This paper presents a generalized Gronwall inequality with singularity. Using the inequality, we study the dependence of the solution on the order and the initial condition of a fractional differential equation.

Some important mechanisms in neuroendocrine-immune (NEI) system are inspired to design a decentralized, evolutionary, scalable, and adaptive system for Web service composition and management. We first abstract a novel intelligent network model inspired from the NEI system. Based on this model, we then propose a method for Web service emergence by designing a bio-entity as an autonomous agent to represent Web service. As such, automatic composition and dynamic management of Web services can be achieved. Also, we build its computation platform which allows the bio-entities to cooperate over Web services and exploits capabilities of their partners. Finally, the simulation results on the platform show that Web service emergence can be achieved through self-organizing, cooperating, and compositing. The proposed method provides a novel solution for intelligent composition and management of Web services.

The function of eukaryotic protein is closely correlated with its subcellular location. The number of newly found protein sequences entering into data banks is rapidly increasing with the success of human genome project. It is highly desirable to predict a protein subcellular automatically from its amino acid sequence. In this paper, amino acid hydrophobic patterns and average power-spectral density (APSD) are introduced to define pseudo amino acid composition. The covariant-discriminant predictor is used to predict subcellular location. Immune-genetic algorithm (IGA) is used to find the fittest weight factors which are very important in this method. As such, high success rates are obtained by both self-consistency test (86%) and jackknife test (73%). More than 80% predictive accuracy is achieved in independent dataset test. The results demonstrate that the proposed method is practical. And, the method illuminates that the protein subcellular location can be predicted from its surface physio-chemical characteristic of protein folding.

In this paper, based on microfluidic systems, we propose a DNA algorithm for solving the special 0-1 integer programming problem, which has n variables and m constraint terms. In our method, capillary electrophoresis (CE) is used to transfer and separate DNA strands, and the solutions are distinguished by analyzing the fluorescence imaging obtained by laser-induced fluorescence (LIF). Under the control of CE workstation, DNA strands with different lengths are separated and transferred according to an advanced program. This method has advantages such as low cost, low error, short operation time, and simple experimental steps. Moreover, there is no need to reconstruct probes and the size of biochip is linearly increased with the complexity of the problem.

It is a critical challenge to develop automated methods for fast and accurately determining the structures of proteins because of the increasingly widening gap between the number of sequence-known proteins and that of structureknown proteins in the post-genomic age. The knowledge of protein structural class can provide useful information towards the determination of protein structure. Thus, it is highly desirable to develop computational methods for identifying the structural classes of newly found proteins based on their primary sequence. In this study, according to the concept of Chou’s pseudo amino acid composition (PseAA), eight PseAA vectors are used to represent protein samples. Each of the PseAA vectors is a 40-D (dimensional) vector, which is constructed by the conventional amino acid composition (AA) and a series of sequence-order correlation factors as original introduced by Chou. The difference among the eight PseAA representations is that different physicochemical properties are used to incorporate the sequence-order effects for the protein samples. Based on such a framework, a dual-layer fuzzy support vector machine (FSVM) network is proposed to predict protein structural classes. In the first layer of the FSVM network, eight FSVM classifiers trained by different PseAA vectors are established. The 2nd layer FSVM classifier is applied to reclassify the outputs of the first layer. The results thus obtained are quite promising, indicating that the new method may become a useful tool for predicting not only the structural classification of proteins but also their other attributes.

In this article, we propose a new approach to the virus DNA–based evolutionary algorithm (VDNA-EA) to implement self-learning of a class of Takagi-Sugeno (T-S) fuzzy controllers. The fuzzy controllers use T-S fuzzy rules with linear consequent, the generalized input fuzzy sets, Zadeh fuzzy logic and operators, and the generalized defuzzifier. The fuzzy controllers are proved to be nonlinear proportional-integral (PI) controllers with variable gains. The fuzzy rules are discovered automatically and the design parameters in the input fuzzy sets and the linear rule consequent are optimized simultaneously by the VDNA-EA. The VDNA-EA uses the VDNA encoding method that stemmed from the structure of the VDNA to encode the design parameters of the fuzzy controllers. We use the frameshift decoding method of the VDNA to decode the DNA chromosome into the design parameters of the fuzzy controllers. In addition, the gene transfer operation and bacterial mutation operation inspired by a microbial evolution phenomenon are introduced into the VDNA-EA. Moreover, frameshift mutation operations based on the DNA genetic operations are used in the VDNA-EA to add and delete adaptively fuzzy rules. Our encoding method can significantly shorten the code length of the DNA chromosomes and improve the encoding efficiency. The length of the chromosome is variable and it is easy to insert and delete parts of the chromosome. It is suitable for complex knowledge representation and is easy for the genetic operations at gene level to be introduced into the VDNA-EA. We show how to implement the new method to self-learn a T-S fuzzy controller in the control of a nonlinear system. The fuzzy controller can be constructed automatically by the VDNA-EA. Computer simulation results indicate that the new method is effective and the designed fuzzy controller is satisfactory.

