This paper provides a unified point of view on fractional perimeters and Riesz potentials. Denoting byH? - for ? 2 .0; 1/ - the ?-fractional perimeter and by J ? - for ? 2 .(d; 0)- the ?-Riesz energies acting on characteristic functions, we prove that both functionals can be seen as limits of renormalized self-attractive energies as well as limits of repulsive interactions between a set and its complement. We also show that the functionals H? and J ? , up to a suitable additive renormalization diverging when ? ? 0, belong to a continuous one-parameter family of functionals, which for ? D 0 gives back a new object we refer to as 0-fractional perimeter. All the convergence results with respect to the parameter ? and to the renormalization procedures are obtained in the framework of A-convergence. As a byproduct of our analysis, we obtain the isoperimetric inequality for the 0-fractional perimeter.

Multiple emulsions are a class of soft fluid in which small drops are immersed within a larger one and stabilized over long periods of time by a surfactant. We recently showed that, if a monodisperse multiple emulsion is subject to a pressure-driven flow, a wide variety of nonequilibrium steady states emerges at late times, whose dynamics relies on a complex interplay between hydrodynamic interactions and multibody collisions among internal drops. In this work, we use lattice Boltzmann simulations to study the dynamics of polydisperse double emulsions driven by a Poiseuille flow within a microfluidic channel. Our results show that their behavior is critically affected by multiple factors, such as initial position, polydispersity index, and area fraction occupied within the emulsion. While at low area fraction inner drops may exhibit either a periodic rotational motion (at low polydispersity) or arrange into nonmotile configurations (at high polydispersity) located far from each other, at larger values of area fraction they remain in tight contact and move unidirectionally. This decisively conditions their close-range dynamics, quantitatively assessed through a time-efficiency-like factor. Simulations also unveil the key role played by the capsule, whose shape changes can favor the formation of a selected number of nonequilibrium states in which both motile and nonmotile configurations are found.

Up-to-date computational glaciology is very often basing its investigations about glacier flow on the intensive use of the large amount of data, gathered in (alpine or polar) on-field campaigns, and on the "brute force" adaptation of the Glen's law via phenomenological multi-parametrical functional factors and/or addenda. Although, reasonable to fully satisfactory numerical results have been being obtained with this approach adopted by the most popular open-source computational glaciology codes, a modelling effort is worth in order to include the normal stress gradient effects which are not covered by such a power law model and are indeed physically significant in the case of moraine ice and rock glaciers. In this trend Kannan, Mansutti and Rajagopal have proposed (2021) a mathematical numerical model which has been successfully challenged on the reproduction of borehole deformation measurements of the Murtel-Corvatsch rock glacier on the Grisons Alps, Switzerland. This case, and possibly other numerical results at the present time in progress, will be discussed.

Spectral residual methods are derivative-free and low-cost per iteration procedures for solving nonlinear systems of equations. They are generally coupled with a nonmonotone linesearch strategy and compare well with Newton-based methods for large nonlinear systems and sequences of nonlinear systems. The residual vector is used as the search direction and choosing the steplength has a crucial impact on the performance. In this work we address both theoretically and experimentally the steplength selection and provide results on a real application such as a rolling contact problem.

In this paper, we numerically investigate the breakup dynamics of droplets in an emulsion flowing in a tapered microchannel with a narrow constriction. The mesoscale approach for multicomponent fluids with near contact interactions is shown to capture the deformation and breakup dynamics of droplets interacting within the constriction, in agreement with experimental evidence. In addition, it permits us to investigate in detail the hydrodynamic phenomena occurring during breakup stages. Finally, a suitable deformation parameter is introduced and analyzed to characterize the state of deformation of the system by inspecting pairs of interacting droplets flowing in the narrow channel.

We study numerically the effect of thermal fluctuations and of variable fluid-substrate interactions on the spontaneous dewetting of thin liquid films. To this aim, we use a recently developed lattice Boltzmann method for thin liquid film flows, equipped with a properly devised stochastic term. While it is known that thermal fluctuations yield shorter rupture times, we show that this is a general feature of hydrophilic substrates, irrespective of the contact angle $\theta$. The ratio between deterministic and stochastic rupture times, though, decreases with $\theta$. Finally, we discuss the case of fluctuating thin film dewetting on chemically patterned substrates and its dependence on the form of the wettability gradients.

