Approximation of Nonlinear Functionals Using Deep ReLU Networks

In recent years, functional neural networks have been proposed and studied in order to approximate nonlinear continuous functionals defined on $L^p([-1, 1]^s)$ for integers $s\ge1$ and $1\le p<\infty$. However, their theoretical properties are largely unknown beyond universality of approximation or the existing analysis does not apply to the rectified linear unit (ReLU) activation function. To fill in this void, we investigate here the approximation power of functional deep neural networks associated with the ReLU activation function by constructing a continuous piecewise linear interpolation under a simple triangulation. In addition, we establish rates of approximation of the proposed functional deep ReLU networks under mild regularity conditions. Finally, our study may also shed some light on the understanding of functional data learning algorithms

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

Bis(2,2′-bipyridine)(2-hy­droxy-2,2-diphenyl­acetato)­copper(II) nitrate dihydrate

In the title complex, [Cu(C14H11O3)(C10H8N2)2]NO3·2H2O, the CuII atom is coordinated by four N atoms from two 2,2′-bipyridine ligands and two O atoms from one benzilate ligand in a distorted octa­hedral geometry. A supra­molecular network is formed via inter­molecular O—H⋯O and C—H⋯O hydrogen-bonding inter­actions. π–π stacking inter­actions between neighboring pyridine rings are also present, the centroid—centroid distance being 3.808 (2) Å

Core Collapse Supernova Explosions in Active Galactic Nucleus Accretion Disks

Astrophysical events that occur in active galactic nucleus (AGN) disks are believed to differ significantly from the ordinary in the interstellar medium. We show that stars located in the outer region of the AGN disk would explode near the original migration starting points instead of being accreted by the central supermassive black hole due to the effect of viscosity. AGN disks provide a dense environment for supernova (SN) explosions, which inevitably involve ejecta-disk interactions. In this paper, we investigate the light curves (LCs) of core-collapse SN exploded in AGN disks. In addition to the fundamental energy source of $^{56} \mathrm{Ni}$--$^{56} \mathrm{Co}$--$^{56} \mathrm{Fe}$ decay reaction powering the SN LCs, the forward-reverse shock produced during interactions may contribute significantly to the observed flux. If the stellar winds manage to create a cavity surrounded by a shell near the star before the SN explosion, the ejecta-winds-disk configurations are expected. We present various SN LCs from different types of progenitors and find that the SN LCs are dominated by the radiation of ejecta-disk interaction-induced shocks. The resulting SNe in the AGN disk is a promising transient source for UV and optical band detection by the Neil Gehrels Swift Observatory (Swift), the Ultraviolet Explorer (UVEX) and wide field survey telescopes such as Ultraviolet Transient Astronomy Satellite (ULTRASAT), Wide Field Survey Telescope (WFST) and Legacy Survey of Space and Time (LSST) at the Vera C. Rubin Observatory. These detections could aid in the investigation of AGN discs and the associated high-energy transient occurrences.Comment: 16 pages, 6 figures, 2 tables, matches the published version in Ap

Identification of MicroRNAs in Two Species of Tomato, \u3ci\u3eSolanum lycopersicum\u3c/i\u3e and \u3ci\u3eSolanum habrochaites\u3c/i\u3e, by Deep Sequencing

MicroRNAs (miRNAs) are ~21 nucleotide (nt), endogenous RNAs that regulate gene expression in plants. Increasing evidence suggests that miRNAs play an important role in species-specific development in plants. However, the detailed miRNA profile divergence has not been performed among tomato species. In this study, the small RNA (sRNA) profiles of Solanum lycopersicum cultivar 9706 and Solanum habrochaites species PI 134417 were obtained by deep sequencing. Sixty-three known miRNA families were identified from these two species, of which 39 were common. Further miRNA profile comparison showed that 24 known non-conserved miRNA families were species-specific between these two tomato species. In addition, six conserved miRNA families displayed an apparent divergent expression pattern between the two tomato species. Our results suggested that species-specific, non-conserved miRNAs and divergent expression of conserved miRNAs might contribute to developmental changes and phenotypic variation between the two tomato species. Twenty new miRNAs were also identified in S. lycopersicum. This research significantly increases the number of known miRNA families in tomato and provides the first set of small RNAs in S. habrochaites. It also suggests that miRNAs have an important role in species-specific plant developmental regulation

Anti-hyperuricemia effect of hesperetin is mediated by inhibiting the activity of xanthine oxidase and promoting excretion of uric acid

