The Multilevel Structures of NURBs and NURBlets on Intervals

This dissertation is concerned with the problem of constructing biorthogonal wavelets based on non-uniform rational cubic B-Splines on intervals. We call non-uniform rational B-Splines ``NURBs , and such biorthogonal wavelets ``NURBlets . Constructing NURBlets is useful in designing and representing an arbitrary shape of an object in the industry, especially when exactness of the shape is critical such as the shape of an aircraft. As we know presently most popular wavelet models in the industry are approximated at boundaries. In this dissertation a new model is presented that is well suited for generating arbitrary shapes in the industry with mathematical exactness throughout intervals; it fulfills interpolation at boundaries as well

A brief review of hybrid skin-topological effect

The finding of non-Hermitian skin effect has revolutionized our understanding of non-Hermitian topological phases, where the usual bulk-boundary correspondence is broken and new topological phases specific to non-Hermitian system are uncovered. Hybrid skin-topological effect (HSTE) is a class of newly discovered non-Hermitian topological states that simultaneously supports skin-localized topological edge states and extended bulk states. Here we provide a brief review of HSTE, starting from different mechanics that have been used to realize HSTE, including non-reciprocal couplings, onsite gain/loss, and non-Euclidean lattice geometries. We also review some theoretical developments closely related to the HSTE, including the concept of higher-order non-Hermitian skin effect, parity-time symmetry engineering, and non-Hermitian chiral skin effect. Finally, we summarize recent experimental exploration of HSTE, including its realization in electric circuits systems, non-Hermitian photonic crystals, and active matter systems. We hope this review can make the concept of hybrid-skin effect clearer and inspire new finding of non-Hermitian topological states in higher dimensional systems.Comment: A review article with 13 pages and 9 figures. Comments are welcom

Facilitating Technology Transfer by Patent Knowledge Graph

Technologies are one of the most important driving forces of our societal development and realizing the value of technologies heavily depends on the transfer of technologies. Given the importance of technologies and technology transfer, an increasingly large amount of money has been invested to encourage technological innovation and technology transfer worldwide. However, while numerous innovative technologies are invented, most of them remain latent and un-transferred. The comprehension of technical documents and the identification of appropriate technologies for given needs are challenging problems in technology transfer due to information asymmetry and information overload problems. There is a lack of common knowledge base that can reveal the technical details of technical documents and assist with the identification of suitable technologies. To bridge this gap, this research proposes to construct knowledge graph for facilitating technology transfer. A case study is conducted to show the construction of a patent knowledge graph and to illustrate its benefit to finding relevant patents, the most common and important form of technologies

A Semantic Graph-Based Approach for Mining Common Topics From Multiple Asynchronous Text Streams

In the age of Web 2.0, a substantial amount of unstructured content are distributed through multiple text streams in an asynchronous fashion, which makes it increasingly difficult to glean and distill useful information. An effective way to explore the information in text streams is topic modelling, which can further facilitate other applications such as search, information browsing, and pattern mining. In this paper, we propose a semantic graph based topic modelling approach for structuring asynchronous text streams. Our model in- tegrates topic mining and time synchronization, two core modules for addressing the problem, into a unified model. Specifically, for handling the lexical gap issues, we use global semantic graphs of each timestamp for capturing the hid- den interaction among entities from all the text streams. For dealing with the sources asynchronism problem, local semantic graphs are employed to discover similar topics of different entities that can be potentially separated by time gaps. Our experiment on two real-world datasets shows that the proposed model significantly outperforms the existing ones