The Multi-Soliton Solutions to The KdV Equation by Hirota Method

The Hirota bilinear method is used to solve the KdV model. As a result, the exact expression of multi-soliton solutions of the KdV equation is obtained

The Applications of ISM Model

The students' interest refers to the knowledge of a positive emotional state, is caused by the motivation to learn, an important factor to promote student learning. Students of weariness largely depend of students' interest. There are many factors that a ect students' interest in learning, both objective factors and subjective factors. The reasons that a ect students learning interest are analyzed by using the interpretative structural modeling (ISM)

Embeddings Among Toruses and Meshes

Toruses and meshes include graphs of many varieties of topologies, with lines, rings, and hypercubes being special cases. Given a d-dimensional torus or mesh G and a c-dimensional torus or mesh H of the same size, we study the problem of embedding G in H to minimize the dilation cost. For increasing dimension cases (d \u3c c) in which the shapes of G and H satisfy the condition of expansion, the dilation costs of our embeddings are either 1 or 2, depending on the types of graphs of G and H. These embeddings a,re optimal except when G is a torus of even size and H is a mesh. For lowering dimension cases (d \u3e c) in which the shapes of G and H satisfy the condition of reduction, the dilation costs of our embeddings depend on the shapes of G and H. These embeddings, however, are not optimal in general. For the special cases in which G and H are square, the embedding results above can always be used to construct embeddings of G in H: these embeddings are all optimal for increasing dimension cases in which the dimension of H is divisible by the dimension of G, and all optimal to within a constant for fixed values of d and c for lowering dimension cases. Our main analysis technique is based on a generalization of Gray code for radix-2 (binary) numbering system to similar sequences for mixed-radix numbering systems

Development of Absorption and Fluorescence Probes Based on Mouse Model for Molecular Optical Imaging [abstract]

Comparative Medicine - OneHealth and Comparative Medicine Poster SessionIn this work we summarize our collaborative research on a project to develop absorption and fluorescence targeting probes. Several groups from University of Missouri and Harry S. Truman Memorial Veteran's Hospital including Dr. Ma's group, Dr. Yu's group, Dr. Smith's group, Dr. Hoffman's group, and Professor Wynn Volkert have been involved in the project. Our goal is to develop probes based on mouse model for molecular optical imaging. In vivo imaging of targeted fluorescence molecular probes, or molecular imaging, is an emerging field in biomedical imaging. During the past forty years, three dimensional biomedical imaging technologies such as CT and MRI have been extensively used in human health and diseases. However, the human body is a complex and interactive biological system. A fundamental scientific barrier in previous biomedical imaging technologies is their limited ability to study physiological processes in vivo at the cellular and molecular levels. Molecular imaging technologies can overcome this barrier. Optical imaging modalities have the highest sensitivity compared to other imaging techniques. So they are good candidates for molecular imaging. We develop probes for two biomedical optical imaging techniques. The first technique is coherence domain imaging. This technique can be used to monitor interactions between targeted peptide conjugates and cancer cells at a tissue level. It requires absorption properties of the probe for effective molecular imaging. The second technique is fluorescence mediated tomographic imaging using an image-intensified CCD camera. This technique uses fluorescence of the probe for molecular imaging. Dye bombesin conjugates are synthesized for site-specific absorption and fluorescence imaging in human prostate and breast cancer cells. Bombesin (BBN), an amphibian analog to the endogenous ligand, binds to the gastrin releasing peptide receptors (GRPr) with high specificity and affinity. BBN conjugates have a specific significance in cancer detection and therapy due to high over-expression levels of GRPrs in human cancer cells. Previously, we have developed an Alexa Fluor 680 BBN peptide conjugate. This probe can not be used as an absorption probe in near-infrared imaging since its absorption peak is in the visible wavelength range. In addition, long wavelength fluorescence is desired because long wavelength photons can penetrate deeper into tissue when using the conjugates as a fluorescent probe. The new absorption and fluorescent probe we developed is based on the last eight-residues of BBN and labeled with Alexa Fluor 750 through an effective linker. The developed probe, AF750-BetaAla-BBN[7-14]NH2, exhibits optimal pharmacokinetic properties for targeting GRPr over-expressing cancer cells in mice. Absorption spectra have been measured and showed absorption peaks at 690nm, 720nm and 735nm. Fluorescent band is located at 755nm. Fluorescent microscopic imaging of the conjugates in human PC-3 prostate cancer and T-47D breast cancer cells indicated specific uptake and internalization in vitro. In vivo optical and MR imaging was performed in SCID mice bearing human breast and prostate xenografts. In vitro and in vivo studies have demonstrated the effectiveness of the fluorescent probe Alexa Fluor 750-BetaAla-BBN[7-14]NH2 to specifically target GRPr overexpressed cancer tissues

Variational Iteration Method for Solving the Generalized Degasperis-Procesi Equation

