Mutagenic evidence for the optimal control of evolutionary dynamics

Elucidating the fitness measures optimized during the evolution of complex biological systems is a major challenge in evolutionary theory. We present experimental evidence and an analytical framework demonstrating how biochemical networks exploit optimal control strategies in their evolutionary dynamics. Optimal control theory explains a striking pattern of extremization in the redox potentials of electron transport proteins, assuming only that their fitness measure is a control objective functional with bounded controls.     

Optimal identification of Hamiltonian information by closed-loop laser control of quantum systems

A closed loop learning control concept is introduced for teaching lasers to manipulate quantum systems for the purpose of optimally identifying Hamiltonian information. The closed loop optimal identification algorithm operates by revealing the distribution of Hamiltonians consistent with the data. The control laser is guided to perform additional experiments, based on minimizing the dispersion of the distribution. Operation of such an apparatus is simulated for two model finite dimensional quantum systems.     

Pressure broadening in the 0–4 through 0–7 overtone bands of H35Cl and H37Cl

We have measured the pressure broadening coefficients of a number of rotation-vibration lines in the 0–4 through 0–7 overtone bands of HCl utilizing a Fourier transform spectrometer and a 409 m path length White cell. These data, when included with previous measurements on the fundamental and lower overtone bands, show a systematic variation of pressure broadening with increasing overtone band. This result reflects a change in the collision dynamics between molecules in the upper state of the transition with ground state molecules.     

Efficient chemical kinetic modeling through neural network maps

An approach to modeling nonlinear chemical kinetics using neural networks is introduced. It is found that neural networks based on a simple multivariate polynomial architecture are useful in approximating a wide variety of chemical kinetic systems. The accuracy and efficiency of these ridge polynomial networks (RPNs) are demonstrated by modeling the kinetics of H(2) bromination, formaldehyde oxidation, and H(2)+O(2) combustion. RPN kinetic modeling has a broad range of applications, including kinetic parameter inversion, simulation of reactor dynamics, and atmospheric modeling.     

Optimal dynamic discrimination of similar quantum systems with time series data

Optimal dynamic discrimination (ODD) was proposed [Li et al., J. Phys. Chem. B 106, 8125 (2002)] as a paradigm for discriminating noninteracting similar quantum systems in a mixture. This paper extends the ODD concept to optimize a laser control pulse for guiding similar quantum systems such that each exhibits a distinct time series signal for maximum discrimination. The use of temporal data addresses various experimental difficulties, including noise in the laser pulse, signal detection errors, and finite time resolution in the signal. Simulations of ODD with time series data are presented to explore these effects. It is found that the use of an optimally chosen control pulse can significantly enhance the discrimination quality. The ODD technique is also adapted to the case where the sample contains an unknown background species.     

High Dimensional Model Representations Generated from Low Dimensional Data Samples. I. mp-Cut-HDMR

High dimensional model representation (HDMR) is a general set of quantitative model assessment and analysis tools for improving the efficiency of deducing high dimensional input–output system behavior. For a high dimensional system, an output f(x) is commonly a function of many input variables x=|x ₁,x ₂,...,x _n } with n10² or larger. HDMR describes f(x) by a finite hierarchical correlated function expansion in terms of the input variables. Various forms of HDMR can be constructed for different purposes. Cut- and RS-HDMR are two particular HDMR expansions. Since the correlated functions in an HDMR expansion are optimal choices tailored to f(x) over the entire domain of x, the high order terms (usually larger than second order, or beyond pair cooperativity) in the expansion are often negligible. When the approximations given by the first and the second order Cut-HDMR correlated functions are not adequate, this paper presents a monomial based preconditioned HDMR method to represent the higher order terms of a Cut-HDMR expansion by expressions similar to the lower order ones with monomial multipliers. The accuracy of the Cut-HDMR expansion can be significantly improved using preconditioning with a minimal number of additional input–output samples without directly invoking the determination of higher order terms. The mathematical foundations of monomial based preconditioned Cut-HDMR is presented along with an illustration of its applicability to an atmospheric chemical kinetics model.     

Convergence properties of a class of boundary element approximations to linear diffusion problems with localized nonlinear reactions

We consider a boundary element (BE) Algorithm for solving linear diffusion desorption problems with localized nonlinear reactions. The proposed BE algorithm provides an elegant representation of the effect of localized nonlinear reactions, which enables the effects of arbitrarily oriented defect structures to be incorporated into BE models without having to perform severe mesh deformations. We propose a one-step recursion procedure to advance the BE solution of linear diffusion localized nonlinear reaction problems and investigate its convergence properties. The separation of the linear and nonlinear effects by the boundary integral formulation enables us to consider the convergence properties of approximations to the linear terms and nonlinear terms of the boundary integral equation separately. For the linear terms we investigate how the degree of piecewise polynomial collocation in space and the size of the spatial mesh relative to the time step affects the accumulation of errors in the one-step recursion scheme. We develop a novel convergence analysis that combines asymptotic methods with Lax's Equivalence Theorem. We identify a dimensionless meshing parameter θ whose magnitudé governs the performance of the one-step BE schemes. In particular, we show that piecewise constant (PWC) and piecewise linear (PWL) BE schemes are conditionally convergent, have lower asymptotic bounds placed on the size of time steps, and which display excess numerical diffusion when small time steps are used. There is no asymptotic bound on how large the tie steps can be–this allows the solution to be advanced in fewer, larger time steps. The piecewise quadratic (PWQ) BE scheme is shown to be unconditionally convergent; there is no asymptotic restriction on the relative sizes of the time and spatial meshing and no numerical diffusion. We verify the theoretical convergence properties in numerical examples. This analysis provides useful information about the appropriate degree of spatial piecewise polynomial and the meshing strategy for a given problem. For the nonlinear terms we investigate the convergence of an explicit algorithm to advance the solution at an active site forward in time by means of Caratheodory iteration combined with piecewise linear interpolation. We consider a model problem comprising a singular nonlinear Volterra equation that represents the effect of the term in the BE formulation that is due to a single defect. We prove the convergence of the piecewise linear Caratheodory iteration algorithm to a solution of the model problem for as long as such a solution can be shown to exist. This analysis provides a theoretical justification for the use of piecewise linear Caratheodory iterates for advancing the effects of localized reactions.     

Parametric scaling of mathematical models

Parametric scaling, the process of extrapolation of a modelling result to new parametric conditions, is often required in model optimization, and can be important if the effects of parametric uncertainty on model predictions are to be quantified. Knowledge of the functional relationship between the model solution (y) and the system parameters (α) may also provide insight into the physical system underlying the model. This paper examines strategies for parametric scaling, assuming that only the nominal model solution y(α) and the associated parametric sensitivity coefficients (?y/?α, ?²y/?α², etc.) are known. The truncated Taylor series is shown to be a poor choice for parametric scaling, when y has known bounds. Alternate formulae are proposed which ‘build-in’ the constraints on y, thus expanding the parametric region in which the extrapolation may be valid. In the case where y has a temporal as well as a parametric dependence, the extrapolation may be further improved by removing from the Taylor series coefficients the ‘secular’ components, which refer to changes in the time scale of y(t), not to changes in y as a function of α.     

Molecular alignment by trains of short laser pulses

We show that a dramatic field-free molecular alignment can be achieved after exciting molecules with proper trains of strong ultrashort laser pulses. Optimal two- and three-pulse excitation schemes are defined, providing an efficient and robust molecular alignment. This opens new prospects for various applications requiring macroscopic ensembles of highly aligned molecules.