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This paper shortly summarises the experimental results obtained since 2011 by a large European academic consortium for the scientific conceptualisation, the definition of the technical requirements, the generation of experimental data, and the validation of a numerical code, for the Pulsating Heat Pipes (PHP) experiment on the International Space Station (ISS). The PHP is a passive, wickless thermal device, whereby a two-phase fluid, forming liquid plugs and vapour slugs, moves with a pulsating or circulating motion inside a meandering tube or channel. The PHP may have a very broad range of geometries (flat, tubular, 3D structured), it can dissipate heat from large areas, and it can be suitable for high power applications with low/medium heat fluxes. PHP functioning is based on the capillary effect, which provides the existence of liquid plugs completely filling the channel cross-section, in a way that any expansion or contraction of the vapour slugs will naturally generate a movement of the fluid along the channel axis. For this, it is important that the channel has a cross-section size below a given threshold, which depends on the liquid surface tension and (for a static fluid) on the gravity acceleration. In space, when only residual accelerations are acting, such a static size threshold is virtually infinite, while a finite dynamic threshold exists even in the absence of gravity. The concept of a ''Space PHP'' was originally developed in 2014 by the team, and from then 17 Parabolic Flight Campaigns (PFC) and 3 Sounding Rocket (SR) experiments have been carried out to generate the data for the preparation of an experiment targeting a Low Earth Orbit (LEO) mission. Both a tubular and a flat plate PHP have been successfully tested in reduced gravity and on ground, by using different combinations of fluids and building materials. The need for having an experiment on a LEO environment is mainly because, during a PFC, only 22sec of reduced gravity are possible, which is a period below the characteristic time for reaching a steady state condition for almost all of the tested devices. Instead, a steady state was reached using the SR campaigns: in this case however, only one experimental condition was achievable, and long-duration data of the PHP performance still remains beyond reach. Several measurement methodologies have been used to characterise the Space PHP, like infrared analysis, high-speed camera visualisation techniques, with data processed with different techniques, from wavelets to inverse heat transfer problem solution. The results clearly showed that PHPs are very interesting for space applications due to their simplicity of construction, the capacity to transfer heat up to several hundred watts, a high power/weight ratio, their geometrical adaptability, and, in particular, the Space PHP will be a breakthrough technology for space thermal management.

Deep learning-based automatic segmentation methods have become state-of-the-art. However, they are often not robust enough for direct clinical application, as domain shifts between training and testing data affect their performance. Failure in automatic segmentation can cause sub-optimal results that require correction. To address these problems, we propose a novel 3D extension of an interactive segmentation framework that represents a segmentation from a convolutional neural network (CNN) as a B-spline explicit active surface (BEAS). BEAS ensures segmentations are smooth in 3D space, increasing anatomical plausibility, while allowing the user to precisely edit the 3D surface. We apply this framework to the task of 3D segmentation of the anal sphincter complex (AS) from transperineal ultrasound (TPUS) images, and compare it to the clinical tool used in the pelvic floor disorder clinic (4D View VOCAL, GE Healthcare; Zipf, Austria). Experimental results show that: 1) the proposed framework gives the user explicit control of the surface contour; 2) the perceived workload calculated via the NASA-TLX index was reduced by 30% compared to VOCAL; and 3) it required 7 0% (170 seconds) less user time than VOCAL (p< 0.00001), Comment: 4 pages, 3 figures, 1 table, conference

We construct a minimal Lefschetz decomposition of the bounded derived category of the odd isotropic Grassmannian $\mathsf{IGr}(3,9)$. The exceptional objects are $\mathsf{Sp}_9$-equivariant vector bundles. This provides further evidence of the Kuznetsov-Smirnov version of Dubrovin conjecture., Comment: 39 pages, 11 figures

