59,351 research outputs found

    Bijections behind the Ramanujan Polynomials

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    The Ramanujan polynomials were introduced by Ramanujan in his study of power series inversions. In an approach to the Cayley formula on the number of trees, Shor discovers a refined recurrence relation in terms of the number of improper edges, without realizing the connection to the Ramanujan polynomials. On the other hand, Dumont and Ramamonjisoa independently take the grammatical approach to a sequence associated with the Ramanujan polynomials and have reached the same conclusion as Shor's. It was a coincidence for Zeng to realize that the Shor polynomials turn out to be the Ramanujan polynomials through an explicit substitution of parameters. Shor also discovers a recursion of Ramanujan polynomials which is equivalent to the Berndt-Evans-Wilson recursion under the substitution of Zeng, and asks for a combinatorial interpretation. The objective of this paper is to present a bijection for the Shor recursion, or and Berndt-Evans-Wilson recursion, answering the question of Shor. Such a bijection also leads to a combinatorial interpretation of the recurrence relation originally given by Ramanujan.Comment: 18 pages, 7 figure

    Projection Measurement of the Maximally Entangled N-Photon State for a Demonstration of N-Photon de Broglie Wavelength

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    We construct a projection measurement process for the maximally entangled N-photon state (the NOON-state) with only linear optical elements and photodetectors. This measurement process will give null result for any N-photon state that is orthogonal to the NOON state. We examine the projection process in more detail for N=4 by applying it to a four-photon state from type-II parametric down-conversion. This demonstrates an orthogonal projection measurement with a null result. This null result corresponds to a dip in a generalized Hong-Ou-Mandel interferometer for four photons. We find that the depth of the dip in this arrangement can be used to distinguish a genuine entangled four-photon state from two separate pairs of photons. We next apply the NOON state projection measurement to a four-photon superposition state from two perpendicularly oriented type-I parametric down-conversion processes. A successful NOON state projection is demonstrated with the appearance of the four-photon de Broglie wavelength in the interference fringe pattern.Comment: 8 pages, 3 figures, new title, some content change, replaced Fig.

    GhostVLAD for set-based face recognition

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    The objective of this paper is to learn a compact representation of image sets for template-based face recognition. We make the following contributions: first, we propose a network architecture which aggregates and embeds the face descriptors produced by deep convolutional neural networks into a compact fixed-length representation. This compact representation requires minimal memory storage and enables efficient similarity computation. Second, we propose a novel GhostVLAD layer that includes {\em ghost clusters}, that do not contribute to the aggregation. We show that a quality weighting on the input faces emerges automatically such that informative images contribute more than those with low quality, and that the ghost clusters enhance the network's ability to deal with poor quality images. Third, we explore how input feature dimension, number of clusters and different training techniques affect the recognition performance. Given this analysis, we train a network that far exceeds the state-of-the-art on the IJB-B face recognition dataset. This is currently one of the most challenging public benchmarks, and we surpass the state-of-the-art on both the identification and verification protocols.Comment: Accepted by ACCV 201

    On the feasibility of speckle reduction in echocardiography using strain compounding

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    Strain compounding has been previously developed as an approach to reducing speckle noise. The technique is based on speckle de-correlation induced by different strain levels applied on the medium and has been demonstrated feasible in the human superficial soft tissues under external quasi-static compression. In this study, the efficacy of strain compounding in echocardiography was investigated. A temporal gate in a cardiac cycle was first defined, with the middle echocardiographic frame selected as the reference image. The in-plane motion of the temporally gated images was then estimated and used for image correction with respect to the reference frame. Finally, the spatially matched images were averaged to form a speckle reduced image. Not only did the prerequisite deformation stem from the natural contraction of the heart, but the computational efficiency could also remain by simply using the strain estimates yielded from cardiac strain imaging, which has become a commonly used tool in the clinic. Ultrasonic images of a normal human heart over six cardiac cycles were acquired by a commercial ultrasound imaging system at a frame rate of 70 fps in the apical four-chamber, long-axis and short-axis views. The results show approximately 7.9%, 8.4%, and 11.3% improvements in the signal-to-noise ratio (SNR) of the septal wall segment of the strain-compounded images in the apical four-chamber and long-axis views, respectively. Comparable performance of strain compounding to that of a well-established method, Speckle Reducing Anisotropic Diffusion (SRAD), was also observed. © 2014 IEEE.published_or_final_versio
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