We investigate nonlinear elliptic Dirichlet problems whose growth is driven by a general anisotropic N-function, which is not necessarily of power-type and need not satisfy the $\Delta_2$ nor the $\nabla_2$ -condition. Fully anisotropic, non-reflexive Orlicz-Sobolev spaces provide a natural functional framework associated with these problems. Minimal integrability assumptions are detected on the datum on the right-hand side of the equation ensuring existence and uniqueness of weak solutions. When merely integrable, or even measure, data are allowed, existence of suitably further generalized solutions--in the approximable sense--is established. Their maximal regularity in Marcinkiewicz-type spaces is exhibited as well. Uniqueness of approximable solutions is also proved in case of L^1-data.

This paper presents the results of an experiment aiming to measure the vibrational frequencies of the main structures of the medieval church of San Domenico (Matera, southern Italy) and relate them to the mechanical properties of geological stratigraphy and construction materials. Vibrational frequencies are measured by means of the ground-based radar inteferometry technique using a Ku-band radar. Time series of ground-based radar data are processed to measure displacements and vibration frequencies of the church structures. Data collected by a seismic triaxal station for the measurement of the H/V ratio are also processed to compare with radar-based frequencies measurements, providing information about the main vibration frequency ranges of the church structures and, more important, disentangle the site and structure vibration frequencies.

We develop and study stability properties of a hybrid approximation of functionals of the Bates jump model with stochastic interest rate that uses a tree method in the direction of the volatility and the interest rate and a finite-difference approach in order to handle the underlying asset price process. We also propose hybrid simulations for the model, following a binomial tree in the direction of both the volatility and the interest rate, and a space-continuous approximation for the underlying asset price process coming from a Euler-Maruyama type scheme. We test our numerical schemes by computing European and American option prices.

We present the first analytical computation of the (conservative) gravitational self-force correction to the periastron advance around a spinning black hole. Our result is accurate to the second order in the rotational parameter and through the 9.5 post-Newtonian level. It has been obtained as the circular limit of the correction to the gyroscope precession invariant along slightly eccentric equatorial orbits in the Kerr spacetime. The latter result is also new and we anticipate here the first few terms only of the corresponding post-Newtonian expansion.

In this paper we present som eremarks about the Hilbert transform on the real line and its numerical approximation, in connection with its application in signal processing.

To investigate the effects of Glatiramer Acetate (GA) on B cells by an integrated computational and experimental approach. GA is an immunomodulatory drug approved for the treatment of multiple sclerosis (MS). GA effect on B cells is yet to be fully elucidated. We compared transcriptional profiles of B cells from treatment-naive relapsing remitting MS patients, treated or not with GA for 6 hours in vitro, and of B cells before and after six months of GA administration in vivo. Microarrays were analyzed with two different computational approaches, one for functional analysis of pathways (Gene Set Enrichment Analysis) and one for the identification of new drug targets (Mode-of-action by Network Analysis). GA modulates the expression of genes involved in immune response and apoptosis. A differential expression of genes encoding ion channels, mostly regulating Ca2+ homeostasis in endoplasmic reticulum (ER) was also observed. Microfluorimetric analysis confirmed this finding, showing a specific GA effect on ER Ca2+ concentration. Our findings unveils a GA regulatory effect on the immune response by influencing B cell phenotype and function. In particular, our results highlight a new functional role for GA in modulating Ca2+ homeostasis in these cells.

Human mesenchymal/stromal stem cells (hMSC) are the most promising cell source for adult cell therapies in regenerative medicine. Many clinical trials have reported the use of autologous transplantation of hMSCs in several disorders, but with limited results. To exert their potential, hMSCs could exhibit efficient homing and migration toward lesion sites among other effects, but the underlying process is not clear enough. To further increase the knowledge, we studied the co-regulation between hypoxia-regulated genes and miRNAs. To this end, we investigated the miRNA expression profile of healthy hMSCs in low oxygen/nutrient conditions to mimic ischemia and compared with cells of patients suffering from critical limb ischemia (CLI). miRNAs are small, highly conserved, non-coding RNAs, skilled in the control of the target's expression level in a fine-tuned way. After analyzing the miRNOme in CLI-derived hMSC cells and healthy controls, and intersecting the results with the mRNA expression dataset under hypoxic conditions, we identified two miRNAs potentially relevant to the disease: miR-29b as a pathological marker of the disease and miR-638 as a therapeutic target. This study yielded a deeper understanding of stem cell biology and ischemic disorders, opening new potential treatments in the future.

