Estimation of rating classes and default probabilities in credit risk models with dependencies

Let Y = m(X) + ε be a regression model with a dichotomous output Y and a one‐step regression function m . In the literature, estimators for the three parameters of m , that is, the breakpoint θ and the levels a and b , are proposed for independent and identically distributed (i.i.d.) observations. We show that these standard estimators also work in a non‐i.i.d. framework, that is, that they are strongly consistent under mild conditions. For that purpose, we use a linear one‐factor model for the input X and a Bernoulli mixture model for the output Y . The estimators for the split point and the risk levels are applied to a problem arising in credit rating systems. In particular, we divide the range of individuals' creditworthiness into two groups. The first group has a higher probability of default and the second group has a lower one. We also stress connections between the standard estimator for the cutoff θ and concepts prevalent in credit risk modeling, for example, receiver operating characteristic. Copyright © 2014 John Wiley & Sons, Ltd.     

Universal point sets for planar three-trees

For every $n\in \mathbb{N}$, we present a set $S_n$ of $O(n^{3/2}\log n)$ points in the plane such that every planar 3-tree with n vertices has a straight-line embedding in the plane in which the vertices are mapped to a subset of $S_n$. This is the first subquadratic upper bound on the cardinality of universal point sets for planar 3-trees, as well as for the class of 2-trees and serial parallel graphs.     

Adaptive lambda square dynamics simulation: An efficient conformational sampling method for biomolecules

A novel, efficient sampling method for biomolecules is proposed. The partial multicanonical molecular dynamics (McMD) was recently developed as a method that improved generalized ensemble (GE) methods to focus sampling only on a part of a system (GEPS); however, it was not tested well. We found that partial McMD did not work well for polylysine decapeptide and gave significantly worse sampling efficiency than a conventional GE. Herein, we elucidate the fundamental reason for this and propose a novel GEPS, adaptive lambda square dynamics (ALSD), which can resolve the problem faced when using partial McMD. We demonstrate that ALSD greatly increases the sampling efficiency over a conventional GE. We believe that ALSD is an effective method and is applicable to the conformational sampling of larger and more complicated biomolecule systems. © 2013 Wiley Periodicals, Inc.     

Ultraviolet light absorber with low surface energy: synthesis and characterization

Novel fluorine-containing ultraviolet absorbers (FBPs) with low surface energy were successfully synthesized based on 2,4-dihydroxy benzophenone (BP-1), and their structures were characterized by ¹H NMR, ¹³C NMR, FTIR, and HRMS. UV absorption of FBPs was studied in 10⁻⁴ M dichloromethane (CH₂Cl₂), which demonstrated the superior UV absorption capability of FBPs (ca. ?=1.7×10⁴ to 2.2×10⁴ at λ_max) over the matrix (?=1.7×10⁴ at λ_max). Quantum chemistry calculation was performed to investigate the stable structure and UV electronic absorption bands of FBPs. The surface chemistry information of high-chlorinated polyethylene (HCPE) coating films embedded with ultraviolet absorbers (UVAs) was given by X-ray photoelectron spectroscopy (XPS) and contact angle measurement. The results show that the surface enrichment capability of FBPs is remarkably better than traditional UVAs (including BP-1, BP-3, BP-12) because of the low surface energy properties of FBPs.     

A general,recursive, and open‐ended response code

We present a new implementation of a recent open‐ended response theory formulation for time‐ and perturbation‐dependent basis sets (Thorvaldsen et al., J. Chem. Phys. 2008, 129, 214108) at the Hartree–Fock and density functional levels of theory. A novel feature of the new implementation is the use of recursive programming techniques, making it possible to write highly compact code for the analytic calculation of any response property at any valid choice of rule for the order of perturbation at which to include perturbed density matrices. The formalism is expressed in terms of the density matrix in the atomic orbital basis, allowing the recursive scheme presented here to be used in linear‐scaling formulations of response theory as well as with two‐ and four‐component relativistic wave functions. To demonstrate the new code, we present calculations of the third geometrical derivatives of the frequency‐dependent second hyperpolarizability for HSOH at the Hartree–Fock level of theory, a seventh‐order energy derivative involving basis sets that are both time and perturbation dependent. © 2014 Wiley Periodicals, Inc.     

