Scaling calculation of isoscalar giant resonances in relativistic Thomas-Fermi theory

We derive analytical expressions for the excitation energy of the isoscalar giant monopole and quadrupole resonances in finite nuclei, by using the scaling method and the extended ThomasFermi approach to relativistic mean-field theory. We study the ability of several nonlinear σω parameter sets of common use in reproducing the experimental data. For monopole oscillations the calculations agree better with experiment when the nuclear matter incompressibility of the relativistic interaction lies in the range 220260 MeV. The breathing-mode energies of the scaling method compare satisfactorily with those obtained in relativistic RPA and time-dependent mean-field calculations. For quadrupole oscillations, all the analyzed nonlinear parameter sets reproduce the empirical trends reasonably well.

Scaling in relativistic Thomas-Fermi approach for nuclei

By using the scaling method we derive the virial theorem for the relativistic mean field model of nuclei treated in the ThomasFermi approach. The ThomasFermi solutions statisfy the stability condition against scaling. We apply the formalism to study the excitation energy of the breathing mode in finite nuclei with several relativistic parameter sets of common use.

Scaling and data collapse for the mean exit time of asset prices

We study theoretical and empirical aspects of the mean exit time (MET) of financial time series. The theoretical modeling is done within the framework of continuous time random walk. We empirically verify that the mean exit time follows a quadratic scaling law and it has associated a prefactor which is specific to the analyzed stock. We perform a series of statistical tests to determine which kind of correlation are responsible for this specificity. The main contribution is associated with the autocorrelation property of stock returns. We introduce and solve analytically both two-state and three-state Markov chain models. The analytical results obtained with the two-state Markov chain model allows us to obtain a data collapse of the 20 measured MET profiles in a single master curve.

Difussion in a titled periodic potential: Enhancement, universality, and scaling

An exact analytical expression for the effective diffusion coefficient of an overdamped Brownian particle in a tilted periodic potential is derived for arbitrary potentials and arbitrary strengths of the thermal noise. Near the critical tilt (threshold of deterministic running solutions) a scaling behavior for weak thermal noise is revealed and various universality classes are identified. In comparison with the bare (potential-free) thermal diffusion, the effective diffusion coefficient in a critically tilted periodic potential may be, in principle, arbitrarily enhanced. For a realistic experimental setup, an enhancement by 14 orders of magnitude is predicted so that thermal diffusion should be observable on a macroscopic scale at room temperature.

Magnetic field scaling of relaxation curves in small particle systems

We study the effects of the magnetic field on the relaxation of the magnetization of smallmonodomain noninteracting particles with random orientations and distribution of anisotropyconstants. Starting from a master equation, we build up an expression for the time dependence of themagnetization which takes into account thermal activation only over barriers separating energyminima, which, in our model, can be computed exactly from analytical expressions. Numericalcalculations of the relaxation curves for different distribution widths, and under different magneticfields H and temperatures T, have been performed. We show how a T ln(t/t0) scaling of the curves,at different T and for a given H, can be carried out after proper normalization of the data to theequilibrium magnetization. The resulting master curves are shown to be closely related to what wecall effective energy barrier distributions, which, in our model, can be computed exactly fromanalytical expressions. The concept of effective distribution serves us as a basis for finding a scalingvariable to scale relaxation curves at different H and a given T, thus showing that the fielddependence of energy barriers can be also extracted from relaxation measurements.

Finite-size scaling investigation of the liquid-liquid critical point in ST2 water and its stability with respect to crystallization.

The liquid-liquid critical point scenario of water hypothesizes the existence of two metastable liq- uid phases low-density liquid (LDL) and high-density liquid (HDL) deep within the supercooled region. The hypothesis originates from computer simulations of the ST2 water model, but the stabil- ity of the LDL phase with respect to the crystal is still being debated. We simulate supercooled ST2 water at constant pressure, constant temperature, and constant number of molecules N for N ≤ 729 and times up to 1 μs. We observe clear differences between the two liquids, both structural and dynamical. Using several methods, including finite-size scaling, we confirm the presence of a liquid-liquid phase transition ending in a critical point. We find that the LDL is stable with respect to the crystal in 98% of our runs (we perform 372 runs for LDL or LDL-like states), and in 100% of our runs for the two largest system sizes (N = 512 and 729, for which we perform 136 runs for LDL or LDL-like states). In all these runs, tiny crystallites grow and then melt within 1 μs. Only for N ≤ 343 we observe six events (over 236 runs for LDL or LDL-like states) of spontaneous crystal- lization after crystallites reach an estimated critical size of about 70 ± 10 molecules.

The relationship of capitalization period length with market portfolio composition and betas

Beta coefficients are not stable if we modify the observation periods of the returns. The market portfolio composition also varies, whereas changes in the betas are the same, whether they are calculated as regression coefficients or as a ratio of the risk premiums. The instantaneous beta, obtained when the capitalization frequency approaches infinity, may be a useful tool in portfolio selection.

