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Journal articles on the topic 'Intrinsic geometry'

Author: Grafiati

Published: 10 March 2023

Last updated: 24 August 2024

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1

Cattani, Carlo, and Ettore Laserra. "Intrinsic geometry of Lax equation." Journal of Interdisciplinary Mathematics 6, no. 3 (January 2003): 291–99. http://dx.doi.org/10.1080/09720502.2003.10700347.

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2

Abou Zeid, M., and C. M. Hull. "Intrinsic geometry of D-branes." Physics Letters B 404, no. 3-4 (July 1997): 264–70. http://dx.doi.org/10.1016/s0370-2693(97)00570-4.

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3

Madore, J., S. Schraml, P. Schupp, and J. Wess. "External fields as intrinsic geometry." European Physical Journal C 18, no. 4 (January 2001): 785–94. http://dx.doi.org/10.1007/s100520100566.

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4

Cushman, Richard, and Jędrzej Śniatycki. "Intrinsic Geometric Structure of Subcartesian Spaces." Axioms 13, no. 1 (December 22, 2023): 9. http://dx.doi.org/10.3390/axioms13010009.

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Every subset S of a Cartesian space Rd, endowed with differential structure C∞(S) generated by restrictions to S of functions in C∞(Rd), has a canonical partition M(S) by manifolds, which are orbits of the family X(S) of all derivations of C∞(S) that generate local one-parameter groups of local diffeomorphisms of S. This partition satisfies the frontier condition, Whitney’s conditions A and B. If M(S) is locally finite, then it satisfies all definitions of stratification of S. This result extends to Hausdorff locally Euclidean differential spaces. The partition M(S) of a subcartesian space S by smooth manifolds provides a measure for the applicability of differential geometric methods to the study of the geometry of S. If all manifolds in M(S) are single points, we cannot expect differential geometry to be an effective tool in the study of S. On the other extreme, if M(S) contains only one manifold M, then the subcartesian space S is a manifold, S=M, and it is a natural domain for differential geometric techniques.

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5

Bellucci, Stefano, and Bhupendra Nath Tiwari. "State-Space Geometry, Statistical Fluctuations, and Black Holes in String Theory." Advances in High Energy Physics 2014 (2014): 1–17. http://dx.doi.org/10.1155/2014/589031.

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We study the state-space geometry of various extremal and nonextremal black holes in string theory. From the notion of the intrinsic geometry, we offer a state-space perspective to the black hole vacuum fluctuations. For a given black hole entropy, we explicate the intrinsic geometric meaning of the statistical fluctuations, local and global stability conditions, and long range statistical correlations. We provide a set of physical motivations pertaining to the extremal and nonextremal black holes, namely, the meaning of the chemical geometry and physics of correlation. We illustrate the state-space configurations for general charge extremal black holes. In sequel, we extend our analysis for various possible charge and anticharge nonextremal black holes. From the perspective of statistical fluctuation theory, we offer general remarks, future directions, and open issues towards the intrinsic geometric understanding of the vacuum fluctuations and black holes in string theory.

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6

Gillespie, Mark, Nicholas Sharp, and Keenan Crane. "Integer coordinates for intrinsic geometry processing." ACM Transactions on Graphics 40, no. 6 (December 2021): 1–13. http://dx.doi.org/10.1145/3478513.3480522.

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This paper describes a numerically robust data structure for encoding intrinsic triangulations of polyhedral surfaces. Many applications demand a correspondence between the intrinsic triangulation and the input surface, but existing data structures either rely on floating point values to encode correspondence, or do not support remeshing operations beyond basic edge flips. We instead provide an integer-based data structure that guarantees valid correspondence, even for meshes with near-degenerate elements. Our starting point is the framework of normal coordinates from geometric topology, which we extend to the broader set of operations needed for mesh processing (vertex insertion, edge splits, etc. ). The resulting data structure can be used as a drop-in replacement for earlier schemes, automatically improving reliability across a wide variety of applications. As a stress test, we successfully compute an intrinsic Delaunay refinement and associated subdivision for all manifold meshes in the Thingi10k dataset. In turn, we can compute reliable and highly accurate solutions to partial differential equations even on extremely low-quality meshes.

