In the description of the relativistic two-body interaction, together with the effects of energy andangular momentum losses due to the emission of gravitational radiation, one has to take into account alsothe loss of linear momentum, which is responsible for the recoil of the center-of-mass of the system. Wecompute higher-order tail (i.e., tail-of-tail and tail-squared) contributions to the linear momentum fluxfor a nonspinning binary system either along hyperboliclike or ellipticlike orbits. The correspondingorbital averages are evaluated at their leading post-Newtonian approximation, using harmoniccoordinates and working in the Fourier domain. The final expressions are given in a large-eccentricity(or large-angular momentum) expansion along hyperboliclike orbits and in a small-eccentricityexpansion along ellipticlike orbits. We thus complete a previous analysis focusing on both energyand angular momentum losses [Phys. Rev. D 104, 104020 (2021)], providing brick-type results whichwill be useful, e.g., in the high-accurate determination of the radiated impulses of the two bodiesundergoing a scattering process.

Gravitational radiation can be decomposed as an infinite sum of radiative multipole moments, which parametrize the waveform at infinity. The multipolar-post-Minkowskian formalism provides a connection between these multipoles and the source multipole moments, known as explicit integrals over the matter source. The gravitational wave energy, angular momentum, and linear momentum fluxes are then expressed as multipolar expansions containing certain combinations of the source moments. We compute several gauge-invariant quantities as "building blocks"entering the multipolar expansion of both radiated energy and angular momentum at the 2.5 post-Newtonian (PN) level of accuracy in the case of hyperboliclike motion, by completing previous studies through the calculation of tail effects up to the fractional 1PN order. We express such multipolar invariants in terms of certain eccentricity enhancement factor functions, which are the counterpart of the well-known enhancement functions already introduced in the literature for ellipticlike motion. Finally, we use the complete 2.5PN-accurate averaged energy and angular momentum fluxes to study the associated adiabatic evolution of orbital elements under gravitational radiation reaction.

We briefly review the known properties of Melvin's magnetic universe and study the propagation of test charged matter waves in this static spacetime. Moreover, the possible correspondence between the wave perturbations on the background Melvin universe and the motion of charged test particles is discussed. Next, we explore a simple scenario for turning Melvin's static universe into one that undergoes gravitational collapse. In the resulting dynamic gravitational field, the formation of cosmic double-jet configurations is emphasized.

We compute the metric fluctuations induced by a turbulent energy-matter tensor within the first orderpost-Minkowskian approximation. It is found that the turbulent energy cascade can in principle interferewith the process of black hole formation, leading to a potentially strong coupling between these two highlynonlinear phenomena. It is further found that a power-law turbulent energy spectrum EðkÞ ~ k-n generatesmetric fluctuations scaling as xn-2, where x is the four-dimensional spacelike distance from an arbitraryorigin in Minkowski spacetime, highlighting the onset of metric singularities whenever n < 2. Finally, theeffect of metric fluctuations on the geodesic motion of test particles is also discussed as a potentialtechnique to extract information on the spectral characteristics of fluctuating spacetime.

In this paper, we consider the problem of estimating the graphs of conditional dependencies between variables (i.e., graphical models) from multiple datasets under Gaussian settings. We present jewel 2.0, which improves our previous method jewel 1.0 by modeling commonality and class-specific differences in the graph structures and better estimating graphs with hubs, making this new approach more appealing for biological data applications. We introduce these two improvements by modifying the regression-based problem formulation and the corresponding minimization algorithm. We also present, for the first time in the multiple graphs setting, a stability selection procedure to reduce the number of false positives in the estimated graphs. Finally, we illustrate the performance of jewel 2.0 through simulated and real data examples. The method is implemented in the new version of the R package jewel

Mathematical models have the potential to contribute to design and evaluate the infectivity spreading and growth of human immunodeficiency virus (HIV). Providing a better understanding of the dynamics of HIV infection in vivo and the immune system interactions with the virus can improve the classification of the infected cells and drive to an early diagnosis of the disease and drug evaluations. We analyze a two-dimensional environment HIV model from a new perspective, in terms of a multi-objective optimization problem, by introducing a linear modeling approach and providing numerical evidence for its suitability by introducing a general Instantaneous Control Algorithm.

In this paper we propose a modeling setting and a numerical Riemann problem solver at the junction of one dimensional shallow-water channel networks. The junction conditions take into account the angles with which the channels intersect and include the possibility of channels with different sections. The solver is illustrated with several numerical tests which underline the importance of the angle dependence to obtain reliable solutions.

