Boundary behaviour of the unique solution to a singular Dirichlet problem with a convection term

AbstractBy Karamata regular variation theory and constructing comparison functions, we derive that the boundary behaviour of the unique solution to a singular Dirichlet problem −Δu=b(x)g(u)+λ|∇u|q, u>0, x∈Ω, u|∂Ω=0, which is independent of λ|∇uλ|q, where Ω is a bounded domain with smooth boundary in RN, λ∈R, q∈(0,2], lims→0+g(s)=+∞, and b is non-negative on Ω, which may be vanishing on the boundary

Active Example Selection for In-Context Learning

With a handful of demonstration examples, large-scale language models show strong capability to perform various tasks by in-context learning from these examples, without any fine-tuning. We demonstrate that in-context learning performance can be highly unstable across samples of examples, indicating the idiosyncrasies of how language models acquire information. We formulate example selection for in-context learning as a sequential decision problem, and propose a reinforcement learning algorithm for identifying generalizable policies to select demonstration examples. For GPT-2, our learned policies demonstrate strong abilities of generalizing to unseen tasks in training, with a $5.8\%$ improvement on average. Examples selected from our learned policies can even achieve a small improvement on GPT-3 Ada. However, the improvement diminishes on larger GPT-3 models, suggesting emerging capabilities of large language models.Comment: EMNLP 2022, code is available at https://github.com/ChicagoHAI/active-example-selectio

Microfluidic assembly of zein microcapsules

Microencapsulation has been widely used for many applications to stabilize functional materials and to control the release of them. With the rapid changes in consumer needs, there are increased and diversified demands for microencapsulation technology in the food industry; for instance, flavor masking, nutrient protection, and probiotics delivery. The controlled release property of core materials from the microcapsules is one of the key factors to achieve the essential goal of incorporating microcapsules in foods. Despite the extensive research on microencapsulation in the past, it is still a challenge for the industry to customize delivery systems to meet the diverse demands, especially when the materials to be used are limited to food-grade materials. In addition, the widely used top-down processes such as high-pressure homogenization and microfluidization cannot provide sufficient control on the properties of microcapsules. Those energy-intensive processes also generate substantial shear and heat, which have negative impacts on vitamins, proteins, and bioactives in microcapsules. Hence, there is a critical need to develop a mild bottom-up process that enables accurate controls over the process and the properties of the microcapsules. Microfluidics drew a great interest as a mean to synthesize or fabricate microcapsules. It features many advantages such as highly homogeneous and tunable product properties and non-invasive process, and makes handling of delicate materials feasible. To date, the majority of materials used in microfluidic process are non-food grade synthetic polymers. In order to apply this technology in the food industry, it is necessary to find suitable food-grade materials. Zein is a water-insoluble protein that has shown a potential as a building block of delivery carriers for functional ingredients and is a good candidate to be used in microfluidic process. Therefore, the overall goal of this study is to develop a methodology to assemble zein microcapsules using microfluidic approach. First, zein nanoparticles were used as building blocks to stabilize emulsions. By tuning the wettability of the zein nanoparticles with sodium caseinate, the emulsion stability was further improved. An optimal zein: caseinate ratio of 10:3 increased the interfacial coverage of oil droplets. This emulsifying ability of zein was improved by tuned wettability, which could be used as a food ingredient. Then, shifting from the conventional process, a microfluidic process was introduced to fabricate hollow zein microcapsules with tunable permeability. The generation of zein microcapsules was driven by self-assembly of zein at the oil-water interface followed by internal phase separation. By controlling the concentration of zein in dispersing phase and the flow rates of continuous and dispersing phases during microfluidic process, the rate of release was accurately adjusted. At the same time, the internal structure of the microcapsules was controlled from single core to multiple cores as well as the particle size of microcapsules. Based on the established microfluidic process, the zein microcapsules were further fabricated to modify mechanical properties and degree of wrinkling. These two properties are critical engineering properties of microcapsules to function properly for many applications. The incorporation of phytic acid significantly changed the plasticity and increased the degree of wrinkling of zein microcapsules, which were confirmed by nanoindentation and image analysis. Finally, an antimicrobial peptide nisin was encapsulated as an example to demonstrate an application of this technology. Nisin is a natural antimicrobial agent that can inhibit the growth of Listeria monocytogenes. However, the application of nisin has the limitation due to its instability in food matrices. Our study showed that the encapsulation of nisin in zein using a microfluidic process was able to control the release of nisin and significantly improved its antimicrobial activity against Listeria monocytogenes in fresh cheese. The efficacy of nisin was also extended from three days with non-encapsulated nisin to more than one week with the encapsulated nisin

Criterion and parameter analysis in aircraft shimmy study

Aircraft shimmy, a dynamic instability phenomenon of the landing gear has been a problem for over half a century. It is important to predict and control nose landing gear shimmy effectively in aircraft design phase. Simulation with typical cases is a better way compared to the tests on real aircraft to investigate early stage design and give modification suggestions at a reasonable cost .In this paper, the simulation for a certain type of aircraft is presented based on actual data. In the rigid-flexible coupling model of aircraft, non-linear factors are considered, such as airframe flexibility, steering clearance and tire parameters. The model is checked with test results of static and modal experiments and proved with sufficient accuracy. Figures of stable region are presented, formed by taxing speed and critical anti-shimmy damping coefficient. Accordingly, details of shimmy criterion are discussed and effects of factors mentioned above are studied. The result shows that self-alignment torque coefficient, relaxation length of tire, and steering clearance of nose landing gear affect critical damping coefficient significantly

DeepMapping2: Self-Supervised Large-Scale LiDAR Map Optimization

LiDAR mapping is important yet challenging in self-driving and mobile robotics. To tackle such a global point cloud registration problem, DeepMapping converts the complex map estimation into a self-supervised training of simple deep networks. Despite its broad convergence range on small datasets, DeepMapping still cannot produce satisfactory results on large-scale datasets with thousands of frames. This is due to the lack of loop closures and exact cross-frame point correspondences, and the slow convergence of its global localization network. We propose DeepMapping2 by adding two novel techniques to address these issues: (1) organization of training batch based on map topology from loop closing, and (2) self-supervised local-to-global point consistency loss leveraging pairwise registration. Our experiments and ablation studies on public datasets (KITTI, NCLT, and Nebula) demonstrate the effectiveness of our method. Our code will be released