Taking wedge products of the p distinct principal null directions (PNDs) associated with the eigen-bivectors of the Weyl tensor associated with the Petrov classification, when linearly independent, one is able to express them in terms of the eigenvalues governing this decomposition. We study here algebraic and differential properties of such p-forms by completing previous geometrical results concerning type I spacetimes and extending that analysis to algebraically special spacetimes with at least two distinct PNDs. A number of vacuum and nonvacuum spacetimes are examined to illustrate the general treatment.

Regular physical exercise and appropriate nutrition affect metabolic and hormonal responses and may reduce the risk of developing chronic non-communicable diseases such as high blood pressure, ischemic stroke, coronary heart disease, some types of cancer, and type 2 diabetes mellitus. Computational models describing the metabolic and hormonal changes due to the synergistic action of exercise and meal intake are, to date, scarce and mostly focussed on glucose absorption, ignoring the contribution of the other macronutrients. We here describe a model of nutrient intake, stomach emptying, and absorption of macronutrients in the gastrointestinal tract during and after the ingestion of a mixed meal, including the contribution of proteins and fats. We integrated this effort to our previous work in which we modeled the effects of a bout of physical exercise on metabolic homeostasis. We validated the computational model with reliable data from the literature. The simulations are overall physiologically consistent and helpful in describing the metabolic changes due to everyday life stimuli such as multiple mixed meals and variable periods of physical exercise over prolonged periods of time. This computational model may be used to design virtual cohorts of subjects differing in sex, age, height, weight, and fitness status, for specialized in silico challenge studies aimed at designing exercise and nutrition schemes to support health.

We consider the problem of interpolating a given function on arbitrary configurations of nodes in a compact interval, with a special focus on the case of equidistant or quasi-equidistant nodes. In this case, instead of polynomial interpolation, a family of rational interpolants introduced by Floater and Hormann in [2] turns out to be very useful . Such interpolants (briefly FH interpolants) generalize Berrut's rational interpolation [1] introducing a fixed integer parameter d >= 1 to speed up the convergence getting, in theory, arbitrarily high approximation orders. In this talk we will further generalize by presenting a whole new family of rational interpolants that depend on an additional parameter ? ? N. When ? = 1 we get the original FH interpolants. For ? > 1 we will see that the new interpolants share a lot of the interesting properties of the original FH interpolants (no real poles, baryentric-type representation, high rates of approximation). But, in addition, we get uniformly bounded Lebesgue constants and a more localized approximation of less smooth functions, compared to the original FH interpolation.

As known, polynomial interpolation is not advisable in the case of equidistant nodes, given the exponential growth of the Lebesgue constants and the consequent stability problems. In [1] Floater and Hormann introduce a family of rational interpolants (briefly FH interpolants) depending on a fixed integer parameter d >= 1. They are based on any configuration of the nodes in [a, b], have no real poles and approximation order O(h^{d+1}) for functions in C^{d+2}[a, b], where h denotes the maximum distance between two consecutive nodes. FH interpolants turn out to be very useful for equidistant or quasi-equidistant configurations of nodes when the Lebesgue constants present only a logarithmic growth as the number of nodes increases [2, 3]. In this talk, we introduce a generalization of FH interpolants depending on an additional parameter ? ? N. If ? = 1 we get the classical FH interpolants, but taking ? > 1 we succeed in getting uniformly bounded Lebesgue constants for quasi-equidistant configurations of nodes. Moreover, in comparison with the original FH interpolants, we show that the new interpolants present a much better error prole when the function is less smooth.

Homophily is the principle whereby "similarity breeds connections."We give a quantitative formulation of this principle within networks. Given a network and a labeled partition of its vertices, the vector indexed by each class of the partition, whose entries are the number of edges of the subgraphs induced by the corresponding classes, is viewed as the observed outcome of the random vector described by picking labeled partitions at random among labeled partitions whose classes have the same cardinalities as the given one. This is the recently introduced random coloring model for network homophily. In this perspective, the value of any homophily score ?, namely, a nondecreasing real-valued function in the sizes of subgraphs induced by the classes of the partition, evaluated at the observed outcome, can be thought of as the observed value of a random variable. Consequently, according to the score ?, the input network is homophillic at the significance level ? whenever the one-sided tail probability of observing a value of ? at least as extreme as the observed one is smaller than ?. Since, as we show, even approximating ? is an NP-hard problem, we resort to classical tails inequality to bound ? from above. These upper bounds, obtained by specializing ?, yield a class of quantifiers of network homophily. Computing the upper bounds requires the knowledge of the covariance matrix of the random vector, which was not previously known within the random coloring model. In this paper we close this gap. Interestingly, the matrix depends on the input partition only through the cardinalities of its classes and depends on the network only through its degrees. Furthermore all the covariances have the same sign, and this sign is a graph invariant. Plugging this structure into the bounds yields a meaningful, easy to compute class of indices for measuring network homophily. As demonstrated in real-world network applications, these indices are effective and reliable, and may lead to discoveries that cannot be captured by the current state of the art.

