A note on fractional linear pure birth and pure death processes in epidemic models

In this note we highlight the role of fractional linear birth and linear death processes recently studied in \citet{sakhno} and \citet{pol}, in relation to epidemic models with empirical power law distribution of the events. Taking inspiration from a formal analogy between the equation of self consistency of the epidemic type aftershock sequences (ETAS) model, and the fractional differential equation describing the mean value of fractional linear growth processes, we show some interesting applications of fractional modelling to study \textit{ab initio} epidemic processes without the assumption of any empirical distribution. We also show that, in the frame of fractional modelling, subcritical regimes can be linked to linear fractional death processes and supercritical regimes to linear fractional birth processes. Moreover we discuss a simple toy model to underline the possible application of these stochastic growth models to more general epidemic phenomena such as tumoral growth

The Space-Fractional Poisson Process

In this paper we introduce the space-fractional Poisson process whose state probabilities $p_k^\alpha(t)$, $t>0$, $\alpha \in (0,1]$, are governed by the equations $(\mathrm d/\mathrm dt)p_k(t) = -\lambda^\alpha (1-B)p_k^\alpha(t)$, where $(1-B)^\alpha$ is the fractional difference operator found in the study of time series analysis. We explicitly obtain the distributions $p_k^\alpha(t)$, the probability generating functions $G_\alpha(u,t)$, which are also expressed as distributions of the minimum of i.i.d.\ uniform random variables. The comparison with the time-fractional Poisson process is investigated and finally, we arrive at the more general space-time fractional Poisson process of which we give the explicit distribution

An Unsupervised Approach for Automotive Driver Identification

The adoption of on-vehicle monitoring devices allows different entities to gather valuable data about driving styles, which can be further used to infer a variety of information for different purposes, such as fraud detection and driver profiling. In this paper, we focus on the identification of the number of people usually driving the same vehicle, proposing a data analytic work-flow specifically designed to address this problem. Our approach is based on unsupervised learning algorithms working on non-invasive data gathered from a specialized embedded device. In addition, we present a preliminary evaluation of our approach, showing promising driver identification capabilities and a limited computational effort

Fractional diffusions with time-varying coefficients

This paper is concerned with the fractionalized diffusion equations governing the law of the fractional Brownian motion $B_H(t)$. We obtain solutions of these equations which are probability laws extending that of $B_H(t)$. Our analysis is based on McBride fractional operators generalizing the hyper-Bessel operators $L$ and converting their fractional power $L^{\alpha}$ into Erd\'elyi--Kober fractional integrals. We study also probabilistic properties of the r.v.'s whose distributions satisfy space-time fractional equations involving Caputo and Riesz fractional derivatives. Some results emerging from the analysis of fractional equations with time-varying coefficients have the form of distributions of time-changed r.v.'s

MRI-based radiomic prognostic signature for locally advanced oral cavity squamous cell carcinoma: development, testing and comparison with genomic prognostic signatures

Background. At present, the prognostic prediction in advanced oral cavity squamous cell carcinoma (OCSCC) is based on the tumor-node-metastasis (TNM) staging system, and the most used imaging modality in these patients is magnetic resonance image (MRI). With the aim to improve the prediction, we developed an MRI-based radiomic signature as a prognostic marker for overall survival (OS) in OCSCC patients and compared it with published gene expression signatures for prognosis of OS in head and neck cancer patients, replicated herein on our OCSCC dataset.MethodsFor each patient, 1072 radiomic features were extracted from T1 and T2-weighted MRI (T1w and T2w). Features selection was performed, and an optimal set of five of them was used to fit a Cox proportional hazard regression model for OS. The radiomic signature was developed on a multi-centric locally advanced OCSCC retrospective dataset (n = 123) and validated on a prospective cohort (n = 108).ResultsThe performance of the signature was evaluated in terms of C-index (0.68 (IQR 0.66-0.70)), hazard ratio (HR 2.64 (95% CI 1.62-4.31)), and high/low risk group stratification (log-rank p < 0.001, Kaplan-Meier curves). When tested on a multi-centric prospective cohort (n = 108), the signature had a C-index of 0.62 (IQR 0.58-0.64) and outperformed the clinical and pathologic TNM stage and six out of seven gene expression prognostic signatures. In addition, the significant difference of the radiomic signature between stages III and IVa/b in patients receiving surgery suggests a potential association of MRI features with the pathologic stage.ConclusionsOverall, the present study suggests that MRI signatures, containing non-invasive and cost-effective remarkable information, could be exploited as prognostic tools

