Normal families of meromorphic functions with multiple zeros

AbstractLet F be a family of meromorphic functions defined in a domain D such that for each f∈F, all zeros of f(z) are of multiplicity at least 3, and all zeros of f′(z) are of multiplicity at least 2 in D. If for each f∈F, f′(z)−1 has at most 1 zero in D, ignoring multiplicity, then F is normal in D

A New Single-Phase Single-Stage AC-DC Stacked Flyback Converter With Active Clamp ZVS

Single-stage AC-DC converters integrate an AC-DC front-end converter with a DC-DC back-end converter. Compared with conventional two-stage AC-DC converters, single-stage AC-DC converters use less components and only one controller, which is used to regulate the output voltage. As a result, the cost, size and complexity of AC-DC converters can be reduced, but single-stage converters do not perform as well as two-stage converters, and most have drawbacks that are related to the fact that the DC bus voltage is not controlled an can become excessive. A new single-phase single-stage AC-DC converter that uses stacked flyback converters is proposed in this thesis. The proposed converter consists of two low power flyback converters stacked on top of each other and an active clamp that helps the main switches operate with ZVS. The stacked structure helps reduce the voltage stresses typical fund in many single-stage converters. In the thesis, the operation of the converter is explained, the steady-state characteristics of the converter are determined and its design is discussed. The feasibility of the new converter is confirmed with experimental results obtained from a 100VAC~220VAC worldwide input, 48V output, 100kHz switching frequency and 200 W output power prototype converter

Normal Families of Zero-Free Meromorphic Functions

Let (≠0),∈ℂ, and and be two positive integers such that ≥2. Let ℱ be a family of zero-free meromorphic functions defined in a domain such that for each ∈ℱ, +(())− has at most zeros, ignoring multiplicity. Then ℱ is normal in

The Hausdorff dimension of directional edge escaping points set

In this paper, we define the directional edge escaping points set of function iteration under a given plane partition and then prove that the upper bound of Hausdorff dimension of the directional edge escaping points set of (S(z)=a e^{z}+b e^{-z}), where (a, bin mathbb{C}) and (|a|^{2}+|b|^{2}neq 0), is no more than 1

Differentially Private Numerical Vector Analyses in the Local and Shuffle Model

Numerical vector aggregation plays a crucial role in privacy-sensitive applications, such as distributed gradient estimation in federated learning and statistical analysis of key-value data. In the context of local differential privacy, this study provides a tight minimax error bound of $O(\frac{ds}{n\epsilon^2})$, where $d$ represents the dimension of the numerical vector and $s$ denotes the number of non-zero entries. By converting the conditional/unconditional numerical mean estimation problem into a frequency estimation problem, we develop an optimal and efficient mechanism called Collision. In contrast, existing methods exhibit sub-optimal error rates of $O(\frac{d^2}{n\epsilon^2})$ or $O(\frac{ds^2}{n\epsilon^2})$. Specifically, for unconditional mean estimation, we leverage the negative correlation between two frequencies in each dimension and propose the CoCo mechanism, which further reduces estimation errors for mean values compared to Collision. Moreover, to surpass the error barrier in local privacy, we examine privacy amplification in the shuffle model for the proposed mechanisms and derive precisely tight amplification bounds. Our experiments validate and compare our mechanisms with existing approaches, demonstrating significant error reductions for frequency estimation and mean estimation on numerical vectors.Comment: Full version of "Hiding Numerical Vectors in Local Private and Shuffled Messages" (IJCAI 2021

Fine-grained Private Knowledge Distillation

Knowledge distillation has emerged as a scalable and effective way for privacy-preserving machine learning. One remaining drawback is that it consumes privacy in a model-level (i.e., client-level) manner, every distillation query incurs privacy loss of one client's all records. In order to attain fine-grained privacy accountant and improve utility, this work proposes a model-free reverse $k$-NN labeling method towards record-level private knowledge distillation, where each record is employed for labeling at most $k$ queries. Theoretically, we provide bounds of labeling error rate under the centralized/local/shuffle model of differential privacy (w.r.t. the number of records per query, privacy budgets). Experimentally, we demonstrate that it achieves new state-of-the-art accuracy with one order of magnitude lower of privacy loss. Specifically, on the CIFAR-$10$ dataset, it reaches $82.1\%$ test accuracy with centralized privacy budget $1.0$; on the MNIST/SVHN dataset, it reaches $99.1\%$/$95.6\%$ accuracy respectively with budget $0.1$. It is the first time deep learning with differential privacy achieve comparable accuracy with reasonable data privacy protection (i.e., $\exp(\epsilon)\leq 1.5$). Our code is available at https://github.com/liyuntong9/rknn