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7

Nurowski, Pawel, and David C. Robinson. "Intrinsic geometry of a null hypersurface." Classical and Quantum Gravity 17, no. 19 (September 19, 2000): 4065–84. http://dx.doi.org/10.1088/0264-9381/17/19/308.

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8

Bachini, Elena, and Mario Putti. "Geometrically intrinsic modeling of shallow water flows." ESAIM: Mathematical Modelling and Numerical Analysis 54, no. 6 (October 12, 2020): 2125–57. http://dx.doi.org/10.1051/m2an/2020031.

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Shallow water models of geophysical flows must be adapted to geometric characteristics in the presence of a general bottom topography with non-negligible slopes and curvatures, such as a mountain landscape. In this paper we derive an intrinsic shallow water model from the Navier–Stokes equations defined on a local reference frame anchored on the bottom surface. The equations resulting are characterized by non-autonomous flux functions and source terms embodying only the geometric information. We show that the proposed model is rotational invariant, admits a conserved energy, is well-balanced, and it is formally a second order approximation of the Navier–Stokes equations with respect to a geometry-based order parameter. We then derive a numerical discretization by means of a first order upwind Godunov finite volume scheme intrinsically defined on the bottom surface. We study convergence properties of the resulting scheme both theoretically and numerically. Simulations on several synthetic test cases are used to validate the theoretical results as well as more experimental properties of the solver. The results show the importance of taking into full consideration the bottom geometry even for relatively mild and slowly varying curvatures.

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9

Liu, Hsueh-Ti Derek, Mark Gillespie, Benjamin Chislett, Nicholas Sharp, Alec Jacobson, and Keenan Crane. "Surface Simplification using Intrinsic Error Metrics." ACM Transactions on Graphics 42, no. 4 (July 26, 2023): 1–17. http://dx.doi.org/10.1145/3592403.

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This paper describes a method for fast simplification of surface meshes. Whereas past methods focus on visual appearance, our goal is to solve equations on the surface. Hence, rather than approximate the extrinsic geometry, we construct a coarse intrinsic triangulation of the input domain. In the spirit of the quadric error metric (QEM) , we perform greedy decimation while agglomerating global information about approximation error. In lieu of extrinsic quadrics, however, we store intrinsic tangent vectors that track how far curvature "drifts" during simplification. This process also yields a bijective map between the fine and coarse mesh, and prolongation operators for both scalar- and vector-valued data. Moreover, we obtain hard guarantees on element quality via intrinsic retriangulation---a feature unique to the intrinsic setting. The overall payoff is a "black box" approach to geometry processing, which decouples mesh resolution from the size of matrices used to solve equations. We show how our method benefits several fundamental tasks, including geometric multigrid, all-pairs geodesic distance, mean curvature flow, geodesic Voronoi diagrams, and the discrete exponential map.

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10

Shaik, Sason S. "Intrinsic selectivity and its geometric significance in SN2 reactions." Canadian Journal of Chemistry 64, no. 1 (January 1, 1986): 96–99. http://dx.doi.org/10.1139/v86-016.

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An intrinsic selectivity is defined for identity SN2 reactions (X− + RX → XR + X−). This selectivity parameter is shown to yield information about: (a) the average looseness of the TS geometry in a reaction series; and (b) the sensitivity of the reaction series to geometric loosening.

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11

MATSUSHITA, YASUYUKI, STEPHEN LIN, HEUNG-YEUNG SHUM, XIN TONG, and SING BING KANG. "LIGHTING AND SHADOW INTERPOLATION USING INTRINSIC LUMIGRAPHS." International Journal of Image and Graphics 04, no. 04 (October 2004): 585–604. http://dx.doi.org/10.1142/s0219467804001555.

