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This paper presents a novel methodology utilizing physics-informed neural network (PINN) as a junction condition for a 1D network model of blood flow in total cavopulmonary connection generated by the Fontan procedure. The technique integrates a 3D mesh generation process based on the parameterization of the junction geometry, along with a sophisticated physically regularized neural network architecture. Synthetic datasets are produced using 3D steady Stokes simulations within fixed boundaries. We use a physically informed feedforward neural network that utilizes a physically regularized loss function, which incorporates the principle of mass conservation. Our PINN achieves a tolerance of 6% on the test set. We develop a 1D-PINN multiscale model based on a previously developed method for multiscale 1D–3D simulations. Comparison with 1D–3D Stokes based model and 3D Navier–Stokes based model verifies the 1D-PINN model. In the first and second comparison, the maximum deviations of the averaged pressures and flows do not exceed 1.48% and 12.26%, respectively. [ABSTRACT FROM AUTHOR]

Nitrogen is one of the most abundant chemical elements on the Earth and plays an important role in global environmental change. Leading Earth system models include coupled carbon and nitrogen cycle modules of varying complexity, but the INM RAS climate model family has not yet included an explicit N-cycle description. This paper presents a parameterization of the terrestrial N-cycle based on a simplification of the JULES-CN model, adapted for coupled use with the INM-CM land C-cycle module. Numerical simulations were carried out with a standalone carbon cycle model with nitrogen feedback disabled and enabled versions for the period 1850–2100. The simulated global pools show good agreement with results of other models with an implemented N-cycle. Taking into account the N-limitation of the C-cycle, the modelled dynamics of total carbon storage in terrestrial ecosystems from 1850 to the mid-20th century is specified. [ABSTRACT FROM AUTHOR]

Consider a source detection problem for a diffusion system at its stationary status, which is stated as the inverse source problem for an elliptic equation from the measurement of the solution specified only in part of the domain. For this linear ill-posed problem, we propose to reconstruct the interior source applying neural network algorithm, which projects the problem into a finite-dimensional space by approximating both the unknown source and the corresponding solution in terms of two neural networks. By minimizing a novel loss function consisting of PDE-fit and data-fit terms but without the boundary condition fit, the modified deep Galerkin method (MDGM) is applied to solve this problem numerically. Based on the stability result for the analytic extension of the solution, we strictly estimate the generalization error caused by the MDGM algorithm employing the property of conditional stability and the regularity of the solution. Numerical experiments show that we can obtain satisfactory reconstructions even in higher-dimensional cases, and validate the effectiveness of the proposed algorithm for different model configurations. Moreover, our algorithm is stable with respect to noisy inversion input data for the noise in various structures. [ABSTRACT FROM AUTHOR]

Many researchers have tried to predict the impact of the COVID-19 outbreak on morbidity, in order to help policy-makers find optimal isolation policies. However, despite the development and use of many models and sophisticated tools, these forecasting attempts have largely failed. We present a model that considers the severity of the disease and the heterogeneity of contacts between the population in complex space–time dynamics. Using mathematical and computational methods, the applied tool was developed to analyze and manage the COVID-19 pandemic (from an epidemiological point of view), with a particular focus on population heterogeneity in terms of age, susceptibility, and symptom severity. We show improved strategies to prevent an epidemic outbreak. We evaluated the model in three countries, obtaining an average mean square error of 0.067 over a full month of the basic reproduction number (R0). The goal of this study is to create a theoretical framework for crisis management that integrates accumulated epidemiological considerations. An applied result is an open-source program for predicting the outcome of an isolation strategy for future researchers and developers who can use and extend our model. [ABSTRACT FROM AUTHOR]

The paper is devoted to one possible way of the model construction for the stationary Gaussian process with given accuracy and reliability in functional space C ⁢ ([ 0 , T ]) . [ABSTRACT FROM AUTHOR]

This paper deals with the problem of the collaborative mapping of unknown indoor environments by a homogeneous mobile robot team. For this aim, a distributed multi-agent coordination approach is proposed for the mapping process to offer a global view of the entire environment. First, the scheme starts by assigning the most suitable robots to the different zones of the environment to be mapped based on a bidding strategy. Then, while a Robot agent of the group explores its local surroundings and collects information about its neighborhood, it sends mapping data to the Human/Machine Interface agent to integrate them into a single global map. Furthermore, a geometric map representation and an algorithm based on obstacles and environment limits detection are used to provide an explicitly geometric representation of the workspace. For validation purposes, Player/Stage simulator is used to show the effectiveness of the proposed distributed approach and algorithms without needing a real multi-robot system and environment. Finally, various scenarios have been carried out and results are compared in terms of (i) required mapping time, (ii) accuracy of the global generated map, and (iii) number of exchanged messages between the agents.

The paper is devoted to the complexity analysis of binary floating point pseudorandom generators. We start with a stochastic model of a 'usual' pseudorandom generator (PRNG). Then integer outputs of this generator are transformed into i.i.d. random variables, agreed with an abstract binary floating point system. Additionally, these random variables are approximately uniformly distributed on the interval [0,1]. Therefore, they can interpreted as (random) outputs of a binary floating point pseudorandom generator (flPRNG). The simulation complexity of such a transformation is defined as the average number of PRNG's outputs necessary to produce the unique output of flPRNG. Several transformations with minimal or approximately minimal complexities are presented and discussed. [ABSTRACT FROM AUTHOR]

In this paper, we obtain an explicit representation of the transition density of the one-dimensional skew Brownian motion with (a constant drift and) two semipermeable barriers. Moreover, we propose a rejection sampling method to simulate this density in an exact way. [ABSTRACT FROM AUTHOR]

In this paper, we research the thermo-mechanical reliability of lead-free solder joints in WLCSP assembly subjected to an accelerated thermal cyclic loading based on finite element simulation and Taguchi method. Effects of different control factors, including solder materials, height of solder ball, chip thickness and substrates thickness on the reliability of the lead-free solder joints were examined and calculated. The corner solder joint is the most critical solder joints in the assembly, the top surface of the solder joint is the crack propagated location. The optimal design in the WLCSP assembly has the combination of the SnAgCuAl, height of solder ball at 0.25 mm, chip thickness at 0.6 mm, substrate thickness at 1.0 mm. Moreover, the solder materials is the most important factor among the control factors in the WLCSP assembly. [ABSTRACT FROM AUTHOR]

With the addition CNTs, the properties of SnAgCu solders and solder joints can be improved remarkably. In this paper, based on the creep testing, the Dorn creep model was used to represent the creep behavior of SnAgCuCNT solder, and the parameters were determined with the fitting analysis. Moreover, the Dorn creep model of SnAgCu and SnAgCuCNT was incorporated into finite element code for calculating the creep strain response of solder joints in FCBGA (Flip Chip Ball Grid Array) device during thermal cycle loading. The results indicated that the CNTs can enhance the creep resistance of SnAgCu solder, which demonstrates the SnAgCuCNT solders can replace the SnAgCu solder in electronic industry for highreliability requirement. [ABSTRACT FROM AUTHOR]