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Register a new userTwo-dimensional nonseparable discrete linear canonical transform based on CM-CC-CM-CC decomposition
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As a generalization of the two-dimensional Fourier transform (2D FT) and 2D fractional Fourier transform, the 2D nonseparable linear canonical transform (2D NsLCT) is useful in optics, signal and image processing. To reduce the digital implementation complexity of the 2D NsLCT, some previous works decomposed the 2D NsLCT into several low-complexity operations, including 2D FT, 2D chirp multiplication (2D CM) and 2D affine transformations. However, 2D affine transformations will introduce interpolation error. In this paper, we propose a new decomposition called CM-CC-CM-CC decomposition, which decomposes the 2D NsLCT into two 2D CMs and two 2D chirp convolutions (2D CCs). No 2D affine transforms are involved. Simulation results show that the proposed methods have higher accuracy, lower computational complexity and smaller error in the additivity property compared with the previous works. Plus, the proposed methods have perfect reversibility property that one can reconstruct the input signal/image losslessly from the output.
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In this paper, a discrete LCT (DLCT) irrelevant to the sampling periods and without oversampling operation is developed. This DLCT is based on the well-known CM-CC-CM decomposition, that is, implemented by two discrete chirp multiplications (CMs) and one discrete chirp convolution (CC). This decomposition doesnt use any scaling operation which will change the sampling period or cause the interpolation error. Compared with previous works, DLCT calculated by direct summation and DLCT based on center discrete dilated Hermite functions (CDDHFs), the proposed method implemented by FFTs has much lower computational complexity. The relation between the proposed DLCT and the continuous LCT is also derived to approximate the samples of the continuous LCT. Simulation results show that the proposed method somewhat outperforms the CDDHFs-based method in the approximation accuracy. Besides, the proposed method has approximate additivity property with error as small as the CDDHFs-based method. Most importantly, the proposed method has perfect reversibility, which doesnt hold in many existing DLCTs. With this property, it is unnecessary to develop the inverse DLCT additionally because it can be replaced by the forward DLCT.
We calculate the semileptonic and a subclass of sixteen nonleptonic two-body decays of the double charm baryon ground states $Xi_{cc}^{++},,Xi_{cc}^{+}$ and $Omega_{cc}^+$ where we concentrate on the nonleptonic decay modes. We identify those nonleptonic decay channels in which the decay proceeds solely via the factorizing contribution precluding a contamination from $W$-exchange. We use the covariant confined quark model previously developed by us to calculate the various helicity amplitudes which describe the dynamics of the $1/2^+ to 1/2^+$ and $1/2^+ to 3/2^+$ transitions induced by the Cabibbo favored effective $(c to s)$ and $(d to u)$ currents. We then proceed to calculate the rates of the decays as well as polarization effects and angular decay distributions of the prominent decay chains resulting from the nonleptonic decays of the double heavy charm baryon parent states.
Fabry-Perot cavities are central to many optical measurement systems. In high precision experiments, such as aLIGO and AdV, coupled cavities are often required leading to complex optical dynamics, particularly when optical imperfections are considered. We show, for the first time, that discrete LCTs can be used to compute circulating optical fields for cavities in which the optics have arbitrary apertures, reflectance and transmittance profiles, and shape. We compare the predictions of LCT models with those of alternative methods. To further highlight the utility of the LCT, we present a case study of point absorbers on the aLIGO mirrors and compare with recently published results.
The loss function is a key component in deep learning models. A commonly used loss function for classification is the cross entropy loss, which is a simple yet effective application of information theory for classification problems. Based on this loss, many other loss functions have been proposed,~emph{e.g.}, by adding intra-class and inter-class constraints to enhance the discriminative ability of the learned features. However, these loss functions fail to consider the connections between the feature distribution and the model structure. Aiming at addressing this problem, we propose a channel correlation loss (CC-Loss) that is able to constrain the specific relations between classes and channels as well as maintain the intra-class and the inter-class separability. CC-Loss uses a channel attention module to generate channel attention of features for each sample in the training stage. Next, an Euclidean distance matrix is calculated to make the channel attention vectors associated with the same class become identical and to increase the difference between different classes. Finally, we obtain a feature embedding with good intra-class compactness and inter-class separability.Experimental results show that two different backbone models trained with the proposed CC-Loss outperform the state-of-the-art loss functions on three image classification datasets.
In this work we study the weak decays of $Xi_{cc}toXi_c$ and $Xi_{cc}toXi_c$ in the light-front quark model. Generally, a naive, but reasonable conjecture suggests that the $cc$ subsystem in $Xi_{cc}$ ( $us$ pair in $Xi^{()}_c$) stands as a diquark with definite spin and color assignments. During the concerned processes, the diquark of the initial state is not a spectator, and must be broken. A Racah transformation would decompose the original $(cc)q$ into a combination of $c(cq)$ components. Thus we may deal with the decaying $c$ quark alone while keeping the $(cq)$ subsystem as a spectator. With the re-arrangement of the inner structure we calculate the form factors numerically and then obtain the rates of semi-leptonic decays and non-leptonic decays, which will be measured in the future.
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