New perspectives in the use of ink evidence in forensic science: Part II. Development and testing of mathematical algorithms for the automatic comparison of ink samples analysed by HPTLC

In the first part of this research, three stages were stated for a program to increase the information extracted from ink evidence and maximise its usefulness to the criminal and civil justice system. These stages are (a) develop a standard methodology for analysing ink samples by high-performance thin layer chromatography (HPTLC) in reproducible way, when ink samples are analysed at different time, locations and by different examiners; (b) compare automatically and objectively ink samples; and (c) define and evaluate theoretical framework for the use of ink evidence in forensic context. This report focuses on the second of the three stages. Using the calibration and acquisition process described in the previous report, mathematical algorithms are proposed to automatically and objectively compare ink samples. The performances of these algorithms are systematically studied for various chemical and forensic conditions using standard performance tests commonly used in biometrics studies. The results show that different algorithms are best suited for different tasks. Finally, this report demonstrates how modern analytical and computer technology can be used in the field of ink examination and how tools developed and successfully applied in other fields of forensic science can help maximising its impact within the field of questioned documents.

Implementation of zonal control algorithms in adaptive optical systems with sparse control matrices

Miralls deformables més i més grans, amb cada cop més actuadors estan sent utilitzats actualment en aplicacions d'òptica adaptativa. El control dels miralls amb centenars d'actuadors és un tema de gran interès, ja que les tècniques de control clàssiques basades en la seudoinversa de la matriu de control del sistema es tornen massa lentes quan es tracta de matrius de dimensions tan grans. En aquesta tesi doctoral es proposa un mètode per l'acceleració i la paral.lelitzacó dels algoritmes de control d'aquests miralls, a través de l'aplicació d'una tècnica de control basada en la reducció a zero del components més petits de la matriu de control (sparsification), seguida de l'optimització de l'ordenació dels accionadors de comandament atenent d'acord a la forma de la matriu, i finalment de la seva posterior divisió en petits blocs tridiagonals. Aquests blocs són molt més petits i més fàcils de fer servir en els càlculs, el que permet velocitats de càlcul molt superiors per l'eliminació dels components nuls en la matriu de control. A més, aquest enfocament permet la paral.lelització del càlcul, donant una com0onent de velocitat addicional al sistema. Fins i tot sense paral. lelització, s'ha obtingut un augment de gairebé un 40% de la velocitat de convergència dels miralls amb només 37 actuadors, mitjançant la tècnica proposada. Per validar això, s'ha implementat un muntatge experimental nou complet , que inclou un modulador de fase programable per a la generació de turbulència mitjançant pantalles de fase, i s'ha desenvolupat un model complert del bucle de control per investigar el rendiment de l'algorisme proposat. Els resultats, tant en la simulació com experimentalment, mostren l'equivalència total en els valors de desviació després de la compensació dels diferents tipus d'aberracions per als diferents algoritmes utilitzats, encara que el mètode proposat aquí permet una càrrega computacional molt menor. El procediment s'espera que sigui molt exitós quan s'aplica a miralls molt grans.

Modeling of hybrid systems by piecewise decomposition

Piecewise linear models systems arise as mathematical models of systems in many practical applications, often from linearization for nonlinear systems. There are two main approaches of dealing with these systems according to their continuous or discrete-time aspects. We propose an approach which is based on the state transformation, more particularly the partition of the phase portrait in different regions where each subregion is modeled as a two-dimensional linear time invariant system. Then the Takagi-Sugeno model, which is a combination of local model is calculated. The simulation results show that the Alpha partition is well-suited for dealing with such a system

The building blocks of international ecological footprint inequality: a regression-based decomposition

This paper performs an empirical Decomposition of International Inequality in Ecological Footprint in order to quantify to what extent explanatory variables such as a country’s affluence, economic structure, demographic characteristics, climate and technology contributed to international differences in terms of natural resource consumption during the period 1993-2007. We use a Regression-Based Inequality Decomposition approach. As a result, the methodology extends qualitatively the results obtained in standard environmental impact regressions as it comprehends further social dimensions of the Sustainable Development concept, i.e. equity within generations. The results obtained point to prioritizing policies that take into account both future and present generations.

