A one-dimensional modified TASEP model on a track of variable length: analytical and computational results

We present analytical solutions and Monte Carlo simulation results for a one-dimensional modified TASEP model inspired by the interplay between molecular motors and their cellular tracks of variable lengths, known as microtubules. Our TASEP model incorporates rules for changes in the length of the track based on the occupation of the first two sites. Using mean-field theory, we derive analytical results for the particle densities and particle currents and compare them with Monte Carlo simulations. These results show the limited range of mean-field methods for models with localized high correlation between particles. The variability in length adds to the complexity of the model, leading to emergent features for the evolution of particle densities and particle currents compared to the traditional TASEP model.

Review of Sublinear Modeling in Probabilistic Graphical Models by Statistical Mechanical Informatics and Statistical Machine Learning Theory

We review sublinear modeling in probabilistic graphical models by statistical mechanical informatics and statistical machine learning theory. Our statistical mechanical informatics schemes are based on advanced mean-field methods including loopy belief propagations. This chapter explores how phase transitions appear in loopy belief propagations for prior probabilistic graphical models. The frameworks are mainly explained for loopy belief propagations in the Ising model which is one of the elementary versions of probabilistic graphical models. We also expand the schemes to quantum statistical machine learning theory. Our framework can provide us with sublinear modeling based on the momentum space renormalization group methods.

A unifying framework for mean-field theories of asymmetric kinetic Ising systems

Kinetic Ising models are powerful tools for studying the non-equilibrium dynamics of complex systems. As their behavior is not tractable for large networks, many mean-field methods have been proposed for their analysis, each based on unique assumptions about the system’s temporal evolution. This disparity of approaches makes it challenging to systematically advance mean-field methods beyond previous contributions. Here, we propose a unifying framework for mean-field theories of asymmetric kinetic Ising systems from an information geometry perspective. The framework is built on Plefka expansions of a system around a simplified model obtained by an orthogonal projection to a sub-manifold of tractable probability distributions. This view not only unifies previous methods but also allows us to develop novel methods that, in contrast with traditional approaches, preserve the system’s correlations. We show that these new methods can outperform previous ones in predicting and assessing network properties near maximally fluctuating regimes.

Comparison between the Thomas–Fermi and Hartree–Fock–Bogoliubov Methods in the Inner Crust of a Neutron Star: The Role of Pairing Correlations

We investigated the role of a pairing correlation in the chemical composition of the inner crust of a neutron star with the extended Thomas–Fermi method, using the Strutinsky integral correction. We compare our results with the fully self-consistent Hartree–Fock–Bogoliubov approach, showing that the resulting discrepancy, apart from the very low density region, is compatible with the typical accuracy we can achieve with standard mean-field methods.