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We study optimal strategies in two-player stochastic games that are played on a finite graph, equipped with a general payoff function. The existence of optimal strategies that do not make use of memory and randomisation is a desirable property that vastly simplifies the algorithmic analysis of such games. Our main theorem gives a sufficient condition for the maximizer to possess such a simple optimal strategy. The condition is imposed on the payoff function, saying the payoff does not depend on any finite prefix (shift-invariant) and combining two trajectories does not give higher payoff than the payoff of the parts (submixing). The core technical property that enables the proof of the main theorem is that of the existence of ϵ -subgame-perfect strategies when the payoff function is shift-invariant. Furthermore, the same techniques can be used to prove a finite-memory transfer-type theorem: namely that for shift-invariant and submixing payoff functions, the existence of optimal finite-memory strategies in one-player games for the minimizer implies the existence of the same in two-player games. We show that numerous classical payoff functions are submixing and shift-invariant. [ABSTRACT FROM AUTHOR]

We show that every closed shift-invariant subspace of L( K) is generated by the Λ-translates of a countable number of functions, where K is a local field of positive characteristic and Λ is an appropriate translation set. We use this result to provide a characterization of wavelets on such a field. [ABSTRACT FROM AUTHOR]

The rotating machinery, as a typical example of large and complex mechanical systems, is prone to diversified sorts of mechanical faults, especially on their rotating components. Although they can be collected via vibration measurements, the critical fault signatures are always masked by overwhelming interfering contents, therefore difficult to be identified. Moreover, owing to the distinguished time-frequency characteristics of the machinery fault signatures, classical dyadic wavelet transforms (DWTs) are not perfect for detecting them in noisy environments. In order to address the deficiencies of DWTs, a pseudo wavelet system (PWS) is proposed based on the filter constructing strategies of wavelet tight frames. The presented PWS is implemented via a specially devised shift-invariant filterbank structure, which generates non-dyadic wavelet subbands as well as dyadic ones. The PWS offers a finer partition of the vibration signal into the frequency-scale plane. In addition, in order to correctly identify the essential transient signatures produced by the faulty mechanical components, a new signal impulsiveness measure, named spatial spectral ensemble kurtosis (SSEK), is put forward. SSEK is used for selecting the optimal analyzing parameters among the decomposed wavelet subbands so that the masked critical fault signatures can be explicitly recognized. The proposed method has been applied to engineering fault diagnosis cases, in which the processing results showed its effectiveness and superiority to some existing methods. [ABSTRACT FROM AUTHOR]

novel adaptive and approximate shift-invariant wavelet packet feature extraction scheme for event-related potentials (ERPs) in the electroencephalogram (EEG) is introduced in this paper. In this algorithm, the shift-invariant wavelet packed decomposition is done by integrating a cost function for decimation decision in each sub-band expansion. Additionally, a shape adaptation of the wavelet is implemented to find the best adapted wavelet shape for a given class of ERPs. This scheme is used to analyze the time course of the impact of single-pulse transcranial magnetic stimulation (TMS) to the auditory ERPs. We show that the proposed scheme is able to extract even slightest impacts of TMS, making it a promising tool for the extraction of weak ERPs components, particularly in hybrid TMS-EEG/ERP setups. [ABSTRACT FROM AUTHOR]