Loss of leptin-induced modulation of hippocampal synaptic trasmission and signal transduction in high-fat diet-fed mice

Hippocampal plasticity is triggered by a variety of stimuli including sensory inputs, neurotrophins and inflammation. Leptin, whose primary function is to regulate food intake and energy expenditure, has been recently shown to affect hippocampal neurogenesis and plasticity. Interestingly, mice fed a high-fat diet (HFD) exhibit impaired hippocampal function, but the underlying mechanisms are poorly understood. To address this issue, we compared leptin responsiveness of hippocampal neurons in control and HFD-fed mice by combining single-cell electrophysiology and biochemical assays. We found that leptin modulated spontaneous and evoked synaptic transmission in control, but not HFD, mice. This functional impairment was paralleled by blunted activation of STAT-3, one of the key signal transduction pathways controlled by the fully functional isoform of the leptin receptor, ObRb. In addition, SOCS-3 expression was non-responsive to leptin, indicating that modulation of negative feedback impinging on ObRb was also altered. Our results advance the understanding of leptin action on hippocampal plasticity and, more importantly, suggest that leptin resistance is a key determinant of hippocampal dysfunction associated with hypercaloric diet

Assessment of the dynamics of atrial signals and local atrial period series during atrial fibrillation: effects of isoproterenol administration

BACKGROUND: The autonomic nervous system (ANS) plays an important role in the genesis and maintenance of atrial fibrillation (AF), but quantification of its electrophysiologic effects is extremely complex and difficult. Aim of the study was to evaluate the capability of linear and non-linear indexes to capture the fine changing dynamics of atrial signals and local atrial period (LAP) series during adrenergic activation induced by isoproterenol (a sympathomimetic drug) infusion. METHODS: Nine patients with paroxysmal or persistent AF (aged 60 ± 6) underwent electrophysiological study in which isoproterenol was administered to patients. Atrial electrograms were acquired during i) sinus rhythm (SR); ii) sinus rhythm during isoproterenol (SRISO) administration; iii) atrial fibrillation (AF) and iv) atrial fibrillation during isoproterenol (AFISO) administration. The level of organization between two electrograms was assessed by the synchronization index (S), whereas the degree of recurrence of a pattern in a signal was defined by the regularity index (R). In addition, the level of predictability (LP) and regularity of LAP series were computed. RESULTS: LAP series analysis shows a reduction of both LP and R index during isoproterenol infusion in SR and AF (R(SR )= 0.75 ± 0.07 R(SRISO )= 0.69 ± 0.10, p < 0.0001; R(AF )= 0.31 ± 0.08 R(AFISO )= 0.26 ± 0.09, p < 0.0001; LP(SR )= 99.99 ± 0.001 LP(SRISO )= 99.97 ± 0.03, p < 0.0001; LP(AF )= 69.46 ± 21.55 LP(AFISO )= 55 ± 24.75; p < 0.0001). Electrograms analysis shows R index reductions both in SR (R(SR )= 0.49 ± 0.08 R(SRISO )= 0.46 ± 0.09 p < 0.0001) and in AF (R(AF )= 0.29 ± 0.09 R(AFISO )= 0.28 ± 0.08 n.s.). CONCLUSIONS: The proposed parameters succeeded in discriminating the subtle changes due to isoproterenol infusion during both the rhythms especially when considering LAP series analysis. The reduced value of analyzed parameters after isoproterenol administration could reflect an important pro-arrhythmic influence of adrenergic activation on favoring maintenance of AF