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Densely-sampled image representations such as the light field or Lumigraph have been effective in enabling photorealistic image synthesis. Unfortunately, lighting interpolation with such representations has not been shown to be possible without the use of accurate 3D geometry and surface reflectance properties. In this paper, we propose an approach to image-based lighting interpolation that is based on estimates of geometry and shading from relatively few images. We decompose light fields captured at different lighting conditions into intrinsic images (reflectance and illumination images), and estimate view-dependent scene geometries using multi-view stereo. We call the resulting representation an Intrinsic Lumigraph. In the same way that the Lumigraph uses geometry to permit more accurate view interpolation, the Intrinsic Lumigraph uses both geometry and intrinsic images to allow high-quality interpolation at different views and lighting conditions. The joint use of geometry and intrinsic images is effective in computing shadow masks for shadow prediction at new lighting conditions. We illustrate our approach with images of real scenes.

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12

Weiss, Gunter. "GEOMETRY. WHAT ELSE !? - MORE OF “ENVIRONMENTAL GEOMETRY”." Boletim da Aproged, no. 34 (December 2018): 9–20. http://dx.doi.org/10.24840/2184-4933_2018-0034_0001.

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This paper is an addendum to a previous article [01] in which several examples demonstrate that “all natural or artificial objects have a shape or form resulting from a natural (bio-physical) or technical (design) process, and therefore have an intrinsic (immanent) geometric constituent”, focusing on the fact that “reality reveals geometry and geometry creates reality”. Since many objects are metaphors for geometric and mathematical content and the starting point for mathematical abstraction, one can conclude that geometry is simply everywhere. This sort of “Appendix” focuses on the symbiotic terms “grasping via senses” and “meaning” in connection with geometry and its visualisation and interpretation, from objects found in our usual environment. A real object that we see or recognize may even gain spiritual meaning, because it is extraordinary and rare and has, therefore, besides its somehow practical purpose, a symbolic one. Here, simplicity, symmetry, smoothness and regularity play an essential role beyond simple aesthetics. In our mainly secular culture, the aesthetic point of view stands in the foreground. KEYWORDS: elementary geometry, intuitive geometry, right angle, cross and square, proofs without words.

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13

Corman, Etienne, Justin Solomon, Mirela Ben-Chen, Leonidas Guibas, and Maks Ovsjanikov. "Functional Characterization of Intrinsic and Extrinsic Geometry." ACM Transactions on Graphics 36, no. 2 (April 21, 2017): 1–17. http://dx.doi.org/10.1145/2999535.

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14

Rodríguez-Laguna, Javier, Silvia N. Santalla, and Rodolfo Cuerno. "Intrinsic geometry approach to surface kinetic roughening." Journal of Statistical Mechanics: Theory and Experiment 2011, no. 05 (May 31, 2011): P05032. http://dx.doi.org/10.1088/1742-5468/2011/05/p05032.

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15

Corman, Etienne, Justin Solomon, Mirela Ben-Chen, Leonidas Guibas, and Maks Ovsjanikov. "Functional Characterization of Intrinsic and Extrinsic Geometry." ACM Transactions on Graphics 36, no. 4 (July 20, 2017): 1. http://dx.doi.org/10.1145/3072959.2999535.

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16

Corman, Etienne, Justin Solomon, Mirela Ben-Chen, Leonidas Guibas, and Maks Ovsjanikov. "Functional characterization of intrinsic and extrinsic geometry." ACM Transactions on Graphics 36, no. 4 (July 20, 2017): 1. http://dx.doi.org/10.1145/3072959.3126796.

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17

Tavakkoli, S., and S. G. Dhande. "Shape Synthesis and Optimization Using Intrinsic Geometry." Journal of Mechanical Design 113, no. 4 (December 1, 1991): 379–86. http://dx.doi.org/10.1115/1.2912793.

