Deep learning is a research hot topic in the field of machine learning. Real-value neural networks (Real NNs), especially deep real networks (DRNs), have been widely used in many research fields. In recent years, the deep complex networks (DCNs) and the deep quaternion networks (DQNs) have attracted more and more attentions. The octonion algebra, which is an extension of complex algebra and quaternion algebra, can provide more efficient and compact expression. This paper constructs a general framework of deep octonion networks (DONs) and provides the main building blocks of DONs such as octonion convolution, octonion batch normalization and octonion weight initialization; DONs are then used in image classification tasks for CIFAR-10 and CIFAR-100 data sets. Compared with the DRNs, the DCNs, and the DQNs, the proposed DONs have better convergence and higher classification accuracy. The success of DONs is also explained by multi-task learning. IntroductionReal-value neural networks (Real NNs) [1][2][3][4][5][6][7][8][9][10][11][12] attracted the attention of many researchers and recently made major breakthroughs in many areas such as signal processing, image processing, natural language processing, etc.Many models of Real NNs have been constructed in the literature. These models can generally be categorized into two kinds: non-deep models and deep models. The non-deep models are mainly constructed by multilayer perceptron module [13] and hard to train, if we only use the real-valued back propagation (BP) algorithm [14], when their layers are larger than 4. The deep models can be roughly constructed by the following two strategies: multilayer perceptron models assisted by the unsupervised pretrained methods (for example, deep belief nets [15], deep auto-encoder [16], etc.) and real-value convolutional neural networks (Real CNNs), including LeNet-5 [17], AlexNet [18], Inception [19-22], VGGNet [23], HighwayNet [24], ResNet [25], ResNeXt [26], DenseNet [27], FractalNet [28], PolyNet [29], SENet [30], CliqueNet [31], BinaryNet [32], SqueezeNet [33], MobileNet [34], etc.Although Real CNNs have achieved great success in various applications, the correlations between convolution kernels generally do not take into consideration, that is, there are no connections or no special relationships considering between convolution kernels. The opposite of Real CNNs is real-value recurrent neural networks (Real RNNs) [35][36][37][38], who obtain the correlations by adding the connections between convolution kernels and then learn the weights of these connections, which, however, increased significantly the training difficulty and was easier to encounter converge problems. The first question has been raised: Can we consider the correlations between convolution kernels by some special relationships, which do not need to learn, instead of adding the connections between convolution kernels?Many researchers find that the performance can be improved when the relationships between convolution kernels are modeled by complex algebra, quaterni...
One of the key challenges in the area of signal processing on graphs is to design transforms and dictionary methods to identify and exploit structure in signals on weighted graphs. In this paper, we first generalize graph Fourier transform (GFT) to spectral graph fractional Fourier transform (SGFRFT), which is then used to define a novel transform named spectral graph fractional wavelet transform (SGFRWT), which is a generalized and extended version of spectral graph wavelet transform (SGWT). A fast algorithm for SGFRWT is also derived and implemented based on Fourier series approximation. Some potential applications of SGFRWT are also presented.
Background: The micro-autologous fat transplantation (MAFT) technique has demonstrated its feasibility in multiple medical fields, such as facial rejuvenation. Advanced platelet-rich fibrin (APRF), an autologous platelet concentrated on a fibrin membrane without added external factors, has shown significant potential for tissue restoration. However, the role of APRF in the modulation of MAFT remains unclear. Here, we aimed to explore the effect of APRF on MAFT. Methods: Adipose-derived stem cells (ASCs) were isolated from human gastric subcutaneous fat and treated with APRF. ELISA assays measured cytokines. The proliferation of ASCs was analyzed by CCK-8 assays. The levels of hypoxia-inducible factor-1α (HIF-1α), heat shock protein 70 (HSP70), insulin like growth factor 2 (IGF-2), interleukin-6 (IL-6), interleukin-8 (IL-8), and vascular endothelial growth factor (VEGF) were measured by ELISA assays, quantitative reverse transcription-PCR (qRT-PCR), and Western blot analysis. The effect of APRF/HIF-1α/VEGF on MAFT in vivo was analyzed in Balb/c nude mice. The BALB/c mice were subcutaneously co-transplanted with fat, APRF, and control shRNA, HIF-1α shRNA, or VEGF shRNA into the dorsal area. The serum and protein levels of the above cytokines were analyzed by ELISA assays and Western blot analysis. Lipid accumulation was measured by Oil Red O staining. The expression of CD34 was assessed by immunohistochemical staining.Results: APRF continuously secreted multiple cytokines, including epidermal growth factor (EGF), FGF-2, insulin like growth factor 1 (IGF-1), interleukin-1beta (IL-1β), interleukin-4 (IL-4), platelet-derived growth factor alpha polypeptide b (PDGF-AB), platelet-derived growth factor beta polypeptide b (PDGF-BB), transforming growth factor-beta (TGF-β), and VEGF. APRF was able to promote the proliferation of ASCs.
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