On Connection between Characterestic Functions and the Caratheodori Class Functions

2000 Mathematics Subject Classification: 47A65, 45S78.

A Bayesian latent class safety performance function for identifying motor vehicle crash blackspots

The current state of the practice in Blackspot Identification (BSI) utilizes safety performance functions based on total crash counts to identify transport system sites with potentially high crash risk. This paper postulates that total crash count variation over a transport network is a result of multiple distinct crash generating processes including geometric characteristics of the road, spatial features of the surrounding environment, and driver behaviour factors. However, these multiple sources are ignored in current modelling methodologies in both trying to explain or predict crash frequencies across sites. Instead, current practice employs models that imply that a single underlying crash generating process exists. The model mis-specification may lead to correlating crashes with the incorrect sources of contributing factors (e.g. concluding a crash is predominately caused by a geometric feature when it is a behavioural issue), which may ultimately lead to inefficient use of public funds and misidentification of true blackspots. This study aims to propose a latent class model consistent with a multiple crash process theory, and to investigate the influence this model has on correctly identifying crash blackspots. We first present the theoretical and corresponding methodological approach in which a Bayesian Latent Class (BLC) model is estimated assuming that crashes arise from two distinct risk generating processes including engineering and unobserved spatial factors. The Bayesian model is used to incorporate prior information about the contribution of each underlying process to the total crash count. The methodology is applied to the state-controlled roads in Queensland, Australia and the results are compared to an Empirical Bayesian Negative Binomial (EB-NB) model. A comparison of goodness of fit measures illustrates significantly improved performance of the proposed model compared to the NB model. The detection of blackspots was also improved when compared to the EB-NB model. In addition, modelling crashes as the result of two fundamentally separate underlying processes reveals more detailed information about unobserved crash causes.

An adaptive controller for a class of nonlinear system using direction basis function

For a class of nonlinear dynamical systems, the adaptive controllers are investigated using direction basis function (DBF) in this paper. Based on the criterion of Lyapunov' stability, DBF is designed which guarantees that the output of the controlled system asymptotically tracks the reference signals. Finally, the simulation shows the good tracking effectiveness of the adaptive controller.

Approximating a class of combinatorial problems with rational objective function

In the late seventies, Megiddo proposed a way to use an algorithm for the problem of minimizing a linear function a(0) + a(1)x(1) + ... + a(n)x(n) subject to certain constraints to solve the problem of minimizing a rational function of the form (a(0) + a(1)x(1) + ... + a(n)x(n))/(b(0) + b(1)x(1) + ... + b(n)x(n)) subject to the same set of constraints, assuming that the denominator is always positive. Using a rather strong assumption, Hashizume et al. extended Megiddo`s result to include approximation algorithms. Their assumption essentially asks for the existence of good approximation algorithms for optimization problems with possibly negative coefficients in the (linear) objective function, which is rather unusual for most combinatorial problems. In this paper, we present an alternative extension of Megiddo`s result for approximations that avoids this issue and applies to a large class of optimization problems. Specifically, we show that, if there is an alpha-approximation for the problem of minimizing a nonnegative linear function subject to constraints satisfying a certain increasing property then there is an alpha-approximation (1 1/alpha-approximation) for the problem of minimizing (maximizing) a nonnegative rational function subject to the same constraints. Our framework applies to covering problems and network design problems, among others.

The Operators Aγ = γA + -γA for a Class of Nondissipative Operators A with a Limit of the Corresponding Correlation Function

2000 Mathematics Subject Classification: Primary 47A48, Secondary 60G12

A Rare Loss-of-Function Variant in Scavenger Receptor Class B Type I (SCARB1) Raises HDL Cholesterol and Increases Risk of Coronary Disease

Scavenger receptor BI (SR-BI) is the major receptor for high-density lipoprotein (HDL)
cholesterol (HDL-C). In humans, high amounts of HDL-C in plasma are associated with a
lower risk of coronary heart disease (CHD). Mice that have depleted Scarb1 (SR-BI
knockout mice) have markedly elevated HDL-C levels but, paradoxically, increased
atherosclerosis. The impact of SR-BI on HDL metabolism and CHD risk in humans remains
unclear. Through targeted sequencing of coding regions of lipid-modifying genes in 328
individuals with extremely high plasma HDL-C levels, we identified a homozygote for a lossof-function
variant, in which leucine replaces proline 376 (P376L), in SCARB1, the gene
encoding SR-BI. The P376L variant impairs posttranslational processing of SR-BI and
abrogates selective HDL cholesterol uptake in transfected cells, in hepatocyte-like cells
derived from induced pluripotent stem cells from the homozygous subject, and in mice.
Large population-based studies revealed that subjects who are heterozygous carriers of
the P376L variant have significantly increased levels of plasma HDL-C. P376L carriers have
a profound HDL-related phenotype and an increased risk of CHD (odds ratio = 1.79, which is
statistically significant).

