Quantum traces for SLnSL_n-skein algebras

We establish the existence of several quantum trace maps. The simplest one is an algebra map between two quantizations of the algebra of regular functions on the $SL_n$-character variety of a surface $\mathfrak{S}$ equipped with an ideal triangulation $\lambda$. The first is the (stated) $SL_n$-skein algebra $\mathscr{S}(\mathfrak{S})$. The second $\overline{\mathcal{X}}(\mathfrak{S},\lambda)$ is the Fock and Goncharov's quantization of their $X$-moduli space. The quantum trace is an algebra homomorphism $\bar{tr}^X:\overline{\mathscr{S}}(\mathfrak{S})\to\overline{\mathcal{X}}(\mathfrak{S},\lambda)$ where the reduced skein algebra $\overline{\mathscr{S}}(\mathfrak{S})$ is a quotient of $\mathscr{S}(\mathfrak{S})$. When the quantum parameter is 1, the quantum trace $\bar{tr}^X$ coincides with the classical Fock-Goncharov homomorphism. This is a generalization of the Bonahon-Wong quantum trace map for the case $n=2$. We then define the extended Fock-Goncharov algebra $\mathcal{X}(\mathfrak{S},\lambda)$ and show that $\bar{tr}^X$ can be lifted to $tr^X:\mathscr{S}(\mathfrak{S})\to\mathcal{X}(\mathfrak{S},\lambda)$. We show that both $\bar{tr}^X$ and $tr^X$ are natural with respect to the change of triangulations. When each connected component of $\mathfrak{S}$ has non-empty boundary and no interior ideal point, we define a quantization of the Fock-Goncharov $A$-moduli space $\overline{\mathcal{A}}(\mathfrak{S},\lambda)$ and its extension $\mathcal{A}(\mathfrak{S},\lambda)$. We then show that there exist quantum traces $\bar{tr}^A:\overline{\mathscr{S}}(\mathfrak{S})\to\overline{\mathcal{A}}(\mathfrak{S},\lambda)$ and $tr^A:\mathscr{S}(\mathfrak{S})\hookrightarrow\mathcal{A}(\mathfrak{S},\lambda)$, where the second map is injective, while the first is injective at least when $\mathfrak{S}$ is a polygon. They are equivalent to the $X$-versions but have better algebraic properties.Comment: 111 pages, 35 figure

Segmental Spatiotemporal CNNs for Fine-grained Action Segmentation

Joint segmentation and classification of fine-grained actions is important for applications of human-robot interaction, video surveillance, and human skill evaluation. However, despite substantial recent progress in large-scale action classification, the performance of state-of-the-art fine-grained action recognition approaches remains low. We propose a model for action segmentation which combines low-level spatiotemporal features with a high-level segmental classifier. Our spatiotemporal CNN is comprised of a spatial component that uses convolutional filters to capture information about objects and their relationships, and a temporal component that uses large 1D convolutional filters to capture information about how object relationships change across time. These features are used in tandem with a semi-Markov model that models transitions from one action to another. We introduce an efficient constrained segmental inference algorithm for this model that is orders of magnitude faster than the current approach. We highlight the effectiveness of our Segmental Spatiotemporal CNN on cooking and surgical action datasets for which we observe substantially improved performance relative to recent baseline methods.Comment: Updated from the ECCV 2016 version. We fixed an important mathematical error and made the section on segmental inference cleare

Solutions to the Jaynes-Cummings model without the rotating-wave approximation

By using extended bosonic coherent states, the solution to the Jaynes-Cummings model without the rotating-wave approximation can be mapped to that of a polynomial equation with a single variable. The solutions to this polynomial equation can give all eigenvalues and eigenfunctions of this model with all values of the coupling strength and the detuning exactly, which can be readily applied to recent circuit quantum electrodynamic systems operating in the ultra-strong coupling regime.Comment: 6 pages,3 figure

Perceptually Motivated Wavelet Packet Transform for Bioacoustic Signal Enhancement