In this paper we study derived categories of nodal singularities. We show that for all nodal singularities there is a categorical resolution whose kernel is generated by a $2$ or $3$-spherical object, depending on the dimension. We apply this result to the case of nodal cubic fourfolds, where we describe the kernel generator of the categorical resolution as an object in the bounded derived category of the associated degree six K3 surface. This paper originated from one of the problem sessions at the Interactive Workshop and Hausdorff School "Hyperk\"ahler Geometry", Bonn, September 6-10, 2021., Comment: 30 pages, final version to appear in Rendiconti del Circolo Matematico di Palermo Series 2

We define a novel time-frequency analyzing tool, namely linear canonical wavelet transform (LCWT) and study some of its important properties like inner product relation, reconstruction formula and also characterize its range. We obtain Donoho-Stark's and Lieb's uncertainty principle for the LCWT and give a lower bound for the measure of its essential support. We also give Shapiro's mean dispersion theorem for the proposed LCWT.

When a new environmental policy or a specific intervention is taken in order to improve air quality, it is paramount to assess and quantify - in space and time - the effectiveness of the adopted strategy. The lockdown measures taken worldwide in 2020 to reduce the spread of the SARS-CoV- 2 virus can be envisioned as a policy intervention with an indirect effect on air quality. In this paper we propose a statistical spatio-temporal model as a tool for intervention analysis, able to take into account the effect of weather and other confounding factors, as well as the spatial and temporal correlation existing in the data. In particular, we focus here on the 2019/2020 relative change in nitrogen dioxide (NO$_2$) concentrations in the north of Italy, for the period of March and April during which the lockdown measure was in force. As an output, we provide a collection of weekly continuous maps, describing the spatial pattern of the NO$_2$ 2019/2020 relative changes. We found that during March and April 2020 most of the studied area is characterized by negative relative changes (median values around -25%), with the exception of the first week of March and the fourth week of April (median values around 5%). As these changes cannot be attributed to a weather effect, it is likely that they are a byproduct of the lockdown measures.

Automatic medical image segmentation via convolutional neural networks (CNNs) has shown promising results. However, they may not always be robust enough for clinical use. Sub-optimal segmentation would require clinician's to manually delineate the target object, causing frustration. To address this problem, a novel interactive CNN-based segmentation framework is proposed in this work. The aim is to represent the CNN segmentation contour as B-splines by utilising B-spline explicit active surfaces (BEAS). The interactive element of the framework allows the user to precisely edit the contour in real-time, and by utilising BEAS it ensures the final contour is smooth and anatomically plausible. This framework was applied to the task of 2D segmentation of the levator hiatus from 2D ultrasound (US) images, and compared to the current clinical tools used in pelvic floor disorder clinic (4DView, GE Healthcare; Zipf, Austria). Experimental results show that: 1) the proposed framework is more robust than current state-of-the-art CNNs; 2) the perceived workload calculated via the NASA-TLX index was reduced more than half for the proposed approach in comparison to current clinical tools; and 3) the proposed tool requires at least 13 seconds less user time than the clinical tools, which was significant (p=0.001)., Comment: 11 pages, 3 figures, 2 tables

We explore four approaches to the question of defectivity for a complex projective toric variety $X_A$ associated with an integral configuration $A$. The explicit tropicalization of the dual variety $X_A^\vee$ due to Dickenstein, Feichtner, and Sturmfels allows for the computation of the defect in terms of an affine combinatorial invariant $\rho(A)$. We express $\rho(A)$ in terms of affine invariants $\iota(A)$ associated to Esterov's iterated circuits and $\lambda(A)$, an invariant defined by Curran and Cattani in terms of a Gale dual of $A$. Thus we obtain formulae for the dual defect in terms of iterated circuits and Gale duals. An alternative expression for the dual defect of $X_A$ is given by Furukawa-Ito in terms of Cayley decompositions of $A$. We give a Gale dual interpretation of these decompositions and apply it to the study of defective configurations., Comment: Several small improvements throughout the manuscript. 30 pages, 1 figure

