On the existence of solutions to nonlinear systems of higher order Poisson type

In this paper, we study the existence of higher order Poisson type systems. In detail, we prove a Residue type phenomenon for the fundamental solution of Laplacian in \RR^n, n\ge 3. This is analogous to the Residue theorem for the Cauchy kernel in \CC. With the aid of the Residue type formula for the fundamental solution, we derive the higher order derivative formula for the Newtonian potential and obtain its appropriate \s C^{k, \alpha} estimates. The existence of solutions to higher order Poisson type nonlinear systems is concluded as an application of the fixed point theorem.Comment: 33 page

DYNAMIC ATOMISTIC STUDY OF TUNNEL FUNCTIONS IN NANOSTRUCTURED TRANSITIONAL METAL OXIDES

Alpha (α-) MnO2 is a well know transitional metal oxide possessing one dimensional 2×2 (4.6 × 4.6 Å2) tunnels for accommodation of various ions. Such a characteristic tunneled structure has enabled the wide applications of α-MnO2 in the fields of ion exchange, molecular sieves, biosensor, catalysis and energy storage. This PhD dissertation focuses on the dynamic study of ion transport functionality of α-MnO2 at atomic level using an aberration corrected scanning transmission electron microscopy equipped with a special holder with a scanning tunneling microscopy probe. The wide application of in situ TEM studying the dynamic behaviors/reactions in rechargeable lithium ion battery is first reviewed. Li+-tunnel interaction during lithiation of a single α-MnO2 nanowire was then systematically studied in situ at sub-Å resolution. An asynchronous tunnel expansion was for the first time captured with an ordered Jahn-Teller distortion theory proposed and confirmed further by DFT. Reversible Na+ insertion in the 2×2 tunnels of α-MnO2 is also explored and the tunneled structure is found to be less stable during sodiation than lithiation, which is explained by the larger Na+ ionic size and thus stronger Na+-tunnel interaction. The effect of large cations (K+) occupying the center of 2×2 tunnels on the electrochemical performance of α-MnO2 as a LIB cathode is systematically studied by controlling K+ concentration. It is found that the presence of K+ improves both the electronic conductivity and Li+ diffusivity of α-MnO2 nanowires, leading to superior discharge rate performance compared to the ones without K+ presence. The last project explores the oriented attachment (OA) growth mechanism of α-MnO2 in aqueous solution. The atomistic formation mechanism of the OA interface is demonstrated based on sub-Å analysis of the edge structures of related planes of α-MnO2. The tunnel-based nature of OA interface is evidenced by direct atomic imaging. The role of surface atomic arrangement at single-tunnel level in directing the self assembly of α-MnO2 nanowires is clearly illustrated with strong DFT theory support

High-Level Abstractions for Programming Network Policies

The emergence of network programmability enabled by innovations such as active network- ing, SDN and NFV offers tremendous flexibility to program network policies. However, it also poses a new demand to network operators on programming network policies. The motivation of this dissertation is to study the feasibility of using high-level abstractions to simplify the programming of network policies. First, we propose scenario-based programming, a framework that allows network operators to program stateful network policies by describing example behaviors in representative scenarios. Given these scenarios, our scenario-based programming tool NetEgg automatically infers the controller state that needs to be maintained along with the rules to process network events and update state. The NetEgg interpreter can execute the generated policy implementation on top of a centralized controller, but also automatically infers flow-table rules that can be pushed to switches to improve throughput. We study a range of policies considered in the literature and report our experience regarding specifying these policies using scenarios. We evaluate NetEgg based on the computational requirements of our synthesis algorithm as well as the overhead introduced by the generated policy implementation. Our results show that our synthesis algorithm can generate policy implementations in seconds, and the automatically generated policy implementations have performance comparable to their hand-crafted implementations. Our preliminary user study results show that NetEgg was able to reduce the programming time of the policies we studied. Second, we propose NetQRE, a high-level declarative language for programming quantitative network policies that require monitoring a stream of network packets. Based on a novel theoretical foundation of parameterized quantitative regular expressions, NetQRE integrates regular-expression-like pattern matching at flow-level as well as application-level payloads with aggregation operations such as sum and average counts. We describe a compiler for NetQRE that automatically generates an efficient implementation from the specification in NetQRE. Our evaluation results demonstrate that NetQRE is expressive to specify a wide range of quantitative network policies that cannot be naturally specified in other systems. The performance of the generated implementations is comparable with that of the manually-optimized low-level code. NetQRE can be deployed in different settings. Our proof-of-concept deployment shows that NetQRE can provide timely enforcement of quantitative network policies

Continuous solutions of nonlinear Cauchy-Riemann equations and pseudoholomorphic curves in normal coordinates

We establish elliptic regularity for nonlinear inhomogeneous Cauchy-Riemann equations under minimal assumptions, and give a counterexample in a borderline case. In some cases where the inhomogeneous term has a separable factorization, the solution set can be explicitly calculated. The methods also give local parametric formulas for pseudoholomorphic curves with respect to some continuous almost complex structures.Comment: Version 3 with new Section 4.2 based on suggestions of referee. Accepted to appear in Transactions AM

Social Media Fashion Knowledge Extraction as Captioning

Social media plays a significant role in boosting the fashion industry, where a massive amount of fashion-related posts are generated every day. In order to obtain the rich fashion information from the posts, we study the task of social media fashion knowledge extraction. Fashion knowledge, which typically consists of the occasion, person attributes, and fashion item information, can be effectively represented as a set of tuples. Most previous studies on fashion knowledge extraction are based on the fashion product images without considering the rich text information in social media posts. Existing work on fashion knowledge extraction in social media is classification-based and requires to manually determine a set of fashion knowledge categories in advance. In our work, we propose to cast the task as a captioning problem to capture the interplay of the multimodal post information. Specifically, we transform the fashion knowledge tuples into a natural language caption with a sentence transformation method. Our framework then aims to generate the sentence-based fashion knowledge directly from the social media post. Inspired by the big success of pre-trained models, we build our model based on a multimodal pre-trained generative model and design several auxiliary tasks for enhancing the knowledge extraction. Since there is no existing dataset which can be directly borrowed to our task, we introduce a dataset consisting of social media posts with manual fashion knowledge annotation. Extensive experiments are conducted to demonstrate the effectiveness of our model.Comment: Accepted by SIGIR-AP 202