The hardness profile as a tool to detect spurious stationary points in the potential energy surface

The energy and hardness profile for a series of inter and intramolecular conformational changes at several levels of calculation were computed. The hardness profiles were found to be calculated as the difference between the vertical ionization potential and electron affinity. The hardness profile shows the correct number of stationary points independently of the basis set and methodology used. It was found that the hardness profiles can be used to check the reliability of the energy profiles for those chemical system

Estimation of electronic coupling in π -stacked donor-bridge-acceptor systems: correction of the two-state model

Comparison of donor-acceptor electronic couplings calculated within two-state and three-state models suggests that the two-state treatment can provide unreliable estimates of Vda because of neglecting the multistate effects. We show that in most cases accurate values of the electronic coupling in a π stack, where donor and acceptor are separated by a bridging unit, can be obtained as Ṽ da = (E2 - E1) μ12 Rda + (2 E3 - E1 - E2) 2 μ13 μ23 Rda2, where E1, E2, and E3 are adiabatic energies of the ground, charge-transfer, and bridge states, respectively, μij is the transition dipole moments between the states i and j, and Rda is the distance between the planes of donor and acceptor. In this expression based on the generalized Mulliken-Hush approach, the first term corresponds to the coupling derived within a two-state model, whereas the second term is the superexchange correction accounting for the bridge effect. The formula is extended to bridges consisting of several subunits. The influence of the donor-acceptor energy mismatch on the excess charge distribution, adiabatic dipole and transition moments, and electronic couplings is examined. A diagnostic is developed to determine whether the two-state approach can be applied. Based on numerical results, we showed that the superexchange correction considerably improves estimates of the donor-acceptor coupling derived within a two-state approach. In most cases when the two-state scheme fails, the formula gives reliable results which are in good agreement (within 5%) with the data of the three-state generalized Mulliken-Hush model

Avoiding transcription factor competition at promoter level increases the chances of obtaining oscillations

Background: The ultimate goal of synthetic biology is the conception and construction of genetic circuits that are reliable with respect to their designed function (e.g. oscillators, switches). This task remains still to be attained due to the inherent synergy of the biological building blocks and to an insufficient feedback between experiments and mathematical models. Nevertheless, the progress in these directions has been substantial. Results: It has been emphasized in the literature that the architecture of a genetic oscillator must include positive (activating) and negative (inhibiting) genetic interactions in order to yield robust oscillations. Our results point out that the oscillatory capacity is not only affected by the interaction polarity but by how it is implemented at promoter level. For a chosen oscillator architecture, we show by means of numerical simulations that the existence or lack of competition between activator and inhibitor at promoter level affects the probability of producing oscillations and also leaves characteristic fingerprints on the associated period/amplitude features. Conclusions: In comparison with non-competitive binding at promoters, competition drastically reduces the region of the parameters space characterized by oscillatory solutions. Moreover, while competition leads to pulse-like oscillations with long-tail distribution in period and amplitude for various parameters or noisy conditions, the non-competitive scenario shows a characteristic frequency and confined amplitude values. Our study also situates the competition mechanism in the context of existing genetic oscillators, with emphasis on the Atkinson oscillator.

Weak approximations. A Malliavin calculus approach

We introduce a variation of the proof for weak approximations that issuitable for studying the densities of stochastic processes which areevaluations of the flow generated by a stochastic differential equation on a random variable that maybe anticipating. Our main assumption is that the process and the initial random variable have to be smooth in the Malliavin sense. Furthermore if the inverse of the Malliavin covariance matrix associated with the process under consideration is sufficiently integrable then approximations fordensities and distributions can also be achieved. We apply theseideas to the case of stochastic differential equations with boundaryconditions and the composition of two diffusions.

What other sciences look like

In order to have references for discussing mathematical menus in political science, Ireview the most common types of mathematical formulae used in physics andchemistry, as well as some mathematical advances in economics. Several issues appearrelevant: variables should be well defined and measurable; the relationships betweenvariables may be non-linear; the direction of causality should be clearly identified andnot assumed on a priori grounds. On these bases, theoretically-driven equations onpolitical matters can be validated by empirical tests and can predict observablephenomena.

A new chance-constrained maximum capture location problem

The paper presents a new model based on the basic Maximum Capture model,MAXCAP. The New Chance Constrained Maximum Capture modelintroduces astochastic threshold constraint, which recognises the fact that a facilitycan be open only if a minimum level of demand is captured. A metaheuristicbased on MAX MIN ANT system and TABU search procedure is presented tosolve the model. This is the first time that the MAX MIN ANT system isadapted to solve a location problem. Computational experience and anapplication to 55 node network are also presented.