A Numerical Solution Using an Adaptively Preconditioned Lanczos Method for a Class of Linear Systems Related with the Fractional Poisson Equation

This study considers the solution of a class of linear systems related with the fractional Poisson equation (FPE) (−∇2)α/2φ=g(x,y) with nonhomogeneous boundary conditions on a bounded domain. A numerical approximation to FPE is derived using a matrix representation of the Laplacian to generate a linear system of equations with its matrix A raised to the fractional power α/2. The solution of the linear system then requires the action of the matrix function f(A)=A−α/2 on a vector b. For large, sparse, and symmetric positive definite matrices, the Lanczos approximation generates f(A)b≈β0Vmf(Tm)e1. This method works well when both the analytic grade of A with respect to b and the residual for the linear system are sufficiently small. Memory constraints often require restarting the Lanczos decomposition; however this is not straightforward in the context of matrix function approximation. In this paper, we use the idea of thick-restart and adaptive preconditioning for solving linear systems to improve convergence of the Lanczos approximation. We give an error bound for the new method and illustrate its role in solving FPE. Numerical results are provided to gauge the performance of the proposed method relative to exact analytic solutions.

An analytical method to solve a general class of nonlinear reactive transport models

Three recent papers published in Chemical Engineering Journal studied the solution of a model of diffusion and nonlinear reaction using three different methods. Two of these studies obtained series solutions using specialized mathematical methods, known as the Adomian decomposition method and the homotopy analysis method. Subsequently it was shown that the solution of the same particular model could be written in terms of a transcendental function called Gauss’ hypergeometric function. These three previous approaches focused on one particular reactive transport model. This particular model ignored advective transport and considered one specific reaction term only. Here we generalize these previous approaches and develop an exact analytical solution for a general class of steady state reactive transport models that incorporate (i) combined advective and diffusive transport, and (ii) any sufficiently differentiable reaction term R(C). The new solution is a convergent Maclaurin series. The Maclaurin series solution can be derived without any specialized mathematical methods nor does it necessarily involve the computation of any transcendental function. Applying the Maclaurin series solution to certain case studies shows that the previously published solutions are particular cases of the more general solution outlined here. We also demonstrate the accuracy of the Maclaurin series solution by comparing with numerical solutions for particular cases.

Loss-of-function fibroblast growth factor receptor-2 mutations in melanoma

We report that 10% of melanoma tumors and cell lines harbor mutations in the fibroblast growth factor receptor 2 (FGFR2) gene. These novel mutations include three truncating mutations and 20 missense mutations occurring at evolutionary conserved residues in FGFR2 as well as among all four FGFRs. The mutation spectrum is characteristic of those induced by UV radiation. Mapping of these mutations onto the known crystal structures of FGFR2 followed by in vitro and in vivo studies show that these mutations result in receptor loss of function through several distinct mechanisms, including loss of ligand binding affinity, impaired receptor dimerization, destabilization of the extracellular domains, and reduced kinase activity. To our knowledge, this is the first demonstration of loss-of-function mutations in a class IV receptor tyrosine kinase in cancer. Taken into account with our recent discovery of activating FGFR2 mutations in endometrial cancer, we suggest that FGFR2 may join the list of genes that play context-dependent opposing roles in cancer.

Structure and function of DsbA, a key bacterial oxidative folding catalyst

Since its discovery in 1991, the bacterial periplasmic oxidative folding catalyst DsbA has been the focus of intense research. Early studies addressed why it is so oxidizing and how it is maintained in its less stable oxidized state. The crystal structure of Escherichia coli DsbA (EcDsbA) revealed that the oxidizing periplasmic enzyme is a distant evolutionary cousin of the reducing cytoplasmic enzyme thioredoxin. Recent significant developments have deepened our understanding of DsbA function, mechanism, and interactions: the structure of the partner membrane protein EcDsbB, including its complex with EcDsbA, proved a landmark in the field. Studies of DsbA machineries from bacteria other than E. coli K-12 have highlighted dramatic differences from the model organism, including a striking divergence in redox parameters and surface features. Several DsbA structures have provided the first clues to its interaction with substrates, and finally, evidence for a central role of DsbA in bacterial virulence has been demonstrated in a range of organisms. Here, we review current knowledge on DsbA, a bacterial periplasmic protein that introduces disulfide bonds into diverse substrate proteins and which may one day be the target of a new class of anti-virulence drugs to treat bacterial infection. Antioxid. Redox Signal. 14, 1729–1760.