Petr Plecháč

Vagelis Harmandaris, Evangelia Kalligiannaki, Markos A. Katsoulakis et al.

In this paper, we discuss information-theoretic tools for obtaining optimized coarse-grained molecular models for both equilibrium and non-equilibrium molecular dynamics. The latter are ubiquitous in physicochemical and biological applications, where they are typically associated with coupling mechanisms, multi-physics and/or boundary conditions. In general the non-equilibrium steady states are not known explicitly as they do not necessarily have a Gibbs structure. The presented approach can compare microscopic behavior of molecular systems to parametric and non-parametric coarse-grained one using the relative entropy between distributions on the path space and setting up a corresponding path space variational inference problem. The methods can become entirely data-driven when the microscopic dynamics are replaced with corresponding correlated data in the form of time series. Furthermore, we present connections and generalizations of force matching methods in coarse-graining with path-space information methods, as well as demonstrate the enhanced transferability of information-based parameterizations to general observables due to information inequalities. We further discuss methodological connections between information-based coarse-graining of molecular systems and variational inference methods primarily developed in the machine learning community. However, we note that the work presented here addresses variational inference for correlated time series due to the focus on dynamics. The applicability of the proposed methods is demonstrated on high-dimensional stochastic processes given by Langevin, overdamped and driven Langevin dynamics of interacting particles.

Brittan A Farmer, Mitchell Luskin, Petr Plecháč et al.

Metastable condensed matter typically fluctuates about local energy minima at the femtosecond time scale before transitioning between local minima after nanoseconds or microseconds. This vast scale separation limits the applicability of classical molecular dynamics methods and has spurned the development of a host of approximate algorithms. One recently proposed method is diffusive molecular dynamics which aims to integrate a system of ordinary differential equations describing the likelihood of occupancy by one of two species, in the case of a binary alloy, while quasistatically evolving the locations of the atoms. While diffusive molecular dynamics has shown to be efficient and provide agreement with observations, it is fundamentally a model, with unclear connections to classical molecular dynamics. In this work, we formulate a spin-diffusion stochastic process and show how it can be connected to diffusive molecular dynamics. The spin-diffusion model couples a classical overdamped Langevin equation to a kinetic Monte Carlo model for exchange amongst the species of a binary alloy. Under suitable assumptions and approximations, spin-diffusion can be shown to lead to diffusive molecular molecular dynamics type models. The key assumptions and approximations include a well defined time scale separation, a choice of spin exchange rates, a low temperature approximation, and a mean field type approximation. We derive several models from different assumptions and show their relationship to diffusive molecular dynamics. Differences and similarities amongst the models are explored in a simple test problem.

Christian Bayer, Håkon Hoel, Petr Plecháč et al.

Born-Oppenheimer dynamics is shown to provide an accurate approximation of time-independent Schrödinger observables for a molecular system with an electron spectral gap, in the limit of large ratio of nuclei and electron masses, without assuming that the nuclei are localized to vanishing domains. The derivation, based on a Hamiltonian system interpretation of the Schrödinger equation and stability of the corresponding Hamilton-Jacobi equation, bypasses the usual separation of nuclei and electron wave functions, includes caustic states and gives a different perspective on the Born-Oppenheimer approximation, Schrödinger Hamiltonian systems and numerical simulation in molecular dynamics modeling at constant energy microcanonical ensembles.

Ting Wang, Petr Plecháč

Stochastic reaction networks that exhibit bistability are common in many fields such as systems biology and materials science. Sampling of the stationary distribution is crucial for understanding and characterizing the long term dynamics of bistable stochastic dynamical systems. However, this is normally hindered by the insufficient sampling of the rare transitions between the two metastable regions. In this paper, we apply the parallel replica (ParRep) method for continuous time Markov chain to accelerate the stationary distribution sampling of bistable stochastic reaction networks. The proposed method uses parallel computing to accelerate the sampling of rare transitions and it is very easy to implement. We combine ParRep with the path space information bounds for parametric sensitivity analysis. We demonstrate the efficiency and accuracy of the method by studying the Schlögl model and the genetic switches network.

Lenka Jungmannová, Petr Plecháč

In addition to being a widely recognised novelist, Milan Kundera has also authored three pieces for theatre: The Owners of the Keys (Majitelé klíčů, 1961), The Blunder (Ptákovina, 1967), and Jacques and his Master (Jakub a jeho pán, 1971). In recent years, however, the hypothesis has been raised that Kundera is the true author of a fourth play: Juro Jánošík, first performed in a 1974 production under the name of Karel Steigerwald, who was Kundera's student at the time. In this study, we make use of supervised machine learning to settle the question of authorship attribution in the case of Juro Jánošík, with results strongly supporting the hypothesis of Kundera's authorship.

