Computer Vision and 3D printing have rapidly evolved in the last 10 years but interactions among them have been very limited so far, despite the fact that they share several mathematical techniques. We try to fill the gap presenting an overview of some techniques for Shape-from-Shading problems as well as for 3D printing with an emphasis on the approaches based on nonlinear partial differential equations and optimization. We also sketch possible couplings to complete the process of object manufacturing starting from one or more images of the object and ending with its final 3D print. We will give some practical examples of this procedure.

Presents several mathematical problems for 3D and 3D printing plus a survey that gives the links between the two areas Contains contributions from highly reputed academic and industrial researchers with a long experience Shows several techniques, applications and benchmarks that can be useful for young researchers approaching the field

Bi-allelic hypomorphic mutations in DNMT3B disrupt DNA methyltransferase activity and lead to immunodeficiency, centromeric instability, facial anomalies syndrome, type 1 (ICF1). Although several ICF1 phenotypes have been linked to abnormally hypomethylated repetitive regions, the unique genomic regions responsible for the remaining disease phenotypes remain largely uncharacterized. Here we explored two ICF1 patient-derived induced pluripotent stem cells (iPSCs) and their CRISPR-Cas9-corrected clones to determine whether DNMT3B correction can globally overcome DNA methylation defects and related changes in the epigenome. Hypomethylated regions throughout the genome are highly comparable between ICF1 iPSCs carrying different DNMT3B variants, and significantly overlap with those in ICF1 patient peripheral blood and lymphoblastoid cell lines. These regions include large CpG island domains, as well as promoters and enhancers of several lineage-specific genes, in particular immune-related, suggesting that they are premarked during early development. CRISPR-corrected ICF1 iPSCs reveal that the majority of phenotype-related hypomethylated regions reacquire normal DNA methylation levels following editing. However, at the most severely hypomethylated regions in ICF1 iPSCs, which also display the highest increases in H3K4me3 levels and/or abnormal CTCF binding, the epigenetic memory persists, and hypomethylation remains uncorrected. Overall, we demonstrate that restoring the catalytic activity of DNMT3B can reverse the majority of the aberrant ICF1 epigenome. However, a small fraction of the genome is resilient to this rescue, highlighting the challenge of reverting disease states that are due to genome-wide epigenetic perturbations. Uncovering the basis for the persistent epigenetic memory will promote the development of strategies to overcome this obstacle.

CRC is an adult-onset carcinoma representing the third most common cancer and the second leading cause of cancer-related deaths in the world. EO-CRC (<45 years of age) accounts for 5% of the CRC cases and is associated with cancer-predisposing genetic factors in half of them. Here, we describe the case of a woman affected by BWSp who developed EO-CRC at age 27. To look for a possible molecular link between BWSp and EO-CRC, we analysed her whole-genome genetic and epigenetic profiles in blood, and peri-neoplastic and neoplastic colon tissues. The results revealed a general instability of the tumor genome, including copy number and methylation changes affecting genes of the WNT signaling pathway, CRC biomarkers and imprinted loci. At the germline level, two missense mutations predicted to be likely pathogenic were found in compound heterozygosity affecting the Cystic Fibrosis (CF) gene CFTR that has been recently classified as a tumor suppressor gene, whose dysregulation represents a severe risk factor for developing CRC. We also detected constitutional loss of methylation of the KCNQ1OT1:TSS-DMR that leads to bi-allelic expression of the lncRNA KCNQ1OT1 and BWSp. Our results support the hypothesis that the inherited CFTR mutations, together with constitutional loss of methylation of the KCNQ1OT1:TSS-DMR, initiate the tumorigenesis process. Further somatic genetic and epigenetic changes enhancing the activation of the WNT/beta-catenin pathway likely contributed to increase the growth advantage of cancer cells. Although this study does not provide any conclusive cause-effect relationship between BWSp and CRC, it is tempting to speculate that the imprinting defect of BWSp might accelerate tumorigenesis in adult cancer in the presence of predisposing genetic variants.

Epigenetic modifications are correlated to environmental factors. Exposure to ambient air pollution may contribute to the development of different diseases such as cancer, cardiovascular diseases, and neurological and metabolic disorders. Looking for the association between DNA methylation and exposure biomarkers may help in the prevention of adverse effects. Association analysis can be carried out through regression modeling. When dealing with the association between DNA methylation and pollutants, the response variable is beta-distributed, and linear regression models are not appropriate when the range is limited to (0, 1). Beta regression models are more suitable for this situation. Methylation levels can also be measured through the M-value statistic and association studies may be performed using classical linear regression models or robust linear regression models in the presence of outliers. An alternative to these models when the variable of interest does not behave linearly in all the predictors is given by a generalized linear model framework that incorporates non-linear terms and interactions. In this paper, we applied these models to a case study constituted of a cohort of healthy people living in regions exposed to different levels of pollution to investigate the association between DNA methylation and cadmium exposure.

