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For a random walk on a confined one-dimensional domain, we consider mean first-passage times (MFPT) in the presence of a mobile trap. The question we address is whether a mobile trap can improve capture times over a stationary trap. We consider two scenarios: a randomly moving trap and an oscillating trap. In both cases, we find that a stationary trap(More)
On a finite three-dimensional domain Ω, a hybrid asymptotic-numerical method is employed to analyze the existence, linear stability, and slow dynamics of localized quasi-equilibrium multi-spot patterns of the Schnakenberg activatorinhibitor model with bulk feed rate A in the singularly perturbed limit of small diffusivity ε of the activator component. By(More)
We continue our investigations of Word-Phrase-Entity (WPE) Language Models that unify words, phrases and classes, such as named entities, into a single probabilistic framework for the purpose of language modeling. In the present study we show how WPE LMs can be adapted to work in a personalized scenario where class definitions change from user to user or(More)
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