Path graphs are intersection graphs of paths in a tree. We start from the characterization of path graphs by Monma and Wei (1986) [14] and we reduce it to some 2-coloring subproblems, obtaining the first characterization that directly leads to a polynomial recognition algorithm. Then we introduce the collection of the attachedness graphs of a graph and we exhibit a list of minimal forbidden 2-edge colored subgraphs in each of the attachedness graph.

We study the asymptotic behavior, as the lattice spacing ? tends to zero, of the discrete elastic energy induced by topological singularities in an inhomogeneous ? periodic medium within a two-dimensional model for screw dislocations in the square lattice. We focus on the |log?| regime which, as ?->0 allows the emergence of a finite number of limiting topological singularities. We prove that the ?-limit of the |log?| scaled functionals as ?->0 is equal to the total variation of the so-called "limiting vorticity measure" times a factor depending on the homogenized energy density of the unscaled functionals.

This paper deals with the limit cases for s-fractional heat flows in a cylindrical domain, with homogeneous Dirichlet boundary conditions, as s-> 0+ and s-> 1-. We describe the fractional heat flows as minimizing move-ments of the corresponding Gagliardo seminorms, with re-spect to the L2 metric. To this end, we first provide a Gamma-convergence analysis for the s-Gagliardo seminorms as s-+ 0+ and s-+ 1-; then, we exploit an abstract stability result for minimizing movements in Hilbert spaces, with respect to a sequence of Gamma-converging uniformly lambda-convex energy function-als. We prove that s-fractional heat flows (suitably scaled in time) converge to the standard heat flow as s-+ 1-, and to a de-generate ODE type flow as s-+ 0+. Moreover, looking at the next order term in the asymptotic expansion of the s -fractional Gagliardo seminorm, we show that suitably forced s-fractional heat flows converge, as s-+ 0+, to the parabolic flow of an energy functional that can be seen as a sort of renormalized 0-Gagliardo seminorm: the resulting parabolic equation involves the first variation of such an energy, that can be understood as a zero (or logarithmic) Laplacian.(c) 2023 Elsevier Inc. All rights reserved.

We present and release in open source format a sparse linear solver which efficiently exploits heterogeneous parallel computers. The solver can be easily integrated into scientific applications that need to solve large and sparse linear systems on modern parallel computers made of hybrid nodes hosting Nvidia Graphics Processing Unit (GPU) accelerators. The work extends previous efforts of some of the authors in the exploitation of a single GPU accelerator and proposes an implementation, based on the hybrid MPI-CUDA software environment, of a Krylov-type linear solver relying on an efficient Algebraic MultiGrid (AMG) preconditioner already available in the BootCMatchG library. Our design for the hybrid implementation has been driven by the best practices for minimizing data communication overhead when multiple GPUs are employed, yet preserving the efficiency of the GPU kernels. Strong and weak scalability results of the new version of the library on well-known benchmark test cases are discussed. Comparisons with the Nvidia AmgX solution show a speedup, in the solve phase, up to 2.0x.

In this paper, a complete picture of the different plastic failure modes that can be predicted by the strain gradient plasticity model proposed in Del Piero et al. (J. Mech. Mater. Struct. 8:109-151, 2013) is drawn. The evolution problem of the elasto-plastic strain is formulated in Del Piero et al. (J. Mech. Mater. Struct. 8:109-151, 2013) as an incremental minimization problem acting on an energy functional which includes a local plastic term and a non-local gradient contribution. Here, an approximate analytical solution of the evolution problem is determined in the one-dimensional case of a tensile bar. Different solutions are found describing specific plastic strain processes, and correlations between the different evolution modes and the convexity/concavity properties of the plastic energy density are established. The variety of solutions demonstrates the large versatility of the model in describing many failure mechanisms, ranging from brittle to ductile. Indeed, for a convex plastic energy, the plastic strain diffuses in the body, while, for a concave plastic energy, it localizes in regions whose amplitude depends on the internal length parameter included into the non-local energy term, and, depending on the convexity properties of the first derivative of the plastic energy, the localization band expands or contracts. Complex failure processes combining different modes can be reproduced by assuming plastic energy functionals with specific convex and concave branches. The quasi-brittle failure of geomaterials in simple tension tests was reproduced by assuming a convex-concave plastic energy, and the accuracy of the analytical predictions was checked by comparing them with the numerical results of finite element simulations.

