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Delayed‐release and extended‐release methylphenidate hydrochloride (JORNAY PM®) is a novel capsule formulation of methylphenidate hydrochloride, used to treat attention deficit hyperactivity disorder in patients 6 years and older. In this paper, we develop a Level A in vitro‐in vivo correlation (IVIVC) model for extended‐release methylphenidate hydrochloride to support post‐approval manufacturing changes by evaluating a point‐to‐point correlation between the fraction of drug dissolved in vitro and the fraction of drug absorbed in vivo. Dissolution data from an in vitro study of three different release formulations: fast, medium, and slow, and pharmacokinetic data from two in vivo studies were used to develop an IVIVC model using a convolution‐based approach. The time‐course of the drug concentration resulting from an arbitrary dose was considered as a function of the in vivo drug absorption and the disposition and elimination processes defined by the unit impulse response function using the convolution integral. An IVIVC was incorporated in the model due to the temporal difference seen in the scatterplots of the estimated fraction of drug absorbed in vivo and the fraction of drug dissolved in vitro and Levy plots. Finally, the IVIVC model was subjected to evaluation of internal predictability. This IVIVC model can be used to predict in vivo profiles for different in vitro profiles of extended‐release methylphenidate hydrochloride.

It is a common experience that rainfall is intermittent in space and time. This is reflected by the fact that the statistics of area‐ and/or time‐averaged rain rate is described by a mixed distribution with a nonzero probability of having a sharp value zero. In this paper we have explored the dependence of the probability of zero rain on the averaging space and time scales in large multiyear data sets based on radar and rain gauge observations. A stretched exponential formula fits the observed scale dependence of the zero‐rain probability. The proposed formula makes it apparent that the space‐time support of the rain field is not quite a set of measure zero as is sometimes supposed. We also give an explanation of the observed behavior in terms of a simple probabilistic model based on the premise that rainfall process has an intrinsic memory. Key Points We present a simple empirical formula for the zero‐rain probability The formula captures the space‐time scale dependence of the zeroes of rain rate We also give an explanation of the formula from a simple probabilistic model

A correlation spectrum‐based approach is used to express the theoretical predictability limits of multifractal processes as an analytical function of their anisotropy parameters. This spatially anisotropic power law function is then used to investigate the general impact of anisotropy on the predictability of atmospheric fields in the weather regime. The investigation reveals that (i) vertical stratification of a field increases and decreases its super and subsphero‐scale predictability limits, respectively; (ii) trivial horizontal anisotropy slightly improves predictability at all scales; and (iii) horizontal anisotropy together with vertical stratification significantly enhances its predictability over almost the entire scale range. Applying these general results to the case of horizontal wind fields suggests that the interplay between spatial‐anisotropy and atmospheric predictability could account for improvements in forecast skill, commonly observed during the occurrence of rotating thunderstorms and breaks in the Indian summer monsoon. Plain Language Summary Quantifying theoretical atmospheric predictability limits is necessary to understand the possibility of making reliable weather predictions. Since atmospheric fields are multifractal and frequently anisotropic with roundish structures near the sphero‐scale, this study expresses the predictability limits via their multifractal and anisotropy parameters for theoretically investigating how spatial anisotropy of a filed impacts its predictability. The investigation shows that horizontal anisotropy moderately increases predictability at all scales, whereas vertical stratification diminishes predictability at scales roughly smaller than the sphero‐scale while enhancing it at larger scales; horizontal anisotropy with vertical stratification, on the other hand, further improves predictability. The spatial anisotropy of horizontal winds seems to be responsible for the extended predictability of organized thunderstorms and monsoon breaks. Key Points The theoretical predictability limits of atmospheric fields follow spatially anisotropic scaling laws Vertical stratification of these fields increases their supersphero‐scale predictability, while trivial horizontal anisotropy slightly improves predictability at all scales Spatial anisotropy of horizontal wind fields seems to play a crucial role in the extended predictability of supercell thunderstorms and monsoon breaks

This study analyses power spectral density (PSD) of a pulse train where the pulses take from a prototype pulse but randomly take an independently and identically distributed time scaling and an independent stationary amplitude. A closed-form expression of PSD is obtained, which is an implicit function of the Fourier transform of the prototype pulse without time scaling, the probability distribution of time scaling, and the first and the second moment means of amplitude. In the special case when the time scaling and amplitude are fixed with probability one, the PSD is degenerated to the well-known PSD of a periodic signal. Results of numerical evaluation and simulation for pulse trains with three rates as well as with Gaussian rates demonstrate that the analytical formula well predicts the data PSD.

We develop a finite- N matched-asymptotic theory for Smoluchowski coagulation. Starting from the infinite system of ODEs, we use conservation laws to obtain closed scalar evolution equations for suitable moments. For the constant kernel a j , k = K , this leads to an exact early-time decay law for the cluster number and the linear coalescence-time scaling T N ≍ N when the volume scales as V ∼ N . For the sum kernel a j , k = j + k , the same reduction yields an exponential decay regime for the number of clusters and a logarithmic finite- N coalescence time. For the multiplicative kernel a j , k = j k , we recover the classical finite-time blowup of the second moment and show that finite N produces a sharp gelation cutoff preceding the mean-field gelation time by a window of order N − 2 . In all kernels considered, the late-time dynamics involve only finitely many clusters and contribute only lower-order corrections. The resulting structure closely parallels that of finite- N two-species annihilation: a conserved quantity reduces the dynamics to a scalar ODE, asymptotic matching at a characteristic time yields the finite-size scaling laws, and post-matching effects do not alter the leading behaviour.

