Victoria Vampa

A hybrid method using wavelets for the numerical solution of boundary value problems on the interval

Abstract In this work, various aspects of wavelet-based methods for second order boundary value problems under Galerkin framework are investigated. Based on the B-spline multiresolution analysis (MRA) on the line we propose a hybrid method on the interval which combines different treatments for interior and boundary splines. By using this procedure, the MRA structure was conserved and hierarchical representations of the solution at different scales were obtained without much computational effort. Numerical examples are given to verify the effectiveness of the proposed method and the comparison with other techniques is presented.

A Maximum Entropy Approach for Predicting Epileptic Tonic-Clonic Seizure

The development of methods for time series analysis and prediction has always been and continues to be an active area of research. In this work, we develop a technique for modelling chaotic time series in parametric fashion. In the case of tonic-clonic epileptic electroencephalographic (EEG) analysis, we show that appropriate information theory tools provide valuable insights into the dynamics of neural activity. Our purpose is to demonstrate the feasibility of the maximum entropy principle to anticipate tonic-clonic seizure in patients with epilepsy.

A NEW REFINEMENT WAVELET–GALERKIN METHOD IN A SPLINE LOCAL MULTIRESOLUTION ANALYSIS SCHEME FOR BOUNDARY VALUE PROBLEMS

In this work, a new Wavelet–Galerkin method for boundary value problems is presented. It improves the approximation in terms of scaling functions obtained through a collocation scheme combined with variational equations. A B-spline multiresolution structure on the interval is designed in order to refine the solution recursively and efficiently using wavelets. Numerical examples are given to verify good convergence properties of the proposed method.

LIBOR Troubles: Anomalous Movements Detection Based on Maximum Entropy

According to the definition of the London Interbank Offered Rate (LIBOR), contributing banks should give fair estimates of their own borrowing costs in the interbank market. Between 2007 and 2009, several banks made inappropriate submissions of LIBOR, sometimes motivated by profit-seeking from their trading positions. In 2012, several newspapers’ articles began to cast doubt on LIBOR integrity, leading surveillance authorities to conduct investigations on banks’ behavior. Such procedures resulted in severe fines imposed to involved banks, who recognized their financial inappropriate conduct. In this paper, we uncover such unfair behavior by using a forecasting method based on the Maximum Entropy principle. Our results are robust against changes in parameter settings and could be of great help for market surveillance.

Effect of Water Content on Thermo-Physical Properties and Freezing Times of Foods

For the prediction of temperature change in different foodstuffs during freezing and thawing processes, accurate estimation of the thermo-physical properties of the product is necessary, such as specific heat, density, freezable water content, enthalpy, and initial freezing temperature. These data allow the adequate design and optimization of equipment and processes. Water is a main component in all foods and greatly influences the behavior of these properties, depending on its concentration. During the freezing process, which involves the phase change of water into ice, the specific heat, thermal conductivity, and density undergo abrupt changes due to the latent heat release. This complex process does not have an analytical solution and it can be described as a highly nonlinear mathematical problem. Many difficulties arise when trying to numerically simulate the freezing process, especially when using the finite element method (FEM), which is especially useful when dealing with irregular-shaped foodstuffs. Several techniques have been applied to consider the large latent heat release when using FEM. One traditional method is the use of the apparent specific heat, where the sensible heat is merged with the latent heat to produce a specific heat curve with a large peak around the freezing point, which can be considered a quasi-delta-Dirac function with temperature (depending on the amount of water in the food product) (Pham 2008). However, this method usually destabilizes the numerical solution. Implementation of the enthalpy method, which can be obtained through the integration of the specific heat with temperature (Fikiin 1996; Comini et al. 1990; Pham 2008; Santos et al. 2010), and the Kirchhoff function, which is the integral of the thermal conductivity, allows the reformulation of the heat transfer differential equation into a transformed partial differential system with two mutually related dependent variables H (enthalpy) and E (Kirchhoff function) (Scheerlinck et al. 2001). These functions, H and E versus temperature, are smoother mathematical functions compared to the specific heat, thermal conductivity, and density versus temperature, avoiding inaccuracies and/or divergence of the numerical method. Even though it brings great advantage to the resolution of the problem, with the simultaneous enhancement of the computational speed of the program, this transformation of variables is not widely used in the literature. Unleavened dough and cooked minced meat were selected due to their significant difference in water content in order to explore the performance of the computational code written using the enthalpy-Kirchhoff formulation. Another important reason is because cooked minced meat and dough are both present in several ready-to-eat meals, therefore contributing valuable information to food processors interested in optimizing cooling and freezing operating conditions of semi- or fully processed goods. The objectives of this work are (1) to experimentally determine by differential scanning calorimetry (DSC) the thermo-physical properties of dough and cooked minced meat in the freezing range: specific heat as a function of temperature, bound water, heat of melting, initial freezing temperature, etc.; (2) to develop and validate a finite element algorithm to simulate the freezing process in regular and irregularly shaped foodstuffs; and (3) to introduce appropriate equations of the thermo-physical properties in the numerical program to assess the effect of total water content, bound water, and surface heat transfer coefficient on freezing times in an irregular food system.