Algorithmic foundations

K.D.M. Harris, R.L. Johnston and B.M. Kariuki, The genetie algorithm Foundations and applications in structure solution from powder diffraction data, Acta Cryst. A54, 632 (1998) K. Shankland, B. David, and T. Csoka, Crystal structure determination from powder difffaetion data by the applieation of a genetie algorithm, Z. Kristallogr. 212, 550 (1997). 

The existence of already proven algorithms, foundation software and a computing environment that could be used as building blocks. 

Algorithmic Foundations of Robotics VIII - Selected Contributions of the Eighth International Workshop on the Algorithmic Foundations of Robotics 680 p. 2010 [978-3-642-00311-0]... 

Vose, M.D. (1999). The Simple Genetic Algorithm Foundations and Theory, MIT Press, Cambridge (MA), 251 p. 

The discovery of the phenomenon that is now known as extended X-ray absorption fine structure (EXAFS) was made in the 1920s, however, it wasn t until the 1970s that two developments set the foundation for the theory and practice of EXAFS measurements. The first was the demonstration of mathematical algorithms for the analysis of EXAFS data. The second was the advent of intense synchrotron radiation of X-ray wavelengths that immensely facilitated the acquisition of these data. During the past two decades, the use of EXAFS has become firmly established as a practical and powerfiil analytical capability for structure determination. ... 

Section III introduces the concept of nonmonotonic planning and outlines its basic features. It is shown that the tractability of nonmonotonic planning is directly related to the form of the operators employed simple propositional operators lead to polynomial-time algorithms, whereas conditional and functional operators lead to NP-hard formulations. In addition, three specific subsections establish the theoretical foundation for the conversion of operational constraints on the plans into temporal orderings of primitive operations. The three classes of constraints considered are (1) temporal ordering of abstract operations, (2) avoidable mixtures of chemical species, and (3) quantitative bounding constraints on the state of processing systems. 

The ideas presented in Section III are used to develop a concise and efficient methodology for the compression of process data, which is presented in Section IV. Of particular importance here is the conceptual foundation of the data compression algorithm instead of seeking noninterpretable, numerical compaction of data, it strives for an explicit retention of distinguished features in a signal. It is shown that this approach is both numerically efficient and amenable to explicit interpretations of historical process trends. 

The Monte Carlo method as described so far is useful to evaluate equilibrium properties but says nothing about the time evolution of the system. However, it is in some cases possible to construct a Monte Carlo algorithm that allows the simulated system to evolve like a physical system. This is the case when the dynamics can be described as thermally activated processes, such as adsorption, desorption, and diffusion. Since these processes are particularly well defined in the case of lattice models, these are particularly well suited for this approach. The foundations of dynamical Monte Carlo (DMC) or kinetic Monte Carlo (KMC) simulations have been discussed by Eichthom and Weinberg (1991) in terms of the theory of Poisson processes. The main idea is that the rate of each process that may eventually occur on the surface can be described by an equation of the Arrhenius type ... 

A helpful starting point for further investigation is Learning Classifier Systems From Foundations to Applications.1 The literature in classifier systems is far thinner than that in genetic algorithms, artificial neural networks, and other methods discussed in this book. A productive way to uncover more... 

Shor, P. W. Polynomial time algorithms for prime factorization and discrete logarithms on a quantum computer. Proc. 35th Annual Symposium on the Foundations of Computer Science Goldwasser, S. Ed. IEEE Computer Society Press Los Alamos, CA, 1994, p. 124. 

C. A. Floudas and I. E. Grossmann. Algorithmic approaches to process synthesis logic and global optimization. In Proceedings of Foundations of Computer-Aided Design, FOCAPD 94, Snowmass, Colorado, 1994. 

I. E. Grossmann. MINLP optimization strategies and algorithms for process synthesis. In Proc. 3rd. Int. Conf. on Foundations of Computer-Aided Process Design, page 105, 1990. 

Physics-based synthesis can provide extremely high quality and expressivity in a very compact algorithm. Such computational models can provide extremely low bit rates at very high quality levels for certain sounds. In addition to data compression applications, such models can also provide a foundation for the future evolution of musical instruments, moving it from the real world of wood and metal into the virtual world where formerly impossible modifications are easily tried out. 

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