Continuity of set-valued maps revisited in the light of tame geometry

Continuity of set-valued maps is hereby revisited: after recalling some basic concepts of variational analysis and a short description of the State-of-the-Art, we obtain as by-product two Sard type results concerning local minima of scalar and vector valued functions. Our main result though, is inscribed in the framework of tame geometry, stating that a closed-valued semialgebraic set-valued map is almost everywhere continuous (in both topological and measure-theoretic sense). The result –depending on stratification techniques– holds true in a more general setting of o-minimal (or tame) set-valued maps. Some applications are briefly discussed at the end.

Basis set superposition error-counterpoise corrected potential energy surfaces : application to hydrogen peroxide ... X (X=F-, Cl-, Br-, Li+, Na+) complexes

Møller-Plesset (MP2) and Becke-3-Lee-Yang-Parr (B3LYP) calculations have been used to compare the geometrical parameters, hydrogen-bonding properties, vibrational frequencies and relative energies for several X- and X+ hydrogen peroxide complexes. The geometries and interaction energies were corrected for the basis set superposition error (BSSE) in all the complexes (1-5), using the full counterpoise method, yielding small BSSE values for the 6-311 + G(3df,2p) basis set used. The interaction energies calculated ranged from medium to strong hydrogen-bonding systems (1-3) and strong electrostatic interactions (4 and 5). The molecular interactions have been characterized using the atoms in molecules theory (AIM), and by the analysis of the vibrational frequencies. The minima on the BSSE-counterpoise corrected potential-energy surface (PES) have been determined as described by S. Simón, M. Duran, and J. J. Dannenberg, and the results were compared with the uncorrected PES

The relevance of the Laplacian of intracule and extracule density distributions for analyzing electron-electron interactions in molecules

A topological analysis of intracule and extracule densities and their Laplacians computed within the Hartree-Fock approximation is presented. The analysis of the density distributions reveals that among all possible electron-electron interactions in atoms and between atoms in molecules only very few are located rigorously as local maxima. In contrast, they are clearly identified as local minima in the topology of Laplacian maps. The conceptually different interpretation of intracule and extracule maps is also discussed in detail. An application example to the C2H2, C2H4, and C2H6 series of molecules is presented

Intramolecular basis set superposition error effects on the planarity of benzene and other aromatic molecules: A solution to the problem

Recently, the surprising result that ab initio calculations on benzene and other planar arenes at correlated MP2, MP3, configuration interaction with singles and doubles (CISD), and coupled cluster with singles and doubles levels of theory using standard Pople’s basis sets yield nonplanar minima has been reported. The planar optimized structures turn out to be transition states presenting one or more large imaginary frequencies, whereas single-determinant-based methods lead to the expected planar minima and no imaginary frequencies. It has been suggested that such anomalous behavior can be originated by two-electron basis set incompleteness error. In this work, we show that the reported pitfalls can be interpreted in terms of intramolecular basis set superposition error (BSSE) effects, mostly between the C–H moieties constituting the arenes. We have carried out counterpoise-corrected optimizations and frequency calculations at the Hartree–Fock, B3LYP, MP2, and CISD levels of theory with several basis sets for a number of arenes. In all cases, correcting for intramolecular BSSE fixes the anomalous behavior of the correlated methods, whereas no significant differences are observed in the single-determinant case. Consequently, all systems studied are planar at all levels of theory. The effect of different intramolecular fragment definitions and the particular case of charged species, namely, cyclopentadienyl and indenyl anions, respectively, are also discussed

Asymptotic analysis of the Gunn effect with realistic boundary conditions

A general asymptotic analysis of the Gunn effect in n-type GaAs under general boundary conditions for metal-semiconductor contacts is presented. Depending on the parameter values in the boundary condition of the injecting contact, different types of waves mediate the Gunn effect. The periodic current oscillation typical of the Gunn effect may be caused by moving charge-monopole accumulation or depletion layers, or by low- or high-field charge-dipole solitary waves. A new instability caused by multiple shedding of (low-field) dipole waves is found. In all cases the shape of the current oscillation is described in detail: we show the direct relationship between its major features (maxima, minima, plateaus, etc.) and several critical currents (which depend on the values of the contact parameters). Our results open the possibility of measuring contact parameters from the analysis of the shape of the current oscillation.

Enhanced electron-electron correlations in nanometric epitaxial SrRuO3 epitaxial films

Epitaxial and fully strained SrRuO3 thin films have been grown on SrTiO3(100). At initial stages the growth mode is three-dimensional- (3D-)like, leading to a finger-shaped structure aligned with the substrate steps and that eventually evolves into a 2D step-flow growth. We study the impact that the defect structure associated with this unique growth mode transition has on the electronic properties of the films. Detailed analysis of the transport properties of nanometric films reveals that microstructural disorder promotes a shortening of the carrier mean free path. Remarkably enough, at low temperatures, this results in a reinforcement of quantum corrections to the conductivity as predicted by recent models of disordered, strongly correlated electronic systems. This finding may provide a simple explanation for the commonly observed¿in conducting oxides-resistivity minima at low temperature. Simultaneously, the ferromagnetic transition occurring at about 140 K, becomes broader as film thickness decreases down to nanometric range. The relevance of these results for the understanding of the electronic properties of disordered electronic systems and for the technological applications of SrRuO3¿and other ferromagnetic and metallic oxides¿is stressed.

