A system to reduce the effect of CCDs saturation

Colour image segmentation based on the hue component presents some problems due to the physical process of image formation. One of that problems is colour clipping, which appear when at least one of the sensor components is saturated. We have designed a system, that works for a trained set of colours, to recover the chromatic information of those pixels on which colour has been clipped. The chromatic correction method is based on the fact that hue and saturation are invariant to the uniform scaling of the three RGB components. The proposed method has been validated by means of a specific colour image processing board that has allowed its execution in real time. We show experimental results of the application of our method

Shape complexity based on mutual information

Shape complexity has recently received attention from different fields, such as computer vision and psychology. In this paper, integral geometry and information theory tools are applied to quantify the shape complexity from two different perspectives: from the inside of the object, we evaluate its degree of structure or correlation between its surfaces (inner complexity), and from the outside, we compute its degree of interaction with the circumscribing sphere (outer complexity). Our shape complexity measures are based on the following two facts: uniformly distributed global lines crossing an object define a continuous information channel and the continuous mutual information of this channel is independent of the object discretisation and invariant to translations, rotations, and changes of scale. The measures introduced in this paper can be potentially used as shape descriptors for object recognition, image retrieval, object localisation, tumour analysis, and protein docking, among others

Universal complex structures in written language

Quantitative linguistics has provided us with a number of empirical laws that characterise the evolution of languages and competition amongst them. In terms of language usage, one of the most influential results is Zipf’s law of word frequencies. Zipf’s law appears to be universal, and may not even be unique to human language. However, there is ongoing controversy over whether Zipf’s law is a good indicator of complexity. Here we present an alternative approach that puts Zipf’s law in the context of critical phenomena (the cornerstone of complexity in physics) and establishes the presence of a large-scale “attraction” between successive repetitions of words. Moreover, this phenomenon is scale-invariant and universal – the pattern is independent of word frequency and is observed in texts by different authors and written in different languages. There is evidence, however, that the shape of the scaling relation changes for words that play a key role in the text, implying the existence of different “universality classes” in the repetition of words. These behaviours exhibit striking parallels with complex catastrophic phenomena.

KAM theory for conformally symplectic systems

We present a KAM theory for some dissipative systems (geometrically, these are conformally symplectic systems, i.e. systems that transform a symplectic form into a multiple of itself). For systems with n degrees of freedom depending on n parameters we show that it is possible to find solutions with n-dimensional (Diophantine) frequencies by adjusting the parameters. We do not assume that the system is close to integrable, but we use an a-posteriori format. Our unknowns are a parameterization of the solution and a parameter. We show that if there is a sufficiently approximate solution of the invariance equation, which also satisfies some explicit non–degeneracy conditions, then there is a true solution nearby. We present results both in Sobolev norms and in analytic norms. The a–posteriori format has several consequences: A) smooth dependence on the parameters, including the singular limit of zero dissipation; B) estimates on the measure of parameters covered by quasi–periodic solutions; C) convergence of perturbative expansions in analytic systems; D) bootstrap of regularity (i.e., that all tori which are smooth enough are analytic if the map is analytic); E) a numerically efficient criterion for the break–down of the quasi–periodic solutions. The proof is based on an iterative quadratically convergent method and on suitable estimates on the (analytical and Sobolev) norms of the approximate solution. The iterative step takes advantage of some geometric identities, which give a very useful coordinate system in the neighborhood of invariant (or approximately invariant) tori. This system of coordinates has several other uses: A) it shows that for dissipative conformally symplectic systems the quasi–periodic solutions are attractors, B) it leads to efficient algorithms, which have been implemented elsewhere. Details of the proof are given mainly for maps, but we also explain the slight modifications needed for flows and we devote the appendix to present explicit algorithms for flows.

Modeling of hybrid systems by piecewise decomposition

Piecewise linear models systems arise as mathematical models of systems in many practical applications, often from linearization for nonlinear systems. There are two main approaches of dealing with these systems according to their continuous or discrete-time aspects. We propose an approach which is based on the state transformation, more particularly the partition of the phase portrait in different regions where each subregion is modeled as a two-dimensional linear time invariant system. Then the Takagi-Sugeno model, which is a combination of local model is calculated. The simulation results show that the Alpha partition is well-suited for dealing with such a system

Sales restriction, quality selection and the mode of competition

A regulator imposing “sales restrictions” on firms competing in oligopolistic markets may enhance quality provision by the firms. Moreover, for most restrictions levels, the impact on quality selection is invariant to the mode of competition

Kuranishi type Moduli Spaces for proper CR submersions fibering over the circle

Kuranishi's fundamental result (1962) associates to any compact complex manifold X&sub&0&/sub& a finite-dimensional analytic space which has to be thought of as a local moduli space of complex structures close to X&sub&0&/sub&. In this paper, we give an analogous statement for Levi-flat CR manifolds fibering properly over the circle by describing explicitely an infinite-dimensional Kuranishi type local moduli space of Levi-flat CR structures. We interpret this result in terms of Kodaira-Spencer deformation theory making clear the likenesses as well as the differences with the classical case. The article ends with applications and examples.

