Lattices for 3-Dimensional Fuzzy Data generated by Fuzzy Galois Connections

Vagueness and high dimensional space data are usual features of current data. The paper is an approach to identify conceptual structures among fuzzy three dimensional data sets in order to get conceptual hierarchy. We propose a fuzzy extension of the Galois connections that allows to demonstrate an isomorphism theorem between fuzzy sets closures which is the basis for generating lattices ordered-sets

Contribution biplots

In order to interpret the biplot it is necessary to know which points usually variables are the ones that are important contributors to the solution, and this information is available separately as part of the biplot s numerical results. We propose a new scaling of the display, called the contribution biplot, which incorporates this diagnostic directly into the graphical display, showing visually the important contributors and thus facilitating the biplot interpretation and often simplifying the graphical representation considerably. The contribution biplot can be applied to a wide variety of analyses such as correspondence analysis, principal component analysis, log-ratio analysis and the graphical results of a discriminant analysis/MANOVA, in fact to any method based on the singular-value decomposition. In the contribution biplot one set of points, usually the rows of the data matrix, optimally represent the spatial positions of the cases or sample units, according to some distance measure that usually incorporates some form of standardization unless all data are comparable in scale. The other set of points, usually the columns, is represented by vectors that are related to their contributions to the low-dimensional solution. A fringe benefit is that usually only one common scale for row and column points is needed on the principal axes, thus avoiding the problem of enlarging or contracting the scale of one set of points to make the biplot legible. Furthermore, this version of the biplot also solves the problem in correspondence analysis of low-frequency categories that are located on the periphery of the map, giving the false impression that they are important, when they are in fact contributing minimally to the solution.

The Standard Biplot

Biplots are graphical displays of data matrices based on the decomposition of a matrix as the product of two matrices. Elements of these two matrices are used as coordinates for the rows and columns of the data matrix, with an interpretation of the joint presentation that relies on the properties of the scalar product. Because the decomposition is not unique, there are several alternative ways to scale the row and column points of the biplot, which can cause confusion amongst users, especially when software packages are not united in their approach to this issue. We propose a new scaling of the solution, called the standard biplot, which applies equally well to a wide variety of analyses such as correspondence analysis, principal component analysis, log-ratio analysis and the graphical results of a discriminant analysis/MANOVA, in fact to any method based on the singular-value decomposition. The standard biplot also handles data matrices with widely different levels of inherent variance. Two concepts taken from correspondence analysis are important to this idea: the weighting of row and column points, and the contributions made by the points to the solution. In the standard biplot one set of points, usually the rows of the data matrix, optimally represent the positions of the cases or sample units, which are weighted and usually standardized in some way unless the matrix contains values that are comparable in their raw form. The other set of points, usually the columns, is represented in accordance with their contributions to the low-dimensional solution. As for any biplot, the projections of the row points onto vectors defined by the column points approximate the centred and (optionally) standardized data. The method is illustrated with several examples to demonstrate how the standard biplot copes in different situations to give a joint map which needs only one common scale on the principal axes, thus avoiding the problem of enlarging or contracting the scale of one set of points to make the biplot readable. The proposal also solves the problem in correspondence analysis of low-frequency categories that are located on the periphery of the map, giving the false impression that they are important.

Freeze-out in hydrodynamical models

We study the effects of strict conservation laws and the problem of negative contributions to final momentum distribution during the freeze-out through 3-dimensional hypersurfaces with spacelike normal. We study some suggested solutions for this problem, and demonstrate it in one example.

Supergravity models of (3+1)-dimensional QCD

The most general black M5-brane solution of eleven-dimensional supergravity (with a flat R4 spacetime in the brane and a regular horizon) is characterized by charge, mass and two angular momenta. We use this metric to construct general dual models of large-N QCD (at strong coupling) that depend on two free parameters. The mass spectrum of scalar particles is determined analytically (in the WKB approximation) and numerically in the whole two-dimensional parameter space. We compare the mass spectrum with analogous results from lattice calculations, and find that the supergravity predictions are close to the lattice results everywhere on the two dimensional parameter space except along a special line. We also examine the mass spectrum of the supergravity Kaluza-Klein (KK) modes and find that the KK modes along the compact D-brane coordinate decouple from the spectrum for large angular momenta. There are however KK modes charged under a U(1)×U(1) global symmetry which do not decouple anywhere on the parameter space. General formulas for the string tension and action are also given.

Periodic orbits near a heteroclinic loop formed by one dimensional orbit and a 2-dimensional manifold: application to the charged collinear 3-body problem

The paper is devoted to the study of a type of differential systems which appear usually in the study of some Hamiltonian systems with 2 degrees of freedom. We prove the existence of infinitely many periodic orbits on each negative energy level. All these periodic orbits pass near the total collision. Finally we apply these results to study the existence of periodic orbits in the charged collinear 3–body problem.

