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Machine learning potentials (MLP) have revolutionized the field of atomistic simulations by describing the atomic interactions with the accuracy of electronic structure methods at a small fraction of the costs. Most current MLPs construct the energy of a system as a sum of atomic energies, which depend on information about the atomic environments provided in form of predefined or learnable feature vectors. If, in addition, non-local phenomena like long-range charge transfer are important, fourth-generation MLPs need to be used, which include a charge equilibration (Qeq) step to take the global structure of the system into account. This Qeq can significantly increase the computational cost and thus can become the computational bottleneck for large systems. In this paper we present a highly efficient formulation of Qeq that does not require the explicit computation of the Coulomb matrix elements resulting in a quasi-linearly scaling method. Moreover, our approach also allows for the efficient calculation of energy derivatives, which explicitly consider the global structure-dependence of the atomic charges as obtained from Qeq. Due to its generality, the method is not restricted to MLPs but can also be applied within a variety of other force fields.

The past decade has seen tremendous breakthroughs in computation and there is no indication that this will slow any time soon. Machine learning, large-scale computing resources, and increased industry focus have resulted in rising investments in computer-driven solutions for data management, simulations, and model generation. However, with this growth in computation has come an even larger expansion of data and with it, complexity in data storage, sharing, and tracking. In this work, we introduce ZnTrack, a Python-driven data versioning tool. ZnTrack builds upon established version control systems to provide a user-friendly and easy-to-use interface for tracking parameters in experiments, designing workflows, and storing and sharing data. From this ability to reduce large datasets to a simple Python script emerges the concept of Data as Code, a core component of the work presented here and an undoubtedly important concept as the age of computation continues to evolve. ZnTrack offers an open-source, FAIR data compatible Python package to enable users to harness these concepts of the future., Comment: 22 pages, 10 figures, 2MB PDF

In this study, we present an integro-differential model to simulate the local spread of infections. The model incorporates a standard susceptible-infected-recovered (\textit{SIR}-) model enhanced by an integral kernel, allowing for non-homogeneous mixing between susceptibles and infectives. We define requirements for the kernel function and derive analytical results for both the \textit{SIR}- and a reduced susceptible-infected-susceptible (\textit{SIS}-) model, especially the uniqueness of solutions. In order to optimize the balance between disease containment and the social and political costs associated with lockdown measures, we set up requirements for the implementation of control function, and show examples for three different formulations for the control: continuous and time-dependent, continuous and space- and time-dependent, and piecewise constant space- and time-dependent. Latter represent reality more closely as the control cannot be updated for every time and location. We found the optimal control values for all of those setups, which are by nature best for a continuous and space-and time dependent control, yet found reasonable results for the discrete setting as well. To validate the numerical results of the integro-differential model, we compare them to an established agent-based model that incorporates social and other microscopical factors more accurately and thus acts as a benchmark for the validity of the integro-differential approach. A close match between the results of both models validates the integro-differential model as an efficient macroscopic proxy. Since computing an optimal control strategy for agent-based models is computationally very expensive, yet comparatively cheap for the integro-differential model, using the proxy model might have interesting implications for future research.

In this study, we present an integro-differential model to simulate the local spread of infections. The model incorporates a standard susceptible-infected-recovered (\textit{SIR}-) model enhanced by an integral kernel, allowing for non-homogeneous mixing between susceptibles and infectives. We define requirements for the kernel function and derive analytical results for both the \textit{SIR}- and a reduced susceptible-infected-susceptible (\textit{SIS}-) model, especially the uniqueness of solutions. In order to optimize the balance between disease containment and the social and political costs associated with lockdown measures, we set up requirements for the implementation of control functions, and show examples for continuous and time-dependent, continuous and space- and time-dependent, and piecewise constant space- and time-dependent controls. Latter represent reality more closely as the control cannot be updated for every time and location. We found the optimal control values for all of those setups, which are by nature best for a continuous and space-and time dependent control, yet found reasonable results for the discrete setting as well. To validate the numerical results of the integro-differential model, we compare them to an established agent-based model that incorporates social and other microscopical factors more accurately and thus acts as a benchmark for the validity of the integro-differential approach. A close match between the results of both models validates the integro-differential model as an efficient macroscopic proxy. Since computing an optimal control strategy for agent-based models is computationally very expensive, yet comparatively cheap for the integro-differential model, using the proxy model might have interesting implications for future research.

Households play an important role in disease dynamics. Many infections happening there due to the close contact, while mitigation measures mainly target the transmission between households. Therefore, one can see households as boosting the transmission depending on household size. To study the effect of household size and size distribution, we differentiated the within and between household reproduction rate. There are basically no preventive measures, and thus the close contacts can boost the spread. We explicitly incorporated that typically only a fraction of all household members are infected. Thus, viewing the infection of a household of a given size as a splitting process generating a new, small fully infected sub-household and a remaining still susceptible sub-household we derive a compartmental ODE-model for the dynamics of the sub-households. In this setting, the basic reproduction number as well as prevalence and the peak of an infection wave in a population with given households size distribution can be computed analytically. We compare numerical simulation results of this novel household-ODE model with results from an agent--based model using data for realistic household size distributions of different countries. We find good agreement of both models showing the catalytic effect of large households on the overall disease dynamics., Comment: 17 pages,10 figures

Currently, due to the COVID-19 pandemic the public life in most European countries stopped almost completely due to measures against the spread of the virus. Efforts to limit the number of new infections are threatened by the advent of new variants of the SARS-COV-2 virus, most prominent the B.1.1.7 strain with higher infectivity. In this article we consider a basic two-strain SIR model to explain the spread of those variants in Germany on small time scales. For a linearized version of the model we calculate relevant variables like the time of minimal infections or the dynamics of the share of variants analytically. These analytical approximations and numerical simulations are in a good agreement to data reported by the Robert Koch Institute (RKI) in Germany.

Since the beginning of the corona pandemic in March 2020, various parameters for describing the spread of the disease have been specified for Germany in addition to the daily infection figures (new infections and total infections), which are also used for political decisions. In addition to excess mortality and the weekly incidence, these include the doubling time $T_2$ and the reproduction number $R_t$. For the latter, various estimates can be found on the website of the Robert-Koch-Institute, see \cite{EstR:RKI}, which are calculated from the case numbers for all of Germany; local differences are not taken into account here. In the present article, the calculations of the RKI on a local level are examined using the example of northern Rhineland-Palatinate and its districts. Here, not the reporting date but the onset of illness is used as a reference for the calculation of $R_t$. For cases where the onset of illness is not known, an adjusted generalized extreme value distribution (GEV) is first fitted to the data for which the reporting delay (difference between the onset of illness and the reporting date) is available and examined for further characteristics such as local as well as demographic differences. This GEV distribution is then used to calculate the reporting delays of incomplete data points. The calculation of the daily value of $R_t$ between the end of February and the end of October showed a similar course of the reproductive rate compared to the nationwide figures. Expectably larger statistical fluctuations were observed in the summer, mainly due to lower case numbers. The values for northern Rhineland-Palatinate have been consistently above $1$ since about mid-September. The calculations can also be transferred to other regions and administrative districts., Comment: 16 pages, 23 figures, in German