Splitting method for elliptic equations with line sources

In this paper, we study the mathematical structure and numerical approximation of elliptic problems posed in a (3D) domain $\Omega$ when the right-hand side is a (1D) line source $\Lambda$. The analysis and approximation of such problems is known to be non-standard as the line source causes the solution to be singular. Our main result is a splitting theorem for the solution; we show that the solution admits a split into an explicit, low regularity term capturing the singularity, and a high-regularity correction term $w$ being the solution of a suitable elliptic equation. The splitting theorem states the mathematical structure of the solution; in particular, we find that the solution has anisotropic regularity. More precisely, the solution fails to belong to $H^1$ in the neighbourhood of $\Lambda$, but exhibits piecewise $H^2$-regularity parallel to $\Lambda$. The splitting theorem can further be used to formulate a numerical method in which the solution is approximated via its correction function $w$. This approach has several benefits. Firstly, it recasts the problem as a 3D elliptic problem with a 3D right-hand side belonging to $L^2$, a problem for which the discretizations and solvers are readily available. Secondly, it makes the numerical approximation independent of the discretization of $\Lambda$; thirdly, it improves the approximation properties of the numerical method. We consider here the Galerkin finite element method, and show that the singularity subtraction then recovers optimal convergence rates on uniform meshes, i.e., without needing to refine the mesh around each line segment. The numerical method presented in this paper is therefore well-suited for applications involving a large number of line segments. We illustrate this by treating a dataset (consisting of $\sim 3000$ line segments) describing the vascular system of the brain

Directional flow in perivascular networks: Mixed finite elements for reduced-dimensional models on graphs

The flow of cerebrospinal fluid through the perivascular spaces of the brain is believed to play a crucial role in eliminating toxic waste proteins. While the driving forces of this flow have been enigmatic, experiments have shown that arterial wall motion is central. In this work, we present a network model for simulating pulsatile fluid flow in perivascular networks. We establish the well-posedness of this model in the primal and dual mixed variational settings, and show how it can be discretized using mixed finite elements. Further, we utilize this model to investigate fundamental questions concerning the physical mechanisms governing perivascular fluid flow. Notably, our findings reveal that arterial pulsations can induce directional flow in branching perivascular networks

Calibration to American options: numerical investigation of the de-Americanization method.

American options are the reference instruments for the model calibration of a large and important class of single stocks. For this task, a fast and accurate pricing algorithm is indispensable. The literature mainly discusses pricing methods for American options that are based on Monte Carlo, tree and partial differential equation methods. We present an alternative approach that has become popular under the name de-Americanization in the financial industry. The method is easy to implement and enjoys fast run-times (compared to a direct calibration to American options). Since it is based on ad hoc simplifications, however, theoretical results guaranteeing reliability are not available. To quantify the resulting methodological risk, we empirically test the performance of the de-Americanization method for calibration. We classify the scenarios in which de-Americanization performs very well. However, we also identify the cases where de-Americanization oversimplifies and can result in large errors

Landwirt*innen nutzen Citizen Science Praktiken zur Unterstützung der Artenvielfalt am Land

Das EU-Projekt FRAMEwork fördert bottom-up Innovationen getragen von Landwirt*innen via elf "Farmer Cluster" in neun Ländern Europas. Anhand zweier Farmer Cluster im Mostviertel und im Burgenland in Österreich veranschaulicht das Poster zwei komplementäre Citizen Science Praktiken, die einen evidenzbasierten, lokal eingebetteten, gemeinschaftlichen Ansatz zum Schutz und zur Verbesserung der biologischen Vielfalt unterstützen und strukturiertes Monitoring mit adaptiven Landmanagementpraktiken kombinieren

An X-Ray Absorption Spectroscopy Study of Ball-Milled Lithium Tantalate and Lithium Titanate Nanocrystals

