PCA Tomography: how to extract information from data cubes

Astronomy has evolved almost exclusively by the use of spectroscopic and imaging techniques, operated separately. With the development of modern technologies, it is possible to obtain data cubes in which one combines both techniques simultaneously, producing images with spectral resolution. To extract information from them can be quite complex, and hence the development of new methods of data analysis is desirable. We present a method of analysis of data cube (data from single field observations, containing two spatial and one spectral dimension) that uses Principal Component Analysis (PCA) to express the data in the form of reduced dimensionality, facilitating efficient information extraction from very large data sets. PCA transforms the system of correlated coordinates into a system of uncorrelated coordinates ordered by principal components of decreasing variance. The new coordinates are referred to as eigenvectors, and the projections of the data on to these coordinates produce images we will call tomograms. The association of the tomograms (images) to eigenvectors (spectra) is important for the interpretation of both. The eigenvectors are mutually orthogonal, and this information is fundamental for their handling and interpretation. When the data cube shows objects that present uncorrelated physical phenomena, the eigenvector`s orthogonality may be instrumental in separating and identifying them. By handling eigenvectors and tomograms, one can enhance features, extract noise, compress data, extract spectra, etc. We applied the method, for illustration purpose only, to the central region of the low ionization nuclear emission region (LINER) galaxy NGC 4736, and demonstrate that it has a type 1 active nucleus, not known before. Furthermore, we show that it is displaced from the centre of its stellar bulge.

A Survey on Graphical Methods for Classification Predictive Performance Evaluation

Predictive performance evaluation is a fundamental issue in design, development, and deployment of classification systems. As predictive performance evaluation is a multidimensional problem, single scalar summaries such as error rate, although quite convenient due to its simplicity, can seldom evaluate all the aspects that a complete and reliable evaluation must consider. Due to this, various graphical performance evaluation methods are increasingly drawing the attention of machine learning, data mining, and pattern recognition communities. The main advantage of these types of methods resides in their ability to depict the trade-offs between evaluation aspects in a multidimensional space rather than reducing these aspects to an arbitrarily chosen (and often biased) single scalar measure. Furthermore, to appropriately select a suitable graphical method for a given task, it is crucial to identify its strengths and weaknesses. This paper surveys various graphical methods often used for predictive performance evaluation. By presenting these methods in the same framework, we hope this paper may shed some light on deciding which methods are more suitable to use in different situations.

On the cutting stock problem under stochastic demand

This paper addresses the one-dimensional cutting stock problem when demand is a random variable. The problem is formulated as a two-stage stochastic nonlinear program with recourse. The first stage decision variables are the number of objects to be cut according to a cutting pattern. The second stage decision variables are the number of holding or backordering items due to the decisions made in the first stage. The problem`s objective is to minimize the total expected cost incurred in both stages, due to waste and holding or backordering penalties. A Simplex-based method with column generation is proposed for solving a linear relaxation of the resulting optimization problem. The proposed method is evaluated by using two well-known measures of uncertainty effects in stochastic programming: the value of stochastic solution-VSS-and the expected value of perfect information-EVPI. The optimal two-stage solution is shown to be more effective than the alternative wait-and-see and expected value approaches, even under small variations in the parameters of the problem.

A linear optimization approach to the combined production planning model

Two fundamental processes usually arise in the production planning of many industries. The first one consists of deciding how many final products of each type have to be produced in each period of a planning horizon, the well-known lot sizing problem. The other process consists of cutting raw materials in stock in order to produce smaller parts used in the assembly of final products, the well-studied cutting stock problem. In this paper the decision variables of these two problems are dependent of each other in order to obtain a global optimum solution. Setups that are typically present in lot sizing problems are relaxed together with integer frequencies of cutting patterns in the cutting problem. Therefore, a large scale linear optimizations problem arises, which is exactly solved by a column generated technique. It is worth noting that this new combined problem still takes the trade-off between storage costs (for final products and the parts) and trim losses (in the cutting process). We present some sets of computational tests, analyzed over three different scenarios. These results show that, by combining the problems and using an exact method, it is possible to obtain significant gains when compared to the usual industrial practice, which solve them in sequence. (C) 2010 The Franklin Institute. Published by Elsevier Ltd. All rights reserved.

A Lagrangian relaxation approach to a coupled lot-sizing and cutting stock problem

Industrial production processes involving both lot-sizing and cutting stock problems are common in many industrial settings. However, they are usually treated in a separate way, which could lead to costly production plans. In this paper, a coupled mathematical model is formulated and a heuristic method based on Lagrangian relaxation is proposed. Computational results prove its effectiveness. (C) 2009 Elsevier B.V. All rights reserved.

