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Within the so-called scaled quantum theory, the standard bouncing ball problem is analyzed under the presence of a gravitational field and harmonic potential. In this framework, the quantum-classical transition of the density matrix is described by the linear scaled von Neumann equation for mixed states and after it has been particularized to the case of pure states. The main purpose of this work is to show how this theory works for conservative systems and the quantum-classical transition is carried out in a continuous and smooth way, being equivalent to a nonlinear differential wave equation which contains a transition parameter ranging continuously from one to zero and covering all dynamical regimes in-between the two extreme quantum and classical regimes. This parameter can be seen as a degree of quantumness where all intermediate dynamical regimes show quantum features but are fading gradually when approaching to the classical value., Comment: Accepted for publication in Euro. Phys. J. Plus

In this work we characterize all the static and spherically symmetric vacuum solutions in $f(R)$ gravity when the principal null directions of the Weyl tensor are non-expanding. In contrast to General Relativity, we show that the Nariai spacetime is not the only solution of this type when general $f(R)$ theories are considered. In particular, we find four different solutions for the non-constant Ricci scalar case, all of them corresponding to the same theory, given by $f(R) = r_0^{-1}\left\lvert R-3/r_0^2\right\rvert^{1/2}$, where $r_0$ is a non-null constant. Finally, we briefly present some geometric properties of these solutions., Comment: 7 pages, 4 figures, published in EPJC

In this work, we consider different theoretical aspects and simple applications of the Milburn equation which is governed by a parameter controlling what is known as intrinsic decoherence. The main goal is to show some similarities also observed when external decoherence is considered. Linear entropy, Ehrenfest relations, probability density current, the Wigner representation as well as the relation to a Lindbladian master equation are analyzed in terms of this intrinsic decoherence, leading to new insights on the Milburn dynamics. Interference of two wave packets, tunneling and the bouncing ball problem are also studied under this perspective., Comment: Accepted for publication in EPJ Plus

This paper presents a global study of the class $\bf{Q}{\widehat{ES}}$ of all real quadratic polynomial differential systems possessing exactly one elemental infinite singular point and one triple infinite singular point, which is either an infinite nilpotent elliptic-saddle or a nilpotent saddle. This class can be divided into three different families, namely, $\bf{Q}{{\widehat{ES}(A)}}$ of phase portraits possessing three real finite singular points, $\bf{Q}{{\widehat{ES}(B)}}$ of phase portraits possessing one real and two complex finite singular points, and $\bf{Q}{{\widehat{ES}(C)}}$ of phase portraits possessing one real triple finite singular point. Here we provide the complete study of the geometry of these three families. Modulo the action of the affine group and time homotheties, families $\bf{Q}{{\widehat{ES}(A)}}$ and $\bf{Q}{{\widehat{ES}(B)}}$ are three-dimensional and family $\bf{Q}{{\widehat{ES}(C)}}$ is two-dimensional. We study the respective bifurcation diagrams of their closures with respect to specific normal forms, in subsets of real Euclidean spaces. The bifurcation diagram of family $\bf{Q}{{\widehat{ES}(A)}}$ (respectively, $\bf{Q}{{\widehat{ES}(B)}}$ and $\bf{Q}{{\widehat{ES}(C)}}$) yields 1274 (respectively, 89 and 14) subsets with 91 (respectively, 27 and 12) topologically distinct phase portraits for systems in the closure $\overline{\bf{Q}{{\widehat{ES}(A)}}}$ (respectively, $\overline{\bf{Q}{{\widehat{ES}(B)}}}$ and $\overline{\bf{Q}{{\widehat{ES}(C)}}}$) within the representatives of $\bf{Q}{{\widehat{ES}(A)}}$ (respectively, $\bf{Q}{{\widehat{ES}(B)}}$ and $\bf{Q}{{\widehat{ES}(C)}}$) given by a specific normal form., Comment: 112 pages. arXiv admin note: text overlap with arXiv:1303.2525

In this work, we proposed a smooth transition wave equation from a quantum to classical regime in the framework of von Neumann formalism for ensembles and then obtained an equivalent scaled equation. This led us to develop a scaled statistical theory following the well-known Wigner-Moyal approach of quantum mechanics. This scaled nonequilibrium statistical mechanics has in it all the ingredients of the classical and quantum theory described in terms of a continuous parameter displaying all the dynamical regimes in between the two extreme cases. Finally, a simple application of our scaled formalism consisting of reflection from a mirror by computing various quantities, including probability density plots, scaled trajectories, and arrival times, was analyzed.

