The existence of periodic solutions of a two dimensional Lattice

We consider a two dimensional lattice coupled with nearest neighbor interaction potential of power type. The existence of infinite many periodic solutions is shown by using minimax methods.

Mejora diagnóstica de hepatopatías de afectación difusa mediante técnicas de inteligencia artificial

The automatic diagnostic discrimination is an application of artificial intelligence techniques that can solve clinical cases based on imaging. Diffuse liver diseases are diseases of wide prominence in the population and insidious course, yet early in its progression. Early and effective diagnosis is necessary because many of these diseases progress to cirrhosis and liver cancer. The usual technique of choice for accurate diagnosis is liver biopsy, an invasive and not without incompatibilities one. It is proposed in this project an alternative non-invasive and free of contraindications method based on liver ultrasonography. The images are digitized and then analyzed using statistical techniques and analysis of texture. The results are validated from the pathology report. Finally, we apply artificial intelligence techniques as Fuzzy k-Means or Support Vector Machines and compare its significance to the analysis Statistics and the report of the clinician. The results show that this technique is significantly valid and a promising alternative as a noninvasive diagnostic chronic liver disease from diffuse involvement. Artificial Intelligence classifying techniques significantly improve the diagnosing discrimination compared to other statistics.

Profiling of counterfeit medicines by vibrational spectroscopy

Counterfeit pharmaceutical products have become a widespread problem in the last decade. Various analytical techniques have been applied to discriminate between genuine and counterfeit products. Among these, Near-infrared (NIR) and Raman spectroscopy provided promising results.The present study offers a methodology allowing to provide more valuable information fororganisations engaged in the fight against counterfeiting of medicines.A database was established by analyzing counterfeits of a particular pharmaceutical product using Near-infrared (NIR) and Raman spectroscopy. Unsupervised chemometric techniques (i.e. principal component analysis - PCA and hierarchical cluster analysis - HCA) were implemented to identify the classes within the datasets. Gas Chromatography coupled to Mass Spectrometry (GC-MS) and Fourier Transform Infrared Spectroscopy (FT-IR) were used to determine the number of different chemical profiles within the counterfeits. A comparison with the classes established by NIR and Raman spectroscopy allowed to evaluate the discriminating power provided by these techniques. Supervised classifiers (i.e. k-Nearest Neighbors, Partial Least Squares Discriminant Analysis, Probabilistic Neural Networks and Counterpropagation Artificial Neural Networks) were applied on the acquired NIR and Raman spectra and the results were compared to the ones provided by the unsupervised classifiers.The retained strategy for routine applications, founded on the classes identified by NIR and Raman spectroscopy, uses a classification algorithm based on distance measures and Receiver Operating Characteristics (ROC) curves. The model is able to compare the spectrum of a new counterfeit with that of previously analyzed products and to determine if a new specimen belongs to one of the existing classes, consequently allowing to establish a link with other counterfeits of the database.

Vacancy-driven ordering in a two-dimensional binary alloy

Domain growth in a system with nonconserved order parameter is studied. We simulate the usual Ising model for binary alloys with concentration 0.5 on a two-dimensional square lattice by Monte Carlo techniques. Measurements of the energy, jump-acceptance ratio, and order parameters are performed. Dynamics based on the diffusion of a single vacancy in the system gives a growth law faster than the usual Allen-Cahn law. Allowing vacancy jumps to next-nearest-neighbor sites is essential to prevent vacancy trapping in the ordered regions. By measuring local order parameters we show that the vacancy prefers to be in the disordered regions (domain boundaries). This naturally concentrates the atomic jumps in the domain boundaries, accelerating the growth compared with the usual exchange mechanism that causes jumps to be homogeneously distributed on the lattice.

Monte Carlo simulation of interface alloying

An Ising-like model, with interactions ranging up to next-nearest-neighbor pairs, is used to simulate the process of interface alloying. Interactions are chosen to stabilize an intermediate "antiferromagnetic" ordered structure. The dynamics proceeds exclusively by atom-vacancy exchanges. In order to characterize the process, the time evolution of the width of the intermediate ordered region and the diffusion length is studied. Both lengths are found to follow a power-law evolution with exponents depending on the characteristic features of the model.

