Statistical Analysis and Parameter Selection for Mapper

In this article, we study the question of the statistical convergence of the 1-dimensional Mapper to its continuous analogue, the Reeb graph. We show that the Mapper is an optimal estimator of the Reeb graph, which gives, as a byproduct, a method to automatically tune its parameters and compute confidence regions on its topological features, such as its loops and flares. This allows to circumvent the issue of testing a large grid of parameters and keeping the most stable ones in the brute-force setting, which is widely used in visualization, clustering and feature selection with the Mapper.Comment: Minor modification

Statistical analysis of Mapper for stochastic and multivariate filters

Reeb spaces, as well as their discretized versions called Mappers, are common descriptors used in Topological Data Analysis, with plenty of applications in various fields of science, such as computational biology and data visualization, among others. The stability and quantification of the rate of convergence of the Mapper to the Reeb space has been studied a lot in recent works [BBMW19, CO17, CMO18, MW16], focusing on the case where a scalar-valued filter is used for the computation of Mapper. On the other hand, much less is known in the multivariate case, when the codomain of the filter is $\mathbb{R}^p$, and in the general case, when it is a general metric space $(Z, d_Z)$, instead of $\mathbb{R}$. The few results that are available in this setting [DMW17, MW16] can only handle continuous topological spaces and cannot be used as is for finite metric spaces representing data, such as point clouds and distance matrices. In this article, we introduce a slight modification of the usual Mapper construction and we give risk bounds for estimating the Reeb space using this estimator. Our approach applies in particular to the setting where the filter function used to compute Mapper is also estimated from data, such as the eigenfunctions of PCA. Our results are given with respect to the Gromov-Hausdorff distance, computed with specific filter-based pseudometrics for Mappers and Reeb spaces defined in [DMW17]. We finally provide applications of this setting in statistics and machine learning for different kinds of target filters, as well as numerical experiments that demonstrate the relevance of our approac

Growth and organization of (3-Trimethoxysilylpropyl) diethylenetriamine within reactive amino-terminated self-assembled monolayer on silica

Alkane chains are the most commonly used molecules for monolayer fabrication. Long chains are used for their strong van der Waals interactions inducing good layer organization. Amine function-terminated alkyl chains are of great interest and are widely used for further surface functionalization. Since it is mandatory that such layers be organized to provide amine moieties at the surface, the present study deals with exploring amine-terminated SAM formation as an alternative to the usual aminopropylalkylsilane SAM. Additionally, using a long NH2terminated alkyl chain allows the formation of hydrogen bonding thanks to the two NH moieties born along the chain. Furthermore, such hydrogen bonding makes possible to shorten the molecule length while preserving a well-organized monolayer. For this purpose we performed a complete study of the grafting of (3-Trimethoxysilylpropyl) diethylenetriamine (DETAS) on native silicon oxide using various solvents, relative humidity and temperature values. Grafting kinetics was monitored by ellipsometry and goniometry, and SAM structure and organization using AFM and ATR-FTIR spectroscopy. Hydrogen bonding was evidenced within the SAM growth process and in the final complete SAM. We believe such study enables a better control of good quality DETAS SAM in order to improve their efficiency in further surface functionalization applications

: Rapport final

Three factors are likely to change daily mobilities in sparsely populated rural areas and diminish the attractiveness of such areas: fuels cost increase; sustainable development necessities which aim at reducing fossil energies dependence; public policies (Grenelle II) in favor of the development of areas best-served by public transport. Then, how could everyone be guaranteed rights to the mobility and the territory wherever they are? How could we develop mobilities which are more sustainable and less car dependent in areas where car is currently the main mean of transport? The laboratory CNRS-CITERES of Tours University tried to provide answers to this last question as part of the research program MOUR (MObilité et Urbanisme Rural). This program is co-funded by the Région Centre and the Regional Natural Park "Loire-Anjou-Touraine", in partnership with ADEME.Trois phénomènes risquent de modifier les conditions de mobilité quotidienne dans les espaces ruraux de faible densité, et de limiter l'attractivité de ces territoires : l'augmentation du coût des carburants ; les impératifs de développement durable qui cherchent à réduire la dépendance aux énergies fossiles ; et des politiques publiques (Grenelle II) qui favorisent le développement des seuls espaces desservis par des transports en commun. Comment alors garantir un droit à la mobilité et un droit au territoire partout et pour tous ? La question posée est celle du développement de mobilités plus durables et moins dépendantes de la voiture, dans des espaces aujourd'hui dépendants à l'automobile. C'est cette question qui a été analysée au cours du programme de recherche MOUR (MObilité et Urbanisme Rural), mené par le laboratoire CNRS-CITERES de l'université de Tours en partenariat Parc naturel régional Loire-Anjou-Touraine ; développé dans le cadre de l'Appel à Projet de Recherche d'Intérêt Régional de la Région Centre, ce projet est cofinancé par la Région Centre et l'ADEME

