Convergence to stable laws for multidimensional stochastic recursions: the case of regular matrices

Given a sequence $(M_{n},Q_{n})_{n\ge 1}$ of i.i.d.\ random variables with generic copy $(M,Q) \in GL(d, \R) \times \R^d$, we consider the random difference equation (RDE) $$R_{n}=M_{n}R_{n-1}+Q_{n},$$ $n\ge 1$, and assume the existence of $\kappa >0$ such that \lim_{n \to \infty}(\E{\norm{M_1 ... M_n}^\kappa})^{\frac{1}{n}} = 1 . We prove, under suitable assumptions, that the sequence $S_n = R_1 + ... + R_n$, appropriately normalized, converges in law to a multidimensional stable distribution with index $\kappa$. As a by-product, we show that the unique stationary solution $R$ of the RDE is regularly varying with index $\kappa$, and give a precise description of its tail measure. This extends the prior work http://arxiv.org/abs/1009.1728v3 .Comment: 15 page

Therapeutic Hypothermia for Neonatal Encephalopathy Results in Improved Microstructure and Metabolism in the Deep Gray Nuclei

BACKGROUND AND PURPOSE: Therapeutic hypothermia has reduced morbidity and mortality and is associated with a lower burden of lesions on conventional imaging in NE. However, its effects on brain microstructure and metabolism have not been fully characterized. We hypothesized that therapeutic hypothermia improves measures of brain microstructure and metabolism. MATERIALS AND METHODS: Forty-one neonates with moderate/severe NE (29 treated with hypothermia, 12 nontreated) and 12 healthy neonates underwent MR imaging, DTI, and (1)H-MR spectroscopy. MR imaging scans were scored by the predominant pattern of brain injury: normal, watershed, and BG/thalamus. ADC, FA, Lac:NAA, and NAA:Cho values from bilateral BG and thalamus ROIs were averaged. T test and linear regression analysis were used to determine the association between hypothermia and MR imaging quantitative measures. RESULTS: Conventional MR imaging findings were normal in 41% of treated neonates; all nontreated neonates had brain injury. Values of MR imaging metrics were closer to normal in treated neonates compared with nontreated neonates: ADC was 63% higher in the BG and 116% higher in the thalamus (both P < .05), and Lac:NAA was 76% lower (P = .04) in the BG. Treated neonates with normal MR imaging findings had normal (1)H-MR spectroscopy metabolites, and ADC was higher by 35% in the thalamus (P = .03) compared with healthy neonates. CONCLUSIONS: Therapeutic hypothermia may reduce disturbances of brain metabolism and preserve its microstructure in the setting of NE, possibly by minimizing cytotoxic edema and cell death. Long-term follow-up studies are required to determine whether early post-treatment DTI and (1)H-MR spectroscopy will be useful biomarkers of treatment response

Validation and reconstruction of flow meter data in the Barcelona water distribution network

12 páginas, 16 figuras, 1 tabla.-- El PDF es la versión pre-print.-- et al.This paper presents a signal analysis methodology to validate (detect) and reconstruct the missing and false data of a large set of flow meters in the telecontrol system of a water distribution network. The proposed methodology is based on two time-scale forecasting models: a daily model based on a ARIMA time series, while the 10-min model is based on distributing the daily flow using a 10-min demand pattern. The demand patterns have been determined using two methods: correlation analysis and an unsupervised fuzzy logic classification, named LAMDA algorithm. Finally, the proposed methodology has been applied to the Barcelona water distribution network, providing very good results.This work is part of a applied research project granted by ADASA and AGBAR companies. The authors also wish to thank the support received by the Research Commission of the Generalitat of Catalunya (Group SAC Ref. 2009 SGR 1491) and by CICYT (Ref. HYFA DPI2008-01996 and WATMAN DPI2009-13744) of Spanish Ministry of Education.Peer reviewe

Validation and reconstruction of flow meter data in the Barcelona water distribution network

This paper presents a signal analysis methodology to validate (detect) and reconstruct the missing and false data of a large set of flow meters in the telecontrol system of a water distribution network. The proposed methodology is based on two time-scale forecasting models: a daily model based on a ARIMA time series, while the 10-min model is based on distributing the daily flow using a 10-min demand pattern. The demand patterns have been determined using two methods: correlation analysis and an unsupervised fuzzy logic classification, named LAMDA algorithm. Finally, the proposed methodology has been applied to the Barcelona water distribution network, providing very good results.Peer ReviewedPostprint (author’s final draft

