Automated estimation of rare event probabilities in biochemical systems

In biochemical systems, the occurrence of a rare event can be accompanied by catastrophic consequences. Precise characterization of these events using Monte Carlo simulation methods is often intractable, as the number of realizations needed to witness even a single rare event can be very large. The weighted stochastic simulation algorithm (wSSA) [J. Chem. Phys. 129, 165101 (2008)] and its subsequent extension [J. Chem. Phys. 130, 174103 (2009)] alleviate this difficulty with importance sampling, which effectively biases the system toward the desired rare event. However, extensive computation coupled with substantial insight into a given system is required, as there is currently no automatic approach for choosing wSSA parameters. We present a novel modification of the wSSA--the doubly weighted SSA (dwSSA)--that makes possible a fully automated parameter selection method. Our approach uses the information-theoretic concept of cross entropy to identify parameter values yielding minimum variance rare event probability estimates. We apply the method to four examples: a pure birth process, a birth-death process, an enzymatic futile cycle, and a yeast polarization model. Our results demonstrate that the proposed method (1) enables probability estimation for a class of rare events that cannot be interrogated with the wSSA, and (2) for all examples tested, reduces the number of runs needed to achieve comparable accuracy by multiple orders of magnitude. For a particular rare event in the yeast polarization model, our method transforms a projected simulation time of 600 years to three hours. Furthermore, by incorporating information-theoretic principles, our approach provides a framework for the development of more sophisticated influencing schemes that should further improve estimation accuracy.     

Heizung

Ohne Zusammenfassung     

On Hadamard differentiability in k-sample semiparametric models—with applications to the assessment of structural relationships

Semiparametric models to describe the functional relationship between k groups of observations are broadly applied in statistical analysis, ranging from nonparametric ANOVA to proportional hazard (ph) rate models in survival analysis. In this paper we deal with the empirical assessment of the validity of such a model, which will be denoted as a “structural relationship model”. To this end Hadamard differentiability of a suitable goodness-of-fit measure in the k-sample case is proved. This yields asymptotic limit laws which are applied to construct tests for various semiparametric models, including the Cox ph model. Two types of asymptotics are obtained, first when the hypothesis of the semiparametric model under investigation holds true, and second for the case when a fixed alternative is present. The latter result can be used to validate the presence of a semiparametric model instead of simply checking the null hypothesis “the model holds true”. Finally, various bootstrap approximations are numerically investigated and a data example is analyzed.     

Surface microstructure/miniature mass spectrometer:.processing and applications

3 . Its fabrication is based on techniques used in microsystem processing and in particular anisotropic etching, thin film deposition, electroplating, and anodic bonding. The mass spectrometer consists of a plasma electron source for measurand ionisation as well as an ion optic and a mass separator specifically designed for the system’s small dimensions. Received: 27 February 1998/Accepted: 11 March 1998     

Fast identification by FAB-mass spectrometry of building blocks for oligonucleotide synthesis

Negative ion FAB-MS is recommended for the rapid routine identification of monomeric as well as oligomeric building blocks used in the phosphotriester synthesis of DNA fragments.     

Begründung einer Integralgleichung für die Bewegung eines strahlenden Elektrons II: Nicht-lineare Näherung

Foundation of a Functional Equation of Motion for the Radiating Electron II: Non Linear Approximation The radiation reaction of an extended, classical particle is analysed in 3^rd order approximation. From this we obtain a relativistic equation of motion, in structure similar to the one given in part I. But there are differences in the relation between the charge distribution and the kernel of the integro-differential equation.     

Notizen zur Cerimetrie. I

Ohne Zusammenfassung