Geometry of the matching distance for 2D filtering functions

In this paper we exploit the concept of extended Pareto grid to study the geometric properties of the matching distance for R^2-valued regular functions defined on a closed Riemannian manifold. In particular, we prove that in this case the matching distance is realised either at special values or at values corresponding to vertical, horizontal or slope 1 lines

Persistence modules, shape description, and completeness

Persistence modules are algebraic constructs that can be used to describe the shape of an object starting from a geometric representation of it. As shape descriptors, persistence modules are not complete, that is they may not distinguish non-equivalent shapes. In this paper we show that one reason for this is that homomorphisms between persistence modules forget the geometric nature of the problem. Therefore we introduce geometric homomorphisms between persistence modules, and show that in some cases they perform better. A combinatorial structure, the $H_0$-tree, is shown to be an invariant for geometric isomorphism classes in the case of persistence modules obtained through the 0th persistent homology functor

Careggi Smart Hospital: A mobile app for patients, citizens and healthcare staff

This paper presents a mobile app called “Careggi Smart Hospital” which has been developed for the Careggi Polyclinic in Florence. The application is designed for Android smartphones and tablets and it is freely downloadable from the Google Play Store. It provides various useful tools to the hospital's users such as personnel and structures finding, way-finding and the possibility to access personal medical records collected on regional electronic health record

Integrated HTA and FMECA methodology for the evaluation of robotic surgery

Robotic surgery has been strongly improved since the beginning of the twenty-first century and chased important level of technical and clinical performances. Within the robotic area, the most worldwide used surgical robot is the da Vinci® system made by Intuitive Surgical Inc. The aim of this study was to evaluate at the hospital scale the robotic surgery (Hospital –Based Health Technology Assessment) in comparison to the open and laparoscopic procedures yet combining a FMECA analysis to accurately assess all those aspects involving patient and staff safety. The total number of robotic procedures directly observed by the surgical department and reported in the following study was 44, including 28 urology interventions and 16 general surgeries. The study confirmed clinical benefits carried out with the robot but bigger complexity in managing the whole surgical system in terms of structural needs, staff and technology. For the future, further steps regard the necessity to dispose of a wider number of robotic procedures in order to strength the analysis reliability and complete the socio-economic assessment with medium and long terms observation. Finally a new FMECA application will be essential to monitor the real effects of the suggested actions on the evaluated risks according to the already known and new failure modes

Graphic-based concept retrieval

Two ways of expressing concepts in the context of image retrieval are presented. One, Keypics, is on the side of an image owner, who wants the image itself to be found on the Web; the second, Trittico, is on the side of the image searcher. Both are based on the paradigm of human intermediation for overcoming the semantic gap. Both require tools capable of qualitative analysis, and have been experimented by using persistent homology

Decentralisation and performance: Autonomy and incentives in Local Health Economies

This project will examine the inter-relationship between governance mechanisms, autonomy and incentives in local health economies (LHEs). This interaction shapes decentralisation policies in the NHS and is thought to shape LHE performance. Recently, English health policy has been implementing new forms of decentralisation (eg. earned autonomy, Foundation Trusts) by altering the mix of governance mechanisms (command, collaboration and competition) and making explicit use of autonomy and incentives, thereby aiming to improve NHS performance. Local contextual factors might also shape performance outcomes. The project involves a synergy between the multi-disciplinary teams involved in 2 previous NCC-SDO funded studies. The aim is to investigate the inter-relationship between decentralisation and performance in LHEs. The project has 5 objectives: a. To examine the impact of decentralisation upon performance through analysis of selected 'tracers (as examples of current priorities) in 3 case-studies; b. To describe the local interaction of governance mechanisms; c. To evaluate the degree of autonomy available to local health-care organisations; d. To assess the (financial and non-financial) incentives associated with different policy initiatives; e. To provide lessons for policy-makers and managers at all levels in implementing decentralisation, managing the implications of autonomy and incentives, and addressing performance management through incentives. The study will use mixed methods. First, analysis of policy and performance data will generate the broad pattern of decentralisation and performance across England. Analysis of these data will aid selection of case-studies and 'tracers (examples within case-studies). Second, three case-studies will be selected which represent a maximum variety of pre-defined criteria. Longitudinal, comparative case-study methods include (a) 'mapping LHE performance and organisational characteristics (using local performance and activity data, and published reports); (b) a survey of senior staff in 3 LHEs (n=c.180) to provide their perceptions of current LHE issues and constraints (especially relating to tracer examples); (c) interviews with a sample of stakeholders (n=c.120) will identify the strengths and effects of organisational relationships across the LHE (such as the impact of service developments in the tracer examples); (d) observation of local planning meetings. Parts (a) and (b) will be conducted in year 1, parts (c) and (d) in years 2 and 3. Quantitative analysis will provide descriptive statistics of broad patterns and association. Qualitative analysis will provide thematic comparisons by LHE, organisational type and tracer example. Analysis will identify the pathways by which governance, autonomy and incentives can facilitate improved performance and also the conditions under which the optimal balance of these may be achieved in different contexts. The study will also consider conceptual frameworks (including 'decision space , resource dependency and principal-agent) to improve understanding of the inter-relationships within LHE and the intersection of national/vertical and local/horizontal pressures affecting performance. The study will engage decision-makers at all stages (via data collection, formative and summative feedback and as members of an Advisory Group). Formative feedback to LHEs (and NCC-SDO) will help validate emergent findings and sharpen subsequent fieldwork. Final dissemination will include such (oral and written) feedback, NCC-SDO report, presentations and publications to practitioner and research communities

The Theory of the Interleaving Distance on Multidimensional Persistence Modules

In 2009, Chazal et al. introduced $\epsilon$-interleavings of persistence modules. $\epsilon$-interleavings induce a pseudometric $d_I$ on (isomorphism classes of) persistence modules, the interleaving distance. The definitions of $\epsilon$-interleavings and $d_I$ generalize readily to multidimensional persistence modules. In this paper, we develop the theory of multidimensional interleavings, with a view towards applications to topological data analysis. We present four main results. First, we show that on 1-D persistence modules, $d_I$ is equal to the bottleneck distance $d_B$. This result, which first appeared in an earlier preprint of this paper, has since appeared in several other places, and is now known as the isometry theorem. Second, we present a characterization of the $\epsilon$-interleaving relation on multidimensional persistence modules. This expresses transparently the sense in which two $\epsilon$-interleaved modules are algebraically similar. Third, using this characterization, we show that when we define our persistence modules over a prime field, $d_I$ satisfies a universality property. This universality result is the central result of the paper. It says that $d_I$ satisfies a stability property generalizing one which $d_B$ is known to satisfy, and that in addition, if $d$ is any other pseudometric on multidimensional persistence modules satisfying the same stability property, then $d\leq d_I$. We also show that a variant of this universality result holds for $d_B$, over arbitrary fields. Finally, we show that $d_I$ restricts to a metric on isomorphism classes of finitely presented multidimensional persistence modules.Comment: Major revision; exposition improved throughout. To appear in Foundations of Computational Mathematics. 36 page