Estimating Multidimensional Persistent Homology through a Finite Sampling

An exact computation of the persistent Betti numbers of a submanifold $X$ of a Euclidean space is possible only in a theoretical setting. In practical situations, only a finite sample of $X$ is available. We show that, under suitable density conditions, it is possible to estimate the multidimensional persistent Betti numbers of $X$ from the ones of a union of balls centered on the sample points; this even yields the exact value in restricted areas of the domain. Using these inequalities we improve a previous lower bound for the natural pseudodistance to assess dissimilarity between the shapes of two objects from a sampling of them. Similar inequalities are proved for the multidimensional persistent Betti numbers of the ball union and the one of a combinatorial description of it

Multidimensional persistent homology is stable

Multidimensional persistence studies topological features of shapes by analyzing the lower level sets of vector-valued functions. The rank invariant completely determines the multidimensional analogue of persistent homology groups. We prove that multidimensional rank invariants are stable with respect to function perturbations. More precisely, we construct a distance between rank invariants such that small changes of the function imply only small changes of the rank invariant. This result can be obtained by assuming the function to be just continuous. Multidimensional stability opens the way to a stable shape comparison methodology based on multidimensional persistence.Comment: 14 pages, 3 figure

Estimating multidimensional persistent homology through a finite sampling

An exact computation of the persistent Betti numbers of a submanifold X of a Euclidean space is possible only in a theoretical setting. In practical situations, only a finite sample of X is available. We show that, under suitable density conditions, it is possible to estimate the multidimensional persistent Betti numbers of X from the ones of a union of balls centered on the sample points; this even yields the exact value in restricted areas of the domain. Similar inequalities are proved for the multidimensional persistent Betti numbers of the ball union and the one of a combinatorial description of it

A Spatial Analysis to evaluate the Farm's structure and the Geography of Rural Areas: The case study of Mugello Area

In order to promote rural development public agricultural policies need to constantly adapt to the continuous change of socio-economic conditions of rural areas, related to both farm and territorial dynamics. Hence beyond the zoning provided by the European Commission and developed by Member States [art. 11 Reg. Ce 1698/2005], policy makers should take into account geography, farms characteristics and farmers attitude to acquire a deeper knowledge of these rural areas. This paper aims at supporting the design of proper agricultural policies focusing on the case-study of Mugello territory, a rural area located in the North of Tuscany, which includes both: intermediate rural areas and areas with development problems. This purpose is firstly pursued by generating a geo-referenced database able to develop a deeper analysis on the existing interactions between socio - economic attributes of farms, land use and agricultural policies. The study combined several sources of data: the 2010 Italian Agriculture Census, the Tuscany Regional Agency for Payments in Agriculture (ARTEA) database, and cover land data from the database Corine Land Cover (CLC-06), as updated to 2007 by LaMMA (Laboratory for Environment Monitoring and Modeling). The resulting sample is composed by 821 farms operating in the Mugello area which are split in four different farm styles according to their level of multifunctionality and enterpreunership capacity. Results show that Mugello territory is characterized by an internal differentiation, that determines the prevalence of different farm structure according to the sub-areas characteristics. Especially analyzing the distribution of payments related to area with development problems we note that there are still margins of improvement

A spatial analysis of terrain features and farming styles in a disadvantaged area of Tuscany (Mugello): implications for the evaluation and the design of CAP payments

In recent times there has been a growing awareness of the role of agriculture in providing public goods and services, in particular in less favoured areas. However, since agriculture is an economic activity, its permanence implies that it should be able to generate a satisfactory income for farmers. Where this is not possible, due to natural constraints or adverse economic and market conditions, in order to maintain an adequate use of farmland it is necessary to provide public aid to farmers. In this framework, the design of proper interventions aimed to promote rural development in less favoured areas should be based on a deep knowledge at the farm and territorial level. As regards the territorial level, the RDP zoning [art. 11 Reg. Ce 1698/2005] developed by Member States on the base of the guidelines provided by the European Commission is very often not sufficient to adequately define the territorial characteristics of rural areas. The use of GIS techniques may help to handle this issue by providing a better and more detailed knowledge at the territorial level. Farm level is important insofar as aid effectiveness is usually strongly depending on the type of farm that is receiving it. Thus, a careful selection of beneficiaries could determine a more effective and efficient distribution of resources. This paper aims to provide a spatial analysis of natural constraints and types of farming style in Mugello area and to analyse their relations with CAP aid distribution. Both Single Payment Scheme (SPS) and Rural Development Programme (RDP) payments have been taken into account. The paper combines a GIS analysis of terrain features with the theoretical approach of farming styles. For this purpose, the study integrates several sources of data: the 2010 Italian Agriculture Census, the Tuscany Regional Agency for Payments in Agriculture (ARTEA) database, and land cover data from the database Corine Land Cover (CLC-06), as updated to 2007 by LAMMA (Laboratory for Environment Monitoring and Modelling). A geo-referenced database including socioeconomic attributes of farms, land use, and terrain characteristics has been generated in order to merge information at territorial and farm level. The results of this integrated analysis confirm that Mugello is a very heterogeneous area as regards terrain characteristics despite the fact that it is totally included in less favoured areas. On the other side, farm strategies and economic results seem to be related to entrepreneurial characteristics as much as to natural constraints. The analysis of Pillar I payments and RDP payments for farms located in this mountainous area shows a very complex situation where the strategies implemented by farmers of the strongest farming styles may successfully counteract natural constraints. Besides, in the Authors' opinion, the analyses performed highlight the importance of spatial analysis as a tool for evaluating how public resources are distributed on a territory, thus providing also useful information on the way this distribution could be improved, e.g. for ensuring a higher level of environmental services