A significant and often unavoidable problem in bioacoustic signal processing is the presence of background noise due to an adverse recording environment. This paper proposes a new bioacoustic signal enhancement technique which can be used on a wide range of species. The technique is based on a perceptually scaled wavelet packet decomposition using a species-specific Greenwood scale function. Spectral estimation techniques, similar to those used for human speech enhancement, are used for estimation of clean signal wavelet coefficients under an additive noise model. The new approach is compared to several other techniques, including basic bandpass filtering as well as classical speech enhancement methods such as spectral subtraction, Wiener filtering, and Ephraim–Malah filtering. Vocalizations recorded from several species are used for evaluation, including the ortolan bunting (Emberiza hortulana), rhesus monkey (Macaca mulatta), and humpback whale (Megaptera novaeanglia), with both additive white Gaussian noise and environment recording noise added across a range of signal-to-noise ratios (SNRs). Results, measured by both SNR and segmental SNR of the enhanced wave forms, indicate that the proposed method outperforms other approaches for a wide range of noise conditions

Elastic net hypergraph learning for image clustering and semi-supervised classification

© 1992-2012 IEEE. Graph model is emerging as a very effective tool for learning the complex structures and relationships hidden in data. In general, the critical purpose of graph-oriented learning algorithms is to construct an informative graph for image clustering and classification tasks. In addition to the classical K -nearest-neighbor and r-neighborhood methods for graph construction, l1-graph and its variants are emerging methods for finding the neighboring samples of a center datum, where the corresponding ingoing edge weights are simultaneously derived by the sparse reconstruction coefficients of the remaining samples. However, the pairwise links of l1-graph are not capable of capturing the high-order relationships between the center datum and its prominent data in sparse reconstruction. Meanwhile, from the perspective of variable selection, the l1 norm sparse constraint, regarded as a LASSO model, tends to select only one datum from a group of data that are highly correlated and ignore the others. To simultaneously cope with these drawbacks, we propose a new elastic net hypergraph learning model, which consists of two steps. In the first step, the robust matrix elastic net model is constructed to find the canonically related samples in a somewhat greedy way, achieving the grouping effect by adding the l2 penalty to the l1 constraint. In the second step, hypergraph is used to represent the high order relationships between each datum and its prominent samples by regarding them as a hyperedge. Subsequently, hypergraph Laplacian matrix is constructed for further analysis. New hypergraph learning algorithms, including unsupervised clustering and multi-class semi-supervised classification, are then derived. Extensive experiments on face and handwriting databases demonstrate the effectiveness of the proposed method

Mitigating laser imprint with a foam overcoating

Foam has been suggested to reduce laser imprint because of its low density. In this paper, the two-dimensional radiation hydrodynamic code FLASH is applied to investigate and characterize the strength of laser imprint through analyzing areal density perturbation. There are two important factors for the mitigation of laser imprint besides the thermal smoothing of the conduction region (between the ablation front and the critical density surface) and the mass ablation of the ablation front. First, radiation ablation dynamically modulates density distribution not only to increase the frequency of the perturbed ablation front oscillation but also to decrease the amplitude of oscillation. Second, a larger length of the shocked compression region reduces the amplitude of the perturbed shock front oscillation. The smaller the perturbation of both ablation front and shock front, the smaller the areal density perturbation. Based on the above physical mechanisms, the optimal way of mitigating laser imprint with foam is that the dynamically modulated density distribution further reduces the amplitude of perturbation reaching the solid CH when the areal density perturbation of foam oscillates to the first minimum value. The optimal ranges of foam parameters to mitigate laser imprint are proposed with the aid of dimensional analysis: the foam thickness is about 2~3 times the perturbation wavelength, and the foam density is about 1/2~3/2 times the mass density corresponding to the critical density

Evaluating quasilocal energy and solving optimal embedding equation at null infinity

We study the limit of quasilocal energy defined in [7] and [8] for a family of spacelike 2-surfaces approaching null infinity of an asymptotically flat spacetime. It is shown that Lorentzian symmetry is recovered and an energy-momentum 4-vector is obtained. In particular, the result is consistent with the Bondi-Sachs energy-momentum at a retarded time. The quasilocal mass in [7] and [8] is defined by minimizing quasilocal energy among admissible isometric embeddings and observers. The solvability of the Euler-Lagrange equation for this variational problem is also discussed in both the asymptotically flat and asymptotically null cases. Assuming analyticity, the equation can be solved and the solution is locally minimizing in all orders. In particular, this produces an optimal reference hypersurface in the Minkowski space for the spatial or null exterior region of an asymptotically flat spacetime.Comment: 22 page

In-shoe plantar prressure measurement and analysis system based on fabric pressure sensing array

Author name used in this publication: David Dagan Feng2009-2010 > Academic research: refereed > Publication in refereed journalVersion of RecordPublishe