A proposal for a new specification for a conditionally heteroskedastic variance model: the Quadratic Moving-Average Conditional Heteroskedasticity and an application to the D. Mark-U.S. dollar Exchange Rate

Ever since the appearance of the ARCH model [Engle(1982a)], an impressive array of variance specifications belonging to the same class of models has emerged [i.e. Bollerslev's (1986) GARCH; Nelson's (1990) EGARCH]. This recent domain has achieved very successful developments. Nevertheless, several empirical studies seem to show that the performance of such models is not always appropriate [Boulier(1992)]. In this paper we propose a new specification: the Quadratic Moving Average Conditional heteroskedasticity model. Its statistical properties, such as the kurtosis and the symmetry, as well as two estimators (Method of Moments and Maximum Likelihood) are studied. Two statistical tests are presented, the first one tests for homoskedasticity and the second one, discriminates between ARCH and QMACH specification. A Monte Carlo study is presented in order to illustrate some of the theoretical results. An empirical study is undertaken for the DM-US exchange rate.

A mathematical model to describe fat oxidation kinetics during graded exercise.

PURPOSE: The purpose of this study was to develop a mathematical model (sine model, SIN) to describe fat oxidation kinetics as a function of the relative exercise intensity [% of maximal oxygen uptake (%VO2max)] during graded exercise and to determine the exercise intensity (Fatmax) that elicits maximal fat oxidation (MFO) and the intensity at which the fat oxidation becomes negligible (Fatmin). This model included three independent variables (dilatation, symmetry, and translation) that incorporated primary expected modulations of the curve because of training level or body composition. METHODS: Thirty-two healthy volunteers (17 women and 15 men) performed a graded exercise test on a cycle ergometer, with 3-min stages and 20-W increments. Substrate oxidation rates were determined using indirect calorimetry. SIN was compared with measured values (MV) and with other methods currently used [i.e., the RER method (MRER) and third polynomial curves (P3)]. RESULTS: There was no significant difference in the fitting accuracy between SIN and P3 (P = 0.157), whereas MRER was less precise than SIN (P < 0.001). Fatmax (44 +/- 10% VO2max) and MFO (0.37 +/- 0.16 g x min(-1)) determined using SIN were significantly correlated with MV, P3, and MRER (P < 0.001). The variable of dilatation was correlated with Fatmax, Fatmin, and MFO (r = 0.79, r = 0.67, and r = 0.60, respectively, P < 0.001). CONCLUSIONS: The SIN model presents the same precision as other methods currently used in the determination of Fatmax and MFO but in addition allows calculation of Fatmin. Moreover, the three independent variables are directly related to the main expected modulations of the fat oxidation curve. SIN, therefore, seems to be an appropriate tool in analyzing fat oxidation kinetics obtained during graded exercise.

Patterns of oxygen consumption during establishment of cephalocaudal polarity in the early chick embryo.

Oxygen uptake was studied during the establishment of cephalocaudal polarity in the very early chick embryo, i.e., 10 hr before (stage VI) and at laying (stage X). Oxygen fluxes in minute regions of the intact blastoderms were measured in vitro by scanning microspectrophotometry in the presence or absence of glucose. The oxygen consumption of the whole blastoderm remained constant (6 nmol O2 X hr-1) throughout the period studied, although the number of cells increased more than twofold. The regional oxygen fluxes varied from 0.41 to 1.13 nmol O2 X hr-1 X mm-2 at stage VI and from 0.42 to 0.70 nmol O2 X hr-1 X mm-2 at stage X. At stage VI, the oxygen flux in the center of the blastoderm was significantly higher than that in its periphery. This pattern remained evident when the values were corrected for cell number or for cytoplasmic volume. At stage X, there was a tendency for the oxygen fluxes to decrease from the posterior to the anterior regions of the area pellucida. Thus the pattern of oxidative metabolism in the late uterine embryos seems to change from radial to bilateral. This change of symmetry probably reflects the process of formation of the embryonic axis. In addition, the fact that the oxygen uptake was similar in the presence or absence of glucose suggests that early chick embryos metabolize essentially intracellular stores.

The choice of banking firm: Are the interest rate a significant criteria?

The objective of the research is to know the factors that in Spain determine the choice of banking organization. The obtained results indicate that the dimension of the network of branches is the reason more valued. In spite of the increasing symmetry of the Spanish banking market, the preferences of the clients of the savings banks and those of the banks are not absolutely coincident, being the proximity - the main reason for election- much more valued by the former than by the latter. The existence of divergences in the preferences has also been detected according to the region and the typology of city of residence.

