Transgenic mice as probes into complex systems

The transfer of genetic information into mouse embryos to stably alter the genetic constitution of mice is affording new insights into and opportunities in a wide variety of biological problems. Higher eukaryotes are composed of many interacting cells and organs. The properties of individual cell systems are often discernible only by studying natural or induced disruptions in their functions. Transgenic mice represent a new form of perturbation analysis whereby the selective expression of novel or altered genes can be used to perturb complex systems in ways that are informative about their development, their functions, and their malfunctions. The utility of this strategy is illustrated by recent research into immunological self-tolerance, oncogenes and cancer, and development.     

Homeokinetics: a physical science for complex systems

A physical basis for reductionism is put forth in the form of five propositions that bridge levels of organization in natural phenomena. The outlook is that complex systems and processes all have to be traced back to physical law, which applies the only general scientific constraint on reality, but that out of physical law a hierarchy of organization emerges. The basic extension of normal physics in this homeokinetic field form is to complex systems. In such systems the repetitive units of concern are internally complex and exhibit elaborate internal time-delayed processes, for example, memory.     

Mathematics

Current research in mathematics involves a wide variety of interlocking ideas, old and new. For example, results about the curves and surfaces defined by polynomial equations, as in algebraic geometry, appear in the study of solitary waves and also in the gauge theories in physics. Centuries-old problems in number theory have been solved, while others have been revealed as insoluble. The classification of all finite simple groups is nearly achieved (and the full treatment will be voluminous); the representation of groups aids in their application to the study of symmetry. These developments, and many others, attest to the vitality of mathematics.     

Pattern-oriented modeling of agent-based complex systems: lessons from ecology

Agent-based complex systems are dynamic networks of many interacting agents; examples include ecosystems, financial markets, and cities. The search for general principles underlying the internal organization of such systems often uses bottom-up simulation models such as cellular automata and agent-based models. No general framework for designing, testing, and analyzing bottom-up models has yet been established, but recent advances in ecological modeling have come together in a general strategy we call pattern-oriented modeling. This strategy provides a unifying framework for decoding the internal organization of agent-based complex systems and may lead toward unifying algorithmic theories of the relation between adaptive behavior and system complexity.     

Analysis of complex vascular systems in plants: optical shuttle method

The "optical shuttle" is an improved method of photographing with a motion-picture camera, one by one, sequential sections mounted on separate slides. The optical output from two microscopes is combined so that the images can be focused on a single film plane. Slides are photographed alternately through the microscopes. Simultaneous viewing of two successive sections in the microscopes enables initial precise alignment of images. Complex anatomical structures can thus be analyzed with relative ease.     

数学概念的学习

数学的一个显著特点就是它的抽象性.抽象的主要表现是:定义了一系列新的概念.谈了数学概念学习的步骤,数学概念理解程度的体现,以及学习概念应抓住的几个环节.     

几个数学建模案例在高等数学教学中的应用

本文主要研究了几个数学建模案例在高等数学教学中的应用,通过案例能够更好地理解高等数学中零点定理、微分方程的概念以及数学期望的知识点。进一步分析了将数学建模思想融入高等数学教学过程中的必要性,提升了学生学习高等数学的意识,进而培养学生利用数学思想去解决实际问题的能力。