Recent advances in deep learning have enabled us to address the curse of dimensionality (COD) by solving problems in higher dimensions. A subset of such approaches of addressing the COD has led us to solving high-dimensional PDEs. This has resulted in opening doors to solving a variety of real-world problems ranging from mathematical finance to stochastic control for industrial applications. Although feasible, these deep learning methods are still constrained by training time and memory. Tackling these shortcomings, Tensor Neural Networks (TNN) demonstrate that they can provide significant parameter savings while attaining the same accuracy as compared to the classical Dense Neural Network (DNN). In addition, we also show how TNN can be trained faster than DNN for the same accuracy. Besides TNN, we also introduce Tensor Network Initializer (TNN Init), a weight initialization scheme that leads to faster convergence with smaller variance for an equivalent parameter count as compared to a DNN. We benchmark TNN and TNN Init by applying them to solve the parabolic PDE associated with the Heston model, which is widely used in financial pricing theory.

部分微分方程（PDE）用于对科学和工程中的各种动力系统进行建模。深度学习的最新进展使我们能够以新的方式解决维度的诅咒，从而在更高的维度中解决它们。但是，深度学习方法受到训练时间和记忆的约束。为了解决这些缺点，我们实施了张量神经网络（TNN），这是一种量子启发的神经网络体系结构，利用张量网络的想法来改进深度学习方法。我们证明，与经典密集神经网络（DNN）相比，TNN提供了明显的参数节省，同时获得了与经典密集的神经网络相同的准确性。此外，我们还展示了如何以相同的精度来比DNN更快地训练TNN。我们通过将它们应用于求解抛物线PDE，特别是Black-Scholes-Barenblatt方程，该方程广泛用于金融定价理论，基于基准测试。还讨论了进一步的例子，例如汉密尔顿 - 雅各比 - 贝尔曼方程。

Objective: Despite numerous studies proposed for audio restoration in the literature, most of them focus on an isolated restoration problem such as denoising or dereverberation, ignoring other artifacts. Moreover, assuming a noisy or reverberant environment with limited number of fixed signal-to-distortion ratio (SDR) levels is a common practice. However, real-world audio is often corrupted by a blend of artifacts such as reverberation, sensor noise, and background audio mixture with varying types, severities, and duration. In this study, we propose a novel approach for blind restoration of real-world audio signals by Operational Generative Adversarial Networks (Op-GANs) with temporal and spectral objective metrics to enhance the quality of restored audio signal regardless of the type and severity of each artifact corrupting it. Methods: 1D Operational-GANs are used with generative neuron model optimized for blind restoration of any corrupted audio signal. Results: The proposed approach has been evaluated extensively over the benchmark TIMIT-RAR (speech) and GTZAN-RAR (non-speech) datasets corrupted with a random blend of artifacts each with a random severity to mimic real-world audio signals. Average SDR improvements of over 7.2 dB and 4.9 dB are achieved, respectively, which are substantial when compared with the baseline methods. Significance: This is a pioneer study in blind audio restoration with the unique capability of direct (time-domain) restoration of real-world audio whilst achieving an unprecedented level of performance for a wide SDR range and artifact types. Conclusion: 1D Op-GANs can achieve robust and computationally effective real-world audio restoration with significantly improved performance. The source codes and the generated real-world audio datasets are shared publicly with the research community in a dedicated GitHub repository1.

Continuous long-term monitoring of motor health is crucial for the early detection of abnormalities such as bearing faults (up to 51% of motor failures are attributed to bearing faults). Despite numerous methodologies proposed for bearing fault detection, most of them require normal (healthy) and abnormal (faulty) data for training. Even with the recent deep learning (DL) methodologies trained on the labeled data from the same machine, the classification accuracy significantly deteriorates when one or few conditions are altered. Furthermore, their performance suffers significantly or may entirely fail when they are tested on another machine with entirely different healthy and faulty signal patterns. To address this need, in this pilot study, we propose a zero-shot bearing fault detection method that can detect any fault on a new (target) machine regardless of the working conditions, sensor parameters, or fault characteristics. To accomplish this objective, a 1D Operational Generative Adversarial Network (Op-GAN) first characterizes the transition between normal and fault vibration signals of (a) source machine(s) under various conditions, sensor parameters, and fault types. Then for a target machine, the potential faulty signals can be generated, and over its actual healthy and synthesized faulty signals, a compact, and lightweight 1D Self-ONN fault detector can then be trained to detect the real faulty condition in real time whenever it occurs. To validate the proposed approach, a new benchmark dataset is created using two different motors working under different conditions and sensor locations. Experimental results demonstrate that this novel approach can accurately detect any bearing fault achieving an average recall rate of around 89% and 95% on two target machines regardless of its type, severity, and location.

Gathering properly labelled, adequately rich, and case-specific data for successfully training a data-driven or hybrid model for structural health monitoring (SHM) applications is a challenging task. We posit that a Transfer Learning (TL) method that utilizes available data in any relevant source domain and directly applies to the target domain through domain adaptation can provide substantial remedies to address this issue. Accordingly, we present a novel TL method that differentiates between the source's no-damage and damage cases and utilizes a domain adaptation (DA) technique. The DA module transfers the accumulated knowledge in contrasting no-damage and damage cases in the source domain to the target domain, given only the target's no-damage case. High-dimensional features allow employing signal processing domain knowledge to devise a generalizable DA approach. The Generative Adversarial Network (GAN) architecture is adopted for learning since its optimization process accommodates high-dimensional inputs in a zero-shot setting. At the same time, its training objective conforms seamlessly with the case of no-damage and damage data in SHM since its discriminator network differentiates between real (no damage) and fake (possibly unseen damage) data. An extensive set of experimental results demonstrates the method's success in transferring knowledge on differences between no-damage and damage cases across three strongly heterogeneous independent target structures. The area under the Receiver Operating Characteristics curves (Area Under the Curve - AUC) is used to evaluate the differentiation between no-damage and damage cases in the target domain, reaching values as high as 0.95. With no-damage and damage cases discerned from each other, zero-shot structural damage detection is carried out. The mean F1 scores for all damages in the three independent datasets are 0.978, 0.992, and 0.975.

