Learning Theory of Distribution Regression with Neural Networks

In this paper, we aim at establishing an approximation theory and a learning theory of distribution regression via a fully connected neural network (FNN). In contrast to the classical regression methods, the input variables of distribution regression are probability measures. Then we often need to perform a second-stage sampling process to approximate the actual information of the distribution. On the other hand, the classical neural network structure requires the input variable to be a vector. When the input samples are probability distributions, the traditional deep neural network method cannot be directly used and the difficulty arises for distribution regression. A well-defined neural network structure for distribution inputs is intensively desirable. There is no mathematical model and theoretical analysis on neural network realization of distribution regression. To overcome technical difficulties and address this issue, we establish a novel fully connected neural network framework to realize an approximation theory of functionals defined on the space of Borel probability measures. Furthermore, based on the established functional approximation results, in the hypothesis space induced by the novel FNN structure with distribution inputs, almost optimal learning rates for the proposed distribution regression model up to logarithmic terms are derived via a novel two-stage error decomposition technique

Can overfitted deep neural networks in adversarial training generalize? -- An approximation viewpoint

Adversarial training is a widely used method to improve the robustness of deep neural networks (DNNs) over adversarial perturbations. However, it is empirically observed that adversarial training on over-parameterized networks often suffers from the \textit{robust overfitting}: it can achieve almost zero adversarial training error while the robust generalization performance is not promising. In this paper, we provide a theoretical understanding of the question of whether overfitted DNNs in adversarial training can generalize from an approximation viewpoint. Specifically, our main results are summarized into three folds: i) For classification, we prove by construction the existence of infinitely many adversarial training classifiers on over-parameterized DNNs that obtain arbitrarily small adversarial training error (overfitting), whereas achieving good robust generalization error under certain conditions concerning the data quality, well separated, and perturbation level. ii) Linear over-parameterization (meaning that the number of parameters is only slightly larger than the sample size) is enough to ensure such existence if the target function is smooth enough. iii) For regression, our results demonstrate that there also exist infinitely many overfitted DNNs with linear over-parameterization in adversarial training that can achieve almost optimal rates of convergence for the standard generalization error. Overall, our analysis points out that robust overfitting can be avoided but the required model capacity will depend on the smoothness of the target function, while a robust generalization gap is inevitable. We hope our analysis will give a better understanding of the mathematical foundations of robustness in DNNs from an approximation view

Nonlinear functional regression by functional deep neural network with kernel embedding

With the rapid development of deep learning in various fields of science and technology, such as speech recognition, image classification, and natural language processing, recently it is also widely applied in the functional data analysis (FDA) with some empirical success. However, due to the infinite dimensional input, we need a powerful dimension reduction method for functional learning tasks, especially for the nonlinear functional regression. In this paper, based on the idea of smooth kernel integral transformation, we propose a functional deep neural network with an efficient and fully data-dependent dimension reduction method. The architecture of our functional net consists of a kernel embedding step: an integral transformation with a data-dependent smooth kernel; a projection step: a dimension reduction by projection with eigenfunction basis based on the embedding kernel; and finally an expressive deep ReLU neural network for the prediction. The utilization of smooth kernel embedding enables our functional net to be discretization invariant, efficient, and robust to noisy observations, capable of utilizing information in both input functions and responses data, and have a low requirement on the number of discrete points for an unimpaired generalization performance. We conduct theoretical analysis including approximation error and generalization error analysis, and numerical simulations to verify these advantages of our functional net

Therapeutic Effects of Chinese Medicine Herb Pair, Huzhang and Guizhi, on Monosodium Urate Crystal-Induced Gouty Arthritis in Rats Revealed by Anti-Inflammatory Assessments and NMR-Based Metabonomics

