Comparison of certain value-at-risk estimation methods for the two-parameter Weibull loss distribution

The Weibull distribution is one of the most important distributions that is utilized as a probability model for loss amounts in connection with actuarial and financial risk management problems. This paper considers the Weibull distribution and its quantiles in the context of estimation of a risk measure called Value-at-Risk (VaR). VaR is simply the maximum loss in a specified period with a pre-assigned probability level. We attempt to present certain estimation methods for VaR as a quantile of a distribution and compare these methods with respect to their deficiency (Def) values. Along this line, the results of some Monte Carlo simulations, that we have conducted for detailed investigations on the efficiency of the estimators as compared to MLE, are provided.     

The maximum surplus in a finite‐time interval for a discrete‐time risk model with exchangeable,dependent claim occurrences

This paper investigates a discrete‐time risk model that involves exchangeable dependent loss generating claim occurrences and compound binomially distributed aggregate loss amounts. First, a general framework is presented to derive the distribution of a surplus sequence using the model. This framework is then applied to obtain the distribution of any function of a surplus sequence in a finite‐time interval. Specifically, the distribution of the maximum surplus is obtained under nonruin conditions. Based on this distribution, the computation of the minimum surplus distribution is given. Asset and risk management–oriented implications are discussed for the obtained distributions based on numerical evaluations. In addition, comparisons are made involving the corresponding results of the classical discrete‐time compound binomial risk model, for which claim occurrences are independent and identically distributed.     

Assessing the Impact of Bridging Analogies in Mechanics

The effects of bridging analogies teaching strategy and gender on Turkish high school students' misconceptions in mechanics were investigated. After a pilot study with 67 students in a nearby high school, the researchers administered the revised Mechanics Misconception Test to 119 high school students as a pretest. Students in the experimental group were instructed by using bridging analogies teaching strategy. At the end of a 3‐week treatment period, the same test was administered to all students as a posttest. The data were analyzed by using analysis of covariance (ANCOVA). The statistical results showed that bridging analogies teaching strategy was an effective means of reducing the number of misconceptions students held about normal forces, frictional forces, tension, gravity, inertia, and Newton's third law.     

Brownian motion never increases: A new proof to a result of Dvoretzky,Erdős and Kakutani

Dvoretzky, Erdős and Kakutani discovered that the Brownian motion is almost surely nowhere increasing. This is proved here in a relatively easy way.     

SemanticEye: a semantic web application to rationalize and enhance chemical electronic publishing

SemanticEye, an ontology with associated tools, improves the classification and open accessibility of chemical information in electronic publishing. In a manner analogous to digital music management, RDF metadata encoded as Adobe XMP can be extracted from a variety of document formats, such as PDF, and managed in an RDF repository called Sesame. Users upload electronic documents containing XMP to a central server by "dropping" them into WebDAV folders. The documents can then be navigated in a Web browser via their metadata, and multiple documents containing identical metadata can then be aggregated. SemanticEye does not actually store any documents. By including unique identifiers within the XMP, such as the DOI, associated documents can be retrieved from the Web with the help of resolving agents. The power of this metadata driven approach is illustrated by including, within the XMP, InChI identifiers for molecular structures and finding relationships between articles based on their InChIs. SemanticEye will become increasingly more comprehensive as usage becomes more widespread. Furthermore, following the Semantic Web architecture enables the reuse of open software tools, provides a "semantically intuitive" alternative to search engines, and fosters a greater sense of trust in Web-based scientific information.     

An integer programming approach for the search of discretization orders in distance geometry problems

Optimization Letters - Discretizable distance geometry problems (DDGPs) constitute a class of graph realization problems where the vertices can be ordered in such a way that the search space of...     

Neural network closures for nonlinear model order reduction

Many reduced-order models are neither robust with respect to parameter changes nor cost-effective enough for handling the nonlinear dependence of complex dynamical systems. In this study, we put forth a robust machine learning framework for projection-based reduced-order modeling of such nonlinear and nonstationary systems. As a demonstration, we focus on a nonlinear advection-diffusion system given by the viscous Burgers equation, which is a prototypical setting of more realistic fluid dynamics applications due to its quadratic nonlinearity. In our proposed methodology the effects of truncated modes are modeled using a single layer feed-forward neural network architecture. The neural network architecture is trained by utilizing both the Bayesian regularization and extreme learning machine approaches, where the latter one is found to be more computationally efficient. A significant emphasis is laid on the selection of basis functions through the use of both Fourier bases and proper orthogonal decomposition. It is shown that the proposed model yields significant improvements in accuracy over the standard Galerkin projection methodology with a negligibly small computational overhead and provide reliable predictions with respect to parameter changes.     

A search method for optimal control of a flow shop system of traditional machines

We consider a convex and nondifferentiable optimization problem for deterministic flow shop systems in which the arrival times of the jobs are known and jobs are processed in the order they arrive. The decision variables are the service times that are to be set only once before processing the first job, and cannot be altered between processes. The cost objective is the sum of regular costs on job completion times and service costs inversely proportional to the controllable service times. A finite set of subproblems, which can be solved by trust-region methods, are defined and their solutions are related to the optimal solution of the optimization problem under consideration. Exploiting these relationships, we introduce a two-phase search method which converges in a finite number of iterations. A numerical study is held to demonstrate the solution performance of the search method compared to a subgradient method proposed in earlier work.     

Vertices of given degree in series‐parallel graphs

We show that the numbers of vertices of a given degree k ≥ 1 in several kinds of series‐parallel labeled graphs of size n satisfy a central limit theorem with mean and variance proportional to n, and quadratic exponential tail estimates. We further prove a corresponding theorem for the number of nodes of degree two in labeled planar graphs. The proof method is based on generating functions and singularity analysis. In particular, we need systems of equations for multivariate generating functions and transfer results for singular representations of analytic functions. © 2009 Wiley Periodicals, Inc. Random Struct. Alg., 2010     

Generation of 287 W, 5.5 ps pulses at 78 MHz repetition rate from a cryogenically cooled Yb:YAG amplifier seeded by a fiber chirped-pulse amplification system

We generate linearly polarized, 287 W average-power, 5.5 ps pulses using a cryogenically cooled Yb:YAG amplifier at a repetition rate of 78 MHz. An optical-to-optical efficiency of 41% is obtained at 700 W pump power. A 6 W, 0.4 nm bandwidth picosecond seed source at 1029 nm wavelength is constructed using a chirped-pulse fiber amplification chain based on chirped volume Bragg gratings. The combination of a fiber amplifier system and a cryogenically cooled Yb:YAG amplifier results in good spatial beam quality at large average power. Low nonlinear phase accumulation as small as 5.1 x 10(-3) rad in the bulk Yb:YAG amplifier supports power scalability to a > 10 kW level without being affected by self-phase modulation. This amplification system is well suited for pumping high-power high-repetition-rate optical parametric chirped-pulse amplifiers.