Related papers: A New Angle on L2 Regularization
From the basic concepts of general relativity, we investigate the rotation of the polarization angle by a moving gravitational lens. Particularly, we clarify the existing confusion in the literature by showing and explaining why such…
This paper is devoted to the description of complex finite-dimensional algebras of level two. We obtain the classification of algebras of level two in the varieties of Jordan, Lie and associative algebras.
We review a range of stastistical methods for analyzing the structures of star clusters, and derive a new measure ${\cal Q}$ which both quantifies, and distinguishes between, a (relatively smooth) large-scale radial density gradient and…
Lung cancer ranks as one of the leading causes of cancer diagnosis and is the foremost cause of cancer-related mortality worldwide. The early detection of lung nodules plays a pivotal role in improving outcomes for patients, as it enables…
Let n,d be positive integers, with d even (say d=2e). Let X_(n,d) denote the locus of degree d hypersurfaces in P^n which consist of two e-fold hyperplanes. We bound the regularity of the ideal of this variety. Moreover, we show that this…
A complete characterization of proper holomorphic mappings between domains from the class of all pseudoconvex Reinhardt domains in $\C^2$ with the logarithmic image equal to a strip or a half-plane is given.
This paper develops the exact linear relationship between the leading eigenvector of the unnormalized modularity matrix and the eigenvectors of the adjacency matrix. We propose a method for approximating the leading eigenvector of the…
Self-propelled particles with anti-aligning interactions generally do not form a polar order. However, in this Letter, we show that when multiple types of such particles coexist and interact through aligning interactions between different…
State-of-the-art subspace clustering methods are based on expressing each data point as a linear combination of other data points while regularizing the matrix of coefficients with $\ell_1$, $\ell_2$ or nuclear norms. $\ell_1$…
I review progress in understanding the evolution of normal field and cluster galaxies through the combination of HST imaging and ground-based spectroscopy. These data suggest that the bulk of the star formation producing the present-day…
We consider commuting pairs of holomorphic endomorphisms of P^2 with disjoint sequence of iterates. The remaining case to be studied is when their degrees coincide after some number of iterations. We show in this case that they are either…
This paper presents DeepI2P: a novel approach for cross-modality registration between an image and a point cloud. Given an image (e.g. from a rgb-camera) and a general point cloud (e.g. from a 3D Lidar scanner) captured at different…
We study the spectral function of the 2D Hubbard model using cluster perturbation theory, and the density matrix renormalization group as a cluster solver. We reconstruct the two-dimensional dispersion at, and away from half-filling using…
Subspace clustering methods based on $\ell_1$, $\ell_2$ or nuclear norm regularization have become very popular due to their simplicity, theoretical guarantees and empirical success. However, the choice of the regularizer can greatly impact…
In this article we classify normal forms and unfoldings of linear maps in eigenspaces of (anti)-automorphisms of order two. Our main motivation is provided by applications to linear systems of ordinary differential equations, general and…
In this paper, congruences between holomorphic Hilbert modular forms are studied. We show the best possible level optimization result outside l for l > 2 by solving the remaining case of Mazur principle when the degree of the totally real…
After generalizing the concept of clusters to incorporate clusters that are linked to other clusters through some relatively narrow bridges, an approach for detecting patches of separation between these clusters is developed based on an…
In hyperbolic space, the angle of intersection and distance classify pairs of totally geodesic hyperplanes. A similar algebraic invariant classifies pairs of hyperplanes in the Einstein universe. In dimension 3, symplectic splittings of a…
We completely classify all plane curves of degree at most 30 with a unique cuspidal (locally unibranch) singular point and rational normalization in terms of the Newton pairs parameterizing the cusp. We distinguish between prime and…
We study the validity of cosmic distance duality relation between angular diameter and luminosity distances. To test this duality relation we use the latest Union2 Supernovae Type Ia (SNe Ia) data for estimating the luminosity distance. The…