arXiv subjects

Álvaro González

Publications and source records attributed to Álvaro González.

5 recordsLinked to original sources

arXiv2024

Moduli of Continuity in Metric Models and Extension of Liveability Indices

Index spaces serve as valuable metric models for studying properties relevant to various applications, such as social science or economics. These properties are represented by real Lipschitz functions that describe the degree of association with each element within the underlying metric space. After determining the index value within a given sample subset, the classic McShane and Whitney formulas allow a Lipschitz regression procedure to be performed to extend the index values over the entire metric space. To improve the adaptability of the metric model to specific scenarios, this paper introduces the concept of a composition metric, which involves composing a metric with an increasing, positive and subadditive function $ϕ$. The results presented here extend well-established results for Lipschitz indices on metric spaces to composition metrics. In addition, we establish the corresponding approximation properties that facilitate the use of this functional structure. To illustrate the power and simplicity of this mathematical framework, we provide a concrete application involving the modelling of livability indices in North American cities.

stat.ME↗

arXiv2019

Universality of power-law exponents by means of maximum likelihood estimation

Power-law type distributions are extensively found when studying the behaviour of many complex systems. However, due to limitations in data acquisition, empirical datasets often only cover a narrow range of observation, making it difficult to establish power-law behaviour unambiguously. In this work we present a statistical procedure to merge different datasets with the aim of obtaining a broader fitting range for the statistics of different experiments or observations of the same system or the same universality class. This procedure is applied to the Gutenberg-Richter law for earthquakes and for synthetic earthquakes (acoustic emission events) generated in the laboratory: labquakes. Different earthquake catalogs have been merged finding a Gutenberg-Ricther law holding for more than eight orders of magnitude in seismic moment. The value of the exponent of the energy distribution of labquakes depends on the material used in the compression experiments. By means of the procedure exposed in this manuscript, it has been found that the Gutenberg-Richter law for earthquakes and charcoal labquakes can be characterized by the same power-law exponent.

physics.data-an↗

arXiv2019

Power-law size distributions in geoscience revisited

The size or energy of diverse structures or phenomena in geoscience appears to follow power-law distributions. A rigorous statistical analysis of such observations is tricky, though. Observables can span several orders of magnitude, but the range for which the power law may be valid is typically truncated, usually because the smallest events are too tiny to be detected and the largest ones are limited by the system size. We revisit several examples of proposed power-law distributions dealing with potentially damaging natural phenomena. Adequate fits of the distributions of sizes are especially important in these cases, given that they may be used to assess long-term hazard. After reviewing the theoretical background for power-law distributions, we improve an objective statistical fitting method and apply it to diverse data sets. The method is described in full detail and it is easy to implement. Our analysis elucidates the range of validity of the power-law fit and the corresponding exponent, and whether a power-law tail is improved by a truncated log-normal. We confirm that impact fireballs and Californian earthquakes show untruncated power-law behavior, whereas global earthquakes follow a double power law. Rain precipitation over space and time and tropical cyclones show a truncated power-law regime. Karst sinkholes and wildfires, in contrast, are better described by truncated log-normals, although wildfires also may show power-law regimes. Our conclusions only apply to the analyzed data sets, but show the potential of applying this robust statistical technique in the future.

physics.geo-ph↗

arXiv2009

Measurement of areas on a sphere using Fibonacci and latitude-longitude lattices

The area of a spherical region can be easily measured by considering which sampling points of a lattice are located inside or outside the region. This point-counting technique is frequently used for measuring the Earth coverage of satellite constellations, employing a latitude-longitude lattice. This paper analyzes the numerical errors of such measurements, and shows that they could be greatly reduced if the Fibonacci lattice were used instead. The latter is a mathematical idealization of natural patterns with optimal packing, where the area represented by each point is almost identical. Using the Fibonacci lattice would reduce the root mean squared error by at least 40%. If, as is commonly the case, around a million lattice points are used, the maximum error would be an order of magnitude smaller.

math.MG↗

arXiv2004

Using synchronization to improve earthquake forecasting in a cellular automaton model

A new forecasting strategy for stochastic systems is introduced. It is inspired by the concept of anticipated synchronization between pairs of chaotic oscillators, recently developed in the area of Dynamical Systems, and by the earthquake forecasting algorithms in which different pattern recognition functions are used for identifying seismic premonitory phenomena. In the new strategy, copies (clones) of the original system (the master) are defined, and they are driven using rules that tend to synchronize them with the master dynamics. The observation of definite patterns in the state of the clones is the signal for connecting an alarm in the original system that efficiently marks the impending occurrence of a catastrophic event. The power of this method is quantitatively illustrated by forecasting the occurrence of characteristic earthquakes in the so-called Minimalist Model.

cond-mat.dis-nn↗