Influence function

Thompson K and Makri N 1999 Influence functionals with semiclassical propagators in combined fonA/ard-backward time J. Chem. Phys. 110 1343... 

The influence functional theory, as it was formulated by Feyman and Vernon, relies on the additional assumption concerning factorization of the total (system and bath) density matrix in the past. Without this assumption the theory requires a triple path integral, with one thermal integration over the imaginary time axis [Grabert et al. 1988]. 

A difference with single DM AO is that there is a propagation between the DMs. But since Fresnel diffraction is distributive, influence functions remain proportional to the command after propagation. 

Le Louam and Tallon, 2002 consider triangular influence functions after propagation ... 

Hampel FR, Roncetti EM, Rousseeuw PJ, Stahel WA (1986) Robust statistics the approach based on influence functions. Wiley, New York... 

Steroid hormone receptors are phosphoproteins that have a DNA-binding domain and a steroid-binding domain. All steroid receptors have a molecular weight of 55,000-120,000. The state of phosphorylation appears to influence functional activity. 

Occasionally it is convenient to refer to the p function in (11.21), but generally the form (11.22) is used in robust M-estimation. The use of the t(r form is due to Hampel s concept of the influence function (Hampel et al., 1986). According to the IF concept, the value of it represents the effect of the residuals on the parameter estimation. If iff is unbounded, it means that an outlier has an infinite effect on the estimation. Thus, the most important requirement for robustness is that iff must be bounded and should have a small value when the residual is large. In fact, the value of the iff function corresponds to the gross error sensitivity (Hampel etal., 1986), which measures the worst (approximate) influence that a small amount of contamination of fixed size can have on the value of the estimator. 

For least squares estimation, p is the errors squared function, and the influence function ft =u. For a very large residual, u — oo, and r also grows to infinity this means that a single outlier has a large influence on the estimation. That is, for least squares estimation, every observation is treated equally and has the same weight. 

An alternative approach to these methods is to obtain the influence function directly from the error distribution. In this case, for the maximum likelihood estimation of the parameters, the i/ function can be chosen as follows ... 

The exponential term which represents the effect of a point source is sometimes called the influence function or Green function of this diffusion problem. The method of sources and sinks easily produces solutions for an infinite medium or for systems of finite dimension when their boundary is kept at zero concentration. Different boundary conditions require a more elaborate formulation (Carslaw and Jaeger, 1959). 

One more structural dilferentiation that can influence functionalization is the tip vs. sidewall region. The tips are the two ending parts of the tube in these two regions, the curvature is increased and the shape more resembles that of a hemisphere, with reactivity expected to be similar to that of fullerenes. In contrast, sidewalls present reduced pyramidalization angles and therefore different behaviors towards functionalization. Reactions involving the use of harsh conditions can result in a fracture of the tubes, enabling production of shorter tubes with open tips, where the aromatic pattern is interrupted and carbon atoms are more reactive. 

The switch function of protein phosphorylation is based on different mechanisms that may work alone or in combination. Phosphorylation by protein kinases influences function and activity of the protein substrate, especially in the following ways ... 

Functional Evaluation - An evaluation of the basic physico-chemical properties that influence functionality. (By this definition the functional tests of enzymic properties are functional evaluations.)... 

Drying - The methods of drying influence functionality through the temperature used. Modifications of porosity... 

One can study the spin dynamics integrating out the environment and using the effective action for the spin. We derive the effective action using the Feynman-Vernon-Keldysh technique. For the interaction —Xsz with the z-component of the spin, the effective action (the influence functional) reads... 

So far, one can be much more successful in calculating a rate constant when one knows in advance that it exists, than in answering the question of whether it exists. A considerable breakthrough in this area was the solution of the spin-boson problem, which, however, has only limited relevance to any problem in chemistry because it neglects the effects of intrawell dynamics (vibrational relaxation) and does not describe thermally activated transitions. A number of attempts have been made to go beyond the two-level system approximation, but the basic question of how vibrational relaxation affects the transition from coherent oscillations to exponential decay awaits a quantitative solution. Such a solution might be obtained by numerical computation of real-time path integrals for the density matrix using the influence functional technique. 

Q. Shi and E. Geva. A derivation of the mixed quantum-classical Liouville equation from the influence functional formalism. J. Chem. Phys., 121(8) 3393-3404, 2004. 

Hampel, F.R., Ronchetti, E.M., Rousseeuw, P.J., Stahel, W.A. Robust Statistics The Approach Based on Influence Functions, Wiley, New York, 1986 Huber, P.J. Robust Statistics, Wiley, New York, 1981... 

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