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

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

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

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

Assessing the Influence of Different ROI Selection Strategies on Functional Connectivity Analyses of fMRI Data Acquired During Steady-State Conditions

In blood oxygen level dependent (BOLD) functional magnetic resonance imaging (fMRI), assessing functional connectivity between and within brain networks from datasets acquired during steady-state conditions has become increasingly common. However, in contrast to connectivity analyses based on task-evoked signal changes, selecting the optimal spatial location of the regions of interest (ROIs) whose timecourses will be extracted and used in subsequent analyses is not straightforward. Moreover, it is also unknown how different choices of the precise anatomical locations within given brain regions influence the estimates of functional connectivity under steady-state conditions. The objective of the present study was to assess the variability in estimates of functional connectivity induced by different anatomical choices of ROI locations for a given brain network. We here targeted the default mode network (DMN) sampled during both resting-state and a continuous verbal 2-back working memory task to compare four different methods to extract ROIs in terms of ROI features (spatial overlap, spatial functional heterogeneity), signal features (signal distribution, mean, variance, correlation) as well as strength of functional connectivity as a function of condition. We show that, while different ROI selection methods produced quantitatively different results, all tested ROI selection methods agreed on the final conclusion that functional connectivity within the DMN decreased during the continuous working memory task compared to rest

Assessing non-Mendelian inheritance in inherited axonopathies

PURPOSE: Inherited axonopathies (IA) are rare, clinically and genetically heterogeneous diseases that lead to length-dependent degeneration of the long axons in central (hereditary spastic paraplegia [HSP]) and peripheral (Charcot–Marie–Tooth type 2 [CMT2]) nervous systems. Mendelian high-penetrance alleles in over 100 different genes have been shown to cause IA; however, about 50% of IA cases do not receive a genetic diagnosis. A more comprehensive spectrum of causative genes and alleles is warranted, including causative and risk alleles, as well as oligogenic multilocus inheritance. METHODS: Through international collaboration, IA exome studies are beginning to be sufficiently powered to perform a pilot rare variant burden analysis. After extensive quality control, our cohort contained 343 CMT cases, 515 HSP cases, and 935 non-neurological controls. We assessed the cumulative mutational burden across disease genes, explored the evidence for multilocus inheritance, and performed an exome-wide rare variant burden analysis. RESULTS: We replicated the previously described mutational burden in a much larger cohort of CMT cases, and observed the same effect in HSP cases. We identified a preliminary risk allele for CMT in the EXOC4 gene (p value= 6.9 × 10-6, odds ratio [OR] = 2.1) and explored the possibility of multilocus inheritance in IA. CONCLUSION: Our results support the continuing emergence of complex inheritance mechanisms in historically Mendelian disorders

Should UI Eligibility Be Expanded to Low-Earning Workers? Evidence on Employment, Transfer Receipt, and Income from Administrative Data

Recent efforts to expand unemployment insurance (UI) eligibility are expected to increase low-earning workers’ access to UI. Although the expansion’s aim is to smooth the income and consumption of previously ineligible workers, it is possible that UI benefits simply displace other sources of income. Standard economic models predict that UI delays reemployment, thereby reducing wage income. Additionally, low-earning workers are often eligible for benefits from means-tested programs, which may decrease with UI benefits. In this paper, we estimate the impact of UI eligibility on employment, means-tested program participation, and income after job loss using a unique individual-level administrative data set from the state of Michigan. To identify a causal effect, we implement a fuzzy regression discontinuity design around the minimum earnings threshold for UI eligibility. Our main finding is that while UI eligibility increases jobless durations by up to 25 percent and temporarily lowers receipt of cash assistance (TANF) by 63 percent, the net impact on total income is still positive and large. In the quarter immediately following job loss, UI-eligible workers have 46-61 percent higher incomes than ineligibles

Colloids as Mobile Substrates for the Implantation and Integration of Differentiated Neurons into the Mammalian Brain

Neuronal degeneration and the deterioration of neuronal communication lie at the origin of many neuronal disorders, and there have been major efforts to develop cell replacement therapies for treating such diseases. One challenge, however, is that differentiated cells are challenging to transplant due to their sensitivity both to being uprooted from their cell culture growth support and to shear forces inherent in the implantation process. Here, we describe an approach to address these problems. We demonstrate that rat hippocampal neurons can be grown on colloidal particles or beads, matured and even transfected in vitro, and subsequently transplanted while adhered to the beads into the young adult rat hippocampus. The transplanted cells have a 76% cell survival rate one week post-surgery. At this time, most transplanted neurons have left their beads and elaborated long processes, similar to the host neurons. Additionally, the transplanted cells distribute uniformly across the host hippocampus. Expression of a fluorescent protein and the light-gated glutamate receptor in the transplanted neurons enabled them to be driven to fire by remote optical control. At 1-2 weeks after transplantation, calcium imaging of host brain slice shows that optical excitation of the transplanted neurons elicits activity in nearby host neurons, indicating the formation of functional transplant-host synaptic connections. After 6 months, the transplanted cell survival and overall cell distribution remained unchanged, suggesting that cells are functionally integrated. This approach, which could be extended to other cell classes such as neural stem cells and other regions of the brain, offers promising prospects for neuronal circuit repair via transplantation of in vitro differentiated, genetically engineered neurons