http://hdl.handle.net/10256/1528 Wed, 10 Dec 2025 00:25:55 GMT 2025-12-10T00:25:55Z http://hdl.handle.net/10256/27830 Entropy stability and Milnor–Thurston invariants for Bowen–Series-like maps Alsedà i Soler, Lluís; Juher, David; Los, Jérôme; Mañosas, Francesc We define a family of discontinuous maps on the circle, called Bowen–Series-like maps, for geometric presentations of surface groups. The family has 2N parameters, where 2N is the number of generators of the presentation. We prove that all maps in the family have the same topological entropy, which coincides with the volume entropy of the group presentation. This approach allows a simple algorithmic computation of the volume entropy from the presentation only, using the Milnor–Thurston theory for one-dimensional maps Wed, 01 Jan 2025 00:00:00 GMT http://hdl.handle.net/10256/27830 2025-01-01T00:00:00Z http://hdl.handle.net/10256/27800 Longitudinal Prediction of Mental Health Outcomes in Vulnerable Youth using Machine Learning Ruiz Pujadas, Esmeralda; Díaz-Caneja, Covadonga M.; Stevanovic, Dejan; Ferrer Quintero, Marta; Martín Isla, Carlos; Hernández-González, Jerónimo; Atehortúa, Angelica; Lazrak, Noussair; Pries, Lotta; Delespaul, Philippe; Camacho, Marina; Gülöksüz, Sinan; Rutten, Bart P. F.; Lekadir, Karim Mental illnesses affect almost 15% of the world's population, with half of the cases emerging before age 14. Improved methods for predicting mental distress among adolescents, particularly in vulnerable populations, are needed. This study utilized traditional machine learning techniques to predict mental health status at age 17. We assessed the correlates of mental health outcomes in a sample of 632 adolescents with general mental distress (i.e., total difficulties score of 17 or higher) at age 11, who participated in the UK Millennium Cohort Study. Predictors measured at ages 11 and 14 were included in the analysis. Mental health status at age 17 was best predicted using a Balanced Random Forest model (AUC 0.75). Explainability techniques enabled the identification of several critical factors, such as school environment, emotional distress, sleep patterns, patience, and social network at ages 11 or 14, which were able to differentiate participants with poor or good mental health outcomes at age 17. Individuals experiencing persistent mental distress between the ages 11 and 17 were most likely to suffer from unhappiness and academic struggles. Our results point to potentially modifiable factors associated with the progression of mental distress in adolescents at high risk. These factors could pave the way for improved early intervention and preventive strategies for vulnerable young people during adolescence Wed, 08 Oct 2025 00:00:00 GMT http://hdl.handle.net/10256/27800 2025-10-08T00:00:00Z http://hdl.handle.net/10256/27736 Characterizing the role of early life factors in machine learning-based multimorbidity risk prediction Dang, VienNgoc; Cecil, Charlotte; Pariante, Carmine M.; Hernández-González, Jerónimo; Lekadir, Karim Recent evidence suggests that psycho-cardio-metabolic (PCM) multimorbidity finds its origins in exposure to early-life factors (ELFs), making the exploration of this association crucial for understanding and effective management of these complex health issues. Moreover, risk prediction models for cardiovascular diseases (CVD) and diabetes, as recommended by current clinical guidelines, typically demonstrate sub-optimal performance in clinically relevant sub-populations where these ELFs may play a substantial role. Our methodological approach investigates the contribution of ELFs to machine-learning-based risk prediction models for comorbid populations, incorporating a wide set of early-life and proximal variables, with a special focus on prenatal and postnatal ELFs. To address the complexity of integrating diverse early-life and proximal factors, we leverage models capable of handling high-dimensional, heterogeneous data sources to enhance prediction accuracy in complex clinical populations. The long-term predictive ability of ELFs, along with their influence on model decisions, is assessed with the learned models, and global and local model-agnostic interpretative techniques allow us to elucidate some interactions leading to multimorbidity. The data for this study is derived from the UK Biobank, showcasing both the strengths and limitations inherent in utilizing a single, large-scale database for such research. Our results show enhanced predictive performance for CVD (AUC-ROC: +7.9%, Acc: +14.7%, Cohen’s d: 1.5) among individuals with concurrent mental health issues (depression or anxiety) and diabetes. Similarly, we demonstrate improved diabetes risk prediction (AUC-ROC: +12.3%, Acc: +13.5%, Cohen’s d: 2.5) in those with concurrent mental health conditions and CVD. The inspection of these models, which integrate a large set of ELFs and other predictors (including the 7-core Framingham and UKDiabetes variables), provides key information that could lead to a more profound understanding of psycho-cardio-metabolic multimorbidity. Our findings highlight the utility of incorporating life-course factors into risk models. Integrating a diverse range of physiological, psychological, and ELFs becomes particularly pertinent in the context of multimorbidity Mon, 18 Aug 2025 00:00:00 GMT http://hdl.handle.net/10256/27736 2025-08-18T00:00:00Z http://hdl.handle.net/10256/27683 Semi-algebraic geometry and generic Hamiltonian stability Barbieri, Santiago The steepness property is a local geometric transversality condition on the gradient of a -function which proves fundamental in order to ensure the stability of sufficiently-regular nearly-integrable Hamiltonian systems over long timespans. Steep functions were originally introduced by Nekhoroshev, who also proved their genericity. Namely, given a pair of positive integers , with r high enough, and a point , the Taylor polynomials of those functions which are not steep around are contained in a semi-algebraic set of positive codimension in the space of polynomials of n variables and degree bounded by r. The demonstration of this result was originally published in 1973 and has been hardly studied ever since, probably due to the fact that it involves no arguments of dynamical systems: it makes use of quantitative reasonings of real-algebraic geometry and complex analysis. The aim of the present work is two-fold. In the first part, the original proof of the genericity of steepness is rewritten by making use of modern tools of real-algebraic geometry: this allows to clarify the original reasonings, that were obscure or sketchy in many parts. In particular, Yomdin's Lemma on the analytic reparameterization of semi-algebraic sets, together with non trivial estimates on the codimension of certain algebraic varieties, turns out to be the fundamental ingredients to prove the genericity of steepness. The second part of this work is entirely new and is devoted to the formulation of explicit algebraic criteria to check steepness of any given sufficiently regular function, which constitutes a very important result for applications, as the original definition of steepness is not constructive. These criteria involve both the derivatives of the studied function up to any given order and external real parameters that, generically, belong to compact sets Mon, 01 Dec 2025 00:00:00 GMT http://hdl.handle.net/10256/27683 2025-12-01T00:00:00Z