Gianluca Frasso

L- and V-curves for optimal smoothing

The L-curve is a tool for the selection of the regularization parameter in ill-posed inverse problems. It is a parametric plot of the size of the residuals vs that of the penalty. The corner of the L indicates the right amount of regularization. In the context of smoothing the L-curve is easy to compute and works surprisingly well, even for data with correlated noise. We present the theoretical background and applications to real data together with an alternative criterion for finding the corner automatically. We introduce as simplification, the V-curve, which replaces finding the corner of the L-curve by locating a minimum.

Function-structure connectivity in patients with severe brain injury as measured by MRI-DWI and FDG-PET.

A vast body of literature exists showing functional and structural dysfunction within the brains of patients with disorders of consciousness. However, the function (fluorodeoxyglucose FDG‐PET metabolism)–structure (MRI‐diffusion‐weighted images; DWI) relationship and how it is affected in severely brain injured patients remains ill‐defined. FDG‐PET and MRI‐DWI in 25 severely brain injured patients (19 Disorders of Consciousness of which 7 unresponsive wakefulness syndrome, 12 minimally conscious; 6 emergence from minimally conscious state) and 25 healthy control subjects were acquired here. Default mode network (DMN) function–structure connectivity was assessed by fractional anisotropy (FA) and metabolic standardized uptake value (SUV). As expected, a profound decline in regional metabolism and white matter integrity was found in patients as compared with healthy subjects. Furthermore, a function–structure relationship was present in brain‐damaged patients between functional metabolism of inferior‐parietal, precuneus, and frontal regions and structural integrity of the frontal‐inferiorparietal, precuneus‐inferiorparietal, thalamo‐inferioparietal, and thalamofrontal tracts. When focusing on patients, a stronger relationship between structural integrity of thalamo‐inferiorparietal tracts and thalamic metabolism in patients who have emerged from the minimally conscious state as compared with patients with disorders of consciousness was found. The latter finding was in line with the mesocircuit hypothesis for the emergence of consciousness. The findings showed a positive function–structure relationship within most regions of the DMN. Hum Brain Mapp 37:3707–3720, 2016.

Parsimonious time series clustering using P-splines

A new parsimonious way to cluster time (data) series is provided.We deal with P-spline framework and non-hierarchical clustering.Simulation studies and two well-known real world case studies are performed. We introduce a parsimonious model-based framework for clustering time course data. In these applications the computational burden becomes often an issue due to the large number of available observations. The measured time series can also be very noisy and sparse and an appropriate model describing them can be hard to define. We propose to model the observed measurements by using P-spline smoothers and then to cluster the functional objects as summarized by the optimal spline coefficients. According to the characteristics of the observed measurements, our proposal can be combined with any suitable clustering method. In this paper we provide applications based on non-hierarchical clustering algorithms. We evaluate the accuracy and the efficiency of our proposal by simulations and by analyzing two real data examples.

Modelling the potential of focal screening and treatment as elimination strategy for Plasmodium falciparum malaria in the Peruvian Amazon Region

BackgroundFocal screening and treatment (FSAT) of malaria infections has recently been introduced in Peru to overcome the inherent limitations of passive case detection (PCD) and further decrease the malaria burden. Here, we used a relatively straightforward mathematical model to assess the potential of FSAT as elimination strategy for Plasmodium falciparum malaria in the Peruvian Amazon Region.MethodsA baseline model was developed to simulate a scenario with seasonal malaria transmission and the effect of PCD and treatment of symptomatic infections on the P. falciparum malaria transmission in a low endemic area of the Peruvian Amazon. The model was then adjusted to simulate intervention scenarios for predicting the long term additional impact of FSAT on P. falciparum malaria prevalence and incidence. Model parameterization was done using data from a cohort study in a rural Amazonian community as well as published transmission parameters from previous studies in similar areas. The effect of FSAT timing and frequency, using either microscopy or a supposed field PCR, was assessed on both predicted incidence and prevalence rates.ResultsThe intervention model indicated that the addition of FSAT to PCD significantly reduced the predicted P. falciparum incidence and prevalence. The strongest reduction was observed when three consecutive FSAT were implemented at the beginning of the low transmission season, and if malaria diagnosis was done with PCR. Repeated interventions for consecutive years (10 years with microscopy or 5 years with PCR), would allow reaching near to zero incidence and prevalence rates.ConclusionsThe addition of FSAT interventions to PCD may enable to reach P. falciparum elimination levels in low endemic areas of the Amazon Region, yet the progression rates to those levels may vary substantially according to the operational criteria used for the intervention.