Acute myeloid leukemia (AML) arises from a complex sequence of biological and finely orchestrated events that are still poorly understood. Increasingly, epigenetic studies are providing exciting findings that may be exploited in promising and personalized cutting-edge therapies. A more appropriate and broader screening of possible players in cancer could identify a master molecular mechanism in AML. Here, we build on our previously published study by evaluating a histone deacetylase (HDAC)2-mediated miRNA regulatory network in U937 leukemic cells. Following a comparative miRNA profiling analysis in genetically and enzymatically HDAC2-downregulated AML cells, we identified miR-96-5p and miR-92a-3p as potential regulators in AML etiopathology by targeting defined genes. Our findings support the potentially beneficial role of alternative physiopathological interventions.

The MagnetoEncephaloGraphy (MEG) has gained great interest in neurorehabilitation training due to its high temporal resolution. The challenge is to localize the active regions of the brain in a fast and accurate way. In this paper we use an inversion method based on random spatial sampling to solve the real-time MEG inverse problem. Several numerical tests on synthetic but realistic data show that the method takes just a few hundredths of a second on a laptop to produce an accurate map of the electric activity inside the brain. Moreover, it requires very little memory storage. For these reasons the random sampling method is particularly attractive in real-time MEG applications.

Magnetoencephalography (MEG) aims at reconstructing the unknown neuroelectric activity in the brain from non-invasive measurements of the magnetic field induced by neural sources. The solution of this ill-posed, ill-conditioned inverse problem is usually dealt with using regularization techniques that are often time-consuming, and computationally and memory storage demanding. In this paper we analyze how a slimmer procedure, random sampling, affects the estimation of the brain activity generated by both synthetic and real sources.

We present Visbrain, a Python open-source package that offers a comprehensive visualization suite for neuroimaging and electrophysiological brain data. Visbrain consists of two levels of abstraction: (1) objects which represent highly configurable neurooriented visual primitives (3D brain, sources connectivity, etc.) and (2) graphical user interfaces for higher level interactions. The object level offers flexible and modular tools to produce and automate the production of figures using an approach similar to that of Matplotlib with subplots. The second level visually connects these objects by controlling properties and interactions through graphical interfaces. The current release of Visbrain (version 0.4.2) contains 14 different objects and three responsive graphical user interfaces, built with PyQt: Signal, for the inspection of time-series and spectral properties, Brain for any type of visualization involving a 3D brain and Sleep for polysomnographic data visualization and sleep analysis. Each module has been developed in tight collaboration with end-users, i.e., primarily neuroscientists and domain experts, who bring their experience to make Visbrain as transparent as possible to the recording modalities (e.g., intracranial EEG, scalp-EEG, MEG, anatomical and functional MRI). Visbrain is developed on top of VisPy, a Python package providing high-performance 2D and 3D visualization by leveraging the computational power of the graphics card. Visbrain is available on Github and comes with a documentation, examples, and datasets (http://visbrain.org).

Imputation of methylation data

Here we present some studies on the behavior of individuals in a biological networks. The first study is about Physarum polycephalum slime mold and its ability to find the shortest path in a maze. Here we present a PDE chemotaxis model that reproduce its behavior in a network, schematized as a planar graph, (1). In particular, suitable transmission and boundary conditions at each node of the graph are considered to mimic the choice of such an organism to move from an arc to another arc of the network, motivated by the search for food. Several numerical tests are presented for special network geometries to show the qualitative agreement between our model and the laboratory observed behavior of the mold. The second study is about tumor associated macrophages and the mathematical modeling of the behavior of cell populations in a microfluidic chip, an environment constructed in laboratory to mimic complex biological systems. In particular, the developed model consists of reaction-diffusion-transport equations with chemotaxis: birth/death processes, interaction with chemoattractant, interaction and competition between species. Suitable transmission conditions are included in the algorithm and numerical tests are presented.

We consider the generalization of discrete de la Vallée Poussin means on the square, obtained via tensor product by the univariate case. Pros and cons of such a kind of filtered approximation are discussed. In particular, under simple, we get near-best discrete approximation polynomials in the space of all locally continuous functions on the square with possible algebraic singularities on the boundary, equipped with the weighted uniform norm. In the four Chebychev cases, these polynomials also interpolate the function. Moreover, for almost everywhere smooth functions, the Gibbs phenomenon appears reduced. Comparison with other interpolating polynomials are proposed.

