for the first homology of the double cover.

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31

ROBERTS, LAWRENCE. "ON KNOT FLOER HOMOLOGY FOR SOME FIBERED KNOTS." Communications in Contemporary Mathematics 15, no. 01 (January 22, 2013): 1250053. http://dx.doi.org/10.1142/s0219199712500538.

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We use knot Floer surgery exact sequences and torsion invariants to compute the knot Floer homology of certain fibered knots in the double cover of S3 branched along the closure of an alternating braid.

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32

Ibrahim, Ahmad S., Ahmad M. Yacoub, and Daniel N. Aloi. "A 3-Dimensional Multiband Antenna for Vehicular 5G Sub-6 GHz/GNSS/V2X Applications." International Journal of Antennas and Propagation 2022 (July 5, 2022): 1–13. http://dx.doi.org/10.1155/2022/5609110.

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A compact multiband monopole antenna is proposed for vehicular roof top shark-fin applications. The proposed multiband antenna covers 5G sub-6 GHz and LTE bands starting at 617 MHz to 5000 MHz and the higher GNSS band from 1559 to 1606 MHz as well as the V2X band at 5900 MHz. The presented antenna is a three-dimensional monopole antenna with two branches to cover the required bands with compact size to fit inside a roof top shark-fin. The long antenna branch covers the lower cellular frequency band from 617 to 960 MHz, while the short branch covers the higher frequency band from 1559 to 6000 MHz. The presented antenna is mounted on a double-sided FR4 PCB and is feeded through a short cable. The proposed antenna covers multiple frequency bands with compact size (H x L x W) of 58 × 37 × 17 mm3. The antenna is simulated and optimized, and then, a prototype is fabricated, and its radiation characteristics are measured when mounted on one-meter ground plane and on a vehicle’s roof. The maximum measured linear average gain is 3 dBi at 1900 MHz, and the maximum measured efficiency is 88% at 787 MHz. The active GNSS antenna gain is measured using an LNA with good isolation. A good agreement is achieved between the simulated and measured results when compared in terms of voltage standing wave ratio (VSWR), radiation patterns, linear average gain (LAG), and antenna efficiency.

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33

Lipshitz, Robert, Peter S. Ozsváth, and Dylan P. Thurston. "Bordered Floer homology and the spectral sequence of a branched double cover I." Journal of Topology 7, no. 4 (July 30, 2014): 1155–99. http://dx.doi.org/10.1112/jtopol/jtu012.

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34

Greene, Joshua Evan. "A spanning tree model for the Heegaard Floer homology of a branched double-cover." Journal of Topology 6, no. 2 (March 29, 2013): 525–67. http://dx.doi.org/10.1112/jtopol/jtt007.

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35

Goodhill, Sarah, Adam M. Lowrance, Valeria Munoz Gonzales, Jessica Rattray, and Amelia Zeh. "The multi-region index of a knot." Journal of Knot Theory and Its Ramifications 29, no. 04 (March 19, 2020): 2050022. http://dx.doi.org/10.1142/s0218216520500224.

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Using region crossing changes, we define a new invariant called the multi-region index of a knot. We prove that the multi-region index of a knot is bounded from above by twice the crossing number of the knot. In addition, we show that the minimum number of generators of the first homology of the double branched cover of [Formula: see text] over the knot is strictly less than the multi-region index. Our proof of this lower bound uses Goeritz matrices.

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36

Tweedy, Eamonn. "On the anti-diagonal filtration for the Heegaard Floer chain complex of a branched double-cover." Journal of Symplectic Geometry 12, no. 2 (2014): 313–63. http://dx.doi.org/10.4310/jsg.2014.v12.n2.a4.

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37

Machon, Thomas, and Gareth P. Alexander. "Global defect topology in nematic liquid crystals." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 472, no. 2191 (July 2016): 20160265. http://dx.doi.org/10.1098/rspa.2016.0265.

