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Fields Institute Communications
We present several sharp inequalities for the SL(n) invariant Ω 2,n (K) introduced in our earlier work on centro-affine invariants for smooth convex bodies containing the origin. ... The technique employed prompts us to conjecture that any SL(n) invariant of convex bodies with continuous and positive centro-affine curvature function can be obtained as a limit of normalized p-affine ... Inequalities for a second order centro-affine invariant In  , we introduced a class of SL(n) invariants for smooth convex bodies in R n . ...doi:10.1007/978-1-4614-6406-8_16 fatcat:do7s37hkbnazrn5dlmzxc3fna4
We present several sharp inequalities for the SL(n) invariant Ω_2,n(K) introduced in our earlier work on centro-affine invariants for smooth convex bodies containing the origin. ... The technique employed prompts us to conjecture that any SL(n) invariant of convex bodies with continuous and positive centro-affine curvature function can be obtained as a limit of normalized p-affine ... Inequalities for a second order centro-affine invariant In  , we introduced a class of SL(n) invariants for smooth convex bodies in R n . ...arXiv:1208.0783v1 fatcat:4uabanb7qfck3exb7jsbxn6sti
The utility of this framework is shown in a number of affine invariant clustering algorithms on image point data. ... This paper proposes a Riemannian geometric framework to compute averages and distributions of point configurations so that different configurations up to affine transformations are considered to be the ... Previous work treating affine invariance in computer vision can be generally divided into two approaches: invariants and normalization. ...doi:10.1109/cvpr.2006.50 dblp:conf/cvpr/BegelforW06 fatcat:57wfmw256bf23hvucajprzwmwm
Such features include for instance trajectory smoothness, periodicity, affine velocity, or more generally, all affine-invariant features, which are of particular importance in humancentered applications ... Building on the presented affine deformation framework, we finally revisit the concept of trajectory redundancy from the viewpoint of group theory. * The paper on which this extended abstract is based ... Finally, the origin of affine invariance in human movements was theorized in relation to the previously established existence of affine invariance in the human visual system (which guarantees the unity ...doi:10.1109/tro.2015.2450413 fatcat:xh7ote3nhvcb3hcgpop74dddry
Many algorithms in numerical analysis are affine equivariant: they are immune to changes of affine coordinates. This is because those algorithms are defined using affine invariant constructions. ... As a result, they are also invariant with respect to non-invertible affine transformation from spaces of different dimensions. ... We first motivate on an examples why full affine equivariance is needed. Example 2.1 (Downhill simplex minimization algorithm revisited). We revisit Example 1.6. ...arXiv:1605.07344v1 fatcat:5kpnkyrfmncajazld62ketrvvu
An equivalent way of defining such a structure is as an equivalence class of conformally related metrics with a unique affine connection Γ_ω, which is invariant under Weyl transformations. ... However, the invariance of the compatibility condition suggests that the affine connection remains invariant under a Weyl transformation. ... In Sect. 4 we revisit the fundamental physical meanings of these transformations and demonstrate how the use of non-Riemannian geometries allows one to extend the usual diffeomorphism invariance to diffeomorphism ...doi:10.1140/epjc/s10052-019-7394-z fatcat:2orszogu4ndthcmdjovfwssmwm
Bose in 1953, is revisited in the context of modern developments in high energy physics. ... Unification of gravity and electromagnetism based on a theory with an affine non-symmetric connection Γ^λ_μν≠Γ^λ_νμ and Γ_μ = Γ^λ_[μλ]≠ 0, proposed by S. N. ... In the projective invariant premetric phase the fourth dimension of the manifold E with negative signature cannot be identified with physical time. Also, this manifold is affine and has no origin. ...arXiv:1302.3324v3 fatcat:ldzctt5wenel7mfck7hg6u64le
affine invariant segmentation. ... We propose to compute texture features using affine invariant intrinsic neighborhoods and affine invariant intrinsic ori- entation matrices. ...
Journal of Geometry
Thus all lines parallel to this one are s s invariant under all affinities of J and every orbit of J is s subset of such an invariant line. ... invariant belongs to J. See [1, 280] or Theorem 23 in [15, 126] for results similar to the following s LEMMA. ...doi:10.1007/bf01222894 fatcat:lpsscet3avcz3nfyhdjwqs5w4u
Springer, 1993] that uses the inverse of the covariance matrix of S to define an affine invariant norm, denoted A_S, and an affine invariant triangulation, denoted DT_A_S[S]. ... In addition, we provide different affine invariant sorting methods of a point set S and of the vertices of a polygon P that can be combined with known algorithms to obtain other affine invariant triangulation ... Conclusions In this paper we revisited Nielson's affine invariant norm, whose unit disk represents how spread the point set is with respect to its mean. ...arXiv:2011.02197v1 fatcat:e3itntpbirbetdfxygpuevnvmy
In order to resolve some conflicts between the recent calculation and the conventional ones in the well-known literatures, the calculation of the free-fall energy density is revisited and some differences ... The affine connections in the Kruskal coordinates are straightforwardly calculated as Γ ... However, the affine connections vanish at x ± = 0 corresponding to the bifurcation point. ...doi:10.1142/s0217732316500334 fatcat:vvt4lo2n6rdsxnfat4uk7h7yqa
It is substituted by the world continuum endowed only with the affine connection. ... The metric, accompanied by the tensor Goldstone boson, is to emerge during the spontaneous breaking of the global affine symmetry. Implications for gravity and the Universe are indicated. ... Under the affine symmetry, the background metric ceases to be invariant. But it still possesses an invariance subgroup. ...arXiv:gr-qc/0409067v1 fatcat:sblncsgnhnfmjjpm5pdlufdjnq
This process must encompass strategies for distinguishing affinity, triggering the TCR, and incorporating both sensitivity and specificity ... However, a static depiction of this signaling cascade fails to capture the complex and dynamic process by which individual T cells discriminate TCR:peptide-MHC affinity, then integrate signals over time ... We speculate that revisiting established signaling components and transcriptional regulators of T and B cells with these approaches in hand will unmask new biology. ...doi:10.1016/j.coi.2015.01.012 pmid:25660212 pmcid:PMC4397149 fatcat:v77eqsvynregdhg3554htoct6e
Summary: “Affine invariants of complex hypersurfaces are defined. These invariants characterize the complex hypersurface up to a complex affine motion.” ... Koutroufiotis [same journal 28 (1988), no. 2, 153-169; MR 90g:53005; “The pedal revisited”, Tech. Rep. 100, Dept. Math., Univ. Ioannina, Ioannina, 1984; per bibl.].} ...
Complex Kleinian Groups
Loxodromic Transformations in PSL(3, C) . . . . . . . . . . 105 4.3 The classification theorems . . . . . . . . . . . . . . . . . . . . . . 112 5 Kleinian Groups with a Control Group 119 5.1 PSL(2, C) revisited ... . . . 28 1.3.2 Mostow's rigidity theorem . . . . . . . . . . . . . . . . . . . 29 1.3.3 On the Patterson-Sullivan measure . . . . . . . . . . . . . . 31 1.3.4 Sullivan's theorem on nonexistence of invariant ...doi:10.1007/978-3-0348-0481-3_3 fatcat:ydd3efculfbxzmnjyhg3nlrlti
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