peak escape.pdf

The Exponentially Modified Gaussian (EMG) peak shape [1] is widely used for peak approximation in chromatography. We constructed the EMG peak deconvolution routine for chromatography, using a combination of two EMG formulas [1,2] and linear optimization methods. This routine accounts for the maximum linear range of the detector and can work with out-of range peaks.

Indian Journal of physics, 691,1995

A b s tr a c t : In Rictveld's method of structure refinement from powder diffraction data all the peaks in a X-ray diffractogram ore fitted with same type o f analytical function usually termed as profile shape function (PSF). Present authors investigated if a single profile shape function could be fitted to all the peaks in a X-ray diffractogram and found that no single PSF could properly fit all the peaks in a given diffraction pattern. This conclusion was arrived at using tw o probes viz (i) calculation o f /L . where Mn being the n-th order central moment o f the profile and (li) R(x) test where R(x) = j j / {x)dx being the PSF in question describing the profile. These two probes were applied Lo the observed line profiles o f copper-nickel alloys and found that peaks are best fitted with different PSFS viz, G aussian, Lorentzian, Intermediate Lorentzian, M odified Lorentzian, Pearson IV type and Pearson VII type. K e y w o r d s Powder diffractogram, profile shape function, Rietveld method P A C S N o . i 6 1 .1 0 U In the original work of Rietveld [11, the profile shape function was assumed to be Gaussian and the standard deviation of the Gaussian function was considered to be proportional tp FWHM (Full width at half maxima). Later workers made various assumptions regarding the profile shape function. The Lorentzian, the Voigt, sum of Lorentzians, sum of

2017

aporc.org

We study the transition time between different metastable states in the continuous Wright-Fisher (diffusion) model. We construct an adaptive landscape for describing the system both qualitatively and quantitatively. When strong genetic drift and weak mutation generate infinite adaptive peaks, we calculate the expected time to escape from such peak states. We find a new way to analytically approximate the escape time, which extends the application of Kramer's classical formulae to the cases of non-Gaussian equilibrium distribution and bridges previous results in two limits. Our adaptive landscape, compared to the classical fitness landscape or other scalar functions, is directly related to system's middle-and-long-term dynamics and is self-consistent in the whole parameter space. Our work provides a complete description for the bi-stabilities in the present model.

aporc.org

We study the transition time between different metastable states in the continuous Wright-Fisher (diffusion) model. We construct an adaptive landscape for describing the system both qualitatively and quantitatively. When strong genetic drift and weak mutation generate infinite adaptive peaks, we calculate the expected time to escape from such peak states. We find a new way to analytically approximate the escape time, which extends the application of Kramer's classical formulae to the cases of non-Gaussian equilibrium distribution and bridges previous results in two limits. Our adaptive landscape, compared to the classical fitness landscape or other scalar functions, is directly related to system's middle-and-long-term dynamics and is self-consistent in the whole parameter space. Our work provides a complete description for the bi-stabilities in the present model.

Computational and Mathematical Methods in Medicine, 2017

In many cases relevant to biomedicine, a variable time, which features a certain distribution, is required for objects of interest to pass from an initial to an intermediate state, out of which they exit at random to a final state. In such cases, the distribution of variable times between exiting the initial and entering the final state must conform to the convolution of the first distribution and a negative exponential distribution. A common example is the exponentially modified Gaussian (EMG), which is widely used in chromatography for peak analysis and is long known as ex-Gaussian in psychophysiology, where it is applied to times from stimulus to response. In molecular and cell biology, EMG, compared with commonly used simple distributions, such as lognormal, gamma, and Wald, provides better fits to the variabilities of times between consecutive cell divisions and transcriptional bursts and has more straightforwardly interpreted parameters. However, since the range of definition ...