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We give the global homotopy classification of nematic textures for a general domain with weak anchoring boundary conditions and arbitrary defect set in terms of twisted cohomology, and give an explicit computation for the case of knotted and linked defects in R 3 , showing that the distinct homotopy classes have a 1–1 correspondence with the first homology group of the branched double cover, branched over the disclination loops. We show further that the subset of those classes corresponding to elements of order 2 in this group has representatives that are planar and characterize the obstruction for other classes in terms of merons. The planar textures are a feature of the global defect topology that is not reflected in any local characterization. Finally, we describe how the global classification relates to recent experiments on nematic droplets and how elements of order 4 relate to the presence of τ lines in cholesterics.

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38

Moon, Han-Bom, and Luca Schaffler. "KSBA compactification of the moduli space of K3 surfaces with a purely non-symplectic automorphism of order four." Proceedings of the Edinburgh Mathematical Society 64, no. 1 (February 2021): 99–127. http://dx.doi.org/10.1017/s001309152100002x.

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We describe a compactification by KSBA stable pairs of the five-dimensional moduli space of K3 surfaces with a purely non-symplectic automorphism of order four and $U(2)\oplus D_4^{\oplus 2}$ lattice polarization. These K3 surfaces can be realized as the minimal resolution of the double cover of $\mathbb {P}^{1}\times \mathbb {P}^{1}$ branched along a specific $(4,\,4)$ curve. We show that, up to a finite group action, this stable pairs compactification is isomorphic to Kirwan's partial desingularization of the GIT quotient $(\mathbb {P}^{1})^{8}{/\!/}\mathrm {SL}_2$ with the symmetric linearization.

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39

Egsgaard, Jens Kristian, and Søren Fuglede Jørgensen. "The homological content of the Jones representations at q = −1." Journal of Knot Theory and Its Ramifications 25, no. 11 (October 2016): 1650062. http://dx.doi.org/10.1142/s0218216516500620.

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We generalize a discovery of Kasahara and show that the Jones representations of braid groups, when evaluated at [Formula: see text], are related to the action on homology of a branched double cover of the underlying punctured disk. As an application, we prove for a large family of pseudo-Anosov mapping classes a conjecture put forward by Andersen, Masbaum, and Ueno [Topological quantum field theory and the Nielsen–Thurston classification of [Formula: see text], Math. Proc. Cambridge Philos. Soc. 141(3) (2006) 477–488] by extending their original argument for the sphere with four marked points to our more general case.

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40

Lipshitz, Robert, Peter S. Ozsváth, and Dylan P. Thurston. "Bordered Floer homology and the spectral sequence of a branched double cover II: the spectral sequences agree." Journal of Topology 9, no. 2 (June 2016): 607–86. http://dx.doi.org/10.1112/jtopol/jtw003.

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41

Firdausi, Ahmad, Galang Hakim, and Mudrik Alaydrus. "Designing a tri-band microstrip antenna for targetting 5g broadband communications." MATEC Web of Conferences 218 (2018): 03015. http://dx.doi.org/10.1051/matecconf/201821803015.

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One of the technologies that has wireless application nowadays was 5G mobile communication.This paper presents the designing of a Tri-band microstrip antenna for targeting 5G broadband communications, This element antenna has 3x3 rectangular patches with feeding line structures are branched. With the use of double feeding proximity coupling structure, we intend to maximize antenna bandwidth, therefore the antenna cover range tri-band frequency from 40 GHz to 70 GHz. The reflection factor comparation between simulation and measurement has a minimum with respective frequency at 45.3 GHz, 57 GHz, and 66 GHz. The total measurement bandwith 11.5 Ghz. With this combination tecnique, the proposed antenna is a promising candidate for 5G communication systems.

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42

Stella, Nazzareno, Roberta Ficarelli, Raffaele Dito, Domitilla Brancadoro, Michele Rossi, and Maurizio Taurino. "A Double Nellix and Chimney Covered Stents: Challenging Treatment of Pararenal Aortic Aneurysm." Vascular and Endovascular Surgery 51, no. 4 (April 4, 2017): 209–14. http://dx.doi.org/10.1177/1538574417702772.