Betti numbers in multidimensional persistent homology are stable functions

Multidimensional persistence mostly studies topological features of shapes by analyzing the lower level sets of vector-valued functions, called filtering functions. As is well known, in the case of scalar-valued filtering functions, persistent homology groups can be studied through their persistent Betti numbers, i.e. the dimensions of the images of the homomorphisms induced by the inclusions of lower level sets into each other. Whenever such inclusions exist for lower level sets of vector-valued filtering functions, we can consider the multidimensional analogue of persistent Betti numbers. Varying the lower level sets, we get that persistent Betti numbers can be seen as functions taking pairs of vectors to the set of non-negative integers. In this paper we prove stability of multidimensional persistent Betti numbers. More precisely, we prove that small changes of the vector-valued filtering functions imply only small changes of persistent Betti numbers functions. This result can be obtained by assuming the filtering functions to be just continuous. Multidimensional stability opens the way to a stable shape comparison methodology based on multidimensional persistence. In order to obtain our stability theorem, some other new results are proved for continuous filtering functions. They concern the finiteness of persistent Betti numbers for vector-valued filtering functions, and the representation via persistence diagrams of persistent Betti numbers, as well as their stability, in the case of scalar-valued filtering functions. Finally, from the stability of multidimensional persistent Betti numbers we obtain a lower bound for the natural pseudo-distance

The perception of allergen-specific immunotherapy among pediatricians in the primary care setting

Background: Allergic respiratory diseases are constantly increasing in prevalence. Allergen Immunotherapy (AIT) represent a valuable therapeutic tool as symptomatic and preventative approach, expecially in children. In Italy, primary care pediatricians (PCP) represent the first-line contact and interface for prescription, use and management of AIT. We attempted to evaluate the perception of AIT practice among PCP. Methods: A questionnaire was built-up, based on literature, guidelines and with the contribution of pediatricians. The questionnaire, including 12 items, was e-mailed to 180 PCP, randomly chosen from mailing lists. The questionnaire explored the personal perception of AIT, the comparison between subcutaneous and sublingual AIT and the overall awareness about the treatment. Results: 130 questionnaires were eligible for analysis. There was a satisfactory knowledge of the characteristics of AIT, its aims and limits, although the positioning of the treatment in guidelines was insufficiently known. Overall, the prescription of AIT made by other specialists was accepted and agreed (78 %). The majority of pediatricians felt that a more intense divulgation and information about AIT would be needed (90 %). Conclusion: AIT is in general well known and accepted among PCP, although a more intense divulgation effort is required

El papel pragmático de la citología nasal: una prueba en el punto de atención para implementar la medicina de precisión en la práctica clínica

Antecedentes: La medicina de precisión es una estrategia actualizada que apunta a individualizar los mecanismos fisiopatológicos precisos. Entonces, la medicina de precisión es la base de la medicina personalizada, como definir el tratamiento apropiado en cada paciente. La citología nasal solo necesita un microscopio óptico, tinturas, gafas y curetas. El procedimiento puede durar muy pocos minutos usando tinción rápida, por lo tanto, se puede considerar una prueba confiable en el punto de atención en el consultorio.Métodos: Estudio transversal que incluyó 5030 pacientes ambulatorios con trastornos nasales: 2612 hombres y 2418 mujeres, edad promedio de 36.8 ± 17.1 años, quienes fueron atendidos en un periodo de cinco años. Los pacientes se subdividieron conforme a la prueba cutánea y la citología nasal en sujetos con rinitis alérgica y con rinitis no alérgica. Las formas celulares se subdividieron en función del citotipo: rinitis no alérgica con predominio de infiltración eosinofílica (NARNE, neutrófilos > 50 % con esporas y bacterias ausentes); rinitis no alérgica con eosinófilos (NARES, eosinófilos > 20%); rinitis no alérgica con predominio de infiltrado de mastocitos (NARMA, mastocitos > 10 %) y rinitis no alérgica con eosinófilos y mastocitos (NARESMA, eosinófilos > 20 % y mastocitos > 10 %).Resultados: 453 (9 %) sujetos tuvieron citología negativa a nasal, 1056 (21 %) rinitis alérgica, 538 (10.7%) NARES, 493 (9.8%) poliposis nasal, 251 (5%) rinosinusitis, 221 (4.4%) NARESMA, 201 (4%) rinitis infecciosa; 131 (2.6%) NARMA y 89 (1.8%) NARNE; los sujetos restantes tenían un perfil inflamatorio-infeccioso misceláneo.Conclusiones: La citología nasal proporciona información rápida sobre el fenotipo y endotipo y puede repetirse en el seguimiento para evaluar los cambios posteriores al tratamiento

Nasal Cytology: A Easy Diagnostic Tool in Precision Medicine for Inflammation in Epithelial Barrier Damage in the Nose. A Perspective Mini Review

Nasal cytology is a diagnostic tool that can be used in precision rhinology medicine. Particularly in non-allergic rhinitis and chronic rhinosinusitis forms it can be useful to evaluate biomarkers of both surgical or biological therapy and especially in the follow-up it must be used to predict the prognostic index of recurrence of nasal polyposis. All inflammatory cytokines are also linked to the presence of cells such as eosinophils and mastcells and nasal cytology is a non-invasive and repeatable method to assess the situation in real life