We investigate rare semileptonic B -> K* l(+) l(-) by looking at a specific long distance contribution. Our analysis is limited to the very small values of physical accessible range of invariant mass of the leptonic couple q(2). We show that the light quarks loop has to be accounted for, along with the charming penguin contribution, in order to accurately compute the q(2)-spectrum in the Standard Model. Such a long distance contribution may also play a role in the analysis of the lepton flavor universality violation in this process. (c) 2023 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).

The properties of semiflexible active ring polymers are studied by numerical simulations. The two-dimensionally confined polymer is modeled as a closed bead-spring chain subject to tangential active forces, and the interaction with the fluid is described by the Brownian multiparticle collision dynamics approach. Both phantom polymers and chains with excluded-volume interactions are considered. The size and shape strongly depend on the relative ratio of the persistence length to the ring length as well as on the active force. The long-time dynamics is characterized by a rotational motion whose frequency increases with the active force.

The aim of this work is to propose a fast and reliable algorithm for computingintegrals of the type$$\int_{-\infty}^{\infty} f(x) e^{\scriptstyle -x^2 -\frac{\scriptstyle 1}{\scriptstyle x^2}} dx,$$where $f(x)$ is a sufficiently smooth function, in floating point arithmetic.The algorithm is based on a product integration rule, whose rate of convergencedepends only on the regularity of $f$, since the coefficients of the rule are ``exactly'' computed by means of suitable recurrence relations here derived.We prove stability and convergence in the space of locally continuous functions on $\RR$ equipped with weighted uniform norm.By extensive numerical tests, the accuracy of the proposed product rule is compared with that of the Gauss--Hermite quadrature formula w.r.t. the function $f(x) e^{-\frac{\scriptstyle 1}{\scriptstyle x^2}}$. The numerical results confirm the effectiveness of the method, supporting the proven theoretical estimates.

In this paper, we discuss the convergence of an Algebraic MultiGrid (AMG) method for general symmetric positive-definite matrices. The method relies on an aggregation algorithm, named coarsening based on compatible weighted matching, which exploits the interplay between the principle of compatible relaxation and the maximum product matching in undirected weighted graphs. The results are based on a general convergence analysis theory applied to the class of AMG methods employing unsmoothed aggregation and identifying a quality measure for the coarsening; similar quality measures were originally introduced and applied to other methods as tools to obtain good quality aggregates leading to optimal convergence for M-matrices. The analysis, as well as the coarsening procedure, is purely algebraic and, in our case, allows an a posteriori evaluation of the quality of the aggregation procedure which we apply to analyze the impact of approximate algorithms for matching computation and the definition of graph edge weights. We also explore the connection between the choice of the aggregates and the compatible relaxation convergence, confirming the consistency between theories for designing coarsening procedures in purely algebraic multigrid methods and the effectiveness of the coarsening based on compatible weighted matching. We discuss various completely automatic algorithmic approaches to obtain aggregates for which good convergence properties are achieved on various test cases.

We numerically study the dynamics of quasi-two dimensional cholesteric liquid crystal droplets in the presence of a time-dependent electric field, rotating at constant angular velocity. A surfactant sitting at the droplet interface is also introduced to prevent droplet coalescence. The dynamics is modeled following a hybrid numerical approach, where a standard lattice Boltzmann technique solves the Navier-Stokes equation and a finite difference scheme integrates the evolution equations of liquid crystal and surfactant. Our results show that, once the field is turned on, the liquid crystal rotates coherently triggering a concurrent orbital motion of both droplets around each other, an effect due to the momentum transfer to the surrounding fluid. In addition the topological defects, resulting from the conflict orientation of the liquid crystal within the drops, exhibit a chaotic-like motion in cholesterics with a high pitch, in contrast with a regular one occurring along circular trajectories observed in nematics drops. Such behavior is found to depend on magnitude and frequency of the applied field as well as on the anchoring of the liquid crystal at the droplet interface. These findings are quantitatively evaluated by measuring the angular velocity of fluid and drops for various frequencies of the applied field.

