arXiv subjects

Petr Plecháč

Publications and source records attributed to Petr Plecháč.

At least 19 recordsLinked to original sources

arXiv2026

Training Data Size Sensitivity in Unsupervised Rhyme Recognition

Rhyme is deceptively intuitive: what is or is not a rhyme is constructed historically, scholars struggle with rhyme classification, and people disagree on whether two words are rhymed or not. This complicates automated rhymed recognition and evaluation, especially in multilingual context. This article investigates how much training data is needed for reliable unsupervised rhyme recognition using RhymeTagger, a language-independent tool that identifies rhymes based on repeating patterns in poetry corpora. We evaluate its performance across seven languages (Czech, German, English, French, Italian, Russian, and Slovene), examining how training size and language differences affect accuracy. To set a realistic performance benchmark, we assess inter-annotator agreement on a manually annotated subset of poems and analyze factors contributing to disagreement in expert annotations: phonetic similarity between rhyming words and their distance from each other in a poem. We also compare RhymeTagger to three large language models using a one-shot learning strategy. Our findings show that, once provided with sufficient training data, RhymeTagger consistently outperforms human agreement, while LLMs lacking phonetic representation significantly struggle with the task.

cs.CL↗

arXiv2025

Source identification via pathwise gradient estimation

In the context of PDE-constrained optimization theory, source identification problems traditionally entail particles emerging from an unknown source distribution inside a domain, moving according to a prescribed stochastic process, e.g.~Brownian motion, and then exiting through the boundary of a compact domain. Given information about the flux of particles through the boundary of the domain, the challenge is to infer as much as possible about the source. In the PDE setting, it is usually assumed that the flux can be observed without error and at all points on the boundary. Here we consider a different, more statistical presentation of the problem, in which the data has the form of discrete counts of particles arriving at a set of disjoint detectors whose union is a strict subset of the boundary. In keeping with the primacy of the stochastic processes in the generation of the model, we present a stochastic gradient descent algorithm in which exit rates and parameter sensitivities are computed by simulations of particle paths. We present examples for both Itô diffusion and piecewise-deterministic Markov processes, noting that the form of the sensitivities depends only on the parameterization of the source distribution and is universal among a large class of Markov processes.

math.OC↗

arXiv2024

Metronome: tracing variation in poetic meters via local sequence alignment

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.

cs.CL↗

arXiv2022

Unsigned Play by Milan Kundera? An Authorship Attribution Study

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.

cs.CL↗

arXiv2022

On the time-domain full waveform inversion for time-dissipative and dispersive poroelastic media

This paper concerns the Time-Domain Full Waveform Inversion (FWI) for dispersive and dissipative poroelastic materials. The forward problem is an initial boundary value problem (IBVP) of the poroelastic equations with a memory term; the FWI is formulated as a minimization problem of a least-square misfit function with the (IBVP) as the constraint. In this paper, we derive the adjoint problem of this minimization problem, whose solution can be applied to computed the direction of steepest descent in the iterative process for minimization. The adjoint problem has a similar numerical structure as the forward problem and hence can be solved by the same numerical solver. Because the tracking of the energy evolution plays an important role in the FWI for dissipative and dispersive equations, the energy analysis of the forward system is also carried out in this paper.

math.NA↗

arXiv2021

Semantics of European poetry is shaped by conservative forces: The relationship between poetic meter and meaning in accentual-syllabic verse

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.

cs.CL↗

arXiv2021

Smaller generalization error derived for a deep residual neural network compared to shallow networks

Estimates of the generalization error are proved for a residual neural network with $L$ random Fourier features layers $\bar z_{\ell+1}=\bar z_\ell + \mathrm{Re}\sum_{k=1}^K\bar b_{\ell k}e^{\mathrm{i}ω_{\ell k}\bar z_\ell}+ \mathrm{Re}\sum_{k=1}^K\bar c_{\ell k}e^{\mathrm{i}ω'_{\ell k}\cdot x}$. An optimal distribution for the frequencies $(ω_{\ell k},ω'_{\ell k})$ of the random Fourier features $e^{\mathrm{i}ω_{\ell k}\bar z_\ell}$ and $e^{\mathrm{i}ω'_{\ell k}\cdot x}$ is derived. This derivation is based on the corresponding generalization error for the approximation of the function values $f(x)$. The generalization error turns out to be smaller than the estimate ${\|\hat f\|^2_{L^1(\mathbb{R}^d)}}/{(KL)}$ of the generalization error for random Fourier features with one hidden layer and the same total number of nodes $KL$, in the case the $L^\infty$-norm of $f$ is much less than the $L^1$-norm of its Fourier transform $\hat f$. This understanding of an optimal distribution for random features is used to construct a new training method for a deep residual network. Promising performance of the proposed new algorithm is demonstrated in computational experiments.