Epidemiological investigation, determination of related factors, and spatial-temporal cluster analysis of wild type pseudorabies virus seroprevalence in China during 2022

IntroductionPseudorabies virus (PRV) is a linear DNA virus with a double-stranded structure, capable of infecting a diverse array of animal species, including humans. This study sought to ascertain the seroprevalence of Pseudorabies Virus (PRV) in China by conducting a comprehensive collection of blood samples from 16 provinces over the course of 2022.MethodsThe presence of PRV gE antibodies was detected through the utilization of an enzyme-linked immunosorbent assay (ELISA) technique. Logistic regression analysis was conducted to identify potential related factors associated with the serologic status of PRV gE at the animal level. Additionally, the SaTScan 10.1 software was used to analyze the spatial and temporal clusters of PRV gE seroprevalence.ResultsA comprehensive collection of 161,880 samples was conducted, encompassing 556 swine farms throughout the country. The analysis revealed that the seroprevalence of PRV gE antibodies was 12.36% (95% confidence interval [CI], 12.20% to 12.52%) at the individual animal level. However, at the swine farm level, the seroprevalence was considerably higher, reaching 46.22% (95% CI, 42.08% to 50.37%). Related factors for PRV infection at the farm level included the geographic distribution of farms and seasonal variables. Moreover, five distinct high seroprevalence clusters of PRV gE were identified across China, with the peak prevalence observed during the months of April through June 2022.ConclusionOur findings serve as a valuable addition to existing research on the seroprevalence, related factors, and temporal clustering of PRV gE in China. Furthermore, our study provides a reference point for the development of effective strategies for the prevention and control of pseudorabies and wild virus outbreaks

Characterization of garlic oil/β-cyclodextrin inclusion complexes and application

Garlic oil is a liquid extracted from garlic that has various natural antibacterial and anti-inflammatory properties and is believed to be used to prevent and treat many diseases. However, the main functional components of garlic oil are unstable. Therefore, in this study, encapsulating garlic oil with cyclodextrin using the saturated co-precipitation method can effectively improve its chemical stability and water solubility and reduce its characteristic odor and taste. After preparation, the microcapsules of garlic oil cyclodextrin were characterized, which proved that the encapsulation was successful. Finally, the results showed that the encapsulated garlic oil still had antioxidant ability and slow-release properties. The final addition to plant-based meat gives them a delicious flavor and adds texture and mouthfeel. Provided a new reference for the flavor application of garlic cyclodextrin micro-capsules in plant-based meat patties

Numerical investigations of urban pollutant dispersion and building intake fraction with various 3D building configurations and tree plantings

Rapid urbanisation and rising vehicular emissions aggravate urban air pollution. Outdoor pollutants could diffuse indoors through infiltration or ventilation, leading to residents’ exposure. This study performed CFD simulations with a standard k-ε model to investigate the impacts of building configurations and tree planting on airflows, pollutant (CO) dispersion, and personal exposure in 3D urban micro-environments (aspect ratio = H/W = 30 m, building packing density λp = λf = 0.25) under neutral atmospheric conditions. The numerical models are well validated by wind tunnel data. The impacts of open space, central high-rise building and tree planting (leaf area density LAD= 1 m2/m3) with four approaching wind directions (parallel 0° and non-parallel 15°, 30°, 45°) are explored. Building intake fraction is adopted for exposure assessment. The change rates of demonstrate the impacts of different urban layouts on the traffic exhaust exposure on residents. The results show that open space increases the spatially-averaged velocity ratio (VR) for the whole area by 0.40–2.27%. Central high-rise building (2H) can increase wind speed by 4.73–23.36% and decrease the CO concentration by 4.39–23.00%. Central open space and high-rise building decrease under all four wind directions, by 6.56–16.08% and 9.59–24.70%, respectively. Tree planting reduces wind speed in all cases, raising by 14.89–50.19%. This work could provide helpful scientific references for public health and sustainable urban planning