Noise-Driven Mechanism for Pattern Formation

We extend the mechanism for noise-induced phase transitions proposed by Ibañes et al. [Phys. Rev. Lett. 87, 020601 (2001)] to pattern formation phenomena. In contrast with known mechanisms for pure noise-induced pattern formation, this mechanism is not driven by a short-time instability amplified by collective effects. The phenomenon is analyzed by means of a modulated mean field approximation and numerical simulations.

Colored noise in spatially extended systems

We study the effects of time and space correlations of an external additive colored noise on the steady-state behavior of a time-dependent Ginzburg-Landau model. Simulations show the existence of nonequilibrium phase transitions controlled by both the correlation time and length of the noise. A Fokker-Planck equation and the steady probability density of the process are obtained by means of a theoretical approximation.

Viscous fingering as a paradigm of interfacial pattern formation: Recent results and new challenges

We review recent results on dynamical aspects of viscous fingering. The Saffman¿Taylor instability is studied beyond linear stability analysis by means of a weakly nonlinear analysis and the exact determination of the subcritical branch. A series of contributions pursuing the idea of a dynamical solvability scenario associated to surface tension in analogy with the traditional selection theory is put in perspective and discussed in the light of the asymptotic theory of Tanveer and co-workers. The inherently dynamical singular effects of surface tension are clarified. The dynamical role of viscosity contrast is explored numerically. We find that the basin of attraction of the Saffman¿Taylor finger depends on viscosity contrast, and that the sensitivity to this parameter is maximal in the usual limit of high viscosity contrast. The competing attractors are identified as closed bubble solutions. We briefly report on recent results and work in progress concerning rotating Hele-Shaw flows, topological singularities and wetting effects, and also discuss future directions in the context of viscous fingering

Design of Optical Systems With Extended Depth of Field: an Educational Approach to Wavefront Coding Techniques

A practical activity designed to introduce wavefront coding techniques as a method to extend the depth of field in optical systems is presented. The activity is suitable for advanced undergraduate students since it combines different topics in optical engineering such as optical system design, aberration theory, Fourier optics, and digital image processing. This paper provides the theoretical background and technical information for performing the experiment. The proposed activity requires students able to develop a wide range of skills since they are expected to deal with optical components, including spatial light modulators, and develop scripts to perform some calculations.

Application of fuzzy-rule-based postprocessing to correlation methods in pattern recognition

One of the most important problems in optical pattern recognition by correlation is the appearance of sidelobes in the correlation plane, which causes false alarms. We present a method that eliminate sidelobes of up to a given height if certain conditions are satisfied. The method can be applied to any generalized synthetic discriminant function filter and is capable of rejecting lateral peaks that are even higher than the central correlation. Satisfactory results were obtained in both computer simulations and optical implementation.

Evidence of extended orientational order in amorphous Fe/Sm thin films

Amorphous thin films of Fe/Sm, prepared by evaporation methods, have been magnetically characterized and the results were interpreted in terms of the random magnets theory. The samples behave as 2D and 3D random magnets depending on the total thickness of the film. From our data the existence of orientational order, which greatly influences the magnetic behavior of the films, is also clear.

Pattern selection in a lattice of pulse-coupled oscillators

We study spatio-temporal pattern formation in a ring of N oscillators with inhibitory unidirectional pulselike interactions. The attractors of the dynamics are limit cycles where each oscillator fires once and only once. Since some of these limit cycles lead to the same pattern, we introduce the concept of pattern degeneracy to take it into account. Moreover, we give a qualitative estimation of the volume of the basin of attraction of each pattern by means of some probabilistic arguments and pattern degeneracy, and show how they are modified as we change the value of the coupling strength. In the limit of small coupling, our estimative formula gives a pefect agreement with numerical simulations.

Mechanisms of synchronization and pattern formation in a lattice of pulse-coupled oscillators

We analyze the physical mechanisms leading either to synchronization or to the formation of spatiotemporal patterns in a lattice model of pulse-coupled oscillators. In order to make the system tractable from a mathematical point of view we study a one-dimensional ring with unidirectional coupling. In such a situation, exact results concerning the stability of the fixed of the dynamic evolution of the lattice can be obtained. Furthermore, we show that this stability is the responsible for the different behaviors.

Evidence of extended orientational order in amorphous Fe/Sm thin films

Amorphous thin films of Fe/Sm, prepared by evaporation methods, have been magnetically characterized and the results were interpreted in terms of the random magnets theory. The samples behave as 2D and 3D random magnets depending on the total thickness of the film. From our data the existence of orientational order, which greatly influences the magnetic behavior of the films, is also clear.

