Computing probable maximum loss in catastrophe reinsurance portfolios on multi-core and many-core architectures

In the reinsurance market, the risks natural catastrophes pose to portfolios of properties must be quantified, so that they can be priced, and insurance offered. The analysis of such risks at a portfolio level requires a simulation of up to 800 000 trials with an average of 1000 catastrophic events per trial. This is sufficient to capture risk for a global multi-peril reinsurance portfolio covering a range of perils including earthquake, hurricane, tornado, hail, severe thunderstorm, wind storm, storm surge and riverine flooding, and wildfire. Such simulations are both computation and data intensive, making the application of high-performance computing techniques desirable.

In this paper, we explore the design and implementation of portfolio risk analysis on both multi-core and many-core computing platforms. Given a portfolio of property catastrophe insurance treaties, key risk measures, such as probable maximum loss, are computed by taking both primary and secondary uncertainties into account. Primary uncertainty is associated with whether or not an event occurs in a simulated year, while secondary uncertainty captures the uncertainty in the level of loss due to the use of simplified physical models and limitations in the available data. A combination of fast lookup structures, multi-threading and careful hand tuning of numerical operations is required to achieve good performance. Experimental results are reported for multi-core processors and systems using NVIDIA graphics processing unit and Intel Phi many-core accelerators.

Computing Zeros of Analytic Functions in the Complex Plane without using Derivatives

A new approach to evaluating all multiple complex roots of analytical function f(z) confined to the specified rectangular domain of complex plane has been developed and implemented in Fortran code. Generally f (z), despite being holomorphic function, does not have a closed analytical form thereby inhibiting explicit evaluation of its derivatives. The latter constraint poses a major challenge to implementation of the robust numerical algorithm. This work is at the instrumental level and provides an enabling tool for solving a broad class of eigenvalue problems and polynomial approximations.

Natural three-qubit interactions in one-way quantum computing

We address the effects of natural three-qubit interactions on the computational power of one-way quantum computation. A benefit of using more sophisticated entanglement structures is the ability to construct compact and economic simulations of quantum algorithms with limited resources. We show that the features of our study are embodied by suitably prepared optical lattices, where effective three-spin interactions have been theoretically demonstrated. We use this to provide a compact construction for the Toffoli gate. Information flow and two-qubit interactions are also outlined, together with a brief analysis of relevant sources of imperfection.

Local and semilocal density functional computations for crystals of 1-alkyl-3-methyl-imidazolium salts

The accuracy and reliability of popular density functional approximations for the compounds giving origin to room temperature ionic liquids have been assessed by computing the T=0 K crystal structure of several 1-alkyl-3-methyl-imidazolium salts. Two prototypical exchange-correlation approximations have been considered, i.e., the local density approximation (LDA) and one gradient corrected scheme [PBE-GGA, Phys. Rev. Lett. 77, 3865 (1996)]. Comparison with low-temperature x-ray diffraction data shows that the equilibrium volume predicted by either approximations is affected by large errors, nearly equal in magnitude (~10%), and of opposite sign. In both cases the error can be traced to a poor description of the intermolecular interactions, while the intramolecular structure is fairly well reproduced by LDA and PBE-GGA. The PBE-GGA optimization of atomic positions within the experimental unit cell provides results in good agreement with the x-ray structure. The correct system volume can also be restored by supplementing PBE-GGA with empirical dispersion terms reproducing the r-6 attractive tail of the van der Waals interactions.