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The present paper outlines a method of shape synthesis using intrinsic geometry to be used for two-dimensional shape optimization problems. It is observed that the shape of a curve can be defined in terms of intrinsic parameters such as the curvature as a function of the arc lenght. The method of shape synthesis, proposed here, consists of selecting a shape model, defining a set of shape design variables and then evaluating Cartesian coordinates of a curve. A shape model is conceived as a set of continuous piecewise linear segments of the curvature; each segment defined as a function of the arc length. The shape design variables are the values of curvature and/or arc lengths at some of the end-points of the linear segments. The proposed method of shape synthesis and optimization is general in nature. It has been shown how the proposed method can be used to find the optimal shape of a planar Variable Geometry Truss (VGT) manipulator for a prespecified position and orientation of the end-effector.

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18

Liu, Bingyuan. "The Intrinsic Geometry on Bounded Pseudoconvex Domains." Journal of Geometric Analysis 28, no. 2 (June 27, 2017): 1728–48. http://dx.doi.org/10.1007/s12220-017-9886-0.

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19

Hosseini Mansoori, Seyed Ali, Behrouz Mirza, and Elham Sharifian. "Extrinsic and intrinsic curvatures in thermodynamic geometry." Physics Letters B 759 (August 2016): 298–305. http://dx.doi.org/10.1016/j.physletb.2016.05.096.

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20

Ambjørn, J., P. Bialas, Z. Burda, J. Jurkiewicz, and B. Petersson. "Intrinsic geometry of c=1 random surfaces." Nuclear Physics B - Proceedings Supplements 42, no. 1-3 (April 1995): 701–3. http://dx.doi.org/10.1016/0920-5632(95)00355-d.

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21

Guo, Chang-Yu. "Intrinsic geometry and analysis of Finsler structures." Annali di Matematica Pura ed Applicata (1923 -) 196, no. 5 (February 6, 2017): 1685–93. http://dx.doi.org/10.1007/s10231-017-0634-7.

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22

Jonsson, Thordur. "Intrinsic and extrinsic geometry of random surfaces." Physics Letters B 278, no. 1-2 (March 1992): 89–93. http://dx.doi.org/10.1016/0370-2693(92)90716-h.

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23

Griffin, Lewis D. "The Intrinsic Geometry of the Cerebral Cortex." Journal of Theoretical Biology 166, no. 3 (February 1994): 261–73. http://dx.doi.org/10.1006/jtbi.1994.1024.

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24

Moser, Roger. "Intrinsic Semiharmonic Maps." Journal of Geometric Analysis 21, no. 3 (July 21, 2010): 588–98. http://dx.doi.org/10.1007/s12220-010-9159-7.

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25

Ciaglia, F. M., G. Marmo, and J. M. Pérez-Pardo. "Generalized potential functions in differential geometry and information geometry." International Journal of Geometric Methods in Modern Physics 16, supp01 (January 29, 2019): 1940002. http://dx.doi.org/10.1142/s0219887819400024.

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Potential functions can be used for generating potentials of relevant geometric structures for a Riemannian manifold such as the Riemannian metric and affine connections. We study whether this procedure can also be applied to tensors of rank four and find a negative answer. We study this from the perspective of solving the inverse problem and also from an intrinsic point of view.

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26

BELLUCCI, STEFANO, VINOD CHANDRA, and BHUPENDRA NATH TIWARI. "ON THE THERMODYNAMIC GEOMETRY OF HOT QCD." International Journal of Modern Physics A 26, no. 01 (January 10, 2011): 43–70. http://dx.doi.org/10.1142/s0217751x11051172.

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We study the nature of the covariant thermodynamic geometry arising from the free energy of hot QCD. We systematically analyze the underlying equilibrium thermodynamic configurations of the free energy of two- and three-flavor hot QCD with or without the inclusion of thermal fluctuations in the neighborhood of the QCD transition temperature. We show that there exists a well-defined thermodynamic geometric notion for the QCD thermodynamics. The geometry thus obtained has no singularity as an intrinsic Riemannian manifold. We further show that there is a close connection of this geometric approach with the existing studies of correlations and quark number susceptibilities.

