Feigenbaum graphs: a complex network perspective of chaos

The recently formulated theory of horizontal visibility graphs transforms time series into graphs and allows the possibility of studying dynamical systems through the characterization of their associated networks. This method leads to a natural graph-theoretical description of nonlinear systems with qualities in the spirit of symbolic dynamics. We support our claim via the case study of the period-doubling and band-splitting attractor cascades that characterize unimodal maps. We provide a universal analytical description of this classic scenario in terms of the horizontal visibility graphs associated with the dynamics within the attractors, that we call Feigenbaum graphs, independent of map nonlinearity or other particulars. We derive exact results for their degree distribution and related quantities, recast them in the context of the renormalization group and find that its fixed points coincide with those of network entropy optimization. Furthermore, we show that the network entropy mimics the Lyapunov exponent of the map independently of its sign, hinting at a Pesin-like relation equally valid out of chaos.Comment: Published in PLoS ONE (Sep 2011

W-Curve Alignments for HIV-1 Genomic Comparisons

The W-curve was originally developed as a graphical visualization technique for viewing DNA and RNA sequences. Its ability to render features of DNA also makes it suitable for computational studies. Its main advantage in this area is utilizing a single-pass algorithm for comparing the sequences. Avoiding recursion during sequence alignments offers advantages for speed and in-process resources. The graphical technique also allows for multiple models of comparison to be used depending on the nucleotide patterns embedded in similar whole genomic sequences. The W-curve approach allows us to compare large numbers of samples quickly.We are currently tuning the algorithm to accommodate quirks specific to HIV-1 genomic sequences so that it can be used to aid in diagnostic and vaccine efforts. Tracking the molecular evolution of the virus has been greatly hampered by gap associated problems predominantly embedded within the envelope gene of the virus. Gaps and hypermutation of the virus slow conventional string based alignments of the whole genome. This paper describes the W-curve algorithm itself, and how we have adapted it for comparison of similar HIV-1 genomes. A treebuilding method is developed with the W-curve that utilizes a novel Cylindrical Coordinate distance method and gap analysis method. HIV-1 C2-V5 env sequence regions from a Mother/Infant cohort study are used in the comparison.The output distance matrix and neighbor results produced by the W-curve are functionally equivalent to those from Clustal for C2-V5 sequences in the mother/infant pairs infected with CRF01_AE.Significant potential exists for utilizing this method in place of conventional string based alignment of HIV-1 genomes, such as Clustal X. With W-curve heuristic alignment, it may be possible to obtain clinically useful results in a short time-short enough to affect clinical choices for acute treatment. A description of the W-curve generation process, including a comparison technique of aligning extremes of the curves to effectively phase-shift them past the HIV-1 gap problem, is presented. Besides yielding similar neighbor-joining phenogram topologies, most Mother and Infant C2-V5 sequences in the cohort pairs geometrically map closest to each other, indicating that W-curve heuristics overcame any gap problem

An Updated Algorithm for the Generation of Neutral Landscapes by Spectral Synthesis

Background: Patterns that arise from an ecological process can be driven as much from the landscape over which the process is run as it is by some intrinsic properties of the process itself. The disentanglement of these effects is aided if it possible to run models of the process over artificial landscapes with controllable spatial properties. A number of different methods for the generation of so-called ‘neutral landscapes’ have been developed to provide just such a tool. Of these methods, a particular class that simulate fractional Brownian motion have shown particular promise. The existing methods of simulating fractional Brownian motion suffer from a number of problems however: they are often not easily generalisable to an arbitrary number of dimensions and produce outputs that can exhibit some undesirable artefacts. Methodology: We describe here an updated algorithm for the generation of neutral landscapes by fractional Brownian motion that do not display such undesirable properties. Using Monte Carlo simulation we assess the anisotropic properties of landscapes generated using the new algorithm described in this paper and compare it against a popular benchmark algorithm. Conclusion/Significance: The results show that the existing algorithm creates landscapes with values strongly correlated in the diagonal direction and that the new algorithm presented here corrects this artefact. A number of extensions of the algorithm described here are also highlighted: we describe how the algorithm can be employed to generate landscapes that display different properties in different dimensions and how they can be combined with an environmental gradient to produce landscapes that combine environmental variation at the local and macro scales

Texture classification of proteins using support vector machines and bio-inspired metaheuristics

6th International Joint Conference, BIOSTEC 2013, Barcelona, Spain, February 11-14, 2013[Abstract] In this paper, a novel classification method of two-dimensional polyacrylamide gel electrophoresis images is presented. Such a method uses textural features obtained by means of a feature selection process for whose implementation we compare Genetic Algorithms and Particle Swarm Optimization. Then, the selected features, among which the most decisive and representative ones appear to be those related to the second order co-occurrence matrix, are used as inputs for a Support Vector Machine. The accuracy of the proposed method is around 94 %, a statistically better performance than the classification based on the entire feature set. This classification step can be very useful for discarding over-segmented areas after a protein segmentation or identification process

Definition of a temporal distribution index for high temporal resolution precipitation data over Peninsular Spain and the Balearic Islands: the fractal dimension; and its synoptic implications

Precipitation on the Spanish mainland and in the Balearic archipelago exhibits a high degree of spatial and temporal variability, regardless of the temporal resolution of the data considered. The fractal dimension indicates the property of self-similarity, and in the case of this study, wherein it is applied to the temporal behaviour of rainfall at a fine (10-min) resolution from a total of 48 observatories, it provides insights into its more or less convective nature. The methodology of Jenkinson & Collison which automatically classifies synoptic situations at the surface, as well as an adaptation of this methodology at 500 hPa, was applied in order to gain insights into the synoptic implications of extreme values of the fractal dimension. The highest fractal dimension values in the study area were observed in places with precipitation that has a more random behaviour over time with generally high totals. Four different regions in which the atmospheric mechanisms giving rise to precipitation at the surface differ from the corresponding above-ground mechanisms have been identified in the study area based on the fractal dimension. In the north of the Iberian Peninsula, high fractal dimension values are linked to a lower frequency of anticyclonic situations, whereas the opposite occurs in the central region. In the Mediterranean, higher fractal dimension values are associated with a higher frequency of the anticyclonic type and a lower frequency of the advective type from the east. In the south, lower fractal dimension values indicate higher frequency with respect to the anticyclonic type from the east and lower frequency with respect to the cyclonic type