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A 77-year-old male patient presented with a symptomatic, 66-mm pararenal aortic aneurysm. The patient was classified as unsuitable for open surgery due to significant comorbidities. Fenestrated or branched endografts were contraindicated due to the poor iliac access (6 mm diameter). A double Nellix with chimney endovascular aneurysm sealing (ChEVAS) technique was selected to exclude the pararenal aortic aneurysm and to preserve renal arteries and the superior mesenteric artery. Technical preplanning considered the ideal proximal landing zone to be close to the origin of the almost occluded celiac trunk and the distal common iliac arteries as the ideal distal landing zone. The total length of the aorta to cover was estimated as >180 mm, requiring 2 aortic EVAS systems, bilaterally overlapped. Technical success was achieved, and the patient was discharged on postoperative day 8 in good general condition. Successful aneurysm exclusion and target vessel patency without endoleak or stent-graft kinking or migration were confirmed at angio-computed tomography at 6 months.

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43

Shramov, K. A. "Birational rigidity and ℚ-factoriality of a singular double cover of a quadric branched over a divisor of degree 4." Mathematical Notes 84, no. 1-2 (August 2008): 280–89. http://dx.doi.org/10.1134/s0001434608070274.

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44

Rabbani, K. Siddique-e. "Hypothesis to Explain the Occurrence of Multiple Peaks of DFL in Nerve Conduction Measurement." Bangladesh Journal of Medical Physics 4, no. 1 (April 19, 2013): 27–36. http://dx.doi.org/10.3329/bjmp.v4i1.14675.

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Distribution of F-Latency (DFL) is a new nerve conduction parameter obtained using evoked EMG responses, and was introduced by us earlier. We had established that DFL is simply related to the distribution of conduction velocity (DCV) of motor fibres in a peripheral nerve, as an approximate mirror image. Normally DFL has a single peak for healthy nerves, but double, or sometimes, triple peaks of DFL were observed in the median nerve, recording the evoked EMG responses from the Thenar muscle in the palm of the hand. From observation, we also established that such multiple peaks of DFL are associated with Cervical Spondylosis (CS). Double peaks were also observed on the nerves of legs suggesting association with Lumbo-sacral spondylotic neuropathy. The present work puts forward hypotheses to explain the occurrence of double or triple peaks of DFL from median nerve in CS, based on principles of physics, physiology and mathematics, and relate these to observations. This includes observations reported in our earlier work, and also obtained from hundreds of patients tested at a clinic managed by the author. The hypothesis assumes similar DCV with single peaks for all the nerve branches that combine to form the median nerve. Compression or degeneation of one or two of the above nerve branches will result in differential shifts of DFLs, and therefore a combination in the median nerve will give rise to double or triple peaks. Initially the explanation was based on radiculopathy, but the hypotheses evolved when newer neuropathological conditions like myelopathy, and external nerve injury were observed. Finally a generalized hypothesis has been put forward that would cover all these abnormal conditions that affect a peripheral nerve of a limb, both in the hands and the legs. Experiments have been suggested that may test these hypotheses, which, if successful, will lead to a greater understanding of neurophysiology and provide a simple and sensitive diagnostic test through the use of DFL. DOI: http://dx.doi.org/10.3329/bjmp.v4i1.14675 Bangladesh Journal of Medical Physics Vol.4 No.1 2011 27-36

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NGUYEN, QUANG MINH. "VECTOR BUNDLES, DUALITIES AND CLASSICAL GEOMETRY ON A CURVE OF GENUS TWO." International Journal of Mathematics 18, no. 05 (May 2007): 535–58. http://dx.doi.org/10.1142/s0129167x07004230.