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27

Ito, Sosuke. "Information geometry, trade-off relations, and generalized Glansdorff–Prigogine criterion for stability." Journal of Physics A: Mathematical and Theoretical 55, no. 5 (January 17, 2022): 054001. http://dx.doi.org/10.1088/1751-8121/ac3fc2.

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Abstract We discuss a relationship between information geometry and the Glansdorff–Prigogine criterion for stability. For the linear master equation, we found a relation between the line element and the excess entropy production rate. This relation leads to a new perspective of stability in a nonequilibrium steady-state. We also generalize the Glansdorff–Prigogine criterion for stability based on information geometry. Our information-geometric criterion for stability works well for the nonlinear master equation, where the Glansdorff–Prigogine criterion for stability does not work well. We derive a trade-off relation among the fluctuation of the observable, the mean change of the observable, and the intrinsic speed. We also derive a novel thermodynamic trade-off relation between the excess entropy production rate and the intrinsic speed. These trade-off relations provide a physical interpretation of our information-geometric criterion for stability. We illustrate our information-geometric criterion for stability by an autocatalytic reaction model, where dynamics are driven by a nonlinear master equation.

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28

Wu, Hao, Yongqiang Cheng, and Hongqiang Wang. "Isometric Signal Processing under Information Geometric Framework." Entropy 21, no. 4 (March 27, 2019): 332. http://dx.doi.org/10.3390/e21040332.

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Information geometry is the study of the intrinsic geometric properties of manifolds consisting of a probability distribution and provides a deeper understanding of statistical inference. Based on this discipline, this letter reports on the influence of the signal processing on the geometric structure of the statistical manifold in terms of estimation issues. This letter defines the intrinsic parameter submanifold, which reflects the essential geometric characteristics of the estimation issues. Moreover, the intrinsic parameter submanifold is proven to be a tighter one after signal processing. In addition, the necessary and sufficient condition of invariant signal processing of the geometric structure, i.e., isometric signal processing, is given. Specifically, considering the processing with the linear form, the construction method of linear isometric signal processing is proposed, and its properties are presented in this letter.

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29

Rainio, O., T. Sugawa, and M. Vuorinen. "Intrinsic Geometry and Boundary Structure of Plane Domains." Siberian Mathematical Journal 62, no. 4 (July 2021): 691–706. http://dx.doi.org/10.1134/s0037446621040121.

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30

Galaev, Sergei Vasilievich. "The Intrinsic Geometry of Almost Contact Metric Manifolds." Izvestiya of Saratov University. New Series. Series: Mathematics. Mechanics. Informatics 12, no. 1 (2012): 16–22. http://dx.doi.org/10.18500/1816-9791-2012-12-1-16-22.

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31

Hill, C. Denson, and Paweł Nurowski. "Intrinsic geometry of oriented congruences in three dimensions." Journal of Geometry and Physics 59, no. 2 (February 2009): 133–72. http://dx.doi.org/10.1016/j.geomphys.2008.10.001.

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32

Burago, Dmitri, and Sergei Ivanov. "On intrinsic geometry of surfaces in normed spaces." Geometry & Topology 15, no. 4 (November 25, 2011): 2275–98. http://dx.doi.org/10.2140/gt.2011.15.2275.

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33

López-Bonilla, J. L., G. A. Ovando Z, and J. M. Rivera-Rebolledo. "Intrinsic geometry of curves and the Bonnor’s equation." Proceedings of the Indian Academy of Sciences - Section A 107, no. 1 (February 1997): 43–55. http://dx.doi.org/10.1007/bf02840473.

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34

Youssef, Nabil L., S. H. Abed, and A. Soleiman. "Intrinsic theory of projective changes in Finsler geometry." Rendiconti del Circolo Matematico di Palermo 60, no. 1-2 (June 8, 2011): 263–81. http://dx.doi.org/10.1007/s12215-011-0051-5.

