Uniformly bounded components of normality

Suppose that $f(z)$ is a transcendental entire function and that the Fatou set $F(f)\neq\emptyset$. Set $$B_1(f):=\sup_{U}\frac{\sup_{z\in U}\log(|z|+3)}{\inf_{w\in U}\log(|w|+3)}$$ and $$B_2(f):=\sup_{U}\frac{\sup_{z\in U}\log\log(|z|+30)}{\inf_{w\in U}\log(|w|+3)},$$ where the supremum $\sup_{U}$ is taken over all components of $F(f)$. If $B_1(f)<\infty$ or $B_2(f)<\infty$, then we say $F(f)$ is strongly uniformly bounded or uniformly bounded respectively. In this article, we will show that, under some conditions, $F(f)$ is (strongly) uniformly bounded.Comment: 17 pages, a revised version, to appear in Mathematical Proceedings Cambridge Philosophical Societ

3-Eth­oxy-4-hydroxy­benzaldehyde

The title compound (ethyl vanillin), C9H10O3, an important food additive and flavouring agent approved by FAO/WHO, has a vanilla odor four times that of vanillin and shows anti­­mutagenic activity. There are two mol­ecules in the asymmetric unit, each having a planar conformation and an intramolecular O—H⋯O bond. Mol­ecules are connected side-by-side, building infinite ribbons along c via inter­molecular O—H⋯O hydrogen bonds between the carbonyl and hydroxyl groups. The ribbons are then packed into layers perpendicular to the a axis

PromptCBLUE: A Chinese Prompt Tuning Benchmark for the Medical Domain

Biomedical language understanding benchmarks are the driving forces for artificial intelligence applications with large language model (LLM) back-ends. However, most current benchmarks: (a) are limited to English which makes it challenging to replicate many of the successes in English for other languages, or (b) focus on knowledge probing of LLMs and neglect to evaluate how LLMs apply these knowledge to perform on a wide range of bio-medical tasks, or (c) have become a publicly available corpus and are leaked to LLMs during pre-training. To facilitate the research in medical LLMs, we re-build the Chinese Biomedical Language Understanding Evaluation (CBLUE) benchmark into a large scale prompt-tuning benchmark, PromptCBLUE. Our benchmark is a suitable test-bed and an online platform for evaluating Chinese LLMs' multi-task capabilities on a wide range bio-medical tasks including medical entity recognition, medical text classification, medical natural language inference, medical dialogue understanding and medical content/dialogue generation. To establish evaluation on these tasks, we have experimented and report the results with the current 9 Chinese LLMs fine-tuned with differtent fine-tuning techniques

Simultaneous Detection of Chlamydia Trachomatis, Neisseria Gonorrhoeae, Ureaplasma Urealyticum by Multiplex PCR-Running

Chlamydia trachomatis (CT), Ureaplasma urealyticum (UU) and Neisseria gonorrhoeae (NG) are the most common pathogens of sexually transmitted infections (STIs), frequently founded in urogenital infections, and showed a criminal role in increasing the risk of potential adverse outcomes. In this study a multiplex PCR assay for the simultaneous detection and accurate identification of 3 clinically relevant pathogens of STIs, i.e., CT, NG and UU in a single tube was developed and evaluated. The limits of detection for the multiplex PCR assay were ~10 copies of DNAs per reaction. This assay has comparable clinical sensitivity to the conventional monoplex real-time PCR assay and considerable potential to be routine molecular diagnostic tool for simultaneous identification of STIs at relatively low cost due to multiplexing

Detection and evaluation of abnormal user behavior based on quantum generation adversarial network

Quantum computing holds tremendous potential for processing high-dimensional data, capitalizing on the unique capabilities of superposition and parallelism within quantum states. As we navigate the noisy intermediate-scale quantum (NISQ) era, the exploration of quantum computing applications has emerged as a compelling frontier. One area of particular interest within the realm of cyberspace security is Behavior Detection and Evaluation (BDE). Notably, the detection and evaluation of internal abnormal behaviors pose significant challenges, given their infrequent occurrence or even their concealed nature amidst vast volumes of normal data. In this paper, we introduce a novel quantum behavior detection and evaluation algorithm (QBDE) tailored for internal user analysis. The QBDE algorithm comprises a Quantum Generative Adversarial Network (QGAN) in conjunction with a classical neural network for detection and evaluation tasks. The QGAN is built upon a hybrid architecture, encompassing a Quantum Generator ($G_Q$) and a Classical Discriminator ($D_C$). $G_Q$, designed as a parameterized quantum circuit (PQC), collaborates with $D_C$, a classical neural network, to collectively enhance the analysis process. To address the challenge of imbalanced positive and negative samples, $G_Q$ is employed to generate negative samples. Both $G_Q$ and $D_C$ are optimized through gradient descent techniques. Through extensive simulation tests and quantitative analyses, we substantiate the effectiveness of the QBDE algorithm in detecting and evaluating internal user abnormal behaviors. Our work not only introduces a novel approach to abnormal behavior detection and evaluation but also pioneers a new application scenario for quantum algorithms. This paradigm shift underscores the promising prospects of quantum computing in tackling complex cybersecurity challenges