Ciarlet–Raviart mixed finite element approximation for an optimal control problem governed by the first bi-harmonic equation

AbstractThe Ciarlet–Raviart mixed finite element approximation is constructed to solve the constrained optimal control problem governed by the first bi-harmonic equation. The optimality conditions consisting of the state and the co-state equations is derived. Also, the a priori error estimates are analyzed. In the analysis of the a priori error estimates, the improved convergent rate of the higher order than existed results is proved. Some numerical experiments are performed to confirm the theoretical analysis for the a priori error estimate

Private Model Compression via Knowledge Distillation

The soaring demand for intelligent mobile applications calls for deploying powerful deep neural networks (DNNs) on mobile devices. However, the outstanding performance of DNNs notoriously relies on increasingly complex models, which in turn is associated with an increase in computational expense far surpassing mobile devices' capacity. What is worse, app service providers need to collect and utilize a large volume of users' data, which contain sensitive information, to build the sophisticated DNN models. Directly deploying these models on public mobile devices presents prohibitive privacy risk. To benefit from the on-device deep learning without the capacity and privacy concerns, we design a private model compression framework RONA. Following the knowledge distillation paradigm, we jointly use hint learning, distillation learning, and self learning to train a compact and fast neural network. The knowledge distilled from the cumbersome model is adaptively bounded and carefully perturbed to enforce differential privacy. We further propose an elegant query sample selection method to reduce the number of queries and control the privacy loss. A series of empirical evaluations as well as the implementation on an Android mobile device show that RONA can not only compress cumbersome models efficiently but also provide a strong privacy guarantee. For example, on SVHN, when a meaningful $(9.83,10^{-6})$-differential privacy is guaranteed, the compact model trained by RONA can obtain 20$\times$ compression ratio and 19$\times$ speed-up with merely 0.97% accuracy loss.Comment: Conference version accepted by AAAI'1

Nitrate and pesticide transport under pear production in clay and sandy soil

Groundwater contamination on irrigated land is of concern in this nation and around the world. In order to reduce the potential of groundwater contamination by agricultural practices such as irrigation, fertilizer and pesticide application, vadose-zone monitoring and sampling are needed. The main objective of this study was to evaluate impacts of current irrigation treatments and soil structures on the migration of pollutants to groundwater. Passive CAPillary wick pan Samplers (PCAPS) and suction cups were installed in two cracking clays and one sandy soil under the pear tree root zone. PCAPS and suction cups were used to collect nitrate-nitrogen and tracer samples. Tracers were applied to track the spatial and temporal patterns of compounds that mimic nitrate-nitrogen and pesticide movement. The observed magnitude of water leaching over 3 months differed between irrigation methods and soil structures and decreased in this order: flooding over 3 months in clay soil (22.8 cm) > micro-sprinkler in clay soil (16.1 cm) > over-head sprinkler in sandy soil (4.1 cm). Leaching patterns were varied spatially; soil structures, irrigation methods, preferential flow, and high water table may have been responsible for the spatial variation of leaching. Mass recovery of all three tracers, including bromide, blue dye, and rhodamine had the same decreasing order: flooding in clay soil > micro-sprinkler in clay soil > over-head sprinkler in sandy soil. Average blue dye and rhodamine concentrations had the following order: flooding in clay soil > micro-sprinkler in clay > over-head sprinkler in sandy soil. Since blue dye and rhodamine have similar properties to some moderately adsorbed pesticides, we may infer that the risk of pesticide movement in three sites should also decrease in this order. Presumably pesticide movement in clay soil would have been more pronounced for flooding than sprinkler irrigation. On the annual/seasonal basis, the total mass of nitrate-nitrogen leaching differed between irrigation methods and soil structures and decreased in the following order: over-head sprinkler in sandy soil > flooding in clay soil > micro-sprinkler in clay soil. The annual average nitrate-nitrogen concentration observed under over-head sprinkler in sandy soil was 15 mg/l over the maximum allowed concentration level (10 mg/l) by the EPA while seasonal nitrate-nitrogen concentration was low in clay soil under current irrigation practices. Strong evidence suggested the occurrence of preferential flow in this study. Preferential flow may contribute to high water leachate, nitrate and pesticide migration. High correlation coefficients between paired PCAPS indicated that PCAPS have similar responses to water and solute leaching. Several improvements in PCAPS are needed to obtain representative samples under severe flooding conditions. Limited data suggested that ultra-low rate irrigation devices could reduce the water leaching and the potential of pollutant migration to the groundwater because ultra-low rate application devices minimize the soil macropore flow

Development of an expert system for irrigation and fertilization management in the Pacific Northwest

Recent advances in computer technology have made possible the development of expert systems. Expert systems are computer programs that perform at the level of a human expert. Expert systems can help integrate and apply diverse sources of information and expertise to problems of integrated crop management. A prototype Crop Management eXpert (CMX) system has been developed. The primary goal of CMX is to provide recommendations on optimal irrigation and fertilization scheduling for wheat production in the Pacific Northwest. This system can be used by farmers and/or extension agents. OUS II Shell has been used as a implementation tool. To build this rule - based expert system, a development strategy, commonly used in the construction of expert systems, consisting of 1 ) identification; 2) conceptualization; 3) formalization; 4) implementation; and 5) testing was applied. CMX is composed of modules for irrigation and fertilization management. For irrigation management, CMX is mainly involved in the irrigation scheduling which is the major part of irrigation management. Irrigation strategies have been applied in irrigation decision making. For each strategy, timing criteria which generally consist of management allowed depletion, soil water potential, leaf water potential, and water stress indices have been used. The system provides farmers with irrigation scenarios which determine when and how much water to apply. CMX represents an integration of conventional computing and expert systems technology designed to provide expert recommendations enabling farmers to obtain the best return on their water and fertilizer investment. For fertilization management, a variety of variables have been taken into considered. Crop growth stages, soil moisture, nutrient analysis, protein requirement, and application methods are important factors for the fertilizer decision making. Several constraints have been used in optimal fertilizer advice. CMX can focus only on relevant information, thus reducing the problem space to a manageable size and significantly, improving the efficiency of the system. The facility of the expert system to explain the decision-making process enables users to better understand the underlying assumptions, facts, and reasoning used to generate recommendations. The CMX prototype demonstrates the feasibility of employing expert systems technology in agricultural applications. CMX has been validated and evaluated. The survey results showed that this prototype was successful in capturing domain experts' knowledge as rules and providing advice on the irrigation and fertilization management for wheat

Habermas, China und die "halbierte Moderne" : im Gespräch mit dem chinesischen Sozialphilosophen und Übersetzer Cao Weidong

Seit den 1980er Jahren erfreut sich die kritische Theorie im intellektuellen Diskurs Chinas großer Beliebtheit. Dank der chinesischen Reformpolitik wird die Sozialphilosophie der Frankfurter Schule zunehmend als Methode verwendet, um den politischen Alltag und den gesellschaftlichen Wandel kritisch zu analysieren. Hierbei spielen die Schriften von Jürgen Habermas und besonders seine Ansichten zur Zivilgesellschaft, Öffentlichkeit und zur Schlüsselrolle der Kommunikation eine wichtige Rolle. Im Rahmen der vom Interdisziplinären Zentrum für Ostasienwissenschaften der Goethe-Universität veranstalteten Konferenz »Kritik – Theorie – Kritische Theorie. Die Frankfurter Schule in China« gab der Habermas-Experte und Übersetzer Cao Weidong Einblick in das chinesische »Habermas-Fieber«