Hesperetin is a natural flavonoid with many biological activities. In view of hyperuricemia treatment, the effects of hesperetin in vivo and in vitro, and the underlying mechanisms, were explored. Hyperuricemia models induced by yeast extract (YE) or potassium oxonate (PO) in mice were created, as were models based on hypoxanthine and xanthine oxidase (XOD) in L-O2 cells and sodium urate in HEK293T cells. Serum level of uric acid (UA), creatinine (CRE), and urea nitrogen (BUN) were reduced significantly after hesperetin treatment in vivo. Hesperetin provided hepatoprotective effects and inhibited xanthine oxidase activity markedly, altered the level of malondialdehyde (MDA), glutathione peroxidase (GSH-PX) and catalase (CAT), downregulated the XOD protein expression, toll-like receptor (TLR)4, nucleotide binding oligomerization domain-like receptor family pyrin domain-containing 3 (NLRP3) inflammasome, interleukin-18 (IL-18), upregulated forkhead box O3a (FOXO3a), manganese superoxide dismutase (MnSOD) in a uric acid-synthesis model in mice. Protein expression of organic anion transporter 1 (OAT1), OAT3, organic cationic transporter 1 (OCT1), and OCT2 was upregulated by hesperetin intervention in a uric acid excretion model in mice. Our results proposal that hesperetin exerts a uric acid-lowering effect through inhibiting xanthine oxidase activity and protein expression, intervening in the TLR4-NLRP3 inflammasome signaling pathway, and up-regulating expression of FOXO3a, MnSOD, OAT1, OAT3, OCT1, and OCT2 proteins. Thus, hesperetin could be a promising therapeutic agent against hyperuricemia

Original Article Correlations of IFN-γ-inducible protein-10 with the risk of chronic hepatitis B and the efficacy of interferon therapy in Asians

Abstract: Purpose: The aim of this study was to identify the correlations of IFN-γ-inducible protein-10 (IP-10) with the risk of chronic hepatitis B (CHB) and the efficacy of interferon therapy in Asians. Method: Serum IP-10 levels were assayed using enzyme linked immunosorbent assay (ELISA) in both CHB and control group. CHB group received interferon-α2b treatment to compare the pre-treatment and post-treatment serum IP-10 levels. Relevant studies met predefined inclusion and exclusion criteria were enrolled into further meta-analysis. Stata 12.0 software was applied for data analysis. Result: Our case-control study demonstrated that CHB group had evaluated serum IP-10 levels compared with control group (285.7 ± 41.6 pg/mL vs. 79.1 ± 33.8 pg/mL, t = 21.85, P &lt; 0.001. After treatment for 12 weeks, CHB group had remarkably decreased post-treatment serum IP-10 levels than pre-treatment (78.5 ± 20.4 pg/mL vs. 285.7 ± 41.6 pg/mL, t = 33.76, P &lt; 0.001). No significance was observed on post-treatment serum IP-10 levels between CHB and control group (78.5 ± 20.4 pg/mL vs. 78.1 ± 33.8 pg/mL, t = 0.07, P = 0.947). Meta-analysis results demonstrated that serum IP-10 levels in CHB group were obviously higher than healthy controls (SMD = 2.21, 95% CI = 1.55~2.87, P &lt; 0.001). A subgroup based on the HBeAg states revealed that serum IP-10 levels in both HBeAg-positive and HBeAg-negative CHB patients were notably higher than healthy controls (HBeAg-positive: SMD = 2.00, 95% CI = 1.13-2.87, P &lt; 0.001; HBeAg-negative: SMD = 1.34, 95% CI = 0.97-1.72, P &lt; 0.001). Conclusion: Serum IP-10 may be correlated with the risk of CHB and the efficiency of interferon therapy, thus IP-10 may be a good biomarker for the diagnosis and treatment of CHB

Marine anoxia linked to abrupt global warming during Earths penultimate icehouse.

Piecing together the history of carbon (C) perturbation events throughout Earth’s history has provided key insights into how the Earth system responds to abrupt warming. Previous studies, however, focused on short-term warming events that were superimposed on longer-term greenhouse climate states. Here, we present an integrated proxy (C and uranium [U] isotopes and paleo CO2) and multicomponent modeling approach to investigate an abrupt C perturbation and global warming event (∼304 Ma) that occurred during a paleo-glacial state. We report pronounced negative C and U isotopic excursions coincident with a doubling of atmospheric CO2 partial pressure and a biodiversity nadir. The isotopic excursions can be linked to an injection of ∼9,000 Gt of organic matter–derived C over ∼300 kyr and to near 20% of areal extent of seafloor anoxia. Earth system modeling indicates that widespread anoxic conditions can be linked to enhanced thermocline stratification and increased nutrient fluxes during this global warming within an icehouse