752 publications from this institution
The differentiation and integration we just discussed so far are for functions with a single variable, and they are univariate functions. For functions with more than one variable, partial derivatives and multiple integrals are needed, which will be the main topics of this chapter.
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A new precise experiment has been carried out to investigate Saxl's effect of the electro-static potential on the period of an electrically charged pendulum. Our experiment shows no evidence for any new interactions.
The purpose of classification in medical informatics is to predict the presence or absence of a particular disease as well as disease types from historical data. Medical data often contain irrelevant features and noise, and an appropriate subset of the significant features can improve classification accuracy. Therefore, researchers apply feature selection to identify and remove irrelevant and redundant features. The authors propose a versatile feature selection approach called Swarm Search Feature Selection (SS-FS), based on stochastic swarm intelligence. It is designed to overcome NP-hard combinatorial search problems such as the selection of an optimal feature subset from an extremely large array of features--which is not uncommon in biomedical data. SS-FS is demonstrated to be a feasible computing tool in achieving high accuracy in classification via testing with two empirical biomedical datasets. This article is part of a special issue on life sciences computing.
No abstract is provided for this article.
Mathematical modeling uses mathematics to build proper models for physical, chemical and biological systems. Modeling has becomes an integrated part of modern science and engineering skills. This chapter uses examples to introduce the basic steps of mathematical modeling and related techniques for solving mathematical models.
Cuckoo search is a swarm-intelligence-based algorithm that is very effective for solving highly nonlinear optimization problems. In this paper, the multiobjective cuckoo search is extended so as to obtain high-quality Pareto fronts more accurately for multiobjective optimization problems with complex constraints. The proposed approach uses a combination of the cuckoo search with non-dominated sorting and archiving techniques. The performance of the proposed approach is validated by seven test problems. The convergence property and diversity as well as uniformity are compared with those of the NSGA-II. The results show that the proposed approach can find Pareto fronts with better uniformity and quicker convergence.
Swarm intelligence has becoming a powerful technique in solving design and scheduling tasks. Metaheuristic algorithms are an integrated part of this paradigm, and particle swarm optimization is often viewed as an important landmark. The outstanding performance and efficiency of swarm-based algorithms inspired many new developments, though mathematical understanding of metaheuristics remains partly a mystery. In contrast to the classic deterministic algorithms, metaheuristics such as PSO always use some form of randomness, and such randomization now employs various techniques. This paper intends to review and analyze some of the convergence and efficiency associated with metaheuristics such as firefly algorithm, random walks, and L\'evy flights. We will discuss how these techniques are used and their implications for further research.
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The firefly algorithm has become an increasingly important tool of Swarm Intelligence that has been applied in almost all areas of optimization, as well as engineering practice. Many problems from various areas have been successfully solved using the firefly algorithm and its variants. In order to use the algorithm to solve diverse problems, the original firefly algorithm needs to be modified or hybridized. This paper carries out a comprehensive review of this living and evolving discipline of Swarm Intelligence, in order to show that the firefly algorithm could be applied to every problem arising in practice. On the other hand, it encourages new researchers and algorithm developers to use this simple and yet very efficient algorithm for problem solving. It often guarantees that the obtained results will meet the expectations.
No abstract is provided for this article.
As an introductory mathematics book for engineers, the basic requirement is a good understanding of secondary mathematics (or GCSE level mathematics). All the fundamental concepts of engineering mathematics will gradually be introduced in a self-contained style with plenty of worked examples to aid the understanding of all important concepts. This chapter reviews the fundamentals of real numbers, sets, functions and equations.