Sleep constitutes a key indicator of human health, performance, and quality of life. Sleep deprivation has long been related to the onset, development, and worsening of several mental and metabolic disorders, constituting an essential marker for preventing, evaluating, and treating different health conditions. Sleep Activity Recognition methods can provide indicators to assess, monitor, and characterize subjects' sleep-wake cycles and detect behavioral changes. In this work, we propose a general method that continuously operates on passively sensed data from smartphones to characterize sleep and identify significant sleep episodes. Thanks to their ubiquity, these devices constitute an excellent alternative data source to profile subjects' biorhythms in a continuous, objective, and non-invasive manner, in contrast to traditional sleep assessment methods that usually rely on intrusive and subjective procedures. A Heterogeneous Hidden Markov Model is used to model a discrete latent variable process associated with the Sleep Activity Recognition task in a self-supervised way. We validate our results against sleep metrics reported by tested wearables, proving the effectiveness of the proposed approach and advocating its use to assess sleep without more reliable sources., Comment: v1.0

Decoherence is a well established process for the emergence of classical mechanics in open quantum systems. However, it can have two different origins or mechanisms depending on the dynamics one is considering, speaking then about intrinsic decoherence for isolated systems and environmental decoherence due to dissipation/fluctuations for open systems. This second mechanism can not be considered for backflow since no thermal fluctuation terms can be added in the formalism in order to keep an important requirement for the occurrence of this effect: only contributions of positive momenta along time should be maintained. The purpose of this work is to analyze the backflow effect in the light of the underlying intrinsic decoherence and the dissipative dynamics. For this goal, we first deal with the Milburn approach where a mean frequency of the unitary evolution steps undergone for the system is assumed. A comparative analysis is carried out in terms of the Lindblad master equation. Second, the so-called quantum-to-classical transition wave equation is analyzed from a linear scaled Schr\"odinger equation which is derived and expressed in terms of a continuous parameter covering from the quantum to the classical regime as well as all in-between dynamical non-classical regimes. This theoretical analysis is inspired by the Wentzel-Kramers-Brillouin approximation. And third, in order to complete our analysis, the transition wave equation formalism is also applied to dissipative backflow within the Caldirola-Kanai approach where the dissipative dynamics comes from an effective Hamiltonian. In all the cases treated here, backflow is gradually suppressed as the intrinsic decoherence process is developing, paying a special attention to the classical limit. The route to classicality is not unique., Comment: Accepted for publication in JPA

Psychiatric patients' passive activity monitoring is crucial to detect behavioural shifts in real-time, comprising a tool that helps clinicians supervise patients' evolution over time and enhance the associated treatments' outcomes. Frequently, sleep disturbances and mental health deterioration are closely related, as mental health condition worsening regularly entails shifts in the patients' circadian rhythms. Therefore, Sleep Activity Recognition constitutes a behavioural marker to portray patients' activity cycles and to detect behavioural changes among them. Moreover, mobile passively sensed data captured from smartphones, thanks to these devices' ubiquity, constitute an excellent alternative to profile patients' biorhythm. In this work, we aim to identify major sleep episodes based on passively sensed data. To do so, a Heterogeneous Hidden Markov Model is proposed to model a discrete latent variable process associated with the Sleep Activity Recognition task in a self-supervised way. We validate our results against sleep metrics reported by clinically tested wearables, proving the effectiveness of the proposed approach., Comment: Extended Abstract presented at Machine Learning for Health (ML4H) symposium 2022, November 28th, 2022, New Orleans, United States & Virtual, http://www.ml4h.cc, 10 pages (6 pages + 4 pages of references and appendices)