The non-equilibrium structural and dynamical properties of semiflexible polymers confined to two dimensions are investigated by Brownian multi-particle collision dynamics. Different scenarios will be considered: tethered polymers subject to an external force, chains under steady shear flow [1], and filaments with either both [2] or one fixed end [3] under oscillatory shear flow. The results of the numerical studies will be presented and discussed. [1] A. Lamura and R. G. Winkler, Semiflexible polymers under external fields confined to two dimensions, J. Chem. Phys. 137, 244909 (2012) [2] A. Lamura and R. G. Winkler, Tethered semiflexible polymer under large amplitude oscillatory shear, Polymers 11, 737 (2019) [3] A. Lamura, R. G. Winkler, and G. Gompper, Wall-anchored semiflexible polymer under oscillating shear flow, pre-print (2020)

A mm thick free-standing gel containing lipid vesicles made of 2-oleoyl-1-palmitoyl-sn-glycero-3-phosphocholine (POPC) was studied by scanning Small Angle X-ray Scattering (SAXS) and X-ray Transmission (XT) microscopies. Raster scanning relatively large volumes, besides reducing the risk of radiation damage, allows signal integration, improving the signal-to-noise ratio (SNR), as well as high statistical significance of the dataset. The persistence of lipid vesicles in gel was demonstrated, while mapping their spatial distribution and concentration gradients. Information about lipid aggregation and packing, as well as about gel density gradients, was obtained.A posterioriconfirmation of lipid presence in well-defined sample areas was obtained by studying the dried sample, featuring clear Bragg peaks from stacked bilayers. The comparison between wet and dry samples allowed it to be proved that lipids do not significantly migrate within the gel even upon drying, whereas bilayer curvature is lost by removing water, resulting in lipids packed in ordered lamellae. Suitable algorithms were successfully employed for enhancing transmission microscopy sensitivity to low absorbing objects, and allowing full SAXS intensity normalization as a general approach. In particular, data reduction includes normalization of the SAXS intensity against the local sample thickness derived from absorption contrast maps. The proposed study was demonstrated by a room-sized instrumentation, although equipped with a high brilliance X-ray micro-source, and is expected to be applicable to a wide variety of organic, inorganic, and multicomponent systems, including biomaterials. The employed routines for data reduction and microscopy, including Gaussian filter for contrast enhancement of low absorbing objects and a region growing segmentation algorithm to exclude no-sample regions, have been implemented and made freely available through the updated in-house developed software SUNBIM.

Background: The high contagiousness and rapid spreading of the coronavirus disease 2019 (COVID-19) has caused a high number of critical to severe life-threatening cases, which required urgent hospital admission and treatment in intensive care units (ICUs). The pandemic has been a tough test for all European national health systems and their capability to provide an adequate reaction. Methods: The present work aims to reveal correlations between parameters such as COVID-19 incidence, ICU bed occupancy, ICU excess area, and mortality in Italian regions. Public data for the period of March 1 to July 16, 2020, were analyzed using several mathematical and statistical methods. Results: The analysis defined two separate groups of Italian regions. The examined variables considered within these groups were interlinked and dependent on each other. The regions of the two groups shared the same kind of fitted model (linear) explaining mortality as a function of cumulative incidence, but with higher value of the constant in one group, so characterized by a high intrinsic "strength" of the pandemic, certainly playing a major role in the generation of a large number of severe and life-threatening cases. These results are confirmed at European level. Other factors may condition mortality and be linked to incidence, such as ICU saturation and excess. Conclusions: These quantitative results could be a very helpful tool to set up preventive measures and optimize biomedical interventions before the pandemic, in its recurrent waves, could overcome the reaction capacity of any public health system.

In this paper, the asymptotic behaviour of the numerical solution to the Volterra integralequations is studied. In particular, a technique based on an appropriate splitting of the kernel isintroduced, which allows one to obtain vanishing asymptotic (transient) behaviour in the numericalsolution, consistently with the properties of the analytical solution, without having to operaterestrictions on the integration steplength

Advanced age is the major risk factor for idiopathic Parkinson's disease (PD), but to date the biological relationship between PD and ageing remains elusive. Here we describe the rationale and the design of the H2020 funded project "PROPAG-AGEING", whose aim is to characterize the contribution of the ageing process to PD development. We summarize current evidences that support the existence of a continuum between ageing and PD and justify the use of a Geroscience approach to study PD. We focus in particular on the role of inflammaging, the chronic, low-grade inflammation characteristic of elderly physiology, which can propagate and transmit both locally and systemically. We then describe PROPAG-AGEING design, which is based on the multi-omic characterization of peripheral samples from clinically characterized drug-naïve and advanced PD, PD discordant twins, healthy controls and "super-controls", i.e. centenarians, who never showed clinical signs of motor disability, and their offspring. Omic results are then validated in a large number of samples, including in vitro models of dopaminergic neurons and healthy siblings of PD patients, who are at higher risk of developing PD, with the final aim of identifying the molecular perturbations that can deviate the trajectories of healthy ageing towards PD development.

