The migration of endothelial cells (ECs) is critical for various processes including vascular wound healing, tumor angiogenesis, and the development of viable endovascular implants. Recent observations (time-lapse imaging over 12hr periods) in our laboratory of ECs cultured on line patterns - surfaces where cellular adhesion is limited to 15 ?m wide lines - have demonstrated the presence of three distinct migration phenotypes: a) running - cells are polarized and migrate continuously and persistently on the adhesive lines with possible directional changes, b) undecided - cells are elongated and exhibit periodic changes in the direction of their polarization and minimal net migration, and c) tumbling-like - cells migrate persistently for a certain amount of time but then stop and round up for a few hours before spreading again and resuming migration. Because EC migration is regulated by intracellular ATP levels and cellular elongation induced ATP release, we hypothesize that the three migration phenotypes on line patterns, which translate into different cell length variations in time, are related to different intracellular ATP profiles. Thus, we have developed a mathematical model to provide a description of the complex interactions between cell length, cytoskeletal (F-actin) organization, and intracellular ATP concentration. To identify the parameters that reproduce the experimental observations, we have implemented an optimization procedure that yields the parameter values that best fit the experimental data on cell lengths. The results show that depending on the parameter values adopted for the simulations, the different ATP profiles can indeed be obtained. Future work will focus on providing experimental evidence for the involvement of intracellular ATP in determining the three types of migration behavior.

The aim of this paper is to solve an inverse problem which regards a mass moving in a bounded domain. We assume that the mass moves following an unknown velocity field and that the evolution of the mass density can be described by a partial differential equation, which is also unknown. The input data of the problems are given by some snapshots of the mass distribution at certain times, while the sought output is the velocity field that drives the mass along its displacement. To this aim, we put in place an algorithm based on the combination of two methods: first, we use the dynamic mode decomposition to create a mathematical model describing the mass transfer; second, we use the notion of Wasserstein distance (also known as earth mover's distance) to reconstruct the underlying velocity field that is responsible for the displacement. Finally, we consider a real-life application: the algorithm is employed to study the travel flows of people in large populated areas using, as input data, density profiles (i.e., the spatial distribution) of people in given areas at different time instants. These kinds of data are provided by the Italian telecommunication company TIM and are derived by mobile phone usage.

The impact of vehicular traffic on society is huge and multifaceted, including economic, social, health and environmental aspects. The problems is complex and hard to model since it requires to consider traffic patterns, air pollutant emissions, and the chemical reactions and dynamics of pollutants in the low atmosphere. This paper aims at exploring a comprehensive simulation tool ranging from vehicular traffic all the way to environmental impact. As first step in this direction, we couple a traffic second-order model, tuned on NGSIM data, with an nitrogen oxides (NO) emission model and a set of equations for some of the main chemical reactions behind ozone (O) production.

In the framework of the exact factorization of the time-dependent electron-nuclear wave function, we investigate the possibility of solving the nuclear time-dependent Schrödinger equation based on trajectories. The nuclear equation is separated in a Hamilton-Jacobi equation for the phase of the wave function, and a continuity equation for its (squared) modulus. For illustrative adiabatic and nonadiabatic one-dimensional models, we implement a procedure to follow the evolution of the nuclear density along the characteristics of the Hamilton-Jacobi equation. Those characteristics are referred to as quantum trajectories, since they are generated via ordinary differential equations similar to Hamilton's equations, but including the so-called quantum potential, and they can be used to reconstruct exactly the quantum-mechanical nuclear wave function, provided infinite initial conditions are propagated in time.

Derivations of the Jarzynski equality (JE) appear to be quite general, and applicable to any particle system, whether deterministic or stochastic, under equally general perturbations of an initial equilibrium state at given temperatureT. At the same time, the definitions of the quantities appearing in the JE, in particular the work, have been questioned. Answers have been given, but a deeper understanding of the range of phenomena to which the JE applies is necessary, both conceptually and in order to interpret the experiments in which it is used. In fact, domains in which the JE is not applicable have been identified. To clarify the issue, we scrutinize the applicability of the JE to a Hamiltonian particle system in a variable volume. We find that, in this case, the standard interpretation of the terms appearing in the JE is not adequate.

Background: Mutations of the mitochondrial protein paraplegin cause hereditary spastic paraplegia type 7 (SPG7), a so-far untreatable degenerative disease of the upper motoneuron with still undefined pathomechanism. The intermittent mitochondrial permeability transition pore (mPTP) opening, called flickering, is an essential process that operates to maintain mitochondrial homeostasis by reducing intra-matrix Ca and reactive oxygen species (ROS) concentration, and is critical for efficient synaptic function. Methods: We use a fluorescence-based approach to measure mPTP flickering in living cells and biochemical and molecular biology techniques to dissect the pathogenic mechanism of SPG7. In the SPG7 animal model we evaluate the potential improvement of the motor defect, neuroinflammation and neurodegeneration by means of an mPTP inducer, the benzodiazepine Bz-423. Findings: We demonstrate that paraplegin is required for efficient transient opening of the mPTP, that is impaired in both SPG7 patients-derived fibroblasts and primary neurons from Spg7 mice. We show that dysregulation of mPTP opening at the pre-synaptic terminal impairs neurotransmitter release leading to ineffective synaptic transmission. Lack of paraplegin impairs mPTP flickering by a mechanism involving increased expression and activity of sirtuin3, which promotes deacetylation of cyclophilin D, thus hampering mPTP opening. Pharmacological treatment with Bz-423, which bypasses the activity of CypD, normalizes synaptic transmission and rescues the motor impairment of the SPG7 mouse model. Interpretation: mPTP targeting opens a new avenue for the potential therapy of this form of spastic paraplegia. Funding: Telethon Foundation grant (TGMGCSBX16TT); Dept. of Defense, US Army, grant W81XWH-18-1-0001

