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We construct an ancient solution to planar curve shortening. The solution is at all times compact and embedded. For $t\ll0$ it is approximated by the rotating Yin-Yang soliton, truncated at a finite angle $\alpha(t) = -t$, and closed off by a small copy of the Grim Reaper translating soliton., Comment: The same result was independently obtained by Charyyev, J. in arXiv:2204.05978

We prove a conjecture of Bernstein that the superconvexity of the heat kernel on hyperbolic space holds in all dimensions and, hence, there is an analog of Huisken's monotonicity formula for mean curvature flow in hyperbolic space of all dimensions.

This paper presents a new distributed-memory algorithm called FastSV for finding connected components in an undirected graph. Our algorithm simplifies the classic Shiloach-Vishkin algorithm and employs several novel and efficient hooking strategies for faster convergence. We map different steps of FastSV to linear algebraic operations and implement them with the help of scalable graph libraries. FastSV uses sparse operations to avoid redundant work and optimized MPI communication to avoid bottlenecks. The resultant algorithm shows high-performance and scalability as it can find the connected components of a hyperlink graph with over 134B edges in 30 seconds using 262K cores on a Cray XC40 supercomputer. FastSV outperforms the state-of-the-art algorithm by an average speedup of 2.21x (max 4.27x) on a variety of real-world graphs., Comment: SIAM Conference on Parallel Processing for Scientific Computing (PP20)

Pregel's vertex-centric model allows us to implement many interesting graph algorithms, where optimization plays an important role in making it practically useful. Although many optimizations have been developed for dealing with different performance issues, it is hard to compose them together to optimize complex algorithms, where we have to deal with multiple performance issues at the same time. In this paper, we propose a new approach to composing optimizations, by making use of the \emph{channel} interface, as a replacement of Pregel's message passing and aggregator mechanism, which can better structure the communication in Pregel algorithms. We demonstrate that it is convenient to optimize a Pregel program by simply using a proper channel from the channel library or composing them to deal with multiple performance issues. We intensively evaluate the approach through many nontrivial examples. By adopting the channel interface, our system achieves an all-around performance gain for various graph algorithms. In particular, the composition of different optimizations makes the S-V algorithm 2.20x faster than the current best implementation., Comment: 10 pages, 4 figures, submitted to IPDPS 2019

Pregel is a popular distributed computing model for dealing with large-scale graphs. However, it can be tricky to implement graph algorithms correctly and efficiently in Pregel's vertex-centric model, especially when the algorithm has multiple computation stages, complicated data dependencies, or even communication over dynamic internal data structures. Some domain-specific languages (DSLs) have been proposed to provide more intuitive ways to implement graph algorithms, but due to the lack of support for remote access --- reading or writing attributes of other vertices through references --- they cannot handle the above mentioned dynamic communication, causing a class of Pregel algorithms with fast convergence impossible to implement. To address this problem, we design and implement Palgol, a more declarative and powerful DSL which supports remote access. In particular, programmers can use a more declarative syntax called chain access to naturally specify dynamic communication as if directly reading data on arbitrary remote vertices. By analyzing the logic patterns of chain access, we provide a novel algorithm for compiling Palgol programs to efficient Pregel code. We demonstrate the power of Palgol by using it to implement several practical Pregel algorithms, and the evaluation result shows that the efficiency of Palgol is comparable with that of hand-written code., Comment: 12 pages, 10 figures, extended version of APLAS 2017 paper

Raman intensity of Rhodamine B (RhB) is enhanced by inserting a thin high \k{appa} dielectric layer which reduces the surface plasmon damping at the gold-graphene interface. The results indicate that the Raman intensity increases sharply by plasmonic resonance enhancement while maintaining efficient fluorescence quenching with optimized dielectric layer thickness., Comment: accepted by Nanoscale