The present study was undertaken to evaluate the therapeutic effects of Huzhang-Guizhi herb pair (HG), firstly included in Hu-Zhang Power documented in Taiping Shenghui Fang, on monosodium urate (MSU) crystals-induced gouty arthritis in rats. We found that pretreatment with HG in rats with gouty arthritis could significantly attenuate the ankle joint swelling, and this beneficial antigout effect might be mediated, at least in part, by inhibiting tumor necrosis factor-alpha (TNF-α) and interleukin-1 beta (IL-1β) production in synovial fluid as well as nuclear transcription factor-κB p65 (NF-κB p65) protein expression in synovial tissue. Moreover, metabonomic analysis demonstrated that 5 and 6 potential biomarkers associated with gouty arthritis in plasma and urine, respectively, which were mainly involved in energy metabolism, amino acid metabolism, and gut microbe metabolism, were identified. HG could reverse the pathological process of MSU-induced gouty arthritis through regulating the disturbed metabolic pathways. These results provided important mechanistic insights into the protective effects of HG against MSU-induced gouty arthritis in rats

Cesarean Scar Defect Manifestations during Pregnancy and Delivery

The cesarean scar is a significant risk factor for the following pregnancies and especially deliveries. In this chapter, we discussed the diagnosis, incidence, detection, manifestations, and prognosis of pregnancy and delivery with cesarean scars. A systematic review of current literature showed that a manifestation of cesarean scars during the following pregnancies is not predictable, in general, although modern visualization technologies could reveal some specific features of scar defects that are associated with complications during pregnancy and delivery. However, there is no factor, which could serve as the main prognostic guide for obstetricians to make a decision for VBAC, thus Edwin Cragin’s phrase “once a cesarean, always a cesarean” has represented the essential healthcare issue over the century. At the moment, the most reasonable measurements to prevent uterine scar complications are reducing the rate of Cesarean Sections, opening the uterus transversely in the lower segment, and stitching the uterus with one layer only continuously using a big needle preferable by Stark technique of Cesarean section

Dynamic recruitment of microRNAs to their mRNA targets in the regenerating liver.

BACKGROUND: Validation of physiologic miRNA targets has been met with significant challenges. We employed HITS-CLIP to identify which miRNAs participate in liver regeneration, and to identify their target mRNAs. RESULTS: miRNA recruitment to the RISC is highly dynamic, changing more than five-fold for several miRNAs. miRNA recruitment to the RISC did not correlate with changes in overall miRNA expression for these dynamically recruited miRNAs, emphasizing the necessity to determine miRNA recruitment to the RISC in order to fully assess the impact of miRNA regulation. We incorporated RNA-seq quantification of total mRNA to identify expression-weighted Ago footprints, and developed a microRNA regulatory element (MRE) prediction algorithm that represents a greater than 20-fold refinement over computational methods alone. These high confidence MREs were used to generate candidate \u27competing endogenous RNA\u27 (ceRNA) networks. CONCLUSION: HITS-CLIP analysis provide novel insights into global miRNA:mRNA relationships in the regenerating liver

Fluorescein-guided surgery for high-grade glioma resection: a five-year-long retrospective study at our institute