A P-Spline based clustering approach for portfolio selection

Abstract In the last years, many clustering techniques dealing with time course data have been proposed due to recent interests in studying phenomena that change over time. A new clustering method suitable for time series applications has been recently proposed by exploiting the properties of the P-splines approach. This semi-parametric tool has several advantages, i.e. it facilitates the removal of noise from time series and it ensures a computational time saving. In this paper, we propose to use this clustering approach on financial data with the aim of building a financial portfolio. Our proposal works directly on time series without any pre-processing, except for the computation of the spline coefficients and, eventually, normalizing the series. We show that our strategy is useful to support the investment decisions of financial practitioners.

Regional brain volumetry and brain function in severely brain-injured patients: Regional Brain Volumetry and Function in DOC

The relationship between residual brain tissue in patients with disorders of consciousness (DOC) and the clinical condition is unclear. This observational study aimed to quantify gray (GM) and white matter (WM) atrophy in states of (altered) consciousness.

P-Splines Based Clustering as a General Framework: Some Applications Using Different Clustering Algorithms

A parsimonious clustering method suitable for time course data applications has been recently introduced. The idea behind this proposal is quite simple but efficient. Each series is first summarized by lower dimensional vectors of P-spline coefficients and then, the P-spline coefficients are partitioned by means of a suitable clustering algorithm. In this paper, we investigate the performance of this proposal through several applications showing examples within both hierarchical and non-hierarchical clustering algorithms.

Bayesian inference in an extended SEIR model with nonparametric disease transmission rate: an application to the Ebola epidemic in Sierra Leone

The 2014 Ebola outbreak in Sierra Leone is analyzed using a susceptible-exposed-infectious-removed (SEIR) epidemic compartmental model. The discrete time-stochastic model for the epidemic evolution is coupled to a set of ordinary differential equations describing the dynamics of the expected proportions of subjects in each epidemic state. The unknown parameters are estimated in a Bayesian framework by combining data on the number of new (laboratory confirmed) Ebola cases reported by the Ministry of Health and prior distributions for the transition rates elicited using information collected by the WHO during the follow-up of specific Ebola cases. The time-varying disease transmission rate is modeled in a flexible way using penalized B-splines. Our framework represents a valuable stochastic tool for the study of an epidemic dynamic even when only irregularly observed and possibly aggregated data are available. Simulations and the analysis of the 2014 Sierra Leone Ebola data highlight the merits of the proposed methodology. In particular, the flexible modeling of the disease transmission rate makes the estimation of the effective reproduction number robust to the misspecification of the initial epidemic states and to underreporting of the infectious cases.

Inference in dynamic systems using B-splines and quasilinearized ODE penalties.

Nonlinear (systems of) ordinary differential equations (ODEs) are common tools in the analysis of complex one-dimensional dynamic systems. We propose a smoothing approach regularized by a quasilinearized ODE-based penalty. Within the quasilinearized spline-based framework, the estimation reduces to a conditionally linear problem for the optimization of the spline coefficients. Furthermore, standard ODE compliance parameter(s) selection criteria are applicable. We evaluate the performances of the proposed strategy through simulated and real data examples. Simulation studies suggest that the proposed procedure ensures more accurate estimates than standard nonlinear least squares approaches when the state (initial and/or boundary) conditions are not known.