The societal impact of traffic is a long-standing and complex problem. We focus on the estimation of ground-level ozone production due to vehicular traffic. We propose a comprehensive computational approach combining four consecutive modules: a traffic simulation module, an emission module, a module for the main chemical reactions leading to ozone production, and a module for the diffusion of gases in the atmosphere. The traffic module is based on a second-order traffic flow model, obtained by choosing a special velocity function for the Collapsed Generalized Aw-Rascle-Zhang model. A general emission module is taken from literature, and tuned on NGSIM data together with the traffic module. Last two modules are based on reaction-diffusion partial differential equations. The system of partial differential equations describing the main chemical reactions of nitrogen oxides presents a source term given by the general emission module applied to the output of the traffic module. We use the proposed approach to analyze the ozone impact of various traffic scenarios and describe the effect of traffic light timing. The numerical tests show the negative effect of vehicles restarts on emissions, and the consequent increase in pollutants in the air, suggesting to increase the length of the green phase of traffic lights.

Nonparametric univariate regression via wavelets is usually implemented under the assumptions of dyadic sample size, equally spaced fixed sample points, and i.i.d. normal errors. In this work, we propose, study and compare some wavelet based nonparametric estimation methods designed to recover a one-dimensional regression function for data that not necessary possess the above requirements. These methods use appropriate regularizations by penalizing the decomposition of the unknown regression function on a wavelet basis of functions evaluated on the sampling design. Exploiting the sparsity of wavelet decompositions for signals belonging to homogeneous Besov spaces, we use some efficient proximal gradient descent algorithms, available in recent literature, for computing the estimates with fast computation times. Our wavelet based procedures, in both the standard and the robust regression case have favorable theoretical properties, thanks in large part to the separability nature of the (non convex) regularization they are based on. We establish asymptotic global optimal rates of convergence under weak conditions. It is known that such rates are, in general, unattainable by smoothing splines or other linear nonparametric smoothers. Lastly, we present several experiments to examine the empirical performance of our procedures and their comparisons with other proposals available in the literature. An interesting regression analysis of some real data applications using these procedures unambiguously demonstrate their effectiveness.

The boreal hemisphere has been experiencing increasing extreme hot and dry conditions over the past few decades, consistent with anthropogenic climate change. The continental extension of this phenomenon calls for tools and techniques capable of monitoring the global to regional scales. In this context, satellite data can satisfy the need for global coverage. The main objective we have addressed in the present paper is the capability of infrared satellite observations to monitor the vegetation stress due to increasing drought and heatwaves in summer. We have designed and implemented a new water deficit index (wdi) that exploits satellite observations in the infrared to retrieve humidity, air temperature, and surface temperature simultaneously. These three parameters are combined to provide the water deficit index. The index has been developed based on the Infrared Atmospheric Sounder Interferometer or IASI, which covers the infrared spectral range 645 to 2760 cm with a sampling of 0.25 cm. The index has been used to study the 2017 heatwave, which hit continental Europe from May to October. In particular, we have examined southern Italy, where Mediterranean forests suffer from climate change. We have computed the index's time series and show that it can be used to indicate the atmospheric background conditions associated with meteorological drought. We have also found a good agreement with soil moisture, which suggests that the persistence of an anomalously high water deficit index was an essential driver of the rapid development and evolution of the exceptionally severe 2017 droughts.

The paper uses Level 2 IASI (Infrared Atmospheric Sounder Interferometer) products to analyse long-standing heatwaves and related droughts. The paper is mostly interested in studying and assessing the effect of drought on vegetation. To this end, we have devised a series of indices sensitive to the water deficit. IASI retrievals are used to derive indices from the surface temperature, emissivity, and temperature/humidity atmospheric profiles. We define the emissivity contrast index, which is sensitive to the land cover and type, and the water deficit index, which combines the surface and air dew point temperatures. These two indices are assessed by considering the heatwave, which hit most of Europe and the Mediterranean basin in 2017. The application of the methodology will be shown by considering a target area in Southern Italy, where woodlands are suffering from climate change. It will be shown that the two indices are sensitive to the water deficit caused by long-lasting droughts.

In this paper we propose a multiscale traffic model, based on the family of Generic Second Order Models, which integrates multiple trajectory data into the velocity function. This combination of a second order macro- scopic model with microscopic information allows us to reproduce significant variations in speed and acceleration that strongly influence traffic emissions. We obtain accurate approximations even with a few trajectory data. The pro- posed approach is therefore a computationally efficient and highly accurate tool for calculating macroscopic traffic quantities and estimating emissions.