A discontinuous-Galerkin-based immersed boundary method with non-homogeneous boundary conditions and its application to elasticity

We propose a discontinuous-Galerkin-based immersed boundary method for elasticity problems. The resulting numerical scheme does not require boundary fitting meshes and avoids boundary locking by switching the elements intersected by the boundary to a discontinuous Galerkin approximation. Special emphasis is placed on the construction of a method that retains an optimal convergence rate in the presence of non-homogeneous essential and natural boundary conditions. The role of each one of the approximations introduced is illustrated by analyzing an analog problem in one spatial dimension. Finally, extensive two- and three-dimensional numerical experiments on linear and nonlinear elasticity problems verify that the proposed method leads to optimal convergence rates under combinations of essential and natural boundary conditions. (C) 2009 Elsevier B.V. All rights reserved.

Fast heuristics for the Steiner tree problem with revenues, budget and hop constraints

This article describes and compares three heuristics for a variant of the Steiner tree problem with revenues, which includes budget and hop constraints. First, a greedy method which obtains good approximations in short computational times is proposed. This initial solution is then improved by means of a destroy-and-repair method or a tabu search algorithm. Computational results compare the three methods in terms of accuracy and speed. (C) 2007 Elsevier B.V. All rights reserved.

On S-matrix factorization of the Landau-Lifshitz model

We consider the three-particle scattering S-matrix for the Landau-Lifshitz model by directly computing the set of the Feynman diagrams up to the second order. We show, following the analogous computations for the non-linear Schrdinger model [1, 2], that the three-particle S-matrix is factorizable in the first non-trivial order.

Pressure-induced electrical and structural anomalies in Pb(1-x)Ca(x)TiO(3) thin films grown at various oxygen pressures by chemical solution route

Lead calcium titanate (Pb(1-x)Ca(x)TiO(3) or PCT) thin films have been thermally treated under different oxygen pressures, 10, 40 and 80 bar, by using the so-called chemical solution deposition method. The structural, morphological, dielectric and ferroelectric properties were characterized by x-ray diffraction, FT-infrared and Raman spectroscopy, atomic force microscopy and polarization-electric-field hysteresis loop measurements. By annealing at a controlled pressure of around 10 and 40 bar, well-crystallized PCT thin films were successfully prepared. For the sample submitted to 80 bar, the x-ray diffraction, Fourier transformed-infrared and Raman data indicated deviation from the tetragonal symmetry. The most interesting feature in the Raman spectra is the occurrence of intense vibrational modes at frequencies of around 747 and 820 cm(-1), whose presence depends strongly on the amount of the pyrochlore phase. In addition, the Raman spectrum indicates the presence of symmetry-breaking disorder, which would be expected for an amorphous (disorder) and mixed pyrochlore-perovskite phase. During the high-pressure annealing process, the crystallinity and the grain size of the annealed film decreased. This process effectively suppressed both the dielectric and ferroelectric behaviour. Ferroelectric hysteresis loop measurements performed on these PCT films exhibited a clear decrease in the remanent polarization with increasing oxygen pressure.

Ac and dc magnetotransport properties of the phase-separated La(0.6)Y(0.1)Ca(0.3)MnO(3) manganite

The physical properties of the La(0.6)Y(0.1)Ca(0.3)MnO(3) compound have been investigated, focusing on the magnetoresistance phenomenon studied by both dc and ac electrical transport measurements. X-ray diffraction and scanning electron microscopy analysis of ceramic samples prepared by the sol-gel method revealed that specimens are single phase and have average grain size of similar to 0.5 mu m. Magnetization and 4-probe dc electrical resistivity rho(T,H) experiments showed that a ferromagnetic transition at T(C) similar to 170 K is closely related to a metal-insulator (MI) transition occurring at essentially the same temperature T(MI). The magnetoresistance effect was found to be more pronounced at low applied fields (H <= 2.5 T) and temperatures close to the MI transition. The ac electrical transport was investigated by impedance spectroscopy Z(f,T,H) under applied magnetic field H up to 1 T. The Z(f,T,H) data exhibited two well-defined relaxation processes that exhibit different behaviors depending on the temperature and applied magnetic field. Pronounced effects were observed close to T (C) and were associated with the coexistence of clusters with different electronic and magnetic properties. In addition, the appreciable decrease of the electrical permittivity epsilon`(T,H) is consistent with changes in the concentration of e(g) mobile holes, a feature much more pronounced close to T (C).

Self-adjoint extensions and spectral analysis in the Calogero problem

In this paper, we present a mathematically rigorous quantum-mechanical treatment of a one-dimensional motion of a particle in the Calogero potential alpha x(-2). Although the problem is quite old and well studied, we believe that our consideration based on a uniform approach to constructing a correct quantum-mechanical description for systems with singular potentials and/or boundaries, proposed in our previous works, adds some new points to its solution. To demonstrate that a consideration of the Calogero problem requires mathematical accuracy, we discuss some `paradoxes` inherent in the `naive` quantum-mechanical treatment. Using a self-adjoint extension method, we construct and study all possible self-adjoint operators (self-adjoint Hamiltonians) associated with a formal differential expression for the Calogero Hamiltonian. In particular, we discuss a spontaneous scale-symmetry breaking associated with self-adjoint extensions. A complete spectral analysis of all self-adjoint Hamiltonians is presented.

