arXiv subjects

Hector J. Hortua

Publications and source records attributed to Hector J. Hortua.

15 recordsLinked to original sources

arXiv2025

Conditional Diffusion-Flow models for generating 3D cosmic density fields: applications to f(R) cosmologies

Next-generation galaxy surveys promise unprecedented precision in testing gravity at cosmological scales. However, realising this potential requires accurately modelling the non-linear cosmic web. We address this challenge by exploring conditional generative modelling to create 3D dark matter density fields via score-based (diffusion) and flow-based methods. Our results demonstrate the power of diffusion models to accurately reproduce the matter power spectra and bispectra, even for unseen configurations. They also offer a significant speed-up with slightly reduced accuracy, when flow-based reconstructing the probability distribution function, but they struggle with higher-order statistics. To improve conditional generation, we introduce a novel multi-output model to develop feature representations of the cosmological parameters. Our findings offer a powerful tool for exploring deviations from standard gravity, combining high precision with reduced computational cost, thus paving the way for more comprehensive and efficient cosmological analyses

astro-ph.CO↗

arXiv2025

Enhancing Diagnostic in 3D COVID-19 Pneumonia CT-scans through Explainable Uncertainty Bayesian Quantification

Accurately classifying COVID-19 pneumonia in 3D CT scans remains a significant challenge in the field of medical image analysis. Although deterministic neural networks have shown promising results in this area, they provide only point estimates outputs yielding poor diagnostic in clinical decision-making. In this paper, we explore the use of Bayesian neural networks for classifying COVID-19 pneumonia in 3D CT scans providing uncertainties in their predictions. We compare deterministic networks and their Bayesian counterpart, enhancing the decision-making accuracy under uncertainty information. Remarkably, our findings reveal that lightweight architectures achieve the highest accuracy of 96\% after developing extensive hyperparameter tuning. Furthermore, the Bayesian counterpart of these architectures via Multiplied Normalizing Flow technique kept a similar performance along with calibrated uncertainty estimates. Finally, we have developed a 3D-visualization approach to explain the neural network outcomes based on SHAP values. We conclude that explainability along with uncertainty quantification will offer better clinical decisions in medical image analysis, contributing to ongoing efforts for improving the diagnosis and treatment of COVID-19 pneumonia.

eess.IV↗

arXiv2024

Deep Bayesian segmentation for colon polyps: Well-calibrated predictions in medical imaging

Colorectal polyps are generally benign alterations that, if not identified promptly and managed successfully, can progress to cancer and cause affectations on the colon mucosa, known as adenocarcinoma. Today advances in Deep Learning have demonstrated the ability to achieve significant performance in image classification and detection in medical diagnosis applications. Nevertheless, these models are prone to overfitting, and making decisions based only on point estimations may provide incorrect predictions. Thus, to obtain a more informed decision, we must consider point estimations along with their reliable uncertainty quantification. In this paper, we built different Bayesian neural network approaches based on the flexibility of posterior distribution to develop semantic segmentation of colorectal polyp images. We found that these models not only provide state-of-the-art performance on the segmentation of this medical dataset but also, yield accurate uncertainty estimates. We applied multiplicative normalized flows(MNF) and reparameterization trick on the UNET, FPN, and LINKNET architectures tested with multiple backbones in deterministic and Bayesian versions. We report that the FPN + EfficientnetB7 architecture with MNF is the most promising option given its IOU of 0.94 and Expected Calibration Error (ECE) of 0.004, combined with its superiority in identifying difficult-to-detect colorectal polyps, which is effective in clinical areas where early detection prevents the development of colon cancer.

eess.IV↗

arXiv2021

Constraining cosmological parameters from N-body simulations with Bayesian Neural Networks

In this paper, we use The Quijote simulations in order to extract the cosmological parameters through Bayesian Neural Networks. This kind of model has a remarkable ability to estimate the associated uncertainty, which is one of the ultimate goals in the precision cosmology era. We demonstrate the advantages of BNNs for extracting more complex output distributions and non-Gaussianities information from the simulations.

astro-ph.CO↗

arXiv2020

Accelerating MCMC algorithms through Bayesian Deep Networks

Markov Chain Monte Carlo (MCMC) algorithms are commonly used for their versatility in sampling from complicated probability distributions. However, as the dimension of the distribution gets larger, the computational costs for a satisfactory exploration of the sampling space become challenging. Adaptive MCMC methods employing a choice of proposal distribution can address this issue speeding up the convergence. In this paper we show an alternative way of performing adaptive MCMC, by using the outcome of Bayesian Neural Networks as the initial proposal for the Markov Chain. This combined approach increases the acceptance rate in the Metropolis-Hasting algorithm and accelerate the convergence of the MCMC while reaching the same final accuracy. Finally, we demonstrate the main advantages of this approach by constraining the cosmological parameters directly from Cosmic Microwave Background maps.