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35

Ye, Allen Q., Olusola A. Ajilore, Giorgio Conte, Johnson GadElkarim, Galen Thomas-Ramos, Liang Zhan, Shaolin Yang, et al. "The intrinsic geometry of the human brain connectome." Brain Informatics 2, no. 4 (November 7, 2015): 197–210. http://dx.doi.org/10.1007/s40708-015-0022-2.

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36

Lohkamp, Joachim. "Hyperbolic Unfoldings of Minimal Hypersurfaces." Analysis and Geometry in Metric Spaces 6, no. 1 (August 1, 2018): 96–128. http://dx.doi.org/10.1515/agms-2018-0006.

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Abstract We study the intrinsic geometry of area minimizing hypersurfaces from a new point of view by relating this subject to quasiconformal geometry. Namely, for any such hypersurface H we define and construct a so-called S-structure. This new and natural concept reveals some unexpected geometric and analytic properties of H and its singularity set Ʃ. Moreover, it can be used to prove the existence of hyperbolic unfoldings of H\Ʃ. These are canonical conformal deformations of H\Ʃ into complete Gromov hyperbolic spaces of bounded geometry with Gromov boundary homeomorphic to Ʃ. These new concepts and results naturally extend to the larger class of almost minimizers.

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37

FERNÁNDEZ, V. V., A. M. MOYA, and W. A. RODRIGUES. "GEOMETRIC AND EXTENSOR ALGEBRAS AND THE DIFFERENTIAL GEOMETRY OF ARBITRARY MANIFOLDS." International Journal of Geometric Methods in Modern Physics 04, no. 07 (November 2007): 1117–58. http://dx.doi.org/10.1142/s0219887807002478.

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We give in this paper which is the third in a series of four a theory of covariant derivatives of representatives of multivector and extensor fields on an arbitrary open set U ⊂ M, based on the geometric and extensor calculus on an arbitrary smooth manifold M. This is done by introducing the notion of a connection extensor field γ defining a parallelism structure on U ⊂ M, which represents in a well-defined way the action on U of the restriction there of some given connection ∇ defined on M. Also we give a novel and intrinsic presentation (i.e. one that does not depend on a chosen orthonormal moving frame) of the torsion and curvature fields of Cartan's theory. Two kinds of Cartan's connection operator fields are identified, and both appear in the intrinsic Cartan's structure equations satisfied by the Cartan's torsion and curvature extensor fields. We introduce moreover a metrical extensor g in U corresponding to the restriction there of given metric tensor g defined on M and also introduce the concept of a geometric structure(U, γ ,g) for U ⊂ M and study metric compatibility of covariant derivatives induced by the connection extensor γ. This permits the presentation of the concept of gauge (deformed) derivatives which satisfy noticeable properties useful in differential geometry and geometrical theories of the gravitational field. Several derivatives of operators in metric and geometrical structures, like ordinary and covariant Hodge co-derivatives and some duality identities are exhibited.

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38

Nikkuni, Ryo. "An intrinsic nontriviality of graphs." Algebraic & Geometric Topology 9, no. 1 (February 23, 2009): 351–64. http://dx.doi.org/10.2140/agt.2009.9.351.

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39

Colebunders, E., S. De Wachter, and B. Lowen. "Intrinsic approach spaces on domains." Topology and its Applications 158, no. 17 (November 2011): 2343–55. http://dx.doi.org/10.1016/j.topol.2011.01.025.

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40

Bandelt, Hans-Jürgen. "Graphs with intrinsic s3 convexities." Journal of Graph Theory 13, no. 2 (June 1989): 215–28. http://dx.doi.org/10.1002/jgt.3190130208.

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41

Livingston, Charles. "Intrinsic symmetry groups of links." Algebraic & Geometric Topology 23, no. 5 (July 25, 2023): 2347–68. http://dx.doi.org/10.2140/agt.2023.23.2347.

