Related papers: Evolving the Loeb Scale
It is known that discrete scale invariance leads to log-periodic corrections to scaling. We investigate the correlations of a system with discrete scale symmetry, discuss in detail possible extension of this symmetry such as translation and…
Majority of the current dimensionality reduction or retrieval techniques rely on embedding the learned feature representations onto a computable metric space. Once the learned features are mapped, a distance metric aids the bridging of gaps…
Current convolution neural network (CNN) classification methods are predominantly focused on flat classification which aims solely to identify a specified object within an image. However, real-world objects often possess a natural…
Building accurate and predictive models of the underlying mechanisms of celestial motion has inspired fundamental developments in theoretical physics. Candidate theories seek to explain observations and predict future positions of planets,…
We investigate distality and existence of distal expansions in valued fields and related structures. In particular, we characterize distality in a large class of ordered abelian groups, provide an AKE-style characterization for henselian…
In this short note a differential version of the classical Weil descent is established in all characteristics. This yields a ready-to-deploy tool of differential restriction of scalars for differential varieties over finite differential…
This work establishes a high-precision relativistic theoretical model: start from studying finite speed of light effect based on a coordinate transformation, and further extend the research methods to analyze the overall relativistic…
We present a new, fully generative model of optical telescope image sets, along with a variational procedure for inference. Each pixel intensity is treated as a Poisson random variable, with a rate parameter dependent on latent properties…
There are irreducible differences between the Hubble constant measured locally and the global value. They are due to density perturbations and finite sample volume (cosmic variance) and finite number of objects in the sample (sampling…
The light we observe from distant astrophysical objects including supernovae and quasars allows us to determine large distances in terms of a cosmological model. Despite the success of the standard cosmological model in fitting the data,…
Cosmography, as an integral branch of cosmology, strives to characterize the Universe without relying on pre-determined cosmological models. This model-independent approach utilizes Taylor series expansions around the current epoch,…
We present a novel approach to measuring the expansion rate and the geometry of the Universe, which combine time-delay cosmography in lens galaxy clusters with pure samples of 'cosmic chronometers' (CCs) by probing the member galaxies. The…
The Random Hypersurface Model (RHM) is introduced that allows for estimating a shape approximation of an extended object in addition to its kinematic state. An RHM represents the spatial extent by means of randomly scaled versions of the…
The luminosity distance can be used to determine the properties of large scale structure around the observer. To this purpose we develop a new inversion method to map luminosity distance to a LTB metric based on the use of the exact…
The model of the homogenous and isotropic universe is considered in which the coordinate system of reference is not defined by the matter but is a priori specified. The scale factor of the universe changes following the linear law. The…
The Reeb graph is a construction that studies a topological space through the lens of a real valued function. It has widely been used in applications, however its use on real data means that it is desirable and increasingly necessary to…
Existing and planned optical telescopes and surveys can detect artificially-illuminated objects comparable in total brightness to a major terrestrial city out to the outskirts of the Solar System. Orbital parameters of Kuiper belt objects…
Sequentially obtained dataset usually exhibits different behavior at different data resolutions/scales. Instead of inferring from data at each scale individually, it is often more informative to interpret the data as an ensemble of time…
$\lambda$-Scale is an enrichment of lambda calculus which is adapted to emergent algebras. It can be used therefore in metric spaces with dilations.
We establish a sequential Hopf's Lemma for higher order differential inequalities in one variable and give some applications of this result.