具有非线性种内制约关系和分布时滞竞争模型的稳定性

构造并研究了一类具有分布时滞和非线性种内制约关系的竞争模型.得到了这类模型的边界平衡点和共存平衡点全局渐近稳定的条件,以及分布时滞、非线性种内制约关系对模型的影响.     

Profiling services for resource optimization and capacity planning in distributed systems

The capacity needs of online services are mainly determined by the volume of user loads. For large-scale distributed systems running such services, it is quite difficult to match the capacities of various system components. In this paper, a novel and systematic approach is proposed to profile services for resource optimization and capacity planning. We collect resource consumption related measurements from various components across distributed systems and further search for constant relationships between these measurements. If such relationships always hold under various workloads along time, we consider them as invariants of the underlying system. After extracting many invariants from the system, given any volume of user loads, we can follow these invariant relationships sequentially to estimate the capacity needs of individual components. By comparing the current resource configurations against the estimated capacity needs, we can discover the weakest points that may deteriorate system performance. Operators can consult such analytical results to optimize resource assignments and remove potential performance bottlenecks. In this paper, we propose several algorithms to support capacity analysis and guide operator’s capacity planning tasks. Our algorithms are evaluated with real systems and experimental results are also included to demonstrate the effectiveness of our approach.

Coding of distributed, topographic and non-specific representations within the brain

This article explores the theoretical basis of coding within topographic representations, where neurons encoding specific features such as locations, are arranged into maps. A novel type of representation, termed non-specific, where each neuron does not encode specific features is also postulated. In common with the previously described distributed representations [Rolls, E.T., Treves, A., 1998. Neural Networks and Brain Function. Oxford University Press, Oxford], topographic representations display an exponential relationship between stimuli encoded and both number of neurons and maximum firing rate of those neurons. The non-specific representations described here display a binomial expansion between the number of stimuli encoded and the sum of the number of neurons and the maximum firing rate; therefore groups of non-specific neurons usually encode less stimuli than equivalent topographic layers of neurons. Lower and higher order sensory regions of the brain use either topographic or distributed representations to encode information. It is proposed that non-specific representations may occur in regions of the brain where different types of information may be represented by the same neurons, as occurs in the prefrontal cortex.     

一类具有分布时滞的扩散种群模型行波解的存在性

研究了一类具有分布时滞的扩散种群模型行波解的存在性,证明了当平均时滞充分小时,方程具有连接两个平衡点的单调行波解.     

A delay reaction-diffusion model of the dynamics of botulinum in fish

A model of interaction between fish and a bacterium (Clostridium botulinum) responsible for avian botulism is introduced, considering diffusion of both fish and bacterium in water. The fish population moves randomly in water. Death fish disintegrate in water, at different locations, causing bacteria to diffuse through water and infect other fish. Existence of uniform steady states is investigated and the linearized stability of the positive uniform steady state is analyzed. A Hopf bifurcation is proved to occur from the uniform steady state when the bifurcation parameter, here the time delay, passes through a critical value and diffusion coefficients satisfy some conditions, that induces time oscillations of the populations. Comments on diffusion-driven instability are provided, and numerical simulations are carried out to illustrate the results.     

On the spread of epidemics in a closed heterogeneous population

Heterogeneity is an important property of any population experiencing a disease. Here we apply general methods of the theory of heterogeneous populations to the simplest mathematical models in epidemiology. In particular, an SIR (susceptible-infective-removed) model is formulated and analyzed when susceptibility to or infectivity of a particular disease is distributed. It is shown that a heterogeneous model can be reduced to a homogeneous model with a nonlinear transmission function, which is given in explicit form. The widely used power transmission function is deduced from the model with distributed susceptibility and infectivity with the initial gamma-distribution of the disease parameters. Therefore, a mechanistic derivation of the phenomenological model, which is believed to mimic reality with high accuracy, is provided. The equation for the final size of an epidemic for an arbitrary initial distribution of susceptibility is found. The implications of population heterogeneity are discussed, in particular, it is pointed out that usual moment-closure methods can lead to erroneous conclusions if applied for the study of the long-term behavior of the models.     

