Ting Hian Ann,Christopher
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Publication Chaotic resonance: Two-state model with chaos-induced escape over potential barrier(2005-09) Chew, L.Y.; Ting, C.; Lai, C.H.; PHYSICSWe consider the resonant effects of chaotic fluctuations on a strongly damped particle in a bistable potential driven by weak sinusoidal perturbation. We derive analytical expressions of chaos-induced transition rate between the neighboring potential wells based on the inhomogeneous Smoluchowski equation. Our first-order analysis reveals that the transition rate has the form of the Kramers escape rate except for a perturbed prefactor. This modification to the prefactor is found to arise from the statistical asymmetry of the chaotic noise. By means of the two-state model and the chaos-induced transition rate, we arrive at an analytical expression of the signal-to-noise ratio (SNR). Our first-order SNR shows that chaotic resonance can correspond directly to stochastic resonance. © 2005 The American Physical Society.Publication Monopoles, vortices, and kinks in the framework of noncommutative geometry(1997-08-15) Teo, E.; Ting, C.; PHYSICS; COMPUTATIONAL SCIENCENoncommutative differential geometry allows a scalar field to be regarded as a gauge connection, albeit on a discrete space. We explain how the underlying gauge principle corresponds to the independence of physics on the choice of vacuum state, should it be nonunique. A consequence is that Yang-Mills-Higgs theory can be reformulated as a generalized Yang-Mills gauge theory on Euclidean space with a Z2 internal structure. By extending the Hodge star operation to this noncommutative space, we are able to define the notion of self-duality of the gauge curvature form in arbitrary dimensions. It turns out that BPS monopoles, critically coupled vortices, and kinks are all self-dual solutions in their respective dimensions. We then prove, within this unified formalism, that static soliton solutions to the Yang-Mills-Higgs system exist only in one, two, and three spatial dimensions.Publication Using a Dependency Structure Parser without any Grammar Formalism to Analyse a Software Manual Corpus(1996) Ting, C.H.A.; Shiuan, P.L.; COMPUTATIONAL SCIENCEDESPAR is discussed, a hybrid approach to parsing that is based on an enhanced hidden Markov model & relies on no grammar formalism. The approach is corpus-based & statistical. Implementation builds on the insight of M. Liberman (1993) that dependency parsing is a kind of tagging for parts of speech. DESPAR takes tagged sentences as input, seeks candidate governors for each part of speech, eliminates invalid candidates for governor, & returns a likely dependency structure as output. The enhanced hidden Markov model operates with bigrams & uses a dynamic context algorithm & dependency axioms. The statistical part-of-speech tagger is based on the Brown & Wall Street Journal corpora, totaling almost 180,000 sentences. A module to handle unknown words effectively gives the parser unlimited vocabulary. A divide-and-conquer module simplifies complex sentences before parsing. DESPAR was applied to the software manual corpus in two stages; with original grammar & vocabulary & with added vocabulary. Preprocessing consisted of tokenization. it is concluded that no grammar formalism is required to analyze the dependency structure of a sentence. The performance of the parser could be improved by providing more corpora & by refining the enhanced hidden Markov model to use trigram transitions. L. Lagerquist.Publication Path integral representation of the Artin braid group(1991) Lai, C.H.; Ting, C.; PHYSICSUsing Feynman kernels, a representation of the Artin braid group is explicitly constructed. The Schrödinger equations associated to the kernels turn out to be intimately related to the Knizhnik-Zamolodchikov equations. The representation space includes the space of correlation functions of the Wess-Zumino-Witten models.Publication Spinning braid-group representation and the fractional quantum Hall effect(1993) Ting, C.; Lai, C.H.; PHYSICSThe path-integral approach to representing braid group is generalized for particles with spin. Introducing the notion of charged winding number in the super-plane, we represent the braid-group generators as homotopically constrained Feynman kernels. In this framework, super Knizhnik-Zamolodchikov operators appear naturally in the hamiltonian, suggesting the possibility of spinning nonabelian anyons. We then apply our formulation to the study of fractional quantum Hall effect (FQHE). A systematic discussion of the ground states and their quasi-hole excitations is given. We obtain Laughlin, Halperin and Moore-Read states as exact ground-state solutions to the respective hamiltonians associated to the braid-group representations. The energy gap of the quasi-excitation is also obtainable from this approach.Publication Analysis on the origin of directed current from a class of microscopic chaotic fluctuations(2004-03) Chew, L.Y.; Ting, C.; PHYSICSAn analytical expression of the origin of directed current from a class of microscopic chaotic fluctuations was discussed. The analytical expression was carried out by employing and extending a model by including a generic potential as an additional force field faced by the particle. The results show that the source term gives rise to a directed current for a strongly damped particle in a spatially periodic potential. It was suggested that the in the zeroth-order limit, the position distribution of the particle obeys the Smoluchowski equation even though the fluctuating force is deterministic.Publication Microscopic chaos and Gaussian diffusion processes(2002-05-01) Chew, L.Y.; Ting, C.; PHYSICSIn this paper, we construct and analyze a prototypical model of microscopic chaos. In particular, we extend the results of Beck and Shimizu to the case where the microscopic time scale τ is no longer small. The upshot is that a non-Ornstein-Uhlenbeck deterministic process can generate a Gaussian diffusion process. © 2002 Elsevier Science B.V. All rights reserved.