BackgroundExtrapolation of human absorbed doses (ADs) from biodistribution experiments on laboratory animals is used to predict the efficacy and toxicity profiles of new radiopharmaceuticals. Comparative studies between available animal-to-human dosimetry extrapolation methods are missing. We compared five computational methods for mice-to-human AD extrapolations, using two different radiopharmaceuticals, namely [111In]CHX-DTPA-scFv78-Fc and [68Ga]NODAGA-RGDyK. Human organ-specific time-integrated activity coefficients (TIACs) were derived from biodistribution studies previously conducted in our centre. The five computational methods adopted are based on simple direct application of mice TIACs to human organs (M1), relative mass scaling (M2), metabolic time scaling (M3), combined mass and time scaling (M4), and organ-specific allometric scaling (M5), respectively. For [68Ga]NODAGA-RGDyK, these methods for mice-to-human extrapolations were tested against the ADs obtained on patients, previously published by our group. Lastly, an average [68Ga]NODAGA-RGDyK-specific allometric parameter αnew was calculated from the organ-specific biological half-lives in mouse and humans and retrospectively applied to M3 and M4 to assess differences in human AD predictions with the α = 0.25 recommended by previous studies.ResultsFor both radiopharmaceuticals, the five extrapolation methods showed significantly different AD results (p < 0.0001). In general, organ ADs obtained with M3 were higher than those obtained with the other methods. For [68Ga]NODAGA-RGDyK, no significant differences were found between ADs calculated with M3 and those obtained directly on human subjects (H) (p = 0.99; average M3/H AD ratio = 1.03). All other methods for dose extrapolations resulted in ADs significantly different from those calculated directly on humans (all p ≤ 0.0001). Organ-specific allometric parameters calculated using combined experimental [68Ga]NODAGA-RGDyK mice and human biodistribution data varied significantly. ADs calculated with M3 and M4 after the application of αnew = 0.17 were significantly different from those obtained by the application of α = 0.25 (both p < 0.001).ConclusionsAvailable methods for mouse-to-human dosimetry extrapolations provided significantly different results in two different experimental models. For [68Ga]NODAGA-RGDyK, the best approximation of human dosimetry was shown by M3, applying a metabolic scaling to the mouse organ TIACs. The accuracy of more refined extrapolation algorithms adopting model-specific metabolic scaling parameters should be further investigated.

In a Hilbert setting we aim to study a second order in time differential equation, combining viscous and Hessian-driven damping, containing a time scaling parameter function and a Tikhonov regularization term. The dynamical system is related to the problem of minimization of a nonsmooth convex function. In the formulation of the problem as well as in our analysis we use the Moreau envelope of the objective function and its gradient and heavily rely on their properties. We show that there is a setting where the newly introduced system preserves and even improves the well-known fast convergence properties of the function and Moreau envelope along the trajectories and also of the gradient of Moreau envelope due to the presence of time scaling. Moreover, in a different setting we prove strong convergence of the trajectories to the element of minimal norm from the set of all minimizers of the objective. The manuscript concludes with various numerical results.

Single point incremental forming (SPIF) is one of the most promising technologies for the manufacturing of sheet metal prototypes and parts in small quantities. Similar to other forming processes, the design of the SPIF process is a demanding task. Nowadays, the design process is usually performed using numerical simulations and virtual models. The modelling of the SPIF process faces several challenges, including extremely long computational times caused by long tool paths and the complexity of the problem. Path determination is also a demanding task. This paper presents a finite element (FE) analysis of an incrementally formed truncated pyramid compared to experimental validation. Focus was placed on a possible simplification of the FE process modelling and its impact on the reliability of the results obtained, especially on the geometric accuracy of the part and bottom pillowing effect. The FE modelling of SPIF process was performed with the software ABAQUS, while the experiment was performed on a conventional milling machine. Low-carbon steel DC04 was used. The results confirm that by implementing mass scaling and/or time scaling, the required calculation time can be significantly reduced without substantially affecting the pillowing accuracy. An innovative artificial neural network (ANN) approach was selected to find the optimal values of mesh size and mass scaling in term of minimal bottom pillowing error. However, care should be taken when increasing the element size, as it has a significant impact on the pillow effect at the bottom of the formed part. In the range of selected mass scaling and element size, the smallest geometrical error regarding the experimental part was obtained by mass scaling of 19.01 and tool velocity of 16.49 m/s at the mesh size of 1 × 1 mm. The obtained results enable significant reduction of the computational time and can be applied in the future for other incrementally formed shapes as well.

Rainfall, or more generally the precipitation process (flux), is a clear example of chaotic variables resulting from a highly nonlinear dynamical system, the atmosphere, which is represented by a set of physical equations such as the Navier–Stokes equations, energy balances, and the hydrological cycle, among others. As a generalization of the Euclidean (ordinary) measurements, chaotic solutions of these equations are characterized by fractal indices, that is, non-integer values that represent the complexity of variables like the rainfall. However, observed precipitation is measured as an aggregate variable over time; thus, a physical analysis of observed fluxes is very limited. Consequently, this review aims to go through the different approaches used to identify and analyze the complexity of observed precipitation, taking advantage of its geometry footprint. To address the review, it ranges from classical perspectives of fractal-based techniques to new perspectives at temporal and spatial scales as well as for the classification of climatic features, including the monofractal dimension, multifractal approaches, Hurst exponent, Shannon entropy, and time-scaling in intensity–duration–frequency curves.

For single-input affine control systems, we address the problem of -orbital feedback linearization around singular points of the derived flag of the distribution associated with the control system. By a singular point of a derived flag we mean a point such that at least one of the elements of the derived flag in any neighborhood of this point is not a distribution of constant rank. We prove a local necessary and sufficient condition for A-orbital feedback equivalence of a single-input affine control system to a linear controllable system considered in a neighbourhood of the zero equilibrium point.