Minimum Width of Leaky-ReLU Neural Networks for Uniform Universal Approximation

The study of universal approximation properties (UAP) for neural networks (NN) has a long history. When the network width is unlimited, only a single hidden layer is sufficient for UAP. In contrast, when the depth is unlimited, the width for UAP needs to be not less than the critical width $w^*_{\min}=\max(d_x,d_y)$, where $d_x$ and $d_y$ are the dimensions of the input and output, respectively. Recently, \cite{cai2022achieve} shows that a leaky-ReLU NN with this critical width can achieve UAP for $L^p$ functions on a compact domain $K$, \emph{i.e.,} the UAP for $L^p(K,\mathbb{R}^{d_y})$. This paper examines a uniform UAP for the function class $C(K,\mathbb{R}^{d_y})$ and gives the exact minimum width of the leaky-ReLU NN as $w_{\min}=\max(d_x+1,d_y)+1_{d_y=d_x+1}$, which involves the effects of the output dimensions. To obtain this result, we propose a novel lift-flow-discretization approach that shows that the uniform UAP has a deep connection with topological theory.Comment: ICML2023 camera read

The Prevalence of Cryptosporidium spp. and Giardia duodenalis in Marmota himalayana (Rodentia: Sciuridae) in the Qinghai Tibetan Plateau area, China

Background: Cryptosporidium and Giardia are well-known important intestinal zoonotic pathogens that can infect various hosts and cause diarrhoeal diseases. We aimed to determine the epidemiological prevalence and molecular characterization of Cryptosporidium and Giardia species in Himalayan marmot (Marmota himalayana, class Marmota) in the Qinghai Tibetan Plateau Area of Qinghai Province, Northwest China. Methods: Overall, 243 Himalayan marmot fecal samples were collected in 2017 and in 2019 and a two-step nested PCR technique was performed to amplify the fragments of the SSU rRNA gene of Cryptosporidium and 18S ribosomal RNA gene of Giardia. Molecular characterization of Cryptosporidium was performed with the primary primers N-DIAGF2 and N-DIAGR2, the secondary primers CPB-DIAGF and CPB-DIAGR. Similarly, molecular characterization of Giardia was used the first primers Gia2029 and Gia2150c, the secondary primers RH11 and RH4. The positive PCR products were sequenced and the sequences were processed by Clustal Omega and BLAST. Phylogenetic analysis was achieved by NJ method in MEGA. Results: The infection rate of Cryptosporidium spp. and G. duodenalis was 4.9% (12/243) and 0.8% (2/243) in M. himalayana, respectively. Cryptosporidium spp. are characterized as novel genotypes Cryptosporidium marmot genotype I (n=3) and Cryptosporidium marmot genotype II (n=9); G. duodenalis assemblage A (n=2) was found in M. himalayana. Conclusion: This is the first report of Cryptosporidium spp. and G. duodenalis infections in M. himalayana in Qinghai of Northwest China. The results indicate the existence of Cryptosporidium species and G. duodenalis infections that may have a potential public health significance

Transcriptome analysis of stem development in the tumourous stem mustard Brassica juncea var. tumida Tsen et Lee by RNA sequencing

<p>Abstract</p> <p>Background</p> <p>Tumourous stem mustard (<it>Brassica juncea </it>var. <it>tumida </it>Tsen et Lee) is an economically and nutritionally important vegetable crop of the <it>Cruciferae </it>family that also provides the raw material for <it>Fuling </it>mustard. The genetics breeding, physiology, biochemistry and classification of mustards have been extensively studied, but little information is available on tumourous stem mustard at the molecular level. To gain greater insight into the molecular mechanisms underlying stem swelling in this vegetable and to provide additional information for molecular research and breeding, we sequenced the transcriptome of tumourous stem mustard at various stem developmental stages and compared it with that of a mutant variety lacking swollen stems.</p> <p>Results</p> <p>Using Illumina short-read technology with a tag-based digital gene expression (DGE) system, we performed <it>de novo </it>transcriptome assembly and gene expression analysis. In our analysis, we assembled genetic information for tumourous stem mustard at various stem developmental stages. In addition, we constructed five DGE libraries, which covered the strains <it>Yong'an </it>and <it>Dayejie </it>at various development stages. Illumina sequencing identified 146,265 unigenes, including 11,245 clusters and 135,020 singletons. The unigenes were subjected to a BLAST search and annotated using the GO and KO databases. We also compared the gene expression profiles of three swollen stem samples with those of two non-swollen stem samples. A total of 1,042 genes with significantly different expression levels occurring simultaneously in the six comparison groups were screened out. Finally, the altered expression levels of a number of randomly selected genes were confirmed by quantitative real-time PCR.</p> <p>Conclusions</p> <p>Our data provide comprehensive gene expression information at the transcriptional level and the first insight into the understanding of the molecular mechanisms and regulatory pathways of stem swelling and development in this plant, and will help define new mechanisms of stem development in non-model plant organisms.</p