?1-Antitrypsin (AAT) encoded by the SERPINA1 gene is an acute-phase protein synthesized in the liver and secreted into the circulation. Its primary role is to protect lung tissue by inhibiting neutrophil elastase. The Z allele of SERPINA1 encodes a mutant AAT, named ATZ, that changes the protein structure and leads to its misfolding and polymerization, which cause endoplasmic reticulum (ER) stress and liver disease through a gain-of-function toxic mechanism. Hepatic retention of ATZ results in deficiency of one of the most important circulating proteinase inhibitors and predisposes to early-onset emphysema through a loss-of-function mechanism. The pathogenetic mechanisms underlying the liver disease are not completely understood. C/EBP-homologous protein (CHOP), a transcription factor induced by ER stress, was found among the most up-regulated genes in livers of PiZ mice that express ATZ and in human livers of patients homozygous for the Z allele. Compared with controls, juvenile PiZ/Chop -/- mice showed reduced hepatic ATZ and a transcriptional response indicative of decreased ER stress by RNA-Seq analysis. Livers of PiZ/Chop -/- mice also showed reduced SERPINA1 mRNA levels. By chromatin immunoprecipitations and luciferase reporter-based transfection assays, CHOP was found to up-regulate SERPINA1 cooperating with c-JUN, which was previously shown to up-regulate SERPINA1, thus aggravating hepatic accumulation of ATZ. Increased CHOP levels were detected in diseased livers of children homozygous for the Z allele. In summary, CHOP and c-JUN up-regulate SERPINA1 transcription and play an important role in hepatic disease by increasing the burden of proteotoxic ATZ, particularly in the pediatric population.

Tumor resistance to chemotherapy represents an important challenge in modern oncology. Although platinum (Pt)-based drugs have demonstrated excellent therapeutic potential, their effectiveness in a wide range of tumors is limited by the development of resistance mechanisms. One of these mechanisms includes increased cisplatin sequestration/efflux by the copper-transporting ATPase, ATP7B. However, targeting ATP7B to reduce Pt tolerance in tumors could represent a serious risk because suppression of ATP7B might compromise copper homeostasis, as happens in Wilson disease. To circumvent ATP7B-mediated Pt tolerance we employed a high-throughput screen (HTS) of an FDA/EMA-approved drug library to detect safe therapeutic molecules that promote cisplatin toxicity in the IGROV-CP20 ovarian carcinoma cells, whose resistance significantly relies on ATP7B. Using a synthetic lethality approach, we identified and validated three hits (Tranilast, Telmisartan, and Amphotericin B) that reduced cisplatin resistance. All three drugs induced Pt-mediated DNA damage and inhibited either expression or trafficking of ATP7B in a tumor-specific manner. Global transcriptome analyses showed that Tranilast and Amphotericin B affect expression of genes operating in several pathways that confer tolerance to cisplatin. In the case of Tranilast, these comprised key Pt-transporting proteins, including ATOX1, whose suppression affected ability of ATP7B to traffic in response to cisplatin. In summary, our findings reveal Tranilast, Telmisartan, and Amphotericin B as effective drugs that selectively promote cisplatin toxicity in Pt-resistant ovarian cancer cells and underscore the efficiency of HTS strategy for identification of biosafe compounds, which might be rapidly repurposed to overcome resistance of tumors to Pt-based chemotherapy.

We study the formation of singularities for the problem {u(t) = [phi(u)](xx) + epsilon[psi(u)](txx) in Omega x (0, T) phi(u) + epsilon[psi(u)](t) = 0 in partial derivative Omega x(0, T) u = u(0) >= 0 in Omega x {0}, where epsilon and Tare positive constants, Omega a bounded interval, u(0) a nonnegative Radon measure on Omega, phi a nonmonotone and nonnegative function with phi(0) = phi(infinity) = 0, and psi an increasing bounded function. We show that if u(0) is a bounded or continuous function, singularities may appear spontaneously. The class of singularities which can arise in finite time is remarkably large, and includes infinitely many Dirac masses and singular continuous measures.

We consider a mathematical model describing population dynamics of normal and abnormal cell densities with contact inhibition of cell growth from a theoretical point of view. In the first part of this paper, we discuss the global existence of a solution satisfying the segregation property in one space dimension for general initial data. Here, the term segregation property means that the different types of cells keep spatially segregated when the initial densities are segregated. The second part is devoted to singular limit problems for solutions of the PDE system and traveling wave solutions, respectively. Actually, the contact inhibition model considered in this paper possesses quite similar properties to those of the Fisher-KPP equation. In particular, the limit problems reveal a relation between the contact inhibition model and the Fisher-KPP equation.

We prove existence and uniqueness for a class of signed Radon measure-valued entropy solutions of the Cauchy problem for a first order scalar hyperbolic conservation law in one space dimension. The initial data of the problem is a finite superposition of Dirac masses, whereas the flux is Lipschitz continuous and bounded. The solution class is determined by an additional condition which is needed to prove uniqueness.

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'.