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Extracting relevant predictive variables for COVID-19 severity prognosis: An exhaustive comparison of feature selection techniques
Get PDFWith the COVID-19 pandemic having caused unprecedented numbers of infections and deaths, large research efforts have been undertaken to increase our understanding of the disease and the factors which determine diverse clinical evolutions. Here we focused on a fully data-driven exploration regarding which factors (clinical or otherwise) were most informative for SARS-CoV-2 pneumonia severity prediction via machine learning (ML).
In particular, feature selection techniques (FS), designed to reduce the dimensionality of data, allowed us to characterize which of our variables were the most useful for ML prognosis.
We conducted a multi-centre clinical study, enrolling n=1548 patients hospitalized due to SARS-CoV-2 pneumonia: where 792, 238, and 598 patients experienced low, medium and high-severity evolutions, respectively. Up to 106 patient-specific clinical variables were collected at admission, although 14 of them had to be discarded for containing ⩾60% missing values. Alongside 7 socioeconomic attributes and 32 exposures to air pollution (chronic and acute), these became d=148 features after variable
encoding.
We addressed this ordinal classification problem both as a ML classification and regression task. Two imputation techniques for missing data were explored, along with a total of 166 unique FS algorithm configurations: 46 filters, 100 wrappers and 20 embeddeds. Of these, 21 setups achieved satisfactory bootstrap stability (⩾0.70) with reasonable computation times: 16 filters, 2 wrappers, and 3 embeddeds.
The subsets of features selected by each technique showed modest Jaccard similarities across them. However, they consistently pointed out the importance of certain explanatory variables. Namely: patient’s C-reactive protein (CRP), pneumonia severity index (PSI), respiratory rate (RR) and oxygen levels –saturation SpO2, quotients SpO2/RR and arterial SatO2/FiO2 –, the neutrophil-to-lymphocyte ratio (NLR) –to certain extent, also neutrophil and lymphocyte counts separately–, lactate dehydrogenase (LDH), and procalcitonin (PCT) levels in blood.
A remarkable agreement has been found a posteriori between our strategy and independent clinical research works investigating risk factors for COVID-19 severity. Hence, these findings stress the suitability of this type of fully data-driven approaches for knowledge extraction, as a complementary to clinical perspectives
Generalized plane offsets and rational parameterizations
Get PDFIn the first part of the paper a planar generalization of offset curves is introduced and some properties are derived. In particular, it is seen that these curves exhibit good regularity properties and a study on self-intersection avoidance is performed. The representation of a rational curve as the envelope of its tangent lines, following the approach of Pottmann, is revisited to give the explicit expression of all rational generalized offsets. Other famous shapes, such as constant width curves, bicycle tire-tracks curves and Zindler curves are related to these generalized offsets. This gives rise to the second part of the paper, where the particular case of rational parameterizations by a support function is considered and explicit families of rational constant width curves, rational bicycle tire-track curves and rational Zindler curves are generated and some examples are shown
Microstructural Smoothed Particle Hydrodynamics Model and Simulations of Discontinuous Shear-Thickening Fluids
Get PDFDespite the recent interest in the discontinuous shear-thickening (DST) behaviour, few computational
works tackle the rich hydrodynamics of these fluids. In this work, we present the first implementation
of a microstructural DST model in Smoothed Particle Hydrodynamic (SPH) simulation. The scalar
model was implemented in an SPH scheme and tested in two flow geometries. Three distinct ratios
of local to non-local microstructural effects were probed: weak, moderate, and strong non-locality.
