Related papers: Computing the luminosity distance via optimal homo…
Analyzing high-dimensional data with manifold learning algorithms often requires searching for the nearest neighbors of all observations. This presents a computational bottleneck in statistical manifold learning when observations of…
We revisit the classical polygonal line simplification problem and study it using the Hausdorff distance and Fr\'echet distance. Interestingly, no previous authors studied line simplification under these measures in its pure form, namely:…
We describe a $O(\log n )$-approximation algorithm for computing the homotopic \Frechet distance between two polygonal curves that lie on the boundary of a triangulated topological disk. Prior to this work, algorithms were known only for…
Recent observational evidence of axially symmetric anisotropies in the local cosmic expansion rate motivates an investigation of whether they can be accounted for within the Lema\^itre-Tolman-Bondi (LTB) framework with an off-center…
This article develops a new predictor-corrector algorithm for numerical path tracking in the context of polynomial homotopy continuation. In the corrector step it uses a newly developed Newton corrector algorithm which rejects an initial…
A new, fast second-order method is proposed that achieves the optimal $\mathcal{O}\left(|\log(\epsilon)|\epsilon^{-3/2}\right)$ complexity to obtain first-order $\epsilon$-stationary points. Crucially, this is deduced without assuming the…
Most existing distance metric learning methods assume perfect side information that is usually given in pairwise or triplet constraints. Instead, in many real-world applications, the constraints are derived from side information, such as…
We propose a new framework for formulating optimal transport distances between Markov chains. Previously known formulations studied couplings between the entire joint distribution induced by the chains, and derived solutions via a reduction…
In this work, the relativistic phenomena of Lorentz-Fitzgerald contraction and time dilation are derived using a modified distance formula that is appropriate for discrete space. This new distance formula is different than the Pythagorean…
The correlation between the luminosities and rotation velocities of galaxies can be used to estimate distances to late-type galaxies. It is an appropriate moment to re-evaluate this method given the great deal of new information available.…
The stray light uniformity is one of the important factors affecting the signal-to-noise ratio of the optical astronomical telescope. It will cause regional differences in the background intensity of the detector image, resulting in a…
We present an algorithm to extract the distance list from atomic pair distribution functions (PDFs) in a highly automated way. The algorithm is constructed via curve fitting based on a Debye scattering equation model. Due to the non-convex…
We propose a relativistic version of the cosmological principle and confront it to the Hubble diagram of supernovae and other probes.
The free distance of a convolutional code is a reliable indicator of its performance. However its computation is not an easy task. In this paper, we present some algorithms to compute the free distance with good efficiency that work for…
Most of current cosmological theories are built combining an isotropic and homogeneous manifold with a scale factor that depends on time. If one supposes a hyperconical universe with linear expansion, an inhomogeneous metric can be obtained…
Topological Data Analysis methods can be useful for classification and clustering tasks in many different fields as they can provide two dimensional persistence diagrams that summarize important information about the shape of potentially…
With the distance sum rule in the Friedmann-Lema\^{\i}tre-Robertson-Walker metric, model-independent constraints on both the Hubble constant $H_0$ and spatial curvature $\Omega_{K}$ can be obtained using strong lensing time-delay data and…
A recalibration of the luminosity-linewidth technique is discussed which introduces (i) new cluster calibration data, (ii) new corrections for reddening as a function of inclination, and (iii) a new zero-point calibration using 13 galaxies…
A homotopy method for multi-objective optimization that produces uniformly sampled Pareto fronts by construction is presented. While the algorithm is general, of particular interest is application to simulation-based engineering…
A direct cryptographic computation of the Cosmological Constant {\Omega}{\Lambda} based solely on a physically anchored prime modulus that stands in full agreement with observational data on {\Omega}{\Lambda} and {\Omega}m and the…