BACKGROUND: Network science represents a powerful and increasingly promising method for studying complex real-world problems. In the last decade, it has been applied to psychometric data in the attempt to explain psychopathologies as complex systems of causally interconnected symptoms. One category of mental disorders, relevant for their severity, incidence and multifaceted structure, is that of eating disorders (EDs), serious disturbances that negatively affect a person's eating behavior. AIMS: We aimed to review the corpus of psychometric network analysis methods by scrutinizing a large sample of network-based studies that exploit psychometric data related to EDs. A particular focus is given to the description of the methodologies for network estimation, network description and network stability analysis providing also a review of the statistical software packages currently used to carry out each phase of the network estimation and analysis workflow. Moreover, we try to highlight aspects with potential clinical impact such as core symptoms, influences of external factors, comorbidities, and related changes in network structure and connectivity across both time and subpopulations. METHODS: A systematic search was conducted (February 2022) on three different literature databases to identify 57 relevant research articles. The exclusion criteria comprehended studies not based on psychometric data, studies not using network analysis, studies with different aims or not focused on ED, and review articles. RESULTS: Almost all the selected 57 papers employed the same analytical procedures implemented in a collection of R packages specifically designed for psychometric network analysis and are mostly based on cross-sectional data retrieved from structured psychometric questionnaires, with just few exemptions of panel data. Most of them used the same techniques for all phases of their analysis. In particular, a pervasive use of the Gaussian Graphical Model with LASSO regularization was registered for in network estimation step. Among the clinically relevant results, we can include the fact that all papers found strong symptom interconnections between specific and nonspecific ED symptoms, suggesting that both types should therefore be addressed by clinical treatment. CONCLUSIONS: We here presented the largest and most comprehensive review to date about psychometric network analysis methods. Although these methods still need solid validation in the clinical setting, they have already been able to show many strengths and important results, as well as great potentials and perspectives, which have been analyzed here to provide suggestions on their use and their possible improvement.

A product quadrature rule, based on the filtered de la Vallée Poussin polynomial approximation, is proposed for evaluating the finite weighted Hilbert transform in [-1,1]. Convergence results are stated in weighted uniform norm for functions belonging to suitable Besov type subspaces. Several numerical tests are provided, also comparing the rule with other formulas known in literature.

Image resizing is a basic tool in image processing, and in literature, we have many methods based on different approaches, which are often specialized in only upscaling or downscaling. In this paper, independently of the (reduced or enlarged) size we aim to get, we approach the problem at a continuous scale where the underlying function representing the image is globally approximated by its Lagrange-Chebyshev I kind interpolation polynomial corresponding to suitable (tensor product) grids of first kind Chebyshev zeros. This is a well-known approximation tool widely used in many applicative fields due to the optimal behavior of the related Lebesgue constants. Here we aim to show how Lagrange-Chebyshev interpolation can be fruitfully applied also for resizing any digital image in both downscaling and upscaling at any desired size. The performance of the proposed method has been tested in terms of the standard SSIM (Structured Similarity Index Measurement) and PSNR (Peak Signal to Noise Ratio) metrics. The results indicate that, in upscaling, it is almost comparable with the classical Bicubic resizing method with slightly better metrics, but in downscaling a much higher performance has been observed in comparison with Bicubic and other recent methods too. Moreover, for all downscaling cases with an odd scale factor, we give a theoretical estimate of the MSE (Mean Squared Error) of the output image produced by our method, stating that it is certainly null (hence PSNR equals infinite and SSIM equals one) if the input image's MSE is null.

Endothelial cell (EC) migration is crucial for a wide range of processes including vascular wound healing, tumor angiogenesis, and the development of viable endovascular implants. We have previously demonstrated that ECs cultured on 15-?m wide adhesive line patterns exhibit three distinct migration phenotypes: (a) "running" cells that are polarized and migrate continuously and persistently on the adhesive lines with possible spontaneous directional changes, (b) "undecided" cells that are highly elongated and exhibit periodic changes in the direction of their polarization while maintaining minimal net migration, and (c) "tumbling-like" cells that migrate persistently for a certain amount of time but then stop and round up for a few hours before spreading again and resuming migration. Importantly, the three migration patterns are associated with distinct profles of cell length. Because of the impact of adenosine triphosphate (ATP) on cytoskeletal organization and cell polarization, we hypothesize that the observed diferences in EC length among the three diferent migration phenotypes are driven by diferences in intracellular ATP levels. In the present work, we develop a mathematical model that incorporates the interactions between cell length, cytoskeletal (F-actin) organization, and intracellular ATP concentration. An optimization procedure is used to obtain the model parameter values that best ft the experimental data on EC lengths. The results indicate that a minimalist model based on diferences in intracellular ATP levels is capable of capturing the diferent cell length profiles observed experimentally.

