2063 research outputs found
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Minimax Risk Classifiers for Mislabeled Data: a Study on Patient Outcome Prediction Tasks
No full textHealthcare datasets are often impacted by incorrect or mislabeled data, due to imperfect an-
notations, data collection problems, ambiguity, and subjective interpretations. Incorrectly
classified data, referred to as “noisy labels,” can significantly degrade the performance of supervised learning models. Namely, noisy labels hinder the algorithm’s ability to accurately
capture the true underlying patterns from observed data. More importantly, evaluating
the performance of a classifier when only noisy test labels are available is a significant complication. We hereby tackle the challenge of trusting the labeling process both in training
and testing, as noisy patient outcome labels in healthcare raise methodological and ethical
considerations. We propose a novel adaptation of Minimax Risk Classifiers (MRCs) for
data subject to noisy labels, both in training and evaluation. We show that the upper
bound of the MRC’s expected loss can serve as a useful estimator for the classifier’s performance, especially in situations where clean test data is not available. We demonstrate
the benefits of the proposed methodology in healthcare tasks where patient outcomes are
predicted from mislabeled data. The proposed technique is accurate and stable, avoiding
overly optimistic assessments of prediction error, a significantly harmful burden in patient
outcome prediction tasks in healthcare.PID2022-137063B-I00
CNS2022-13520
C*-Algebraic Formulation of Quantum Mechanics
Full text linkThis manuscript is based on a series of lectures given in the XX Jacques-Louis Lions Spanish-French School on Numerical Simulations in Physics & Engineering. While quantum mechanics is widely presented within the Hilbert space formalism in undergraduate courses, in these notes we give an introduction to its algebraic formulation. It is based on the theory of C^{∗}-algebras, which is shortly outlined here. This viewpoint is more general than the usual formulation of quantum mechanics, because of the the non-uniqueness of irreducible representations of C^{∗}-algebras of infinite dimension. This is related to the Rosenberg theorem and Naimark's problem.W. de Siqueira Pedra has been supported by CNPq (309723/2020-5). J.-B. Bru is supported by the Basque Government through the grant IT1615-22 and the BERC 2022-2025 program, by the COST Action CA18232 financed by the European Cooperation in Science and Technology (COST), and by the grant PID2020-112948GB-I00 funded by MCIN/AEI/10.13039/501100011033 and by "ERDF A way of making Europe"
Depolarization block induction via slow NaV1.1 inactivation in Dravet syndrome
No full textDravet syndrome is a developmental and epileptic encephalopathy, characterized by the early onset of drug-resistant seizures
and various comorbidities. Most cases of this severe and complex pathology are due to mutations of NaV1.1, a sodium
channel mainly expressed in fast-spiking inhibitory neurons. Layer et al. (Front. Cell. Neurosci. 15, 2021) showed that one of
these mutations alters the voltage dependence of channel activation, as well as the voltage dependence and kinetics of slow
inactivation. Implementing the three effects into a computational model, they predict that altered activation has the largest
impact on channel function, as it causes the most severe firing rate reduction. Using a conductance-based model tailored
to the dynamics of fast-spiking inhibitory neurons, we look deeper into slow inactivation. We exploit the timescale difference
between this very slow process and the rest of the system to conduct a multiple-timescale analysis. We find that, upon
prolonged stimulation, the onset of slow inactivation at lower voltage in mutant channels promotes depolarization block, another
possible firing deficit aside from frequency reduction. The accelerated kinetics of slow inactivation in mutant channels hastens
this transition. This suggests that slow inactivation alterations might for some Dravet variant contribute to the pathological
mechanism.PID2023-146683OB-10
Explosive neural networks via higher-order interactions in curved statistical manifolds
No full textHigher-order interactions underlie complex phenomena in systems such as biological and artificial neural networks, but their study is challenging due to the scarcity of tractable models. By leveraging a generalisation of the maximum entropy principle, we introduce curved neural networks as a class of models with a limited number of parameters that are particularly well-suited for studying higher-order phenomena. Through exact mean-field descriptions, we show that these curved neural networks implement a self-regulating annealing process that can accelerate memory retrieval, leading to explosive order-disorder phase transitions with multi-stability and hysteresis effects. Moreover, by analytically exploring their memory-retrieval capacity using the replica trick, we demonstrate that these networks can enhance memory capacity and robustness of retrieval over classical associative-memory networks. Overall, the proposed framework provides parsimonious models amenable to analytical study, revealing higher-order phenomena in complex networks
DMC matters: the role of dimethyl carbonate in SEI formation on oxygen functionalized anodes
No full textUnderstanding the decomposition mechanisms of electrolyte components on functionalized graphite anodes are critical for optimizing solid electrolyte interphase (SEI) formation and enhancing Li-ion battery performance. This study employs first principles calculations and reactive force field (ReaxFF) simulations to examine the thermodynamic and kinetic feasibility of dimethyl carbonate (DMC) decomposition on four functionalized graphite surfaces (−CO, −COH, −CHO, and −COOH functional groups) during early stages of battery operation. Our findings reveal that three distinct Hydrogen Atom Transfer (HAT) mechanisms play a key role in DMC decomposition. Among the studied functional groups, −COH and −COOH exhibit the highest reactivity, enabling multiple favorable decomposition pathways. Besides well-known SEI organic components such as CH3OLi and CH3OCOOLi, we predict the formation of less-reported species, including CH4, CH3OC(OH)OLi, CH3OCHO, CH3OCH3, LiHCO3, and Li2C(OH)O2. Notably, we identify strong competition between DMC and ethylene carbonate/fluoroethylene carbonate decomposition, particularly on −COH and −COOH surfaces, which should profoundly impact SEI formation and evolution. ReaxFF simulations further reveal that inorganic species like LiHCO3 and Li2C(OH)O2 act as precursors to the formation of Li2CO3, a key inorganic SEI component. Moreover, organic decomposition products are found to detach and diffuse from −COH, −CHO, and −COOH functionalized surfaces, supporting a bottom-up SEI formation mechanism. Conversely, −CO strongly binds organic species via Li+ ions, potentially leading to surface poisoning over extended battery operation. These insights provide a comprehensive understanding of how functional groups influence DMC decomposition and general SEI evolution, offering valuable guidance for designing more stable and efficient anode materials for Li-ion batteries.JDC2022-049793-I/MCIN/AEI/10.13039/501100011033, RYC2022-036500-I, MODEL2RESIST (6/12/TT/2024/00003), RES, QHS-2025-1-002
