Numerical probabilistic approach

Numerous studies have been devoted to classification (probabilistic) approaches used in conjunction with fragment descriptors for virtual screening. Here we present several examples. 

The deterministic approach of direct numerical simulation (DNS) and the probabilistic approach of probability density function (PDF) modeling are implemented for prediction of droplet dispersion and polydis-persity in liquid-fuel combustors. For DNS, a multidomain spectral element method was used for the carrier phase while tracking the droplets individually in a Lagrangian frame. The geometry considered here is a backward-facing step flow with and without a countercurrent shear. In PDF modeling, the extension of previous work to the case of evaporating droplets is discussed. 

A brief QRA process htis been depicted in Fig. V/5.4-l. Probabilistic QRAs are also used. In the probabilistic approach, first a deterministic model is developed, then numerical values are replaced by probability structure and distribution patterns to get the output. 

Eor composite materials, due to the complexity of their structure and variability of their properties in both deterministic and probabilistic approaches, experimental results and their quality are of particular importance. They are necessary not only for verification of all theoretical calculations but also they should supply numerical data for factors, coefficients and distributions, which are used in the formulae. 

The probabilistic approach is, in fact, a kind of numerical approach, where a probabilistic theory has been elaborated to eliminate the assumption of an infinite... 

William R. Rhyne received a B.S. in nuclear engineering from the University of Tennessee and M.S. and D.Sc. degrees in nuclear engineering from the University of Virginia. Dr. Rhyne is currently an independent consultant and earlier cofounded H R Technical Associates, Inc., where he remains a member of the board of directors. He has extensive experience in risk and safety analyses associated with nuclear and chemical processes and with the transport of hazardous nuclear materials and chemicals. From 1984 to 1987, he was the project manager and principal investigator for a probabilistic accident analysis of transporting obsolete chemical munitions. Dr. Rhyne has authored or coauthored numerous publications and reports in nuclear and chemical safety and risk analysis areas and is author of the book Hazardous Materials Transportation Risk Analysis Quantitative Approaches for Truck and Train. He is a former member of the NRC Transportation Research Board Hazardous Materials Committee, the Society for Risk Assessment, the American Nuclear... 

As described in detail in this book, the use of assessment factors is an established practice in chemical risk assessment to account for uncertainties inherent in the hazard (effects) assessment and consequently, inherent in the risk assessment. The use of assessment factors to address this uncertainty is part of the conventional approach that has developed over the years. According to the current risk assessment paradigm, the usual approach is simply to multiply these individual assessment factors in order to establish an overall composite numerical assessment factor (Section 5.10). An alternative to the traditional assessment factor approach is to combine estimates of the ranges that these factors may encompass through a probabilistic assessment this is essentially a variation of the standard paradigm. 

Stochastic analysis presents an alternative avenue for dealing with the inherently probabilistic and discontinuous microscopic events that underlie macroscopic phenomena. Many processes of chemical and physical interest can be described as random Markov processes.1,2 Unfortunately, solution of a stochastic master equation can present an extremely difficult mathematical challenge for systems of even modest complexity. In response to this difficulty, Gillespie3-5 developed an approach employing numerical Monte Carlo... 

Simplistic and heuristic similarity-based approaches can hardly produce as good predictive models as modern statistical and machine learning methods that are able to assess quantitatively biological or physicochemical properties. QSAR-based virtual screening consists of direct assessment of activity values (numerical or binary) of all compounds in the database followed by selection of hits possessing desirable activity. Mathematical methods used for models preparation can be subdivided into classification and regression approaches. The former decide whether a given compound is active, whereas the latter numerically evaluate the activity values. Classification approaches that assess probability of decisions are called probabilistic. 

The goal of human error quantification is to produce error probabilities, building on task analysis and error identification techniques to provide a probabilistic risk assessment (PRA). This provides numerical estimates of error likelihood and of the probability of overall likelihood of system breakdown. Quantification of error is the most difficult aspect of HRA, often heavily reliant on expert judgement, rather than the more rigorous approach of actual observation and recording of error frequencies. Such techniques are little used in healthcare but have been successfully applied to anaesthesia (Pate-Cornell and Bea, 1992). Nevertheless, some hospital tasks, such as blood transfusion, are highly structured and the quantification of errors probabilities would seem to be eminently feasible (Lyons et al, 2004). 

The many factors that seem to defy rigorous analysis can be quantified in different ways. One would involve probabilistic estimates and assign hard numerical values to each factor. The size and quality of the reliable database, however, do not support this approach. It becomes a judgmental exercise. Another is to prepare a matrix of the various factors considered to be important in a given analysis. Some of these factors might be ... 

The most common approach to evaluating the probabilistic character of an engineering demand parameter given an intensity measure level is to perform a series of numerical simulations (e.g. Kunnath 2007). In these simulations, the variability of... 

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