Strong and moderate cases yielded excellent agreement with flow curves constructed via the Wyart–
Cates (WC) model, with the moderate case exhibiting banding patterns. Weak non-locality produced
stress-splitting instability, resulting in discontinuous stress fields and poor agreement with the WC
model. The mechanism of the stress-splitting has been explored and contextualised by the interaction
of local microstructure evolution and the stress-control scheme. Velocity profiles obtained in body
force-driven channel flow were found to be in excellent agreement with the analytical solution, yielding
an upward inflection corresponding to the typical S-curve. Simulations carried out at increasing
driving forces exhibited a decrease in flow. We showed that even the simple scalar model can
capture some of the key properties of DST materials, laying the foundation for further SPH study
of instabilities and pattern formation
ENDPOINT ESTIMATES AND OPTIMALITY FOR THE GENERALIZED SPHERICAL MAXIMAL OPERATOR ON RADIAL FUNCTIONS
Get PDFWe find sharp conditions for the maximal operator associated with generalized spherical mean Radon transform on radial functions Mtα,β to be bounded on power weighted Lebesgue spaces. Moreover, we also obtain the corresponding endpoint results in terms of optimal power weighted weak and restricted weak type estimates. All this complements significantly previous partial results existing in the literature
POINTWISE ESTIMATES FOR ROUGH OPERATORS WITH APPLICATIONS TO SOBOLEV INEQUALITIES
Get PDFWe investigate weighted Sobolev inequalities for rough operators. We prove that several operators satisfy a pointwise bound by the Riesz potential applied to the gradient. From this inequality, we derive several new Sobolev type inequalities with an operator on the left-hand side
A TRIBUTE TO POLA HARBOURE: ISOPERIMETRIC INEQUALITIES AND THE HMS EXTRAPOLATION THEOREM
Get PDFWe give a different simpler proof of the Gagliardo estimate with a measure obtained in [FPW00] and improved in [PR19]. This result will be further improved using fractional Poincaré type inequalities with the extra bonus of Bourgain-Brezis-Mironescu as done in [HMPV1] with a new argument. This will be used with the HMS extrapolation theorem to get Lp type result
Double-Weighting for Covariate Shift Adaptation
Get PDFSupervised learning is often affected by a covariate shift in which the marginal distributions of instances (covariates ) of training and testing samples and are different but the label conditionals coincide.
Existing approaches address such covariate shift by either using the ratio to weight training samples (reweighted methods) or using the ratio to weight testing samples (robust methods).
However, the performance of such approaches can be poor under support mismatch or when the above ratios take large values.
We propose a minimax risk classification (MRC) approach for covariate shift adaptation that avoids such limitations by weighting both training and testing samples.
In addition, we develop effective techniques that obtain both sets of weights and generalize the conventional kernel mean matching method.
We provide novel generalization bounds for our method that show a significant increase in the effective sample size compared with reweighted methods.
The proposed method also achieves enhanced classification performance in both synthetic and empirical experiments.CNS2022-135203, “Early Prognosis of COVID-19 Infections via Machine Learning” funded by the AXA Research Fun
The tempered space-fractional Cattaneo equation
No full textWe consider the time-fractional Cattaneo equation involving the tempered Caputo space-fractional derivative. There is an increasing interest in the recent literature for the applications of the fractional-type Cattaneo equations to heat transfer models. Our main aim is to discuss the role played by a fractional tempered operator in this framework. We show that the fundamental solution coincides with the probability law of a time-changed Brownian motion, obtained by means of a tempered stable subordinator. We find the characteristic function of this process and we explain the main differences with previous stochastic treatments of the time-fractional Cattaneo equation. We also provide the solution of a Dirichlet problem for the tempered fractional Cattaneo equation by means of the H-Fox function
Deep Fourier Residual method for solving time-harmonic Maxwell’s equations
No full textSolving PDEs with machine learning techniques has become a popular alternative to conventional
methods. In this context, Neural networks (NNs) are among the most commonly used machine learning
tools, and in those models, the choice of an appropriate loss function is critical. In general, the main
goal is to guarantee that minimizing the loss during training translates to minimizing the error in the
solution at the same rate. In this work, we focus on the time-harmonic Maxwell’s equations, whose weak
formulation takes H0(curl, Ω) as the space of test functions. We propose a NN in which the loss function
is a computable approximation of the dual norm of the weak-form PDE residual. To that end, we employ
the Helmholtz decomposition of the space H0(curl, Ω) and construct an orthonormal basis for this space
in two and three spatial dimensions. Here, we use the Discrete Sine/Cosine Transform to accurately
and efficiently compute the discrete version of our proposed loss function. Moreover, in the numerical
examples we show a high correlation between the proposed loss function and the H(curl)-norm of the
error, even in problems with low-regularity solutions
Regular polygons on isochordal-viewed hedgehogs
Get PDFA curve is called isochordal viewed if there is a smooth motion of a constant length chord with its endpoints along such that their tangents to the curve at these points form a constant angle. In this paper some properties of isochordal-viewed hedgehogs and Holditch curves are studied. It is proved that, under some conditions, the construction of some closed regular polygons whose vertices move smoothly along the curve is possible. The property is illustrated with some examples. Moreover, Holditch curves of isochordal-viewed hedgehogs are considered and it is seen that they feature similar regular polygon properties although they are, in general, not parameterized by a support function. Finally, a recursive iteration of some Holditch curves for isochordal-viewed hedgehogs is shown to converge to the curve of polygon centers