We present and make available novel implementations of the two-dimensional Ising model that is used as a benchmark to show the computational capabilities of modern Graphic Processing Units (GPUs). The rich programming environment now available on GPUs and flexible hardware capabilities allowed us to quickly experiment with several implementation ideas: a simple stencil-based algorithm, recasting the stencil operations into matrix multiplies to take advantage of Tensor Cores available on NVIDIA GPUs, and a highly optimized multi-spin coding approach. Using the managed memory API available in CUDA allows for simple and efficient distribution of these implementations across a multi-GPU NVIDIA DGX-2 server. We show that even a basic GPU implementation can outperform current results published on TPUs (Yang et al., 2019) and that the optimized multi-GPU implementation can simulate very large lattices faster than custom FPGA solutions (Ortega-Zamorano et al., 2016). Program summary: Program title: cuIsing (optimized). CPC Library link to program files: http://dx.doi.org/10.17632/xrb9xtkbcp.1 Licensing provisions: MIT license. Programming languages: CUDA C, Python. Nature of problem: Two dimensional Ising model for spin systems. Solution method: Checkerboard Metropolis algorithm.

Out-of-equilibrium relaxation processes show aging if they become slower as time passes. Aging processes are ubiquitous and play a fundamental role in the physics of glasses and spin glasses and in other applications (e.g., in algorithms minimizing complex cost/loss functions). The theory of aging in the out-of-equilibrium dynamics of mean-field spin glass models has achieved a fundamental role, thanks to the asymptotic analytic solution found by Cugliandolo and Kurchan. However, this solution is based on assumptions (e.g., the weak ergodicity breaking hypothesis) which have never been put under a strong test until now. In the present work, we present the results of an extraordinary large set of numerical simulations of the prototypical mean-field spin glass models, namely the Sherrington-Kirkpatrick and the Viana-Bray models. Thanks to a very intensive use of graphics processing units (GPUs), we have been able to run the latter model for more than 264 spin updates and thus safely extrapolate the numerical data both in the thermodynamical limit and in the large times limit. The measurements of the two-times correlation functions in isothermal aging after a quench from a random initial configuration to a temperature T < T-c provides clear evidence that, at large times, such correlations do not decay to zero as expected by assuming weak ergodicity breaking. We conclude that strong ergodicity breaking takes place in mean-field spin glasses aging dynamics which, asymptotically, takes place in a confined configurational space. Theoretical models for the aging dynamics need to be revised accordingly.

Linear solvers for large and sparse systems are a key element of scientific applications, and their efficient implementation is necessary to harness the computational power of current computers. Algebraic Multigrid (AMG) Preconditioners are a popular ingredient of such linear solvers; this is the motivation for the present work where we examine some recent developments in a package of AMG preconditioners to improve efficiency, scalability, and robustness on extreme-scale problems. The main novelty is the design and implementation of a new parallel coarsening algorithm based on aggregation of unknowns employing weighted graph matching techniques; this is a completely automated procedure, requiring no information from the user, and applicable to general symmetric positive definite (s.p.d.) matrices. The new coarsening algorithm improves in terms of numerical scalability at low operator complexity over decoupled aggregation algorithms available in previous releases of the package. The preconditioners package is built on the parallel software framework PSBLAS, which has also been updated to progress towards exascale. We present weak scalability results on two of the most powerful supercomputers in Europe, for linear systems with sizes up to O(10^10) unknowns.

A challenging task in the management of Protected Areas is to control the spread of invasive species, either floristic or faunistic, and the preservation of indigenous endangered species, typically competing for the use of resources in a fragmented habitat. In this paper, we present some mathematical tools that have been recently applied to contain the worrying diffusion of wolf-wild boars in a Southern Italy Protected Area belonging to the Natura 2000 network. They aim to solve the problem according to three different and in some sense complementary approaches: (i) the qualitative one, based on the use of dynamical systems and bifurcation theory; (ii) the Z-control, an error-based neural dynamic approach; (iii) the optimal control theory. In the case of the wild-boars, the obtained results are illustrated and discussed. To refine the optimal control strategies, a further development is to take into account the spatio-temporal features of the invasive species over large and irregular environments. This approach can be successfully applied, with an optimal allocation of resources, to control an invasive alien species infesting the Alta Murgia National Park: Ailanthus altissima. This species is one of the most invasive species in Europe and its eradication and control is the object of research projects and biodiversity conservation actions in both protected and urban areas [11]. We lastly present, as a further example, the effects of the introduction of the brook trout, an alien salmonid from North America, in naturally fishless lakes of the Gran Paradiso National Park, study site of an on-going H2020 project (ECOPOTENTIAL).