Patterns of burned area by a cellular-automata fire simulator: The role of microscale wind field
No full textWildfire dynamics simulated using PROPAGATOR, a quasi-empirical cellular automaton model,
is studied by investigating the effects of wind-terrain interactions on the predicted burned
area patterns. In order to do so, PROPAGATOR is coupled with WindNinja, a microscale wind
simulator that computes spatially varying wind fields by a solver accounting for the conservation
of mass and a second one assuming also conservation of momentum. Two historical fires are
considered: the first one occurred in quasi-flat terrain in the Molise region of Italy, while the
second ignited in the southern area of Avinyo in Spain. The standard fire simulator incorporating
solely uniform wind fields and that coupled with the solvers of WindNinja predict similar
burning probability maps for the Campomarino fire. The quasi-flatness of the Campomarino
terrain is the main cause since the wind pattern is very weakly affected by its topography
during fire propagation, resulting in only a slight deviation from the initial uniform wind field.
However, in the presence of the complex topography of the Avinyo region, the fire spread
simulations incorporating the spatially-varying wind fields predict significantly different burned
area shapes for long time regimes and intense winds, where secondary fire spots separated
from the main burning zone emerge. Larger spatial extension of the wildfire is observed in
the absence of firefighters’ actions, but the predicted patterns seem to be similar regardless of
the type of wind field input and its resolution. A 10-fold increase of perturbation magnitude
on wind direction yields a contraction of the predicted burned area for all the probability
thresholds considered, while a 2-fold and 10-fold increase of the wind speed perturbations
lead to a significantly larger burned area and fire spread. Further quantitative analysis of
the importance of incorporating spatially-varying wind fields in improving the predictability
of cellular automata models in the case of megafires is mandatory
Multipliers for Hardy-Orlicz spaces and applications
No full textUsing real-variable methods, we characterise multipliers for general
classes ofHardy–Orlicz spaces, unifying and extending several classical results
due to Hardy and Littlewood; Duren and Shields; Paley; and others. Applications
of our results include inequalities involving Fourier coefficients and Fourier
transforms of elements of Hardy–Orlicz spaces and their duals, as well as embeddings
into spaces of generalised smoothness, Sobolev type-embeddings and
Paley–Wiener type theorems
Quadratic Hamiltonians in Fermionic Fock Spaces
Full text linkQuadratic Hamiltonians are important in quantum field theory and quantum statistical mechanics. Their general studies, which go back to the sixties, are relatively incomplete for the fermionic case studied here. Following Berezin, they are quadratic in the fermionic field and in this way well-defined self-adjoint operators acting on the fermionic Fock space. We analyze their diagonalization by applying a novel elliptic operator-valued differential equations on the one-particle Hilbert space studied in a companion paper. This allows for their (N--) diagonalization under much weaker assumptions than before. Last but not least, in 1994 Bach, Lieb and Solovej defined them to be generators of strongly continuous unitary groups of Bogoliubov transformations. This is shown to be an equivalent definition, as soon as the vacuum state belongs to the domain of definition of these Hamiltonians. This second outcome is demonstrated to be reminiscent to the celebrated Shale-Stinespring condition on Bogoliubov transformations.This work is supported by the Basque Government through the grant IT1615-22 and the BERC 2022-2025 program, by the grant PID2020-112948GB-I00 funded by MCIN/AEI/10.13039/501100011033 and by "ERDF A way of making Europe"
Complex non-Markovian dynamics and the dual role of astrocytes in Alzheimer's disease development and propagation
Full text linkAlzheimer’s disease (AD) is a common neurodegenerative disorder nowadays. Amyloid-beta (Aβ)
and tau proteins are among the main contributors to the AD progression. In AD, Aβ proteins clump
together to form plaques and disrupt cell functions. On the other hand, the abnormal chemical change
in the brain helps to build sticky tau tangles that block the neuron’s transport system. Astrocytes
generally maintain a healthy balance in the brain by clearing the Aβ plaques (toxic Aβ). However,
over-activated astrocytes release chemokines and cytokines in the presence of Aβ and react to proinflammatory cytokines, further increasing the production of Aβ. In this paper, we construct a mathematical model that can capture astrocytes’ dual behaviour. Furthermore, we reveal that the disease
progression depends on the current time instance and the disease’s earlier status, called the “memory
effect”. We consider a fractional order network mathematical model to capture the influence of such
memory effect on AD progression. We have integrated brain connectome data into the model and
studied the memory effect, the dual role of astrocytes, and the brain’s neuronal damage. Based on the
pathology, primary, secondary, and mixed tauopathies parameters are considered in the model. Due
to the mixed tauopathy, different brain nodes or regions in the brain connectome accumulate different
toxic concentrations of Aβ and tau proteins. Finally, we explain how the memory effect can slow
down the propagation of such toxic proteins in the brain, decreasing the rate of neuronal damage