N-dimensional dynamical systems exploiting instabilities in full

We report experimental and numerical results showing how certain N-dimensional dynamical systems are able to exhibit complex time evolutions based on the nonlinear combination of N-1 oscillation modes. The experiments have been done with a family of thermo-optical systems of effective dynamical dimension varying from 1 to 6. The corresponding mathematical model is an N-dimensional vector field based on a scalar-valued nonlinear function of a single variable that is a linear combination of all the dynamic variables. We show how the complex evolutions appear associated with the occurrence of successive Hopf bifurcations in a saddle-node pair of fixed points up to exhaust their instability capabilities in N dimensions. For this reason the observed phenomenon is denoted as the full instability behavior of the dynamical system. The process through which the attractor responsible for the observed time evolution is formed may be rather complex and difficult to characterize. Nevertheless, the well-organized structure of the time signals suggests some generic mechanism of nonlinear mode mixing that we associate with the cluster of invariant sets emerging from the pair of fixed points and with the influence of the neighboring saddle sets on the flow nearby the attractor. The generation of invariant tori is likely during the full instability development and the global process may be considered as a generalized Landau scenario for the emergence of irregular and complex behavior through the nonlinear superposition of oscillatory motions

Ratio maps and correspondence analysis

We compare two methods for visualising contingency tables and developa method called the ratio map which combines the good properties of both.The first is a biplot based on the logratio approach to compositional dataanalysis. This approach is founded on the principle of subcompositionalcoherence, which assures that results are invariant to considering subsetsof the composition. The second approach, correspondence analysis, isbased on the chi-square approach to contingency table analysis. Acornerstone of correspondence analysis is the principle of distributionalequivalence, which assures invariance in the results when rows or columnswith identical conditional proportions are merged. Both methods may bedescribed as singular value decompositions of appropriately transformedmatrices. Correspondence analysis includes a weighting of the rows andcolumns proportional to the margins of the table. If this idea of row andcolumn weights is introduced into the logratio biplot, we obtain a methodwhich obeys both principles of subcompositional coherence and distributionalequivalence.

Multiple filtering devices for the estimation of cyclical DSGE models

We propose a method to estimate time invariant cyclical DSGE models using the informationprovided by a variety of filters. We treat data filtered with alternative procedures as contaminated proxies of the relevant model-based quantities and estimate structural and non-structuralparameters jointly using a signal extraction approach. We employ simulated data to illustratethe properties of the procedure and compare our conclusions with those obtained when just onefilter is used. We revisit the role of money in the transmission of monetary business cycles.

On the motive of a quotient variety

We show that the motive of the quotient of a scheme by a finite group coincides with the invariant submotive.

Growth, optical characterization, and laser operation of a stoichiometric crystal KYb(WO4)(2)

We present our recent achievements in the growing and optical characterization of KYb(WO4)2 (hereafter KYbW) crystals and demonstrate laser operation in this stoichiometric material. Single crystals of KYbW with optimal crystalline quality have been grown by the top-seeded-solution growth slow-cooling method. The optical anisotropy of this monoclinic crystal has been characterized, locating the tensor of the optical indicatrix and measuring the dispersion of the principal values of the refractive indices as well as the thermo-optic coefficients. Sellmeier equations have been constructed valid in the visible and near-IR spectral range. Raman scattering has been used to determine the phonon energies of KYbW and a simple physical model is applied for classification of the lattice vibration modes. Spectroscopic studies (absorption and emission measurements at room and low temperature) have been carried out in the spectral region near 1 µm characteristic for the ytterbium transition. Energy positions of the Stark sublevels of the ground and the excited state manifolds have been determined and the vibronic substructure has been identified. The intrinsic lifetime of the upper laser level has been measured taking care to suppress the effect of reabsorption and the intrinsic quantum efficiency has been estimated. Lasing has been demonstrated near 1074 nm with 41% slope efficiency at room temperature using a 0.5 mm thin plate of KYbW. This laser material holds great promise for diode pumped high-power lasers, thin disk and waveguide designs as well as for ultrashort (ps/fs) pulse laser systems.

Multiple edges of a quantum Hall system in a strong electric

In this paper we show that if the electrons in a quantum Hall sample are subjected to a constant electric field in the plane of the material, comparable in magnitude to the background magnetic field on the system of electrons, a multiplicity of edge states localized at different regions of space is produced in the sample. The actions governing the dynamics of these edge states are obtained starting from the well-known Schrödinger field theory for a system of nonrelativistic electrons, where on top of the constant background electric and magnetic fields, the electrons are further subject to slowly varying weak electromagnetic fields. In the regions between the edges, dubbed as the "bulk," the fermions can be integrated out entirely and the dynamics expressed in terms of a local effective action involving the slowly varying electromagnetic potentials. It is further shown how the bulk action is gauge noninvariant in a particular way, and how the edge states conspire to restore the U(1) electromagnetic gauge invariance of the system. In the edge action we obtain a heretofore unnoticed gauge-invariant term that depends on the particular edge. We argue that this term may be detected experimentally as different edges respond differently to a monochromatic probe due to this term

Critical review of K- ppn bound states

We make a thorough study of the process of three-body kaon absorption in nuclei, in connection with a recent FINUDA experiment which claims the existence of a deeply bound kaonic state from the observation of a peak in the Lambdad invariant mass distribution following K- absorption on 6Li. We show that the peak is naturally explained in terms of K- absorption from three nucleons leaving the rest as spectators. We can also reproduce all the other observables measured in the same experiment and used to support the hypothesis of the deeply bound kaon state. Our study also reveals interesting aspects of kaon absorption in nuclei, a process that must be understood in order to make progress in the search for K- deeply bound states in nuclei.