教学课程资源库 更多>>

关键词： branching parameter   firing rate   Fokker-Planck equation   neuronal population model  

摘要： It is important to understand the relationship between spatiotemporal patterns of neuronal populations and information processing of the brain for medical and engineering purposes. Although, there are some methods to record neuronal population, basically only the information about firing rate can be obtained from those methods. Therefore, some methods are suggested to estimate the internal state of the neuronal population from the information about firing. In this research, we investigated the relationship between firing rates and responses to external electrical stimuli by using neuronal population models. We developed a method to manipulate neuronal parameters to make neuronal populations exhibit different dynamical properties while keeping firing rates intact. As a result, we found that there are some cases where the internal states are different even though they share the same firing rate. This result suggests that there is some information that cannot be obtained by using only the information about firing rates.

关键词： Efficiency   friction   preacceleration   railgun  

摘要： Efficiency equations that consider friction and preacceleration of the projectile were derived. Special consideration was taken to distinguish between the loss of performance due to friction and the actual energy lost as heat due to friction. A thorough analysis of the effects of friction was also provided for special cases such as when the friction force is proportional to the Lorentz force, and so on. The equations were then compared with a mathematical simulation of an arbitrary fictitious railgun.

关键词： Perturbative anomalies   Batlin-Vilkovisky formalism   Cohomological methods in quantum field theory   Massless free fermion  

摘要： As is well known to physicists, the axial anomaly of the massless free fermion in Euclidean signature is given by the index of the corresponding Dirac operator. We use the Batalin-Vilkovisky (BV) formalism and the methods of equivariant quantization of Costello and Gwilliam to produce a new, mathematical derivation of this result. Using these methods, we formalize two conventional interpretations of the axial anomaly, the first as a violation of current conservation at the quantum level and the second as the obstruction to the existence of a well-defined fermionic partition function. Moreover, in the formalism of Costello and Gwilliam, anomalies are measured by cohomology classes in a certain obstruction-deformation complex. Our main result shows thatin the case of the axial symmetrythe relevant complex is quasi-isomorphic to the complex of de Rham forms of the space-time manifold and that the anomaly corresponds to a top-degree cohomology class which is trivial if and only if the index of the corresponding Dirac operator is zero.

关键词： Multiscale model   Mathematical model   Viral dynamics   HCV   PDE  

摘要： Mathematical modeling has revealed the quantitative dynamics during the process of viral infection and evolved into an important tool in modern virology. Coupled with analyses of clinical and experimental data, the widely used basic model of viral dynamics described by ordinary differential equations (ODEs) has been well parameterized. In recent years, age-structured models, called multiscale model, formulated by partial differential equations (PDEs) have also been developed and become useful tools for more detailed data analysis. However, in general, PDE models are considerably more difficult to subject to mathematical and numerical analyses. In our recently reported study, we successfully derived a mathematically identical ODE model from a PDE model, which helps to overcome the limitations of the PDE model with regard to clinical data analysis. Here, we derive the basic reproduction number from the identical ODE model and provide insight into the global stability of all possible steady states of the ODE model.

关键词： Lung adenocarcinoma   Gefitinib resistance   MET amplification   Mathematical modeling  

摘要： Gefitinib, one of the tyrosine kinase inhibitors of epidermal growth factor receptor (EGFR), is effective for treating lung adenocarcinoma harboring EGFR mutation;but later, most cases acquire a resistance to gefitinib. One of the mechanisms conferring gefitinib resistance to lung adenocarcinoma is the amplification of the MET gene, which is observed in 5-22% of gefitinib-resistant tumors. A previous study suggested that MET amplification could cause gefitinib resistance by driving ErbB3-dependent activation of the PI3K pathway. In this study, we built a mathematical model of gefitinib resistance caused by MET amplification using lung adenocarcinoma HCC827-GR (gefitinib resistant) cells. The molecular reactions involved in gefitinib resistance consisted of dimerization and phosphorylation of three molecules, EGFR, ErbB3, and MET were described by a series of ordinary differential equations. To perform a computer simulation, we quantified each molecule on the cell surface using flow cytometry and estimated unknown parameters by dimensional analysis. Our simulation showed that the number of active ErbB3 molecules is around a hundred-fold smaller than that of active MET molecules. Limited contribution of ErbB3 in gefitinib resistance by MET amplification is also demonstrated using HCC827-GR cells in culture experiments. Our mathematical model provides a quantitative understanding of the molecular reactions underlying drug resistance. (C) 2019 Published by Elsevier Inc.

