Modelling the Spatial Spread of COVID-19 in a German District using a Diffusion Model

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

Exploiting Exploration: Reintegrating Digital Innovations from Digital Innovation Units

In digital transformation, incumbents are pressured to exploit their core business and simultaneously explore opportunities for digital innovation. When pursuing ambidexterity, organizations establish digital innovation units (DIUs) dedicated to digital innovation. Due to the novelty of the phenomenon, prior studies targeted DIUs' design, objectives, and challenges. However, their value lies in reintegrating digital innovations back into the operational organization for use and commercialization, which has been neglected so far. Thus, we analyze the reintegration based on a single-embedded case study of four heterogeneous DIUs. We identify three phases of reintegration activities and trace differences to the contextual factors: innovation orientation, number of involved entities, and ownership. Our contribution is twofold. First, we shed light on the reintegration of DIUs' innovation outcomes for the first time. Second, we extend research on digital innovation and ambidexterity by outlining drivers and inhibitors of reintegration, enhancing our understanding of how organizations can exploit exploration

Modelling the spatial spread of COVID-19 in a German district using a diffusion model

In this study, we focus on modeling the local spread of COVID-19 infections. As the pandemic continues and new variants or future pandemics can emerge, modelling the early stages of infection spread becomes crucial, especially as limited medical data might be available initially. Therefore, our aim is to gain a better understanding of the diffusion dynamics on smaller scales using partial differential equation (PDE) models. Previous works have already presented various methods to model the spatial spread of diseases, but, due to a lack of data on regional or even local scale, few actually applied their models on real disease courses in order to describe the behaviour of the disease or estimate parameters. We use medical data from both the Robert-Koch-Institute (RKI) and the Birkenfeld district government for parameter estimation within a single German district, Birkenfeld in Rhineland-Palatinate, during the second wave of the pandemic in autumn 2020 and winter 2020–21. This district can be seen as a typical middle-European region, characterized by its (mainly) rural nature and daily commuter movements towards metropolitan areas. A basic reaction-diffusion model used for spatial COVID spread, which includes compartments for susceptibles, exposed, infected, recovered, and the total population, is used to describe the spatio-temporal spread of infections. The transmission rate, recovery rate, initial infected values, detection rate, and diffusivity rate are considered as parameters to be estimated using the reported daily data and least square fit. This work also features an emphasis on numerical methods which will be used to describe the diffusion on arbitrary two-dimensional domains. Two numerical optimization techniques for parameter fitting are used: the Metropolis algorithm and the adjoint method. Two different methods, the Crank-Nicholson method and a finite element method, which are used according to the requirements of the respective optimization method are used to solve the PDE system. This way, the two methods are compared and validated and provide similar results with good approximation of the infected in both the district and the respective sub-districts

Inelastic chaotic scattering on a Bose-Einstein condensate

We devise a microscopic scattering approach to probe the excitation spectrum of a Bose-Einstein condensate. We show that the experimentally accessible scattering cross section exhibits universal Ericson fluctuations, with characteristic properties rooted in the underlying classical field equations.Comment: 11 pages, 5 figure

G-flux and Spectral Divisors

We propose a construction of G-flux in singular elliptic Calabi-Yau fourfold compactifications of F-theory, which in the local limit allow a spectral cover description. The main tool of construction is the so-called spectral divisor in the resolved Calabi-Yau geometry, which in the local limit reduces to the Higgs bundle spectral cover. We exemplify the workings of this in the case of an E_6 singularity by constructing the resolved geometry, the spectral divisor and in the local limit, the spectral cover. The G-flux constructed with the spectral divisor is shown to be equivalent to the direct construction from suitably quantized linear combinations of holomorphic surfaces in the resolved geometry, and in the local limit reduces to the spectral cover flux.Comment: 30 page

Product-Production-CoDesign: An Approach on Integrated Product and Production Engineering Across Generations and Life Cycles

Shorter product life cycles and high product variance nowadays require efficient engineering of products and production systems. Hereby a further challenge is that costs over the entire life cycle of the product and production system are defined early in the process. Existing approaches in literature and practice such as simultaneous engineering and design for manufacturing incorporate aspects of production into product engineering. However, these approaches leave potential for increasing efficiency unused because knowledge from past generations of products, production systems, and business models is not stored and reused in a formalized way and future generations are not considered in the respective current engineering process. This article proposes an approach for integrated product and production engineering across generations and life cycles of products and production systems. This includes the consideration of related business models to successfully establish the products on the market as well as the anticipation of future product and production system characteristics. The presented approach can reduce both development and manufacturing costs as well as time to market and opens the vast technological potential for product design to achieve additional customer benefits. Three case studies elaborate on aspects of the proposed approach and present its benefits