Online Robust 3D Mapping Using Structure from Motion Cues

This paper presents a complete solution for creating accurate 3D textured models from monocular video sequences. The methods are developed within the framework of sequential structure from motion, where a 3D model of the environment is maintained and updated as new visual information becomes available. The camera position is recovered by directly associating the 3D scene model with local image observations. Compared to standard structure from motion techniques, this approach decreases the error accumulation while increasing the robustness to scene occlusions and feature association failures. The obtained 3D information is used to generate high quality, composite visual maps of the scene (mosaics). The visual maps are used to create texture-mapped, realistic views of the scene

One-dimensional solidification of supercooled melts

In this paper a one-phase supercooled Stefan problem, with a nonlinear relation between the phase change temperature and front velocity, is analysed. The model with the standard linear approximation, valid for small supercooling, is first examined asymptotically. The nonlinear case is more difficult to analyse and only two simple asymptotic results are found. Then, we apply an accurate heat balance integral method to make further progress. Finally, we compare the results found against numerical solutions. The results show that for large supercooling the linear model may be highly inaccurate and even qualitatively incorrect. Similarly as the Stefan number β → 1&sup&+&/sup& the classic Neumann solution which exists down to β =1 is far from the linear and nonlinear supercooled solutions and can significantly overpredict the solidification rate.

Risk management under a two-factor model of the term structure of interest rates

This paper presents several applications to interest rate risk managementbased on a two-factor continuous-time model of the term structure of interestrates previously presented in Moreno (1996). This model assumes that defaultfree discount bond prices are determined by the time to maturity and twofactors, the long-term interest rate and the spread (difference between thelong-term rate and the short-term (instantaneous) riskless rate). Several newmeasures of ``generalized duration" are presented and applied in differentsituations in order to manage market risk and yield curve risk. By means ofthese measures, we are able to compute the hedging ratios that allows us toimmunize a bond portfolio by means of options on bonds. Focusing on thehedging problem, it is shown that these new measures allow us to immunize abond portfolio against changes (parallel and/or in the slope) in the yieldcurve. Finally, a proposal of solution of the limitations of conventionalduration by means of these new measures is presented and illustratednumerically.

Auctions of licences and market structure

This paper studies sequential auctions of licences to operate in amarket where those firms that obtain at least one licence then engage ina symmetric market game. I employ a new refinement of Nash equilibrium,the concept of {\sl Markovian recursively undominated equilibrium}.The unique solution satisfies the following properties: (i) when severalfirms own licences before the auction (incumbents), new entrants buylicences in each stage, and (ii) when there is no more than one incumbent,either the single firm preempts entry altogether or entry occurs inevery stage, depending on the parameter configuration.

A two-mean reverting-factor model of the term structure of interest rates

This paper presents a two--factor model of the term structure ofinterest rates. We assume that default free discount bond prices aredetermined by the time to maturity and two factors, the long--term interestrate and the spread (difference between the long--term rate and theshort--term (instantaneous) riskless rate). Assuming that both factorsfollow a joint Ornstein--Uhlenbeck process, a general bond pricing equationis derived. We obtain a closed--form expression for bond prices andexamine its implications for the term structure of interest rates. We alsoderive a closed--form solution for interest rate derivatives prices. Thisexpression is applied to price European options on discount bonds andmore complex types of options. Finally, empirical evidence of the model'sperformance is presented.

Dynamic structure function in 3-4He mixtures

Relevant features of the dynamic structure function S(q,¿) in 3-4He mixtures at zero temperature are investigated starting from known properties of the ground state. Sum rules are used to fix rigorous constraints to the different contributions to S(q,¿), coming from 3He and 4He elementary excitations, as well as to explore the role of the cross term S(3,4)(q,¿). Both the low-q (phonon-roton 4He excitations and 1p-1h 3He excitations) and high-q (deep-inelastic-scattering) ranges are discussed.

Quantum wire with periodic serial structure

Electron wave motion in a quantum wire with periodic structure is treated by direct solution of the Schrödinger equation as a mode-matching problem. Our method is particularly useful for a wire consisting of several distinct units, where the total transfer matrix for wave propagation is just the product of those for its basic units. It is generally applicable to any linearly connected serial device, and it can be implemented on a small computer. The one-dimensional mesoscopic crystal recently considered by Ulloa, Castaño, and Kirczenow [Phys. Rev. B 41, 12 350 (1990)] is discussed with our method, and is shown to be a strictly one-dimensional problem. Electron motion in the multiple-stub T-shaped potential well considered by Sols et al. [J. Appl. Phys. 66, 3892 (1989)] is also treated. A structure combining features of both of these is investigated

Quantum wire with periodic serial structure

Electron wave motion in a quantum wire with periodic structure is treated by direct solution of the Schrödinger equation as a mode-matching problem. Our method is particularly useful for a wire consisting of several distinct units, where the total transfer matrix for wave propagation is just the product of those for its basic units. It is generally applicable to any linearly connected serial device, and it can be implemented on a small computer. The one-dimensional mesoscopic crystal recently considered by Ulloa, Castaño, and Kirczenow [Phys. Rev. B 41, 12 350 (1990)] is discussed with our method, and is shown to be a strictly one-dimensional problem. Electron motion in the multiple-stub T-shaped potential well considered by Sols et al. [J. Appl. Phys. 66, 3892 (1989)] is also treated. A structure combining features of both of these is investigated.

Structure and magnetic properties of Sm/Fe multilayers versus substrate temperature

Three Sm(2 Å)/Fe(3 Å) multilayers have been made using two electron beams in a high vacuum chamber onto very thin Kapton foils at different substrate temperatures, (Ts=40°C, 150°C and 230°C), with the same total thickness of 3000 Å. We have found that the substrate temperature strongly affects structure and magnetic properties of the samples. For a substrate temperature of 150°C the sample behaves as a three dimensional random magnet.