The simulations for the inverse problem of radiative transfer, even if built with a correct Bayesian approach, do not represent the full source of errors present in the experimental data. We point out two categories of errors (atmospheric model errors and non-Gaussian instrumental errors due to the optics and hardware, that are not considered by standard methods. Moreover, we show cases taken from FORUM simulated radiances using an End to End simulator, where se show how the instrument reacts to a non homogeneousneous filed of view.

The non-equilibrium structural and dynamical properties of a flexible polymer pinned to a reflecting wall and subject to oscillatory linear flow are studied by numerical simulations. Polymer is confined in two dimensions and is modeled as a bead-spring chain while the interaction with the fluid is described by the Brownian multiparticle collision dynamics. At low strain the polymer is stretched along the flow direction. When increasing strain, chains are completely elongated and compressed against the wall when the flow is reverted. The conformations are analyzed and compared to the case of stiffer polymers [1]. The dynamics is investigated by looking at the motion of the center of mass which shows a frequency doubling along the shear direction. [1] A. Lamura, R. G. Winkler, and G. Gompper, Wall-Anchored Semiflexible Polymer under Large Amplitude Oscillatory Shear, J. Chem. Phys. 154, 224901 (2021).

After giving some background on neuron physiology, the classical (deterministic) models for the generation of action potentials are briefly introduced and their limitations discussed, so to motivate the need for a stochastic description of the neuronal firing activity. The more relevant stochastic models for single neuron dynamics are reviewed, with particular attention to the phenomenon of spike-frequency adaptation. Then some approaches to the modeling of network dynamics, where populations of excitatory and inhibitory neurons interact, are described. Finally,some recent models applying suitable strategies to reproduce complex neural dynamics emerging from networks of spiking neurons, such as fractional differentiation or other memory effects, are introduced as a perspective for current and future research.

Insieme al teorema dimostrato da Bernoulli nel 1713 e noto oggi come legge dei grandi numeri, il teorema del limite centrale è alla base della statistica inferenziale, che si propone di ricavare informazioni e di trarre conclusioni su una popolazione a partire dall'osservazione di un campione casuale dei suoi elementi.In sintesi, il teorema dice che in ogni situazione in cui i dati da noi osservati sono influenzati da tanti piccoli effetti casuali indipendenti tra loro, la distribuzione risultante sarà approssimativamente una curva gaussiana, detta anche normale. Ciò permette di determinare un valore attendibile per un parametro di interesse, come il valore atteso, con il relativo intervallo di fiducia per la nostra stima; o di valutare la credibilità di un'ipotesi di carattere generale dopo una serie di osservazioni.Le sue applicazione spaziano nei campi più diversi. Per esempio, l'altezza delle donne italiane, la luminosità delle stelle, i valori di colesterolo della popolazione di maschi adulti, le fluttuazioni giornaliere di un indice del mercato azionario, i punteggi registrati in un test preselettivo, fino all'attendibilità dei sondaggi e all'efficacia dei vaccini sulla popolazione.

Mortality shocks, such as pandemics, threaten the consolidated longevity improvements, confirmed in the last decades for the majority of western countries. Indeed, just before the COVID-19 pandemic, mortality was falling for all ages, with a different behavior according to different ages and countries. It is indubitable that the changes in the population longevity induced by shock events, even transitory ones, affecting demographic projections, have financial implications in public spending as well as in pension plans and life insurance. The Short Term Mortality Fluctuations (STMF) data series, providing data of all-cause mortality fluctuations by week within each calendar year for 38 countries worldwide, offers a powerful tool to timely analyze the effects of the mortality shock caused by the COVID-19 pandemic on Italian mortality rates. This dataset, recently made available as a new component of the Human Mortality Database, is described and techniques for the integration of its data with the historical mortality time series are proposed. Then, to forecast mortality rates, the well-known stochastic mortality model proposed by Lee and Carter in 1992 is first considered, to be consistent with the internal processing of the Human Mortality Database, where exposures are estimated by the Lee-Carter model; empirical results are discussed both on the estimation of the model coefficients and on the forecast of the mortality rates. In detail, we show how the integration of the yearly aggregated STMF data in the HMD database allows the Lee-Carter model to capture the complex evolution of the Italian mortality rates, including the higher lethality for males and older people, in the years that follow a large shock event such as the COVID-19 pandemic. Finally, we discuss some key points concerning the improvement of existing models to take into account mortality shocks and evaluate their impact on future mortality dynamics.