Soliton interactions and asymptotic state analysis in a discrete nonlocal nonlinear self-dual network equation of reverse-space type

We propose a reverse-space nonlocal nonlinear self-dual network equation under special symmetry reduction,which may have potential applications in electric circuits.Nonlocal infinitely many conservation laws are constructed based on its Lax pair.Nonlocal discrete generalized(m,N−m)-fold Darboux transformation is extended and applied to solve this system.As an application of the method,we obtain multi-soliton solutions in zero seed background via the nonlocal discrete N-fold Darboux transformation and rational solutions from nonzero-seed background via the nonlocal discrete generalized(1,N−1)-fold Darboux transformation,respectively.By using the asymptotic and graphic analysis,structures of one-,two-,three-and four-soliton solutions are shown and discussed graphically.We find that single component field in this nonlocal system displays unstable soliton structure whereas the combined potential terms exhibit stable soliton structures.It is shown that the soliton structures are quite different between discrete local and nonlocal systems.Results given in this paper may be helpful for understanding the electrical signals propagation.

Novel Multisoliton Solutions of Some Soliton Equations

The novel multisoliton solutions for the nonlinear lumped self-dual network equations, Toda lattice and KP equation were obtained by using the Hirota direct method.

EQUATOR Network Library for health research reporting

Introduction EQUATOR Network provides unique access to collated expertise and resources for good reporting of health research, The resources are aimed at researchers （authors of research articles）, journal editors, peer reviewers, and developers of reporting guidelines,

Pattern dynamics of network-organized system with cross-diffusion

Cross-diffusion is a ubiquitous phenomenon in complex networks, but it is often neglected in the study of reaction–diffusion networks. In fact, network connections are often random. In this paper, we investigate pattern dynamics of random networks with cross-diffusion by using the method of network analysis and obtain a condition under which the network loses stability and Turing bifurcation occurs. In addition, we also derive the amplitude equation for the network and prove the stability of the amplitude equation which is also an effective tool to investigate pattern dynamics of the random network with cross diffusion. In the meantime, the pattern formation consistently matches the stability of the system and the amplitude equation is verified by simulations. A novel approach to the investigation of specific real systems was presented in this paper. Finally, the example and simulation used in this paper validate our theoretical results.

Analytical solutions for the slow neutron capture process of heavy element nucleosynthesis

In this paper, the network equation for the slow neutron capture process （s-process） of heavy element nucleosynthesis is investigated. Dividing the s-process network reaction chains into two standard forms and using the technique of matrix decomposition, a group of analytical solutions for the network equation are obtained. With the analytical solutions, a calculation for heavy element abundance of the solar system is carried out and the results are in good agreement with the astrophysical measurements.

Reporting guidelines of Chinese medicine:Current situation and future development

Objective:Reporting research is as important a part of a study as its design or analysis.Reporting guidelines(RGs)provide structured advice on how to report research studies clearly and adequately.This study aimed to review the development of RGs of Chinese medicine(CM)and to provide recommen-dations for improvement.Methods:Through a systematic search of the Enhancing the QUAlity and Transparency Of health Research(EQUATOR)Network and electronic databases up to January 1,2022,we identified a total of 15 RGs of CM,and further summarized their characteristics and applications.In addition,we reviewed the development of international RGs and analyzed its impact for CM.Results:Compared with the generic RGs,the reporting standards of CM have been rapidly developed over the last 10 years,of which 57%were issued in recent 3 years(2019-2021).Currently,the system of RGs of CM has been established,especially for clinical trials,including various CM interventions and covering the guidelines from trial registration,protocol,results publication to the evidence synthesis and clinical practice guideline.However,the application of RGs of CM is suboptimal.Conclusion:It is necessary to take further measures to promote practical application,improve journals’endorsement,and establish quality monitoring procedures for RGs of CM in the future.

Travelling Wave Solutions of Integro-differential Equations of One-dimensional Neuronal Networks

Travelling wave solutions of integro-differential equations for modeling one-dimensional neuronal networks, are studied. Under moderate continuity assumptions, necessary and sufficient conditions for the existence and uniqueness of monotone increasing（decreasing） Travelling wave solutions are established. Some faults in previous studies are corrected.

A Hybrid Mathematical Model of Tumor-Induced Angiogenesis with Blood Perfusion

Angiogenesis, the growth of new blood vessel from existing ones, is a pivotal stage in cancer development,and is an important target for cancer therapy. We develop a hybrid mathematical model to understand the mechanisms behind tumor-induced angiogenesis. This model describes uptake of Tumor Angiogenic Factor（TAF）at extracellular level, uses partial differential equation to describe the evolution of endothelial cell density including TAF induced proliferation, chemotaxis to TAF, and haptotaxis to extracellular matrix. In addition we also consider the phenomenon of blood perfusion in the micro-vessels. The model produces sprout formation with realistic morphological and dynamical features, including the so-called brush border effect, the dendritic branching and fusing of the capillary sprouts forming a vessel network. The model also demonstrates the effects of individual mechanisms in tumor angiogenesis： Chemotaxis to TAF is the key driving mechanisms for the extension of sprout cell; endothelial proliferation is not absolutely necessary for sprout extension; haptotaxis to Extra Cellular Matrix（ECM） gradient provides additional guidance to sprout extension, suggesting potential targets for anti-angiogenic therapies.