This paper deals with the variational analysis of topological singularities in two dimensions. We consider two canonical zero-temperature models: the core radius approach and the Ginzburg-Landau energy. Denoting by epsilon the length scale parameter in such models, we focus on the vertical bar log epsilon VERBAR; energy regime. It is well known that, for configurations whose energy is bounded by c vertical bar log epsilon vertical bar, the vorticity measures can be decoupled into the sum of a finite number of Dirac masses, each one of them carrying pi vertical bar log epsilon vertical bar energy, plus a mea. sure supported on small zero-average sets. Loosely speaking, on such sets the vorticity measure is close, with respect to the flat norm, to zero-average clusters of positive and negative masses. Here, we perform a compactness and Gamma-convergence analysis accounting also for the presence of such clusters of dipoles (on the range scale epsilon(s), for 0 &lt; s &lt; 1), which vanish in the flat convergence and whose energy contribution has, so far, been neglected. Our results refine and contain as a particular case the classical Gamma-convergence analysis for vortices, extending it also to low energy configurations consisting of just clusters of dipoles, and whose energy is of order c vertical bar log epsilon vertical bar with c &lt; pi.

We prove the existence of weak solutions to the homogeneous wave equation on a suitable class of time-dependent domains. Using the approach suggested by De Giorgi and developed by Serra and Tilli, such solutions are approximated by minimizers of suitable functionals in space-time.

We show that the First-Passage-Time probability distribution of a Lévy time-changed Brownian motion with drift is solution of a time fractional advection-diffusion equation subject to initial and boundary conditions; the Caputo fractional derivative with respect to time is considered. We propose a high order compact implicit discretization scheme for solving this fractional PDE problem and we show that it preserves the structural properties (non-negativity, boundedness, time monotonicity) of the theoretical solution, having to be a probability distribution. Numerical experiments confirming such findings are reported. Simulations of the sample paths of the considered process are also performed and used to both provide suitable boundary conditions and to validate the numerical results.

We numerically investigate the rheological response of a noncoalescing multiple emulsion under a symmetric shear flow. We find that the dynamics significantly depends on the magnitude of the shear rate and on the number of the encapsulated droplets, two key parameters whose control is fundamental to accurately select the resulting nonequiibrium steady states. The double emulsion, for instance, attains a static steady state in which the external droplet stretches under flow and achieves an elliptical shape (closely resembling the one observed in a sheared isolated fluid droplet), while the internal one remains essentially unaffected. Novel nonequiibrium steady states arise in a multiple emulsion. Under low/moderate shear rates, for instance, the encapsulated droplets display a nontrivial planetarylike motion that considerably affects the shape of the external droplet. Some features of this dynamic behavior are partially captured by the Taylor deformation parameter and the stress tensor. Besides a theoretical interest on its own, our results can potentially stimulate further experiments, as most of the predictions could be tested in the lab by monitoring droplets' shapes and position over time. Published under license by AIP Publishing.

The study of the underlying physics of soft flowing materials depends heavily on numerical simulations, due to the complex structure of the governing equations reflecting the competition of concurrent mechanisms acting at widely disparate scales in space and time. A full-scale computational modelling remains a formidable challenge since it amounts to simultaneously handling six or more spatial decades in space and twice as many in time. Coarse-grained methods often provide a viable strategy to significantly mitigate this issue, through the implementation of mesoscale supramolecular forces designed to capture the essential physics at a fraction of the computational cost of a full-detail description. Here, we review some recent advances in the design of a lattice Boltzmann mesoscale approach for soft flowing materials, inclusive of near-contact interactions (NCIs) between dynamic interfaces, as they occur in high packing-fraction soft flowing crystals. The method proves capable of capturing several aspects of the rheology of soft flowing crystals, namely, (i) a 3/2 power-law dependence of the dispersed phase flow rate on the applied pressure gradient, (ii) the structural transition between an ex-two and ex-one (bamboo) configurations with the associated drop of the flow rate, (iii) the onset of interfacial waves once NCI is sufficiently intense. This article is part of the theme issue 'Fluid dynamics, soft matter and complex systems: recent results and new methods'.