Two complementary molecular energy decomposition schemes: the Mayer and Ziegler-Rauk methods in comparison

In the present paper we discuss and compare two different energy decomposition schemes: Mayer's Hartree-Fock energy decomposition into diatomic and monoatomic contributions [Chem. Phys. Lett. 382, 265 (2003)], and the Ziegler-Rauk dissociation energy decomposition [Inorg. Chem. 18, 1558 (1979)]. The Ziegler-Rauk scheme is based on a separation of a molecule into fragments, while Mayer's scheme can be used in the cases where a fragmentation of the system in clearly separable parts is not possible. In the Mayer scheme, the density of a free atom is deformed to give the one-atom Mulliken density that subsequently interacts to give rise to the diatomic interaction energy. We give a detailed analysis of the diatomic energy contributions in the Mayer scheme and a close look onto the one-atom Mulliken densities. The Mulliken density ρA has a single large maximum around the nuclear position of the atom A, but exhibits slightly negative values in the vicinity of neighboring atoms. The main connecting point between both analysis schemes is the electrostatic energy. Both decomposition schemes utilize the same electrostatic energy expression, but differ in how fragment densities are defined. In the Mayer scheme, the electrostatic component originates from the interaction of the Mulliken densities, while in the Ziegler-Rauk scheme, the undisturbed fragment densities interact. The values of the electrostatic energy resulting from the two schemes differ significantly but typically have the same order of magnitude. Both methods are useful and complementary since Mayer's decomposition focuses on the energy of the finally formed molecule, whereas the Ziegler-Rauk scheme describes the bond formation starting from undeformed fragment densities

Density functional energy decomposition into one- and two-atom contributions

The present work provides a generalization of Mayer's energy decomposition for the density-functional theory (DFT) case. It is shown that one- and two-atom Hartree-Fock energy components in Mayer's approach can be represented as an action of a one-atom potential VA on a one-atom density ρ A or ρ B. To treat the exchange-correlation term in the DFT energy expression in a similar way, the exchange-correlation energy density per electron is expanded into a linear combination of basis functions. Calculations carried out for a number of density functionals demonstrate that the DFT and Hartree-Fock two-atom energies agree to a reasonable extent with each other. The two-atom energies for strong covalent bonds are within the range of typical bond dissociation energies and are therefore a convenient computational tool for assessment of individual bond strength in polyatomic molecules. For nonspecific nonbonding interactions, the two-atom energies are low. They can be either repulsive or slightly attractive, but the DFT results more frequently yield small attractive values compared to the Hartree-Fock case. The hydrogen bond in the water dimer is calculated to be between the strong covalent and nonbonding interactions on the energy scale

The Building Blocks of International Ecological Footprint inequality: A Regression-Base Decomposition

This paper performs an empirical Decomposition of International Inequality in Ecological Footprint in order to quantify to what extent explanatory variables such as a country’s affluence, economic structure, demographic characteristics, climate and technology contributed to international differences in terms of natural resource consumption during the period 1993-2007. We use a Regression- Based Inequality Decomposition approach. As a result, the methodology extends qualitatively the results obtained in standard environmental impact regressions as it comprehends further social dimensions of the Sustainable Development concept, i.e. equity within generations. The results obtained point to prioritizing policies that take into account both future and present generations. Keywords: Ecological Footprint Inequality, Regression-Based Inequality Decomposition, Intragenerational equity, Sustainable development.

Simple estimation of incident HIV infection rates in notification cohorts based on window periods of algorithms for evaluation of line-immunoassay result patterns.

BACKGROUND: Tests for recent infections (TRIs) are important for HIV surveillance. We have shown that a patient's antibody pattern in a confirmatory line immunoassay (Inno-Lia) also yields information on time since infection. We have published algorithms which, with a certain sensitivity and specificity, distinguish between incident (< = 12 months) and older infection. In order to use these algorithms like other TRIs, i.e., based on their windows, we now determined their window periods. METHODS: We classified Inno-Lia results of 527 treatment-naïve patients with HIV-1 infection < = 12 months according to incidence by 25 algorithms. The time after which all infections were ruled older, i.e. the algorithm's window, was determined by linear regression of the proportion ruled incident in dependence of time since infection. Window-based incident infection rates (IIR) were determined utilizing the relationship 'Prevalence = Incidence x Duration' in four annual cohorts of HIV-1 notifications. Results were compared to performance-based IIR also derived from Inno-Lia results, but utilizing the relationship 'incident = true incident + false incident' and also to the IIR derived from the BED incidence assay. RESULTS: Window periods varied between 45.8 and 130.1 days and correlated well with the algorithms' diagnostic sensitivity (R(2) = 0.962; P<0.0001). Among the 25 algorithms, the mean window-based IIR among the 748 notifications of 2005/06 was 0.457 compared to 0.453 obtained for performance-based IIR with a model not correcting for selection bias. Evaluation of BED results using a window of 153 days yielded an IIR of 0.669. Window-based IIR and performance-based IIR increased by 22.4% and respectively 30.6% in 2008, while 2009 and 2010 showed a return to baseline for both methods. CONCLUSIONS: IIR estimations by window- and performance-based evaluations of Inno-Lia algorithm results were similar and can be used together to assess IIR changes between annual HIV notification cohorts.

