Here, we propose a simple uniform counting strategy, Paired-Insertion Counting (PIC), that corrects for the peak boundary problem (Methods) along with a probability model that accounts for shared insertion point
A TCSPCS is used to generate a time trace of multiple detection events (mDEs), the histogram of which is matched to a probability model to determine the number of emitters. e, TIRF image of a U2-OS cell transiently transfected with the ProDOL probe. The arrows depict single-molecule ...
In any event, the rate of counting is proportional to the intensity of the light beam, so one writes αI(t)dt for the probability of counting a photon at the time t in the interval dt. The factor α takes account of the atomic variables governing the ionization process as well as ...
Monte Carlo (MC) involves sampling from the distributions on the right axis, with a sample histogram shown as thin black lines for the distributions in (a). Trends in the errors as a function of particle counts can be used in conjunction with errors models. 2.1.2. Probability density ...
In order to rediscover some properties of probability that were inspired by counting, we need to pursue properties of the counting function itself. Let S be a finite set (sample space) with points s l s 2 ,s m when S has size m; the counting function begins with #((s i )) = 1;...
Using the above posterior probability and density estimation map Dest, we can obtain the Bayesian loss function, L Bayes =∑n=1NF(1−∑m=1Mp(yn∣xm)Dest(xm)) (3) The presence of background pixel points will have a great impact on the regression estimation. In order to further elimin...
Statistics and ProbabilityAccuracy of the box-counting algorithm for numerical computation of the fractal exponents is investigated. To this end several sample mathematical fractal sets are analyzed. It is shown that the standard deviation obtained for the fit of the fractal scaling in the log-log ...
To address this challenge, BL [144] proposes Bayesian loss, which constructs a density contribution probability model from point annotations. Specifically, it adds the product of contribu- tion probability and estimated density for each pixel, achieving supervision and counting tasks by computing the ...
σ 212×2 (2) Using the above posterior probability and density estima- tion map Dest , we can obtain the Bayesian loss function, NM L Bayes = F 1 − p yn | xm Dest (xm) n=1 m=1 (3) The presence of background pixel points will have a great impact on the regression estima...
To this end, we introduce a latent variable matrix Ω ∈ R ,mi,j×mi,j where the (u, v)-th element Ωu,v denote the probability that the u-th pedestrian in X is matched with v-th pedestrian in Y. To increase the similarity between the pairs that have a higher matching ...