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The application of kernel-based Machine Learning (ML) techniques to discrete choice modelling using large datasets often faces challenges due to memory requirements and the considerable number of parameters involved in these models. This complexity hampers the efficient training of large-scale models. This paper addresses these problems of scalability by introducing the Nystr\"om approximation for Kernel Logistic Regression (KLR) on large datasets. The study begins by presenting a theoretical analysis in which: i) the set of KLR solutions is characterised, ii) an upper bound to the solution of KLR with Nystr\"om approximation is provided, and finally iii) a specialisation of the optimisation algorithms to Nystr\"om KLR is described. After this, the Nystr\"om KLR is computationally validated. Four landmark selection methods are tested, including basic uniform sampling, a k-means sampling strategy, and two non-uniform methods grounded in leverage scores. The performance of these strategies is evaluated using large-scale transport mode choice datasets and is compared with traditional methods such as Multinomial Logit (MNL) and contemporary ML techniques. The study also assesses the efficiency of various optimisation techniques for the proposed Nystr\"om KLR model. The performance of gradient descent, Momentum, Adam, and L-BFGS-B optimisation methods is examined on these datasets. Among these strategies, the k-means Nystr\"om KLR approach emerges as a successful solution for applying KLR to large datasets, particularly when combined with the L-BFGS-B and Adam optimisation methods. The results highlight the ability of this strategy to handle datasets exceeding 200,000 observations while maintaining robust performance., Comment: 34 pages, 5 figures

Catheter ablation (CA) remains the cornerstone alternative to cardioversion for sinus rhythm (SR) restoration in patients with atrial fibrillation (AF). Unfortunately, despite the last methodological and technological advances, this procedure is not consistently effective in treating persistent AF.

"Objective: The electrocardiogram (ECG) is currently the most widely used recording to diagnose cardiac disorders, including the most common supraventricular arrhythmia, such as atrial fibrillation (AF). However, different types of electrical disturbances, in which power-line interference (PLI) is a major problem, can mask and distort the original ECG morphology. This is a significant issue in the context of AF, because accurate characterization of fibrillatory waves (f-waves) is unavoidably required to improve current knowledge about its mechanisms. This work introduces a new algorithm able to reduce high levels of PLI and preserve, simultaneously, the original ECG morphology. Approach: The method is based on stationary wavelet transform shrinking and makes use of a new thresholding function designed to work successfully in a wide variety of scenarios. In fact, it has been validated in a general context with 48 ECG recordings obtained from pathological and non-pathological conditions, as well as in the particular context of AF, where 380 synthesized and 20 long-term real ECG recordings were analyzed. Main results: In both situations, the algorithm has reported a notably better performance than common methods designed for the same purpose. Moreover, its effectiveness has proven to be optimal for dealing with ECG recordings affected by AF, since f-waves remained almost intact after removing very high levels of noise. Significance: The proposed algorithm may facilitate a reliable characterization of the f-waves, preventing them from not being masked by the PLI nor distorted by an unsuitable filtering applied to ECG recordings with AF."

The liberalisation of the European passenger railway markets through the European Directive EU 91/440/EEC states a new scenario where different Railway Undertakings compete with each other in a bidding process for time slots. The infrastructure resources are provided by the Infrastructure Manager, who analyses and assesses the bids received, allocating the resources to each Railway Undertaking. Time slot allocation is a fact that drastically influences the market equilibrium. In this paper, we address the time slot allocation problem within the context of a liberalized passenger railway market as a multi-objective model. The Infrastructure Manager is tasked with selecting a point from the Pareto front as the solution to the time slot allocation problem. We propose two criteria for making this selection: the first one allocates time slots to each company according to a set of priorities, while the second one introduces a criterion of fairness in the treatment of companies to incentive competition. The assessment of the impact of these rules on market equilibrium has been conducted on a liberalized high-speed corridor within the Spanish railway network., Comment: 32 pages and 6 figures

Surgical ablation (SA) is the most effective procedure to terminate atrial fibrillation (AF) in patients requiring concomitant open heart surgery. However, considering the great stress provoked in the patients heart, along with the benefits of anticipating antiarrhythmic therapeutical decisions, preoperative prediction of long term failure of the procedure is an interesting clinical challenge. Hence, the present work introduces a novel algorithm to anticipate SA outcome after one year of follow up by just analyzing the surface ECG. The method firstly extracts fibrillatory waves reflected on standard lead V1 using an adaptive QRST cancellation approach. The resulting signal is then segmented into 1 s length intervals and wavelet energy is computed for all of them. Finally, the coefficient of variation of the time series obtained for the 7th scale is computed. Analyzing 20 second length preoperative ECG excerpts from 53 persistent AF patients undergoing concomitant openheart surgery, only the proposed method reported statistically significant differences between the patients who relapsed to AF and those who maintained sinus rhythm during the follow up. The algorithm also provided values of sensitivity, specificity, and accuracy between 10 and 20% better than the well established dominant atrial frequency and fibrillatory waves amplitude, thus suggesting to be a promising predictor of AF recurrence after SA.

