Nowcasting COVID-19 incidence indicators during the Italian first outbreak

A novel parametric regression model is proposed to fit incidence data typically collected during epidemics. The proposal is motivated by real-time monitoring and short-term forecasting of the main epidemiological indicators within the first outbreak of COVID-19 in Italy. Accurate short-term predictions, including the potential effect of exogenous or external variables are provided. This ensures to accurately predict important characteristics of the epidemic (e.g., peak time and height), allowing for a better allocation of health resources over time. Parameter estimation is carried out in a maximum likelihood framework. All computational details required to reproduce the approach and replicate the results are provided

Local and global behaviour of nonlinear equations with natural growth terms

This paper concerns a study of the pointwise behaviour of positive solutions to certain quasi-linear elliptic equations with natural growth terms, under minimal regularity assumptions on the underlying coefficients. Our primary results consist of optimal pointwise estimates for positive solutions of such equations in terms of two local Wolff's potentials.Comment: In memory of Professor Nigel Kalto

H^s versus C^0-weighted minimizers

We study a class of semi-linear problems involving the fractional Laplacian under subcritical or critical growth assumptions. We prove that, for the corresponding functional, local minimizers with respect to a C^0-topology weighted with a suitable power of the distance from the boundary are actually local minimizers in the natural H^s-topology.Comment: 15 page

Fractional differentiability for solutions of nonlinear elliptic equations

We study nonlinear elliptic equations in divergence form $${\operatorname{div}}{\mathcal A}(x,Du)={\operatorname{div}}G.$$ When ${\mathcal A}$ has linear growth in $Du$, and assuming that $x\mapsto{\mathcal A}(x,\xi)$ enjoys $B^\alpha_{\frac{n}\alpha, q}$ smoothness, local well-posedness is found in $B^\alpha_{p,q}$ for certain values of $p\in[2,\frac{n}{\alpha})$ and $q\in[1,\infty]$. In the particular case ${\mathcal A}(x,\xi)=A(x)\xi$, $G=0$ and $A\in B^\alpha_{\frac{n}\alpha,q}$, $1\leq q\leq\infty$, we obtain $Du\in B^\alpha_{p,q}$ for each $p<\frac{n}\alpha$. Our main tool in the proof is a more general result, that holds also if ${\mathcal A}$ has growth $s-1$ in $Du$, $2\leq s\leq n$, and asserts local well-posedness in $L^q$ for each $q>s$, provided that $x\mapsto{\mathcal A}(x,\xi)$ satisfies a locally uniform $VMO$ condition

Interpolating the Sherrington-Kirkpatrick replica trick

The interpolation techniques have become, in the past decades, a powerful approach to lighten several properties of spin glasses within a simple mathematical framework. Intrinsically, for their construction, these schemes were naturally implemented into the cavity field technique, or its variants as the stochastic stability or the random overlap structures. However the first and most famous approach to mean field statistical mechanics with quenched disorder is the replica trick. Among the models where these methods have been used (namely, dealing with frustration and complexity), probably the best known is the Sherrington-Kirkpatrick spin glass: In this paper we are pleased to apply the interpolation scheme to the replica trick framework and test it directly to the cited paradigmatic model: interestingly this allows to obtain easily the replica-symmetric control and, synergically with the broken replica bounds, a description of the full RSB scenario, both coupled with several minor theorems. Furthermore, by treating the amount of replicas $n\in(0,1]$ as an interpolating parameter (far from its original interpretation) this can be though of as a quenching temperature close to the one introduce in off-equilibrium approaches and, within this viewpoint, the proof of the attended commutativity of the zero replica and the infinite volume limits can be obtained.Comment: This article is dedicated to David Sherrington on the occasion of his seventieth birthda

Glucagon-like peptide-1 receptor and sarcoglycan delta genetic variants can affect cardiovascular risk in chronic kidney disease patients under hemodialysis

