1,721,101 research outputs found
Decomp2d: An R solution for image decomposition
No full textThe subjects of image processing include feature extraction, compression, denoising, image enhancement, and restoration. Many softwares have been developed for these studies. However, few studies have focused on decomposition in the literature, even though image decomposition is essential for image processing. This paper reviews several two-dimensional methods that can be adapted for image decomposition. Furthermore, we provide an R solution termed Decomp2d, tailored to the viewpoint of image decomposition based on existing R packages. © 2022 The Author(s)Y
Orbit closures of unipotent flows for hyperbolic manifolds with Fuchsian ends
No full textWe establish an analogue of Ratner's orbit closure theorem for any connected closed subgroup generated by unipotent elements in SO(d, 1) acting on the space Gamma\SO(d, 1), assuming that the associated hyperbolic manifold M = Gamma\H-d is a convex cocompact manifold with Fuchsian ends. For d = 3, this was proved earlier by McMullen, Mohammadi and Oh. In a higher-dimensional case, the possibility of accumulation on closed orbits of intermediate subgroups causes serious issues, but, in the end, all orbit closures of unipotent flows are relatively homogeneous. Our results imply the following: for any k >= 1,,(1) the closure of any k-horosphere in M is a properly immersed submanifold;,(2) the closure of any geodesic (k + 1)-plane in M is a properly immersed submanifold;,(3) an infinite sequence of maximal properly immersed geodesic (k + 1)-planes intersecting core M becomes dense in M.,
Invariant Measures for Horospherical Actions and Anosov Groups
No full textLet Gamma be a Zariski dense Anosov subgroup of a connected semisimple real algebraic group G. For a maximal horospherical subgroup N of G, we show that the space of all non-trivial NM-invariant ergodic and A-quasi-invariant Radon measures on Gamma\G, up to proportionality, is homeomorphic to RrankG-1, where A is a maximal real split torus and M is a maximal compact subgroup that normalizes N. One of the main ingredients is to establish the NM-ergodicity of all Burger-Roblin measures.
Dichotomy and Measures on Limit Sets of Anosov Groups
No full textLet G be a connected semisimple real algebraic group. For a Zariski dense Anosov subgroup Γ < G, we show that a Γ-conformal measure is supported on the limit set of Γ if and only if its dimension is Γ-critical. This implies the uniqueness of a Γ-conformal measure for each critical dimension, answering the question posed in our earlier paper with Edwards [13]. We obtain this by proving a higher rank analogue of the Hopf–Tsuji–Sullivan dichotomy for the maximal diagonal action. Other applications include an analogue of the Ahlfors measure conjecture for Anosov subgroups.
Topological proof of benoist-quint’s orbit closure theorem for SO(d, 1)
No full textWe present a new proof of the following theorem of Benoist-Quint: Let G := SO degrees (d, 1), d >= 2 and Delta < G a cocompact lattice. Any orbit of a Zariski dense subgroup Gamma of G is either finite or dense in Delta\G. While Benoist and Quint's proof is based on the classification of stationary measures, our proof is topological, using ideas from the study of dynamics of unipotent flows on the infinite volume homogeneous space Gamma\G.
ERGODIC DECOMPOSITIONS OF GEOMETRIC MEASURES ON ANOSOV HOMOGENEOUS SPACES
No full textLet G be a connected semisimple real algebraic group and Gamma a Zariski dense Anosov subgroup of G with respect to a minimal parabolic subgroup P. Let N be the maximal horospherical subgroup of G given by the unipotent radical of P. We describe the N -ergodic decompositions of all Burger-Roblin measures as well as the A-ergodic decompositions of all Bowen-Margulis-Sullivan measures on Gamma\G. As a consequence, we obtain the following refinement of the main result of [17]: the space of all non-trivial N-invariant ergodic and P degrees-quasi-invariant Radon measures on Gamma\G, up to constant multiples, is homeomorphic to RrankG-1 x {1, ..., k} where k is the number of P degrees-minimal subsets in Gamma\G.
Probabilistic Principal Curves on Riemannian Manifolds
No full textThis paper studies a new curve-fitting approach to data on Riemannian manifolds. We define a principal curve based on a mixture model for observations and unobserved latent variables and propose a new algorithm to estimate the principal curve for given data points on Riemannian manifolds.N
Lifting scheme for streamflow data in river networks
No full textThis paper presents a new multiscale method for analysing water pollutant data located in river networks. The main idea of the proposed method is to adapt the conventional lifting scheme, reflecting the characteristics of streamflow data in the river network domain. Due to the complexity of the data domain structure, it is difficult to apply the lifting scheme to the streamflow data directly. To solve this problem, we propose a new lifting scheme algorithm for streamflow data that incorporates flow-adaptive neighbourhood selection, flow proportional weight generation and flow-length adaptive removal point selection. A nondecimated version of the proposed lifting scheme is also provided. The simulation study demonstrates that the proposed method successfully performs a multiscale analysis of streamflow data. Furthermore, we provide a real data analysis of water pollutant data observed on the Geum-River basin compared to the existing smoothing method.N
Robust coherence analysis for long-memory processes
Full text linkThis paper investigates the linear relationships between two time-series in the frequency domain, termed coherence analysis. It is widely used in various fields, including signal processing, engineering, and meteorology. However, conventional coherence analysis tends to be sensitive to outliers. Laplace cross-periodogram and a corresponding robust coherence analysis based on the least-absolute deviation (LAD) regression have recently been developed to improve this shortcoming. In this paper, to extend the scope of Laplace cross-periodogram, we study a robust cross periodogram for long-memory processes and derive its asymptotic distribution. Through numerical studies, we demonstrate the usefulness of the proposed robust coherence analysis for long-memory processes.N
Pseudo-quantile functional data clustering
No full textThis paper studies the problem of functional data clustering. Functional data have their own characteristics and contain rich information that cannot be obtained when regarding the data as multivariate data. Functional data are inherently infinite-dimensional, so classical clustering techniques for finite-dimensional data may not be suitable for functional data. There are several clustering methods for functional data based on probabilistic models or basis expansion approaches. However, most of these depend on the symmetric structure of the model or the mean response; hence, these cannot reflect characteristics of the distribution of data beyond the mean, such as behavior at the extremes. In this paper, we propose a new approach for functional data clustering based on the concept of an asymmetric norm. For this purpose, we consider pseudo-quantiles, such as M-quantiles and expectiles, and their corresponding curves that can provide rich distributional information about hidden structures in the data at various levels. Moreover, as a theoretical justification for the proposed method, a strong consistency property is investigated. Results from numerical examples, including real data analysis, demonstrate the promising empirical properties of the proposed approach. (C) 2020 Elsevier Inc. All rights reserved.N
- …
