A Note on the periodic orbits and topological entropy of graph maps

This paper deals with the relationship between the periodic orbits of continuous maps on graphs and the topological entropy of the map. We show that the topological entropy of a graph map can be approximated by the entropy of its periodic orbits

Quantum similarity topological indices definition, analysis and comparison with classical molecular topological indices

Es mostra que, gracies a una extensió en la definició dels Índexs Moleculars Topològics, s'arriba a la formulació d'índexs relacionats amb la teoria de la Semblança Molecular Quàntica. Es posa de manifest la connexió entre les dues metodologies: es revela que un marc de treball teòric sòlidament fonamentat sobre la teoria de la Mecànica Quàntica es pot connectar amb una de les tècniques més antigues relacionades amb els estudis de QSPR. Es mostren els resultats per a dos casos d'exemple d'aplicació d'ambdues metodologies

Refinement criteria for global illumination using convex funcions

In several computer graphics areas, a refinement criterion is often needed to decide whether to go on or to stop sampling a signal. When the sampled values are homogeneous enough, we assume that they represent the signal fairly well and we do not need further refinement, otherwise more samples are required, possibly with adaptive subdivision of the domain. For this purpose, a criterion which is very sensitive to variability is necessary. In this paper, we present a family of discrimination measures, the f-divergences, meeting this requirement. These convex functions have been well studied and successfully applied to image processing and several areas of engineering. Two applications to global illumination are shown: oracles for hierarchical radiosity and criteria for adaptive refinement in ray-tracing. We obtain significantly better results than with classic criteria, showing that f-divergences are worth further investigation in computer graphics. Also a discrimination measure based on entropy of the samples for refinement in ray-tracing is introduced. The recursive decomposition of entropy provides us with a natural method to deal with the adaptive subdivision of the sampling region

Compression-based Image Registration

Image registration is an important component of image analysis used to align two or more images. In this paper, we present a new framework for image registration based on compression. The basic idea underlying our approach is the conjecture that two images are correctly registered when we can maximally compress one image given the information in the other. The contribution of this paper is twofold. First, we show that the image registration process can be dealt with from the perspective of a compression problem. Second, we demonstrate that the similarity metric, introduced by Li et al., performs well in image registration. Two different versions of the similarity metric have been used: the Kolmogorov version, computed using standard real-world compressors, and the Shannon version, calculated from an estimation of the entropy rate of the images

Viewpoint-Based Ambient Occlusion

We've developed a new ambient occlusion technique based on an information-theoretic framework. Essentially, our method computes a weighted visibility from each object polygon to all viewpoints; we then use these visibility values to obtain the information associated with each polygon. So, just as a viewpoint has information about the model's polygons, the polygons gather information on the viewpoints. We therefore have two measures associated with an information channel defined by the set of viewpoints as input and the object's polygons as output, or vice versa. From this polygonal information, we obtain an occlusion map that serves as a classic ambient occlusion technique. Our approach also offers additional applications, including an importance-based viewpoint-selection guide, and a means of enhancing object features and producing nonphotorealistic object visualizations

A Monte Carlo-Based Fiber Tracking Algorithm using Diffusion Tensor MRI

Diffusion tensor magnetic resonance imaging, which measures directional information of water diffusion in the brain, has emerged as a powerful tool for human brain studies. In this paper, we introduce a new Monte Carlo-based fiber tracking approach to estimate brain connectivity. One of the main characteristics of this approach is that all parameters of the algorithm are automatically determined at each point using the entropy of the eigenvalues of the diffusion tensor. Experimental results show the good performance of the proposed approach

Critical analysis and extension of the Hirshfeld atoms in molecules

The computational approach to the Hirshfeld [Theor. Chim. Acta 44, 129 (1977)] atom in a molecule is critically investigated, and several difficulties are highlighted. It is shown that these difficulties are mitigated by an alternative, iterative version, of the Hirshfeld partitioning procedure. The iterative scheme ensures that the Hirshfeld definition represents a mathematically proper information entropy, allows the Hirshfeld approach to be used for charged molecules, eliminates arbitrariness in the choice of the promolecule, and increases the magnitudes of the charges. The resulting "Hirshfeld-I charges" correlate well with electrostatic potential derived atomic charges

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

Exploring chromium (VI) dioxodihalides chemistry: is density functional theory the most suitable tool?

