DNA Circular Game of Chaos
31 Mar 2005-Vol. 757, Iss: 1, pp 217-224
TL;DR: It is shown that traditional and well‐known results from the theory of nonlinear dynamics can provide a useful ground to achieve whole genome phylogenies treating DNA as a discrete sequence and then feeding it to a dynamical system.
Abstract: One of the most important aims in evolutionary biology is the search of historical as well as structural relationships among species. In this report, we show that traditional and well‐known results from the theory of nonlinear dynamics can provide a useful ground to achieve this end. In particular, we propose whole genome phylogenies treating DNA as a discrete sequence and then feeding it to a dynamical system.
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TL;DR: A modification to the SOM algorithm is introduced in which neighborhood is contemplated from the point of view of affected units, not from the view of BMUs, and the maps achieved have, in many cases, a lower error measure than the maps formed by SOM.
Abstract: Decreasing neighborhood with distance has been identified as one of a few conditions to achieve final states in the self-organizing map (SOM) that resemble the distribution of high-dimensional input data. In the classic SOM model, best matching units (BMU) decrease their influence area as a function of distance. We introduce a modification to the SOM algorithm in which neighborhood is contemplated from the point of view of affected units, not from the view of BMUs. In our proposal, neighborhood for BMUs is not reduced, instead the rest of the units exclude some BMUs from affecting them. Each neuron identifies, from the set of BMUs that influenced it in previous epochs, those to whom it becomes refractory to for the rest of the process. Despite that the condition of decreasing neighborhood over distance is not maintained, self-organization still persists, as shown by several experiments. The maps achieved by the proposed modification have, in many cases, a lower error measure than the maps formed by SOM. Also, the model is able to remove discontinuities (kinks) from the map in a very small number of epochs, which contrasts with the original SOM model.
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Book•
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TL;DR: Focusing on how fractal geometry can be used to model real objects in the physical world, this up-to-date edition featurestwo 16-page full-color inserts, problems and tools emphasizing fractal applications, and an answers section.
Abstract: Focusing on how fractal geometry can be used to model real objects in the physical world, this up-to-date edition featurestwo 16-page full-color inserts, problems and tools emphasizing fractal applications, and an answers section. A bonus CD of an IFS Generator provides an excellent software tool for designing iterated function systems codes and fractal images.
4,361 citations
"DNA Circular Game of Chaos" refers background in this paper
...Barnsle y [2] was named "The Game of Chaos"....
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Book•
01 Jan 1993
TL;DR: Data compression with fractals is an approach to reach high compression ratios for large data streams related to images, at a cost of large amounts of computation.
Abstract: The top-selling multimedia encyclopedia Encarta, published by Microsoft Corporation, includes on one CD-ROM seven thousand color photographs which may be viewed interactively on a computer screen. The images are diverse; they are of buildings, musical instruments, people’s faces, baseball bats, ferns, etc. What most users do not know is that all of these photographs are based on fractals and that they represent a (seemingly magical) practical success of mathematics. Research on fractal image compression evolved from the mathematical ferment on chaos and fractals in the years 1978–1985 and in particular on the resurgence of interest in Julia sets and dynamical systems. Here I describe briefly some of the underlying ideas. Following Hutchinson [7], see also [5], consider first a finite set of contraction mappings wi, each with contractivity factor s < 1, taking a compact metric space X into itself, i = 1,2, . . .N. Such a setup is called an iterated function system (IFS), [1]. Use this IFS to construct a mapping W from the space H of nonempty compact subsets of X into itself by defining, in the self-explanatory notation, W (B) = N ⋃
867 citations
"DNA Circular Game of Chaos" refers background in this paper
...THE CIRCULAR GAME OF CHAOS Two decades ago, an algorithm first described by M. F. Barnsley [2] was named "The Game of Chaos"....
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...In 1999, Tsuchiya Takashi [13] realized that further insights about a dynamically generated discrete sequence could be obtained by increasing the number of sides of the polygon and getting in the limit what he named The Circular G me of Chaos (it is important, since the very outset, to remark that the denominatio game of chaosis a misnomer because the relationship of the fractal structures first obtained by Barnsley on a triangle to what the community understands by deterministic chaos is tangential)....
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...Barnsley Michael F.,Fractal Image Compression, Ak Peters Ltd., New York, 1993....
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...The details of the fractal compression algorithm can be foun d in [3] but the idea is simple: Consider a hybrid dynamical system (determinist ic rules probabilistically applied):...
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...In this case we showed that the Iterated Functio Systems proposed by Barnsley back in the eighties still have spring to unwind....
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Book•
01 Mar 1993
TL;DR: Fractal Image Compression (FI) as discussed by the authorsractals are geometric or data structures which do not simplify under magnification and can be described in terms of a few succinct rules, while the fractal contains much or all the image information.
Abstract: Fractals are geometric or data structures which do not simplify under magnification. Fractal Image Compression is a technique which associates a fractal to an image. On the one hand, the fractal can be described in terms of a few succinct rules, while on the other, the fractal contains much or all of the image information. Since the rules are described with less bits of data than the image, compression results. Data compression with fractals is an approach to reach high compression ratios for large data streams related to images. The high compression ratios are attained at a cost of large amounts of computation. Both lossless and lossy modes are supported by the technique. The technique is stable in that small errors in codes lead to small errors in image data. Applications to the NASA mission are discussed.
673 citations