Mikhail V. Tamm

Alexander Lobashev, Mikhail V. Tamm

We introduce a new approach to reconstruction of the thermodynamic functions and phase boundaries in two-parametric statistical mechanics systems. Our method is based on expressing the Fisher metric in terms of the posterior distributions over a space of external parameters and approximating the metric field by a Hessian of a convex function. We use the proposed approach to accurately reconstruct the partition functions and phase diagrams of the Ising model and the exactly solvable non-equilibrium TASEP without any a priori knowledge about microscopic rules of the models. We also demonstrate how our approach can be used to visualize the latent space of StyleGAN models and evaluate the variability of the generated images.

Mikhail V. Tamm, Els Heinsalu, Stefano Scialla et al.

We introduce a language competition model that is based on the Abrams-Strogatz model and incorporates the effects of memory and learning in the language shift dynamics. On a coarse grained time scale, the effects of memory and learning can be expressed as thresholds on the speakers fractions of the competing languages. In its simplest form, the resulting model is exactly solvable. Besides the consensus on one of the two languages, the model describes additional equilibrium states that are not present in the Abrams-Strogatz model: a stable dynamical coexistence of the two languages and a frozen state coinciding with the initial state. We show numerically that these results are preserved for threshold functions of a more general shape. The comparison of the model predictions with historical datasets demonstrates that while the Abrams-Strogatz model fails to describe some relevant language competition situations, the proposed model provides a good fitting.