Extinction Effects of Multiplicative Non-Gaussian L′evy Noise in a Tumor Growth System with Immunization

The extinction phenomenon induced by multiplicative non-Gaussian Levy noise in a tumor growth model with immune response is discussed. Under the influence of the stochastic immune rate, the model is analyzed in terms of a stochastic differential equation with multiplicative noise. By means of the theory of the infinitesimal generator of Hunt processes, the escape probability, which is used to measure the noise-induced extinction probability of tumor cells, is explicitly expressed as a function of initial tumor cell density, stability index and noise intensity. Based on the numerical calculations, it is found that for different initial densities of tumor cells, noise parameters play opposite roles on the escape probability. The optimally selected values of the multiplicative noise intensity and the stability index are found to maximize the escape probability.     

Arithmetic Brownian motion and real options

We treat real option value when the underlying process is arithmetic Brownian motion (ABM). In contrast to the more common assumption of geometric Brownian motion (GBM) and multiplicative diffusion, with ABM the underlying project value is expressed as an additive process. Its variance remains constant over time rather than rising or falling along with the project’s value, even admitting the possibility of negative values. This is a more compelling paradigm for projects that are managed as a component of overall firm value. After outlining the case for ABM, we derive analytical formulas for European calls and puts on dividend-paying assets as well as a numerical algorithm for American-style and other more complex options based on ABM. We also provide examples of their use.     

On asymptotic elastodynamic homogenization approaches for periodic media

A fairly large family of asymptotic elastodynamic homogenization methods is shown to be derivable from Willis exact elastodynamic homogenization theory for periodic media under appropriate approximation assumptions about, for example, frequencies, wavelengths and phase contrast. In light of this result, two long-wavelength and low-frequency asymptotic elastodynamic approaches are carefully analyzed and compared in connection with higher-order strain-gradient media. In particular, these approaches are proved to be unable to capture, at least in the one-dimensional setting, the optical branches of the dispersion curve. As an example, a two-phase string is thoroughly studied so as to illustrate the main results of the present work.     

Application of the multireference equation of motion coupled cluster method,including spin–orbit coupling,to the atomic spectra of Cr,Mn, Fe and Co

The recently introduced multireference equation of motion (MR-EOM) approach is combined with a simple treatment of spin–orbit coupling, as implemented in the ORCA program. The resulting multireference equation of motion spin–orbit coupling (MR-EOM-SOC) approach is applied to the first-row transition metal atoms Cr, Mn, Fe and Co, for which experimental data are readily available. Using the MR-EOM-SOC approach, the splittings in each L-S multiplet can be accurately assessed (root mean square (RMS) errors of about 70 cm^?1). The RMS errors for J-specific excitation energies range from 414 to 783 cm^?1 and are comparable to previously reported J-averaged MR-EOM results using the ACESII program. The MR-EOM approach is highly efficient. A typical MR-EOM calculation of a full spin–orbit spectrum takes about 2 CPU hours on a single processor of a 12-core node, consisting of Intel XEON 2.93 GHz CPUs with 12.3 MB of shared cache memory.     

Stochastic delay fractional evolution equations driven by fractional Brownian motion

In this paper, we consider a class of stochastic delay fractional evolution equations driven by fractional Brownian motion in a Hilbert space. Sufficient conditions for the existence and uniqueness of mild solutions are obtained. An application to the stochastic fractional heat equation is presented to illustrate the theory. Copyright © 2014 John Wiley & Sons, Ltd.     

Rapid determination of RMSDs corresponding to macromolecular rigid body motions

Finding the root mean sum of squared deviations (RMSDs) between two coordinate vectors that correspond to the rigid body motion of a macromolecule is an important problem in structural bioinformatics, computational chemistry, and molecular modeling. Standard algorithms compute the RMSD with time proportional to the number of atoms in the molecule. Here, we present RigidRMSD, a new algorithm that determines a set of RMSDs corresponding to a set of rigid body motions of a macromolecule in constant time with respect to the number of atoms in the molecule. Our algorithm is particularly useful for rigid body modeling applications, such as rigid body docking, and also for high‐throughput analysis of rigid body modeling and simulation results. We also introduce a constant‐time rotation RMSD as a similarity measure for rigid molecules. A C++ implementation of our algorithm is available at http://nano‐d.inrialpes.fr/software/RigidRMSD . © 2014 Wiley Periodicals, Inc.