Petr Plecháč, Erik von Schwerin

We propose a Multi-level Monte Carlo technique to accelerate Monte Carlo sampling for approximation of properties of materials with random defects. The computational efficiency is investigated on test problems given by tight-binding models of a single layer of graphene or of $MoS_2$ where the integrated electron density of states per unit area is taken as a representative quantity of interest. For the chosen test problems the multi-level Monte Carlo estimators significantly reduce the computational time of standard Monte Carlo estimators to obtain a given accuracy.

Ting Wang, Petr Plecháč, David Aristoff

We propose two algorithms for simulating continuous time Markov chains in the presence of metastability. We show that the algorithms correctly estimate, under the ergodicity assumption, stationary averages of the process. Both algorithms, based on the idea of the parallel replica method, use parallel computing in order to explore metastable sets more efficiently. The algorithms require no assumptions on the Markov chains beyond ergodicity and the presence of identifiable metastability. In particular, there is no assumption on reversibility. For simpler illustration of the algorithms, we assume that a synchronous architecture is used throughout of the paper. We present error analyses, as well as numerical simulations on multi-scale stochastic reaction network models in order to demonstrate consistency of the method and its efficiency.

Ben Nagy, Artjoms Šeļa, Mirella De Sisto et al.

All poetic forms come from somewhere. Prosodic templates can be copied for generations, altered by individuals, imported from foreign traditions, or fundamentally changed under the pressures of language evolution. Yet these relationships are notoriously difficult to trace across languages and times. This paper introduces an unsupervised method for detecting structural similarities in poems using local sequence alignment. The method relies on encoding poetic texts as strings of prosodic features using a four-letter alphabet; these sequences are then aligned to derive a distance measure based on weighted symbol (mis)matches. Local alignment allows poems to be clustered according to emergent properties of their underlying prosodic patterns. We evaluate method performance on a meter recognition tasks against strong baselines and show its potential for cross-lingual and historical research using three short case studies: 1) mutations in quantitative meter in classical Latin, 2) European diffusion of the Renaissance hendecasyllable, and 3) comparative alignment of modern meters in 18--19th century Czech, German and Russian. We release an implementation of the algorithm as a Python package with an open license.

Artjoms Šeļa, Petr Plecháč, Alie Lassche

Recent advances in cultural analytics and large-scale computational studies of art, literature and film often show that long-term change in the features of artistic works happens gradually. These findings suggest that conservative forces that shape creative domains might be underestimated. To this end, we provide the first large-scale formal evidence of the persistent association between poetic meter and semantics in 18-19th European literatures, using Czech, German and Russian collections with additional data from English poetry and early modern Dutch songs. Our study traces this association through a series of clustering experiments using the abstracted semantic features of 150,000 poems. With the aid of topic modeling we infer semantic features for individual poems. Texts were also lexically simplified across collections to increase generalizability and decrease the sparseness of word frequency distributions. Topics alone enable recognition of the meters in each observed language, as may be seen from highly robust clustering of same-meter samples (median Adjusted Rand Index between 0.48 and 1). In addition, this study shows that the strength of the association between form and meaning tends to decrease over time. This may reflect a shift in aesthetic conventions between the 18th and 19th centuries as individual innovation was increasingly favored in literature. Despite this decline, it remains possible to recognize semantics of the meters from past or future, which suggests the continuity of semantic traditions while also revealing the historical variability of conditions across languages. This paper argues that distinct metrical forms, which are often copied in a language over centuries, also maintain long-term semantic inertia in poetry. Our findings, thus, highlight the role of the formal features of cultural items in influencing the pace and shape of cultural evolution.

Petr Plecháč

The versified play Henry VIII is nowadays widely recognized to be a collaborative work not written solely by William Shakespeare. We employ combined analysis of vocabulary and versification together with machine learning techniques to determine which authors also took part in the writing of the play and what were their relative contributions. Unlike most previous studies, we go beyond the attribution of particular scenes and use the rolling attribution approach to determine the probabilities of authorship of pieces of texts, without respecting the scene boundaries. Our results highly support the canonical division of the play between William Shakespeare and John Fletcher proposed by James Spedding, but also bring new evidence supporting the modifications proposed later by Thomas Merriam.