In the first part of this paper, we investigate explicit structure of the typical Takagi-Sugeno (TS) fuzzy PI and PD controllers. By typical, we mean the use of at least three trapezoidal or triangular input fuzzy sets for each input variable, fuzzy rules with linear consequent, Zadeh fuzzy logic AND operator and the centroid defuzzifier. This configuration covers many TS fuzzy controllers in the literature. We mathematically prove these fuzzy controllers to be nonlinear PI (or PD) controllers with proportional-gain and integral-gain (or derivative-gain) changing with output of the controlled system. We reveal these fuzzy controllers to be inherently nonlinear gain scheduling PI (or PD) controllers with different variable gains in different regions of input space. The gains constantly change even in the same region, and switch continuously and smoothly between adjacent regions. The explicit structural expressions of the fuzzy controllers are derived and their characteristics, including the bounds and geometrical shape of the gain variation, are studied. In the second part of the paper, we apply the Small Gain Theorem to the derived structures of the fuzzy controllers and establish a sufficient global BIBO stability criterion for nonlinear systems controlled by the fuzzy controllers. Local stability is also examined.

Grid technologies facilitate innovative applications among dynamic virtual organizations, while the ability to deploy, manage, and properly remain functioning via traditional approaches has been exceeded by the complexity of the next generation of grid systems. An important method for addressing this challenge may require nature-inspired computing paradigms. This technique will entail construction of a bottom-up multiagent system; however, the appropriate implementation mechanism is under consideration in order for the autonomous and distributed agents to emerge as a controlled grid service or application. A credit card management service in economic interactions is considered in this article for a decentralized control approach. This consideration is based on a preliminarily developed ecological network-based grid middleware that has features desired for the next generation grid systems. The control scheme, design, and implementation of he credit card management service are presented in detail. The simulation results show that (1) agents are accountable for their activities such as behavior invocation, service provision, and resource utilization and (2) generated services or applications adapt well to dynamically changing environments such as agent amounts as well as partial failure of agents. The approach presented herein is beneficial for building autonomous and adaptive grid applications and services.

This paper applies the principles and concepts in social networks to designing a decentralized, survivable and adaptive resource discovery approach in complex grid systems. The simulation results show that our approach can: (i) form relationship among clusters and significantly improve the discovery performance; (ii) adapt well to different resource distributions and user request patterns; (iii) survive from the changes of dynamic environments, including variable-biased user requests and agent amounts as well as partial failure of the agents. Our approach is not only a beneficial experience on dynamic resource discovery of complex grid systems, but also a further attempt to exploit one type of complex systems-inspired approach to build useful services in another type of complex systems.

Recent studies have shown that both Mamdani-type and Takagi-Sugeno-type fuzzy systems are universal approximators in that they can uniformly approximate continuous functions defined on compact domains with arbitrarily high approximation accuracy. In this paper, we investigate necessary conditions for general multiple-input single-output (MISO) Mamdani fuzzy systems as universal approximators with as minimal system configuration as possible. The general MISO fuzzy systems employ almost arbitrary continuous input fuzzy sets, arbitrary singleton output fuzzy sets, arbitrary fuzzy rules, product fuzzy logic AND, and the generalized defuzzifier containing the popular centroid defuzzifier as a special case. Our necessary conditions are developed under the practically sensible assumption that only a finite set of extrema of the multivariate continuous function to be approximated is available. We have first revealed a decomposition property of the general fuzzy systems: A-input fuzzy system can always be decomposed to the sum of simpler fuzzy systems where the first system has only one input variable, the second one two input variables, and the last one r input variables. Utilizing this property, we have derived some necessary conditions for the fuzzy systems to be universal approximators with minimal system configuration. The conditions expose the strength as well as limitation of the fuzzy approximation: 1) only a small number of fuzzy rules may be needed to uniformly approximate multivariate continuous functions that have a complicated formulation but a relatively small number of extrema; and 2) the number of fuzzy rules must be large in order to approximate highly oscillatory continuous functions. A numerical example is given to demonstrate our new results.