Explicit Solutions of Quadratic FBSDEs Arising From Quadratic Term Structure Models

We provide explicit solutions of certain forward-backward stochastic differential equations (FBSDEs) with quadratic growth. These particular FBSDEs are associated with quadratic term structure models of interest rates and characterize the zero-coupon bond price. The results of this paper are naturally related to similar results on affine term structure models of Hyndman (Math. Financ. Econ. 2(2):107–128, 2009) due to the relationship between quadratic functionals of Gaussian processes and linear functionals of affine processes. Similar to the affine case a sufficient condition for the explicit solutions to hold is the solvability in a fixed interval of Riccati-type ordinary differential equations. However, in contrast to the affine case, these Riccati equations are easily associated with those occurring in linear-quadratic control problems. We also consider quadratic models for a risky asset price and characterize the futures price and forward price of the asset in terms of similar FBSDEs. An example is considered, using an approach based on stochastic flows that is related to the FBSDE approach, to further emphasize the parallels between the affine and quadratic models. An appendix discusses solvability and explicit solutions of the Riccati equations.     

Calibration transfer between electronic nose systems for rapid In situ measurement of pulp and paper industry emissions

Electronic nose systems when deployed in network mesh can effectively provide a low budget and onsite solution for the industrial obnoxious gaseous measurement. For accurate and identical prediction capability by all the electronic nose systems, a reliable calibration transfer model needs to be implemented in order to overcome the inherent sensor array variability. In this work, robust regression (RR) is used for calibration transfer between two electronic nose systems using a Box–Behnken (BB) design. Out of the two electronic nose systems, one was trained using industrial gas samples by four artificial neural network models, for the measurement of obnoxious odours emitted from pulp and paper industries. The emissions constitute mainly of hydrogen sulphide (H₂S), methyl mercaptan (MM), dimethyl sulphide (DMS) and dimethyl disulphide (DMDS) in different proportions. A Box–Behnken design consisting of 27 experiment sets based on synthetic gas combinations of H₂S, MM, DMS and DMDS, were conducted for calibration transfer between two identical electronic nose systems. Identical sensors on both the systems were mapped and the prediction models developed using ANN were then transferred to the second system using BB–RR methodology. The results showed successful transmission of prediction models developed for one system to other system, with the mean absolute error between the actual and predicted concentration of analytes in mg L⁻¹ after calibration transfer (on second system) being 0.076, 0.1801, 0.0329, 0.427 for DMS, DMDS, MM, H₂S respectively.     

RNA Cleavage Catalyzed by Amphoteric Bis(acyl)guanidinium Derivatives

Described herein are two series (twelve compounds each) of very closely related guanidinium‐based receptors and their ability to catalyze hydrolytic cleavage of a unique RNA substrate – oligo‐dT flanked t rans‐ A ctivation R esponsive region of the HIV‐1 mRNA, TAR RNA. The significant difference in activities of otherwise very similar compounds is discussed, and direct and indirect evidences supporting our interpretation are presented. The results indicate that improvements in catalytic efficiency could be achieved with little modification of the structure of a relatively weak catalyst, and that a crucial feature could be a finely calibrated interplay between anion‐binding and proton‐donating abilities.     

Performance evaluation of CAESAR–QSAR output using PAHs as a case study

The set of 16 polycyclic aromatic hydrocarbon compounds was examined with the Internet available quantitative structure–activity relationship (QSAR) CAESAR models. For mutagenicity, carcinogenicity, developmental toxicity, and skin sensitization, the report includes the predicted classifications, the analysis of applicability domains, and the similarity sets, which consist of the similar compounds from the training sets. These results were further analyzed with chemometrical methods, that is, hierarchical clustering, principal component analysis, and self‐organizing maps, which were used for clustering and to define the cluster indicators. Such analysis assists the users in planning the application of QSAR models for hazard communication in regulatory compliance and in research of new active compounds. Copyright © 2013 John Wiley & Sons, Ltd.     

Use of a tree‐structured hierarchical model for estimation of location and uncertainty in multivariate spatial data

Analysis and modeling of spatial data are of considerable interest in many applications. However, the prediction of geographical features from a set of chemical measurements on a set of geographically distinct samples has never been explored. We report a new, tree‐structured hierarchical model for the estimation of geographical location of spatially distributed samples from their chemical measurements. The tree‐structured hierarchical modeling used in this study involves a set of geographic regions stored in a hierarchical tree structure, with each nonterminal node representing a classifier and each terminal node representing a regression model. Once the tree‐structured model is constructed, given a sample with only chemical measurements available, the predicted regional location of the sample is gradually restricted as it is passed through a series of classification steps. The geographic location of the sample can be predicted using a regression model within the terminal subregion. We show that the tree‐structured modeling approach provides reasonable estimates of geographical region and geographic location for surface water samples taken across the entire USA. Further, the location uncertainty, an estimate of a probability that a test sample could be located within a pre‐estimated, joint prediction interval that is much smaller than the terminal subregion, can also be assessed. Copyright © 2014 John Wiley & Sons, Ltd.     