Background: DNA methylation is the main epigenetic mechanism driving changes in phenotype without altering genotype. Since the end of the seventies the role of methylation in cancer has become increasingly clear. Objective: The aim of this work is to shed light on the impact of methylation events on cancer cells, providing evidence that differential methylation in small regions, mostly characterized by hypermethylation, affects gene regulation while differential methylation in large genomic regions, mostly characterized by hypomethylation, affects chromosomal organization. Methods: By exploiting a solid computational and statistical analysis, methylation maps of cancer and normal samples in six different cancer types were studied, looking for those genomic regions showing differentially methylated patterns between the two conditions. Results: Through a chromosome sliding windows approach, a set of differentially methylated genomic micro regions of size 2 K bp and macro regions of size 1 M bp, were identified. Micro regions are mostly linked to functional elements while macro regions are mostly linked to nuclear chromosome organization. Results discussed in previous works were confirmed, providing clear evidence that hypermethylation mainly occurs in significant micro regions while hypomethylation mainly occurs in significant macro regions. Interestingly the presence of differentially methylated regions common for six different cancers were identified and some unexpected and previously unexplored peculiar methylation patterns were also found. Conclusions: The effective and robust computational and statistical methodology presented in this work can be used to shed light on the role that DNA methylation plays in cancer and in other non malignant diseases and can be customized to study differentially methylated patterns in specific areas of interest of the genome both at a small scale and at a large scale.

The recent COVID-19 pandemic came alongside with an "infodemic", with online social media flooded by often unreliable information associating the medical emergency with popular subjects of disinformation. In Italy, one of the first European countries suffering a rise in new cases and dealing with a total lockdown, controversial topics such as migrant flows and the 5G technology were often associated online with the origin and diffusion of the virus. In this work we analyze COVID-19 related conversations on the Italian Facebook, collecting over 1.5M posts shared by nearly 80k public pages and groups for a period of four months since January 2020. On the one hand, our findings suggest that well-known unreliable sources had a limited exposure, and that discussions over controversial topics did not spark a comparable engagement with respect to institutional and scientific communication. On the other hand, however, we realize that dis- and counter-information induced a polarization of (clusters of) groups and pages, wherein conversations were characterized by a topical lexicon, by a great diffusion of user generated content, and by link-sharing patterns that seem ascribable to coordinated propaganda. As revealed by the URL-sharing diffusion network showing a "small-world" effect, users were easily exposed to harmful propaganda as well as to verified information on the virus, exalting the role of public figures and mainstream media, as well as of Facebook groups, in shaping the public opinion.

In a computer-aided system for skin cancer diagnosis, hair removal is one of the main challenges to face before applying a process of automatic skin lesion segmentation and classification. In this paper, we propose a straightforward method to detect and remove hair from dermoscopic images. Preliminarily, the regions to consider as candidate hair regions and the border/corner components located on the image frame are automatically detected. Then, the hair regions are determined using information regarding the saliency, shape and image colors. Finally, the detected hair regions are restored by a simple inpainting method. The method is evaluated on a publicly available dataset, comprising 340 images in total, extracted from two commonly used public databases, and on an available specific dataset including 13 images already used by other authors for evaluation and comparison purposes. We propose also a method for qualitative and quantitative evaluation of a hair removal method. The results of the evaluation are promising as the detection of the hair regions is accurate, and the performance results are satisfactory in comparison to other existing hair removal methods.

Targeted drug delivery systems represent a promising strategy to treat localised disease with minimum impact on the surrounding tissue. In particular, polymeric nanocontainers have attracted major interest because of their structural and morphological advantages and the variety of polymers that can be used, allowing the synthesis of materials capable of responding to the biochemical alterations of the environment. While experimental methodologies can provide much insight, the generation of experimental data across a wide parameter space is usually prohibitively time consuming and/or expensive. To better understand the influence of varying design parameters on the release profile and drug kinetics involved, appropriately-designed mathematical models are of great benefit. Here, we developed a continuum-scale mathematical model to describe drug transport within, and release from, a hollow nanocontainer consisting of a core and a pH-responsive polymeric shell. Our two-layer mathematical model accounts for drug dissolution and diffusion and includes a mechanism to account for trapping of drug molecules within the shell. We conduct a sensitivity analysis to assess the effect of varying the model parameters on the overall behaviour of the system. To demonstrate the usefulness of our model, we focus on the particular case of cancer treatment and calibrate the model against release profile data for two anti-cancer therapeutical agents. We show that the model is capable of capturing the experimentally observed pH-dependent release.

