Threshold Dynamics in Stochastic SIRS Epidemic Models with Nonlinear Incidence and Vaccination

In this paper, the dynamical behaviors for a stochastic SIRS epidemic model with nonlinear incidence and vaccination are investigated. In the models, the disease transmission coefficient and the removal rates are all affected by noise. Some new basic properties of the models are found. Applying these properties, we establish a series of new threshold conditions on the stochastically exponential extinction, stochastic persistence, and permanence in the mean of the disease with probability one for the models. Furthermore, we obtain a sufficient condition on the existence of unique stationary distribution for the model. Finally, a series of numerical examples are introduced to illustrate our main theoretical results and some conjectures are further proposed

Patterns of nucleotides that flank substitutions in human orthologous genes

<p>Abstract</p> <p>Background</p> <p>Sequence context is an important aspect of base mutagenesis, and three-base periodicity is an intrinsic property of coding sequences. However, how three-base periodicity is influenced in the vicinity of substitutions is still unclear. The effect of context on mutagenesis should be revealed in the usage of nucleotides that flank substitutions. Relative entropy (also known as Kullback-Leibler divergence) is useful for finding unusual patterns in biological sequences.</p> <p>Results</p> <p>Using relative entropy, we visualized the periodic patterns in the context of substitutions in human orthologous genes. Neighbouring patterns differed both among substitution categories and within a category that occurred at three codon positions. Transition tended to occur in periodic sequences relative to transversion. Periodic signals were stronger in a set of flanking sequences of substitutions that occurred at the third-codon positions than in those that occurred at the first- or second-codon positions. To determine how the three-base periodicity was affected near the substitution sites, we fitted a sine model to the values of the relative entropy. A sine of period equal to 3 is a good approximation for the three-base periodicity at sites not in close vicinity to some substitutions. These periods were interrupted near the substitution site and then reappeared away from substitutions. A comparative analysis between the native and codon-shuffled datasets suggested that the codon usage frequency was not the sole origin of the three-base periodicity, implying that the native order of codons also played an important role in this periodicity. Synonymous codon shuffling revealed that synonymous codon usage bias was one of the factors responsible for the observed three-base periodicity.</p> <p>Conclusions</p> <p>Our results offer an efficient way to illustrate unusual periodic patterns in the context of substitutions and provide further insight into the origin of three-base periodicity. This periodicity is a result of the native codon order in the reading frame. The length of the period equal to 3 is caused by the usage bias of nucleotides in synonymous codons. The periodic features in nucleotides surrounding substitutions aid in further understanding genetic variation and nucleotide mutagenesis.</p

VDIP-TGV: Blind Image Deconvolution via Variational Deep Image Prior Empowered by Total Generalized Variation

Recovering clear images from blurry ones with an unknown blur kernel is a challenging problem. Deep image prior (DIP) proposes to use the deep network as a regularizer for a single image rather than as a supervised model, which achieves encouraging results in the nonblind deblurring problem. However, since the relationship between images and the network architectures is unclear, it is hard to find a suitable architecture to provide sufficient constraints on the estimated blur kernels and clean images. Also, DIP uses the sparse maximum a posteriori (MAP), which is insufficient to enforce the selection of the recovery image. Recently, variational deep image prior (VDIP) was proposed to impose constraints on both blur kernels and recovery images and take the standard deviation of the image into account during the optimization process by the variational principle. However, we empirically find that VDIP struggles with processing image details and tends to generate suboptimal results when the blur kernel is large. Therefore, we combine total generalized variational (TGV) regularization with VDIP in this paper to overcome these shortcomings of VDIP. TGV is a flexible regularization that utilizes the characteristics of partial derivatives of varying orders to regularize images at different scales, reducing oil painting artifacts while maintaining sharp edges. The proposed VDIP-TGV effectively recovers image edges and details by supplementing extra gradient information through TGV. Additionally, this model is solved by the alternating direction method of multipliers (ADMM), which effectively combines traditional algorithms and deep learning methods. Experiments show that our proposed VDIP-TGV surpasses various state-of-the-art models quantitatively and qualitatively.Comment: 13 pages, 5 figure

Reaction Mechanisms and Sensitivity for Silicon Nitrocarbamate and Related Systems from Quantum Mechanics Reaction Dynamics