Optimal management of barcelona water distribution network using non-linear model predictive control

© . This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/This paper presents a non-linear optimal control strategy for the operational management of water distribution networks (WDNs) including both flow and hydraulic head/pressure constraints. The optimal operation of WDNs should guarantee water supply with suitable pressures at all the demand nodes in the network. The challenge for non-linear model predictive control in this context is to compute control strategies for the pumps and valves in a WDN to supply the required demand while optimizing performance goals related to cost and safety. A two-layer scheme is used in order to produce set-points that can be directly sent to the actuators: on-off schedules for pumps and pressure set-points for pressures reducing valves. Finally, the results of applying the proposed control strategy to a portion of the Barcelona real WDN are provided.Peer ReviewedPostprint (author's final draft

Natural history of Charcot-Marie-Tooth disease type 2A: a large international multicentre study

Mitofusin-2 (MFN2) is one of two ubiquitously expressed homologous proteins in eukaryote cells, playing a critical role in mitochondrial fusion. Mutations in MFN2 (most commonly autosomal dominant) cause Charcot-Marie-Tooth disease type 2A (CMT2A), the commonest axonal form of CMT, with significant allelic heterogeneity. Previous, moderately-sized, cross sectional genotype-phenotype studies of CMT2A have described the phenotypic spectrum of the disease, but longitudinal natural history studies are lacking. In this large multicentre prospective cohort study of 196 patients with dominant and autosomal recessive CMT2A, we present an in-depth genotype-phenotype study of the baseline characteristics of patients with CMT2A and longitudinal data (1-2 years) to describe the natural history. A childhood onset of autosomal dominant CMT2A is the most predictive marker of significant disease severity and is independent of the disease duration. When compared to adult onset autosomal dominant CMT2A, it is associated with significantly higher rates of use of ankle-foot orthoses, full-time use of wheelchair, dexterity difficulties and also has significantly higher CMT Examination Score (CMTESv2) and CMT Neuropathy Score (CMTNSv2) at initial assessment. Analysis of longitudinal data using the CMTESv2 and its Rasch-weighted counterpart, CMTESv2-R, show that over 1 year, the CMTESv2 increases significantly in autosomal dominant CMT2A (mean change 0.84 ± 2.42; two-tailed paired t-test P = 0.039). Furthermore, over 2 years both the CMTESv2 (mean change 0.97 ± 1.77; two-tailed paired t-test P = 0.003) and the CMTESv2-R (mean change 1.21 ± 2.52; two-tailed paired t-test P = 0.009) increase significantly with respective standardized response means of 0.55 and 0.48. In the paediatric CMT2A population (autosomal dominant and autosomal recessive CMT2A grouped together), the CMT Pediatric Scale increases significantly both over 1 year (mean change 2.24 ± 3.09; two-tailed paired t-test P = 0.009) and over 2 years (mean change 4.00 ± 3.79; two-tailed paired t-test P = 0.031) with respective standardized response means of 0.72 and 1.06. This cross-sectional and longitudinal study of the largest CMT2A cohort reported to date provides guidance for variant interpretation, informs prognosis and also provides natural history data that will guide clinical trial design

An application of kernel methods to variety identification based on SSR markers genetic fingerprinting

<p>Abstract</p> <p>Background</p> <p>In crop production systems, genetic markers are increasingly used to distinguish individuals within a larger population based on their genetic make-up. Supervised approaches cannot be applied directly to genotyping data due to the specific nature of those data which are neither continuous, nor nominal, nor ordinal but only partially ordered. Therefore, a strategy is needed to encode the polymorphism between samples such that known supervised approaches can be applied. Moreover, finding a minimal set of molecular markers that have optimal ability to discriminate, for example, between given groups of varieties, is important as the genotyping process can be costly in terms of laboratory consumables, labor, and time. This feature selection problem also needs special care due to the specific nature of the data used.</p> <p>Results</p> <p>An approach encoding SSR polymorphisms in a positive definite kernel is presented, which then allows the usage of any kernel supervised method. The polymorphism between the samples is encoded through the Nei-Li genetic distance, which is shown to define a positive definite kernel between the genotyped samples. Additionally, a greedy feature selection algorithm for selecting SSR marker kits is presented to build economical and efficient prediction models for discrimination. The algorithm is a filter method and outperforms other filter methods adapted to this setting. When combined with kernel linear discriminant analysis or kernel principal component analysis followed by linear discriminant analysis, the approach leads to very satisfactory prediction models.</p> <p>Conclusions</p> <p>The main advantage of the approach is to benefit from a flexible way to encode polymorphisms in a kernel and when combined with a feature selection algorithm resulting in a few specific markers, it leads to accurate and economical identification models based on SSR genotyping.</p