In this work we developed a mathematical model describing the crystallization process of salt dissolved in water flowing within a porous medium (in this case the common brick). Starting from this model a numerical tool was developed that allows to describe the effects of salt penetrating inside porous media and to forecast the effects of the application of crystallization inibitors.

t. The present work was inspired by the recent developments in laboratory experiments made on chip, where culturing of multiple cell species waspossible. The model is based on coupled reaction-diffusion-transport equationswith chemotaxis, and takes into account the interactions among cell populations and the possibility of drug administration for drug testing effects.Our effort was devoted to the development of a simulation tool that is able toreproduce the chemotactic movement and the interactions between differentcell species (immune and cancer cells) living in microfluidic chip environment.The main issues faced in this work are the introduction of mass-preservingand positivity-preserving conditions involving the balancing of incoming andoutgoing fluxes passing through interfaces between 2D and 1D domains of thechip and the development of mass-preserving and positivity preserving numerical conditions at the external boundaries and at the interfaces between 2Dand 1D domains

SUNBIM (Supramolecular and sUbmolecular Nano- and Biomaterials X-ray IMaging) is a computer suite of integrated programs which, through a user-friendly graphical interface, is able to perform a number of functions for (GI)SAXS-(GI)WAXS data analysis [1] such as: centering, q-scale calibration, two-dimensional to one-dimensional folding of small- and wide-angle X-ray scattering (SAXS/WAXS) data, also in grazing-incidence (GISAXS/GIWAXS); indexing of two-dimensional GISAXS frames and extraction of one-dimensional GISAXS profiles along specific cuts; quantitative scanning microscopy in absorption and SAXS contrast. SUNBIM consists of five main programs: (1) Calibration package, a set of functions allow one to find all of the geometrical parameters needed to extract a one-dimensional profile out of a two-dimensional image; (2) Batch Script & 2D Mesh Composite, to prepare batch script files (ASCII files) to run a sequential acquisition of two-dimensional frames (in scanning mode) and to perform a composite of the as-collected two-dimensional SAXS frames into a single image; (3) Single-scan (GI)SAXS and (GI)WAXS data analysis, to calibrate and fold the two-dimensional data, in order to extract relevant information from the experimental data and to fold 2D data into 1D profiles; (4) Multi-scan SAXS and WAXS data analysis, to fold each two-dimensional frame of the mesh into a one-dimensional profile and extract scattering features of the sample with a multi-modal imaging approach; (5) One-D Data Analysis Manager, a package that in addition to basic operations on one dimensional profiles (such as change of the plot representation from pixels to q, change from linear scale to logarithmic scale of the axes, choice of colors and plot thickness, inserting the legend, etc. as well as import, trigger, save and export plots) gives the possibility to denoise the folded profile and/or to deconvolute the primary beam angular divergence from the SAXS/WAXS profiles, particularly useful for a complete data analysis. SUNBIM combines in the same package both originally developed algorithms (i.e denoising, beam centering etc.) and reliable methods documented in the literature (multi-modal imaging [2], GIXAXS three-dimensional frame indexing [3]). New tools have been developed to enrich SUNBIM suite. The main novelty is the possibility to perform a deeper data reduction including dark current subtraction, background evaluation and subtraction, normalization of the SAXS intensity against the local sample thickness derived from absorption contrast maps. The advances of the new release with respect to previous one include also an automatic background subtraction from the 1D profile of the azimuthal integration to enhance peak visibility at large scattering angles (WAXS), to correct geometric aberration for small sample-to-detector distance. The previous release of the software has already been used successfully to analyse several nano-structured samples [4][5][6]. We are confident that the new features will allow a more correct and extensive analysis of the (GI)SAXS/(GI)WAXS data. SUNBIM is developed in the MATLAB language and it is distributed free of charge to the academic user (downloadable after a valid registration from http://www.ba.ic.cnr.it/softwareic/sunbimweb/)

Background: High-throughput technologies enable the cost-effective collection and analysis of DNA methylation data throughout the human genome. This naturally entails missing values management that can complicate the analysis of the data. Several general and specific imputation methods are suitable for DNA methylation data. However, there are no detailed studies of their performances under different missing data mechanisms -(completely) at random or not- and different representations of DNA methylation levels (beta andM-value).