Temperature induced instability is an important issue in developing new molecules and materials, but there is no clear understanding about how molecular structure and crystal packing control sensitivity. This is particularly the case for energetic materials (EM) important in propulsion and detonation. We propose here using the quantum mechanics molecular dynamics (QM-MD) based tempereature programmed reaction dynamics for predicting the relative sensitivity of various materials while simultaneously obtaining the reaction mechanisms underlying to provide guidance in improving materials. We illustrate this for four closely related molecules, pentaerythritol tetranitrate, pentaerythritol tetranitrocarbamate, and their silicon analogs, that have minor intramolecular differences but exhibit different sensitivities experimentally. Our study finds dramatic differences in reaction mechanisms and energy variation under heating that suggest explanations for the different sensitivities. Important here are both the initial decomposition and the secondary reactions between products. The higher sensitivity of the Si analogs originates from the highly exothermic Si–O bond formation as a paramount initial reaction that promotes other reactions, leading to the generations of various intermediates and final products, thus accelerating the decomposition process and energy release. The nitrocarbamates have low sensitivity because their large complex branching impedes the exothermic Si/C–O bond formation and triggers multiple initial endothermic reaction pathways with higher reaction barrier, delaying secondary exothermic reactions and energy release. We find two computational measures that correlate well with sensitivity: the temperatures at which the energy changes from endothermic to exothermic and the total absorbed energy. This study provides mechanistic insight on the molecular and structural determinants controlling the sensitivity of EMs and provides a practical way to predict the relative sensitivity in advance of experimental synthesis and characterization, benefiting the design of novel EMs

Analysis of basic pentacysteine6 transcription factor involved in abiotic stress response in Arabidopsis thaliana

Background: Abiotic stress is a significant environmental factor that limits plant growth. Plants have complex and diverse mechanisms for dealing with abiotic stress, and different response mechanisms are interconnected. Our research aims to find key transcription factors that can respond to multiple non -biological stress.Methods: We used gene expression profile data of Arabidopsis in response to abiotic stress, constructed a weighted gene co-expression network, to obtain key modules in the network. The functions and pathways involved in these modules were further explored by Gene Ontology (GO) and Kyoto Encyclopedia of Genes and Genomes (KEGG) enrichment analyses. Through the enrichment analysis of transcription factor, the transcription factor that plays an important regulatory role in the key module. Through gene difference expression analysis and building protein interaction networks, the important role of key transcription factors is verified.Result: In weighted gene co-expression network, identified three gene modules that are primarily associated with cold stress, heat stress, and salt stress. Functional enrichment analysis indicated that the genes in these modules participate in biological processes such as protein binding, stress response, and others. Transcription factor enrichment analysis revealed that the transcription factor Basic Pentacysteine6 (BPC6) plays a crucial regulatory role in these three modules. The expression of the BPC6 gene is dramatically affected under a variety of abiotic stress treatments, according to an analysis of Arabidopsis gene expression data under abiotic stress treatments. Differential expression analysis showed that there were 57 differentially expressed genes in bpc4 bpc6 double mutant Arabidopsis relative to normal Arabidopsis samples, including 14 BPC6 target genes. Protein interaction network analysis indicated that the differentially expressed genes had strong interactions with BPC6 target genes within the key modules.Conclusion: Our findings reveal that the BPC6 transcription factor plays a key regulatory function in Arabidopsis coping with a variety of abiotic stresses, which opens up new ideas and perspectives for us to understand the mechanism of plants coping with abiotic stresses

STUDY ON THE INHIBITORY EFFECT OF DRYNARIA FORTUNEI EXTRACT ON HUMAN MYELOMA SP20 CELLS

The objective of the study was to investigate the inhibitory effect of Drynaria fortunei extract on human myeloma SP2 cells. Three different total extracts of Drynaria fortunei were obtained by reflux extraction method using different organic solvents including ethanol, methanol and petroleum ether. Their anticancer activities on SP20 cells were tested, and the maximum inhibition rate was obtained. The inhibitory effects on tumour cells at 12 h, 24 h, 36 h and 48 h were tested, and the inhibition curves at different time periods were plotted. The results showed that the methanol and ethanol extracts have similar inhibition rates at 24 h, which are around 55%. On the other hand, the maximum inhibition rate of petroleum ether extract is only 36% within 24h. Moreover, within the time periods of 36 h and 48 h, its inhibition rates are all below 10%

Potential advantage of multiple alkali metal doped KNbO3 single crystals

Potassium niobate crystal KNbO3 (KN) is a well-known crystal for lead free piezoelectric or nonlinear optical applications. The KN crystal has been studied in both single crystal form and in thin film form which has resulted in many review articles being published. In order to exceed the KN crystal, it is important to study KN phase forming and doping effects on the K site. This article summarizes the authors\u27 study towards a multiple alkali metal doped KN crystal and related single crystals briefly from the viewpoint of crystal growth

Quantum Attacks on Lai-Massey Structure

Aaram Yun et al. considered that Lai-Massey structure has the same security as Feistel structure. However, Luo et al. showed that 3-round Lai-Massey structure can resist quantum attacks of Simon\u27s algorithm, which is different from Feistel structure. We give quantum attacks against a typical Lai-Massey structure. The result shows that there exists a quantum CPA distinguisher against 3-round Lai-Massey structure and a quantum CCA distinguisher against 4-round Lai-Massey Structure, which is the same as Feistel structure. We extend the attack on Lai-Massey structure to quasi-Feistel structure. We show that if the combiner of quasi-Feistel structure is linear, there exists a quantum CPA distinguisher against 3-round balanced quasi-Feistel structure and a quantum CCA distinguisher against 4-round balanced quasi-Feistel Structure