Eliminació d'artefactes en EGG mitjançant l'ús de la Multivariate Empirical Mode Decomposition

La tècnica de l’electroencefalograma (EEG) és una de les tècniques més utilitzades per estudiar el cervell. En aquesta tècnica s’enregistren els senyals elèctrics que es produeixen en el còrtex humà a través d’elèctrodes col•locats al cap. Aquesta tècnica, però, presenta algunes limitacions a l’hora de realitzar els enregistraments, la principal limitació es coneix com a artefactes, que són senyals indesitjats que es mesclen amb els senyals EEG. L’objectiu d’aquest treball de final de màster és presentar tres nous mètodes de neteja d’artefactes que poden ser aplicats en EEG. Aquests estan basats en l’aplicació de la Multivariate Empirical Mode Decomposition, que és una nova tècnica utilitzada per al processament de senyal. Els mètodes de neteja proposats s’apliquen a dades EEG simulades que contenen artefactes (pestanyeigs), i un cop s’han aplicat els procediments de neteja es comparen amb dades EEG que no tenen pestanyeigs, per comprovar quina millora presenten. Posteriorment, dos dels tres mètodes de neteja proposats s’apliquen sobre dades EEG reals. Les conclusions que s’han extret del treball són que dos dels nous procediments de neteja proposats es poden utilitzar per realitzar el preprocessament de dades reals per eliminar pestanyeigs.

High order hydrodynamical equations

Hydrodynamical equations act as a link between the local observed magnitudes of galactic motion and the general ones accounting for the behaviour of the Galaxy as a whole. Constraints are set usually in order to use them even in the lower order hierarchy. The authors present in this paper the complete expressions up to their fourth order. These equations will be used in the next future in their general form taking into account both the expected increase of kinematic data that the astrometric mission Hipparcos will provide, and some recent results indicating the possibility to obtain estimates for the momenta gradients.

Differential equations driven by fractional Brownian motion

A global existence and uniqueness result of the solution for multidimensional, time dependent, stochastic differential equations driven by a fractional Brownian motion with Hurst parameter H> is proved. It is shown, also, that the solution has finite moments. The result is based on a deterministic existence and uniqueness theorem whose proof uses a contraction principle and a priori estimates.

Irrigation with domestic wastewater: a multivariate analysis of main soil changes

Irrigation with treated domestic sewage wastewater (TSE) is an agricultural practice to reduce water requirements of agroecossystems and the nutrient load impact on freshwaters, but adverse effects on soil chemical (salinization, sodification, etc.) and soil physical properties (alteration in soil porosity and hydraulic conductivity, etc.) have been reported. This study aimed to define some relationships among these changes in an Oxisol using multivariate analysis. Corn (Zea mays L.) and sunflower (Helianthus annuus L.) were grown for two years, irrigated with TSE. The following soil properties were determined: Ca2+; Mg2+; Na+; K+ and H + Al contents, cationic exchangeable capacity (CEC), sum of bases (SB), base saturation (V), texture (sand, silt and clay), macro-, micro-, and cryptoporosity (V MA, V MI and V CRI), water content at soil saturation (θS) and at field capacity (θFC), residual water content (θR), soil bulk density (d s), water dispersed clay (WDC) and saturated hydraulic conductivity (K SAT). Factor analysis revealed the following six principal factors: Fine Porosity (composed of Na+; K+; WDC, θR, θRFC, and V CRI); Large Porosity (θS, d s, V MA, Vs); Soil CEC (Ca2+; Mg2+; CEC, SB, V); Soil Acidity (H + Al); and Soil Texture (factors 5 and 6). A dual pore structure appears clearly to the factors 1 and 2, with an apparent relationship between fine porosity and the monovalent cations Na+ and K+. The irrigation (with potable sodic tap water or sewage wastewater) only had a significant effect on Fine Porosity and Large Porosity factors, while factors 3 and 4 (Soil CEC and Soil Acidity) were correlated with soil depth. The main conclusion was a shift in pore distribution (large to fine pores) during irrigation with TSE, which induces an increase of water storage and reduces the capacity of drainage of salts.

Fluctuations in domain growth: Ginzburg-Landau equations with multiplicative noise

Ginzburg-Landau equations with multiplicative noise are considered, to study the effects of fluctuations in domain growth. The equations are derived from a coarse-grained methodology and expressions for the resulting concentration-dependent diffusion coefficients are proposed. The multiplicative noise gives contributions to the Cahn-Hilliard linear-stability analysis. In particular, it introduces a delay in the domain-growth dynamics.

Numerical algorithm for Ginzburg-Landau equations with multiplicative noise: Application to domain growth

We consider stochastic partial differential equations with multiplicative noise. We derive an algorithm for the computer simulation of these equations. The algorithm is applied to study domain growth of a model with a conserved order parameter. The numerical results corroborate previous analytical predictions obtained by linear analysis.

Bargmann-Wigner method and (6S + 1)-component wave equations

A modified Bargmann-Wigner method is used to derive (6s + 1)-component wave equations. The relation between different forms of these equations is shown.