: Rapport final

Three factors are likely to change daily mobilities in sparsely populated rural areas and diminish the attractiveness of such areas: fuels cost increase; sustainable development necessities which aim at reducing fossil energies dependence; public policies (Grenelle II) in favor of the development of areas best-served by public transport. Then, how could everyone be guaranteed rights to the mobility and the territory wherever they are? How could we develop mobilities which are more sustainable and less car dependent in areas where car is currently the main mean of transport? The laboratory CNRS-CITERES of Tours University tried to provide answers to this last question as part of the research program MOUR (MObilité et Urbanisme Rural). This program is co-funded by the Région Centre and the Regional Natural Park "Loire-Anjou-Touraine", in partnership with ADEME.Trois phénomènes risquent de modifier les conditions de mobilité quotidienne dans les espaces ruraux de faible densité, et de limiter l'attractivité de ces territoires : l'augmentation du coût des carburants ; les impératifs de développement durable qui cherchent à réduire la dépendance aux énergies fossiles ; et des politiques publiques (Grenelle II) qui favorisent le développement des seuls espaces desservis par des transports en commun. Comment alors garantir un droit à la mobilité et un droit au territoire partout et pour tous ? La question posée est celle du développement de mobilités plus durables et moins dépendantes de la voiture, dans des espaces aujourd'hui dépendants à l'automobile. C'est cette question qui a été analysée au cours du programme de recherche MOUR (MObilité et Urbanisme Rural), mené par le laboratoire CNRS-CITERES de l'université de Tours en partenariat Parc naturel régional Loire-Anjou-Touraine ; développé dans le cadre de l'Appel à Projet de Recherche d'Intérêt Régional de la Région Centre, ce projet est cofinancé par la Région Centre et l'ADEME

Meeting the home-care needs of disabled older persons living in the community: does integrated services delivery make a difference?

<p>Abstract</p> <p>Background</p> <p>The PRISMA Model is an innovative coordination-type integrated-service-delivery (ISD) network designed to manage and better match resources to the complex and evolving needs of elders. The goal of this study was to examine the impact of this ISD network on unmet needs among disabled older persons living in the community.</p> <p>Methods</p> <p>Using data from the PRISMA study, we compared unmet needs of elders living in the community in areas with or without an ISD network. Disabilities and unmet needs were assessed with the Functional Autonomy Measurement System (SMAF). We used growth-curve analysis to examine changes in unmet needs over time and the variables associated with initial status and change. Sociodemographic characteristics, level of disability, self-perceived health status, cognitive functioning, level of empowerment, and the hours of care received were investigated as covariates. Lastly, we report the prevalence of needs and unmet needs for 29 activities in both areas at the end of the study.</p> <p>Results</p> <p>On average, participants were 83 years old; 62% were women. They had a moderate level of disability and mild cognitive problems. On average, they received 2.07 hours/day (SD = 1.08) of disability-related care, mostly provided by family. The findings from growth-curve analysis suggest that elders living in the area where ISD was implemented and those with higher levels of disability experience better fulfillment of their needs over time. Besides the area, being a woman, living alone, having a higher level of disability, more cognitive impairments, and a lower level of empowerment were linked to initial unmet needs (r²= 0.25; p < 0.001). At the end of the study, 35% (95% CI: 31% to 40%) of elders with needs living in the ISD area had at least one unmet need, compared to 67% (95% CI: 62% to 71%) in the other area. In general, unmet needs were highest for bathing, grooming, urinary incontinence, walking outside, seeing, hearing, preparing meals, and taking medications.</p> <p>Conclusions</p> <p>In spite of more than 30 years of home-care services in the province of Quebec, disabled older adults living in the community still have unmet needs. ISD networks such as the PRISMA Model, however, appear to offer an effective response to the long-term-care needs of the elderly.</p