Publications (9)
Holonomic Bessel modules and generating functions
Yik Man Chiang, Avery Ching, Xiaoli Lin
We have solved a number of holonomic PDEs derived from the Bessel modules which are related to the generating functions of classical Bessel functions and the difference Bessel func…
Twins: BFT Systems Made Robust
Shehar Bano, Alberto Sonnino, Andrey Chursin +4
This paper presents Twins, an automated unit test generator of Byzantine attacks. Twins implements three types of Byzantine behaviors: (i) leader equivocation, (ii) double voting,…
Solutions of Darboux Equations, its Degeneration and Painlevé VI Equations
Yik-Man Chiang, Avery Ching, Chiu-Yin Tsang
In this paper, we study the Darboux equations in both classical and system form, which give the elliptic Painlevé VI equations by the isomonodromy deformation method. Then we esta…
Symmetries of the Darboux equation
Yik-Man Chiang, Avery Ching, Chiu-Yin Tsang
This paper establishes the symmetries of Darboux's equations (1882) on tori. We extend Ince's work (1940) by developing new infinite series expansions in terms of Jacobi elliptic f…
Noncontiguous I/O through PVFS
Avery Ching, Alok Choudhary, Wei-keng Liao +2
With the tremendous advances in processor and memory technology, I/O has risen to become the bottleneck in high-performance computing for many applications. The development of para…
Resolving singularities and monodromy reduction of Fuchsian connections
Yik-Man Chiang, Avery Ching, Chiu-Yin Tsang
We study monodromy reduction of Fuchsian connections from a sheave theoretic viewpoint, focusing on the case when a singularity of a special connection with four singularities has…
D-module approach to Liouville's Theorem for difference operators
Kam Hang Cheng, Yik-Man Chiang, Avery Ching
We establish analogues of Liouville's theorem in the complex function theory, with the differential operator replaced by various difference operators. This is done generally by the…
Series solutions of linear ODEs by Newton-Raphson method on quotient -modules
Yik Man Chiang, Avery Ching, Chiu Yin Tsang
We develop a module approach to various kinds of solutions to several classes of important differential equations by long divisions of different differential operators. The zer…
Darwini: Generating realistic large-scale social graphs
Sergey Edunov, Dionysios Logothetis, Cheng Wang +2
Synthetic graph generators facilitate research in graph algorithms and processing systems by providing access to data, for instance, graphs resembling social networks, while circum…