The issue of failed weaning is a critical concern in the intensive care unit (ICU) setting. This scenario occurs when a patient experiences difficulty maintaining spontaneous breathing and ensuring a patent airway within the first 48 hours after the withdrawal of mechanical ventilation. Approximately 20 of ICU patients experience this phenomenon, which has severe repercussions on their health. It also has a substantial impact on clinical evolution and mortality, which can increase by 25 to 50. To address this issue, we propose a medical support system that uses a convolutional neural network (CNN) to assess a patients suitability for disconnection from a mechanical ventilator after a spontaneous breathing test (SBT). During SBT, respiratory flow and electrocardiographic activity were recorded and after processed using time-frequency analysis (TFA) techniques. Two CNN architectures were evaluated in this study: one based on ResNet50, with parameters tuned using a Bayesian optimization algorithm, and another CNN designed from scratch, with its structure also adapted using a Bayesian optimization algorithm. The WEANDB database was used to train and evaluate both models. The results showed remarkable performance, with an average accuracy 98 when using CNN from scratch. This model has significant implications for the ICU because it provides a reliable tool to enhance patient care by assisting clinicians in making timely and accurate decisions regarding weaning. This can potentially reduce the adverse outcomes associated with failed weaning events.

Quantum computing has gained a lot of attention in recent years due to its potential to solve complex problems which would take exponential time in classical computers. Most of the research efforts have been focused on constructing quantum computers based on qubits [1]. However, there has been a growing interest in building quantum computers based on qudits, i.e. machines that simulate and operate d-dimensional quantum states, with d > 2. Various physical implementations of high-dimensional quantum states have been proposed, such as photonic states integrated in chips [2, 3], photonic modes encoded in the orbital angular momentum (OAM) [4], ion traps [5], ququarts implemented on a quadrupolar nuclear magnetic resonance (NMR) [6], and molecular quantum magnets [7]. Two of the main advantages of highdimensional quantum computers compared to their qubit-based counterparts are their larger information storage [8], and their higher resilience to noise [9]. One closely related field of quantum computing is quantum machine learning (QML). This field aims to develop novel quantum-inspired machine learning (ML) methods that may run on classical or quantum computers and to implement the existing ML algorithms on quantum computers. For instance, some classical machine learning algorithms like support vector machines and restricted Boltzmann machines can be implemented on qubit-based quantum computers [10, 11], and many of the ML methods have been reformulated in the language of quantum physics like quantum decision trees [12], quantum neural networks [13, 14], and quantum generative adversarial networks [15]. In contrast with QML methods built on qubits, less research has been done on QML based on qudits, i.e. algorithms that run in high-dimensional quantum computers. Some of these methods include protocols with qudits for reinforcement learning [16], and for training quantum neural networks [17, 18, 19].

The paper introduces a non-linear version of the process convolution formalism for building covariance functions for multi-output Gaussian processes. The non-linearity is introduced via Volterra series, one series per each output. We provide closed-form expressions for the mean function and the covariance function of the approximated Gaussian process at the output of the Volterra series. The mean function and covariance function for the joint Gaussian process are derived using formulae for the product moments of Gaussian variables. We compare the performance of the non-linear model against the classical process convolution approach in one synthetic dataset and two real datasets.

A latent force model is a Gaussian process with a covariance function inspired by a differential operator. Such covariance function is obtained by performing convolution integrals between Green's functions associated to the differential operators, and covariance functions associated to latent functions. In the classical formulation of latent force models, the covariance functions are obtained analytically by solving a double integral, leading to expressions that involve numerical solutions of different types of error functions. In consequence, the covariance matrix calculation is considerably expensive, because it requires the evaluation of one or more of these error functions. In this paper, we use random Fourier features to approximate the solution of these double integrals obtaining simpler analytical expressions for such covariance functions. We show experimental results using ordinary differential operators and provide an extension to build general kernel functions for convolved multiple output Gaussian processes.

To survive environmental conditions, cells transcribe their response activities into encoded mRNA sequences in order to produce certain amounts of protein concentrations. The external conditions are mapped into the cell through the activation of special proteins called transcription factors (TFs). Due to the difficult task to measure experimentally TF behaviours, and the challenges to capture their quick-time dynamics, different types of models based on differential equations have been proposed. However, those approaches usually incur in costly procedures, and they present problems to describe sudden changes in TF regulators. In this paper, we present a switched dynamical latent force model for reverse-engineering transcriptional regulation in gene expression data which allows the exact inference over latent TF activities driving some observed gene expressions through a linear differential equation. To deal with discontinuities in the dynamics, we introduce an approach that switches between different TF activities and different dynamical systems. This creates a versatile representation of transcription networks that can capture discrete changes and non-linearities We evaluate our model on both simulated data and real-data (e.g. microaerobic shift in E. coli, yeast respiration), concluding that our framework allows for the fitting of the expression data while being able to infer continuous-time TF profiles.