Heavy rainfall equations for Santa Catarina, Brazil

Knowledge of intensity-duration-frequency (IDF) relationships of rainfall events is extremely important to determine the dimensions of surface drainage structures and soil erosion control. The purpose of this study was to obtain IDF equations of 13 rain gauge stations in the state of Santa Catarina in Brazil: Chapecó, Urussanga, Campos Novos, Florianópolis, Lages, Caçador, Itajaí, Itá, Ponte Serrada, Porto União, Videira, Laguna and São Joaquim. The daily rainfall data charts of each station were digitized and then the annual maximum rainfall series were determined for durations ranging from 5 to 1440 min. Based on these, with the Gumbel-Chow distribution, the maximum rainfall was estimated for durations ranging from 5 min to 24 h, considering return periods of 2, 5, 10, 20, 25, 50, and 100 years,. Data agreement with the Gumbel-Chow model was verified by the Kolmogorov-Smirnov test, at 5 % significance level. For each rain gauge station, two IDF equations of rainfall events were adjusted, one for durations from 5 to 120 min and the other from 120 to 1440 min. The results show a high variability in maximum intensity of rainfall events among the studied stations. Highest values of coefficients of variation in the annual maximum series of rainfall were observed for durations of over 600 min at the stations of the coastal region of Santa Catarina.

From Galilean-invariant to relativistic wave equations

Through an imaginary change of coordinates in the Galilei algebra in 4 space dimensions and making use of an original idea of Dirac and Lvy-Leblond, we are able to obtain the relativistic equations of Dirac and of Bargmann and Wigner starting with the (Galilean-invariant) Schrdinger equation.

Multivariate analysis and geostatistics of the fertility of a humic rhodic hapludox under coffee cultivation

The spatial variability of soil and plant properties exerts great influence on the yeld of agricultural crops. This study analyzed the spatial variability of the fertility of a Humic Rhodic Hapludox with Arabic coffee, using principal component analysis, cluster analysis and geostatistics in combination. The experiment was carried out in an area under Coffea arabica L., variety Catucai 20/15 - 479. The soil was sampled at a depth 0.20 m, at 50 points of a sampling grid. The following chemical properties were determined: P, K+, Ca2+, Mg2+, Na+, S, Al3+, pH, H + Al, SB, t, T, V, m, OM, Na saturation index (SSI), remaining phosphorus (P-rem), and micronutrients (Zn, Fe, Mn, Cu and B). The data were analyzed with descriptive statistics, followed by principal component and cluster analyses. Geostatistics were used to check and quantify the degree of spatial dependence of properties, represented by principal components. The principal component analysis allowed a dimensional reduction of the problem, providing interpretable components, with little information loss. Despite the characteristic information loss of principal component analysis, the combination of this technique with geostatistical analysis was efficient for the quantification and determination of the structure of spatial dependence of soil fertility. In general, the availability of soil mineral nutrients was low and the levels of acidity and exchangeable Al were high.

Kinematic reduction of reaction-diffusion fronts with multiplicative noise. Derivation of stochastic sharp-interface equations

We study the dynamics of generic reaction-diffusion fronts, including pulses and chemical waves, in the presence of multiplicative noise. We discuss the connection between the reaction-diffusion Langevin-like field equations and the kinematic (eikonal) description in terms of a stochastic moving-boundary or sharp-interface approximation. We find that the effective noise is additive and we relate its strength to the noise parameters in the original field equations, to first order in noise strength, but including a partial resummation to all orders which captures the singular dependence on the microscopic cutoff associated with the spatial correlation of the noise. This dependence is essential for a quantitative and qualitative understanding of fluctuating fronts, affecting both scaling properties and nonuniversal quantities. Our results predict phenomena such as the shift of the transition point between the pushed and pulled regimes of front propagation, in terms of the noise parameters, and the corresponding transition to a non-Kardar-Parisi-Zhang universality class. We assess the quantitative validity of the results in several examples including equilibrium fluctuations and kinetic roughening. We also predict and observe a noise-induced pushed-pulled transition. The analytical predictions are successfully tested against rigorous results and show excellent agreement with numerical simulations of reaction-diffusion field equations with multiplicative noise.

Dynamical properties of nonmarkovian stochastic differential equations

We study nonstationary non-Markovian processes defined by Langevin-type stochastic differential equations with an OrnsteinUhlenbeck driving force. We concentrate on the long time limit of the dynamical evolution. We derive an approximate equation for the correlation function of a nonlinear nonstationary non-Markovian process, and we discuss its consequences. Non-Markovicity can introduce a dependence on noise parameters in the dynamics of the correlation function in cases in which it becomes independent of these parameters in the Markovian limit. Several examples are discussed in which the relaxation time increases with respect to the Markovian limit. For a Brownian harmonic oscillator with fluctuating frequency, the non-Markovicity of the process decreases the domain of stability of the system, and it can change an infradamped evolution into an overdamped one.

Poincar wave equations as Fourier transformations of Galilei wave equations

The relationship between the Poincar and Galilei groups allows us to write the Poincar wave equations for arbitrary spin as a Fourier transform of the Galilean ones. The relation between the Lagrangian formulation for both cases is also studied.