Background Chronic kidney disease (CKD) patients under hemodialysis show a higher risk of cardiovascular (CV) mortality and morbidity than the general population. This study aims to identify genetic markers that could explain the increased CV risk in hemodialysis. Methods A total of 245 CKD patients under hemodialysis were recruited and followed up for 5\u2009years to record CV events. Genetic analysis was performed using single-nucleotide polymorphisms (SNPs) genotyping by Infinium Expanded Multi-Ethnic Genotyping Array (Illumina, San Diego, CA, USA) comparing patients with and without a history of CV events [161 cardiovascular diseases (CVDs) and 84 no CVDs]. The fixation index (Fst) measure was used to identify the most differentiated SNPs, and gene ontology analysis [Protein Analysis THrough Evolutionary Relationships (PANTHER) and Ingenuity Pathway Analysis (IPA)] was applied to define the biological/pathological roles of the associated SNPs. Partitioning tree analysis interrogated the genotype\u2013phenotype relationship between discovered genetic variants and CV phenotypes. Cox regression analysis measured the effect of these SNPs on new CV events during the follow-up (FU). Results Fst analysis identified 3218 SNPs that were significantly different between CVD and no CVD. Gene ontology analysis identified two of these SNPs as involved in cardiovascular disease pathways (Ingenuity Pathway) and heart development (Panther) and belonging to 2 different genes: Glucagon-like peptide-1 receptor (GLP1R) and Sarcoglycan delta (SGCD). The phenotype\u2013genotype analysis found a higher percentage of CVD patients carrying the GLP1R rs10305445 allele A (P\u2009=\u20090.03) and lower percentages of CVD patients carrying the SGCD rs145292439 allele A (P\u2009=\u20090.038). Moreover, SGCD rs145292439 was associated with higher levels of high-density lipoprotein (P\u2009=\u20090.015). Cox analysis confirmed the increased frequency of CV events during the 5-year FU in patients carrying GLP1R rs1035445 allele A but it did not show any significant association with SGCD rs145292439. Conclusions This study identified GLP1R rs10305445 and SCGD rs145292439 as potential genetic markers that may explain the higher risk of CVD in hemodialysis patients

Estudio de factores pronósticos en el tratamiento de la carcinomatosis mucinosa peritoneal de origen apendicular mediante citorreducción y quimioterapia intraperitoneal hipertérmica (HIPEC)

Las neoplasias apendiculares son poco frecuentes, suponen el 0,4% de los tumores gastrointestinales, presentan una incidencia de 0,12 casos por 100.000 habitantes-año y cuentan con un amplio espectro histológico. Los tumores epiteliales mucinosos de origen apendicular son característicamente muy proclives a la diseminación por vía peritoneal dando lugar a la denominada Carcinomatosis Mucinosa Peritoneal de Origen Apendicular (CMPOA), objeto de estudio de este trabajo. Desde las primeras descripciones histológicas ha existido un intenso debate en cuanto a su nomenclatura que persiste hasta nuestros días, además, existen distintas clasificaciones histológicas con mayor o menor aceptación que han dificultado la estandarización de los términos en torno a la CMPOA. En la actualidad sigue pendiente la creación de una clasificación de consenso universalmente aplicable. La historia natural de la CMPOA se caracteriza por la liberación de moco y células tumorales epiteliales libres desde el apéndice a la cavidad peritoneal, éstas se van a diseminar al resto de la cavidad siguiendo caminos predefinidos según el “fenómeno de redistribución” descrito por Sugarbaker, depositándose con mayor probabilidad en lugares específicos como son los diafragmas, el omento mayor, la región ileocecal, el rectosigma y la pelvis. Inicialmente el paciente se mantendrá asintomático o con sintomatología limitada, sin embargo con el avance de la enfermedad, el material mucinoso abarcará toda la cavidad peritoneal conduciendo a un estado de caquexia y obstrucción intestinal. El método diagnóstico de elección de la CMPOA es el TC con contraste iv..

Riesz and Wolff potentials and elliptic equations in variable exponent weak Lebesgue spaces

We prove optimal integrability results for solutions of the p(x)-Laplace equation in the scale of (weak) Lebesgue spaces. To obtain this, we show that variable exponent Riesz and Wolff potentials map L1 to variable exponent weak Lebesgue spaces