Final nanoparticle size distribution under unusual parameter regimes.

We explore the large-scale behavior of a stochastic model for nanoparticle growth in an unusual parameter regime. This model encompasses two types of reactions: nucleation, where n monomers aggregate to form a nanoparticle, and growth, where a nanoparticle increases its size by consuming a monomer. Reverse reactions are disregarded. We delve into a previously unexplored parameter regime. Specifically, we consider a scenario where the growth rate of the first newly formed particle is of the same order of magnitude as the nucleation rate, in contrast to the classical scenario where, in the initial stage, nucleation dominates over growth. In this regime, we investigate the final size distribution as the initial number of monomers tends to infinity through extensive simulation studies utilizing state-of-the-art stochastic simulation methods with an efficient implementation and supported by high-performance computing infrastructure. We observe the emergence of a deterministic limit for the particle's final size density. To scale up the initial number of monomers to approximate the magnitudes encountered in real experiments, we introduce a novel approximation process aimed at faster simulation. Remarkably, this approximating process yields a final size distribution that becomes very close to that of the original process when the available monomers approach infinity. Simulations of the approximating process further support the conjecture of the emergence of a deterministic limit.

Asymptotic distributions of kappa statistics and their differences with many raters, many rating categories and two conditions.

In clinical research and in more general classification problems, a frequent concern is the reliability of a rating system. In the absence of a gold standard, agreement may be considered as an indication of reliability. When dealing with categorical data, the well-known kappa statistic is often used to measure agreement. The aim of this paper is to obtain a theoretical result about the asymptotic distribution of the kappa statistic with multiple items, multiple raters, multiple conditions, and multiple rating categories (more than two), based on recent work. The result settles a long lasting quest for the asymptotic variance of the kappa statistic in this situation and allows for the construction of asymptotic confidence intervals. A recent application to clinical endoscopy and to the diagnosis of inflammatory bowel diseases (IBDs) is shortly presented to complement the theoretical perspective.

Errors in estimation of the input signal for integrate-and-fire neuronal models.

Estimation of the input parameters of stochastic (leaky) integrate-and-fire neuronal models is studied. It is shown that the presence of a firing threshold brings a systematic error to the estimation procedure. Analytical formulas for the bias are given for two models, the randomized random walk and the perfect integrator. For the third model considered, the leaky integrate-and-fire model, the study is performed by using Monte Carlo simulated trajectories. The bias is compared with other errors appearing during the estimation, and it is documented that the effect of the bias has to be taken into account in experimental studies.

Estimating input parameters from intracellular recordings in the Feller neuronal model.

We study the estimation of the input parameters in a Feller neuronal model from a trajectory of the membrane potential sampled at discrete times. These input parameters are identified with the drift and the infinitesimal variance of the underlying stochastic diffusion process with multiplicative noise. The state space of the process is restricted from below by an inaccessible boundary. Further, the model is characterized by the presence of an absorbing threshold, the first hitting of which determines the length of each trajectory and which constrains the state space from above. We compare, both in the presence and in the absence of the absorbing threshold, the efficiency of different known estimators. In addition, we propose an estimator for the drift term, which is proved to be more efficient than the others, at least in the explored range of the parameters. The presence of the threshold makes the estimates of the drift term biased, and two methods to correct it are proposed.