Fum i miralls: trobant l'ordre en un món caòtic

El calidoscopi és una joguina que converteix fragments de vidre acolorit en patrons infinitament variats mitjançant l'ús de miralls. Hi ha quelcom satisfactori en els patrons –els necessitem per crear significat, i trobem bellesa en la seva simetria. No obstant, els sistemes complexos desobeeixen les fórmules simples. Per exemple, és impossible descriure una cosa tan prosaica com el comportament del fum mentre ascendeix fent servir les matemàtiques clàssiques. Agafant en préstec idees de diferents disciplines, podem considerar l'alfabetització informacional com una invitació per als nostres estudiants per jugar amb la imprevisible varietat de l'experiència humana i descobrir patrons que els resultin plens de significat.

Shaping fission yeast with microtubules.

For cell morphogenesis, the cell must establish distinct spatial domains at specified locations at the cell surface. Here, we review the molecular mechanisms of cell polarity in the fission yeast Schizosaccharomyces pombe. These are simple rod-shaped cells that form cortical domains at cell tips for cell growth and at the cell middle for cytokinesis. In both cases, microtubule-based systems help to shape the cell by breaking symmetry, providing endogenous spatial cues to position these sites. The plus ends of dynamic microtubules deliver polarity factors to the cell tips, leading to local activation of the GTPase cdc42p and the actin assembly machinery. Microtubule bundles contribute to positioning the division plane through the nucleus and the cytokinesis factor mid1p. Recent advances illustrate how the spatial and temporal regulation of cell polarization integrates many elements, including historical landmarks, positive and negative controls, and competition between pathways.

Estimation of the Spatial Weights Matrix under Structural Constraints

While estimates of models with spatial interaction are very sensitive to the choice of spatial weights, considerable uncertainty surrounds de nition of spatial weights in most studies with cross-section dependence. We show that, in the spatial error model the spatial weights matrix is only partially identi ed, and is fully identifi ed under the structural constraint of symmetry. For the spatial error model, we propose a new methodology for estimation of spatial weights under the assumption of symmetric spatial weights, with extensions to other important spatial models. The methodology is applied to regional housing markets in the UK, providing an estimated spatial weights matrix that generates several new hypotheses about the economic and socio-cultural drivers of spatial di¤usion in housing demand.

Positive solutions of nonlinear problems involving the square root of the Laplacian

We consider nonlinear elliptic problems involving a nonlocal operator: the square root of the Laplacian in a bounded domain with zero Dirichlet boundary conditions. For positive solutions to problems with power nonlinearities, we establish existence and regularity results, as well as a priori estimates of Gidas-Spruck type. In addition, among other results, we prove a symmetry theorem of Gidas-Ni-Nirenberg type.

Complex contact manifolds and S1 actions

We prove rigidity and vanishing theorems for several holomorphic Euler characteristics on complex contact manifolds admitting holomorphic circle actions preserving the contact structure. Such vanishings are reminiscent of those of LeBrun and Salamon on Fano contact manifolds but under a symmetry assumption instead of a curvature condition.

Primordial Perturbations in Einstein-Aether theories

El nostre objectiu es l'estudi d'extensions de la Relativitat General i, en particular, estem interessats en les teories que continguin camps vectorials addicionals. En aquests tipus de teories es necessari imposar que el vector ha de tenir norma fixa per evitar la presència d'un fantasma o grau de llibertat amb terme cinètic negatiu, i això implica que la simetria Lorentz està trencada espontàniament. El camp del aether només interactua gravitatòriament i la seva presència es difícil de detectar, no obstant això, durant inflació les fluctuacions del buit a escales petites d'un camp lleuger pot deixar una empremta en observables com les anisotropies del fons de radiació de microones. Les fluctuacions del Einstein-aether es comporten com els camps sense massa i això fa que inflació generi modes de longitud de ona llarga en els sectors escalar i vectorial. Hem estudiat la signatura del Einstein-aether dins l'espectre de pertorbacions primordials lluny del límit de de Sitter de inflació. Aquests modes escalars i vectorials poden deixar una empremta significativa en la radiació de fons de microones en funció dels paràmetres del model. Les observacions del fons de radiació de microones imposen restriccions fenomenològiques que redueixen els límits existents per aquesta classe de teoria. Amb aquest estudi del aether també esperem millorar el coneixement que tenim de una classe més ampla de teories que exhibeixen el mateix tipus de trencament de simetria.

