Related papers: Fisher information matrix for single molecules wit…
A wide variety of numerical methods are evaluated and compared for solving the stochastic differential equations encountered in molecular dynamics. The methods are based on the application of deterministic impulses, drifts, and Brownian…
Time course measurement of single molecules on a cell surface provides detailed information on the dynamics of the molecules, which is otherwise inaccessible. To extract the quantitative information, single particle tracking (SPT) is…
In quantum multi-parameter estimation, the precision of estimating unknown parameters is bounded by the Cramer-Rao bound (CRB), defined via the inverse of the Fisher information matrix (FIM). However, in certain scenarios such as…
The Fisher information matrix (FIM) plays an important role in the analysis of parameter inference and system design problems. In a number of cases, however, the statistical data distribution and its associated information matrix are either…
The Fisher information matrix (FIM) has long been of interest in statistics and other areas. It is widely used to measure the amount of information and calculate the lower bound for the variance for maximum likelihood estimation (MLE). In…
A deep neural network is a hierarchical nonlinear model transforming input signals to output signals. Its input-output relation is considered to be stochastic, being described for a given input by a parameterized conditional probability…
Stochastic fluctuations of molecule numbers are ubiquitous in biological systems. Important examples include gene expression and enzymatic processes in living cells. Such systems are typically modelled as chemical reaction networks whose…
Conventional Bayesian estimation requires an accurate stochastic model of a system. However, this requirement is not always met in many practical cases where the system is not completely known or may differ from the assumed model. For such…
Investigating the dynamics of learning in machine learning algorithms is of paramount importance for understanding how and why an approach may be successful. The tools of physics and statistics provide a robust setting for such…
The number of resident space objects is rising at an alarming rate. Mega-constellations and breakup events are proliferating in most orbital regimes, and safe navigation is becoming increasingly problematic. It is important to be able to…
Data assimilation methods aim at estimating the state of a system by combining observations with a physical model. When sequential data assimilation is considered, the joint distribution of the latent state and the observations is described…
This paper presents a generic motion model to capture mobile robots' dynamic behaviors (translation and rotation). The model is based on statistical models driven by white random processes and is formulated into a full state estimation…
Synthesis of protein molecules in a cell are carried out by ribosomes. A ribosome can be regarded as a molecular motor which utilizes the input chemical energy to move on a messenger RNA (mRNA) track that also serves as a template for the…
Many biological systems can be described by finite Markov models. A general method for simplifying master equations is presented that is based on merging adjacent states. The approach preserves the steady-state probability distribution and…
Calibrating mathematical models of biological processes is essential for achieving predictive accuracy and gaining mechanistic insight. However, this task remains challenging due to limited and noisy data, significant biological…
Molecular search phenomena are observed in a variety of chemical and biological systems. During the search the participating particles frequently move in complex inhomogeneous environments with random transitions between different dynamic…
In this paper we extend the parametric sensitivity analysis (SA) methodology proposed in Ref. [Y. Pantazis and M. A. Katsoulakis, J. Chem. Phys. 138, 054115 (2013)] to continuous time and continuous space Markov processes represented by…
We investigate three different methods for systematically approximating the diffusion coefficient of a deterministic random walk on the line which contains dynamical correlations that change irregularly under parameter variation. Capturing…
This paper deals with the identification of linear stochastic dynamical systems, where the unknowns include system coefficients and noise variances. Conventional approaches that rely on the maximum likelihood estimation (MLE) require…
Background: The recent explosion of experimental techniques in single molecule biophysics has generated a variety of novel time series data requiring equally novel computational tools for analysis and inference. This article describes in…