Particle methods for PDEs arising in financial modeling

We numerically study convection–diffusion equations arising in financial modeling. We focus on the convection-dominated cases, in which the diffusion coefficients are relatively small. Both finite-difference and Monte-Carlo methods which are widely used in the problems of this kind might be inefficient due to severe restrictions on the meshsize and the number of realizations needed to achieve high resolution.We propose an alternative approach based on particle methods which have extremely low numerical diffusion and thus do not have the aforementioned restrictions. Our approach is based on the operator splitting: The hyperbolic steps are made using the method of characteristics, while the parabolic steps are performed using either a special discretization of the integral representation of the solution (which leads to a deterministic particle method) or a stochastic random walk approach.We apply the designed particle methods to a variety of test problems and the numerical results indicate high accuracy, efficiency and robustness of both the deterministic and stochastic methods. In addition, our numerical experiments clearly demonstrate that the deterministic particle method outperforms its stochastic counterpart.     

A step-by-step guide to building two-population stochastic mortality models

Two-population stochastic mortality models play a crucial role in the securitization of longevity risk. In particular, they allow us to quantify the population basis risk when longevity hedges are built from broad-based mortality indexes. In this paper, we propose and illustrate a systematic process for constructing a two-population mortality model for a pair of populations. The process encompasses four steps, namely (1) determining the conditions for biological reasonableness, (2) identifying an appropriate base model specification, (3) choosing a suitable time-series process and correlation structure for projecting period and/or cohort effects into the future, and (4) model evaluation.For each of the seven single-population models from Cairns et al. (2009), we propose two-population generalizations. We derive criteria required to avoid long-term divergence problems and the likelihood functions for estimating the models. We also explain how the parameter estimates are found, and how the models are systematically simplified to optimize the fit based on the Bayes Information Criterion. Throughout the paper, the results and methodology are illustrated using real data from two pairs of populations.     

Derivatives of molecular surface area and volume: simple and exact analytical formulas

The computational effort of biomolecular simulations can be significantly reduced by means of implicit solvent models in which the energy generally contains a correction depending on the surface area and/or the volume of the molecule. In this article, we present simple derivation of exact, easy-to-use analytical formulas for these quantities and their derivatives with respect to atomic coordinates. In addition, we provide an efficient, linear-scaling algorithm for the construction of the power diagram required for practical implementation of these formulas. Our approach is implemented in a C++ header-only template library.     

A near-infrared spectroscopy method to determine aminoglycosides in pharmaceutical formulations

The analytical determination of aminoglycosides in pharmaceutical formulations is very difficult due to the lack of chromophores or fluorophores. Several analytical methods have been developed along the years mainly based on derivatization reactions. The European Pharmacopeia (EP) and the United States Pharmacopeia (USP) describe a microbiological assay to the quantification of aminoglycosides. Near infrared spectroscopy (NIRS) can be used alternatively to analyse aminoglycosides without the need of derivatization reactions or other type of sample processing. A new NIRS based method was developed for the analysis of the aminoglycoside antibiotic neomycin. The method was developed with samples based on a commercial formulation containing neomycin sulphate and three excipients: lactose, talc and magnesium stearate. Synthetic and doped samples were manufactured for this purpose. Three lots of a commercial solid formulation were also used to assess the validity of the method to quantify neomycin sulphate in the industrial pharmaceutical product. The method proposes measurements in reflectance mode using a Fourier-transform near infrared (FT-NIR) spectrometer. Partial least squares regression was the multivariate method adopted to calibrate the NIR spectra with the neomycin sulphate mass fraction. The concentration of neomycin sulphate present in the commercial samples was confirmed by HPLC with pre-column derivatization with phenylisocyanate. Results show that neomycin sulphate was determined successfully in the commercial samples using the method calibrated with the doped samples (mass fraction error of 6.6%). Moreover, the synthetic samples were found to be unqualified to develop the method, producing a biased calibration.     

基于改进BP神经网络的煤催化气化预测模型研究

采用改进的三层BP神经网络建立了煤催化气化反应失重率、气化初始温度和最大气化速率所对应温度的预测模型。结果表明,采用改进BP神经网络模型在此研究中可达到较高的精度,其最大预测误差分别为5.18% 、5.65% 、2.33%,明显小于归回公式的预测误差。