A heat flow for special metrics

On the space of positive 3-forms on a seven-manifold, we study a natural functional whose critical points induce metrics with holonomy contained in $G_2$. We prove short-time existence and uniqueness for its negative gradient flow. Furthermore, we show that the flow exists for all times and converges modulo diffeomorphisms to some critical point for any initial condition sufficiently $C^\infty$-close to a critical point.Comment: 35 pages, slightly revise

The spinoral energy functional on surfaces

This is a companion paper to [1] where we introduced the spino- rial energy functional and studied its main properties in dimensions equal or greater than three. In this article we focus on the surface case. A salient feature here is the scale invariance of the functional which leads to a plenitude of critical points. Moreover, via the spinorial Weierstraß representation it relates to the Willmore energy of periodic immersions of surfaces into R3

A General Purpose Neural Architecture for Geospatial Systems

Geospatial Information Systems are used by researchers and Humanitarian Assistance and Disaster Response (HADR) practitioners to support a wide variety of important applications. However, collaboration between these actors is difficult due to the heterogeneous nature of geospatial data modalities (e.g., multi-spectral images of various resolutions, timeseries, weather data) and diversity of tasks (e.g., regression of human activity indicators or detecting forest fires). In this work, we present a roadmap towards the construction of a general-purpose neural architecture (GPNA) with a geospatial inductive bias, pre-trained on large amounts of unlabelled earth observation data in a self-supervised manner. We envision how such a model may facilitate cooperation between members of the community. We show preliminary results on the first step of the roadmap, where we instantiate an architecture that can process a wide variety of geospatial data modalities and demonstrate that it can achieve competitive performance with domain-specific architectures on tasks relating to the U.N.'s Sustainable Development Goals.Comment: Presented at AI + HADR Workshop at NeurIPS 202

The Aerosol Deposition Method: A Modified Aerosol Generation Unit to Improve Coating Quality

Owing to its ability to produce dense thick-films at room temperature directly from a ceramic powder, the Aerosol Deposition Method (AD) possesses a unique feature in ceramics processing. For this technology, the aerosol generation of particles is a decisive part of reliable process control. However, there has only been a small amount of work published addressing this topic. In this work, we compare the aerosolization and deposition behavior of a fluidized bed generator with an aerosol generator with the rotary brush principle. While film properties very much depend on deposition time for the fluidized bed generator, films produced with the brush generator show a constant film profile, and their film thickness correlates with the controllable aerosol concentration and the duration of deposition. This type of aerosol generation may improve the setup towards a more reliable AD process

Clinical outcome of hypofractionated breath-hold image-guided SABR of primary lung tumors and lung metastases

Background: Stereotactic Ablative RadioTherapy (SABR) of lung tumors/metastases has been shown to be an effective treatment modality with low toxicity. Outcome and toxicity were retrospectively evaluated in a unique single-institution cohort treated with intensity-modulated image-guided breath-hold SABR (igSABR) without external immobilization. The dose–response relationship is analyzed based on Biologically Equivalent Dose (BED). Patients and methods: 50 lesions in 43 patients with primary NSCLC (n = 27) or lung-metastases of various primaries (n = 16) were consecutively treated with igSABR with Active-Breathing-Coordinator (ABC®) and repeat-breath-hold cone-beam-CT. After an initial dose-finding/-escalation period, 5x12 Gy for peripheral lesions and single doses of 5 Gy to varying dose levels for central lesions were applied. Overall-survival (OS), progression-free-survival (PFS), progression pattern, local control (LC) and toxicity were analyzed. Results: The median BED2 was 83 Gy. 12 lesions were treated with a BED2 of &lt;80 Gy, and 38 lesions with a BED2 of <80 Gy. Median follow-up was 15 months. Actuarial 1- and 2-year OS were 67% and 43%; respectively. Cause of death was non-disease-related in 27%. Actuarial 1- and 2-year PFS was 42% and 28%. Progression site was predominantly distant. Actuarial 1- and 2 year LC was 90% and 85%. LC showed a trend for a correlation to BED2 (p = 0.1167). Pneumonitis requiring conservative treatment occurred in 23%. Conclusion: Intensity-modulated breath-hold igSABR results in high LC-rates and low toxicity in this unfavorable patient cohort with inoperable lung tumors or metastases. A BED2 of <80 Gy was associated with reduced local control

Imaging features of fibrolamellar hepatocellular carcinoma in gadoxetic acid-enhanced MRI

Background: Fibrolamellar hepatocellular carcinoma (FLC) is a rare malignancy occurring in young patients without cirrhosis. Objectives of our study were to analyze contrast material uptake in hepatobiliary phase imaging (HBP) in gadoxetic acid-enhanced liver MRI in patients with FLC and to characterize imaging features in sequence techniques other than HBP. Methods: In this retrospective study on histology-proven FLC, contrast material uptake in HBP was quantitatively assessed by calculating the corrected FLC enhancement index (CEI) using mean signal intensities of FLC and lumbar muscle on pre-contrast imaging and HBP, respectively. Moreover, enhancement patterns in dynamic contrast-enhanced MRI and relative signal intensities compared with background liver parenchyma were determined by two radiologists in consensus for HBP, diffusion-weighted imaging using high b-values (DWI), and T2 and T1 weighted pre-contrast imaging. Results: In 6 of 13 patients with FLC gadoxetic acid-enhanced liver MRI was available. The CEI suggested presence of HBP contrast material uptake in all FLCs. A mean CEI of 1.35 indicated FLC signal increase of 35% in HBP compared with pre-contrast imaging. All FLCs were hypointense in HBP compared with background liver parenchyma. Three of 6 FLCs had arterial hyperenhancement and venous wash-out. In DWI and T2 weighted imaging, 5 of 6 FLCs were hyperintense. In T1 weighted imaging, 5 of 6 FLCs were hypointense. Conclusion: Hepatobiliary uptake of gadoxetic acid was quantitatively measurable in all FLCs investigated in our study. The observation of hypointensity of FLCs in HBP compared with background liver parenchyma emphasizes the role of gadoxetic acid-enhanced liver MRI for non-invasive diagnosis of FLC and its importance in the diagnostic work-up of indeterminate liver lesions