Recycling universe

If the effective cosmological constant is nonzero, our observable universe may enter a stage of exponential expansion. In such a case, regions of it may tunnel back to the false vacuum of an inflaton scalar field, and inflation with a high expansion rate may resume in those regions. An ideal eternal observer would then witness an infinite succession of cycles from false vacuum to true, and back. Within each cycle, the entire history of a hot universe would be replayed. If there were several minima of the inflaton potential, our ideal observer would visit each one of these minima with a frequency which depends on the shape of the potential. We generalize the formalism of stochastic inflation to analyze the global structure of the universe when this recycling process is taken into account.

Properties of resonant activation phenomena

The phenomenon of resonant activation of a Brownian particle over a fluctuating barrier is revisited. We discuss the important distinctions between barriers that can fluctuate among up and down configurations, and barriers that are always up but that can fluctuate among different heights. A resonance as a function of the barrier fluctuation rate is found in both cases, but the nature and physical description of these resonances is quite distinct. The nature of the resonances, the physical basis for the resonant behavior, and the importance of boundary conditions are discussed in some detail. We obtain analytic expressions for the escape time over the barrier that explicitly capture the minima as a function of the barrier fluctuation rate, and show that our analytic results are in excellent agreement with numerical results.

Asymptotic analysis of the Gunn effect with realistic boundary conditions

A general asymptotic analysis of the Gunn effect in n-type GaAs under general boundary conditions for metal-semiconductor contacts is presented. Depending on the parameter values in the boundary condition of the injecting contact, different types of waves mediate the Gunn effect. The periodic current oscillation typical of the Gunn effect may be caused by moving charge-monopole accumulation or depletion layers, or by low- or high-field charge-dipole solitary waves. A new instability caused by multiple shedding of (low-field) dipole waves is found. In all cases the shape of the current oscillation is described in detail: we show the direct relationship between its major features (maxima, minima, plateaus, etc.) and several critical currents (which depend on the values of the contact parameters). Our results open the possibility of measuring contact parameters from the analysis of the shape of the current oscillation.

Reversible and high capacity data hiding in medical images

In this paper we introduce a highly efficient reversible data hiding system. It is based on dividing the image into tiles and shifting the histograms of each image tile between its minimum and maximum frequency. Data are then inserted at the pixel level with the largest frequency to maximize data hiding capacity. It exploits the special properties of medical images, where the histogram of their nonoverlapping image tiles mostly peak around some gray values and the rest of the spectrum is mainlyempty. The zeros (or minima) and peaks (maxima) of the histograms of the image tiles are then relocated to embed the data. The grey values of some pixels are therefore modified.High capacity, high fidelity, reversibility and multiple data insertions are the key requirements of data hiding in medical images. We show how histograms of image tiles of medical images can be exploited to achieve these requirements. Compared with data hiding method applied to the whole image, our scheme can result in 30%-200% capacity improvement and still with better image quality, depending on the medical image content. Additional advantages of the proposed method include hiding data in the regions of non-interest and better exploitation of spatial masking.

Simulated Annealing, High-Order Statistics and Mutual Information for Separation of Sources

In this article, the fusion of a stochastic metaheuristic as Simulated Annealing (SA) with classical criteria for convergence of Blind Separation of Sources (BSS), is shown. Although the topic of BSS, by means of various techniques, including ICA, PCA, and neural networks, has been amply discussed in the literature, to date the possibility of using simulated annealing algorithms has not been seriously explored. From experimental results, this paper demonstrates the possible benefits offered by SA in combination with high order statistical and mutual information criteria for BSS, such as robustness against local minima and a high degree of flexibility in the energy function.

Hydrological evidence for a North Atlantic oscillation during the Little Ice Age outside its range observed since 1850.

An annual-resolved precipitation reconstruction for the last 800 yr in Southern Spain has been performed using stable carbon isotope (δ13C) of Pinus nigra tree rings. The reconstruction exhibits high- to low-frequency variability and distinguishes a Little Ice Age (LIA, AD 13501850) characterized by lower averaged rainfall than both in the transition from the Medieval Climate Anomaly to the LIA and in the 20th century. The driest conditions are recorded during the Maunder solar Minimum (mid 17thearly 18th centuries), in good agreement with the Spanish documentary archive. Similar linkage between solar activity (maximum/minimum) and precipitation (increase/decrease) is observed throughout the entire LIA. Additionally, the relationship between the hydrological pattern in the Iberian Peninsula and Morocco during the LIA suggests different spatial distribution of precipitation in the south-eastern sector of the North Atlantic region such as it is known currently. Whereas in the instrumental record the precipitation evolves similarly in both regions and opposite to the North Atlantic oscillation (NAO) index, the coldest periods of the LIA shows a contrasting pattern with drier conditions in the South of Spain and wetter in Northern Africa. We suggest an extreme negative NAO conditions, accompanied by a southward excursion of the winter rainfall band beyond that observed in the last century, can explain this contrast. The sustained NAO conditions could have been triggered by solar minima and higher volcanic activity during the LIA.