Nodal Solutions for Some Second-Order Semipositone Integral Boundary Value Problems

Using bifurcation techniques, we first prove a global bifurcation theorem for nonlinear second-order semipositone integral boundary value problems. Then the existence and multiplicity of nodal solutions of the above problems are obtained. Finally, an example is worked out to illustrate our main results

Analysis of Maximum Threshold and Quantum Security for Fault-Tolerant Encoding and Decoding Scheme Base on Steane Code

Steane code is one of the most widely studied quantum error-correction codes, which is a natural choice for fault-tolerant quantum computation (FTQC). However, the original Steane code is not fault-tolerant because the CNOT gates in an encoded block may cause error propagation. In this paper, we first propose a fault-tolerant encoding and decoding scheme, which analyzes all possible errors caused by each quantum gate in an error-correction period. In this scheme, we combine the results of measuring redundant qubits with those of syndrome measurements to identify specific errors for different types of errors. But due to the error propagation, there may be cases where different errors produce the same measurement results. Therefore, we introduce the "flag qubits" scheme (providing its usage conditions) to reduce error interference as much as possible, and we consider the errors caused by the introduced quantum gates, realizing the truly fault-tolerant Steane code. Afterwards, we provide the fault-tolerant scheme of the universal quantum gate set, including fault-tolerant preparation and verification of ancillary states. This is the first time that fault tolerance has been considered for every process of FTQC. Finally, We propose an algorithm for a more accurate estimation of thresholds and optimal error-correction period selection. Our simulation results based on this entire scheme demonstrate the effectiveness of this algorithm, satisfying the threshold theorem and the currently widely recognized threshold. We analyze the relationship among the maximum threshold, concatenated levels, and quantum logical depth, showing that quantum operations play a crucial role in increasing the threshold. Furthermore, we analyze the computational theoretical limits of quantum computers from the perspectives of attack and active defense based on our FTQC scheme, thereby assessing the security of a system

Antitumor immunostimulatory activity of the traditional Chinese medicine polysaccharide on hepatocellular carcinoma

Hepatocellular carcinoma (HCC) is a prevalent malignancy, often associated with compromised immune function in affected patients. This can be attributed to the secretion of specific factors by liver cancer cells, which hinder the immune response and lead to a state of immune suppression. Polysaccharides derived from traditional Chinese medicine (TCM) are valuable constituents known for their immunomodulatory properties. This review aims to look into the immunomodulatory effects of TCM polysaccharides on HCC. The immunomodulatory effects of TCM polysaccharides are primarily manifested through the activation of effector T lymphocytes, dendritic cells, NK cells, and macrophages against hepatocellular carcinoma (HCC) both in vivo and in vitro settings. Furthermore, TCM polysaccharides have demonstrated remarkable adjuvant antitumor immunomodulatory effects on HCC in clinical settings. Therefore, the utilization of TCM polysaccharides holds promising potential for the development of novel therapeutic agents or adjuvants with advantageous immunomodulatory properties for HCC

Transfer Learning Applied to Stellar Light Curve Classification

Variability carries physical patterns and astronomical information of objects, and stellar light curve variations are essential to understand the stellar formation and evolution processes. The studies of variations in stellar photometry have the potential to expand the list of known stars, protostars, binary stars, and compact objects, which could shed more light on stages of stellar lifecycles. The progress in machine-learning techniques and applications has developed modern algorithms to detect and condense features from big data, which enables us to classify stellar light curves efficiently and effectively. We explore several deep-learning methods on variable star classifications. The sample of light curves is constructed with $\delta$ Scuti, $\gamma$ Doradus, RR Lyrae, eclipsing binaries, and hybrid variables from \textit{Kepler} observations. Several algorithms are applied to transform the light curves into images, continuous wavelet transform (CWT), Gramian angular fields, and recurrent plots. We also explore the representation ability of these algorithms. The processed images are fed to several deep-learning methods for image recognition, including VGG-19, GoogLeNet, Inception-v3, ResNet, SqueezeNet, and Xception architectures. The best transformation method is CWT, resulting in an average accuracy of 95.6\%. VGG-19 shows the highest average accuracy of 93.25\% among all architectures, while it shows the highest accuracy of 97.2\% under CWT transformation method. The prediction can reach $\sim1000$ light curves per second by using NVIDIA RTX 3090. Our results indicate that the combination of big data and deep learning opens a new path to classify light curves automatically.Comment: 30 pages, 19 figure