astro-ph.CO↗

arXiv2020

Parameters Estimation for the Cosmic Microwave Background with Bayesian Neural Networks

In this paper, we present the first study that compares different models of Bayesian Neural Networks (BNNs) to predict the posterior distribution of the cosmological parameters directly from the Cosmic Microwave Background temperature and polarization maps. We focus our analysis on four different methods to sample the weights of the network during training: Dropout, DropConnect, Reparameterization Trick (RT), and Flipout. We find out that Flipout outperforms all other methods regardless of the architecture used, and provides tighter constraints for the cosmological parameters. Moreover we compare with MCMC posterior analysis obtaining comparable error correlation among parameters, with BNNs being orders of magnitude faster in inference, although less accurate. Thanks to the speed of the inference process with BNNs, the posterior distribution, outcome of the neural network, can be used as the initial proposal for the Markov Chain. We show that this combined approach increases the acceptance rate in the Metropolis-Hasting algorithm and accelerates the convergence of the MCMC, while reaching the same final accuracy. In the second part of the paper, we present a guide to the training and calibration of a successful multi-channel BNN for the CMB temperature and polarization map. We show how tuning the regularization parameter for the standard deviation of the approximate posterior on the weights in Flipout and RT we can produce unbiased and reliable uncertainty estimates, i.e., the regularizer acts like a hyperparameter analogous to the dropout rate in Dropout. Finally, we show how polarization, when combined with the temperature in a unique multi-channel tensor fed to a single BNN, helps to break degeneracies among parameters and provides stringent constraints.

astro-ph.IM↗

arXiv2020

Reliable Uncertainties for Bayesian Neural Networks using Alpha-divergences

Bayesian Neural Networks (BNNs) often result uncalibrated after training, usually tending towards overconfidence. Devising effective calibration methods with low impact in terms of computational complexity is thus of central interest. In this paper we present calibration methods for BNNs based on the alpha divergences from Information Geometry. We compare the use of alpha divergence in training and in calibration, and we show how the use in calibration provides better calibrated uncertainty estimates for specific choices of alpha and is more efficient especially for complex network architectures. We empirically demonstrate the advantages of alpha calibration in regression problems involving parameter estimation and inferred correlations between output uncertainties.

cs.LG↗

arXiv2019

Cosmological Features of Primordial Magnetic Fields

The aim of this thesis is to study the effects on the CMB anisotropy due to primordial magnetic fields and to analyze some favorable scenarios of magnetogenesis constrained by those signatures, including limits on the amplitude of the fields from bounds on CMB non-Gaussianity and background models. In fact, we found out that helicity in the fields plays an important role in the analysis PMFs origin, by generating significant features in the cross-correlation polarization pattern and the increasing of the signal in the reduced CMB bispectrum. In the latter case, we reported that non-causal fields (mainly generated during the inflation epoch) are the most favorable models constrained by CMB observations. Moreover, we have studied the presence of an IR cutoff in the spectra and bispectra finding appealing unique features from primordial magnetic fields. Another important result shown in this thesis is the equivalence between different approaches of cosmological perturbation theory in the magnetized context. In fact, assuming a magnetized Universe and building gauge invariant quantities in both approaches: the 1+3covariant and the gauge invariant; we found out that those invariants represent the same physical meaning. Besides, we define gauge invariant related to the electromagnetic potentials which in future works, could help us to study magnetogenesis models on perturbed scenarios.

astro-ph.CO↗

arXiv2017

Reduced bispectrum seeded by helical primordial magnetic fields

In this paper, we investigate the effects of helical primordial magnetic fields (PMFs) on the cosmic microwave background (CMB) reduced bispectrum. We derive the full three-point statistics of helical magnetic fields and numerically calculate the even contribution in the collinear configuration. We then numerically compute the CMB reduced bispectrum induced by passive and compensated PMF modes on large angular scales. There is a negative signal on the bispectrum due to the helical terms of the fields and we also observe that the biggest contribution to the bispectrum comes from the non-zero IR cut-off for causal fields, unlike the two-point correlation case. For negative spectral indices, the reduced bispectrum is enhanced by the passive modes. This gives a lower value of the upper limit for the mean amplitude of the magnetic field on a given characteristic scale. However, high values of IR cut-off in the bispectrum, and the helical terms of the magnetic field relaxes this bound. This demonstrates the importance of the IR cut-off and helicity in the study of the nature of PMFs from CMB observations.

astro-ph.CO↗

arXiv2015

Contrasting formulations of cosmological perturbations in a magnetic FLRW cosmology