Tight open knots.

The tightest open conformations of a few prime knots (3(1), 4(1), 5(1), 5(2), and 6(3)) found with the use of the SONO algorithm are presented and discussed. The conformations are obtained from the tightest closed conformations of the knots by cutting and opening them at different locations. The length of the rope engaged in each of the open conformations is calculated. The curvature and torsion profiles of the unique tightest conformations of the 3(1) and 4(1) open knots are presented and discussed. In particular, symmetry properties of the knots reflected within their curvature and torsion profiles are analysed. Connections with the physics of polymers are discussed.

Effect of Knotting on the Shape of Polymers

Momentary configurations of long polymers at thermal equilibrium usually deviate from spherical symmetry and can be better described, on average, by a prolate ellipsoid. The asphericity and nature of asphericity (or prolateness) that describe these momentary ellipsoidal shapes of a polymer are determined by specific expressions involving the three principal moments of inertia calculated for configurations of the polymer. Earlier theoretical studies and numerical simulations have established that as the length of the polymer increases, the average shape for the statistical ensemble of random configurations asymptotically approaches a characteristic universal shape that depends on the solvent quality. It has been established, however, that these universal shapes differ for linear, circular, and branched chains. We investigate here the effect of knotting on the shape of cyclic polymers modeled as random isosegmental polygons. We observe that random polygons forming different knot types reach asymptotic shapes that are distinct from the ensemble average shape. For the same chain length, more complex knots are, on average, more spherical than less complex knots.

Estimation of parametric and nonparametric models for univariate claim severity distributions - an approach using R

This paper presents an analysis of motor vehicle insurance claims relating to vehicle damage and to associated medical expenses. We use univariate severity distributions estimated with parametric and non-parametric methods. The methods are implemented using the statistical package R. Parametric analysis is limited to estimation of normal and lognormal distributions for each of the two claim types. The nonparametric analysis presented involves kernel density estimation. We illustrate the benefits of applying transformations to data prior to employing kernel based methods. We use a log-transformation and an optimal transformation amongst a class of transformations that produces symmetry in the data. The central aim of this paper is to provide educators with material that can be used in the classroom to teach statistical estimation methods, goodness of fit analysis and importantly statistical computing in the context of insurance and risk management. To this end, we have included in the Appendix of this paper all the R code that has been used in the analysis so that readers, both students and educators, can fully explore the techniques described

The metaphysics of quantum gravity : a causal approach

The dissertation investigates some relevant metaphysical issues arising in the context of spacetime theories. In particular, the inquiry focuses on general relativity and canonical quantum gravity. A formal definition of spacetime theory is proposed and, against this framework, an analysis of the notions of general covariance, symmetry and background independence is performed. It is argued that many conceptual issues in general relativity and canonical quantum gravity derive from putting excessive emphasis on general covariance as an ontological prin-ciple. An original metaphysical position grounded in scientific essential- ism and causal realism (weak essentialism) is developed and defended. It is argued that, in the context of general relativity, weak essentialism supports spacetime substantivalism. It is also shown that weak essentialism escapes arguments from metaphysical underdetermination by positing a particular kind of causation, dubbed geometric. The proposed interpretive framework is then applied to Bohmian mechanics, pointing out that weak essentialism nicely fits into this theory. In the end, a possible Bohmian implementation of loop quantum gravity is considered, and such a Bohmian approach is interpreted in a geometric causal fashion. Under this interpretation, Bohmian loop quantum gravity straightforwardly commits us to an ontology of elementary extensions of space whose evolution is described by a non-local law. The causal mechanism underlying this evolution clarifies many conceptual issues related to the emergence of classical spacetime from the quantum regime. Although there is as yet no fully worked out physical theory of quantum gravity, it is argued that the proposed approach sets up a standard that proposals for a serious ontology in this field should meet.

Extensional flow of nematic liquid crystal under electric field gradient

Systematic asymptotic methods are used to formulate a model for the extensional flow of a thin sheet of nematic liquid crystal. With no external body forces applied, the model is found to be equivalent to the so-called Trouton model for Newtonian sheets (and fi bers), albeit with a modi fied "Trouton ratio". However, with a symmetry-breaking electric field gradient applied, behavior deviates from the Newtonian case, and the sheet can undergo fi nite-time breakup if a suitable destabilizing field is applied. Some simple exact solutions are presented to illustrate the results in certain idealized limits, as well as sample numerical results to the full model equations.