Abrupt elevation of tumor marker levels in a huge splenic epidermoid cyst, a case report

Epidermoid cyst of the spleen is a rare disease, and relatively few cases were reported by literatures. Most published case reports provided inadequate information on the impact of splenic epidermoid cyst on tumor markers. A 32-year-old woman with a giant splenic epidermoid cyst was reported, for whom the serum concentration of a collection of tumor markers (CA19–9, CEA, CA125, CA242, and CA50) increased abruptly accompanied by left upper abdominal pain for 5 days. After comprehensive preoperative examination and multidisciplinary team discussion, we ruled out any concurrent malignancy and a laparoscopic total splenectomy was performed, during which the splenic cyst spontaneously ruptured unexpectedly. After surgery, the elevated serum tumor marker levels decreased sharply until reaching normal range 3 months later. Learning from the case, we conclude that interval monitoring of serum tumor markers is of critical value for patients with splenic epidermoid cyst. Abrupt elevation of tumor marker levels and abdominal pain may serve as signs of cyst rupture, which is strongly indicative of surgical intervention as soon as possible. Total removal of the splenic cyst is strongly suggested considering the recurrence and malignant potential of the splenic epidermoid cyst

Validation of the Oxford classification of IgA nephropathy for pediatric patients from China

BACKGROUND: The Oxford classification of IgA nephropathy (IgAN) provides a useful tool for prediction of renal prognosis. However, the application of this classification in children with IgAN needs validation in different patient populations. METHODS: A total of 218 children with IgAN from 7 renal centers in China were enrolled. The inclusion criteria was similar to the original Oxford study. RESULTS: There were 98 patients (45%) with mesangial proliferation (M1), 51 patients (23%) with endocapillary proliferation (E1), 136 patients (62%) with segmental sclerosis/adhesion lesion (S1), 13 patients (6%) with moderate tubulointerstitial fibrosis (T1 26-50% of cortex scarred), and only 2 patients (1%) with severe tubulointerstitial fibrosis (T2, >50% of cortex scarred). During a median follow-up duration of 56 months, 24 children (12.4%) developed ESRD or 50% decline in renal function. In univariate COX analysis, we found that tubular atrophy/interstitial fibrosis (HR 4.3, 95%CI 1.8-10.5, P < 0.001) and segmental glomerulosclerosis (HR 9.2 1.2-68.6, P = 0.03) were significant predictors of renal outcome. However, mesangial hypercellularity, endocapillary proliferation, crescents, and necrosis were not associated with renal prognosis. In the multivariate COX regression model, none of these pathologic lesions were shown to be independent risk factors of unfavorable renal outcome except for tubular atrophy/interstitial fibrosis (HR 2.9, 95%CI 1.0-7.9 P = 0.04). CONCLUSIONS: We confirmed tubular atrophy/interstitial fibrosis was the only feature independently associated with renal outcomes in Chinese children with IgAN

