142 research outputs found
Uncertainty Constraint on Headphone Secondary Path Function for Designing Cascade Biquad Feedback Controller with Improved Noise Reduction Performance
No full textThe uncertainty in the secondary path of active noise control (ANC) headphones affects the waterbed effect and stability of the feedback system. This study focuses on the uncertainty of the secondary path when real users wear headphones and proposes a new uncertainty constraint based on the measured results of the secondary path transfer function under different wearing conditions of a dummy head and limited subjects. This constraint and a cascaded second-order infinite impulse response filter with fixed coefficients are used to formulate a control strategic function, which is optimized using the Improved Grey Wolf Optimizer (IGWO) algorithm to obtain the optimal controller with better noise reduction performance. The proposed method and simulation model are validated based on the experimental test results. The results demonstrate that the safety factor and waterbed suppressing factor contained in the proposed uncertainty constraint ensure more stable noise reduction and effective suppression of the waterbed effect for new subjects without a priori data
Cyclic Sieving and Cluster Duality of Grassmannian
No full textWe introduce a decorated configuration space Confˣₙ() with a potential function . We prove the cluster duality conjecture of Fock-Goncharov for Grassmannians, that is, the tropicalization of (Confˣₙ(), ) canonically parametrizes a linear basis of the homogeneous coordinate ring of the Grassmannian Grₐ(n) with respect to the Plücker embedding. We prove that (Confˣₙ(), ) is equivalent to the mirror Landau-Ginzburg model of the Grassmannian considered by Eguchi-Hori-Xiong, Marsh-Rietsch, and Rietsch-Williams. As an application, we show a cyclic sieving phenomenon involving plane partitions under a sequence of piecewise-linear toggles.We are grateful to Alexander Goncharov for the inspiration on the construction of the cluster dual space, and to Jiuzu Hong for many helpful discussions on the representation theoretical aspects of the cyclic sieving problem. We would also like to thank Michael Gekhtman, Li Li, Tim Magee, Gregg Musiker, Brendon Rhoades, Bruce Sagan, Lauren Williams, Eric Zaslow, and Peng Zhou for useful conversations in the process of drafting this paper. Finally, we thank the referees for their very careful reading of this paper and for many useful suggestions
Quantum geometry of moduli spaces of local systems and representation theory
No full textLet G be a split semi-simple adjoint group, and S a colored decorated surface, given by an oriented surface with punctures, special boundary points, and a specified collection of boundary intervals.
We introduce a moduli space P(G,S) parametrizing G-local system on S with some boundary data, and prove that it carries a cluster Poisson structure, equivariant under the action of the cluster modular group M(G,S), containing the mapping class group of S, the group of outer automorphisms of G, and the product of Weyl / braid groups over punctures / boundary components. We prove that the dual moduli space A(G,S) carries a M(G,S)-equivariant cluster structure, and the pair (A(G,S), P(G,S)) is a cluster ensemble. These results generalize the works of V. Fock & the first author, and of I. Le.
We quantize cluster Poisson varieties X for any Planck constant h s.t. h>0 or |h|=1. First, we define a *-algebra structure on the Langlands modular double A(h; X) of the algebra of functions on X. We construct a principal series of representations of the *-algebra A(h; X), equivariant under a unitary projective representation of the cluster modular group M(X). This extends works of V. Fock and the first author when h>0.
Combining this, we get a M(G,S)-equivariant quantization of the moduli space P(G,S), given by the *-algebra A(h; P(G,S)) and its principal series representations. We construct realizations of the principal series *-representations. In particular, when S is punctured disc with two special points, we get a principal series *-representations of the Langlands modular double of the quantum group Uq(g).
We conjecture that there is a nondegenerate pairing between the local system of coinvariants of oscillatory representations of the W-algebra and the one provided by the projective representation of the mapping class group of S.234 pages. Updated following the referee report. Sections 2.4, 13.4, 17.8, 17.9 20.3, 20.4 ne
Spatial structure of temporal coherence scale under the different propagation conditions
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