Comparative effectiveness research (CER) has recently emerged as a key component of health care decision-making, specifically designed to provide evidence of the effectiveness of different health care treatments. The latter are becoming increasingly complex, and there is now intense interest in deploying advanced statistical tools to study and guide the development of such complex systems. Complex interventions might also involve interactions through time, where actions in the past affect the future decision making context. In this case, the temporal dimension should be taken into account into the statistical model, yielding in turn more precise guidelines for health care decision-making. However, current CER methodologies are not well-suited to understand such complex systems or characterise their future behaviour. Statistical methods based on dynamic modelling are therefore needed to advance progress of the state-of-the art of CER research. In particular, this fellowship will tackle the problem by developing novel statistical methodologies for the study of the temporal dynamics of complex health care interventions, both for primary research and evidence synthesis. For primary research, the fellowship will explore the emerging case of pervasive and technology-based interventions, which are by nature dynamic. For evidence synthesis - which is the procedure of summarising evidence from different primary studies of a specific health condition - the innovative tool of network meta-analysis will be deployed and an extension for dynamically monitoring and updating the results of existing network meta-analyses will be developed.

This proposal develops in the framework of applications of set theory to C*-algebras and it is organized into three main themes: (1) the set-theoretic study of the Calkin algebra, (2) Naimark's problem, (3) the Stone-Weierstrass problem for noncommutative C*-algebras. The first part of the project consists of a systematic analysis of the class of the C*-algebras which embed into the Calkin algebra and of how set-theoretic principles influence such class. This study will be achieved by means of forcing techniques and through the adaptation of methods coming from the framework of boolean algebras. The main objectives are to reach a deeper understanding of the structure of the Calkin algebra, and to provide a benchmark for future applications of forcing methods in a more abstract C*-algebraic context. The second part of the proposal is in continuity with the line of research opened by Akemann and Weaver in the study of Naimark's problem, and it involves a series of applications of set-theoretic combinatorial statements in the construction of nonseparable C*-algebras with peculiar properties, specifically for what concerns their representation theory. With these investigations we aim to extend, by means of set theory, the current knowledge on the discrepancies between the nonseparable and the separable framework in operator algebras. The last part of the project regards the Stone-Weierstrass problem for noncommutative C*-algebras, an old open question which asks whether the classical Stone-Weierstrass theorem can be generalized to all C*-algebras. We plan to study this topic using set-theoretic methods, with the objective to find new consistency results, and extend to the nonseparable setting the known theorems holding for separable C*-algebras.

Geometry and dynamics in the moduli spaces proved to be extremely efficient in the study of surface foliations, billiards in polygons and in mathematical models of statistical and solid state physics like Ehrenfest billiards or Novikov's problem on electron transport. Ideas of study of surface dynamics through geometry of moduli spaces originate in works of Thurston, Masur and Veech. The area is flourishing ever since. Contributions of Avila, Eskin, McMullen, Mirzakhani, Kontsevich, Okounkov, Yoccoz, to mention only Fields Medal and Breakthrough Prize winners, made geometry and dynamics in the moduli spaces one of the most active areas of modern mathematics. Moduli spaces of Riemann surfaces and related moduli spaces of Abelian differentials are parametrized by a genus g of the surface. Considering all associated hyperbolic (respectively flat) metrics at once, one observes more and more sophisticated diversity of geometric properties when genus grows. However, most of metrics, on the contrary, progressively share certain similarity. Here the notion of “most of” has explicit quantitative meaning, for example, in terms of the Weil-Petersson measure. Global characteristics of the moduli spaces, like Weil-Petersson and Masur-Veech volumes, Siegel-Veech constants, intersection numbers of ψ-classes were traditionally studied through algebra-geometric tools, where all formulae are exact, but difficult to manipulate in large genus. Most of these quantities admit simple uniform large genus approximate asymptotic formulae. The project aims to study large genus asymptotic geometry and dynamics of moduli spaces and of related objects from probabilistic and asymptotic perspectives. This will provide important applications to enumerative geometry, combinatorics and dynamics, including count of meanders in all genera, solution of Arnold’s problem on statistics of random interval exchange permutations, asymptotics of Lyapunov exponents and of diffusion rates of Ehrenfest billiards.

SEPN1-related myopathy (SEPN1-RM) is a rare, untreatable debilitating congenital myopathy in which SEPN1 mutations impair the antioxidant system, ER stress protection and mitochondrial oxidative function. These altered cellular processes ultimately lead to a significant loss of bioenergetic production and abrogate muscle cellular functions. SEPN1-RM patients experience potentially-lethal respiratory failure and major life burden due to loss of mobility. Currently, there are no high-throughput or appropriate preclinical models to facilitate identification of disease-modifying drugs; this has hampered efforts in devising therapeutic strategies. To overcome these bottlenecks, I aim to use patient-derived cells to establish (1) high-throughput measureable readouts of metabolism, facilitating repurposed drug screen for SEPN1-RM; (2) an original treatment strategy by exploiting potential biased signalings, which bypass SEPN1 defects to restore cellular bioenergetics. I will capitalize on (1) the availability of SEPN1-RM biopsies, (2) host lab expertise for handling and culturing primary SEPN1-RM cells and (3) my experience in muscle biology and innovative tools for analysing metabolic/signalling pathways. I aim to implement transcriptomic analyses by using next-generation RNA-seq, optogenetic based sensors to quantify metabolic activity, real-time clonal analysis of cell fate with dynamic fluorescent time-lapse microscopy and multi-dimensional assessment of intracellular activities at single-cell level via CYTOF technology. This study will not only facilitate the establishment of SEPN1-RM biomarkers and novel therapeutic studies, it will also provide a model paradigm for analysing and treating other inherited or acquired myopathies sharing an underlying bioenergetic deficiency, including sarcopenia and cancer cachexia.

Studying the brain mechanisms behind consciousness is a major challenge for neuroscience and medicine. Accumulating evidence shows that the structural, histological, functional, genetic, and neurochemical inhomogeneities of the mammalian cortex do not follow a modular distribution; instead, these properties change following gradients, understood as axes of variance along which cortical features are ordered continuously. The gradient describing the axis of largest variance (principal gradient) obtained for an ample range of cortical features follows a unimodal-transmodal organization, ranging from externally-oriented sensory and motor regions to multimodal association regions, culminating in regions linked with internally oriented higher-order cognitive functions. In this project we propose a novel approach, constructing, validating and exploring whole-brain computational models combining empirical information including anatomical connectivity, spatial maps of local neuroanatomical features, to reproduce the configuration of human functional gradients, as determined using manifold learning techniques applied to functional magnetic resonance imaging (fMRI) data. This will allow us to investigate the process by which functional gradients emerge from the spatial distribution of cortical anatomical inhomogeneities. The models will also provide the possibility to investigate how different global brain states behave under perturbations. In order to achieve our goals, we propose a highly interdisciplinary project that combines state-of-the-art principal gradient expertise with whole-brain computational modelling proposing a synergy between two groups with large expertise in each area to address a common question: do realistic functional gradients emerge from the dynamical equations when coupled by realistic long-range structural connections, and modulated locally by empirical maps encoding relevant neurochemical data?