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Let C be a curve of genus two. We denote by [Formula: see text] the moduli space of semi-stable vector bundles of rank 3 and trivial determinant over C, and by Jd the variety of line bundles of degree d on C. In particular, J1 has a canonical theta divisor Θ. The space [Formula: see text] is a double cover of ℙ8 = |3Θ| branched along a sextic hypersurface, the Coble sextic. In the dual [Formula: see text], where J1 is embedded, there is a unique cubic hypersurface singular along J1, the Coble cubic. We prove that these two hypersurfaces are dual, inducing a non-abelian Torelli result. Moreover, by looking at some special linear sections of these hypersurfaces, we can observe and reinterpret some classical results of algebraic geometry in a context of vector bundles: the duality of the Segre–Igusa quartic with the Segre cubic, the symmetric configuration of 15 lines and 15 points, the Weddle quartic surface and the Kummer surface.

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Liang, Yan-Wu, and Hao-Miao Zhou. "Small-Size Seven-Band WWAN/LTE Antenna with Distributed LC Resonant Circuit for Smartphone Application." International Journal of Antennas and Propagation 2015 (2015): 1–9. http://dx.doi.org/10.1155/2015/630674.

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A compact small-size coupled-fed antenna composed of an inverted L-shaped feeding strip and a shorting strip with double branches for the WWAN/LTE bands operation in the internal smartphone application is presented. With the help of a novel distributed LC resonant circuit, the proposed antenna can not only realize the miniaturization (15 × 28 × 4 mm3) and multiband to cover 2G/3G/4G bands but also be tuned and optimized easily. The measured bandwidth with 3 : 1 VSWR is 163 MHz (804–967 MHz) at the low-band and 1615 MHz (1665–3280 MHz) at the high-band. What is more, the lowest measured efficiency in the whole frequency band is more than 52% for practical applications. The operating principles and main parameters are detailed below. And successful simulation, fabrication, and measurement of the proposed antenna are shown in this paper.

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Sage, Agata, and Pawel Badura. "Intracranial Hemorrhage Detection in Head CT Using Double-Branch Convolutional Neural Network, Support Vector Machine, and Random Forest." Applied Sciences 10, no. 21 (October 27, 2020): 7577. http://dx.doi.org/10.3390/app10217577.

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Brain hemorrhage is a severe threat to human life, and its timely and correct diagnosis and treatment are of great importance. Multiple types of brain hemorrhage are distinguished depending on the location and character of bleeding. The main division covers five subtypes: subdural, epidural, intraventricular, intraparenchymal, and subarachnoid hemorrhage. This paper presents an approach to detect these intracranial hemorrhage types in computed tomography images of the head. The model trained for each hemorrhage subtype is based on a double-branch convolutional neural network of ResNet-50 architecture. It extracts features from two chromatic representations of the input data: a concatenation of the image normalized in different intensity windows and a stack of three consecutive slices creating a 3D spatial context. The joint feature vector is passed to the classifier to produce the final decision. We tested two tools: the support vector machine and the random forest. The experiments involved 372,556 images from 11,454 CT series of 9997 patients, with each image annotated with labels related to the hemorrhage subtypes. We validated deep networks from both branches of our framework and the model with either of two classifiers under consideration. The obtained results justify the use of a combination of double-source features with the random forest classifier. The system outperforms state-of-the-art methods in terms of F1 score. The highest detection accuracy was obtained in intraventricular (96.7%) and intraparenchymal hemorrhages (93.3%).

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Matsumoto, Takuya, Kentaro Inoue, Shinichi Tanaka, Yukihiko Aoyagi, Yutaka Matsubara, Daisuke Matsuda, Keiji Yoshiya, Ryosuke Yoshiga, Tomoko Ohkusa, and Yoshihiko Maehara. "Radial forces of stents used in thoracic endovascular aortic repair and bare self-expanding nitinol stents measured ex vivo – Rapid rescue for obstruction of the innominate artery using bare self-expanding nitinol stents." Vascular 25, no. 1 (July 9, 2016): 36–41. http://dx.doi.org/10.1177/1708538116640131.