In this paper we contrasted two cosmological perturbation theory formalisms, the 1+3 covariant gauge invariant and the gauge invariant by comparing their gauge invariant variables associated with magnetic field defined in each approach. In the first part we give an introduction to each formalism assuming the presence of a magnetic field. We found that gauge invariant quantities defined by 1+3 covariant approach are related with spatial variations of the magnetic field (defined in the gauge invariant formalism) between two closed fundamental observers. This relation was computed by choosing the comoving gauge in the gauge invariant approach in a magnetized universe. Furthermore, we have derived the gauge transformations for electromagnetic potentials in the gauge invariant approach and the Maxwell's equations have been written in terms of these potentials.

gr-qc↗

arXiv2015

Effects of primordial magnetic fields on CMB

The origin of large-scale magnetic fields is an unsolved problem in cosmology. In order to overcome, a possible scenario comes from the idea that these fields emerged from a small primordial magnetic field (PMF), produced in the early universe. This field could lead to the observed large-scales magnetic fields but also, would have left an imprint on the cosmic microwave background (CMB). In this work we summarize some statistical properties of this PMFs on the FLRW background. Then, we show the resulting PMF power spectrum using cosmological perturbation theory and some effects of PMFs on the CMB anisotropies.

astro-ph.CO↗

arXiv2014

Power spectrum of post-inflationary primordial magnetic fields

The origin of large scale magnetic fields is one of the most puzzling topics in cosmology and astrophysics. It is assumed that the observed magnetic fields result from the amplification of an initial field produced in the early universe. In this paper we compute the exact power spectrum of magnetic fields created after inflation best known as post inflationary magnetic fields, using the first order cosmological perturbation theory. Our treatment differs from others works because we include an infrared cutoff which encodes only causal modes in the spectrum. The cross-correlation between magnetic energy density with Lorentz force and the anisotropic part of the electromagnetic field are exactly computed. We compare our results with previous works finding agreement in cases where the ratio between lower and upper cutoff is very small. However, we found that spectrum is strongly affected when this ratio is greater than 0.2. Moreover, the effect of a post inflationary magnetic field with a lower cutoff on the angular power spectrum in the temperature distribution of CMB was also exactly calculated. The main feature is a shift of the spectrum's peak as function of the infrared cutoff, therefore analyzing this effect we could infer the value of this cutoff and thus constraining the primordial magnetic fields generation models.

gr-qc↗

arXiv2014

Equivalence between formulations in Cosmological Perturbation Theory: The primordial magnetic fields as an example

Nowdays, Cosmological Perturbation Theory is a standard and useful tool in theoretical cosmology. In this work, we compare the 1+3 covariant formalism in perturbation theory (Ellis et al.) to the gauge invariant approach (Bruni et al.), and we show the equivalence of these formalisms to fix the choice of the perturbed variables (gauge choice) in magnetogenesis. We analyze the evolution of primordial magnetic fields through perturbation theory and we discuss the similarities and differences between these two approaches. We get the Maxwell's equations and show a cosmic dynamo like equation written in Poisson gauge, computing the evolution of primordial magnetic fields. Finally, prospects around these formalisms in the study of magnetogenesis are discussed.

gr-qc↗

arXiv2013

Evolution of magnetic fields through cosmological perturbation theory

The origin of galactic and extra-galactic magnetic fields is an unsolved problem in modern cosmology. A possible scenario comes from the idea of these fields emerged from a small field, a seed, which was produced in the early universe (phase transitions, inflation, ...) and it evolves in time. Cosmological perturbation theory offers a natural way to study the evolution of primordial magnetic fields. The dynamics for this field in the cosmological context is described by a cosmic dynamo like equation, through the dynamo term. In this paper we get the perturbed Maxwell's equations and compute the energy momentum tensor to second order in perturbation theory in terms of gauge invariant quantities. Two possible scenarios are discussed, first we consider a FLRW background without magnetic field and we study the perturbation theory introducing the magnetic field as a perturbation. The second scenario, we consider a magnetized FLRW and build up the perturbation theory from this background. We compare the cosmological dynamo like equation in both scenarios.

astro-ph.CO↗

arXiv2009

Temperature for the (2+1)-dimensional Black Hole with Non Linear Electrodynamics from the Generalized Uncertainty Principle

In this paper, we study the thermodynamical properties of the (2+1) dimensional black hole with a non-linear electrodynamics and with a negative cosmological constant, using the Generalized Uncertainty Principle (GUP). This approach shows that there is a minimum mass or remnant for the black hole, corresponding to the minimum radius of the event horizon that has a size of the order of the Planck scale. We also show that the heat capacity for this black hole is always positive.

gr-qc↗