Randomly Stopped Nonlinear Fractional Birth Processes

We present and analyse the nonlinear classical pure birth process \mathpzc{N} (t), $t>0$, and the fractional pure birth process \mathpzc{N}^\nu (t), $t>0$, subordinated to various random times, namely the first-passage time $T_t$ of the standard Brownian motion $B(t)$, $t>0$, the $\alpha$-stable subordinator \mathpzc{S}^\alpha(t), $\alpha \in (0,1)$, and others. For all of them we derive the state probability distribution $\hat{p}_k (t)$, $k \geq 1$ and, in some cases, we also present the corresponding governing differential equation. We also highlight interesting interpretations for both the subordinated classical birth process \hat{\mathpzc{N}} (t), $t>0$, and its fractional counterpart \hat{\mathpzc{N}}^\nu (t), $t>0$ in terms of classical birth processes with random rates evaluated on a stretched or squashed time scale. Various types of compositions of the fractional pure birth process \mathpzc{N}^\nu(t) have been examined in the last part of the paper. In particular, the processes \mathpzc{N}^\nu(T_t), \mathpzc{N}^\nu(\mathpzc{S}^\alpha(t)), \mathpzc{N}^\nu(T_{2\nu}(t)), have been analysed, where $T_{2\nu}(t)$, $t>0$, is a process related to fractional diffusion equations. Also the related process \mathpzc{N}(\mathpzc{S}^\alpha({T_{2\nu}(t)})) is investigated and compared with \mathpzc{N}(T_{2\nu}(\mathpzc{S}^\alpha(t))) = \mathpzc{N}^\nu (\mathpzc{S}^\alpha(t)). As a byproduct of our analysis, some formulae relating Mittag--Leffler functions are obtained

Prospective Latin American cohort evaluating outcomes of patients with COVID-19 and abnormal liver tests on admission

