Search

Stochastic modeling of biochemical processes at the cellular level has been the subject of intense research in recent years. The Chemical Master Equation is a broadly utilized stochastic discrete model of such processes. Numerous important biochemical systems consist of many species subject to many reactions. As a result, their mathematical models depend on many parameters. In applications, some of the model parameters may be unknown, so their values need to be estimated from the experimental data. However, the problem of parameter value inference can be quite challenging, especially in the stochastic setting. To estimate accurately the values of a subset of parameters, the system should be sensitive with respect to variations in each of these parameters and they should not be correlated. In this paper, we propose a technique for detecting collinearity among models' parameters and we apply this method for selecting subsets of parameters that can be estimated from the available data. The analysis relies on finite-difference sensitivity estimations and the singular value decomposition of the sensitivity matrix. We illustrated the advantages of the proposed method by successfully testing it on several models of biochemical systems of practical interest. [ABSTRACT FROM AUTHOR]

This work is devoted to increasing the computational efficiency of numerical methods for the one-way Helmholtz Equation (higher-order parabolic equation) in a heterogeneous underwater environment. The finite-difference rational Padé approximation of the propagation operator is considered, whose artificial computational parameters are the grid cell sizes and reference sound speed. The relationship between the parameters of the propagation medium and the artificial computational parameters is established. An optimized method for automatic determination of the artificial computational parameters is proposed. The optimization method makes it possible to account for any propagation angle and arbitrary variations in refractive index. The numerical simulation results confirm the adequacy and efficiency of the proposed approach. Automating the selection process of the computational parameters makes it possible to eliminate human errors and avoid excessive consumption of computational resources. [ABSTRACT FROM AUTHOR]

Plasma diagnostics is a topic of great interest in the physics and engineering community because the monitoring of plasma parameters plays a fundamental role in the development and optimization of plasma reactors. Towards this aim, microwave diagnostics, such as reflectometric, interferometric, and polarimetric techniques, can represent effective means. Besides the above, microwave imaging profilometry (MIP) may allow the obtaining of tomographic, i.e., volumetric, information of plasma that could overcome some intrinsic limitations of the standard non-invasive diagnostic approaches. However, pursuing MIP is not an easy task due to plasma's electromagnetic features, which strongly depend on the working frequency, angle of incidence, polarization, etc., as well as on the need for making diagnostics in both large (meter-sized) and small (centimeter-sized) reactors. Furthermore, these latter represent extremely harsh environments, wherein different systems and equipment need to coexist to guarantee their functionality. Specifically, MIP entails solution of an inverse scattering problem, which is non-linear and ill-posed, and, in addition, in the one-dimensional case, is also severely limited in terms of achievable reconstruction accuracy and resolution. In this contribution, we address microwave inverse profiling of plasma assuming a high-frequency probing regime when magnetically confined plasma can be approximated as both an isotropic and weak penetrable medium. To this aim, we adopt a finite-difference frequency-domain (FDFD) formulation which allows dealing with non-homogeneous backgrounds introduced by unavoidable presence of plasma reactors. [ABSTRACT FROM AUTHOR]

Polyharmonic spline (PHS) radial basis functions (RBFs) have been used in conjunction with polynomials to create RBF finite-difference (RBF-FD) methods. In 2D, these methods are usually implemented with Cartesian nodes, hexagonal nodes, or most commonly, quasi-uniformly distributed nodes generated through fast algorithms. We explore novel strategies for computing the placement of sampling points for RBF-FD methods in both 1D and 2D while investigating the benefits of using these points. The optimality of sampling points is determined by a novel piecewise-defined Lebesgue constant. Points are then sampled by modifying a simple, robust, column-pivoting QR algorithm previously implemented to find sets of near-optimal sampling points for polynomial approximation. Using the newly computed sampling points for these methods preserves accuracy while reducing computational costs by mitigating stencil size restrictions for RBF-FD methods. The novel algorithm can also be used to select boundary points to be used in conjunction with fast algorithms that provide quasi-uniformly distributed nodes. [ABSTRACT FROM AUTHOR]