math.NA↗

arXiv2021

Spintronics meets density matrix renormalization group: Quantum spin torque driven nonclassical magnetization reversal and dynamical buildup of long-range entanglement

We introduce time-dependent density matrix renormalization group (tDMRG) as a solution to long standing problem in spintronics -- how to describe spin-transfer torque (STT) between flowing spins of conduction electrons and localized spins within a magnetic material by treating the dynamics of both spin species fully quantum-mechanically. In contrast to conventional Slonczewski-Berger STT, where the localized spins are viewed as classical vectors obeying the Landau-Lifshitz-Gilbert equation and where their STT-driven dynamics is initiated only when the spin-polarization of flowing electrons and localized spins are noncollinear, quantum STT can occur when these vectors are collinear but antiparallel. Using tDMRG, we simulate the time evolution of a many-body quantum state of electrons and localized spins, where the former are injected as a spin-polarized current pulse while the latter comprise a quantum Heisenberg ferromagnetic metallic (FM) spin-$\frac{1}{2}$ XXZ chain initially in the ground state with spin-polarization antiparallel to that of injected electrons. The quantum STT reverses the direction of localized spins, but without rotation from the initial orientation, when the number of injected electrons exceeds the number of localized spins. Such nonclassical reversal, which is absent from LLG dynamics, is strikingly inhomogeneous across the FM chain and it can be accompanied by reduction of the magnetization associated with localized spins, even to zero at specific locations. This is because quantum STT generates a highly entangled nonequilibrium many-body state of all flowing and localized spins, despite starting from the initially unentangled ground state of a mundane FM. Furthermore, the mutual information between localized spins at the FM edges remains nonzero even at infinite separation as the signature of dynamical buildup of long-range entanglement.

cond-mat.str-el↗

arXiv2020

Adaptive random Fourier features with Metropolis sampling

The supervised learning problem to determine a neural network approximation $\mathbb{R}^d\ni x\mapsto\sum_{k=1}^K\hatβ_k e^{\mathrm{i}ω_k\cdot x}$ with one hidden layer is studied as a random Fourier features algorithm. The Fourier features, i.e., the frequencies $ω_k\in\mathbb{R}^d$, are sampled using an adaptive Metropolis sampler. The Metropolis test accepts proposal frequencies $ω_k'$, having corresponding amplitudes $\hatβ_k'$, with the probability $\min\big\{1, (|\hatβ_k'|/|\hatβ_k|)^γ\big\}$, for a certain positive parameter $γ$, determined by minimizing the approximation error for given computational work. This adaptive, non-parametric stochastic method leads asymptotically, as $K\to\infty$, to equidistributed amplitudes $|\hatβ_k|$, analogous to deterministic adaptive algorithms for differential equations. The equidistributed amplitudes are shown to asymptotically correspond to the optimal density for independent samples in random Fourier features methods. Numerical evidence is provided in order to demonstrate the approximation properties and efficiency of the proposed algorithm. The algorithm is tested both on synthetic data and a real-world high-dimensional benchmark.

math.NA↗

arXiv2020

Sampling from Rough Energy Landscapes

We examine challenges to sampling from Boltzmann distributions associated with multiscale energy landscapes. The multiscale features, or "roughness," corresponds to highly oscillatory, but bounded, perturbations of a smooth landscape. Through a combination of numerical experiments and analysis we demonstrate that the performance of Metropolis Adjusted Langevin Algorithm can be severely attenuated as the roughness increases. In contrast, we prove that Random Walk Metropolis is insensitive to such roughness. We also formulate two alternative sampling strategies that incorporate large scale features of the energy landscape, while resisting the impact of fine scale roughness; these also outperform Random Walk Metropolis. Numerical experiments on these landscapes are presented that confirm our predictions. Open questions and numerical challenges are also highlighted.

