arXiv subjects

Jaime Gomez

Publications and source records attributed to Jaime Gomez.

7 recordsLinked to original sources

arXiv2026

On multidimensional infinite dihedral group extensions of Gibbs Markov maps

We obtain a local central limit theorem for cocycles associated with a class of non abelian and non compact group extensions of Gibbs Markov maps. This class consists of multidimensional infinite dihedral groups. Unlike in the set up of the random walks on groups, we cannot use the convolution of measures on the group and instead we resort to an approach based on irreducible representations. Depending on the dimension of the group, we obtain either mixing, and thus ergodicity, or dissipativity. Also, we obtain the asymptotics of the first return time of the group extension to the origin.

math.DS↗

arXiv2025

Ratio limits and pressure function for group extensions of Gibbs Markov maps

Ratio limit theorems for random walks on (various) groups are known. We obtain a generalization of this type of ratio limit for deterministic walks on certain groups driven by Gibbs Markov maps. In terms of proofs, the main difficulty comes down to the absence of a convolution structure. Also, for (finitely generated) group extensions of Gibbs Markov maps we obtain a characterization of the pressure function without a symmetry assumption.

math.DS↗

arXiv2024

On the K-theory of magnetic algebras: Iwatsuka case

In the tight-binding approximation, an Iwatsuka magnetic field is modeled by a function on $\mathbb{Z}^2$ with constant, but distinct values in the two parts of the lattice separated by a straight line of slope $\alpha\in [-\infty,\infty]$. In this paper, the $K$-theory of the magnetic $C^*$-algebras generated by an Iwatsuka magnetic field for any possible $\alpha$ is computed. One interesting aspect concerns the analysis of the behavior of the system in the transition from rational to irrational $\alpha$. It turns out that when $\alpha$ is irrational, the magnetic hull associated with the flux operator forms a Cantor set. On the other hand, for rational $\alpha$ this set coincides with the two-point compactification of $\mathbb{Z}$. This characterization, along with the use of the Pimsner-Voiculescu exact sequence, is the main ingredient for the computation of the $K$-theory. Once the $K$-theory is known, with the use of the index theory one can deduce the bulk-interface correspondence for tight-binding Hamiltonians subjected to an Iwatsuka magnetic field. Notably, it occurs that the topological quantization of the interface currents remains independent of the slope $\alpha$.

math.OA↗

arXiv2005

Sub-Optimum Signal Linear Detector Using Wavelets and Support Vector Machines

The problem of known signal detection in Additive White Gaussian Noise is considered. In previous work, a new detection scheme was introduced by the authors, and it was demonstrated that optimum performance cannot be reached in a real implementation. In this paper we analyse Support Vector Machines (SVM) as an alternative, evaluating the results in terms of Probability of detection curves for a fixed Probability of false alarm.

cs.IR↗

arXiv2005

Upgrading Pulse Detection with Time Shift Properties Using Wavelets and Support Vector Machines

Current approaches in pulse detection use domain transformations so as to concentrate frequency related information that can be distinguishable from noise. In real cases we do not know when the pulse will begin, so we need a time search process in which time windows are scheduled and analysed. Each window can contain the pulsed signal (either complete or incomplete) and / or noise. In this paper a simple search process will be introduced, allowing the algorithm to process more information, upgrading the capabilities in terms of probability of detection (Pd) and probability of false alarm (Pfa).

cs.IR↗

arXiv2005

Wavelet Time Shift Properties Integration with Support Vector Machines

This paper presents a short evaluation about the integration of information derived from wavelet non-linear-time-invariant (non-LTI) projection properties using Support Vector Machines (SVM). These properties may give additional information for a classifier trying to detect known patterns hidden by noise. In the experiments we present a simple electromagnetic pulsed signal recognition scheme, where some improvement is achieved with respect to previous work. SVMs are used as a tool for information integration, exploiting some unique properties not easily found in neural networks.

cs.IR↗

arXiv2005

Optimum Signal Linear Detector in the Discrete Wavelet Transform-Domain

The problem of known signal detection in Additive White Gaussian Noise is considered. In this paper a new detection algorithm based on Discrete Wavelet Transform pre-processing and threshold comparison is introduced. Current approaches described in [7] use the maximum value obtained in the wavelet domain for decision. Here, we use all available information in the wavelet domain with excellent results. Detector performance is presented in Probability of detection curves for a fixed probability of false alarm.

cs.IT↗