Relevant bibliographies by topics / Convex projective geometry

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  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers

Academic literature on the topic 'Convex projective geometry'

Author: Grafiati
Published: 16 November 2024

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Journal articles on the topic "Convex projective geometry"

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Wienhard, Anna, and Tengren Zhang. "Deforming convex real projective structures." Geometriae Dedicata 192, no. 1 (May 5, 2017): 327–60. http://dx.doi.org/10.1007/s10711-017-0243-z.

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Weisman, Theodore. "Dynamical properties of convex cocompact actions in projective space." Journal of Topology 16, no. 3 (August 2, 2023): 990–1047. http://dx.doi.org/10.1112/topo.12307.

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AbstractWe give a dynamical characterization of convex cocompact group actions on properly convex domains in projective space in the sense of Danciger–Guéritaud–Kassel: we show that convex cocompactness in is equivalent to an expansion property of the group about its limit set, occurring in different Grassmannians. As an application, we give a sufficient and necessary condition for convex cocompactness for groups that are hyperbolic relative to a collection of convex cocompact subgroups. We show that convex cocompactness in this situation is equivalent to the existence of an equivariant homeomorphism from the Bowditch boundary to the quotient of the limit set of the group by the limit sets of its peripheral subgroups.
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Kapovich, Michael. "Convex projective structures on Gromov–Thurston manifolds." Geometry & Topology 11, no. 3 (September 24, 2007): 1777–830. http://dx.doi.org/10.2140/gt.2007.11.1777.

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Kim, Inkang. "Compactification of Strictly Convex Real Projective Structures." Geometriae Dedicata 113, no. 1 (June 2005): 185–95. http://dx.doi.org/10.1007/s10711-005-0550-7.

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Kohn, Kathlén, and Kristian Ranestad. "Projective Geometry of Wachspress Coordinates." Foundations of Computational Mathematics 20, no. 5 (November 11, 2019): 1135–73. http://dx.doi.org/10.1007/s10208-019-09441-z.

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Abstract We show that there is a unique hypersurface of minimal degree passing through the non-faces of a polytope which is defined by a simple hyperplane arrangement. This generalizes the construction of the adjoint curve of a polygon by Wachspress (A rational finite element basis, Academic Press, New York, 1975). The defining polynomial of our adjoint hypersurface is the adjoint polynomial introduced by Warren (Adv Comput Math 6:97–108, 1996). This is a key ingredient for the definition of Wachspress coordinates, which are barycentric coordinates on an arbitrary convex polytope. The adjoint polynomial also appears both in algebraic statistics, when studying the moments of uniform probability distributions on polytopes, and in intersection theory, when computing Segre classes of monomial schemes. We describe the Wachspress map, the rational map defined by the Wachspress coordinates, and the Wachspress variety, the image of this map. The inverse of the Wachspress map is the projection from the linear span of the image of the adjoint hypersurface. To relate adjoints of polytopes to classical adjoints of divisors in algebraic geometry, we study irreducible hypersurfaces that have the same degree and multiplicity along the non-faces of a polytope as its defining hyperplane arrangement. We list all finitely many combinatorial types of polytopes in dimensions two and three for which such irreducible hypersurfaces exist. In the case of polygons, the general such curves are elliptic. In the three-dimensional case, the general such surfaces are either K3 or elliptic.
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Hildebrand, Roland. "Optimal Inequalities Between Distances in Convex Projective Domains." Journal of Geometric Analysis 31, no. 11 (May 10, 2021): 11357–85. http://dx.doi.org/10.1007/s12220-021-00684-3.

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Benoist, Yves, and Dominique Hulin. "Cubic differentials and finite volume convex projective surfaces." Geometry & Topology 17, no. 1 (April 8, 2013): 595–620. http://dx.doi.org/10.2140/gt.2013.17.595.

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Sioen, M., and S. Verwulgen. "Locally convex approach spaces." Applied General Topology 4, no. 2 (October 1, 2003): 263. http://dx.doi.org/10.4995/agt.2003.2031.

