Global Probability Density Function Research Articles

Modified probabilistic neural network considering heterogeneous probabilistic density functions in the design of breakwater

In this study, a modified probabilistic neural network approach is proposed. The global probability density function (PDF) of variables is reflected by summing the heterogeneous local PDFs automatically determined in the individual standard derivation of each variable. The proposed modified probabilistic neural network (MPNN) is applied to predict the stability number of armor bøcks of break waters using the experiental data of van der Meer, and the estimated results of the MPNN are compared with those of conventional probabilistic neural network. The MPNN shows improved results in predicting the stability number of armor blocks of breakwaters and in providing the promising reliability for stability numbers estimated by using the individual standard deviation in a variable.

A weighted bootstrap method for the determination of probability density functions of freshwater distribution coefficients (Kds) of Co, Cs, Sr and I radioisotopes

The objective of the study was to provide global probability density functions (PDFs) representing the uncertainty of distribution coefficients (Kds) in freshwater for radioisotopes of Co, Cs, Sr and I. A comprehensive database containing Kd values referenced in 61 articles was first built and quality scores were affected to each data point according to various criteria (e.g. presentation of data, contact times, pH, solid-to-liquid ratio, expert judgement). A weighted bootstrapping procedure was then set up in order to build PDFs, in such a way that more importance is given to the most relevant data points (i.e. those corresponding to typical natural environments). However, it was also assessed that the relevance and the robustness of the PDFs determined by our procedure depended on the number of Kd values in the database. Owing to the large database, conditional PDFs were also proposed, for site studies where some parametric information is known (e.g. pH, contact time between radionuclides and particles, solid-to-liquid ratio). Such conditional PDFs reduce the uncertainty on the Kd values. These global and conditional PDFs are useful for end-users of dose models because the uncertainty and sensitivity of Kd values are taking into account.

Assessment of ignition hazard in turbulent flammable gas mixers combining a Lagrangian approach and large eddy simulation

In this article, a Lagrangian approach is adopted to assess both mixing efficiency and ignition hazard of fuel/oxygen flammable gas mixing in a jets-in-cross-flow configuration. Large eddy simulation is used to provide the unsteady fields of turbulent gas mixing. To achieve statistical reliability of the fluid dynamics field, such as velocity, pressure, temperature, and chemical composition, a large number of Lagrangian markers are dumped into the inlet streams of the mixer and their trajectories are determined during the numerical simulation. Those trajectories are stored in a file processed afterward to build up the probability density functions of the fuel molar fraction of Lagrangian markers gauging both mixer efficiency and safety. Flammability limits provided by H.F. Coward and G.W. Jones [U.S. Bur. Mines Bull. 503 (1952)] and autoignition delays from a detailed kinetics scheme are required to define the hazard range. Processing the marker trajectory file allows the calculation of relevant Lagrangian properties such as (i) the critical residence time in flammability areas for the ignition case and (ii) the marker Damköhler number for the autoignition case, both including the subgrid turbulence effects. The latter are accounted for by assuming a presumed beta shape for the large eddy probability density function of subgrid fluctuations of mixture fraction. Analysis of all marker trajectories leads to a computation of global probability density functions of Lagrangian properties that characterize mixer safety.

Localization of the N-terminal Domain in Light-harvesting Chlorophyll a/b Protein by EPR Measurements

The conformational distribution of the N-terminal domain of the major light-harvesting chlorophyll a/b protein (LHCIIb) has been characterized by electron-electron double resonance yielding distances between spin labels placed in various domains of the protein. Distance distributions involving residue 3 near the N terminus turned out to be bimodal, revealing that this domain, which is involved in regulatory functions such as balancing the energy flow through photosystems (PS) I and II, exists in at least two conformational states. Models of the conformational sub-ensembles were generated on the basis of experimental distance restraints from measurements on LHCIIb monomers and then checked for consistency with the experimental distance distribution between residues 3 in trimers. Only models where residue 3 is located above the core of the protein and extends into the aqueous phase on the stromal side fit the trimer data. In the other state, which consequently is populated only in monomers, the N-terminal domain extends sideways from the protein core. The two conformational states may correspond to two functional states of LHCIIb, namely trimeric LHCIIb associated with PSII in stacked thylakoid membranes and presumably monomeric LHCIIb associated with PSI in nonstacked thylakoids. The switch between these two is known to be triggered by phosphorylation of Thr-6. A similar phosphorylation-induced conformational change of the N-terminal domain has been observed by others in bovine annexin IV which, due to the conformational switch, also loses its membrane-aggregating property.

Generalization of Metropolis and heat-bath sampling for Monte Carlo simulations.

For a wide class of applications of the Monte Carlo method, we describe a general sampling methodology that is guaranteed to converge to a specified equilibrium distribution function. The method is distinct from that of Metropolis in that it is sometimes possible to arrange for unconditional acceptance of trial moves. It involves sampling states in a local region of phase space with probability equal to, in the first approximation, the square root of the desired global probability density function. The validity of this choice is derived from the Chapman-Kolmogorov equation, and the utility of the method is illustrated by a prototypical numerical experiment.