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42

Dong, Jinpeng, Yuhao Huang, Songyi Zhang, Shitao Chen, and Nanning Zheng. "Construct Effective Geometry Aware Feature Pyramid Network for Multi-Scale Object Detection." Proceedings of the AAAI Conference on Artificial Intelligence 36, no. 1 (June 28, 2022): 534–41. http://dx.doi.org/10.1609/aaai.v36i1.19932.

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Feature Pyramid Network (FPN) has been widely adopted to exploit multi-scale features for scale variation in object detection. However, intrinsic defects in most of the current methods with FPN make it difficult to adapt to the feature of different geometric objects. To address this issue, we introduce geometric prior into FPN to obtain more discriminative features. In this paper, we propose Geometry-aware Feature Pyramid Network (GaFPN), which mainly consists of the novel Geometry-aware Mapping Module and Geometry-aware Predictor Head.The Geometry-aware Mapping Module is proposed to make full use of all pyramid features to obtain better proposal features by the weight-generation subnetwork. The weights generation subnetwork generates fusion weight for each layer proposal features by using the geometric information of the proposal. The Geometry-aware Predictor Head introduces geometric prior into predictor head by the embedding generation network to strengthen feature representation for classification and regression. Our GaFPN can be easily extended to other two-stage object detectors with feature pyramid and applied to instance segmentation task. The proposed GaFPN significantly improves detection performance compared to baseline detectors with ResNet-50-FPN: +1.9, +2.0, +1.7, +1.3, +0.8 points Average Precision (AP) on Faster-RCNN, Cascade R-CNN, Dynamic R-CNN, SABL, and AugFPN respectively on MS COCO dataset.

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43

Engman, Martin, and Ricardo Cordero-Soto. "Intrinsic spectral geometry of the Kerr-Newman event horizon." Journal of Mathematical Physics 47, no. 3 (March 2006): 033503. http://dx.doi.org/10.1063/1.2174290.

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44

Bélair, Jacques. "Intrinsic Geometry of Biological Surface Growth (Philip H. Todd)." SIAM Review 30, no. 1 (March 1988): 138–39. http://dx.doi.org/10.1137/1030019.

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45

Talmon, Ronen, and Ronald R. Coifman. "Intrinsic modeling of stochastic dynamical systems using empirical geometry." Applied and Computational Harmonic Analysis 39, no. 1 (July 2015): 138–60. http://dx.doi.org/10.1016/j.acha.2014.08.006.

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46

BELLUCCI, STEFANO, and BHUPENDRA NATH TIWARI. "ON REAL INTRINSIC WALL CROSSINGS." International Journal of Modern Physics A 26, no. 30n31 (December 20, 2011): 5171–209. http://dx.doi.org/10.1142/s0217751x11054917.

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We study moduli space stabilization of a class of BPS configurations from the perspective of the real intrinsic Riemannian geometry. Our analysis exhibits a set of implications towards the stability of the D-term potentials, defined for a set of Abelian scalar fields. In particular, we show that the nature of marginal and threshold walls of stabilities may be investigated by real geometric methods. Interestingly, we find that the leading order contributions may easily be accomplished by translations of the Fayet parameter. Specifically, we notice that the various possible linear, planar, hyperplanar and the entire moduli space stability may easily be reduced to certain polynomials in the Fayet parameter. For a set of finitely many real scalar fields, it may be further inferred that the intrinsic scalar curvature defines the global nature and range of vacuum correlations. Whereas, the underlying moduli space configuration corresponds to a noninteracting basis at the zeros of the scalar curvature, where the scalar fields become uncorrelated. The divergences of the scalar curvature provide possible phase structures, viz., wall of stability, phase transition, if any, in the chosen moduli configuration. The present analysis opens up a new avenue towards the stabilization of gauge and string moduli.

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47

BARBERO-LIÑÁN, MARÍA, and ANDREW D. LEWIS. "GEOMETRIC INTERPRETATIONS OF THE SYMMETRIC PRODUCT IN AFFINE DIFFERENTIAL GEOMETRY AND APPLICATIONS." International Journal of Geometric Methods in Modern Physics 09, no. 08 (October 29, 2012): 1250073. http://dx.doi.org/10.1142/s0219887812500739.