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<p>We continue the investigation of suitable structures for quantified functional analysis, by looking at the notion of local convexity in the setting of approach vector spaces as introduced in [6]. We prove that the locally convex objects are exactly the ones generated (in the usual approach sense) by collections of seminorms. Furthermore, we construct a quantified version of the projective tensor product and show that the locally convex objects admitting a decent exponential law with respect to it are precisely the seminormed spaces.</p>
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Bray, Harrison, and David Constantine. "Entropy rigidity for finite volume strictly convex projective manifolds." Geometriae Dedicata 214, no. 1 (May 17, 2021): 543–57. http://dx.doi.org/10.1007/s10711-021-00627-w.

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Zimmer, Andrew. "A higher-rank rigidity theorem for convex real projective manifolds." Geometry & Topology 27, no. 7 (September 19, 2023): 2899–936. http://dx.doi.org/10.2140/gt.2023.27.2899.

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Dissertations / Theses on the topic "Convex projective geometry"

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Fléchelles, Balthazar. "Geometric finiteness in convex projective geometry." Electronic Thesis or Diss., université Paris-Saclay, 2024. http://www.theses.fr/2024UPASM029.

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Cette thèse est consacrée à l’étude des orbivariétés projectives convexes géométriquement finies, et fait suite aux travaux de Ballas, Cooper, Crampon, Leitner, Long, Marquis et Tillmann sur le sujet. Une orbivariété projective convexe est le quotient d’un ouvert convexe et borné d’une carte affine de l’espace projectif réel (appelé aussi ouvert proprement convexe) par un groupe discret de transformations projectives préservant cet ouvert. S’il n’y a pas de segment dans le bord du convexe, on dit que l’orbivariété est strictement convexe, et si de plus il y a un unique hyperplan de support en chaque point du bord, on dit qu’elle est ronde. Suivant Cooper-Long-Tillmann et Crampon-Marquis, on dit qu’une orbivariété strictement convexe est géométriquement finie si son cœur convexe est l’union d’un compact et d’un nombre fini de bouts, appelés pointes, où le rayon d’injectivité est inférieur à une constante ne dépendant que de la dimension. Comprendre la géométrie des pointes est primordial pour l’étude des orbivariétés géométriquement finies. Dans le cas strictement convexe, la seule restriction connue sur l’holonomie des pointes vient d’une généralisation du lemme de Margulis due à Cooper-Long-Tillmann et Crampon-Marquis, qui implique que cette holonomie est virtuellement nilpotente. On donne dans cette thèse une caractérisation de l’holonomie des pointes des orbivariétés strictement convexes et des orbivariétés rondes. En généralisant la méthode de Cooper, qui a produit le seul exemple connu jusqu’ici d’une pointe de variété strictement convexe dont l’holonomie n’est pas virtuellement abélienne, on construit des pointes de variétés strictement convexes et de variétés rondes dont l’holonomie est isomorphe à n’importe quel groupe nilpotent sans torsion de type fini. En collaboration avec M. Islam et F. Zhu, on démontre que dans le cas des groupes relativement hyperboliques sans torsion, les représentations relativement P1-anosoviennes (au sens de Kapovich-Leeb, Zhu et Zhu-Zimmer) qui préservent un ouvert proprement convexe sont exactement les holonomies des variétés rondes géométriquement finies.Dans le cas des orbivariétés projectives convexes non strictement convexes, il n’y a pas pour l’instant de définition satisfaisante de la finitude géométrique. Toutefois, Cooper-Long-Tillmann puis Ballas-Cooper-Leitner ont proposé une définition de pointe généralisée dans ce contexte. Bien qu’ils demandent que l’holonomie des pointes généralisées soit virtuellement nilpotente, tous les exemples connus jusqu’à présent avaient une holonomie virtuellement abélienne. On construit des exemples de pointes généralisées dont l’holonomie peut être n’importe quel groupe nilpotent sans torsion de type fini. On s’autorise également à modifier la définition originale de Cooper-Long-Tillmann en affaiblissant l’hypothèse de nilpotence en une hypothèse naturelle de résolubilité, ce qui nous permet de construire de nouveaux exemples dont l’holonomie n’est pas virtuellement nilpotente.Une orbivariété géométriquement finie qui n’a pas de pointes, c’est-à-dire dont le cœur convexe est compact, est dite convexe cocompacte. On dispose par les travaux de