Neutrino Physics with JUNO

The Jiangmen Underground Neutrino Observatory (JUNO), a 20 kton multi-purposeunderground liquid scintillator detector, was proposed with the determinationof the neutrino mass hierarchy as a primary physics goal. It is also capable ofobserving neutrinos from terrestrial and extra-terrestrial sources, includingsupernova burst neutrinos, diffuse supernova neutrino background, geoneutrinos,atmospheric neutrinos, solar neutrinos, as well as exotic searches such asnucleon decays, dark matter, sterile neutrinos, etc. We present the physicsmotivations and the anticipated performance of the JUNO detector for variousproposed measurements. By detecting reactor antineutrinos from two power plantsat 53-km distance, JUNO will determine the neutrino mass hierarchy at a 3-4sigma significance with six years of running. The measurement of antineutrinospectrum will also lead to the precise determination of three out of the sixoscillation parameters to an accuracy of better than 1\%. Neutrino burst from atypical core-collapse supernova at 10 kpc would lead to ~5000inverse-beta-decay events and ~2000 all-flavor neutrino-proton elasticscattering events in JUNO. Detection of DSNB would provide valuable informationon the cosmic star-formation rate and the average core-collapsed neutrinoenergy spectrum. Geo-neutrinos can be detected in JUNO with a rate of ~400events per year, significantly improving the statistics of existing geoneutrinosamples. The JUNO detector is sensitive to several exotic searches, e.g. protondecay via the $p\to K^++\bar\nu$ decay channel. The JUNO detector will providea unique facility to address many outstanding crucial questions in particle andastrophysics. It holds the great potential for further advancing our quest tounderstanding the fundamental properties of neutrinos, one of the buildingblocks of our Universe

Potential of Core-Collapse Supernova Neutrino Detection at JUNO

JUNO is an underground neutrino observatory under construction in Jiangmen, China. It uses 20kton liquid scintillator as target, which enables it to detect supernova burst neutrinos of a large statistics for the next galactic core-collapse supernova (CCSN) and also pre-supernova neutrinos from the nearby CCSN progenitors. All flavors of supernova burst neutrinos can be detected by JUNO via several interaction channels, including inverse beta decay, elastic scattering on electron and proton, interactions on C12 nuclei, etc. This retains the possibility for JUNO to reconstruct the energy spectra of supernova burst neutrinos of all flavors. The real time monitoring systems based on FPGA and DAQ are under development in JUNO, which allow prompt alert and trigger-less data acquisition of CCSN events. The alert performances of both monitoring systems have been thoroughly studied using simulations. Moreover, once a CCSN is tagged, the system can give fast characterizations, such as directionality and light curve

Detection of the Diffuse Supernova Neutrino Background with JUNO

As an underground multi-purpose neutrino detector with 20 kton liquid scintillator, Jiangmen Underground Neutrino Observatory (JUNO) is competitive with and complementary to the water-Cherenkov detectors on the search for the diffuse supernova neutrino background (DSNB). Typical supernova models predict 2-4 events per year within the optimal observation window in the JUNO detector. The dominant background is from the neutral-current (NC) interaction of atmospheric neutrinos with 12C nuclei, which surpasses the DSNB by more than one order of magnitude. We evaluated the systematic uncertainty of NC background from the spread of a variety of data-driven models and further developed a method to determine NC background within 15\% with {\it{in}} {\it{situ}} measurements after ten years of running. Besides, the NC-like backgrounds can be effectively suppressed by the intrinsic pulse-shape discrimination (PSD) capabilities of liquid scintillators. In this talk, I will present in detail the improvements on NC background uncertainty evaluation, PSD discriminator development, and finally, the potential of DSNB sensitivity in JUNO

Real-time Monitoring for the Next Core-Collapse Supernova in JUNO

Core-collapse supernova (CCSN) is one of the most energetic astrophysical events in the Universe. The early and prompt detection of neutrinos before (pre-SN) and during the SN burst is a unique opportunity to realize the multi-messenger observation of the CCSN events. In this work, we describe the monitoring concept and present the sensitivity of the system to the pre-SN and SN neutrinos at the Jiangmen Underground Neutrino Observatory (JUNO), which is a 20 kton liquid scintillator detector under construction in South China. The real-time monitoring system is designed with both the prompt monitors on the electronic board and online monitors at the data acquisition stage, in order to ensure both the alert speed and alert coverage of progenitor stars. By assuming a false alert rate of 1 per year, this monitoring system can be sensitive to the pre-SN neutrinos up to the distance of about 1.6 (0.9) kpc and SN neutrinos up to about 370 (360) kpc for a progenitor mass of 30$M_{\odot}$ for the case of normal (inverted) mass ordering. The pointing ability of the CCSN is evaluated by using the accumulated event anisotropy of the inverse beta decay interactions from pre-SN or SN neutrinos, which, along with the early alert, can play important roles for the followup multi-messenger observations of the next Galactic or nearby extragalactic CCSN.Comment: 24 pages, 9 figure