Chaos game representation （CGR） is proposed as a scale-independent representation for DNA sequences and provides information about the statistical distribution of oligonucleotides in a DNA sequence. CGR images of DNA sequences represent some kinds of fractal patterns, but the common multifractal analysis based on the box counting method cannot deal with CGR images perfectly. Here, the wavelet transform modulus maxima （WTMM） method is applied to the multifractal analysis of CGR images. The results show that the scale-invariance range of CGR edge images can be extended to three orders of magnitude, and complete singularity spectra can be calculated. Spectrum parameters such as the singularity spectrum span are extracted to describe the statistical character of DNA sequences. Compared with the singularity spectrum span, exon sequences with a minimal spectrum span have the most uniform fractal structure. Also, the singularity spectrum parameters are related to oligonueleotide length, sequence component and species, thereby providing a method of studying the length polymorphism of repeat oligonucleotides.
Objective:The aim of this study was to investigate the effect of adenosine AR in the rostral ventrolateral med...
Mei-Yan JIANG,Cheng-Rong ZHANG,Jin WANG,Lin-Lin SHEN,Yin-Xiang CAO,Da-Nian ZHU Department of Physiology and Pathophysiology,Shanghai Medical College,Fudan University,Shanghai 200032,China
This article studied on five elements system and set general and strict model expectations combining with Traditional Chinese Medicine Zang-fu organs theory,in which absolute stable state,conditional stable state or transient stability and instability in mathematical models were corresponding to human healthy state,sub-healthy state(pathological plateau phase) and health deterioration state respectively.Model parameters were set up according to the mutual generation and restriction relations among five elements.The dynamic model of Five-Elements System was built,of which impulse responses were corresponding to human response under TCM treatment.Analyses of initial value and excitation response were conducted by numerical simulation and results turned out to meet the requirements of general model expectation:five elements system dynamic model had self-organization function;there existed only one non-global stable point and instability region in the five-dimensional space consisting of variables,in which instability was corresponding to pathological deterioration;system stable region was an unbounded domain and it included the stable sub-regions of special straight line-type,ray-type and line segment-type.Among those ray-types,some contained "Regression Peak" were classed as conditional stable regions while others as absolute ones.The existence of this peak indicates that our body must exceed a "Regression Threshold" when transiting from sub-healthy state(pathological plateau phase) to healthy state through self-regulation mechanism.Impulse excitation can reduce certain threshold and then increase the system health level,which is complied with the operating principle of Five-Elements System and the empirical rule of TCM clinical practice.This model has revealed qualitatively the inherent movement law of Five-Elements System and thus provides a new analysis tool for basic theoretical study on TCM.