Danciger-Guéritaud-Kassel d’une définition de la convexe cocompacité pour les orbivariétés projectives convexes sans hypothèse de stricte convexité, contrairement au cas géométriquement fini. Ils démontrent que l’holonomie d’une orbivariété projective convexe convexe cocompacte est Gromov hyperbolique si et seulement si la représentation associée est P1-anosovienne. À l’aide de ce résultat, de la théorie de Vinberg et des travaux d’Agol et Haglund-Wise sur les groupes hyperboliques cubulés, on construit en collaboration avec S. Douba, T. Weisman et F. Zhu des représentations P1-anosoviennes pour tout groupe hyperbolique cubulé. Ceci fournit de nouveaux exemples de groupes hyperboliques admettant des représentations anosoviennes
This thesis is devoted to the study of geometrically finite convex projective orbifolds, following work of Ballas, Cooper, Crampon, Leitner, Long, Marquis and Tillmann. A convex projective orbifold is the quotient of a bounded, convex and open subset of an affine chart of real projective space (called a properly convex domain) by a discrete group of projective transformations that preserve it. We say that a convex projective orbifold is strictly convex if there are no non-trivial segments in the boundary of the convex subset, and round if in addition there is a unique supporting hyperplane at each boundary point. Following work of Cooper-Long-Tillmann and Crampon-Marquis, we say that a strictly convex orbifold is geometrically finite if its convex core decomposes as the union of a compact subset and of finitely many ends, called cusps, all of whose points have an injectivity radius smaller than a constant depending only on the dimension. Understanding what types of cusps may occur is crucial for the study of geometrically finite orbifolds. In the strictly convex case, the only known restriction on cusp holonomies, imposed by a generalization of the celebrated Margulis lemma proven by Cooper-Long-Tillmann and Crampon-Marquis, is that the holonomy of a cusp has to be virtually nilpotent. We give a complete characterization of the holonomies of cusps of strictly convex orbifolds and of those of round orbifolds. By generalizing a method of Cooper, which gave the only previously known example of a cusp of a strictly convex manifold with non virtually abelian holonomy, we build examples of cusps of strictly convex manifolds and round manifolds whose holonomy can be any finitely generated torsion-free nilpotent group. In joint work with M. Islam and F. Zhu, we also prove that for torsion-free relatively hyperbolic groups, relative P1-Anosov representations (in the sense of Kapovich-Leeb, Zhu and Zhu-Zimmer) that preserve a properly convex domain are exactly the holonomies of geometrically finite round manifolds.In the general case of non strictly convex projective orbifolds, no satisfactory definition of geometric finiteness is known at the moment. However, Cooper-Long-Tillmann, followed by Ballas-Cooper-Leitner, introduced a notion of generalized cusps in this context. Although they only require that the holonomy be virtually nilpotent, all previously known examples had virtually abelian holonomy. We build examples of generalized cusps whose holonomy can be any finitely generated torsion-free nilpotent group. We also allow ourselves to weaken Cooper-Long-Tillmann’s original definition by assuming only that the holonomy be virtually solvable, and this enables us to construct new examples whose holonomy is not virtually nilpotent.When a geometrically finite orbifold has no cusps, i.e. when its convex core is compact, we say that the orbifold is convex cocompact. Danciger-Guéritaud-Kassel provided a good definition of convex cocompactness for convex projective orbifolds that are not necessarily strictly convex. They proved that the holonomy of a convex cocompact convex projective orbifold is Gromov hyperbolic if and only if the associated representation is P1-Anosov. Using these results, Vinberg’s theory and work of Agol and Haglund-Wise about cubulated hyperbolic groups, we construct, in collaboration with S. Douba, T. Weisman and F. Zhu, examples of P1-Anosov representations for any cubulated hyperbolic group. This gives new examples of hyperbolic groups admitting Anosov representations
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Ellis, Amanda. "Classification of conics in the tropical projective plane /." Diss., CLICK HERE for online access, 2005. http://contentdm.lib.byu.edu/ETD/image/etd1104.pdf.

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Ellis, Amanda. "Classifcation of Conics in the Tropical Projective Plane." BYU ScholarsArchive, 2005. https://scholarsarchive.byu.edu/etd/697.

