Learning Two-layer Neural Networks with Symmetric Inputs

We give a new algorithm for learning a two-layer neural network under a general class of input distributions. Assuming there is a ground-truth two-layer network $$y = A \sigma(Wx) + \xi,$$ where $A,W$ are weight matrices, $\xi$ represents noise, and the number of neurons in the hidden layer is no larger than the input or output, our algorithm is guaranteed to recover the parameters $A,W$ of the ground-truth network. The only requirement on the input $x$ is that it is symmetric, which still allows highly complicated and structured input. Our algorithm is based on the method-of-moments framework and extends several results in tensor decompositions. We use spectral algorithms to avoid the complicated non-convex optimization in learning neural networks. Experiments show that our algorithm can robustly learn the ground-truth neural network with a small number of samples for many symmetric input distributions

Stabilized SVRG: Simple Variance Reduction for Nonconvex Optimization

Variance reduction techniques like SVRG provide simple and fast algorithms for optimizing a convex finite-sum objective. For nonconvex objectives, these techniques can also find a first-order stationary point (with small gradient). However, in nonconvex optimization it is often crucial to find a second-order stationary point (with small gradient and almost PSD hessian). In this paper, we show that Stabilized SVRG (a simple variant of SVRG) can find an $\epsilon$-second-order stationary point using only $\widetilde{O}(n^{2/3}/\epsilon^2+n/\epsilon^{1.5})$ stochastic gradients. To our best knowledge, this is the first second-order guarantee for a simple variant of SVRG. The running time almost matches the known guarantees for finding $\epsilon$-first-order stationary points

Flood Disaster Assessment Method Based on a Stacked Denoising Autoencoder

In recent years, extreme weather has occurred frequently, and the risk of heavy rainfall and flooding faced by the people has risen. It is therefore an urgent requirement to carry out applied research on heavy rainfall and flooding risk assessment. We took Henan Province, where a major flood disaster occurred in 2021, as an example to analyze the impact factors of urban flooding and conduct a risk assessment. Indicators were first selected from population, housing, and the economy, and correlation analysis was used to optimize the indicator system. Then, a deep clustering network model based on a stacked denoising autoencoder (SDAE) was constructed, the feature information implied in the disaster indicators was abstracted into potential features through the coding and decoding of the network, and a small number of potential features were used to express the complex relationship between the disaster indicators. The results of the study show that the high-risk areas of flood damage in Henan Province in 2021 account for 2.3%, the medium-risk areas account for 9.4%, and the low-risk areas account for 80.3%. These evaluation results are in line with the actual situation in Henan Province, and the division of the grade in some areas is more reasonable compared with the entropy weighting method, which is a commonly used method of disaster assessment. The new model does not need to calculate weights to cope with changes in indicators and disaster conditions. The research results can provide scientific reference for urban flood risk management, disaster prevention and mitigation, and regional planning

Continuous output feedback sliding mode control for underactuated flexible-joint robot

The tracking control based on output feedback for a category of flexible-joint robot (FJR) systems is investigated in this brief. Control performance of the systems is inevitably bearing the brunt of various unknown time-varying disturbances, which can be categorized to be matched and mismatched and generally cover internal parameter uncertainties, couplings, unmodelled dynamics, and external load or changing operating environments. To cope with these disturbances, the mismatched disturbances are first transferred to the matched ones by a flatness method, which eliminates the computational cost of estimating mismatched disturbances. Then, a generalized proportional integral observer (GPIO) is constructed to estimate the unavailable states and disturbances. By integrating the estimated disturbance and states provided by the GPIO, a novel dynamic sliding surface is constructed. Finally, a continuous sliding mode control (CSMC)-based output feedback control framework is further designed. The presented control strategy only requires link position information and is continuous, which can effectively reduce the chattering driven by the high-frequency switching item in the traditional SMC method. Asymptotic convergence of output tracking error is guaranteed by theoretical analysis under some mild conditions. Comparative tests on a two-link FJR verify the claimed control performance

Impacts of Multiwalled Carbon Nanotubes on Nutrient Removal from Wastewater and Bacterial Community Structure in Activated Sludge

<div><p>Background</p><p>The increasing use of multiwalled carbon nanotubes (MWCNTs) will inevitably lead to the exposure of wastewater treatment facilities. However, knowledge of the impacts of MWCNTs on wastewater nutrient removal and bacterial community structure in the activated sludge process is sparse.</p><p>Aims</p><p>To investigate the effects of MWCNTs on wastewater nutrient removal, and bacterial community structure in activated sludge.</p><p>Methods</p><p>Three triplicate sequencing batch reactors (SBR) were exposed to wastewater which contained 0, 1, and 20 mg/L MWCNTs. MiSeq sequencing was used to investigate the bacterial community structures in activated sludge samples which were exposed to different concentrations of MWCNTs.</p><p>Results</p><p>Exposure to 1 and 20 mg/L MWCNTs had no acute (1 day) impact on nutrient removal from wastewater. After long-term (180 days) exposure to 1 mg/L MWCNTs, the average total nitrogen (TN) removal efficiency was not significantly affected. TN removal efficiency decreased from 84.0% to 71.9% after long-term effects of 20 mg/L MWCNTs. After long-term exposure to 1 and 20 mg/L MWCNTs, the total phosphorus removal efficiencies decreased from 96.8% to 52.3% and from 98.2% to 34.0% respectively. Further study revealed that long-term exposure to 20 mg/L MWCNTs inhibited activities of ammonia monooxygenase and nitrite oxidoreductase. Long-term exposure to 1 and 20 mg/L MWCNTs both inhibited activities of exopolyphosphatase and polyphosphate kinase. MiSeq sequencing data indicated that 20 mg/L MWCNTs significantly decreased the diversity of bacterial community in activated sludge. Long-term exposure to 1 and 20 mg/L MWCNTs differentially decreased the abundance of nitrifying bacteria, especially ammonia-oxidizing bacteria. The abundance of PAOs was decreased after long-term exposure to 20 mg/L MWCNTs. The abundance of glycogen accumulating organisms (GAOs) was increased after long-term exposure to 1 mg/L MWCNTs.</p><p>Conclusion</p><p>MWCNTs have adverse effects on biological wastewater nutrient removal, and altered the diversity and structure of bacterial community in activated sludge.</p></div