Despite the international guidelines on the containment of the coronavirus disease 2019 (COVID-19) pandemic, the European scientific community was not sufficiently prepared to coordinate scientific efforts. To improve preparedness for future pandemics, we have initiated a network of nine European-funded Cooperation in Science and Technology (COST) Actions that can help facilitate inter-, multi-, and trans-disciplinary communication and collaboration.

ZBTB2 is a protein belonging to the BTB/POZ zinc-finger family whose members typically contain a BTB/POZ domain at the N-terminus and several zinc-finger domains at the C-terminus. Studies have been carried out to disclose the role of ZBTB2 in cell proliferation, in human cancers and in regulating DNA methylation. Moreover, ZBTB2 has been also described as an ARF, p53 and p21 gene repressor as well as an activator of genes modulating pluripotency. In this scenario, ZBTB2 seems to play many functions likely associated with other proteins. Here we report a picture of the ZBTB2 protein partners in U87MG cell line, identified by high-resolution mass spectrometry (MS) that highlights the interplay between ZBTB2 and chromatin remodeling multiprotein complexes.In particular, our analysis reveals the presence, as ZBTB2 candidate interactors, of SMARCA5 and BAZ1B components of the chromatin remodeling complex WICH and PBRM1, a subunit of the SWI/SNF complex. Intriguingly, we identified all the subunits of the NuRD complex among the ZBTB2 interactors. By co-immunoprecipitation experiments and ChIP-seq analysis we definitely identify ZBTB2 as a new partner of the NuRD complex. Highlightso ZBTB2 co-associate with the NuRD complex.o The multiple ZBTB2 functions can be explained because of its interplay with NuRD.o ZBTB2 can be a bridge between NuRD and DNA-sequence specific transcription factors.o ZBTB2 interactome by mass-spectrometry reveals the presence of many chromatin remodeling complex subunits.o ZBTB2 interacts with ZNF639, a sequence-specific DNA-binding zinc-finger protein.

A recently introduced approach to the classical gravitational dynamics of binary systems involves intricate integrals (linked to a combination of nonlocal-in-time interactions with iterated 1r-potential scattering) which have so far resisted attempts at their analytical evaluation. By using computing techniques developed for the evaluation of multiloop Feynman integrals (notably harmonic polylogarithms and Mellin transform) we show how to analytically compute all the integrals entering the nonlocal-in-time contribution to the classical scattering angle at the sixth post-Newtonian accuracy, and at the seventh order in Newton's constant, G (corresponding to six-loop graphs in the diagrammatic representation of the classical scattering angle).

The linear-order effects of radiation-reaction on the classical scattering of two point masses, in general relativity, are derived by a variation-of-constants method. Explicit expressions for the radiation-reaction contributions to the changes of 4-momentum during scattering are given to linear order in the radiative losses of energy, linear-momentum, and angular momentum. The polynomial dependence on the masses of the 4-momentum changes is shown to lead to nontrivial identities relating the various radiative losses. At order G3 our results lead to a streamlined classical derivation of results recently derived within a quantum approach. At order G4 we compute the needed radiative losses to next-to-next-to-leading-order in the post-Newtonian expansion, thereby reaching the absolute fourth and a half post-Newtonian level of accuracy in the 4-momentum changes. We also provide explicit expressions, at the absolute sixth post-Newtonian accuracy, for the radiation-graviton contribution to conservative O(G4) scattering. At orders G5 and G6 we derive explicit theoretical expressions for the last two hitherto undetermined parameters describing the fifth-post-Newtonian dynamics. Our results at the fifth-post-Newtonian level confirm results of [Nucl. Phys. B965, 115352 (2021)NUPBBO0550-321310.1016/j.nuclphysb.2021.115352] but exhibit some disagreements with results of [Phys. Rev. D 101, 064033 (2020)PRVDAQ2470-001010.1103/PhysRevD.101.064033].

The energy radiated (without the 1.5PN tail contribution which requires a different treatment) by a binary system of compact objects moving in a hyperboliclike orbit is computed in the frequency domain through the second post-Newtonian level as an expansion in the large-eccentricity parameter up to next-to-next-to-leading order, completing the time domain corresponding information (fully known in closed form at the second post-Newtonian of accuracy). The spectrum contains quadratic products of the modified Bessel functions of the first kind (Bessel K functions) with frequency-dependent order (and argument) already at Newtonian level, so preventing the direct evaluation of Fourier integrals. However, as the order of the Bessel functions tends to zero for large eccentricities, a large-eccentricity expansion of the spectrum allows for analytical computation beyond the lowest order.