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This paper defines tropical projective space, TP^n, and the tropical general linear group TPGL(n). After discussing some simple examples of tropical polynomials and their hypersurfaces, a strategy is given for finding all conics in the tropical projective plane. The classification of conics and an analysis of the coefficient space corresponding to such conics is given.
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Alessandrini, Daniele. "A tropical compactification for character spaces of convex projective structures." Doctoral thesis, Scuola Normale Superiore, 2007. http://hdl.handle.net/11384/85709.

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Baratov, Rishat. "Efficient conic decomposition and projection onto a cone in a Banach ordered space." Thesis, University of Ballarat, 2005. http://researchonline.federation.edu.au/vital/access/HandleResolver/1959.17/61401.

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Sim, Kristy Karen Wan Yen. "Multiple view geometry and convex optimization." Phd thesis, 2007. http://hdl.handle.net/1885/149870.

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Ballas, Samuel Aaron. "Flexibility and rigidity of three-dimensional convex projective structures." 2013. http://hdl.handle.net/2152/21681.

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This thesis investigates various rigidity and flexibility phenomena of convex projective structures on hyperbolic manifolds, particularly in dimension 3. Let M[superscipt n] be a finite volume hyperbolic n-manifold where [mathematical equation] and [mathematical symbol] be its fundamental group. Mostow rigidity tells us that there is a unique conjugacy class of discrete faithful representation of [mathematical symbol] into PSO(subscript n, 1). In light of this fact we examine when this representations can be non-trivially deformed into the larger Lie group of PGL[subscript n+1](R) as well as the relationship between these deformations and convex projective structures on M. Specifically, we show that various two-bridge knots do not admit such deformations into PGL[subscript 4](R) satisfying certain boundary conditions. We subsequently use this result to show that certain orbifold surgeries on amphicheiral knot complements do admit deformations.
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Books on the topic "Convex projective geometry"

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Choi, Suhyoung. The Convex and concave decomposition of manifolds with real projective structures. [Paris, France]: Société mathématique de France, 1999.

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Huybrechts, D. Spherical and Exceptional Objects. Oxford University Press, 2007. http://dx.doi.org/10.1093/acprof:oso/9780199296866.003.0008.

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Spherical objects — motivated by considerations in the context of mirror symmetry — are used to construct special autoequivalences. Their action on cohomology can be described precisely, considering more than one spherical object often leads to complicated (braid) groups acting on the derived category. The results related to Beilinson are almost classical. Section 3 of this chapter gives an account of the Beilinson spectral sequence and how it is used to deduce a complete description of the derived category of the projective space. This will use the language of exceptional sequences and semi-orthogonal decompositions encountered here. The final section gives a simplified account of the work of Horja, which extends the theory of spherical objects and their associated twists to a broader geometric context.
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Book chapters on the topic "Convex projective geometry"

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Oda, Tadao. "Integral Convex Polytopes and Toric Projective Varieties." In Convex Bodies and Algebraic Geometry, 66–114. Berlin, Heidelberg: Springer Berlin Heidelberg, 1988. http://dx.doi.org/10.1007/978-3-642-72547-0_2.

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Hibi, Takayuki. "Ehrhart polynomials of convex polytopes, ℎ-vectors of simplicial complexes, and nonsingular projective toric varieties." In Discrete and Computational Geometry: Papers from the DIMACS Special Year, 165–78. Providence, Rhode Island: American Mathematical Society, 1991. http://dx.doi.org/10.1090/dimacs/006/09.

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Li, Hongbo. "Projective geometric theorem proving with Grassmann–Cayley algebra." In From Past to Future: Graßmann's Work in Context, 275–85. Basel: Springer Basel, 2010. http://dx.doi.org/10.1007/978-3-0346-0405-5_24.

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Feferman, Solomon, John W. Dawson, Stephen C. Kleene, Gregory H. Moore, Robert M. Solovay, and Jean van Heijenoort. "Introductory note to 1999b, c, d, g and h." In Kurt GöDel Collected Works Volume I, 272–75. Oxford University PressNew York, NY, 2001. http://dx.doi.org/10.1093/oso/9780195147209.003.0055.

