902 research outputs found
Shannon entropy analysis of the genome code
This paper studies the chromosome information of twenty five species, namely, mammals, fishes,
birds, insects, nematodes, fungus, and one plant. A quantifying scheme inspired in the state space
representation of dynamical systems is formulated. Based on this algorithm, the information of
each chromosome is converted into a bidimensional distribution. The plots are then analyzed and
characterized by means of Shannon entropy. The large volume of information is integrated by
averaging the lengths and entropy quantities of each species. The results can be easily visualized
revealing quantitative global genomic information
Optimal controllers with complex order derivatives
This paper studies the optimization of complex-order algorithms for the
discrete-time control of linear and nonlinear systems. The fundamentals of fractional
systems and genetic algorithms are introduced. Based on these concepts, complexorder
control schemes and their implementation are evaluated in the perspective
of evolutionary optimization. The results demonstrate not only that complex-order
derivatives constitute a valuable alternative for deriving control algorithms, but also
the feasibility of the adopted optimization strategy
Fractional dynamics of genetic algorithms using hexagonal space tessellation
The paper formulates a genetic algorithm that evolves two types of objects in a plane. The fitness function promotes a relationship between the objects that is optimal when some kind of interface between them occurs. Furthermore, the algorithm adopts an hexagonal tessellation of the two-dimensional space for promoting an efficient method of the neighbour modelling. The genetic algorithm produces special patterns with resemblances to those revealed in percolation phenomena or in the symbiosis found in lichens. Besides the analysis of the spacial layout, a modelling of the time evolution is performed by adopting a distance measure and the modelling in the Fourier domain in the perspective of fractional calculus. The results reveal a consistent, and easy to interpret, set of model parameters for distinct operating conditions
Root locus of fractional linear systems
In this paper an algorithm for the calculation of the root locus of fractional linear systems is
presented. The proposed algorithm takes advantage of present day computational
resources and processes directly the characteristic equation, avoiding the limitations
revealed by standard methods. The results demonstrate the good performance for different
types of expressions
Calculation of fractional derivatives of noisy data with genetic algorithms
This paper addresses the calculation of derivatives of fractional order for non-smooth data. The noise is avoided by adopting an optimization formulation using genetic algorithms (GA). Given the flexibility of the evolutionary schemes, a hierarchical GA composed by a series of two GAs, each one with a distinct fitness function, is established
Fractional derivatives: probability interpretation and frequency response of rational approximations
The theory of fractional calculus (FC) is a useful mathematical tool in many applied sciences. Nevertheless, only in the last decades researchers were motivated for the adoption of the FC concepts. There are several reasons for this state of affairs, namely the co-existence of different definitions and interpretations, and the necessity of approximation methods for the real time calculation of fractional derivatives (FDs). In a first part, this paper introduces a probabilistic interpretation of the fractional derivative based on the Grünwald-Letnikov definition. In a second part, the calculation of fractional derivatives through Padé fraction approximations is analyzed. It is observed that the probabilistic interpretation and the frequency response of fraction approximations of FDs reveal a clear correlation between both concepts
Multidimensional Scalling Analysis of the World Economy During the Period 1972-2012
The last 40 years of the world economy are analyzed by means of computer visualization methods. Multidimensional scaling and the hierarchical clustering tree techniques are used. The current Western downturn in favor of Asian partners may still be reversed in the coming decades
Complex dynamics of financial indices
This paper presents a novel method for the
analysis of nonlinear financial and economic systems.
The modeling approach integrates the classical concepts
of state space representation and time series regression.
The analytical and numerical scheme leads
to a parameter space representation that constitutes a
valid alternative to represent the dynamical behavior.
The results reveal that business cycles can be clearly
revealed, while the noise effects common in financial
indices can elegantly be filtered out of the results
Accessing complexity from genome information
This paper studies the information content of the chromosomes of 24 species. In a first
phase, a scheme inspired in dynamical system state space representation is developed.
For each chromosome the state space dynamical evolution is shed into a two dimensional
chart. The plots are then analyzed and characterized in the perspective of fractal dimension.
This information is integrated in two measures of the species’ complexity addressing
its average and variability. The results are in close accordance with phylogenetics pointing
quantitative aspects of the species’ genomic complexity
Time-delay and fractional derivatives
This paper proposes the calculation of fractional algorithms based on time-delay systems. The
study starts by analyzing the memory properties of fractional operators and their relation with
time delay. Based on the Fourier analysis an approximation of fractional derivatives through timedelayed
samples is developed. Furthermore, the parameters of the proposed approximation are
estimated by means of genetic algorithms. The results demonstrate the feasibility of the new
perspective
- …