ObjectiveThis study investigates the extent of resection, duration of surgery, intraoperative blood loss, and postoperative complications in patients with high-grade glioma who received surgery with or without sodium fluorescein guidance.MethodsA single-center retrospective cohort study was conducted on 112 patients who visited our department and underwent surgery between July 2017 and June 2022, with 61 in the fluorescein group and 51 in the non-fluorescein group. Baseline characteristics, intraoperative blood loss, surgery duration, resection extent, and postoperative complications were documented.ResultsThe duration of surgery was significantly shorter in the fluorescein group than in the non-fluorescein group (P = 0.022), especially in patients with tumors in the occipital lobes (P = 0.013). More critically, the gross total resection (GTR) rate was significantly higher in the fluorescein group than in the non-fluorescein group (45.9% vs. 19.6%, P = 0.003). The postoperative residual tumor volume (PRTV) was also significantly lower in the fluorescein group than in the non-fluorescein group (0.40 [0.12-7.11] cm3 vs. 4.76 [0.44-11.00] cm3, P = 0.020). Particularly in patients with tumors located in the temporal and occipital lobes (temporal, GTR 47.1% vs. 8.3%, P = 0.026; PRTV 0.23 [0.12-8.97] cm3 vs. 8.35 [4.05-20.59] cm3, P = 0.027; occipital, GTR 75.0% vs. 0.0%, P = 0.005; PRTV 0.15 [0.13-1.50] cm3 vs. 6.58 [3.70-18.79] cm3, P = 0.005). However, the two groups had no significant difference in intraoperative blood loss (P = 0.407) or postoperative complications (P = 0.481).ConclusionsFluorescein-guided resection of high-grade gliomas using a special operating microscope is a feasible, safe, and convenient technique that significantly improves GTR rates and reduces postoperative residual tumor volume when compared to conventional white light surgery without fluorescein guidance. This technique is particularly advantageous for patients with tumors located in non-verbal, sensory, motor, and cognitive areas such as the temporal and occipital lobes, and does not increase the incidence of postoperative complications

Characterization of Aquifex aeolicus ribonuclease III and the reactivity epitopes of its pre-ribosomal RNA substrates

Ribonuclease III cleaves double-stranded (ds) structures in bacterial RNAs and participates in diverse RNA maturation and decay pathways. Essential insight on the RNase III mechanism of dsRNA cleavage has been provided by crystallographic studies of the enzyme from the hyperthermophilic bacterium, Aquifex aeolicus. However, the biochemical properties of A. aeolicus (Aa)-RNase III and the reactivity epitopes of its substrates are not known. The catalytic activity of purified recombinant Aa-RNase III exhibits a temperature optimum of ∼70–85°C, with either Mg2+ or Mn2+ supporting efficient catalysis. Small hairpins based on the stem structures associated with the Aquifex 16S and 23S rRNA precursors are cleaved at sites that are consistent with production of the immediate precursors to the mature rRNAs. Substrate reactivity is independent of the distal box sequence, but is strongly dependent on the proximal box sequence. Structural studies have shown that a conserved glutamine (Q157) in the Aa-RNase III dsRNA-binding domain (dsRBD) directly interacts with a proximal box base pair. Aa-RNase III cleavage of the pre-16S substrate is blocked by the Q157A mutation, which reflects a loss of substrate binding affinity. Thus, a highly conserved dsRBD-substrate interaction plays an important role in substrate recognition by bacterial RNase III

Extensive Crosstalk between O-GlcNAcylation and Phosphorylation Regulates Akt Signaling

O-linked N-acetylglucosamine glycosylations (O-GlcNAc) and O-linked phosphorylations (O-phosphate), as two important types of post-translational modifications, often occur on the same protein and bear a reciprocal relationship. In addition to the well documented phosphorylations that control Akt activity, Akt also undergoes O-GlcNAcylation, but the interplay between these two modifications and the biological significance remain unclear, largely due to the technique challenges. Here, we applied a two-step analytic approach composed of the O-GlcNAc immunoenrichment and subsequent O-phosphate immunodetection. Such an easy method enabled us to visualize endogenous glycosylated and phosphorylated Akt subpopulations in parallel and observed the inhibitory effect of Akt O-GlcNAcylations on its phosphorylation. Further studies utilizing mass spectrometry and mutagenesis approaches showed that O-GlcNAcylations at Thr 305 and Thr 312 inhibited Akt phosphorylation at Thr 308 via disrupting the interaction between Akt and PDK1. The impaired Akt activation in turn resulted in the compromised biological functions of Akt, as evidenced by suppressed cell proliferation and migration capabilities. Together, this study revealed an extensive crosstalk between O-GlcNAcylations and phosphorylations of Akt and demonstrated O-GlcNAcylation as a new regulatory modification for Akt signaling