Related papers: Finite-temperature local protein sequence alignmen…
This dissertation develops, for several families of statistical mechanical and random growth models, techniques for analyzing infinite-volume asymptotics. In the statistical mechanical setting, we focus on the low-temperature phases of spin…
Using analytical calculations and computer simulations we consider both the lateral diffusion of a membrane protein and the fluctuation spectrum of the membrane in which the protein is embedded. The membrane protein interacts with the…
The parallel dynamics of the fully connected Blume-Emery-Griffiths neural network model is studied at zero temperature for arbitrary using a probabilistic approach. A recursive scheme is found determining the complete time evolution of the…
This contribution is devoted to cover some technical aspects related to the use of the recently proposed energy probability distribution zeros in the study of phase transitions. This method is based on the partial knowledge of the partition…
The free energy of globular protein chain is considered to be a functional defined on smooth curves in three dimensional Euclidean space. From the requirement of geometrical invariance, together with basic facts on conformation of helical…
The exact evolution in time and space of a distribution of the temperature (or density of diffusing matter) in an isotropic homogeneous medium is determined where the initial distribution is described by a piecewise polynomial. In two…
Free energy calculation is critical in predictive tasks such as protein folding, docking and design. However, rigorous calculation of free energy change is prohibitively expensive in these practical applications. The minimum potential…
In statistical physics, the efficiency of tempering approaches strongly depends on ingredients such as the number of replicas $R$, reliable determination of weight factors and the set of used temperatures, ${\mathcal T}_R = \{T_1, T_2,…
During their evolution, proteins explore sequence space via an interplay between random mutations and phenotypic selection. Here we build upon recent progress in reconstructing data-driven fitness landscapes for families of homologous…
In this paper we discuss how the information contained in atomistic simulations of homogeneous nucleation should be used when fitting the parameters in macroscopic nucleation models. We show how the number of solid and liquid atoms in such…
In efforts to determine phase transitions in the disintegration of highly excited heavy nuclei, a popular practice is to parametrise the yields of isotopes as a function of temperature in the form $Y(z)=z^{-\tau}f(z^{\sigma}(T-T_0))$, where…
Temperature scaling is a popular technique for tuning the sharpness of a model distribution. It is used extensively for sampling likely generations and calibrating model uncertainty, and even features as a controllable parameter to many…
We investigate the parameter space of transformer models trained on protein sequence data using a statistical mechanics framework, sampling the loss landscape at varying temperatures by Langevin dynamics to characterize the low-loss…
We develop a geometric account of sequence modelling that links patterns in the data to measurable properties of the loss landscape in transformer networks. First, we cast conditional sequence distributions into a Hilbert-space framework…
Linked cluster expansions provide a useful tool for both analytical and numerical investigations of lattice field theories. The expansion parameter(s) being the interaction strength(s) fields at neighboured lattice sites are coupled, they…
The probability distribution of sequences with maximum entropy that satisfies a given amino acid composition at each site and a given pairwise amino acid frequency at each site pair is a Boltzmann distribution with $\exp(-\psi_N)$, where…
The free energy functional has recently been proposed as a variational principle for bounded rational decision-making, since it instantiates a natural trade-off between utility gains and information processing costs that can be…
The folding ability of a heteropolymer model for proteins subject to Monte Carlo dynamics on a simple cubic lattice is shown to be strongly correlated with the energy gap between the native state and the structurally dissimilar part of the…
In this paper, we address the logarithmic corrections to the leading power laws that govern thermodynamic quantities as a second-order phase transition point is approached. For phase transitions of spin systems on d-dimensional lattices,…
To address the large gap between time scales that can be easily reached by molecular simulations and those required to understand protein dynamics, we propose a rapid self-consistent approximation of the side chain free energy at every…