Bacterial Community Dynamics and Taxa-Time Relationships within Two Activated Sludge Bioreactors

<div><p>Background</p><p>Biological activated sludge process must be functionally stable to continuously remove contaminants while relying upon the activity of complex microbial communities. However the dynamics of these communities are as yet poorly understood. A macroecology metric used to quantify community dynamic is the taxa-time relationship (TTR). Although the TTR of animal and plant species has been well documented, knowledge is still lacking in regard to TTR of microbial communities in activated sludge bioreactors.</p><p>Aims</p><p>1) To characterize the temporal dynamics of bacterial taxa in activated sludge from two bioreactors of different scale and investigate factors affecting such dynamics; 2) to evaluate the TTRs of activated sludge microbial communities in two bioreactors of different scale.</p><p>Methods</p><p>Temporal variation of bacterial taxa in activated sludge collected from a full- and lab-scale activated sludge bioreactor was monitored over a one-year period using pyrosequencing of 16S rRNA genes. TTR was employed to quantify the bacterial taxa shifts based on the power law equation <i>S = cT^w</i>.</p><p>Results</p><p>The power law exponent <i>w</i> for the full-scale bioreactor was 0.43 (<i>R²</i> = 0.970), which is lower than that of the lab-scale bioreactor (<i>w</i> = 0.55, <i>R²</i> = 0.971). The exponents for the dominant phyla were generally higher than that of the rare phyla. Canonical correspondence analysis (CCA) result showed that the bacterial community variance was significantly associated with water temperature, influent (biochemical oxygen demand) BOD, bioreactor scale and dissolved oxygen (DO). Variance partitioning analyses suggested that wastewater characteristics had the greatest contribution to the bacterial community variance, explaining 20.3% of the variance of bacterial communities independently, followed by operational parameters (19.9%) and bioreactor scale (3.6%).</p><p>Conclusions</p><p>Results of this study suggest bacterial community dynamics were likely driven partly by wastewater and operational parameters and provide evidence that the TTR may be a fundamental ecological pattern in macro- and microbial systems.</p></div

Taxa-time relationships for a full-scale bioreactor (circles) and lab-scale bioreactor (triangles).

<p>The lines are fitted to a power law equation <i>S</i> = <i>cT^w</i>, where <i>S</i> is the number of observed taxa, <i>c</i> is the constant, <i>T</i> is the time, and <i>w</i> is the taxa-time relationship exponent.</p

Number of taxa classified by different taxonomic levels from the full-and lab-scale bioreactor.

a<p>Full-scale bioreactor.</p>b<p>Lab-scale bioreactor.</p

Clinicopathological characteristics of androgen receptor splicing variant 7 (AR-V7) expression in patients with castration resistant prostate cancer: A systematic review and meta‐analysis

Background:  Studies have shown that AR-V7 may be correlated with the poor prognosis of castration resistant prostate cancer (CRPC), however, clinicopathological characteristics of AR-V7 have not been fully elucidated. Objective: This study aimed at evaluating the clinicopathological features of AR-V7 in CRPC patients. Materials and methods: To evaluate the clinicopathological features of AR-V7 in CRPC patients. A search of PubMed, Embase, and Web of Science was performed using the keywords prostate cancer, prostate tumor, prostate neoplasm, prostate carcinoma, AR-V7, AR3, androgen receptor splicing variant-7, or androgen receptor-3. Twenty-four trials published by February 2020 were included in this study. Results: The proportion of Gleason score ≥ 8 was found to be significantly higher in AR-V7-positive CRPC (69.5%) than negative (54.9%) (OR 1.68, 95% CI 1.25–2.25, p < 0.001), while the rates of T3/T4 stage (OR 1.16, 95% CI 0.60–2.24, p = 0.65) and N1 stage (OR 0.99, 95% CI 0.65–1.51, p = 0.96) were not statistically correlated with AR-V7 status. The AR-V7-positive patients exhibited a significantly higher proportion of any site metastasis (61.3% versus 35.0%; OR 2.19, 95% CI 1.57–3.05, p < 0.001) and bone metastasis (81.7% versus 69.0%; OR 1.97, 95% CI 1.44–2.69, p < 0.001), and a trend close to significance was expected in visceral metastasis (28.8% versus 22.1%; OR 1.29, 95% CI 0.96–1.74, p = 0.09). Incidences of pain in AR-V7-positive CRPC (54.6%) were significantly higher than in negative CRPC (28.1%; OR 4.23, 95% CI 2.52–7.10, p < 0.001), line with worse ECOG performance status (56.7% versus 35.0%, OR 2.18, 95% CI 1.51–3.16, P < 0.001). Limitations of the study include differences in sample sizes and designs, AR-V7 detection assays, as well as disease characteristics of the included studies. Conclusions: AR-V7 positivity is associated with a higher Gleason score, bone or any site metastasis, pain and worse ECOG performance scores in CRPC. However, it is not correlated with tumor stage or lymph node metastasis. More studies are needed to confirm these findings