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Abstract In addition to the many important logical results on which Gödel reported in Karl Menger’s Ergebnisse eines mathematischen Kolloquiums at the University of Vienna, there are five lesser known ones on geometry. In fact, Gödel had taken courses with Menger, and these notes are best seen within the framework of a program for reforming and purifying differential and projective geometry developed by Menger in the colloquium. In order to free the notion of “curvature” from “the complicated conceptual machinery” (Menger 1952) of classical differential geometry, in particular from coordinates, parameterizations and differentiability assumptions, Menger proposed to study suitable n-tuples of points in compact convex metric spaces. The triangle inequality implies the existence of three points in the Euclidean plane isometric to any triple of points in such a space, and their curvature is taken to be the reciprocal of the radius of the circle circumscribed around them. Menger then defined the curvature at a point of a curve in his space as the number from which the curvature of any three sufficiently close isometric points in the Euclidean plane differs arbitrarily little. Several results were based on this definition as well as on modifications of it by Franz Alt and by Gödel himself (Alt 1933). For surfaces the problem of curvature is more ambiguous and difficult. One now considers quadruples of points in Menger’s spaces; but points isometric to them may not exist at all in Euclidean space, and even when they do exist, the reciprocal of the radius of their circumscribed sphere is of no particular significance for the problem of curvature. Gödel (1993b) shows, however, in answer to a question of Laura Klanfer, that this reciprocal can be used to prove that, if an isometric Euclidean quadruple exists and is non-coplanar, then the metric quadruple is isometric, under the geodesic metric, to four points of a metricized sphere of suitable radius.
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"Curves with Locally Convex Projection." In Differential Geometry and Topology of Curves, 91–95. CRC Press, 2001. http://dx.doi.org/10.1201/9781420022605.ch20.

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Goebel, Kazimierz, and Stanisław Prus. "Projections on balls and convex sets." In Elements of Geometry of Balls in Banach Spaces, 70–84. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198827351.003.0006.

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Radial projection on the unit ball and its Lipschitz constant are discussed. Special attention is paid to nonexpansive projections on balls and other sets. The cases of Hilbert spaces and spaces with uniform norm are studied in more detail.
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"On the road between polar projection bodies and intersection bodies." In The Interface between Convex Geometry and Harmonic Analysis, 75–85. Providence, Rhode Island: American Mathematical Society, 2007. http://dx.doi.org/10.1090/cbms/108/07.

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Conference papers on the topic "Convex projective geometry"

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Akhter, Muhammad Awais, Rob Heylen, and Paul Scheunders. "Hyperspectral unmixing with projection onto convex sets using distance geometry." In IGARSS 2015 - 2015 IEEE International Geoscience and Remote Sensing Symposium. IEEE, 2015. http://dx.doi.org/10.1109/igarss.2015.7326970.

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Stark, Henry, and Peyma Oskoui-Fard. "Geometry-Free X-Ray Reconstruction Using the Theory of Convex Projections." In Machine Vision. Washington, D.C.: Optica Publishing Group, 1987. http://dx.doi.org/10.1364/mv.1987.tha5.

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In problems involving inspection by x-ray tomography it may not always be possible to obtain a full set of parallel-beam or fan-beam views from which to reconstruct an image. This may occur because of: 1) external obstructions; 2) internal obstruction; and 3) restricted data acquisition times. Yet typical reconstruction algorithms such as convolution-back projection (CBP) or the direct Fourier method (DFM) are based on specific geometries and a full set of views.
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Stark, Henry, and Peyma Oskoui-Fard. "Image reconstruction in tomography using convex projections." In OSA Annual Meeting. Washington, D.C.: Optica Publishing Group, 1986. http://dx.doi.org/10.1364/oam.1986.mr4.