Monte Carlo Study of the Growth of L12 ordered domains in fcc A3B binary alloys

A Monte Carlo study of the late time growth of L12-ordered domains in a fcc A3B binary alloy is presented. The energy of the alloy has been modeled by a nearest-neighbor interaction Ising Hamiltonian. The system exhibits a fourfold degenerated ground state and two kinds of interfaces separating ordered domains: flat and curved antiphase boundaries. Two different dynamics are used in the simulations: the standard atom-atom exchange mechanism and the more realistic vacancy-atom exchange mechanism. The results obtained by both methods are compared. In particular we study the time evolution of the excess energy, the structure factor and the mean distance between walls. In the case of atom-atom exchange mechanism anisotropic growth has been found: two characteristic lengths are needed in order to describe the evolution. Contrarily, with the vacancyatom exchange mechanism scaling with a single length holds. Results are contrasted with existing experiments in Cu3Au and theories for anisotropic growth.

Lattice-gas model of particles with orientational and positional degrees of freedom: Mean-field treatment

We consider a lattice-gas model of particles with internal orientational degrees of freedom. In addition to antiferromagnetic nearest-neighbor (NN) and next-nearest-neighbor (NNN) positional interactions we also consider NN and NNN interactions arising from the internal state of the particles. The system then shows positional and orientational ordering modes with associated phase transitions at Tp and To temperatures at which long-range positional and orientational ordering are, respectively, lost. We use mean-field techniques to obtain a general approach to the study of these systems. By considering particular forms of the orientational interaction function we study coupling effects between both phase transitions arising from the interplay between orientational and positional degrees of freedom. In mean-field approximation coupling effects appear only for the phase transition taking place at lower temperatures. The strength of the coupling depends on the value of the long-range order parameter that remains finite at that temperature.

Automatic Mapping and Classification of Spatial Environmental Data

The paper deals with the development and application of the generic methodology for automatic processing (mapping and classification) of environmental data. General Regression Neural Network (GRNN) is considered in detail and is proposed as an efficient tool to solve the problem of spatial data mapping (regression). The Probabilistic Neural Network (PNN) is considered as an automatic tool for spatial classifications. The automatic tuning of isotropic and anisotropic GRNN/PNN models using cross-validation procedure is presented. Results are compared with the k-Nearest-Neighbours (k-NN) interpolation algorithm using independent validation data set. Real case studies are based on decision-oriented mapping and classification of radioactively contaminated territories.

Comparison between detailed digital and conventional soil maps of an area with complex geology

Since different pedologists will draw different soil maps of a same area, it is important to compare the differences between mapping by specialists and mapping techniques, as for example currently intensively discussed Digital Soil Mapping. Four detailed soil maps (scale 1:10.000) of a 182-ha sugarcane farm in the county of Rafard, São Paulo State, Brazil, were compared. The area has a large variation of soil formation factors. The maps were drawn independently by four soil scientists and compared with a fifth map obtained by a digital soil mapping technique. All pedologists were given the same set of information. As many field expeditions and soil pits as required by each surveyor were provided to define the mapping units (MUs). For the Digital Soil Map (DSM), spectral data were extracted from Landsat 5 Thematic Mapper (TM) imagery as well as six terrain attributes from the topographic map of the area. These data were summarized by principal component analysis to generate the map designs of groups through Fuzzy K-means clustering. Field observations were made to identify the soils in the MUs and classify them according to the Brazilian Soil Classification System (BSCS). To compare the conventional and digital (DSM) soil maps, they were crossed pairwise to generate confusion matrices that were mapped. The categorical analysis at each classification level of the BSCS showed that the agreement between the maps decreased towards the lower levels of classification and the great influence of the surveyor on both the mapping and definition of MUs in the soil map. The average correspondence between the conventional and DSM maps was similar. Therefore, the method used to obtain the DSM yielded similar results to those obtained by the conventional technique, while providing additional information about the landscape of each soil, useful for applications in future surveys of similar areas.

