培养神经元网络自发活动规律性和复杂度分析

采用近似熵（approximate entropy,ApEn）的新统计方法衡量神经元不同自发放电活动时间序列数据的规律性和复杂度,对多电极阵列上培养的海马神经元网络自发活动的复杂度进行研究．结果表明不同自发放电活动的近似熵动态变化曲线有明显差别．静息期时近似熵值范围1．0-1．2;典型爆发活动时近似熵值呈现迅速下降而后上升再下降小幅振荡（0．2-0．6）;而伪爆发活动时近似熵值在0．2—0．7范围,沿平行时间轴的某一直线上下波动;连续发放锋电位时近似熵值在0．8-0．9范围;而随机单发锋电位时近似熵值0．6—0．8范围．以上分析结果说明近似熵动态变化曲线能够体现爆发活动和锋电位发放过程的规律性和复杂度变化,并可以有效地识别培养神经元网络自发的不同电生理信号,因而在神经元电信号分析中有着潜在的应用价值．     

心率变异性的复杂性与分形维数分析

发挥非线性动力学的潜力，提出了心率变异性（ＨＲＶ）信号的复杂度分析法和分形维数分析法。由于这两种方法能从较短的ＨＲＶ信号中提取信息，因此作者又进一步把这两种分析方法发展成动态分析法。用这两种方法分别对一个改变体位的ＨＲＶ信号和一个发生心肌缺血的ＨＲＶ信号的过程进行了动态分析。分析结果表明，它们都成功地检测出了ＨＲＶ信号的生理和病理变化。可见，动态复杂度分析法和动态分形维数分析法对ＨＲＶ信号及类似于ＨＲＶ的信号是很有前途的分析方法。     

The k-Error Linear Complexity and the Linear Complexity for pq^n-Periodic Binary Sequences

The k-error linear complexity and the linear complexity of the keystream of a stream cipher are two important standards to scale the randomness of the key stream. For a pq^n-periodic binary sequences where p, q are two odd primes satisfying that 2 is a primitive root module p and q^2 and gcd（p-1, q-1） = 2, we analyze the relationship between the linear complexity and the minimum value k for which the k-error linear complexity is strictly less than the linear complexity.     

城市结构的多维性和复杂性

通过对城市、社会、人之间相关关系的分析 ,探讨城市的本质和城市结构的含义 ,从城市结构与形态、城市发展演化和城市的整体性等视角 ,论叙城市结构的多维性和复杂性。     

股票市场的复杂性与有效性(英文)

对金融市场提出有效性指标和复杂性指标,利用"滑动窗技术"研究了上海和深圳股票市场有效性与复杂性之间的关联.结果显示,上海股票市场的复杂性和有效性之间以及复杂性之间存在双向的Granger因果关系,深圳股票市场亦是如此;两个市场的有效性之间存在双向的Granger因果关系,两个市场的复杂性之间亦是如此;上海股票市场的有效性之间以及复杂性之间相互影响强于深圳股票市场,两个市场有效性之间的相互影响强于复杂性之间的相互影响.论文的实证结果支持了刘维奇关于金融复杂性可以改进金融市场效率的理论研究的论断.     

基于统计复杂度的非对称双稳系统的动力学复杂性研究

本文运用统计复杂度和标准Shannon熵研究了乘性色噪声和加性白噪声共同作用下非对称双稳系统的动力学复杂性.考虑到系统势函数的非对称性,借助于Bandt-Pompe算法分别计算了系统总的以及左、右势阱的统计复杂度和标准Shannon熵,并在此基础上详细讨论了势阱的非对称性、加性白噪声、乘性色噪声及周期信号等对系统动力学复杂性的影响.结果表明,当这些因素变化时,系统总的统计复杂度和标准Shannon熵与系统单个势阱中的统计复杂度和标准Shannon熵呈现出明显不同的趋势,反映了其动力学复杂性的不同.     

The energetics of genome complexity

All complex life is composed of eukaryotic (nucleated) cells. The eukaryotic cell arose from prokaryotes just once in four billion years, and otherwise prokaryotes show no tendency to evolve greater complexity. Why not? Prokaryotic genome size is constrained by bioenergetics. The endosymbiosis that gave rise to mitochondria restructured the distribution of DNA in relation to bioenergetic membranes, permitting a remarkable 200,000-fold expansion in the number of genes expressed. This vast leap in genomic capacity was strictly dependent on mitochondrial power, and prerequisite to eukaryote complexity: the key innovation en route to multicellular life.     

