Differentiable Programming Tensor Networks

Differentiable programming is a fresh programming paradigm which composes parameterized algorithmic components and trains them using automatic differentiation (AD). The concept emerges from deep learning but is not only limited to training neural networks. We present theory and practice of programming tensor network algorithms in a fully differentiable way. By formulating the tensor network algorithm as a computation graph, one can compute higher order derivatives of the program accurately and efficiently using AD. We present essential techniques to differentiate through the tensor networks contractions, including stable AD for tensor decomposition and efficient backpropagation through fixed point iterations. As a demonstration, we compute the specific heat of the Ising model directly by taking the second order derivative of the free energy obtained in the tensor renormalization group calculation. Next, we perform gradient based variational optimization of infinite projected entangled pair states for quantum antiferromagnetic Heisenberg model and obtain start-of-the-art variational energy and magnetization with moderate efforts. Differentiable programming removes laborious human efforts in deriving and implementing analytical gradients for tensor network programs, which opens the door to more innovations in tensor network algorithms and applications.Comment: Typos corrected, discussion and refs added; revised version accepted for publication in PRX. Source code available at https://github.com/wangleiphy/tensorgra

Dynamical self-assembly of dipolar active Brownian particles in two dimensions

Based on Brownian Dynamics (BD) simulations, we study the dynamical self-assembly of active Brownian particles with dipole–dipole interactions, stemming from a permanent point dipole at the particle center. The propulsion direction of each particle is chosen to be parallel to its dipole moment. We explore a wide range of motilities and dipolar coupling strengths and characterize the corresponding behavior based on several order parameters. At low densities and low motilities, the most important structural phenomenon is the aggregation of the dipolar particles into chains. Upon increasing the particle motility, these chain-like structures break, and the system transforms into a weakly correlated isotropic fluid. At high densities, we observe that the motility-induced phase separation is strongly suppressed by the dipolar coupling. Once the dipolar coupling dominates the thermal energy, the phase separation disappears, and the system rather displays a flocking state, where particles form giant clusters and move collective along one direction. We provide arguments for the emergence of the flocking behavior, which is absent in the passive dipolar system.TU Berlin, Open-Access-Mittel - 2020DFG, 65143814, GRK 1524: Self-Assembled Soft-Matter Nanostructures at Interface

MIMO-OFDM channel estimation in the presence of carrier frequency offset

A multiple-input multiple-output (MIMO) wireless communication system with orthogonal frequency division multiplexing (OFDM) is expected to be a promising scheme. However, the estimation of the carrier frequency offset (CFO) and the channel parameters is a great challenging task. In this paper, a maximum-likelihood- (ML-) based algorithm is proposed to jointly estimate the frequency-selective channels and the CFO in MIMO-OFDM by using a block-type pilot. The proposed algorithm is capable of dealing with the CFO range nearly ±1/2 useful OFDM signal bandwidth. Furthermore, the cases with timing error and unknown channel order are discussed. The Cramér-Rao bound (CRB) for the problem is developed to evaluate the performance of the algorithm. Computer simulations show that the proposed algorithm can exploit the gain from multiantenna to improve effectively the estimation performance and achieve the CRB in high signal-to-noise ratio (SNR). © 2005 Hindawi Publishing Corporation

An Edge-Preserved Image Denoising Algorithm Based on Local Adaptive Regularization

Image denoising methods are often based on the minimization of an appropriately defined energy function. Many gradient dependent energy functions, such as Potts model and total variation denoising, regard image as piecewise constant function. In these methods, some important information such as edge sharpness and location is well preserved, but some detailed image feature like texture is often compromised in the process of denoising. For this reason, an image denoising method based on local adaptive regularization is proposed in this paper, which can adaptively adjust denoising degree of noisy image by adding spatial variable fidelity term, so as to better preserve fine scale features of image. Experimental results show that the proposed denoising method can achieve state-of-the-art subjective visual effect, and the signal-noise-ratio (SNR) is also objectively improved by 0.3–0.6 dB

Astrocyte elevated gene-1 (AEG-1) is a marker for aggressive salivary gland carcinoma

<p>Abstract</p> <p>Background</p> <p>Astrocyte elevated gene-1 (AEG-1) is associated with tumorigenesis and progression in diverse human cancers. The present study was aimed to investigate the clinical and prognostic significance of AEG-1 in salivary gland carcinomas (SGC).</p> <p>Methods</p> <p>Real-time PCR and western blot analyses were employed to examine AEG-1 expression in two normal salivary gland tissues, eight SGC tissues of various clinical stages, and five pairs of primary SGC and adjacent salivary gland tissues from the same patient. Immunohistochemistry (IHC) was performed to examine AEG-1 protein expression in paraffin-embedded tissues from 141 SGC patients. Statistical analyses was applies to evaluate the diagnostic value and associations of AEG-1 expression with clinical parameters.</p> <p>Results</p> <p>AEG-1 expression was evidently up-regulated in SGC tissues compared with that in the normal salivary gland tissues and in matched adjacent salivary gland tissues. AEG-1 protein level was positively correlated with clinical stage (<it>P </it>< 0.001), T classification (<it>P </it>= 0.008), N classification (<it>P </it>= 0.008) and M classifications (<it>P </it>= 0.006). Patients with higher AEG-1 expression had shorter overall survival time, whereas those with lower tumor AEG-1 expression had longer survival time.</p> <p>Conclusions</p> <p>Our results suggest that AEG-1 expression is associated with SGC progression and may represent a novel and valuable predictor for prognostic evaluation of SGC patients.</p