Accelerated tumor invasion under non-isotropic cell dispersal in glioblastomas

Glioblastomas are highly diffuse, malignant tumors that have so far evaded clinical treatment. The strongly invasive behavior of cells in these tumors makes them very resistant to treatment, and for this reason both experimental and theoretical efforts have been directed toward understanding the spatiotemporal pattern of tumor spreading. Although usual models assume a standard diffusion behavior, recent experiments with cell cultures indicate that cells tend to move in directions close to that of glioblastoma invasion, thus indicating that a biasedrandom walk model may be much more appropriate. Here we show analytically that, for realistic parameter values, the speeds predicted by biased dispersal are consistent with experimentally measured data. We also find that models beyond reaction–diffusion–advection equations are necessary to capture this substantial effect of biased dispersal on glioblastoma spread

Dispersal probability distributions and the wave-front speed problem

The speed and width of front solutions to reaction-dispersal models are analyzed both analytically and numerically. We perform our analysis for Laplace and Gaussian distribution kernels, both for delayed and nondelayed models. The results are discussed in terms of the characteristic parameters of the models

Predicting the potential for lightning activity in mediterranean storms based on the WRF model dynamic and microphysical fields

A new parameter is introduced: the lightning potential index (LPI), which is a measure of the potential for charge generation and separation that leads to lightning flashes in convective thunderstorms. The LPI is calculated within the charge separation region of clouds between 0 C and 20 C, where the noninductive mechanism involving collisions of ice and graupel particles in the presence of supercooled water is most effective. As shown in several case studies using the Weather Research and Forecasting (WRF) model with explicit microphysics, the LPI is highly correlated with observed lightning. It is suggested that the LPI may be a useful parameter for predicting lightning as well as a tool for improving weather forecasting of convective storms and heavy rainfall.

Modelling of weather radar echoes from anomalous propagation using a hybrid parabolic equation method and NWP model data

Contamination of weather radar echoes by anomalous propagation (anaprop) mechanisms remains a serious issue in quality control of radar precipitation estimates. Although significant progress has been made identifying clutter due to anaprop there is no unique method that solves the question of data reliability without removing genuine data. The work described here relates to the development of a software application that uses a numerical weather prediction (NWP) model to obtain the temperature, humidity and pressure fields to calculate the three dimensional structure of the atmospheric refractive index structure, from which a physically based prediction of the incidence of clutter can be made. This technique can be used in conjunction with existing methods for clutter removal by modifying parameters of detectors or filters according to the physical evidence for anomalous propagation conditions. The parabolic equation method (PEM) is a well established technique for solving the equations for beam propagation in a non-uniformly stratified atmosphere, but although intrinsically very efficient, is not sufficiently fast to be practicable for near real-time modelling of clutter over the entire area observed by a typical weather radar. We demonstrate a fast hybrid PEM technique that is capable of providing acceptable results in conjunction with a high-resolution terrain elevation model, using a standard desktop personal computer. We discuss the performance of the method and approaches for the improvement of the model profiles in the lowest levels of the troposphere.

Valores medios del coeficiente de atenuación de las ondas Rayleigh para Europa occidental

En este estudio presentamos los valores medios del coeficiente de atenuación de las ondas Rayleigh para Europa occidental, obtenidos a partir del estudio de tres terremotos situados en las Azores, Sicilia y Mar Negro y registrados por estaciones europeas. Los resultados presentan una gran dispersión, mostrando claramente la inhomogeneidad de la zona. Para el terremoto del Atlántico, los resultados son muy coherentes y presentan unos valores del coeficiente de atenuación comparables, aunque ligeramente superiores para periodos cortos, a los haliados para la region estable de la placa Euroasiática.

Anelasticidad de la zona estable euroasiática y de la zona europea occidental

La teoria de inversión en su forma estocastica ha sido aplicada a dos conjuntos de coeficientes de atenuación de las ondas de Rayleigh correspondientes a la zona estable Euroasiatica y a la zona Europea Occidental. Los resultados obtenidos muestran que las propiedades anelásticas bajo dichas zonas son distintas. Europa Occidental se halla caracterizada por valores mas bajos de los factores especificos de calidad de las ondas de cizalla(Qbeta) que los correspondientes a la zona Estable Euroasiática. Las profundiades a las que los valores de Qbeta decrecen más rápidamente son alrededorde 60 km para Europa Occidental y de 40 km para la zona Estable Euroasiática. La comparación con un estudio de atenuación en el Océano Atlántico muestra que los coeficientes de atenuación correspondientes a la zona Europea Occidental pueden ser considerados representativos para dicha zona.

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.

The mean-variance model from the inverse of the variance-covariance matrix

En este artículo, a partir de la inversa de la matriz de varianzas y covarianzas se obtiene el modelo Esperanza-Varianza de Markowitz siguiendo un camino más corto y matemáticamente riguroso. También se obtiene la ecuación de equilibrio del CAPM de Sharpe.