Trojan Horse Method: a useful tool for electron screening effect investigation

Direct measurements in the last decades have highlighted a new problem related to the lowering of the Coulomb barrier between the interacting nuclei due to the presence of the ""electron screening"" in the laboratory measurements. It was systematically observed that the presence of the electronic cloud around the interacting ions in measurements of nuclear reactions cross sections at astrophysical energies gives rise to an enhancement of the astrophysical S(E)-factor as lower and lower energies are explored [1]. Moreover, at present Such an effect is not well understood as the value of the potential for screening extracted from these measurements is higher than the tipper limit of theoretical predictions (adiabatic limit). On the other hand, the electron screening potential in laboratory measurement is different from that occurring in stellar plasmas thus the quantity of interest in astrophysics is the so-called ""bare nucleus cross section"". This quantity can only be extrapolated in direct measurements. These are the reasons that led to a considerable growth on interest in indirect measurement techniques and in particular the Trojan Horse Method (THM) [2,3]. Results concerning the bare nucleus cross sections measurements will be shown in several cases of astrophysical interest. In those cases the screening potential evaluated by means of the THM will be compared with the adiabatic limit and results arising from extrapolation in direct measurements.

Self-adjoint extensions and spectral analysis in the generalized Kratzer problem

We present a mathematically rigorous quantum-mechanical treatment of a one-dimensional non-relativistic motion of a particle in the potential field V(x) = g(1)x(-1) + g(2)x(-2), x is an element of R(+) = [0, infinity). For g(2) > 0 and g(1) < 0, the potential is known as the Kratzer potential V(K)(x) and is usually used to describe molecular energy and structure, interactions between different molecules and interactions between non-bonded atoms. We construct all self-adjoint Schrodinger operators with the potential V(x) and represent rigorous solutions of the corresponding spectral problems. Solving the first part of the problem, we use a method of specifying self-adjoint extensions by (asymptotic) self-adjoint boundary conditions. Solving spectral problems, we follow Krein`s method of guiding functionals. This work is a continuation of our previous works devoted to the Coulomb, Calogero and Aharonov-Bohm potentials.

Detection of phenolic compounds using impedance spectroscopy measurements

Langmuir-Blodgett (LB) and layer-by-layer films (LbL) of a PPV (p-phenylenevinylene) derivative, an azo compound and tetrasulfonated phthalocyanines were successfully employed as transducers in an ""electronic tongue"" system for detecting trace levels of phenolic compounds in water. The choice of the materials was based on their distinct electrical natures, which enabled the array to establish a fingerprint of very similar liquids. Impedance spectroscopy measurements were taken in the frequency range from 10 Hz to 1 MHz, with the data analysed with principal component analysis (PCA). The sensing units were obtained from five-layer LB films of (poly[(2-methoxy-5-n-hexyloxy)-p-phenylenevinylene]), OC(1)OC(18)-PPV (poly(2-methoxy,5-(n-octadecyl)-p-phenylenevinylene)), DR (HEMA-co-DR13MA (poly-(hydroxyethylmethacrylate-co-[4`-[[2-(methacryloyloxy)-ethyl]ethylamino]-2-chloro-4-nitroazobenzene]))) and five-bilayer LbL films of tetrasulfonated metallic phthalocyanines deposited onto gold interdigitated electrodes. The sensors were immersed into phenol, 2-chloro-4-methoxyphenol, 2-chlorophenol and 3-chlorophenol (isomers) solutions at 1 x 10(-9) mol L(-1), with control experiments carried out in ultra pure water. Samples could be distinguished if the principal component analysis (PCA) plots were made with capacitance values taken at 10(3) Hz, which is promising for detection of trace amounts of phenolic pollutants in natural water.

On the generalized eigenvalue method for energies and matrix elements in lattice field theory

We discuss the generalized eigenvalue problem for computing energies and matrix elements in lattice gauge theory, including effective theories such as HQET. It is analyzed how the extracted effective energies and matrix elements converge when the time separations are made large. This suggests a particularly efficient application of the method for which we can prove that corrections vanish asymptotically as exp(-(E(N+1) - E(n))t). The gap E(N+1) - E(n) can be made large by increasing the number N of interpolating fields in the correlation matrix. We also show how excited state matrix elements can be extracted such that contaminations from all other states disappear exponentially in time. As a demonstration we present numerical results for the extraction of ground state and excited B-meson masses and decay constants in static approximation and to order 1/m(b) in HQET.