On the relationship between connections and the asymptotic properties of predictive distributions

In a recent paper, Komaki studied the second-order asymptotic properties of predictive distributions, using the Kullback-Leibler divergence as a loss function. He showed that estimative distributions with asymptotically efficient estimators can be improved by predictive distributions that do not belong to the model. The model is assumed to be a multidimensional curved exponential family. In this paper we generalize the result assuming as a loss function any f divergence. A relationship arises between alpha connections and optimal predictive distributions. In particular, using an alpha divergence to measure the goodness of a predictive distribution, the optimal shift of the estimate distribution is related to alpha-covariant derivatives. The expression that we obtain for the asymptotic risk is also useful to study the higher-order asymptotic properties of an estimator, in the mentioned class of loss functions.

Fifth-order cyclicity and organic matter contents relationship (Lower Eocene, Pyrenees)

The Upper Limestone Member of the Corones Formation of the Spanish Pyrenees consists of various units (Lower and Upper Foraminifera Units, Shale Unit, Cherty-ostracode Unit, Ostracode Unit and Chara-ostracode Unit) and offers strong facies and lateral thickness (20 to 80 m) variations. Detailed facies analyses, fifth-order cycles and organic geochemical determinations in the central domain of the Corones platform carbonates (Cherty-ostracode Unit), lower Eocene in age, were carried out to establish a case of close relationship between variations in organic matter productivity and cyclicity with annual period. The Cherty-ostracode Unit displays a continuous and pervasive fifth-order cyclicity, represented by 5 cycles. Each cycle consists of a lower part (mollusc facies) and an upper part (laminated ostracode facies). The calculated fifth-order cycle period ranges from about 17,000 to 28,000 years, which falls within the Milankovitch Band. Variations in organic matter content related to these carbonate cycles have been established. The lower mollusc facies members show a low organic carbon content and Hydrogen Index (HI) below 0.6% in weight and 261, respectively. By contrast, the upper laminated ostracode facies members show high organic carbon contents (up to 2% in weight) and high HI (between 164 and 373), and are also characterized by important silicification processes (the content in chert is up to 30%). The organic geochemistry resulting from these organic rich levels reflects a contribution of algal marine input.

Relationship between squamous cell carcinoma of the anterior two thirds of the tongue and removable denture use - a pioneer study in a Portuguese

The aim of the study was to determine whether there is any relationship between the presence of removable dentures and squamous cell carcinoma of the anterior two thirds of the tongue in a Portuguese population. A retrospective cross-sectional study was conducted on patients with a biopsy-proven diagnosis of squamous cell carcinoma of the tongue, who were seen and treated at the Department of Head and Neck Surgery of the Portuguese Institute of Oncology 'Francisco Gentil', Lisbon, Portugal, during a 3-year period. Several factors were examined: gender, use of removable dentures, age, location of the lesion, and alcohol and tobacco consumption. One hundred and six cases were selected from the initial 151 cases, with a male:female ratio of 3:1 and the lateral borders being the most commonly affected site. The prevalence in both genders was between the sixth and seventh decade of life. Men were more likely to consume alcohol and tobacco than women, and no relationship was observed between denture use and presence of carcinoma of the tongue. In light of the data obtained, it may be considered that female use of a denture plays an important role, but it cannot be identified as a remarkable etiologic factor.

Solid phase crystallization under continuous heating: kinetic and microstructure scaling laws

The kinetics and microstructure of solid-phase crystallization under continuous heating conditions and random distribution of nuclei are analyzed. An Arrhenius temperature dependence is assumed for both nucleation and growth rates. Under these circumstances, the system has a scaling law such that the behavior of the scaled system is independent of the heating rate. Hence, the kinetics and microstructure obtained at different heating rates differ only in time and length scaling factors. Concerning the kinetics, it is shown that the extended volume evolves with time according to αex = [exp(κCt′)]m+1, where t′ is the dimensionless time. This scaled solution not only represents a significant simplification of the system description, it also provides new tools for its analysis. For instance, it has been possible to find an analytical dependence of the final average grain size on kinetic parameters. Concerning the microstructure, the existence of a length scaling factor has allowed the grain-size distribution to be numerically calculated as a function of the kinetic parameters

The changing relationship between commodity prices and equity prices in commodity exporting

We explore the linkage between equity and commodity markets, focusing in particular on its evolution over time. We document that a country's equity market valuehas significant out-of-sample predictive ability for the future global commodity priceindex for several primary commodity-exporting countries. The out-of-sample predictive ability of the equity market appears around 2000s. The results are robust to usingseveral control variables as well as firm-level equity data. Finally, our results indicatethat exchange rates are a better predictor of commodity prices than equity markets,especially at very short horizons.