The rate of drug delivery to cells and the subsequent rate of drug metabolism are dependent on the cell membrane permeability to the drug. In some cases, tissue may be composed of different types of cells that exhibit order of magnitude differences in their membrane permeabilities. This paper presents a brief review of the components of the tissue scale three-compartment pharmacokinetic model of drug delivery to single-cell-type populations. The existing model is extended to consider tissue composed of two different cell types. A case study is presented of infusion mediated delivery of doxorubicin to a tumor that is composed of a drug reactive cell type and of a drug resistive cell type. The membrane permeabilities of the two cell types differ by an order of magnitude. A parametric investigation of the population composition is conducted and it is shown that the drug metabolism of the low permeability cells are negatively influenced by the fraction of the tissue composed of the permeable drug reactive cells. This is because when the population is composed mostly of drug permeable cells, the extracellular space is rapidly depleted of the drug. This has two compounding effects: (i) locally there is simply less drug available to the neighboring drug resistant cells, and (ii) the depletion of the drug from the extracellular space near the vessel-tissue interface leaves less drug to be transported to both cell types farther away from the vessel.

Controlled release of a drug contained in a spherical polymer capsule is of significant interest in many fields of medicine. There is growing interest in tailoring the erosion properties of the drug to help control and optimize the drug release process. Theoretical understanding of the nature of drug release from a bioerodible capsule is, therefore, important for designing effective drug delivery systems. While drug release from a fixed-radius capsule is relatively easier to model, the shrinking nature of a bioerodible capsule due to surface erosion presents several difficulties in theoretical modeling. This work presents a closed-form solution for the drug concentration distribution and drug delivery characteristics from a spherical capsule undergoing linear surface erosion. This problem is solved by a transformation that converts the moving boundary problem into a fixed boundary problem. For uniform initial drug distribution, the solution is shown to depend on a single non-dimensional parameter. The theoretical model is used to develop an understanding of the impact of varying the drug diffusion coefficient and rate of erosion on drug delivery characteristics. It is found that, in general, the nature of drug release in a bioerodible sphere is determined by a delicate balance between two simultaneously occurring processes - erosion and diffusion. This work improves the theoretical understanding of diffusion in drug delivery systems by accounting for the practical erosion phenomena, and may contribute towards the design and optimization of drug delivery systems.

Objective: Customization of the rate of drug delivered based on individual patient requirements is of paramount importance in the design of drug delivery devices. Advances in manufacturing may enable multilayer drug delivery devices with different initial drug distributions in each layer. However, a robust mathematical understanding of how to optimize such capabilities is critically needed. The objective of this work is to determine the initial drug distribution needed in a spherical drug delivery device such as a capsule in order to obtain a desired drug release profile. Methods: This optimization problem is posed as an inverse mass transfer problem, and optimization is carried out using the solution of the forward problem. Both non-erodible and erodible multilayer spheres are analyzed. Cases with polynomial forms of initial drug distribution are also analyzed. Optimization is also carried out for a case where an initial burst in drug release rate is desired, followed by a constant drug release rate. Results: More than 60% reduction in root-mean-square deviation of the actual drug release rate from the ideal constant drug release rate is reported. Typically, the optimized initial drug distribution in these cases prevents or minimizes large drug release rate at early times, leading to a much more uniform drug release overall. Conclusions: Results demonstrate potential for obtaining a desired drug delivery profile over time by carefully engineering the drug distribution in the drug delivery device. These results may help engineer devices that offer customized drug delivery by combining advanced manufacturing with mathematical optimization.

The rate of drug delivery to cells and the subsequent rate of drug metabolism are dependent on the cell membrane permeability to the drug. In some cases, tissue may be composed of different types of cells that exhibit order of magnitude differences in their membrane permeabilities. This paper presents a brief review of the components of the tissue scale three-compartment pharmacokinetic model of drug delivery to single-cell-type populations. The existing model is extended to consider tissue composed of two different cell types. A case study is presented of infusion mediated delivery of doxorubicin to a tumor that is composed of a drug reactive cell type and of a drug resistive cell type. The membrane permeabilities of the two cell types differ by an order of magnitude. A parametric investigation of the population composition is conducted and it is shown that the drug metabolism of the low permeability cells are negatively influenced by the fraction of the tissue composed of the permeable drug reactive cells. This is because when the population is composed mostly of drug permeable cells, the extracellular space is rapidly depleted of the drug. This has two compounding effects: (i) locally there is simply less drug available to the neighboring drug resistant cells, and (ii) the depletion of the drug from the extracellular space near the vessel-tissue interface leaves less drug to be transported to both cell types farther away from the vessel.