Optimization Under Uncertainty Using the Generalized Inverse Distribution Function

A framework for robust optimization under uncertainty based on the use of the generalized inverse distribution function (GIDF), also called quantile function, is here proposed. Compared to more classical approaches that rely on the usage of statistical moments as deterministic attributes that define the objectives of the optimization process, the inverse cumulative distribution function allows for the use of all the possible information available in the probabilistic domain. Furthermore, the use of a quantile based approach leads naturally to a multi-objective methodology which allows an a-posteriori selection of the candidate design based on risk/opportunity criteria defined by the designer. Finally, the error on the estimation of the objectives due to the resolution of the GIDF will be proven to be quantifiableComment: 20 pages, 25 figure

Quasi-Monte Carlo, Discrepancies and Error Estimates

We discuss the problem of defining an estimate for the error in quasi-Monte Carlo integration. The key issue is the definition of an ensemble of quasi-random point sets that, on the one hand, includes a sufficiency of equivalent point sets, and on the other hand uses information on the degree of uniformity of the point set actually used, in the form of a discrepancy or diaphony. A few examples of such discrepancies are given. We derive the distribution of our error estimate in the limit of large number of points. In many cases, Gaussian central limits are obtained. We also present numerical results for the quadratic star-discrepancy for a number of quasi-random sequences

Multifractal properties of power-law time sequences; application to ricepiles

We study the properties of time sequences extracted from a self-organized critical system, within the framework of the mathematical multifractal analysis. To this end, we propose a fixed-mass algorithm, well suited to deal with highly inhomogeneous one dimensional multifractal measures. We find that the fixed mass (dual) spectrum of generalized dimensions depends on both the system size L and the length N of the sequence considered, being however stable when these two parameters are kept fixed. A finite-size scaling relation is proposed, allowing us to define a renormalized spectrum, independent of size effects.We interpret our results as an evidence of extremely long-range correlations induced in the sequence by the criticality of the systemComment: 12 pages, RevTex, includes 9 PS figures, Phys. Rev. E (in press

ON COMPUTER SIMULATION AS A COMPONENT IN INFORMATION SYSTEMS RESEARCH

Computer simulation is widely regarded as a useful activity during various phases of research. However, depending on its context, the meaning, definition, and focus of the term can vary: In traffic planning, for example, simulation is used to determine useful configurations of a road network, thus focusing on the environment. An entirely different perspective is used within multi-agent systems. In such settings, the environment of the agents remains static, while the interesting research questions concern the behavior of the agents themselves. The research focuses on the microscopic level and the resulting emergent behavior. This article puts such diverse meanings in the context of a research process that treats descriptive and prescriptive research as two sides of the same coin. We develop a framework to classify different types of simulation, based on the actual research activity they are intended to be used for. Two case studies supplement the framework

Library Design in Combinatorial Chemistry by Monte Carlo Methods

Strategies for searching the space of variables in combinatorial chemistry experiments are presented, and a random energy model of combinatorial chemistry experiments is introduced. The search strategies, derived by analogy with the computer modeling technique of Monte Carlo, effectively search the variable space even in combinatorial chemistry experiments of modest size. Efficient implementations of the library design and redesign strategies are feasible with current experimental capabilities.Comment: 5 pages, 3 figure

Hurst's Rescaled Range Statistical Analysis for Pseudorandom Number Generators used in Physical Simulations

The rescaled range statistical analysis (R/S) is proposed as a new method to detect correlations in pseudorandom number generators used in Monte Carlo simulations. In an extensive test it is demonstrated that the RS analysis provides a very sensitive method to reveal hidden long run and short run correlations. Several widely used and also some recently proposed pseudorandom number generators are subjected to this test. In many generators correlations are detected and quantified.Comment: 12 pages, 12 figures, 6 tables. Replaces previous version to correct citation [19

Radiation thermo-chemical models of protoplanetary disks II. Line diagnostics

Methods. We use the recently developed disk code ProDiMo to calculate the physico-chemical structure of protoplanetary disks and apply the Monte-Carlo line radiative transfer code RATRAN to predict observable line profiles and fluxes. We consider a series of Herbig Ae type disk models ranging from 10^-6 M_Sun to 2.2 10^-2 M_Sun (between 0.5 and 700 AU) to discuss the dependency of the line fluxes and ratios on disk mass for otherwise fixed disk parameters. Results. We find the [CII] 157.7 mum line to originate in LTE from the surface layers of the disk, where Tg > Td . The total emission is dominated by surface area and hence depends strongly on disk outer radius. The [OI] lines can be very bright (> 10^-16 W/m^2) and form in slightly deeper and closer regions under non-LTE conditions. The high-excitation [OI] 145.5 mum line, which has a larger critical density, decreases more rapidly with disk mass than the 63.2 mum line. Therefore, the [OI] 63.2 mum/145.5 mum ratio is a promising disk mass indicator, especially as it is independent of disk outer radius for Rout > 200 AU. CO is abundant only in deeper layers A_V >~ 0.05. For too low disk masses (M_disk <~10^-4 M_Sun) the dust starts to become transparent, and CO is almost completely photo-dissociated. For masses larger than that the lines are an excellent independent tracer of disk outer radius and can break the outer radius degeneracy in the [OI] 63.2 mum/[CII]157.7 mum line ratio. Conclusions. The far-IR fine-structure lines of [CII] and [OI] observable with Herschel provide a promising tool to measure the disk gas mass, although they are mainly generated in the atomic surface layers. In spatially unresolved observations, none of these lines carry much information about the inner, possibly hot regions < 30 AU.Comment: accepted for publication in A&

Static Hedging of Multivariate Derivatives by Simulation

We propose an approximate static hedging procedure for multivariate derivatives. The hedging portfolio is composed of statically held simple univariate options, optimally weighted minimizing the variance of the difference between the target claim and the approximate replicating portfolio. The method uses simulated paths to estimate the weights of the hedging portfolio and is related to Monte Carlo control variates techniques. We report numerical results showing the performance of this static hedging procedure on bivariate options on the maximum of two assets and on 2- and 7-dimensional portfolio options. It is shown that, in the presence of transaction costs, Value at Risk and Expected Shortfall of the dynamically hedged positions can be higher than the ones obtained by a static hedge