We consider low-energy configurations for the Heitmann-Radin sticky discs functional, in the limit of diverging number of discs. More precisely, we renormalize the Heitmann-Radin potential by subtracting the minimal energy per particle, i.e. the so-called kissing number. For configurations whose energy scales like the perimeter, we prove a compactness result which shows the emergence of polycrystalline structures: The empirical measure converges to a set of finite perimeter, while a microscopic variable, representing the orientation of the underlying lattice, converges to a locally constant function. Whenever the limit configuration is a single crystal, i.e. it has constant orientation, we show that the Gamma-limit is the anisotropic perimeter, corresponding to the Finsler metric determined by the orientation of the single crystal.

The aim of this paper is to study relaxation rates for the Cahn-Hilliard equation in dimension larger than one. We follow the approach of Otto and Westdickenberg based on the gradient flow structure of the equation and establish differential and algebraic relationships between the energy, the dissipation, and the squared H -1 distance to a kink. This leads to a scale separation of the dynamics into two different stages: a first fast phase of the order t- where one sees convergence to some kink, followed by a slow relaxation phase with rate t< where convergence to the centered kink is observed.

Background and limitations Impaired wound healing (WH) and chronic inflammation are hallmarks of non-communicable diseases (NCDs). However, despite WH being a recognized player in NCDs, mainstream therapies focus on (un)targeted damping of the inflammatory response, leaving WH largely unaddressed, owing to three main factors. The first is the complexity of the pathway that links inflammation and wound healing; the second is the dual nature, local and systemic, of WH; and the third is the limited acknowledgement of genetic and contingent causes that disrupt physiologic progression of WH. Proposed approach Here, in the frame of Predictive, Preventive, and Personalized Medicine (PPPM), we integrate and revisit current literature to offer a novel systemic view on the cues that can impact on the fate (acute or chronic inflammation) of WH, beyond the compartmentalization of medical disciplines and with the support of advanced computational biology. Conclusions This shall open to a broader understanding of the causes for WH going awry, offering new operational criteria for patients' stratification (prediction and personalization). While this may also offer improved options for targeted prevention, we will envisage new therapeutic strategies to reboot and/or boost WH, to enable its progression across its physiological phases, the first of which is a transient acute inflammatory response versus the chronic low-grade inflammation characteristic of NCDs.

Results: We present a simple and computationally efficient imputation method, metyhLImp, based on linear regression. The rationale of the approach lies in the observation that methylation levels show a high degree of inter-sample correlation. We performed a comparative study of our approach with other imputation methods on DNA methylation data of healthy and disease samples from different tissues. Performances have been assessed both in terms of imputation accuracy and in terms of the impact imputed values have on mAge estimation. In comparison to existing methods, our linear regression model proves to perform equally or better and with good computational efficiency. The results of our analysis provide recommendations for accurate estimation of missing methylation values. Motivation: DNA methylation is a stable epigenetic mark with major implications in both physiological (development, aging) and pathological conditions (cancers and numerous diseases). Recent research involving methylation focuses on the development of molecular age estimation methods based on DNA methylation levels (mAge). An increasing number of studies indicate that divergences between mAge and chronological age may be associated to age-related diseases. Current advances in high-throughput technologies have allowed the characterization of DNA methylation levels throughout the human genome. However, experimental methylation profiles often contain multiple missing values that can affect the analysis of the data and also mAge estimation. Although several imputation methods exist, a major deficiency lies in the inability to cope with large datasets, such as DNA methylation chips. Specific methods for imputing missing methylation data are therefore needed.

Chronic inflammatory autoimmune disorders are systemic diseases with increasing incidence and still lack a cure. More recently, attention has been placed in understanding gastrointestinal (GI) dysbiosis and, although important progress has been made in this area, it is currently unclear to what extent microbiome manipulation can be used in the treatment of autoimmune disorders. Via the use of appropriate models, rheumatoid arthritis (RA), a well-known exemplar of such pathologies, can be exploited to shed light on the currently overlooked effects of existing therapies on the GI microbiome. In this direction, we here explore the crosstalk between the GI microbiome and the host immunity in model arthritis (collagen induced arthritis, CIA). By exploiting omics from samples of limited invasiveness (blood and stools), we assess the host-microbiome responses to standard therapy (methotrexate, MTX) combined with mechanical subcutaneous stimulation (MS) and to mechanical stimulation alone. When MS is involved, results reveal the sphingolipid metabolism as the trait d'union among known hallmarks of (model) RA, namely: Imbalance in the S1P-S1PR1 axis, expansion of Prevotella sp., and invariant Natural Killer T (iNKT)-penia, thus offering the base of a rationale to mechanically modulate this pathway as a therapeutic target in RA.