As the interest to Graph Neural Networks (GNNs) is growing, the importance of benchmarking and performance characterization studies of GNNs is increasing. So far, we have seen many studies that investigate and present the performance and computational efficiency of GNNs. However, the work done so far has been carried out using a few high-level GNN frameworks. Although these frameworks provide ease of use, they contain too many dependencies to other existing libraries. The layers of implementation details and the dependencies complicate the performance analysis of GNN models that are built on top of these frameworks, especially while using architectural simulators. Furthermore, different approaches on GNN computation are generally overlooked in prior characterization studies, and merely one of the common computational models is evaluated. Based on these shortcomings and needs that we observed, we developed a benchmark suite that is framework independent, supporting versatile computational models, easily configurable and can be used with architectural simulators without additional effort. Our benchmark suite, which we call gSuite, makes use of only hardware vendor's libraries and therefore it is independent of any other frameworks. gSuite enables performing detailed performance characterization studies on GNN Inference using both contemporary GPU profilers and architectural GPU simulators. To illustrate the benefits of our new benchmark suite, we perform a detailed characterization study with a set of well-known GNN models with various datasets; running gSuite both on a real GPU card and a timing-detailed GPU simulator. We also implicate the effect of computational models on performance. We use several evaluation metrics to rigorously measure the performance of GNN computation.

Communication and computation are often viewed as separate tasks. This approach is very effective from the perspective of engineering as isolated optimizations can be performed. On the other hand, there are many cases where the main interest is a function of the local information at the devices instead of the local information itself. For such scenarios, information theoretical results show that harnessing the interference in a multiple-access channel for computation, i.e., over-the-air computation (OAC), can provide a significantly higher achievable computation rate than the one with the separation of communication and computation tasks. Besides, the gap between OAC and separation in terms of computation rate increases with more participating nodes. Given this motivation, in this study, we provide a comprehensive survey on practical OAC methods. After outlining fundamentals related to OAC, we discuss the available OAC schemes with their pros and cons. We then provide an overview of the enabling mechanisms and relevant metrics to achieve reliable computation in the wireless channel. Finally, we summarize the potential applications of OAC and point out some future directions.

An activation function has a significant impact on the efficiency and robustness of the neural networks. As an alternative, we evolved a cutting-edge non-monotonic activation function, Negative Stimulated Hybrid Activation Function (Nish). It acts as a Rectified Linear Unit (ReLU) function for the positive region and a sinus-sigmoidal function for the negative region. In other words, it incorporates a sigmoid and a sine function and gaining new dynamics over classical ReLU. We analyzed the consistency of the Nish for different combinations of essential networks and most common activation functions using on several most popular benchmarks. From the experimental results, we reported that the accuracy rates achieved by the Nish is slightly better than compared to the Mish in classification.

恢复质量差的图像与一组混合伪影对于可靠的诊断起着至关重要的作用。现有的研究集中在特定的恢复问题上，例如图像过度，去核和暴露校正，通常对伪影类型和严重性有很强的假设。作为盲X射线恢复的先驱研究，我们提出了一个通用图像恢复和分类的联合模型：恢复分类为分类的生成对抗网络（R2C-GAN）。这种共同优化的模型使恢复后保持任何疾病完整。因此，由于X射线图像质量的提高，这自然会导致更高的诊断性能。为了实现这一关键目标，我们将恢复任务定义为图像到图像的翻译问题，从差异，模糊或暴露不足/暴露不足的图像到高质量的图像域。提出的R2C-GAN模型能够使用未配对的训练样本在两个域之间学习前进和逆变换。同时，联合分类在恢复过程中保留了疾病标签。此外，R2C-GAN配备了操作层/神经元，可降低网络深度，并进一步增强恢复和分类性能。拟议的联合模型对2019年冠状病毒病（COVID-19）分类的卡塔-COV19数据集进行了广泛的评估。拟议的恢复方法达到了90％以上的F1得分，这显着高于任何深层模型的性能。此外，在定性分析中，R2C-GAN的恢复性能得到了一群医生的批准。我们在https://github.com/meteahishali/r2c-gan上共享软件实施。

在这项研究中，提出了用于实现连续值梯度聚合的数字空地计算方案。结果表明，可以使用相应的数字的平均值来计算一组实价参数的平均值，其中数字是根据平衡数字系统获得的。通过使用此属性，提出的方案将局部梯度编码为一组数字。然后，它通过使用数字值来确定激活的正交频分多路复用（OFDM）子载波的位置。为了消除需要精确的样本级时同步，通道估计开销和由于通道倒置而引起的功率不稳定性，提出的方案还使用Edge Server（ES）的非连接接收器，并且不利用Pre-Pre-Pre-pre-pre-边缘设备（EDS）处的均等化。最后，得出了所提出的方案的理论均衡误差（MSE）性能，并展示了其在联合边缘学习（FEES）的性能。