Non-adaptive origins of interactome complexity

The boundaries between prokaryotes, unicellular eukaryotes and multicellular eukaryotes are accompanied by orders-of-magnitude reductions in effective population size, with concurrent amplifications of the effects of random genetic drift and mutation. The resultant decline in the efficiency of selection seems to be sufficient to influence a wide range of attributes at the genomic level in a non-adaptive manner. A key remaining question concerns the extent to which variation in the power of random genetic drift is capable of influencing phylogenetic diversity at the subcellular and cellular levels. Should this be the case, population size would have to be considered as a potential determinant of the mechanistic pathways underlying long-term phenotypic evolution. Here we demonstrate a phylogenetically broad inverse relation between the power of drift and the structural integrity of protein subunits. This leads to the hypothesis that the accumulation of mildly deleterious mutations in populations of small size induces secondary selection for protein-protein interactions that stabilize key gene functions. By this means, the complex protein architectures and interactions essential to the genesis of phenotypic diversity may initially emerge by non-adaptive mechanisms.     

单向副集的区间生成及其生成粒度

针对单向S-粗集副集的动态性和单向迁移特性,基于单向副集的α-生成与α-生成粒度的基础上提出单向副集AS(X°)的区间生成、区间生成粒度、区间集生成、区间集生成粒度的概念.并对其性质进行了讨论,单向副集的区间生成及其生成粒度拓展为S-粗集的应用范围.     

连接型自动机的极小化及其复杂性

通过定义确定型有穷自动机在状态集上的等价关系,可以构造一类非确定型有穷自动机在状态集上的等价关系,利用这个等价关系可以对这类非确定型有穷自动机进行极小化。     

Functional complexity and regulation through RNA dynamics

Changes to the conformation of coding and non-coding RNAs form the basis of elements of genetic regulation and provide an important source of complexity, which drives many of the fundamental processes of life. Although the structure of RNA is highly flexible, the underlying dynamics of RNA are robust and are limited to transitions between the few conformations that preserve favourable base-pairing and stacking interactions. The mechanisms by which cellular processes harness the intrinsic dynamic behaviour of RNA and use it within functionally productive pathways are complex. The versatile functions and ease by which it is integrated into a wide variety of genetic circuits and biochemical pathways suggests there is a general and fundamental role for RNA dynamics in cellular processes.     

改进的堆排序算法及其复杂度分析

给出了传统堆排序算法的改进算法，该算法降低了原算法的复杂度，在元素个数较大时，能较明显地提高算法的效率。     

司期为2^n的线性复杂度为2^n-9二元序列的k错线性复杂度分布

线性复杂度和k错线性复杂度分别是度量密钥流序列的密码强度和稳定性的重要指标。通过研究周期为2^n的二元序列线性复杂度．提出将k错线性复杂度的计算转化为求Hamming重量最小的错误序列。基于Games-Chan算法．讨论周期为2^n的线性复杂度为2^n-9的二元序列的4错线性复杂度分布,并给出了其对应4错线性复杂度序列的计数公式。     

The complexity of variable minimal formulas

Based on the common properties of logic formulas: equivalence and satisfiability, the concept of variable minimal formulas with property preservation is introduced. A formula is variable minimal if the resulting sub-formulas with any variable omission will change the given property. Some theoretical results of two classes: variable minimal equivalence (VME) and variable minimal satisfiability (VMS) are studied. We prove that VME is NP-complete, and VMS is in D^P and coNP-hard.     

Kerr-AdS黑洞的复杂度

规范/引力对偶为人们提供了一个研究物理的全新视角.由规范/引力对偶可知,边界上的共形场论等价于其内部的Anti-de Sitter时空.这个对偶为人们研究边界共形场论带来了极大的方便.最近,Susskind团队提出了一个复杂度/作用量对偶假设:认为黑洞边界上态的量子计算复杂度等价于其在Wheeler-DeWitt片中的作用量.复杂度代表了进行量子计算的困难程度,这意味着黑洞也许与量子计算有联系,这也加深了人们对黑洞的认识.基于这个假设,考虑类光关节项的贡献,改进了Susskind团队的原有方案,更精确地计算了Kerr-AdS黑洞的Wheeler-DeWitt片的作用量增长率,最终得到了边界态复杂度的增长率.