Meta-analysis is a powerful means for leveraging the hundreds of experiments being run worldwide into more statistically powerful analyses. This is also true for the analysis of omic data, including genome-wide DNA methylation. In particular, thousands of DNA methylation profiles generated using the Illumina 450k are stored in the publicly accessible Gene Expression Omnibus (GEO) repository. Often, however, the intensity values produced by the BeadChip (raw data) are not deposited, therefore only pre-processed values-obtained after computational manipulation-are available. Pre-processing is possibly different among studies and may then affect meta-analysis by introducing non-biological sources of variability. Introduction

We discuss the well-posedness of the "transient eddy current" magneto-quasi-static approximation of Maxwell's initial value problem with bounded and measurable conductivity, with sources, on a domain. We prove the existence and uniqueness of weak solutions, and we provide global Hölder estimates for the magnetic part.

The ongoing COVID-19 pandemic still requires fast and effective efforts from all fronts, including epidemiology, clinical practice, molecular medicine, and pharmacology. A comprehensive molecular framework of the disease is needed to better understand its pathological mechanisms, and to design successful treatments able to slow down and stop the impressive pace of the outbreak and harsh clinical symptomatology, possibly via the use of readily available, off-the-shelf drugs. This work engages in providing a wider picture of the human molecular landscape of the SARS-CoV-2 infection via a network medicine approach as the ground for a drug repurposing strategy. Grounding on prior knowledge such as experimentally validated host proteins known to be viral interactors, tissue-specific gene expression data, and using network analysis techniques such as network propagation and connectivity significance, the host molecular reaction network to the viral invasion is explored and exploited to infer and prioritize candidate target genes, and finally to propose drugs to be repurposed for the treatment of COVID-19. Ranks of potential target genes have been obtained for coherent groups of tissues/organs, potential and distinct sites of interaction between the virus and the organism. The normalization and the aggregation of the different scores allowed to define a preliminary, restricted list of genes candidates as pharmacological targets for drug repurposing, with the aim of contrasting different phases of the virus infection and viral replication cycle.

Systems medicine (SM) has emerged as a powerful tool for studying the human body at the systems level with the aim of improving our understanding, prevention and treatment of complex diseases. Being able to automatically extract relevant features needed for a given task from high-dimensional, heterogeneous data, deep learning (DL) holds great promise in this endeavour. This review paper addresses the main developments of DL algorithms and a set of general topics where DL is decisive, namely, within the SM landscape. It discusses how DL can be applied to SM with an emphasis on the applications to predictive, preventive and precision medicine. Several key challenges have been highlighted including delivering clinical impact and improving interpretability. We used some prototypical examples to highlight the relevance and significance of the adoption of DL in SM, one of them is involving the creation of a model for personalized Parkinson's disease. The review offers valuable insights and informs the research in DL and SM.

Simulated data are crucial for evaluating epistasis detection tools in genome-wide association studies. Existing simulators are limited, as they do not account for linkage disequilibrium (LD), support limited interaction models of single nucleotide polymorphisms (SNPs) and only dichotomous phenotypes or depend on proprietary software. In contrast, EpiGEN supports SNP interactions of arbitrary order, produces realistic LD patterns and generates both categorical and quantitative phenotypes.EpiGEN is implemented in Python 3 and is freely available at https://github.com/baumbachlab/epigen.Supplementary data are available at Bioinformatics online.

This paper describes the effect of perturbation of the kernel on the solutions of linear Volterra integral equations on time scales and proposes a new perspective for the stability analysis of numerical methods.

Introduction: Network and systems medicine has rapidly evolved over the past decade, thanks to computational and integrative tools, which stem in part from systems biology. However, major challenges and hurdles are still present regarding validation and translation into clinical application and decision making for precision medicine. Methods: In this context, the Collaboration on Science and Technology Action on Open Multiscale Systems Medicine (OpenMultiMed) reviewed the available advanced technologies for multidimensional data generation and integration in an open-science approach as well as key clinical applications of network and systems medicine and the main issues and opportunities for the future. Results: The development of multi-omic approaches as well as new digital tools provides a unique opportunity to explore complex biological systems and networks at different scales. Moreover, the application of findable, applicable, interoperable, and reusable principles and the adoption of standards increases data availability and sharing for multiscale integration and interpretation. These innovations have led to the first clinical applications of network and systems medicine, particularly in the field of personalized therapy and drug dosing. Enlarging network and systems medicine application would now imply to increase patient engagement and health care providers as well as to educate the novel generations of medical doctors and biomedical researchers to shift the current organ- and symptom-based medical concepts toward network- and systems-based ones for more precise diagnoses, interventions, and ideally prevention. Conclusion: In this dynamic setting, the health care system will also have to evolve, if not revolutionize, in terms of organization and management.