关键词： Plasmonic resonance   Photonic crystal   Quasi-periodic Neumann-Poincare operator   Quasi-periodic layer potential   Drude model   Quasi-static regime  

摘要： In this article, we study the plasmonic resonance of infinite photonic crystal mounted by the double negative nanoparticles in two dimensions. The corresponding physical model is described by the Helmholz equation with so called Bloch wave condition in a periodic domain. By using the quasi-periodic layer potential techniques and the spectral theorem of quasi-periodic Neumann-Poincare operator, the quasi-static expansion of the near field in the presence of nanoparticles is derived. Furthermore, when the magnetic permeability of nanoparticles satisfies the Drude model, we give the conditions under which the plasmonic resonance occurs, and the rate of blow up of near field energy with respect to nanoparticle's bulk electron relaxation rate and filling factor are also obtained. It indicates that one can appropriately control the bulk electron relaxation rate or filling factor of nanoparticle in photonic crystal structure such that the near field energy attains its maximum, and enhancing the efficiency of energy utilization. (C) 2018 Elsevier Inc. All rights reserved.

关键词： 多元非线性数学分析   混凝土   强度预测  

摘要： 从多元非线性数学分析方法的要点入手,构建了混凝土强度预测模型,并通过试验制作了两种不同的混凝土,应用混凝土强度预测模型进行强度预测,预测结果与实际结果存在较小的误差,可以忽略不计,表明构建的数学模型具有较强的精度。

关键词： 艾滋病病毒   自然向量   Python   Mega   进化树  

摘要： 本文通过运用Yau 2011提出的自然向量法,对艾滋病病毒HIV-1, HIV-2, PLV三类病毒进行进化分析。采用Python计算序列的自然向量以及序列间两两的距离,之后利用Mega对计算好的距离矩阵画进化树。为了测试本文方法的可行性,本文选取了HIV Sequence Database的20条全基因数据进行研究,分别用我们的方法和传统的MSA(多序列比对)画进化树。得到的结果显示我们的方法明显优于MSA,而且在耗时上我们也优于MSA。因此,我们的方法能为艾滋病病毒在进化方面的研究提供有利的工具。

关键词： 刚体   转动   角速度  

摘要： 自然界中,刚体的转动是一种常见的物理现象,依据转动的特点可分为定轴转动和非定轴转动。在高中阶段,定轴转动问题较容易处理,但是复杂的非定轴转动问题对于学生来说较困难。本文利用利用初等数学方法分析非定轴转动问题,不仅弱化问题的解决的难度,而且通过对非定轴转动问题特点总结,为学生解决此类问题开辟了新的思路。

关键词： 新课改   高中数学   分析   解决  

摘要： 对于高中数学来讲,提高学生的分析和解决问题的能力具有非常重要的意义,通过提高学生的分析和解决问题的能力,可以使其获得更大的成长。而在新课改不断深化的过程中,会对学生的这一能力提出更高的要求。本文就相关内容展开了综合性的阐述与分析,首先介绍了分析与解决问题能力的内容,并阐述了新课改下高中数学分析和解决问题能力的提升措施。希望通过本文对相关内容的阐述与分析,能够进一步提升其实际效果,为我国高中生的发展提供更大的动力,使其可以利用有关知识解决更多的问题。