Electro-spinning/netting: A strategy for the fabrication of three-dimensional polymer nano-fiber/nets.

Since 2006, a rapid development has been achieved in a subject area, so called electro-spinning/netting (ESN), which comprises the conventional electrospinning process and a unique electro-netting process. Electro-netting overcomes the bottleneck problem of electrospinning technique and provides a versatile method for generating spider-web-like nano-nets with ultrafine fiber diameter less than 20 nm. Nano-nets, supported by the conventional electrospun nanofibers in the nano-fiber/nets (NFN) membranes, exhibit numerious attractive characteristics such as extremely small diameter, high porosity, and Steiner tree network geometry, which make NFN membranes optimal candidates for many significant applications. The progress made during the last few years in the field of ESN is highlighted in this review, with particular emphasis on results obtained in the author's research units. After a brief description of the development of the electrospinning and ESN techniques, several fundamental properties of NFN nanomaterials are addressed. Subsequently, the used polymers and the state-of-the-art strategies for the controllable fabrication of NFN membranes are highlighted in terms of the ESN process. Additionally, we highlight some potential applications associated with the remarkable features of NFN nanostructure. Our discussion is concluded with some personal perspectives on the future development in which this wonderful technique could be pursued

Ricci Curvature of the Internet Topology

Analysis of Internet topologies has shown that the Internet topology has negative curvature, measured by Gromov's "thin triangle condition", which is tightly related to core congestion and route reliability. In this work we analyze the discrete Ricci curvature of the Internet, defined by Ollivier, Lin, etc. Ricci curvature measures whether local distances diverge or converge. It is a more local measure which allows us to understand the distribution of curvatures in the network. We show by various Internet data sets that the distribution of Ricci cuvature is spread out, suggesting the network topology to be non-homogenous. We also show that the Ricci curvature has interesting connections to both local measures such as node degree and clustering coefficient, global measures such as betweenness centrality and network connectivity, as well as auxilary attributes such as geographical distances. These observations add to the richness of geometric structures in complex network theory.Comment: 9 pages, 16 figures. To be appear on INFOCOM 201

Focal surfaces of discrete geometry

The differential geometry of smooth three-dimensional surfaces can be interpreted from one of two perspectives: in terms of oriented frames located on the surface, or in terms of a pair of associated focal surfaces. These focal surfaces are swept by the loci of the principal curvatures' radii. In this article, we develop a focal-surface-based differential geometry interpretation for discrete mesh surfaces. Focal surfaces have many useful properties. For instance, the normal of each focal surface indicates a principal direction of the corresponding point on the original surface. We provide algorithms to robustly approximate the focal surfaces of a triangle mesh with known or estimated normals. Our approach locally parameterizes the surface normals about a point by their intersections with a pair of parallel planes. We show neighboring normal triplets are constrained to pass simultaneously through two slits, which are parallel to the specified parametrization planes and rule the focal surfaces. We develop both CPU and GPU-based algorithms to efficiently approximate these two slits and, hence, the focal meshes. Our focal mesh estimation also provides a novel discrete shape operator that simultaneously estimates the principal curvatures and principal directions.Engineering and Applied Science

SPAN: A Stochastic Projected Approximate Newton Method

Second-order optimization methods have desirable convergence properties. However, the exact Newton method requires expensive computation for the Hessian and its inverse. In this paper, we propose SPAN, a novel approximate and fast Newton method. SPAN computes the inverse of the Hessian matrix via low-rank approximation and stochastic Hessian-vector products. Our experiments on multiple benchmark datasets demonstrate that SPAN outperforms existing first-order and second-order optimization methods in terms of the convergence wall-clock time. Furthermore, we provide a theoretical analysis of the per-iteration complexity, the approximation error, and the convergence rate. Both the theoretical analysis and experimental results show that our proposed method achieves a better trade-off between the convergence rate and the per-iteration efficiency.Comment: Appeared in the AAAI 2020, 25 pages, 6 figure

Topological holographic quench dynamics in a synthetic dimension

The notion of topological phases extended to dynamical systems stimulates extensive studies, of which the characterization of non-equilibrium topological invariants is a central issue and usually necessitates the information of quantum dynamics in both the time and spatial dimensions. Here we combine the recently developed concepts of the dynamical classification of topological phases and synthetic dimension, and propose to efficiently characterize photonic topological phases via holographic quench dynamics. A pseudo spin model is constructed with ring resonators in a synthetic lattice formed by frequencies of light, and the quench dynamics is induced by initializing a trivial state which evolves under a topological Hamiltonian. Our key prediction is that the complete topological information of the Hamiltonian is extracted from quench dynamics solely in the time domain, manifesting holographic features of the dynamics. In particular, two fundamental time scales emerge in the quench dynamics, with one mimicking the Bloch momenta of the topological band and the other characterizing the residue time evolution of the state after quench. For this a dynamical bulk-surface correspondence is obtained in time dimension and characterizes the topology of the spin model. This work also shows that the photonic synthetic frequency dimension provides an efficient and powerful way to explore the topological non-equilibrium dynamics.Comment: Compared to the previous submission, we made changes to figures and revised some discussion