We introduce the variational iteration method for solving the generalized Degasperis-Procesi equation. Firstly, according to the variational iteration, the Lagrange multiplier is found after making the correction functional. Furthermore, several approximations of un+1(x,t) which is converged to u(x,t) are obtained, and the exact solutions of Degasperis-Procesi equation will be obtained by using the traditional variational iteration method with a suitable initial approximation u0(x,t). Finally, after giving the perturbation item, the approximate solution for original equation will be expressed specifically

UniMAP: Universal SMILES-Graph Representation Learning

Molecular representation learning is fundamental for many drug related applications. Most existing molecular pre-training models are limited in using single molecular modality, either SMILES or graph representation. To effectively leverage both modalities, we argue that it is critical to capture the fine-grained 'semantics' between SMILES and graph, because subtle sequence/graph differences may lead to contrary molecular properties. In this paper, we propose a universal SMILE-graph representation learning model, namely UniMAP. Firstly, an embedding layer is employed to obtain the token and node/edge representation in SMILES and graph, respectively. A multi-layer Transformer is then utilized to conduct deep cross-modality fusion. Specially, four kinds of pre-training tasks are designed for UniMAP, including Multi-Level Cross-Modality Masking (CMM), SMILES-Graph Matching (SGM), Fragment-Level Alignment (FLA), and Domain Knowledge Learning (DKL). In this way, both global (i.e. SGM and DKL) and local (i.e. CMM and FLA) alignments are integrated to achieve comprehensive cross-modality fusion. We evaluate UniMAP on various downstream tasks, i.e. molecular property prediction, drug-target affinity prediction and drug-drug interaction. Experimental results show that UniMAP outperforms current state-of-the-art pre-training methods.We also visualize the learned representations to demonstrate the effect of multi-modality integration

A novel and simple method for construction of recombinant adenoviruses

Recombinant adenoviruses have been widely used for various applications, including protein expression and gene therapy. We herein report a new and simple cloning approach to an efficient and robust construction of recombinant adenoviral genomes based on the mating-assisted genetically integrated cloning (MAGIC) strategy. The production of recombinant adenovirus serotype 5-based vectors was greatly facilitated by the use of the MAGIC procedure and the development of the Adeasy™ adenoviral vector system. The recombinant adenoviral plasmid can be generated by a direct and seamless substitution, which replaces the stuff fragment in a full-length adenoviral genome with the gene of interest in a small plasmid in Escherichia coli. Recombinant adenoviral plasmids can be rapidly constructed in vivo by using the new method, without manipulations of the large adenoviral genome. In contrast to other traditional systems, it reduces the need for multiple in vitro manipulations, such as endonuclease cleavage, ligation and transformation, thus achieving a higher efficiency with negligible background. This strategy has been proven to be suitable for constructing an adenoviral cDNA expression library. In summary, the new method is highly efficient, technically less demanding and less labor-intensive for constructing recombinant adenoviruses, which will be beneficial for functional genomic and proteomic researches in mammalian cells

Combining Artificial Intelligence with Traditional Chinese Medicine for Intelligent Health Management

The growth of artificial intelligence (AI) is being referred to as the beginning of "the fourth industrial revolution". With the rapid development of hardware, algorithms, and applications, AI not only provides a new concept and relevant solutions to solve the problem of complexity science but also provides a new concept and method to promote the development of traditional Chinese medicine (TCM). In this study, based on the research and development of AI technology applications in biomedical and clinical diagnosis and treatment, we introduce AI technologies in current TCM research. This can have applications in intelligent clinical information acquisition, intelligent clinical decision, and efficacy evaluation of TCM; intelligent classification management, intelligent prescription, and drug research in Chinese herbal medicine; and health management. Furthermore, we propose a framework of "intelligent TCM" and outline its development prospects

Spatio-Temporal Relation and Attention Learning for Facial Action Unit Detection

Spatio-temporal relations among facial action units (AUs) convey significant information for AU detection yet have not been thoroughly exploited. The main reasons are the limited capability of current AU detection works in simultaneously learning spatial and temporal relations, and the lack of precise localization information for AU feature learning. To tackle these limitations, we propose a novel spatio-temporal relation and attention learning framework for AU detection. Specifically, we introduce a spatio-temporal graph convolutional network to capture both spatial and temporal relations from dynamic AUs, in which the AU relations are formulated as a spatio-temporal graph with adaptively learned instead of predefined edge weights. Moreover, the learning of spatio-temporal relations among AUs requires individual AU features. Considering the dynamism and shape irregularity of AUs, we propose an attention regularization method to adaptively learn regional attentions that capture highly relevant regions and suppress irrelevant regions so as to extract a complete feature for each AU. Extensive experiments show that our approach achieves substantial improvements over the state-of-the-art AU detection methods on BP4D and especially DISFA benchmarks