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The method of projections onto convex sets (POCS) has been widely used in image recovery and synthesis problems but it has never been used as an actual reconstruction algorithm in tomography. Yet POCS offers certain advantages over methods such as convolution backprojection or direct Fourier inversion. What are these advantages? First, POCS does not require a particular data gathering geometry (e.g., parallel beam or fan beam projections); it can be used with any arbitrary set of projection data. Second, POCS furnishes a systematic technique for incorporating a priori information about the image. It is interesting to note that when POCS is used in its most primitive mode, i.e., the only constraints are those imposed by the line-integral projections, it becomes the well-known ART algorithm. We describe how POCS is used to reconstruct images in tomography and present computer simulations to verify the feasibility of the procedure.
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van Holland, Winfried, and Willem F. Bronsvoort. "Assembly Features and Visibility Maps." In ASME 1995 15th International Computers in Engineering Conference and the ASME 1995 9th Annual Engineering Database Symposium collocated with the ASME 1995 Design Engineering Technical Conferences. American Society of Mechanical Engineers, 1995. http://dx.doi.org/10.1115/cie1995-0799.

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Abstract Feature modelling is now being used quite extensively in the context of manufacturing of parts. It is shown that the use of features in product models, instead of geometric information only, can be very useful in assembly as well. This is done by introducing two types of assembly features, handling and connection features, and by outlining their usability in several assembly planning modules. It is also shown that in assembly feature modelling the concept of internal freedom of motion can be profitably used. Internal freedom of motion can be represented with visibility maps, which can be transformed using the central projection method. An extension of the central projection method, projecting a visibility map onto a cube, is described.
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Reyes, L., and E. Bayro-Corrochano. "Geometric approach for simultaneous projective reconstruction of points, lines, planes, quadrics, plane conies and degenerate quadrics." In Proceedings of the 17th International Conference on Pattern Recognition, 2004. ICPR 2004. IEEE, 2004. http://dx.doi.org/10.1109/icpr.2004.1333705.

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Smith, Hollis, and Julian Norato. "A Topology Optimization Method for the Design of Orthotropic Plate Structures." In ASME 2020 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2020. http://dx.doi.org/10.1115/detc2020-22400.

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Abstract This work introduces a topology optimization method for the design of structures composed of rectangular plates each of which is made of a predetermined anisotropic material. This work builds upon the geometry projection method with two notable additions. First, a novel geometric parameterization of plates represented by offset surfaces is formulated that is simpler than the one used in previous works. Second, the formulation presented herein adds support to the geometry projection method for geometric components with general anisotropic material properties. A design-generation framework is formulated that produces optimal designs composed exclusively of rectangular plates that may be made of a predetermined, generally anisotropic material. The efficacy of the proposed method is demonstrated with a numerical example comparing optimal cantilever beam designs obtained using isotropic- and orthotropic-material plates. For this example, we maximize the stiffness of the structure for a fixed amount of material. The example reveals the importance of considering material anisotropy in the design of plate structures. Moreover, it is demonstrated that an optimally stiff design for plates made of an isotropic material can exhibit detrimental performance if the plates are naively replaced with an anisotropic material. Although the example given in this work is in the context of orthotropic plates, since the formulation presented in this work supports arbitrary anisotropic materials, it may be readily extended to support the design of each component’s material anisotropy as a part of the optimization routine.
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Dumitrescu, Adrian, Scott J. I. Walker, and Atul Bhaskar. "Modelling of the Hypervelocity Impact Performance of a Corrugated Shield with an Integrated Honeycomb Geometry." In 2022 16th Hypervelocity Impact Symposium. American Society of Mechanical Engineers, 2022. http://dx.doi.org/10.1115/hvis2022-13.

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Abstract In the context of spacecraft protection from orbital debris, a wide variety of shield designs revolving around multi shock panels (MSP) has been previously investigated. In parallel with these purpose-built shields there has been work done on understanding the protection capabilities of CFRP-AL honeycomb structures which are also impacted. A widely held view is that a honeycomb core sandwich panel performs poorly under hypervelocity impact (HVI), especially at low impact angles. By contrast, an MSP is very effective in dispersing the impact energy and stopping the projectile across a wide range of impact angles. The objective of this paper is to better understand the relative impact performance between multi shock panels and shields which contain honeycomb geometries in order to more effectively make use of the satellite structure in protecting the components inside a satellite. This research explores a novel shield geometry which combines a multi shock panel with corrugated walls with a honeycomb core in a design that can perform well both structurally and in impact.
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Sharpe, Conner, Carolyn Conner Seepersad, Seth Watts, and Dan Tortorelli. "Design of Mechanical Metamaterials via Constrained Bayesian Optimization." In ASME 2018 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2018. http://dx.doi.org/10.1115/detc2018-85270.

