Related papers: Learning the nonlinear interactions from particle …
An old problem in multivariate statistics is that linear Gaussian models are often unidentifiable, i.e. some parameters cannot be uniquely estimated. In factor (component) analysis, an orthogonal rotation of the factors is unidentifiable,…
Transport of molecules across membrane channels is investigated theoretically using exactly solvable discrete stochastic site-binding models. It is shown that the interaction potential between molecules and the channel has a strong effect…
Water molecules confined between biological membranes exhibit a distinctive non-Gaussian displacement distribution, far different from bulk water. Here, we introduce a new transport equation for water molecules in the intermembrane space,…
In the standard picture of structure formation, initially random-phase fluctuations are amplified by non-linear gravitational instability to produce a final distribution of mass which is highly non-Gaussian and has highly coupled Fourier…
Gas transport across cell membrane is a very important process in biochemistry which is essential for many crucial tasks, including cell respiration pH regulation in the cell. In the late 1990's, the suggestion that gasses are transported…
The behaviour of many real-world phenomena can be modelled by nonlinear dynamical systems whereby a latent system state is observed through a filter. We are interested in interacting subsystems of this form, which we model by a set of…
We introduce a simulation strategy to consistently couple continuum biomembrane dynamics to the motion of discrete biological macromolecules residing within or on the membrane. The methodology is used to study the diffusion of integral…
We investigate nonlinear transport properties of quantum conductors in response to both electrical and thermal driving forces. Within scattering approach, we determine the nonequilibrium screening potential of a generic mesoscopic system…
Random walks are the simplest way to explore or search a graph, and have revealed a very useful tool to investigate and characterize the structural properties of complex networks from the real world, e.g. they have been used to identify the…
Diffusion of colloidal particles in a complex environment such as polymer networks or biological cells is a topic of high complexity with significant biological and medical relevance. In such situations, the interaction between the…
The statistics of multi-field inflation are investigated using the stochastic approach. We analytically obtain the probability distribution function of fields with the scaling approximation by extending the previous work by Amendola. The…
Spatial fields in the Earth and environmental sciences are often available at multiple scales or resolutions. While coarse-scale data (e.g., from global circulation models) are often abundant, they lack the local detail provided by…
We derive the stationary probability distribution for a non-equilibrium system composed by an arbitrary number of degrees of freedom that are subject to Gaussian colored noise and a conservative potential. This is based on a…
All living cells transport molecules and ions across membranes, often against concentration gradients. This active transport requires continual energy expenditure and is clearly a nonequilibrium process for which standard equilibrium…
Determining the different conformational states of a protein and the transition paths between them is key to fully understanding the relationship between biomolecular structure and function. This can be accomplished by sampling protein…
We propose a new semiparametric approach for modelling nonlinear univariate diffusions, where the observed process is a nonparametric transformation of an underlying parametric diffusion (UPD). This modelling strategy yields a general class…
We propose a reaction-transport model for CTRW with non-linear reactions and non-exponential waiting time distributions. We derive non-linear evolution equation for mesoscopic density of particles. We apply this equation to the problem of…
A plethora of networks is being collected in a growing number of fields, including disease transmission, international relations, social interactions, and others. As data streams continue to grow, the complexity associated with these highly…
Collective behavior of proteins on biomembranes is usually studied within the spontaneous curvature model. Here we consider an alternative phenomenological approach, which accounts consistently for partial ordering of proteins as well as…
A multivariate distribution can be described by a triangular transport map from the target distribution to a simple reference distribution. We propose Bayesian nonparametric inference on the transport map by modeling its components using…