Previous work has shown that nanocrystalline samples of lithium tantalate and titanate prepared by high-energy milling show unusually high lithium ion conductivity. Here, we report an X-ray absorption spectroscopy (XAS) study at the Ti K-edge and the Ta L3 edge of samples that have been milled for various lengths of time. For both systems the results show that milling creates amorphous material whose quantity increases with the milling time. The more extensive data for the tantalate shows that milling for only 30 minutes generates ~25% amorphous content in the sample. The content rises to ~60% after 16 hours. It is suggested that it is the motion of the lithium ions through the amorphous content that provides the mechanism for the high ionic conductivity

A prospective randomised phase III trial of adjuvant chemotherapy with 5-fluorouracil and leucovorin in patients with stage II colon cancer

The purpose of this trial was to investigate the efficacy of adjuvant chemotherapy with 5-fluorouracil (5-FU) and leucovorin (LV) in stage II colon cancer. Patients with stage II colon cancer were randomised to either adjuvant chemotherapy with 5-FU/LV (100 mg m−2 LV+450 mg m−2 5-FU weekly, weeks 1–6, in 8 weeks cycles × 7) or surveillance only. Five hundred patients were evaluable for analyses. After a median follow-up of 95.6 months, 55 of 252 patients (21.8%) have died in the 5-FU/LV arm and 58 of 248 patients (23.4%) in the surveillance arm. There was no statistically significant difference in overall survival (OS) between the two treatment arms (hazard ratios, HR 0.88, 95% CI 0.61–1.27, P=0.49). The relative risk for tumour relapse was higher for patients on the surveillance arm than for those on the 5-FU/LV arm; however, this difference was not statistically significant (HR 0.69, 95% CI 0.45–1.06, P=0.09). Consequently, disease-free survival (DFS) was not significantly different between the two trial arms. In conclusion, results of this trial demonstrate a trend to a lower risk for relapse in patients treated with adjuvant 5-FU/LV for stage II colon cancer. However, in this study with limited power to detect small differences between the study arms, adjuvant chemotherapy failed to significantly improve DFS and OS

Ginger Stimulates Hematopoiesis via Bmp Pathway in Zebrafish

) has been widely used in traditional medicine; however, to date there is no scientific research documenting the potential of ginger to stimulate hematopoiesis. expression in the caudal hematopoietic tissue area. We further confirmed that Bmp/Smad pathway mediates this hematopoiesis promoting effect of ginger by using the Bmp-activated Bmp type I receptor kinase inhibitors dorsomorphin, LND193189 and DMH1.Our study provides a strong foundation to further evaluate the molecular mechanism of ginger and its bioactive components during hematopoiesis and to investigate their effects in adults. Our results will provide the basis for future research into the effect of ginger during mammalian hematopoiesis to develop novel erythropoiesis promoting agents

Business constraints and growth potential of micro and small manufacturing enterprises in Uganda

Ugandan micro and small enterprises (MSEs) still perform poorly. Studies associating poor performance of manufacturers with lack of finance and low investment ignore micro enterprises. Those focusing on MSEs are either exploratory in nature or employ a descriptive analysis, which cannot show the extent to which business constraints explain the performance of MSEs. Thus, this paper tries to examine the extent to which the growth of MSEs is associated with business constraints while controlling for owners’ attributes and firms’ characteristics. The results reveal that MSEs’ growth potential is negatively associated with limited access to productive resources (finance and business development services), high taxes and lack of market access

Social Order and Adaptability in Animal and Human Cultures as Analogues for Agent Communities: Toward a Policy-Based Approach

Abstract. In this paper we discuss some of the ways social order is maintained in animal and human realms, with the goal of enriching our thinking about mechanisms that might be employed in developing similar means of ordering communities of agents. We present examples from our current work in human-agent teamwork, and we speculate about some new directions this kind of research might take. Since communities also need to change over time to cope with changing circumstances, we also speculate on means that regulatory bodies can use to adapt. 1