Yohsuke T. Fukai

Despite similarities between models exhibiting absorbing phase transitions (APTs) and those showing Kardar-Parisi-Zhang (KPZ) growth, the relationship between these universal fluctuations has remained elusive. We numerically study (1+1)-dimensional interfaces of (2+1)-dimensional models showing APTs of directed percolation (DP) and compact directed percolation (CDP) classes with an active boundary, finding a universal crossover from short-time APT-governed fluctuations to long-time KPZ fluctuations. Upon rescaling time and length by the APT correlation time and length, the cumulants of the interface height distributions collapse onto a single scaling function. The fluctuation properties of the discrete Domany-Kinzel model and the continuum stochastic Fisher-Kolmogorov-Petrovsky-Piskunov (sFKPP) equation coincide, indicating that the KPZ growth parameters are determined solely by fundamental properties of the APT. For the CDP sFKPP equation, a dimensionless parameter tunes both the critical interface distribution and the KPZ parameters, with the interface properties of the biased voter model recovered in a limiting case. These results uncover a universal crossover in which KPZ fluctuations emerge from APT fluctuations at long times, linking paradigmatic universality classes of nonequilibrium scale-invariant phenomena.

Understanding how epigenetic modifications intrinsically shape gene-scale chromatin architecture remains challenging due to difficulties in reconstituting and characterizing sufficiently long arrays with defined modification patterns. Here, we overcome this barrier by reconstituting 20-kilobase (96-nucleosome) chromatin arrays with modification patterns precisely controlled at 12-nucleosome resolution. Single-molecule microscopy reveals the dynamics governed by hydrodynamic interactions, demonstrating that increasing histone H4 acetylation density enhances structural fluctuations and relaxation times. In vitro Hi-C reveals power-law decay of the nucleosome contacts consistent with the Gaussian chain, which is globally reduced by acetylation. We also observe that heterogeneous modification patterns alone are sufficient to create distinct structural domains reminiscent of higher-order chromatin organization. These findings establish how histone modifications modulate chromatin architecture via changes in local stiffness and nucleosome interactions, providing a quantitative framework for genome organization.

Particle tracking is an important step of analysis in a variety of scientific fields and is particularly indispensable for the construction of cellular lineages from live images. Although various supervised machine learning methods have been developed for cell tracking, the diversity of the data still necessitates heuristic methods that require parameter estimations from small amounts of data. For this, solving tracking as a linear assignment problem (LAP) has been widely applied and demonstrated to be efficient. However, there has been no implementation that allows custom connection costs, parallel parameter tuning with ground truth annotations, and the functionality to preserve ground truth connections, limiting the application to datasets with partial annotations.We developed LapTrack, a LAP-based tracker which allows including arbitrary cost functions and inputs, parallel parameter tuning and ground-truth track preservation. Analysis of real and artificial datasets demonstrates the advantage of custom metric functions for tracking score improvement from distance-only cases. The tracker can be easily combined with other Python-based tools for particle detection, segmentation and visualization.LapTrack is available as a Python package on PyPi, and the notebook examples are shared at https://github.com/yfukai/laptrack. The data and code for this publication are hosted at https://github.com/NoneqPhysLivingMatterLab/laptrack-optimisation.Supplementary data are available at Bioinformatics online.

Infinitesimal perturbations in various systems showing spatiotemporal chaos (STC) evolve following the power laws of the Kardar–Parisi–Zhang (KPZ) universality class. While universal properties beyond the power-law exponents, such as distributions and correlations and their geometry dependence, are established for random growth and related KPZ systems, the validity of these findings to deterministic chaotic perturbations is unknown. Here, we fill this gap between stochastic KPZ systems and deterministic STC perturbations by conducting extensive simulations of a prototypical STC system, namely, the logistic coupled map lattice. We show that the perturbation interfaces, defined by the logarithm of the modulus of the perturbation vector components, exhibit the universal, geometry-dependent statistical laws of the KPZ class despite the deterministic nature of STC. We demonstrate that KPZ statistics for three established geometries arise for different initial profiles of the perturbation, namely, point (local), uniform, and “pseudo-stationary” initial perturbations, the last being the statistically stationary state of KPZ interfaces given independently of the Lyapunov vector. This geometry dependence lasts until the KPZ correlation length becomes comparable to the system size. Thereafter, perturbation vectors converge to the unique Lyapunov vector, showing characteristic meandering, coalescence, and annihilation of borders of piece-wise regions that remain different from the Lyapunov vector. Our work implies that the KPZ universality for stochastic systems generally characterizes deterministic STC perturbations, providing new insights for STC, such as the universal dependence on initial perturbation and beyond.

We study fluctuations of interfaces in the Kardar-Parisi-Zhang (KPZ) universality class with curved initial conditions. By simulations of a cluster growth model and experiments with liquid-crystal turbulence, we determine the universal scaling functions that describe the height distribution and the spatial correlation of the interfaces growing outward from a ring. The scaling functions, controlled by a single dimensionless time parameter, show crossover from the statistical properties of the flat interfaces to those of the circular interfaces. Moreover, employing the KPZ variational formula to describe the case of the ring initial condition, we find that the formula, which we numerically evaluate, reproduces the numerical and experimental results precisely without adjustable parameters. This demonstrates that precise numerical evaluation of the variational formula is possible at all, and underlines the practical importance of the formula, which is able to predict the one-point distribution of KPZ interfaces for general initial conditions.