A comparative systematic study of the CrO2F2 compound has been performed using different conventional ab initio methodologies and density functional procedures. Two points have been analyzed: first, the accuracy of results yielded by each method under study, and second, the computational cost required to reach such results. Weighing up both aspects, density functional theory has been found to be more appropriate than the Hartree-Fock (HF) and the analyzed post-HF methods. Hence, the structural characterization and spectroscopic elucidation of the full CrO2X2 series (X=F,Cl,Br,I) has been done at this level of theory. Emphasis has been given to the unknown CrO2I2 species, and specially to the UV/visible spectra of all four compounds. Furthermore, a topological analysis in terms of charge density distributions has revealed why the valence shell electron pair repulsion model fails in predicting the molecular shape of such CrO2X2 complexes

Internal test sets studies in a group of antimalarials

Topological indices have been applied to build QSAR models for a set of 20 antimalarial cyclic peroxy cetals. In order to evaluate the reliability of the proposed linear models leave-n-out and Internal Test Sets (ITS) approaches have been considered. The proposed procedure resulted in a robust and consensued prediction equation and here it is shown why it is superior to the employed standard cross-validation algorithms involving multilinear regression models

Distinct Unfolding and Refolding Pathways of Ribonuclease A Revealed by Heating and Cooling Temperature Jumps

Heating and cooling temperature jumps (T-jumps) were performed using a newly developed technique to trigger unfolding and refolding of wild-type ribonuclease A and a tryptophan-containing variant (Y115W). From the linear Arrhenius plots of the microscopic folding and unfolding rate constants, activation enthalpy (ΔH#), and activation entropy (ΔS#) were determined to characterize the kinetic transition states (TS) for the unfolding and refolding reactions. The single TS of the wild-type protein was split into three for the Y115W variant. Two of these transition states, TS1 and TS2, characterize a slow kinetic phase, and one, TS3, a fast phase. Heating T-jumps induced protein unfolding via TS2 and TS3; cooling T-jumps induced refolding via TS1 and TS3. The observed speed of the fast phase increased at lower temperature, due to a strongly negative ΔH# of the folding-rate constant. The results are consistent with a path-dependent protein folding/unfolding mechanism. TS1 and TS2 are likely to reflect X-Pro114 isomerization in the folded and unfolded protein, respectively, and TS3 the local conformational change of the β-hairpin comprising Trp115. A very fast protein folding/unfolding phase appears to precede both processes. The path dependence of the observed kinetics is suggestive of a rugged energy protein folding funne

Relacions estructura-propietat per un conjunt d'hidrocarburs a partir de nous descriptors tridimensionals derivats de la semblança molecular quàntica

En aquest article es defineixen uns nous índexs tridimensionals per a la descripció de les molècules a partir de paràmetres derivats de la Teoria de la Semblança Molecular i de les distàncies euclidianes entre els àtoms i les càrregues atòmiques efectives. Aquests indexs, anomenats 3D, s'han aplicat a l'estudi de les relacions estructura-propietat d'una família d'hidrocarburs, i han demostrat una capacitat de descripció de tres propietats de la família (temperatura d'ebullició, temperatura de fusió i densitat) molt més acurada que quan s'utilitzen els indexs 2D clàssics

Estudi Qsar d'una família de Quinolones utilitzant índex de semblança i índex topològics de semblança i índexs topològics de semblanç

En aquest treball es presenta un exemple d'aplicació de la semblança molecular quàntica en l'àmbit de la determinació de relacions entre l'estructura i les propietats o activitats biològiques de molècules. La família estudiada està formada per un conjunt de divuit quinolones de les quals es coneixen dues propietats relacionades amb l'activitat biològica: la concentració mínima inhibitòria de la reproducció en E. Coli i I'escissió de l'ADN per la girasa, també en E. Coli. L'estudi s'ha realitzat emprant dues metodologies diferents, fonamentades ambdues en el desenvolupament de la semblança molecular quàntica. Aquestes dues metodologies es basen, respectivament, en el càlcul i l'aplicació dels índexs de semblança i dels índexs topològics de semblança

Robustness against large-scale failures in communications networks

This thesis studies robustness against large-scale failures in communications networks. If failures are isolated, they usually go unnoticed by users thanks to recovery mechanisms. However, such mechanisms are not effective against large-scale multiple failures. Large-scale failures may cause huge economic loss. A key requirement towards devising mechanisms to lessen their impact is the ability to evaluate network robustness. This thesis focuses on multilayer networks featuring separated control and data planes. The majority of the existing measures of robustness are unable to capture the true service degradation in such a setting, because they rely on purely topological features. One of the major contributions of this thesis is a new measure of functional robustness. The failure dynamics is modeled from the perspective of epidemic spreading, for which a new epidemic model is proposed. Another contribution is a taxonomy of multiple, large-scale failures, adapted to the needs and usage of the field of networking.