Rapid radiation in spiny lobsters (Palinurus spp) as revealed by classic and ABC methods using mtDNA and microsatellite data

Background: Molecular tools may help to uncover closely related and still diverging species from a wide variety of taxa and provide insight into the mechanisms, pace and geography of marine speciation. There is a certain controversy on the phylogeography and speciation modes of species-groups with an Eastern Atlantic-Western Indian Ocean distribution, with previous studies suggesting that older events (Miocene) and/or more recent (Pleistocene) oceanographic processes could have influenced the phylogeny of marine taxa. The spiny lobster genus Palinurus allows for testing among speciation hypotheses, since it has a particular distribution with two groups of three species each in the Northeastern Atlantic (P. elephas, P. mauritanicus and P. charlestoni) and Southeastern Atlantic and Southwestern Indian Oceans (P. gilchristi, P. delagoae and P. barbarae). In the present study, we obtain a more complete understanding of the phylogenetic relationships among these species through a combined dataset with both nuclear and mitochondrial markers, by testing alternative hypotheses on both the mutation rate and tree topology under the recently developed approximate Bayesian computation (ABC) methods. Results Our analyses support a North-to-South speciation pattern in Palinurus with all the South-African species forming a monophyletic clade nested within the Northern Hemisphere species. Coalescent-based ABC methods allowed us to reject the previously proposed hypothesis of a Middle Miocene speciation event related with the closure of the Tethyan Seaway. Instead, divergence times obtained for Palinurus species using the combined mtDNA-microsatellite dataset and standard mutation rates for mtDNA agree with known glaciation-related processes occurring during the last 2 my. Conclusion The Palinurus speciation pattern is a typical example of a series of rapid speciation events occurring within a group, with very short branches separating different species. Our results support the hypothesis that recent climate change-related oceanographic processes have influenced the phylogeny of marine taxa, with most Palinurus species originating during the last two million years. The present study highlights the value of new coalescent-based statistical methods such as ABC for testing different speciation hypotheses using molecular data.

Genesis and evolution of the Evx and Mox genes and the extended Hox and ParaHox gene clusters

Background: Hox and ParaHox gene clusters are thought to have resulted from the duplication of a ProtoHox gene cluster early in metazoan evolution. However, the origin and evolution of the other genes belonging to the extended Hox group of homeobox-containing genes, that is, Mox and Evx, remains obscure. We constructed phylogenetic trees with mouse, amphioxus and Drosophila extended Hox and other related Antennapedia-type homeobox gene sequences and analyzed the linkage data available for such genes.Results: We claim that neither Mox nor Evx is a Hox or ParaHox gene. We propose a scenariothat reconciles phylogeny with linkage data, in which an Evx/Mox ancestor gene linked to aProtoHox cluster was involved in a segmental tandem duplication event that generated an arrayof all Hox-like genes, referred to as the `coupled¿ cluster. A chromosomal breakage within thiscluster explains the current composition of the extended Hox cluster (with Evx, Hox and Moxgenes) and the ParaHox cluster.Conclusions: Most studies dealing with the origin and evolution of Hox and ParaHox clustershave not included the Hox-related genes Mox and Evx. Our phylogenetic analyses and theavailable linkage data in mammalian genomes support an evolutionary scenario in which anancestor of Evx and Mox was linked to the ProtoHox cluster, and that a tandem duplication of alarge genomic region early in metazoan evolution generated the Hox and ParaHox clusters, plusthe cluster-neighbors Evx and Mox. The large `coupled¿ Hox-like cluster EvxHox/MoxParaHox wassubsequently broken, thus grouping the Mox and Evx genes to the Hox clusters, and isolating theParaHox cluster.

Discriminant ECOC: a heuristic method for application dependent design of error correcting output codes

We present a heuristic method for learning error correcting output codes matrices based on a hierarchical partition of the class space that maximizes a discriminative criterion. To achieve this goal, the optimal codeword separation is sacrificed in favor of a maximum class discrimination in the partitions. The creation of the hierarchical partition set is performed using a binary tree. As a result, a compact matrix with high discrimination power is obtained. Our method is validated using the UCI database and applied to a real problem, the classification of traffic sign images.

Dynamics of transient pattern formation in nematic liquid crystals

We analyze the dynamics of a transient pattern formation in the Fréedericksz transition corresponding to a twist geometry. We present a calculation of the time-dependent structure factor based on a dynamical model which incorporates consistently the coupling of the director field with the velocity flow and also the effect of fluctuations. The appearance and development of a characteristic periodicity is described in terms of the time dependence of the maximum of the structure factor. We find a well-defined time for the appearance of the pattern and a subsequent stage of pattern development in which the characteristic periodicity tends to an asymptotic value.