In this review we deal with open (dissipative and stochastic) quantum systems within the Bohmian mechanics framework which has the advantage to provide a clear picture of quantum phenomena in terms of trajectories, originally in configuration space. The gradual decoherence process is studied from linear and nonlinear Schr\"odinger equations through Bohmian trajectories as well as by using the so-called quantum-classical transition differential equation through scaled trajectories. This transition is governed by a continuous parameter, the transition parameter, covering these two extreme open dynamical regimes. Thus, two sources of decoherence of different nature are going to be considered. Several examples will be presented and discussed in order to illustrate the corresponding theory behind each case, namely: the so-called Brownian-Bohmian motion leading to quantum diffusion coefficients, dissipative diffraction in time, dissipative tunnelling for a parabolic barrier under the presence of an electric field and stochastic early arrivals for the same type of barrier. In order to simplify the notations and physical discussion, the theoretical developments will be carried out in one dimension throughout all this wok. One of the main goals is to analyze the gradual decoherence process existing in these open dynamical regimes in terms of trajectories, leading to a more intuitive way of understanding the underlying physics in order to gain new insights., Comment: Review Article; accepted for publication in Found. Phys

We introduce PyHHMM, an object-oriented open-source Python implementation of Heterogeneous-Hidden Markov Models (HHMMs). In addition to HMM's basic core functionalities, such as different initialization algorithms and classical observations models, i.e., continuous and multinoulli, PyHHMM distinctively emphasizes features not supported in similar available frameworks: a heterogeneous observation model, missing data inference, different model order selection criterias, and semi-supervised training. These characteristics result in a feature-rich implementation for researchers working with sequential data. PyHHMM relies on the numpy, scipy, scikit-learn, and seaborn Python packages, and is distributed under the Apache-2.0 License. PyHHMM's source code is publicly available on Github (https://github.com/fmorenopino/HeterogeneousHMM) to facilitate adoptions and future contributions. A detailed documentation (https://pyhhmm.readthedocs.io/en/latest), which covers examples of use and models' theoretical explanation, is available. The package can be installed through the Python Package Index (PyPI), via 'pip install pyhhmm'.

Some unexplored decoherence aspects within the Caldeira-Leggett master equation are analyzed and discussed. The decoherence process is controlled by the two environment parameters, the relaxation rate or friction and the temperature, leading to a gradual transition from the quantum to classical regime. Arrival time distributions, nonminimum-uncertainty-product or stretching Gaussian wave packets, identical particles and diffraction in time display interesting features during the decoherence process undergone by the time dependent interference patterns. We show that the presence of a constant force field does not affect the decoherence, {\it positive} values of the stretching parameter reduces the rate of decoherence, the symmetry of the wave function for identical particles plays no role when open dynamics are considered; and diffraction in time and space is gradually washed out by increasing the temperature and/or relaxation rate in the zero dissipation limit within the so-called quantum shutter problem., Comment: Accepted for publication in EPJP

In this work, momentum-space decoherence using minimum and nonminimum-uncertainty-product (stretched) Gaussian wave packets in the framework of Caldeira-Leggett formalism and under the presence of a linear potential is studied. As a dimensionless measure of decoherence, purity, a quantity appearing in the definition of the {\it linear entropy}, is studied taking into account the role of the stretching parameter. Special emphasis is on the open dynamics of the well-known cat states and bosons and fermions compared to distinguishable particles. For the cat state, while the stretching parameter speeds up the decoherence, the external linear potential strength does not affect the decoherence time; only the interference pattern is shifted. Furthermore, the interference pattern is not observed for minimum-uncertainty-product-Gaussian wave packets in the momentum space. Concerning bosons and fermions, the question we have addressed is how the symmetry of the wave functions of indistinguishable particles is manifested in the decoherence process, which is understood here as the loss of being indistinguishable due to the gradual emergence of classical statistics with time. We have observed that the initial bunching and anti-bunching character of bosons and fermions, respectively, in the momentum space are not preserved as a function of the environmental parameters, temperature and damping constant. However, fermionic distributions are slightly broader than the distinguishable ones and these similar to the bosonic distributions. This general behavior could be interpreted as a residual reminder of the symmetry of the wave functions in the momentum space for this open dynamics., Comment: Accepted for publication in Entropy