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The symmetric product of vector fields on a manifold arises when one studies the controllability of certain classes of mechanical control systems. A novel geometric description of the symmetric product is provided using parallel transport, along the lines of the flow interpretation of the Lie bracket. This geometric interpretation of the symmetric product yields two different applications. First, an intrinsic proof is provided of the fact that the distributions closed under the symmetric product are exactly those distributions invariant under the geodesic flow. Second, some applications in geometric control theory for mechanical systems are clarified.

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48

Yang, Fan, Hui Chen, Yuwei He, Sicheng Zhao, Chenghao Zhang, Kai Ni, and Guiguang Ding. "Geometry-Guided Domain Generalization for Monocular 3D Object Detection." Proceedings of the AAAI Conference on Artificial Intelligence 38, no. 6 (March 24, 2024): 6467–76. http://dx.doi.org/10.1609/aaai.v38i6.28467.

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Monocular 3D object detection (M3OD) is important for autonomous driving. However, existing deep learning-based methods easily suffer from performance degradation in real-world scenarios due to the substantial domain gap between training and testing. M3OD's domain gaps are complex, including camera intrinsic parameters, extrinsic parameters, image appearance, etc. Existing works primarily focus on the domain gaps of camera intrinsic parameters, ignoring other key factors. Moreover, at the feature level, conventional domain invariant learning methods generally cause the negative transfer issue, due to the ignorance of dependency between geometry tasks and domains. To tackle these issues, in this paper, we propose MonoGDG, a geometry-guided domain generalization framework for M3OD, which effectively addresses the domain gap at both camera and feature levels. Specifically, MonoGDG consists of two major components. One is geometry-based image reprojection, which mitigates the impact of camera discrepancy by unifying intrinsic parameters, randomizing camera orientations, and unifying the field of view range. The other is geometry-dependent feature disentanglement, which overcomes the negative transfer problems by incorporating domain-shared and domain-specific features. Additionally, we leverage a depth-disentangled domain discriminator and a domain-aware geometry regression attention mechanism to account for the geometry-domain dependency. Extensive experiments on multiple autonomous driving benchmarks demonstrate that our method achieves state-of-the-art performance in domain generalization for M3OD.

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CANARUTTO, DANIEL. ""MINIMAL GEOMETRIC DATA" APPROACH TO DIRAC ALGEBRA, SPINOR GROUPS AND FIELD THEORIES." International Journal of Geometric Methods in Modern Physics 04, no. 06 (September 2007): 1005–40. http://dx.doi.org/10.1142/s0219887807002417.

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The first three sections contain an updated, not-so-short account of a partly original approach to spinor geometry and field theories introduced by Jadczyk and myself [3–5]; it is based on an intrinsic treatment of 2-spinor geometry in which the needed background structures do not need to be assumed, but rather arise naturally from a unique geometric datum: a vector bundle with complex 2-dimensional fibers over a real 4-dimensional manifold. The following two sections deal with Dirac algebra and 4-spinor groups in terms of two spinors, showing various aspects of spinor geometry from a different perspective. The last section examines particle momenta in 2-spinor terms and the bundle structure of 4-spinor space over momentum space.

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Vitale, Richard A. "Intrinsic volumes and Gaussian processes." Advances in Applied Probability 33, no. 2 (June 2001): 354–64. http://dx.doi.org/10.1017/s0001867800010831.

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Intrinsic volumes are key functionals in convex geometry and have also appeared in several stochastic settings. Here we relate them to questions of regularity in Gaussian processes with regard to Itô–Nisio oscillation and metrization of GB/GC indexing sets. Various bounds and estimates are presented, and questions for further investigation are suggested. From alternate points of view, much of the discussion can be interpreted in terms of (i) random sets and (ii) properties of (deterministic) infinite-dimensional convex bodies.

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