Analysis of the fetal heart rate during pregnancy is essential for monitoring the proper development of the fetus. Current fetal heart monitoring techniques lack the accuracy in fetal heart rate monitoring and features acquisition, resulting in diagnostic medical issues. The challenge lies in the extraction of the fetal ECG from the mother's ECG during pregnancy. This approach has the advantage of being a reliable and non-invasive technique. For this aim, we propose in this paper a wavelet/multi-wavelet method allowing to extract perfectly the feta ECG parameters from the abdominal mother ECG. The method is essentially due to the exploitation of Clifford wavelets as recent variants in the field. We prove that these wavelets are more efficient and performing against classical ones. The experimental results are therefore due to two basic classes of wavelets and multi-wavelets. A first-class is the classical Haar Schauder, and a second one is due to Clifford valued wavelets and multi-wavelets. These results showed that wavelets/multiwavelets are already good bases for the FECG processing, provided that Clifford ones are the best., Comment: 21 pages, 8 figures, 1 table

This paper illustrates the main results of a spatio-temporal interpolation process of $\text{PM}_{10}$ concentrations at daily resolution using a set of 410 monitoring sites, distributed throughout the Italian territory, for the year 2015. The interpolation process is based on a Bayesian hierarchical model where the spatial-component is represented through the Stochastic Partial Differential Equation (SPDE) approach with a lag-1 temporal autoregressive component (AR1). Inference is performed through the Integrated Nested Laplace Approximation (INLA). Our model includes 11 spatial and spatio-temporal predictors, including meteorological variables and Aerosol Optical Depth. As the predictors' impact varies across months, the regression is based on 12 monthly models with the same set of covariates. The predictive model performance has been analyzed using a cross-validation study. Our results show that the predicted and the observed values are well in accordance (correlation range: 0.79 - 0.91; bias: 0.22 - 1.07 $\mu \text{g}/\text{m}^3$; RMSE: 4.9 - 13.9 $\mu \text{g}/\text{m}^3$). The model final output is a set of 365 gridded (1km $\times$ 1km) daily $\text{PM}_{10}$ maps over Italy equipped with an uncertainty measure. The spatial prediction performance shows that the interpolation procedure is able to reproduce the large scale data features without unrealistic artifacts in the generated $\text{PM}_{10}$ surfaces. The paper presents also two illustrative examples of practical applications of our model, exceedance probability and population exposure maps.

Computational models lie at the intersection of basic neuroscience and healthcare applications because they allow researchers to test hypotheses \textit{in silico} and predict the outcome of experiments and interactions that are very hard to test in reality. Yet, what is meant by "computational model" is understood in many different ways by researchers in different fields of neuroscience and psychology, hindering communication and collaboration. In this review, we point out the state of the art of computational modeling in Electroencephalography (EEG) and outline how these models can be used to integrate findings from electrophysiology, network-level models, and behavior. On the one hand, computational models serve to investigate the mechanisms that generate brain activity, for example measured with EEG, such as the transient emergence of oscillations at different frequency bands and/or with different spatial topographies. On the other hand, computational models serve to design experiments and test hypotheses \emph{in silico}. The final purpose of computational models of EEG is to obtain a comprehensive understanding of the mechanisms that underlie the EEG signal. This is crucial for an accurate interpretation of EEG measurements that may ultimately serve in the development of novel clinical applications.

Capturing solution near the singular point of any nonlinear SBVPs is challenging because coefficients involved in the differential equation blow up near singularities. In this article, we aim to construct a general method based on orthogonal polynomials as wavelets. We discuss multiresolution analysis for wavelets generated by orthogonal polynomials, e.g., Hermite, Legendre, Chebyshev, Laguerre, and Gegenbauer. Then we use these wavelets for solving nonlinear SBVPs. These wavelets can deal with singularities easily and efficiently. To deal with the nonlinearity, we use both Newton's quasilinearization and the Newton-Raphson method. To show the importance and accuracy of the proposed methods, we solve the Lane-Emden type of problems and compare the computed solutions with the known solutions. As the resolution is increased the computed solutions converge to exact solutions or known solutions. We observe that the proposed technique performs well on a class of Lane-Emden type BVPs. As the paper deals with singularity, non-linearity significantly and different wavelets are used to compare the results.