Although catheter ablation (CA) is still the first-line treatment for persistent atrial fibrillation (AF) patients, its limited long-term success rate has motivated clinical interest in preoperative prediction on the procedures outcome to provide optimized patient selection, limit repeated procedures, hospitalization rates, and treatment costs. To this respect, dominant frequency (DF) and amplitude of fibrillatory waves (f-waves) reflected on the ECG have provided promising results. Hence this work explores the ability of a novel set of frequency and amplitud f-waves features, such as spectral entropy (SE), spectral flatness measure (SFM), and amplitud spectrum area (AMSA), along with DF and normalized f-wave amplitude (NFWA), to improve CA outcome prediction. Despite all single indices reported statistically significant differences between patients who relapsed to AF and those who maintained sinus rhythm after a follow up of 9 months for 204 6 s-length ECG intervals extracted from 51 persistent AF patients, they obtained a limited discriminant ability ranging between 55 and 62%, which was overcome by 15 - 23% when NFWA, SE and AMSA were combined. Consequently, this combination of frequency and amplitude features of the fwaves seems to provide new insights about the atrial substrate remodeling, which could be helpful in improving preoperative CA outcome prediction.

Analysis of intra-atrial electrograms (EGMs) nowadays constitutes the most common way to gain new insights about the mechanisms triggering and maintaining atrial fibrillation (AF). However, these recordings are highly contaminated by powerline interference (PLI) due to the large amount of electrical devices operating simultaneously in the electrophysiology laboratory. To remove this perturbation, conventional notch filtering has been widely used. However, this method adds artificial fractionation to the EGMs, thus concealing their accurate interpretation. Hence, the development of novel algorithms for PLI suppression in EGMs is still an unresolved challenge. Within this context, the present work introduces the joint application of common notch filtering and Wavelet denoising for enhanced PLI removal in AF EGMs. The algorithm was validated on a set of 100 unipolar EGM signals, which were synthesized with different noise levels. Original and denoised EGMs were compared in terms of a signed correlation index (SCI), computed both in time and frequency domains. Compared with the single use of notch filtering, improvements between 4 and 15% were reached with Wavelet denoising in both domains. As a consequence, the proposed algorithm was able to efficiently reduce high levels of PLI and simultaneously preserve the original morphology of AF EGMs.

Nowadays, the electrocardiogram (ECG) is still the most widely used signal for the diagnosis of cardiac pathologies. However, this recording is often disturbed by the powerline interference (PLI), its removal being mandatory to avoid misdiagnosis. Although a broad variety of methods have been proposed for that purpose, often they substantially alter the original signal morphology or are computationally expensive. Hence, the present work introduces a simple and efficient algorithm to suppress the PLI from the ECG. Briefly, the input signal is decomposed into four Wavelet levels and the resulting coefficients are thresholded to remove the PLI estimated from the TQ intervals. The denoised ECG signal is then reconstructed by computing the inverse Wavelet transform. The method has been validated making use of fifty 10-min length clean ECG segments obtained from the MIT BIH Normal Sinus Rhythm database, which were contaminated with a sinusoidal signal of 50 Hz and variable harmonic content. Comparing the original and denoised ECG signals through a signed correlation index, improvements between 10 - 72% have been observed with respect to common adaptive notch filtering, implemented for comparison. These results suggest that the proposed method is featured by an enhanced trade-off between noise reduction and signal morphology preservation.

In the current industry, the development of optimized mechanical components able to satisfy the customer requirements evolves quickly. Therefore, companies are asked for efficient solutions to improve their products in terms of stiffness and strength. In this sense, Topology Optimization has been extensively used to determine the best topology of structural components from the mechanical point of view. Its main objective is to distribute a given amount of material into a predefined domain to reach the maximum overall stiffness of the component. Besides, high-resolution solutions are essential to define the final distribution of material. Standard Topological Optimization tools are able to propose an optimal topology for the whole component, but when small topological details are required (i.e. trabecular-type structures) the computational cost is prohibitive. In order to mitigate this issue, the present work proposes a two-level topology optimization method to solve high-resolution problems by using density-based methods. The proposed methodology includes three steps: The first one subdivides the whole component in cells and generates a coarse optimized low-definition material distribution assigning one different density to each cell. The second one uses an equilibrating technique that provides tractions continuity between adjacent cells, thus ensuring the material inter-cell continuity after the cells optimization process. Finally, each cell is optimized at fine scale taking as input data the densities and the equilibrated tractions obtained from the macro problem. The main goal of this work is to efficiently solve high-resolution topology optimization problems using density-based methods, which would be unaffordable with standard computing facilities and the current methodologies., Comment: 23 pages

The emergence of a variety of Machine Learning (ML) approaches for travel mode choice prediction poses an interesting question to transport modellers: which models should be used for which applications? The answer to this question goes beyond simple predictive performance, and is instead a balance of many factors, including behavioural interpretability and explainability, computational complexity, and data efficiency. There is a growing body of research which attempts to compare the predictive performance of different ML classifiers with classical random utility models. However, existing studies typically analyse only the disaggregate predictive performance, ignoring other aspects affecting model choice. Furthermore, many studies are affected by technical limitations, such as the use of inappropriate validation schemes, incorrect sampling for hierarchical data, lack of external validation, and the exclusive use of discrete metrics. We address these limitations by conducting a systematic comparison of different modelling approaches, across multiple modelling problems, in terms of the key factors likely to affect model choice (out-of-sample predictive performance, accuracy of predicted market shares, extraction of behavioural indicators, and computational efficiency). We combine several real world datasets with synthetic datasets, where the data generation function is known. The results indicate that the models with the highest disaggregate predictive performance (namely extreme gradient boosting and random forests) provide poorer estimates of behavioural indicators and aggregate mode shares, and are more expensive to estimate, than other models, including deep neural networks and Multinomial Logit (MNL). It is further observed that the MNL model performs robustly in a variety of situations, though ML techniques can improve the estimates of behavioural indices such as Willingness to Pay., Comment: 44 pages and 13 figures