Deep brain stimulation (DBS) is a surgical treatment for Parkinson's Disease. Static models based on quasi-static approximation are common approaches for DBS modeling. While this simplification has been validated for bioelectric sources, its application to rapid stimulation pulses, which contain more high-frequency power, may not be appropriate, as DBS therapeutic results depend on stimulus parameters such as frequency and pulse width, which are related to time variations of the electric field. We propose an alternative hybrid approach based on probabilistic models and differential equations, by using Gaussian processes and wave equation. Our model avoids quasi-static approximation, moreover, it is able to describe dynamic behavior of DBS. Therefore, the proposed model may be used to obtain a more realistic phenomenon description. The proposed model can also solve inverse problems, i.e. to recover the corresponding source of excitation, given electric potential distribution. The electric potential produced by a time-varying source was predicted using proposed model. For static sources, the electric potential produced by different electrode configurations were modeled. Four different sources of excitation were recovered by solving the inverse problem. We compare our outcomes with the electric potential obtained by solving Poisson's equation using the Finite Element Method (FEM). Our approach is able to take into account time variations of the source and the produced field. Also, inverse problem can be addressed using the proposed model. The electric potential calculated with the proposed model is close to the potential obtained by solving Poisson's equation using FEM.

Linear autoregressive models serve as basic representations of discrete time stochastic processes. Different attempts have been made to provide non-linear versions of the basic autoregressive process, including different versions based on kernel methods. Motivated by the powerful framework of Hilbert space embeddings of distributions, in this paper we apply this methodology for the kernel embedding of an autoregressive process of order $p$. By doing so, we provide a non-linear version of an autoregressive process, that shows increased performance over the linear model in highly complex time series. We use the method proposed for one-step ahead forecasting of different time-series, and compare its performance against other non-linear methods.

Power quality (PQ) analysis describes the non-pure electric signals that are usually present in electric power systems. The automatic recognition of PQ disturbances can be seen as a pattern recognition problem, in which different types of waveform distortion are differentiated based on their features. Similar to other quasi-stationary signals, PQ disturbances can be decomposed into time-frequency dependent components by using time-frequency or time-scale transforms, also known as dictionaries. These dictionaries are used in the feature extraction step in pattern recognition systems. Short-time Fourier, Wavelets and Stockwell transforms are some of the most common dictionaries used in the PQ community, aiming to achieve a better signal representation. To the best of our knowledge, previous works about PQ disturbance classification have been restricted to the use of one among several available dictionaries. Taking advantage of the theory behind sparse linear models (SLM), we introduce a sparse method for PQ representation, starting from overcomplete dictionaries. In particular, we apply Group Lasso. We employ different types of time-frequency (or time-scale) dictionaries to characterize the PQ disturbances, and evaluate their performance under different pattern recognition algorithms. We show that the SLM reduce the PQ classification complexity promoting sparse basis selection, and improving the classification accuracy.

Approximate Bayesian Computation (ABC) are likelihood-free Monte Carlo methods. ABC methods use a comparison between simulated data, using different parameters drew from a prior distribution, and observed data. This comparison process is based on computing a distance between the summary statistics from the simulated data and the observed data. For complex models, it is usually difficult to define a methodology for choosing or constructing the summary statistics. Recently, a nonparametric ABC has been proposed, that uses a dissimilarity measure between discrete distributions based on empirical kernel embeddings as an alternative for summary statistics. The nonparametric ABC outperforms other methods including ABC, kernel ABC or synthetic likelihood ABC. However, it assumes that the probability distributions are discrete, and it is not robust when dealing with few observations. In this paper, we propose to apply kernel embeddings using an smoother density estimator or Parzen estimator for comparing the empirical data distributions, and computing the ABC posterior. Synthetic data and real data were used to test the Bayesian inference of our method. We compare our method with respect to state-of-the-art methods, and demonstrate that our method is a robust estimator of the posterior distribution in terms of the number of observations.

Multi-output Gaussian processes have received increasing attention during the last few years as a natural mechanism to extend the powerful flexibility of Gaussian processes to the setup of multiple output variables. The key point here is the ability to design kernel functions that allow exploiting the correlations between the outputs while fulfilling the positive definiteness requisite for the covariance function. Alternatives to construct these covariance functions are the linear model of coregionalization and process convolutions. Each of these methods demand the specification of the number of latent Gaussian process used to build the covariance function for the outputs. We propose in this paper, the use of an Indian Buffet process as a way to perform model selection over the number of latent Gaussian processes. This type of model is particularly important in the context of latent force models, where the latent forces are associated to physical quantities like protein profiles or latent forces in mechanical systems. We use variational inference to estimate posterior distributions over the variables involved, and show examples of the model performance over artificial data, a motion capture dataset, and a gene expression dataset.