Search results for " Geometry."
showing 10 items of 2189 documents
New Error Measures to Evaluate Features on Three-Dimensional Scenes
2011
In this paper new error measures to evaluate image features in three-dimensional scenes are proposed and reviewed. The proposed error measures are designed to take into account feature shapes, and ground truth data can be easily estimated. As other approaches, they are not error-free and a quantitative evaluation is given according to the number of wrong matches and mismatches in order to assess their validity
Metric Lie groups admitting dilations
2019
We consider left-invariant distances $d$ on a Lie group $G$ with the property that there exists a multiplicative one-parameter group of Lie automorphisms $(0, \infty)\rightarrow\mathtt{Aut}(G)$, $\lambda\mapsto\delta_\lambda$, so that $ d(\delta_\lambda x,\delta_\lambda y) = \lambda d(x,y)$, for all $x,y\in G$ and all $\lambda>0$. First, we show that all such distances are admissible, that is, they induce the manifold topology. Second, we characterize multiplicative one-parameter groups of Lie automorphisms that are dilations for some left-invariant distance in terms of algebraic properties of their infinitesimal generator. Third, we show that an admissible left-invariant distance on a Lie …
An efficient algorithm to estimate the sparse group structure of an high-dimensional generalized linear model
2014
Massive regression is one of the new frontiers of computational statistics. In this paper we propose a generalization of the group least angle regression method based on the differential geometrical structure of a generalized linear model specified by a fixed and known group structure of the predictors. An efficient algorithm is also proposed to compute the proposed solution curve.
Rational normal curves and Hadamard products
2021
AbstractGiven $$r>n$$ r > n general hyperplanes in $$\mathbb P^n,$$ P n , a star configuration of points is the set of all the n-wise intersection of the hyperplanes. We introduce contact star configurations, which are star configurations where all the hyperplanes are osculating to the same rational normal curve. In this paper, we find a relation between this construction and Hadamard products of linear varieties. Moreover, we study the union of contact star configurations on a same conic in $$\mathbb P^2$$ P 2 , we prove that the union of two contact star configurations has a special h-vector and, in some cases, this is a complete intersection.
Halogen bond directionality translates tecton geometry into self-assembled architecture geometry
2013
The structures of halogen-bonded infinite chains involving two diiodoperfluoroalkanes and a bent bis(pyrid-4′-yl)oxadiazole show that the geometry of the pyridyl pendant rings is translated into the angle between the formed halogen bonds.
The Poincar\'e-Cartan Form in Superfield Theory
2018
An intrinsic description of the Hamilton-Cartan formalism for first-order Berezinian variational problems determined by a submersion of supermanifolds is given. This is achieved by studying the associated higher-order graded variational problem through the Poincar\'e-Cartan form. Noether theorem and examples from superfield theory and supermechanics are also discussed.
Electronic structure of tetraphenyldithiapyranylidene : A valence effective Hamiltonian theoretical investigation
1992
We present a theoretical investigation of the electronic structure of tetraphenyldithiapyranylidene (DIPSΦ4) using the nonempirical valence effective Hamiltonian (VEH) method. Molecular geometries are optimized at the semiempirical PM3 level which predicts an alternating nonaromatic structure for the dithiapyranylidene (DIPS) framework. The VEH one‐electron energy level distribution calculated for DIPSΦ4 is presented as a theoretical XPS simulation and is analyzed by comparison to the electronic structure of its molecular components DIPS and benzene. The theoretical VEH spectrum is found to be fully consistent with the experimental solid‐state x‐ray photoelectron spectroscopy (XPS) spectrum…
Hardy spaces and quasiconformal maps in the Heisenberg group
2023
We define Hardy spaces $H^p$, $00$ such that every $K$-quasiconformal map $f:B \to f(B) \subset \mathbb{H}^1$ belongs to $H^p$ for all $0<p<p_0(K)$. Second, we give two equivalent conditions for the $H^p$ membership of a quasiconformal map $f$, one in terms of the radial limits of $f$, and one using a nontangential maximal function of $f$. As an application, we characterize Carleson measures on $B$ via integral inequalities for quasiconformal mappings on $B$ and their radial limits. Our paper thus extends results by Astala and Koskela, Jerison and Weitsman, Nolder, and Zinsmeister, from $\mathbb{R}^n$ to $\mathbb{H}^1$. A crucial difference between the proofs in $\mathbb{R}^n$ and $\mathbb{…
$n$-harmonic coordinates and the regularity of conformal mappings
2014
This article studies the smoothness of conformal mappings between two Riemannian manifolds whose metric tensors have limited regularity. We show that any bi-Lipschitz conformal mapping or $1$-quasiregular mapping between two manifolds with $C^r$ metric tensors ($r > 1$) is a $C^{r+1}$ conformal (local) diffeomorphism. This result was proved in [12, 27, 33], but we give a new proof of this fact. The proof is based on $n$-harmonic coordinates, a generalization of the standard harmonic coordinates that is particularly suited to studying conformal mappings. We establish the existence of a $p$-harmonic coordinate system for $1 < p < \infty$ on any Riemannian manifold.
Conformality and $Q$-harmonicity in sub-Riemannian manifolds
2016
We prove the equivalence of several natural notions of conformal maps between sub-Riemannian manifolds. Our main contribution is in the setting of those manifolds that support a suitable regularity theory for subelliptic $p$-Laplacian operators. For such manifolds we prove a Liouville-type theorem, i.e., 1-quasiconformal maps are smooth. In particular, we prove that contact manifolds support the suitable regularity. The main new technical tools are a sub-Riemannian version of p-harmonic coordinates and a technique of propagation of regularity from horizontal layers.