Statistical Optimality of Deep Wide Neural Networks

In this paper, we consider the generalization ability of deep wide feedforward ReLU neural networks defined on a bounded domain $\mathcal X \subset \mathbb R^{d}$. We first demonstrate that the generalization ability of the neural network can be fully characterized by that of the corresponding deep neural tangent kernel (NTK) regression. We then investigate on the spectral properties of the deep NTK and show that the deep NTK is positive definite on $\mathcal{X}$ and its eigenvalue decay rate is $(d+1)/d$. Thanks to the well established theories in kernel regression, we then conclude that multilayer wide neural networks trained by gradient descent with proper early stopping achieve the minimax rate, provided that the regression function lies in the reproducing kernel Hilbert space (RKHS) associated with the corresponding NTK. Finally, we illustrate that the overfitted multilayer wide neural networks can not generalize well on $\mathbb S^{d}$. We believe our technical contributions in determining the eigenvalue decay rate of NTK on $\mathbb R^{d}$ might be of independent interests

Beyond Fairness: Age-Harmless Parkinson's Detection via Voice

Parkinson's disease (PD), a neurodegenerative disorder, often manifests as speech and voice dysfunction. While utilizing voice data for PD detection has great potential in clinical applications, the widely used deep learning models currently have fairness issues regarding different ages of onset. These deep models perform well for the elderly group (age $>$ 55) but are less accurate for the young group (age $\leq$ 55). Through our investigation, the discrepancy between the elderly and the young arises due to 1) an imbalanced dataset and 2) the milder symptoms often seen in early-onset patients. However, traditional debiasing methods are impractical as they typically impair the prediction accuracy for the majority group while minimizing the discrepancy. To address this issue, we present a new debiasing method using GradCAM-based feature masking combined with ensemble models, ensuring that neither fairness nor accuracy is compromised. Specifically, the GradCAM-based feature masking selectively obscures age-related features in the input voice data while preserving essential information for PD detection. The ensemble models further improve the prediction accuracy for the minority (young group). Our approach effectively improves detection accuracy for early-onset patients without sacrificing performance for the elderly group. Additionally, we propose a two-step detection strategy for the young group, offering a practical risk assessment for potential early-onset PD patients

Experimental determination of forces applied by liquid water drops at high drop velocities impacting a glass plate with and without a shallow water layer using wavelet deconvolution

Time-dependent forces applied by 2 and 4.5 mm diameter drops of water (with velocities up to terminal velocity) impacting upon a glass plate with or without a water layer (up to 10 mm depth) have been measured using two different approaches, force transduction and wavelet deconvolution. Both approaches are in close agreement for drops falling on dry glass. However, only the wavelet approach is able to measure natural features of the splash on shallow water layers that impart forces to the plate after the initial impact. At relatively high velocities (including terminal velocity) the measured peak force from the initial impact is significantly higher than that predicted by idealised drop shape models and models from Roisman et al. and Marengo et al. Hence empirical formulae are developed for the initial time-dependent impact force from drops falling at (a) different velocities up to and including terminal velocity onto a dry glass surface, (b) terminal velocity onto dry glass or glass with a water layer and (c) different velocities below terminal velocity onto dry glass or glass with a water layer. For drops on dry glass, the empirical formulae are applicable to a glass plate or a composite layered plate with a glass surface, although they apply to other plate thicknesses and are applicable to any plate material with a similar surface roughness and wettability. The measurements also indicate that after the initial impact there can be high level forces when bubbles are entrained in the water layer

Phycocyanin relieves myocardial ischemia-reperfusion injury in rats by inhibiting oxidative stress

Purpose: To investigate the effect of phycocyanin on myocardial ischemia-reperfusion injury, and the possible mechanisms involved. Methods: Twenty-four Sprague-Dawley (SD) rats were randomly divided into Sham group (only threading without ligation), IRI group (myocardial ischemia-reperfusion injury group) and phycocyanin group (phycocyanin pretreatment + myocardial ischemia-reperfusion injury group). The heart was harvested and cardiomyocytes were isolated. Colorimetry was used to determine the contents of cardiomyocyte serum creatine phospho-MB (CK-MB), lactate dehydrogenase (LDH) and malondialdehyde (MDA), and the activities of total antioxidant capacity (T-AOC), catalase (CAT), glutathione (GSH), total superoxide dismutase (SOD) and other related oxidative stress indicators. Furthermore, apoptosis was evaluated using TUNEL staining. Protein levels of cardiac factor E2 related factor 2 (Nrf2), heme oxygenase-1 (HO-1), human NADPH dehydrogenase 1 (NQO1) and nuclear factor-κB (NF-κB) were evaluated by Western blot and immunohistochemistry. Results: Compared with the myocardial IRI group, the contents of CK-MB, LDH, MAD and ROS in the treated group were significantly decreased (p < 0.05), but the activities of SOD, GSH, SOD, CAT, and T-AOC in the myocardial tissues were significantly enhanced (p < 0.05). Moreover, the pathological changes in myocardial tissue were significantly reduced. In addition, the expression levels of Nrf2, HO-1 and NQO-1 were significantly up-regulated after phycocyanin pretreatment, while expression of NF-κB was significantly down-regulated (p < 0.05). Conclusion: Phycocyanin improves myocardial anti-oxidative stress via activation of Nrf2 signaling pathway, and also protects rats from myocardial ischemia-reperfusion injury by reducing inflammatory response via inhibition of NF-κB signaling pathway