Abstract. Electroencephalography (EEG) source imaging aims to reconstruct brainactivity maps from the neuroelectric potential difference measured on the skull. Toobtain the brain activity map, we need to solve an ill-posed and ill-conditionedinverse problem that requires regularization techniques to make the solution viable.When dealing with real-time applications, dimensionality reduction techniques can beused to reduce the computational load required to evaluate the numerical solutionof the EEG inverse problem. To this end, in this paper we use the random dipolesampling method, in which a Monte Carlo technique is used to reduce the numberof neural sources. This is equivalent to reducing the number of the unknownsin the inverse problem and can be seen as a first regularization step. Then, wesolve the reduced EEG inverse problem with two popular inversion methods, theweighted Minimum Norm Estimate (wMNE) and the standardized LOw Resolutionbrain Electromagnetic TomogrAphy (sLORETA). The main result of this paper is theerror estimates of the reconstructed activity map obtained with the randomized versionof wMNE and sLORETA. Numerical experiments on synthetic EEG data demonstratethe effectiveness of the random dipole sampling method.

Understanding brain function from magneto-electroencephalographic (M/EEG) measurements requires advanced mathematical and signal processing tools. Although the analysis of M/EEG data at sensors level sheds light on important brain mechanisms, full exploitation of the information contained in such brain data could be achieved by reconstructing the active neural sources from M/EEG measurements. This involves solving an ill-posed and ill-conditioned inverse problem in which not only the identification of the most suitable inversion method [1, 2] but also the calibration of the regularization parameters is of paramount importance. Once time series representing brain activity are available, a next step is to develop tools to extract meaningful information that characterizes brain activity [3, 4], for example, when the subject under study is affected by diseases that impair brain function. The mini-symposium brings together researchers from various disciplines who have developed methodologies that are being successfully used for the analysis of the M/EEG data, the solution of the underlying inverse problem and in the definition of brain fingerprint. The purpose is not only to present the latest research results in this area but also to create a fruitful environment for the development of new ideas.

Following the methodology of Brasco (Adv Math 394:108029, 2022), we study the long-time behavior for the signed fractional porous medium equation in open bounded sets with smooth boundary. Homogeneous exterior Dirichlet boundary conditions are considered. We prove that if the initial datum has sufficiently small energy, then the solution, once suitably rescaled, converges to a nontrivial constant sign solution of a sublinear fractional Lane-Emden equation. Furthermore, we give a nonlocal sufficient energetic criterion on the initial datum, which is important to identify the exact limit profile, namely the positive solution or the negative one

Image scaling methods allows us to obtain a given image at a different, higher (upscaling) or lower (downscaling), resolution with the aim of preserving as much as possible the original content and the quality of the image. In this paper, we focus on interpolation methods for scaling three-dimensional grayscale images. Within a unified framework, we introduce two different scaling methods, respectively based on the Lagrange and filtered de la Vall\'ee Poussin type interpolation at the 1st kind's Chebyshev zeros. In both cases, using a non-standard sampling model, we take (via tensor product) the associated trivariate polynomial interpolating the input image. It represents a continuous approximate 3D image to resample at the desired resolution. Using discrete linf and l2 norms, we theoretically estimate the error achieved in output, showing how it depends on the error in input and on the smoothness of the specific image we are processing. Finally, taking the special case of medical images as a case study, we experimentally compare the performances of the proposed methods among them and with the classical multivariate cubic and Lanczos interpolation methods.

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PRISMA is a hyperspectral pushbroom sensor, launched by the Italian Space Agency in 2019. PRISMA collects the reflected Earth signal from VNIR to the SWIR with 230 spectral bands with a variable FWHM according to the prism dispersion element. This work intends to develop a procedure suitable to monitor the consistency of photon and thermal noise components across a times series of L1 radiance images collected on different Mediterranean scenarios (i.e. rural and coastal). To improve the retrieval of the useful signal and the random noise on PRISMA images the spatial variability of the scenes has been considered in the new version of the HYperspectral Noise Parameters Estimation (HYNPE) algorithm. The procedure, tested on two PRISMA time series, has assessed quite stable and coherent values for the retrieved noise coefficients, not significantly affected by seasonal radiance variations and scene characteristics