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Purpose Our objective was to compare the radial forces of several stents ex vivo to identify stents suitable for rescue of the unexpected coverage of aortic arch branches in thoracic endovascular aortic repair. Methods We measured the radial forces of two types of self-expanding bare nitinol stents (E-luminexx and Epic) used singly or as double-walled pairs, and of three endoprostheses used in thoracic endovascular aortic repair (TEVAR, Gore c-TAG, Relay, and Valiant) by compressing the stent using an MTS Instron universal testing machine (model #5582). We also examined the compressive effects of the TEVAR endoprostheses and the bare nitinol stents on each other. Results The radial force was greater in the center than at the edge of each stent. In all stents tested, the radial force decreased incrementally with increasing stent diameter. The radial force at the center was two times greater when using two stents than with a single stent. In the compression test, only E-luminexx used as a pair was not compressed after compressing a Relay endoprosthesis by 12 mm. Conclusion Two E-luminexx stents are appropriate to restore the blood flow if a TEVAR endoprosthesis covers the innominate artery following innominate–carotid–left subclavian arterial bypass.

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Filipuk, Galina, and Alexander Stokes. "Takasaki’s rational fourth Painlevé-Calogero system and geometric regularisability of algebro-Painlevé equations." Nonlinearity 36, no. 10 (September 18, 2023): 5661–97. http://dx.doi.org/10.1088/1361-6544/acf266.

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Abstract We propose a notion of regularisation which extends Okamoto’s construction of spaces of initial conditions for the Painlevé differential equations to the class of systems with globally finite branching about movable singularities in the sense of the algebro-Painlevé property. We illustrate this regularisation first in the case of a Hamiltonian system obtained by Takasaki as part of the Painlevé-Calogero correspondence, which is related by an algebraic transformation to the fourth Painlevé equation. Through a combination of compactification, blowups and removal of certain curves we obtain a space on which the system is everywhere either regular or regularisable by certain algebraic transformations. We provide an atlas for this space in which the system has a global Hamiltonian structure, with all Hamiltonian functions being polynomial in coordinates just as in the case of the Painlevé equations on Okamoto’s spaces. We also compare the surface associated with the Takasaki system with that of the fourth Painlevé equation, showing that they are related by a combination of blowdowns and a branched double cover. We provide more examples of algebro-Painlevé equations regularised in this way and also discuss applications of this generalised construction of the space of initial conditions to the identification and classification of algebro-Painlevé equations.

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Xiong, Lu, Zhenwen Deng, Yuyao Huang, Weixin Du, Xiaolong Zhao, Chengyu Lu, and Wei Tian. "Traffic Intersection Re-Identification Using Monocular Camera Sensors." Sensors 20, no. 22 (November 14, 2020): 6515. http://dx.doi.org/10.3390/s20226515.

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Perception of road structures especially the traffic intersections by visual sensors is an essential task for automated driving. However, compared with intersection detection or visual place recognition, intersection re-identification (intersection re-ID) strongly affects driving behavior decisions with given routes, yet has long been neglected by researchers. This paper strives to explore intersection re-ID by a monocular camera sensor. We propose a Hybrid Double-Level re-identification approach which exploits two branches of Deep Convolutional Neural Network to accomplish multi-task including classification of intersection and its fine attributes, and global localization in topological maps. Furthermore, we propose a mixed loss training for the network to learn the similarity of two intersection images. As no public datasets are available for the intersection re-ID task, based on the work of RobotCar, we propose a new dataset with carefully-labeled intersection attributes, which is called “RobotCar Intersection” and covers more than 30,000 images of eight intersections in different seasons and day time. Additionally, we provide another dataset, called “Campus Intersection” consisting of panoramic images of eight intersections in a university campus to verify our updating strategy of topology map. Experimental results demonstrate that our proposed approach can achieve promising results in re-ID of both coarse road intersections and its global pose, and is well suited for updating and completion of topological maps.

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