A longitudinal study of CMT1A using Rasch analysis based CMT neuropathy and examination scores

Objective: To evaluate the sensitivity of Rasch analysis-based, weighted Charcot-Marie-Tooth Neuropathy and Examination Scores (CMTNS-R and CMTES-R) to clinical progression in patients with Charcot-Marie-Tooth disease type 1A (CMT1A). Methods: Patients with CMT1A from 18 sites of the Inherited Neuropathies Consortium were evaluated between 2009 and 2018. Weighted CMTNS and CMTES modified category responses were developed with Rasch analysis of the standard scores. Change from baseline for CMTNS-R and CMTES-R was estimated with longitudinal regression models. Results: Baseline CMTNS-R and CMTES-R scores were available for 517 and 1,177 participants, respectively. Mean ± SD age of participants with available CMTES-R scores was 41 ± 18 (range 4–87) years, and 56% were female. Follow-up CMTES-R assessments at 1, 2, and 3 years were available for 377, 321, and 244 patients. A mixed regression model showed significant change in CMTES-R score at years 2 through 6 compared to baseline (mean change from baseline 0.59 points at 2 years, p = 0.0004, n = 321). Compared to the original CMTES, the CMTES-R revealed a 55% improvement in the standardized response mean (mean change/SD change) at 2 years (0.17 vs 0.11). Change in CMTES-R at 2 years was greatest in mildly to moderately affected patients (1.48-point mean change, 95% confidence interval 0.99–1.97, p < 0.0001, for baseline CMTES-R score 0–9). Conclusion: The CMTES-R demonstrates change over time in patients with CMT1A and is more sensitive than the original CMTES. The CMTES-R was most sensitive to change in patients with mild to moderate baseline disease severity and failed to capture progression in patients with severe CMT1A. ClinicalTrials.gov identifier NCT01193075

Genetic analysis and natural history of Charcot-Marie-Tooth disease CMTX1 due to GJB1 variants

Charcot-Marie-Tooth disease (CMT) due to GJB1 variants (CMTX1) is the second most common form of CMT. It is an X-linked disorder characterised by progressive sensory and motor neuropathy with males affected more severely than females. Many reported GJB1 variants remain classified as variants of uncertain significance (VUS). In this large, international, multicentre study we prospectively collected demographic, clinical and genetic data on patients with CMT associated with GJB1 variants. Pathogenicity for each variant was defined using adapted American College of Medical Genetics criteria. Baseline and longitudinal analyses were conducted to study genotype-phenotype correlations, to calculate longitudinal change using the CMT Examination Score (CMTES), to compare males versus females, and pathogenic/likely pathogenic (P/LP) variants versus VUS. We present 387 patients from 295 families harbouring 154 variants in GJB1. Of these, 319 patients (82.4%) were deemed to have P/LP variants, 65 had VUS (16.8%) and 3 benign variants (0.8%; excluded from analysis); an increased proportion of patients with P/LP variants compared with using ClinVar's classification (74.6%). Male patients (166/319, 52.0%, P/LP only) were more severely affected at baseline. Baseline measures in patients with P/LP variants and VUS showed no significant differences, and regression analysis suggested the disease groups were near identical at baseline. Genotype-phenotype analysis suggested c.-17G>A produces the most severe phenotype of the five most common variants, and missense variants in the intracellular domain are less severe than other domains. Progression of disease was seen with increasing CMTES over time up to 8 years follow-up. Standard response mean (SRM), a measure of outcome responsiveness, peaked at 3 years with moderate responsiveness (change in CMTES (ΔCMTES) = 1.3 ± 2.6, p = 0.00016, SRM = 0.50). Males and females progressed similarly up to 8 years, but baseline regression analysis suggested that over a longer period, females progress more slowly. Progression was most pronounced for mild phenotypes (CMTES = 0-7; 3-year ΔCMTES = 2.3 ± 2.5, p = 0.001, SRM = 0.90). Enhanced variant interpretation has yielded an increased proportion of GJB1 variants classified as P/LP and will aid future variant interpretation in this gene. Baseline and longitudinal analysis of this large cohort of CMTX1 patients describes the natural history of the disease including the rate of progression; CMTES showed moderate responsiveness for the whole group at 3 years and higher responsiveness for the mild group at 3, 4 and 5 years. These results have implications for patient selection for upcoming clinical trials