Introduction & objectives: The independent effect of liver biochemistries as a prognostic factor in patients with COVID-19 has not been completely addressed. We aimed to evaluate the prognostic value of abnormal liver tests on admission of hospitalized patients with COVID-19. Materials & methods: We performed a prospective cohort study including 1611 hospitalized patients with confirmed SARS-CoV-2 infection from April 15, 2020 through July 31, 2020 in 38 different Hospitals from 11 Latin American countries. We registered clinical and laboratory parameters, including liver function tests, on admission and during hospitalization. All patients were followed until discharge or death. We fit multivariable logistic regression models, further post-estimation effect through margins and inverse probability weighting. Results: Overall, 57.8% of the patients were male with a mean age of 52.3 years, 8.5% had chronic liver disease and 3.4% had cirrhosis. Abnormal liver tests on admission were present on 45.2% (CI 42.7–47.7) of the cohort (n = 726). Overall, 15.1% (CI 13.4–16.9) of patients died (n = 244). Patients with abnormal liver tests on admission presented higher mortality 18.7% (CI 15.9–21.7), compared to those with normal liver biochemistries 12.2% (CI 10.1–14.6); P 30. Conclusions: The presence of abnormal liver tests on admission is independently associated with mortality and severe COVID-19 in hospitalized patients with COVID-19 infection and may be used as surrogate marker of inflammation.Fil: Mendizabal, Manuel. Universidad Austral. Hospital Universitario Austral; ArgentinaFil: Piñero, Federico. Universidad Austral. Hospital Universitario Austral; ArgentinaFil: Ridruejo, Ezequiel. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Parque Centenario. CEMIC-CONICET. Centro de Educaciones Médicas e Investigaciones Clínicas "Norberto Quirno". CEMIC-CONICET; ArgentinaFil: Anders, Margarita. Hospital Aleman; ArgentinaFil: Silveyra, María Dolores. Sanatorio Anchorena; ArgentinaFil: Torre, Aldo. Centro Médico ABC; MéxicoFil: Montes, Pedro. Hospital Nacional Daniel A. Carrión; PerúFil: Urzúa, Alvaro. Hospital Clínico de la Universidad de Chile; ChileFil: Pages, Josefina. Universidad Austral. Hospital Universitario Austral; ArgentinaFil: Toro, Luis G.. Hospitales de San Vicente Fundación de Medellín y Rionegro; ColombiaFil: Díaz, Javier. Hospital Nacional Edgardo Rebagliati Martins; PerúFil: Gonzalez Ballerga, Esteban. Universidad de Buenos Aires. Facultad de Medicina. Hospital de Clínicas General San Martín; ArgentinaFil: Miranda Zazueta, Godolfino. Instituto Nacional de Ciencias Médicas y Nutrición; MéxicoFil: Peralta, Mirta. Gobierno de la Ciudad de Buenos Aires. Hospital de Infecciosas "Dr. Francisco Javier Muñiz"; ArgentinaFil: Gutiérrez, Isabel. Centro Médico ABC; MéxicoFil: Michelato, Douglas. Hospital Especializado en Enfermedades Infecciosas Instituto Couto Maia; BrasilFil: Venturelli, Maria Grazia. Hospital Nacional Guillermo Almenara Irigoyen; PerúFil: Varón, Adriana. Fundación Cardio-Infantil; ColombiaFil: Vera Pozo, Emilia. Hospital Regional Dr. Teodoro Maldonado Carbo; EcuadorFil: Tagle, Martín. Clínica Anglo-Americana; PerúFil: García, Matías. Centro de Educación Médica e Investigaciones Clínicas "Norberto Quirno"; ArgentinaFil: Tassara, Alfredo. Hospital Aleman; ArgentinaFil: Brutti, Julia. Sanatorio Anchorena; ArgentinaFil: Ruiz García, Sandro. Hospital de Víctor Lazarte Echegaray; PerúFil: Bustios, Carla. Clínica Delgado; PerúFil: Escajadillo, Nataly. Hospital Nacional Almanzor Aguinaga Asenjo; PerúFil: Macias, Yuridia. No especifíca;Fil: Higuera de la Tijera, Fátima. Hospital General de México “Dr. Eduardo Liceaga"; MéxicoFil: Gómez, Andrés J.. Hospital Universitario Fundación Santa Fé de Bogotá; ColombiaFil: Dominguez, Alejandra. Hospital Padre Hurtado; ChileFil: Castillo Barradas, Mauricio. Hospital de Especialidades del Centro Médico Nacional La Raza; MéxicoFil: Contreras, Fernando. No especifíca;Fil: Scarpin, Aldana. Centro de Educación Médica e Investigaciones Clínicas "Norberto Quirno"; ArgentinaFil: Schinoni, Maria Isabel. Hospital Alianza; BrasilFil: Toledo, Claudio. Universidad Austral de Chile; ChileFil: Girala, Marcos. Universidad Nacional de Asunción; ParaguayFil: Mainardi, Victoria. Hospital Central De las Fuerzas Armadas; UruguayFil: Sanchez, Abel. Hospital Roosevelt; GuatemalaFil: Bessone, Fernando. Provincia de Santa Fe. Ministerio de Salud y Medio Ambiente - Rosario. Hospital Provincial del Centenario; ArgentinaFil: Rubinstein, Fernando Adrian. Instituto de Efectividad Clínica y Sanitaria; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Silva, Marcelo Oscar. Universidad Austral. Hospital Universitario Austral; Argentin

Phenotype and genotype of 87 patients with Mowat-Wilson syndrome and recommendations for care

Mowat-Wilson syndrome (MWS) is a rare intellectual disability/multiple congenital anomalies syndrome caused by heterozygous mutation of the ZEB2 gene. It is generally underestimated because its rarity and phenotypic variability sometimes make it difficult to recognize. Here, we aimed to better delineate the phenotype, natural history, and genotype-phenotype correlations of MWS.MethodsIn a collaborative study, we analyzed clinical data for 87 patients with molecularly confirmed diagnosis. We described the prevalence of all clinical aspects, including attainment of neurodevelopmental milestones, and compared the data with the various types of underlying ZEB2 pathogenic variations.ResultsAll anthropometric, somatic, and behavioral features reported here outline a variable but highly consistent phenotype. By presenting the most comprehensive evaluation of MWS to date, we define its clinical evolution occurring with age and derive suggestions for patient management. Furthermore, we observe that its severity correlates with the kind of ZEB2 variation involved, ranging from ZEB2 locus deletions, associated with severe phenotypes, to rare nonmissense intragenic mutations predicted to preserve some ZEB2 protein functionality, accompanying milder clinical presentations.ConclusionKnowledge of the phenotypic spectrum of MWS and its correlation with the genotype will improve its detection rate and the prediction of its features, thus improving patient care.GENETICS in MEDICINE advance online publication, 4 January 2018; doi:10.1038/gim.2017.221