Spatially-resolved eigenmode decomposition of red blood cells membrane fluctuations questions the role of ATP in flickering.

Red blood cells (RBCs) present unique reversible shape deformability, essential for both function and survival, resulting notably in cell membrane fluctuations (CMF). These CMF have been subject of many studies in order to obtain a better understanding of these remarkable biomechanical membrane properties altered in some pathological states including blood diseases. In particular the discussion over the thermal or metabolic origin of the CMF has led in the past to a large number of investigations and modeling. However, the origin of the CMF is still debated. In this article, we present an analysis of the CMF of RBCs by combining digital holographic microscopy (DHM) with an orthogonal subspace decomposition of the imaging data. These subspace components can be reliably identified and quantified as the eigenmode basis of CMF that minimizes the deformation energy of the RBC structure. By fitting the observed fluctuation modes with a theoretical dynamic model, we find that the CMF are mainly governed by the bending elasticity of the membrane and that shear and tension elasticities have only a marginal influence on the membrane fluctations of the discocyte RBC. Further, our experiments show that the role of ATP as a driving force of CMF is questionable. ATP, however, seems to be required to maintain the unique biomechanical properties of the RBC membrane that lead to thermally excited CMF.

A pseudo-spectral method for the simulation of poro-elastic seismic wave propagation in 2D polar coordinates using domain decomposition

We present a novel numerical approach for the comprehensive, flexible, and accurate simulation of poro-elastic wave propagation in 2D polar coordinates. An important application of this method and its extensions will be the modeling of complex seismic wave phenomena in fluid-filled boreholes, which represents a major, and as of yet largely unresolved, computational problem in exploration geophysics. In view of this, we consider a numerical mesh, which can be arbitrarily heterogeneous, consisting of two or more concentric rings representing the fluid in the center and the surrounding porous medium. The spatial discretization is based on a Chebyshev expansion in the radial direction and a Fourier expansion in the azimuthal direction and a Runge-Kutta integration scheme for the time evolution. A domain decomposition method is used to match the fluid-solid boundary conditions based on the method of characteristics. This multi-domain approach allows for significant reductions of the number of grid points in the azimuthal direction for the inner grid domain and thus for corresponding increases of the time step and enhancements of computational efficiency. The viability and accuracy of the proposed method has been rigorously tested and verified through comparisons with analytical solutions as well as with the results obtained with a corresponding, previously published, and independently bench-marked solution for 2D Cartesian coordinates. Finally, the proposed numerical solution also satisfies the reciprocity theorem, which indicates that the inherent singularity associated with the origin of the polar coordinate system is adequately handled.

A general decomposition formula for derivative prices in stochastic volatility models

We see that the price of an european call option in a stochastic volatilityframework can be decomposed in the sum of four terms, which identifythe main features of the market that affect to option prices: the expectedfuture volatility, the correlation between the volatility and the noisedriving the stock prices, the market price of volatility risk and thedifference of the expected future volatility at different times. We alsostudy some applications of this decomposition.

Allowing for heterogeneity in the decomposition of measures of inequality in health

This paper shows how recently developed regression-based methods for the decomposition ofhealth inequality can be extended to incorporate heterogeneity in the responses of health to the explanatory variables. We illustrate our method with an application to the GHQ measure of psychological well-being taken from the British Household Panel Survey. The results suggest that there is an important degree of heterogeneity in the association of health to explanatory variables across birth cohorts and genders which, in turn, accounts for a substantial percentage of the inequality in observed health.