Center problem for a class of degenerate quartic systems

This paper, using pseudo-division algorithm, introduces a method for computing resonant focus numbers of a class of complex polynomial differential systems, establishes the necessary and sufficient conditions for existence of a center for a class of complex quartic systems with a degenerate resonant singular point

Precise Request Tracing and Performance Debugging for Multi-tier Services of Black Boxes

As more and more multi-tier services are developed from commercial components or heterogeneous middleware without the source code available, both developers and administrators need a precise request tracing tool to help understand and debug performance problems of large concurrent services of black boxes. Previous work fails to resolve this issue in several ways: they either accept the imprecision of probabilistic correlation methods, or rely on knowledge of protocols to isolate requests in pursuit of tracing accuracy. This paper introduces a tool named PreciseTracer to help debug performance problems of multi-tier services of black boxes. Our contributions are two-fold: first, we propose a precise request tracing algorithm for multi-tier services of black boxes, which only uses application-independent knowledge; secondly, we present a component activity graph abstraction to represent causal paths of requests and facilitate end-to-end performance debugging. The low overhead and tolerance of noise make PreciseTracer a promising tracing tool for using on production systems

Quasi-Eigenstate Evolution in Open Chaotic Billiards

We experimentally studied evolution of quasi-eigenmodes as classical dynamics undergoing a transition from being regular to chaotic in open quantum billiards. In a deformation-variable microcavity we traced all high-Q cavity modes in a wide range of frequency as the cavity deformation increased. By employing an internal parameter we were able to obtain a mode-dynamics diagram at a given deformation, showing avoided crossings between different mode groups, and could directly observe the coupling strengths induced by ray chaos among encountering modes. We also show that the observed mode-dynamics diagrams reflect the underlying classical ray dynamics in the phase space.Comment: 4 pages, 4 figure