On the induced‐fit mechanism of substrate‐enzyme binding structures of nylon‐oligomer hydrolase

We present a detailed computational investigation of the induced‐fit motion in a nylon‐oligomer hydrolase (NylB) upon substrate binding. To this aim, we resort on the recently introduced parallel cascade selection molecular dynamics approach, allowing for an accelerated access to the set of conformational changes from an open‐ to a closed‐state structure to form the enzyme‐substrate complex in a specific induce‐fit mechanism. The structural investigation is quantitatively complemented by free energy analyses within the umbrella sampling algorithm accompanied by weighted histogram analysis. We find that the stabilization free energy is about 1.4 kcal/mol, whereas the highest free energy barrier to be overcome is about 2.3 kcal/mol. Conversely, the energetic contribution for the substrate binding is about 20 kcal/mol, as estimated from Generalized Born/Surface Area. This means that the open‐close induced‐fit motion could occur frequently once the substrate binds to the open state of NylB. © 2014 Wiley Periodicals, Inc.     

The READY program: Building a global potential energy surface and reactive dynamic simulations for the hydrogen combustion

READY (REActive DYnamics) is a program for studying reactive dynamic systems using a global potential energy surface (PES) built from previously existing PESs corresponding to each of the most important elementary reactions present in the system. We present an application to the combustion dynamics of a mixture of hydrogen and oxygen using accurate PESs for all the systems involving up to four oxygen and hydrogen atoms. Results at the temperature of 4000 K and pressure of 2 atm are presented and compared with model based on rate constants. Drawbacks and advantages of this approach are discussed and future directions of research are pointed out. © 2014 Wiley Periodicals, Inc.     

Molecular dynamics simulation of configurational ensembles compatible with experimental FRET efficiency data through a restraint on instantaneous FRET efficiencies

Förster resonance energy transfer (FRET) measurements are widely used to investigate (bio)molecular interactions or/and association. FRET efficiencies, the primary data obtained from this method, give, in combination with the common assumption of isotropic chromophore orientation, detailed insight into the lengthscale of molecular phenomena. This study illustrates the application of a FRET efficiency restraint during classical atomistic molecular dynamics simulations of a mutant mastoparan X peptide in either water or 7 M aqueous urea. The restraint forces acting on the donor and acceptor chromophores ensure that the sampled peptide configurational ensemble satisfies the experimental primary data by modifying interchromophore separation and chromophore transition dipole moment orientations. By means of a conformational cluster analysis, it is seen that indeed different configurational ensembles may be sampled without and with application of the restraint. In particular, while the FRET efficiency and interchromophore distances monitored in an unrestrained simulation may differ from the experimentally‐determined values, they can be brought in agreement with experimental data through usage of the FRET efficiency restraining potential. Furthermore, the present results suggest that the assumption of isotropic chromophore orientation is not always justified. The FRET efficiency restraint allows the generation of configurational ensembles that may not be accessible with unrestrained simulations, and thereby supports a meaningful interpretation of experimental FRET results in terms of the underlying molecular degrees of freedom. Thus, it offers an additional tool to connect the realms of computer and wet‐lab experimentation. © 2014 Wiley Periodicals, Inc.     

TiS2 and ZrS2 single‐ and double‐wall nanotubes: First‐principles study

Hybrid density functional theory has been applied for investigations of the electronic and atomic structure of bulk phases, nanolayers, and nanotubes based on titanium and zirconium disulfides. Calculations have been performed on the basis of the localized atomic functions by means of the CRYSTAL‐2009 computer code. The full optimization of all atomic positions in the regarded systems has been made to study the atomic relaxation and to determine the most favorable structures. The different layered and isotropic bulk phases have been considered as the possible precursors of the nanotubes. Calculations on single‐walled TiS₂ and ZrS₂ nanotubes confirmed that the nanotubes obtained by rolling up the hexagonal crystalline layers with octahedral 1T morphology are the most stable. The strain energy of TiS₂ and ZrS₂ nanotubes is small, does not depend on the tube chirality, and approximately obeys to D^–2 law (D is nanotube diameter) of the classical elasticity theory. It is greater than the strain energy of the similar TiO₂ and ZrO₂ nanotubes; however, the formation energy of the disulfide nanotubes is considerably less than the formation energy of the dioxide nanotubes. The distance and interaction energy between the single‐wall components of the double‐wall nanotubes is proved to be close to the distance and interaction energy between layers in the layered crystals. Analysis of the relaxed nanotube shape using radial coordinate of the metal atoms demonstrates a small but noticeable deviation from completely cylindrical cross‐section of the external walls in the armchair‐like double‐wall nanotubes. © 2013 Wiley Periodicals, Inc.