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Advances in additive manufacturing processes have made it possible to build mechanical metamaterials with bulk properties that exceed those of naturally occurring materials. One class of these metamaterials is structural lattices that can achieve high stiffness to weight ratios. Recent work on geometric projection approaches has introduced the possibility of optimizing these architected lattice designs in a drastically reduced parameter space. The reduced number of design variables enables application of a new class of methods for exploring the design space. This work investigates the use of Bayesian optimization, a technique for global optimization of expensive non-convex objective functions through surrogate modeling. We utilize formulations for implementing probabilistic constraints in Bayesian optimization to aid convergence in this highly constrained engineering problem, and demonstrate results with a variety of stiff lightweight lattice designs.
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Maywald, Thomas, Thomas Backhaus, Sven Schrape, and Arnold Kühhorn. "Geometric Model Update of Blisks and its Experimental Validation for a Wide Frequency Range." In ASME Turbo Expo 2017: Turbomachinery Technical Conference and Exposition. American Society of Mechanical Engineers, 2017. http://dx.doi.org/10.1115/gt2017-63446.

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The contribution discusses a model update procedure and its experimental validation in the context of blisk mistuning. Object of investigation is an industrial test blisk of an axial compressor which is milled from solid using a state of the art 5-axis milling machine. First, the blisk geometry is digitized by a blue light fringe projector. Digitization is largely automated using an industrial robot cell in order to guarantee high repeatability of the measurement results. Additionally, frequency mistuning patterns are identified based on vibration measurements. Here, the system excitation is realized by a modal impact hammer. The blade response is detected using a laser scanning vibrometer. Furthermore, all blades except the currently excited one are detuned with additional masses. Applying these masses allows to identify a blade dominated natural frequency for each blade and every mode of interest. Finally, these blade dominated frequencies are summarized to mode specific mistuning patterns. The key part of the contribution presents a model update approach which is focused on small geometric deviations between real engine parts and idealized simulation models. Within this update procedure the nodal coordinates of an initially tuned finite element blisk model were modified in order to match the geometry of the real part measured by blue light fringe projection. All essential pre- and post-processing steps of the mesh morphing procedure are described and illustrated. It could be proven that locally remaining geometric deviations between updated finite element model and the optical measurement results are below 5 μm. For the purpose of validation blade dominated natural frequencies of the updated finite element blisk model are calculated for each sector up to a frequency of 17 kHz. Finally, the numerically predicted mistuning patterns are compared against the experimentally identified counterparts. At this point a very good agreement between experimentally identified and numerically predicted mistuning patterns can be proven across several mode families. Even mistuning patterns of higher modes at about 17 kHz are well predicted by the geometrically mistuned finite element model. Within the last section of the paper, possible uncertainties of the presented model update procedure are analyzed. As a part of the study the digitization of the investigated blisk has been repeated for ten times. These measurement results serve as input for the model update procedure described before. In the context of this investigation ten independent geometrical mistuned simulation models are created and the corresponding mistuning patterns are calculated.
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Guo, Yuxiao, and Xin Tong. "View-Volume Network for Semantic Scene Completion from a Single Depth Image." In Twenty-Seventh International Joint Conference on Artificial Intelligence {IJCAI-18}. California: International Joint Conferences on Artificial Intelligence Organization, 2018. http://dx.doi.org/10.24963/ijcai.2018/101.

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We introduce a View-Volume convolutional neural network (VVNet) for inferring the occupancy and semantic labels of a volumetric 3D scene from a single depth image. Our method extracts the detailed geometric features from the input depth image with a 2D view CNN and then projects the features into a 3D volume according to the input depth map via a projection layer. After that, we learn the 3D context information of the scene with a 3D volume CNN for computing the result volumetric occupancy and semantic labels. With combined 2D and 3D representations, the VVNet efficiently reduces the computational cost, enables feature extraction from multi-channel high resolution inputs, and thus significantly improve the result accuracy. We validate our method and demonstrate its efficiency and effectiveness on both synthetic SUNCG and real NYU dataset.
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