多维球面模型应用于草原监测数据分析的探讨

 提出分析归纳草原监测多元数据的新数学方法,多维球面模型。M个物种所组成的草原的状态可以用M元向量来表示,向量的长度用来表示草原的量值,向量的方向表示草原组成。从草原监测的角度,草原的相对组成是更重要的,成份变化的比率更能说明问题。在处理草原监测数据中使用向量等比系列和向量等差系列是可行的。等比系列比较能反映生物几何增长的本质。为了纠正中间过程被忽略的弱点,要坚持逐年监测,逐步分析,或使用滑动平均。二阶趋势值可尝试用于解决时间滞后问题,卡门滤波用于降低预报误差。因为草原监测需要使用分种数据,必须以人工监测记录为主,再辅以其它高科技手段,如遥感。     

Arithmetic inside the universal genetic code

The first information system emerged on the earth as primordial version of the genetic code and genetic texts. The natural appearance of arithmetic power in such a linguistic milieu is theoretically possible and practical for producing information systems of extremely high efficiency. In this case, the arithmetic symbols should be incorporated into an alphabet, i.e. the genetic code. A number is the fundamental arithmetic symbol produced by the system of numeration. If the system of numeration were detected inside the genetic code, it would be natural to expect that its purpose is arithmetic calculation e.g., for the sake of control, safety, and precise alteration of the genetic texts. The nucleons of amino acids and the bases of nucleic acids seem most suitable for embodiments of digits. These assumptions were used for the analyzing the genetic code.

The compressed, life-size, and split representation of the Escherichia coli and Euplotes octocarinatus code versions were considered simultaneously. An exact equilibration of the nucleon sums of the amino acid standard blocks and/or side chains was found repeatedly within specified sets of the genetic code. Moreover, the digital notations of the balanced sums acquired, in decimal representation, the unique form 111, 222, …, 999. This form is a consequence of the criterion of divisibility by 037. The criterion could simplify some computing mechanism of a cell if any and facilitate its computational procedure. The cooperative symmetry of the genetic code demonstrates that possibly a zero was invented and used by this mechanism. Such organization of the genetic code could be explained by activities of some hypothetical molecular organelles working as natural biocomputers of digital genetic texts.

It is well known that if mutation replaces an amino acid, the change of hydrophobicity is generally weak, while that of size is strong. The antisymmetrical correlation between the amino acid size and the degeneracy number is known as well. It is shown that these and some other familiar properties may be a physicochemical effect of arithmetic inside the genetic code.

The “frozen accident” model, giving unlimited freedom to the mapping function, could optimally support the appearance of both arithmetic symbols and physicochemical protection inside the genetic code.     

The slow process: A hypothetical cognitive adaptation for distributed cognitive networks

Human cognitive evolution is characterized by two special features that are truly novel in the primate line. The first is the emergence of "mindsharing" cultures that perform cooperative cognitive work, and serve as distributed cognitive networks. The second is the emergence of a brain that is specifically adapted for functioning within those distributed networks, and cannot realize its design potential without them. This paper proposes a hypothetical neural process at the core of this brain adaptation, called the "slow process". It enables the human brain to comprehend social events of much longer duration and complexity than those that characterize primate social life. It runs in the background of human cognitive life, with the faster moving sensorimotor interface running in the foreground. Most mammals can integrate events in the shorter time zone that corresponds to working memory. However, very few can comprehend complex events that extend over several hours (for example, a game or conversation) in what may be called the "intermediate" time zone. Adult humans typically live, plan, and imagine their lives in this time range, which seems to exceed the capabilities of our closest relatives, bonobos and chimpanzees. In summary, human cognition has both an individual and a collective dimension. Individual brains and minds function within cognitive-cultural networks, or CCNs, that store and transmit knowledge. The human brain relies on cultural input even to develop the basic cognitive capacities needed to gain access to that knowledge in the first place. The postulated slow process is a top-down executive capacity that evolved specifically to manage the cultural connection, and handle the cognitive demands imposed by increasingly complex distributed systems.     

An adaptive dual control framework for QoS design

The widespread deployment of the advanced computer technology in business and industries has demanded the high standard on quality of service (QoS). For example, many Internet applications, i.e. online trading, e-commerce, and real-time databases, etc., execute in an unpredictable general-purpose environment but require performance guarantees. Failure to meet performance specifications may result in losing business or liability violations. As systems become distributed and complex, it has become a challenge for QoS design. The ability of on-line identification and auto-tuning of adaptive control systems has made the adaptive control theoretical design an attractive approach for QoS design. However, there is an inherent constraint in adaptive control systems, i.e. a conflict between asymptotically good control and asymptotically good on-line identification. This paper first identifies and analyzes the limitations of adaptive control for network QoS by extensive simulation studies. Secondly, as an approach to mitigate the limitations, we propose an adaptive dual control framework. By incorporating the existing uncertainty of on-line prediction into the control strategy and accelerating the parameter estimation process, the adaptive dual control framework optimizes the tradeoff between the control goal and the uncertainty, and demonstrates robust and cautious behavior. The experimental study shows that the adaptive dual control framework mitigate the limitations of the conventional adaptive control framework. Compared with the conventional adaptive control framework under the medium uncertainty, the adaptive dual control framework reduces the deviation from the desired hit-rate ratio from 40% to 13%.