Branched covers of the sphere and the prime-degree conjecture

To a branched cover between closed, connected and orientable surfaces one associates a "branch datum", which consists of the two surfaces, the total degree d, and the partitions of d given by the collections of local degrees over the branching points. This datum must satisfy the Riemann-Hurwitz formula. A "candidate surface cover" is an abstract branch datum, a priori not coming from a branched cover, but satisfying the Riemann-Hurwitz formula. The old Hurwitz problem asks which candidate surface covers are realizable by branched covers. It is now known that all candidate covers are realizable when the candidate covered surface has positive genus, but not all are when it is the 2-sphere. However a long-standing conjecture asserts that candidate covers with prime degree are realizable. To a candidate surface cover one can associate one Y -> X between 2-orbifolds, and in a previous paper we have completely analyzed the candidate surface covers such that either X is bad, spherical, or Euclidean, or both X and Y are rigid hyperbolic orbifolds, thus also providing strong supporting evidence for the prime-degree conjecture. In this paper, using a variety of different techniques, we continue this analysis, carrying it out completely for the case where X is hyperbolic and rigid and Y has a 2-dimensional Teichmueller space. We find many more realizable and non-realizable candidate covers, providing more support for the prime-degree conjecture.Comment: Some slips in the first version have been corrected, and a reference to the omitted proofs now fully available online has been added; 44 pages, 14 figure

AI for Health and Well Being @SI Lab

This presentation was delivered in the framework of a bilateral meeting between CNR and IVI on September 5, 2023

Monitoring Ancient Buildings: Real Deployment of an IoT System Enhanced by UAVs and Virtual Reality

The historical buildings of a nation are the tangible signs of its history and culture. Their preservation deserves considerable attention, being of primary importance from a historical, cultural, and economic point of view. Having a scalable and reliable monitoring system plays an important role in the Structural Health Monitoring (SHM): therefore, this paper proposes an Internet Of Things (IoT) architecture for a remote monitoring system that is able to integrate, through the Virtual Reality (VR) paradigm, the environmental and mechanical data acquired by a wireless sensor network set on three ancient buildings with the images and context information acquired by an Unmanned Aerial Vehicle (UAV). Moreover, the information provided by the UAV allows to promptly inspect the critical structural damage, such as the patterns of cracks in the structural components of the building being monitored. Our approach opens new scenarios to support SHM activities, because an operator can interact with real-time data retrieved from a Wireless Sensor Network (WSN) by means of the VR environment

Mirror mirror on the wall... an unobtrusive intelligent multisensory mirror for well-being status self-assessment and visualization

A person’s well-being status is reflected by their face through a combination of facial expressions and physical signs. The SEMEOTICONS project translates the semeiotic code of the human face into measurements and computational descriptors that are automatically extracted from images, videos and 3D scans of the face. SEMEOTICONS developed a multisensory platform in the form of a smart mirror to identify signs related to cardio-metabolic risk. The aim was to enable users to self-monitor their well-being status over time and guide them to improve their lifestyle. Significant scientific and technological challenges have been addressed to build the multisensory mirror, from touchless data acquisition, to real-time processing and integration of multimodal data

Wize Mirror - a smart, multisensory cardio-metabolic risk monitoring system

In the recent years personal health monitoring systems have been gaining popularity, both as a result of the pull from the general population, keen to improve well-being and early detection of possibly serious health conditions and the push from the industry eager to translate the current significant progress in computer vision and machine learning into commercial products. One of such systems is the Wize Mirror, built as a result of the FP7 funded SEMEOTICONS (SEMEiotic Oriented Technology for Individuals CardiOmetabolic risk self-assessmeNt and Self-monitoring) project. The project aims to translate the semeiotic code of the human face into computational descriptors and measures, automatically extracted from videos, multispectral images, and 3D scans of the face. The multisensory platform, being developed as the result of that project, in the form of a smart mirror, looks for signs related to cardio-metabolic risks. The goal is to enable users to self-monitor their well-being status over time and improve their life-style via tailored user guidance. This paper is focused on the description of the part of that system, utilising computer vision and machine learning techniques to perform 3D morphological analysis of the face and recognition of psycho-somatic status both linked with cardio-metabolic risks. The paper describes the concepts, methods and the developed implementations as well as reports on the results obtained on both real and synthetic datasets

SURFACE BRANCHED COVERS AND GEOMETRIC 2-ORBIFOLDS

Let ˜ Σ and Σ be closed, connected, and orientable surfaces, and let f: ˜ Σ → Σ be a branched cover. For each branching point x ∈ Σ the set of local degrees of f at f −1 (x) is a partition of the total degree d. The total length of the various partitions is determined by χ(˜Σ), χ(Σ), d and the number of branching points via the Riemann-Hurwitz formula. A very old problem asks whether a collection of partitions of d having the appropriate total length (that we call a candidate cover) always comes from some branched cover. The answer is known to be in the affirmative whenever Σ is not the 2-sphere S, while for Σ = S exceptions do occur. A long-standing conjecture however asserts that when the degree d is a prime number a candidate cover is always realizable. In this paper we analyze the question from the point of view of the geometry of 2-orbifolds, and we provide strong supporting evidence for the conjecture. In particular, we exhibit three different sequences of candidate covers, indexed by their degree, such that for each sequence: • The degrees giving realizable covers have asymptotically zero density in the naturals. • Each prime degree gives a realizable cover