We present a framework for transfer learning based on modular variational Gaussian processes (GP). We develop a module-based method that having a dictionary of well fitted GPs, one could build ensemble GP models without revisiting any data. Each model is characterised by its hyperparameters, pseudo-inputs and their corresponding posterior densities. Our method avoids undesired data centralisation, reduces rising computational costs and allows the transfer of learned uncertainty metrics after training. We exploit the augmentation of high-dimensional integral operators based on the Kullback-Leibler divergence between stochastic processes to introduce an efficient lower bound under all the sparse variational GPs, with different complexity and even likelihood distribution. The method is also valid for multi-output GPs, learning correlations a posteriori between independent modules. Extensive results illustrate the usability of our framework in large-scale and multi-task experiments, also compared with the exact inference methods in the literature., Comment: Accepted at Advances in Neural Information Processing Systems (NeurIPS) 2021. arXiv admin note: substantial text overlap with arXiv:2010.02554

Language models (LM) have grown with non-stop in the last decade, from sequence-to-sequence architectures to the state-of-the-art and utter attention-based Transformers. In this work, we demonstrate how the inclusion of deep generative models within BERT can bring more versatile models, able to impute missing/noisy words with richer text or even improve BLEU score. More precisely, we use a Gaussian Mixture Variational Autoencoder (GMVAE) as a regularizer layer and prove its effectiveness not only in Transformers but also in the most relevant encoder-decoder based LM, seq2seq with and without attention.

Time series forecasting is an important problem across many domains, playing a crucial role in multiple real-world applications. In this paper, we propose a forecasting architecture that combines deep autoregressive models with a Spectral Attention (SA) module, which merges global and local frequency domain information in the model's embedded space. By characterizing in the spectral domain the embedding of the time series as occurrences of a random process, our method can identify global trends and seasonality patterns. Two spectral attention models, global and local to the time series, integrate this information within the forecast and perform spectral filtering to remove time series's noise. The proposed architecture has a number of useful properties: it can be effectively incorporated into well-know forecast architectures, requiring a low number of parameters and producing interpretable results that improve forecasting accuracy. We test the Spectral Attention Autoregressive Model (SAAM) on several well-know forecast datasets, consistently demonstrating that our model compares favorably to state-of-the-art approaches., Comment: Errors in Eq. 2 and Eq. 3 corrected

In this work, our purpose is to show how the symmetry of identical particles can influence the time evolution of free particles in the nonrelativistic and relativistic domains. For this goal, we consider a system of either two distinguishable or indistinguishable (bosons and fermions) particles. Two classes of initial conditions have been studied: different initial locations with the same momenta, and the same locations with different momenta. The flight time distribution of particles arriving at a `screen' is calculated in each case. Fermions display broader distributions as compared with either distinguishable particles or bosons, leading to earlier and later arrivals for all the cases analyzed here. The symmetry of the wave function seems to speed up or slow down propagation of particles. Due to the cross terms, certain initial conditions lead to bimodality in the fermionic case. Within the nonrelativistic domain and when the short-time survival probability is analyzed, if the cross term becomes important, one finds that the decay of the overlap of fermions is faster than for distinguishable particles which in turn is faster than for bosons. These results are of interest in the short time limit since they imply that the well-known quantum Zeno effect would be stronger for bosons than for fermions.Fermions also arrive earlier than bosons when they are scattered by a delta barrier. Furthermore, the particle symmetry does not affect the mean tunneling flight time and it is given by the phase time for the distinguishable particle., Comment: 25 pages, 1 table, 5 figures

Medical data sets are usually corrupted by noise and missing data. These missing patterns are commonly assumed to be completely random, but in medical scenarios, the reality is that these patterns occur in bursts due to sensors that are off for some time or data collected in a misaligned uneven fashion, among other causes. This paper proposes to model medical data records with heterogeneous data types and bursty missing data using sequential variational autoencoders (VAEs). In particular, we propose a new methodology, the Shi-VAE, which extends the capabilities of VAEs to sequential streams of data with missing observations. We compare our model against state-of-the-art solutions in an intensive care unit database (ICU) and a dataset of passive human monitoring. Furthermore, we find that standard error metrics such as RMSE are not conclusive enough to assess temporal models and include in our analysis the cross-correlation between the ground truth and the imputed signal. We show that Shi-VAE achieves the best performance in terms of using both metrics, with lower computational complexity than the GP-VAE model, which is the state-of-the-art method for medical records., Comment: Accepted for publication in IEEE Journal of Biomedical and Health Informatics (JBHI)