math.NA↗

arXiv2019

Relative contributions of Shakespeare and Fletcher in Henry VIII: An Analysis Based on Most Frequent Words and Most Frequent Rhythmic Patterns

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.

cs.CL↗

arXiv2019

Reply to: Large-scale quantitative profiling of the Old English verse tradition

In Nature Human Behaviour 3/2019, an article was published entitled "Large-scale quantitative profiling of the Old English verse tradition" dealing with (besides other things) the question of the authorship of the Old English poem Beowulf. The authors provide various textual measurements that they claim present "serious obstacles to those who would advocate for composite authorship or scribal recomposition" (p. 565). In what follows we raise doubts about their methods and address serious errors in both their data and their code. We show that reliable stylometric methods actually identify significant stylistic heterogeneity in Beowulf. In what follows we discuss each method separately following the order of the original article.

stat.AP↗

arXiv2019

The classical limit of quantum observables in the conservation laws of fluid dynamics

In the classical work by Irving and Zwanzig [Irving J.H. and Zwanzig R.W., J. Chem. Phys. 19 (1951), 1173-1180 ] it has been shown that quantum observables for macroscopic density, momentum and energy satisfy the conservation laws of fluid dynamics. This work derives the corresponding classical molecular dynamics limit by extending Irving and Zwanzig's result to matrix-valued potentials for a general quantum particle system. The matrix formulation provides the semi-classical limit of the quantum observables in the conservation laws, also in the case where the temperature is large compared to the electron eigenvalue gaps. The classical limit of the quantum observables in the conservation laws is useful in order to determine the constitutive relations for the stress tensor and the heat flux by molecular dynamics simulations. The main new steps to obtain the molecular dynamics limit is to: (i) approximate the dynamics of quantum observables accurately by classical dynamics, by diagonalizing the Hamiltonian using a non linear eigenvalue problem, (ii) define the local energy density by partitioning a general potential, applying perturbation analysis of the electron eigenvalue problem, (iii) determine the molecular dynamics stress tensor and heat flux in the case of several excited electron states, and (iv) construct the initial particle phase-space density as a local grand canonical quantum ensemble determined by the initial conservation variables.

math-ph↗

arXiv2018

First-principles quantum transport modeling of spin-transfer and spin-orbit torques in magnetic multilayers

We review a unified approach for computing: (i) spin-transfer torque in magnetic trilayers like spin-valves and magnetic tunnel junction, where injected charge current flows perpendicularly to interfaces; and (ii) spin-orbit torque in magnetic bilayers of the type ferromagnet/spin-orbit-coupled-material, where injected charge current flows parallel to the interface. Our approach requires to construct the torque operator for a given Hamiltonian of the device and the steady-state nonequilibrium density matrix, where the latter is expressed in terms of the nonequilibrium Green's functions and split into three contributions. Tracing these contributions with the torque operator automatically yields field-like and damping-like components of spin-transfer torque or spin-orbit torque vector, which is particularly advantageous for spin-orbit torque where the direction of these components depends on the unknown-in-advance orientation of the current-driven nonequilibrium spin density in the presence of spin-orbit coupling. We provide illustrative examples by computing spin-transfer torque in a one-dimensional toy model of a magnetic tunnel junction and realistic Co/Cu/Co spin-valve, both of which are described by first-principles Hamiltonians obtained from noncollinear density functional theory calculations; as well as spin-orbit torque in a ferromagnetic layer described by a tight-binding Hamiltonian which includes spin-orbit proximity effect within ferromagnetic monolayers assumed to be generated by the adjacent monolayer transition metal dichalcogenide.

cond-mat.mes-hall↗

arXiv2017

Stationary averaging for multi-scale continuous time Markov chains using parallel replica dynamics

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.

math.NA↗

arXiv2017

Spin-Diffusions and Diffusive Molecular Dynamics

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.

physics.comp-ph↗

arXiv2017

Parallel replica dynamics method for bistable stochastic reaction networks: simulation and sensitivity analysis

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.

math.NA↗

arXiv2016

Multi-level Monte Carlo acceleration of computations on multi-layer materials with random defects

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.

math.NA↗