Study of defects in directed energy deposited Vanadis 4 Extra tool steel

A cold work tool steel with varied number of layers was deposited on a substrate of hot work tool steel for hard-facing by directed energy deposition technique. This study deals with the defects and microstructure in the as-cladded tool steels. Defects, including pores and cracks, were found in the deposited zone, the number of which increased with the building height or number of layers deposited. Large irregular pores were mainly located at the lower regions of the deposited layers. The formation of this type of pores was attributed to the segregation of alloy elements on the pore surface and insufficient heat input. Non-equilibrium eutectic microstructure was a characteristic feature in the regions adjacent to the pores. Cracking, on the other hand, tended to occur in the upper part of the deposited layers. Two important contributing factors were identified for cracking. The first one was the microstructural gradient, which was modified from fine cellular dendrite to columnar dendrite when moving from the bottom to the top deposited layer. Second, the deposited cold work tool steel exhibited a relatively large temperature range of solidification, as simulated by Thermocalc software, leading to high sensitivity to hot cracking

Time and temperature dependent softening of a novel maraging steel fabricated by laser metal deposition

Durability is a critical factor for hot stamping dies from an economic point of view. Refurbishing the dies by depositing new material instead of replacement is a promising method to reduce the cost. For this reason, a newly developed maraging steel (NMS) was cladded on a hot work tool steel by means of directed energy deposition. After an optimized tempering, exposures at high temperatures were carried out on the cladded NMS in order to examine the softening resistance. The microstructural evolution of the material was systematically characterized using a combination of optical microscopy (OM), X-ray diffraction (XRD), scanning electron microscopy (SEM), Auger electron spectroscopy (AES) and transmission electron microscopy (TEM). The precipitate in the cladded steel was identified as Laves phase. The coarsening of this phase is considered as the main reason for the thermal softening of the steel at high temperatures. The coarsening behavior was also simulated by using the revised Langer-Schwartz-Wagner (LSW) model, which was in good agreement with experimental observations. Moreover, a mathematical model of precipitate strengthening was successfully applied to evaluate the softening behavior of the steel. This model can be used to predict the hardness/strength evolution of the investigated tool steel during its high-temperature service

Displacement mechanism of polymeric surfactant in chemical cold flooding for heavy oil based on microscopic visualization experiments

 In order to study the microscopic oil displacement mechanism of polymeric surfactant in chemical cold flooding for heavy oil, the indoor microscopic visualization displacement experiments were carried out. The flooding experiment of heavy oil was conducted by using water, osmotic modified oil displacing agent (a kind of polymeric surfactant) and water-in-oil emulsion (obtained by mixing polymeric surfactant and heavy oil) as displacing phases to study the mechanism of polymeric surfactant to enhance oil recovery in heavy oil reservoir. The experimental results show that the polymeric surfactant can increase the viscosity of the water phase, reduce the water-oil mobility ratio, expand the swept area, and there is no obvious fingering phenomenon which occurs during water flooding. The polymeric surfactant has the surfactant characteristics which can reduce the interfacial tension between oil and water to promote the formation of oil droplets with smaller droplet diameter. And the interfacial film composed of polymeric surfactant molecules will be formed on the surface of oil droplets to prevent the coalescence of oil droplets and improve the flow ability of oil phase. The water-in-oil emulsion can be miscible with the oil in heavy oil displacement process, and thus sweeps the areas such as the dead pores which cannot be swept by water and polymeric surfactant flooding, which increases the sweep efficiency to a certain extent.Cited as: Xu, F., Chen, Q., Ma, M., Wang, Y., Yu, F., Li, J. Displacement mechanism of polymeric surfactant in chemical cold flooding for heavy oil based on microscopic visualization experiments. Advances in Geo-Energy Research, 2020, 4(1): 77-85, doi: 10.26804/ager.2020.01.0