Squared interaction matrix Sherrington-Kirkpatrick model for a spin glass

The mean-field theory of a spin glass with a specific form of nearest- and next-nearest-neighbor interactions is investigated. Depending on the sign of the interaction matrix chosen we find either the continuous replica symmetry breaking seen in the Sherrington-Kirkpartick model or a one-step solution similar to that found in structural glasses. Our results are confirmed by numerical simulations and the link between the type of spin-glass behavior and the density of eigenvalues of the interaction matrix is discussed.

Statistics of depth probed by cw measurement of photons in a turbid medium

Photon migration in a turbid medium has been modeled in many different ways. The motivation for such modeling is based on technology that can be used to probe potentially diagnostic optical properties of biological tissue. Surprisingly, one of the more effective models is also one of the simplest. It is based on statistical properties of a nearest-neighbor lattice random walk. Here we develop a theory allowing one to calculate the number of visits by a photon to a given depth, if it is eventually detected at an absorbing surface. This mimics cw measurements made on biological tissue and is directed towards characterizing the depth reached by photons injected at the surface. Our development of the theory uses formalism based on the theory of a continuous-time random walk (CTRW). Formally exact results are given in the Fourier-Laplace domain, which, in turn, are used to generate approximations for parameters of physical interest.

Variational localized-site cluster expansions. X. Dimerization in linear Heisenberg chains

Ground-state instability to bond alternation in long linear chains is considered from the point of view of valence-bond (VB) theory. This instability is viewed as the consequence of a long-range order (LRO) which is expected if the ground state is reasonably described in terms of the Kekulé states (with nearest-neighbor singlet pairing). It is argued that the bond alternation and associated LRO predicted by this simple, VB picture is retained for certain linear Heisenberg models; many-body VB calculations on spin s=1 / 2 and s=1 chains are carried out in a test of this argument.

Tuning synchronization of integrate-and-fire oscillators through mobility

We analyze the emergence of synchronization in a population of moving integrate-and-fire oscillators. Oscillators, while moving on a plane, interact with their nearest neighbor upon firing time. We discover a nonmonotonic dependence of the synchronization time on the velocity of the agents. Moreover, we find that mechanisms that drive synchronization are different for different dynamical regimes. We report the extreme situation where an interplay between the time scales involved in the dynamical processes completely inhibits the achievement of a coherent state. We also provide estimators for the transitions between the different regimes.

Resonating-valence-bond theory for the square-planar lattice

The short-range resonating-valence-bond (RVB) wave function with nearest-neighbor (NN) spin pairings only is investigated as a possible description for the Heisenberg model on a square-planar lattice. A type of long-range order associated to this RVB Ansatz is identified along with some qualitative consequences involving lattice distortions, excitations, and their coupling.

Ab Initio study of magnetic interactions in the KCuF3 and K2CuF4 low-dimensional Systems

The ab initio cluster model approach has been used to study the electronic structure and magnetic coupling of KCuF3 and K2CuF4 in their various ordered polytype crystal forms. Due to a cooperative Jahn-Teller distortion these systems exhibit strong anisotropies. In particular, the magnetic properties strongly differ from those of isomorphic compounds. Hence, KCuF3 is a quasi-one-dimensional (1D) nearest neighbor Heisenberg antiferromagnet whereas K2CuF4 is the only ferromagnet among the K2MF4 series of compounds (M=Mn, Fe, Co, Ni, and Cu) behaving all as quasi-2D nearest neighbor Heisenberg systems. Different ab initio techniques are used to explore the magnetic coupling in these systems. All methods, including unrestricted Hartree-Fock, are able to explain the magnetic ordering. However, quantitative agreement with experiment is reached only when using a state-of-the-art configuration interaction approach. Finally, an analysis of the dependence of the magnetic coupling constant with respect to distortion parameters is presented.