@inproceedings{22002, abstract = {Topological simplification is the process of reducing complexity of a function while maintaining its essential features. Its goal is to find a new filter function, which reorders cells of the input complex in a way which eliminates some persistent homological features, without affecting the rest. We present a new approach to simplification based on the concept of forbidden regions and combinatorial dynamics. It allows us to reorder and cancel critical values, whose cancellation is not possible using existing methods because they are not consecutive in the total order. Each such cancellation takes O(c⋅n) time in the worst case, where c is the number of birth-death pairs and n is the size of the input complex.}, author = {Leśkiewicz, Jakub and Furmanek, Bartosz and Lipiński, Michał and Morozov, Dmitriy}, booktitle = {42nd International Symposium on Computational Geometry}, isbn = {9783959774185}, issn = {1868-8969}, keywords = {persistent homology, topological simplification, depth posets}, location = {New Brunswick, NJ, United States}, publisher = {Schloss Dagstuhl - Leibniz-Zentrum für Informatik}, title = {{Topological simplification guided by forbidden regions}}, doi = {10.4230/LIPIcs.SoCG.2026.72}, volume = {367}, year = {2026}, } @article{21015, abstract = {Early embryo geometry is one of the most invariant species-specific traits, yet its role in ensuring developmental reproducibility and robustness remains underexplored. Here we show that in zebrafish, the geometry of the fertilized egg—specifically its curvature and volume—serves as a critical initial condition triggering a cascade of events that influence development. The embryo geometry guides patterned asymmetric cell divisions in the blastoderm, generating radial gradients of cell volume and nucleocytoplasmic ratio. These gradients generate mitotic phase waves, with the nucleocytoplasmic ratio determining individual cell cycle periods independently of other cells. We demonstrate that reducing cell autonomy reshapes these waves, emphasizing the instructive role of geometry-derived volume patterns in setting the intrinsic period of the cell cycle oscillator. In addition to organizing cell cycles, early embryo geometry spatially patterns zygotic genome activation at the midblastula transition, a key step in establishing embryonic autonomy. Disrupting the embryo shape alters the zygotic genome activation pattern and causes ectopic germ layer specification, underscoring the developmental significance of geometry. Together, our findings reveal a symmetry-breaking function of early embryo geometry in coordinating cell cycle and transcriptional patterning.}, author = {Mishra, Nikhil and Li, Yuting I and Hannezo, Edouard B and Heisenberg, Carl-Philipp J}, issn = {1745-2481}, journal = {Nature Physics}, pages = {139--150}, publisher = {Springer Nature}, title = {{Geometry-driven asymmetric cell divisions pattern cell cycles and zygotic genome activation in the zebrafish embryo}}, doi = {10.1038/s41567-025-03122-1}, volume = {22}, year = {2026}, } @article{21018, abstract = {In this paper, we review recent results on stability and instability in logarithmic Sobolev inequalities, with a particular emphasis on strong norms. We consider several versions of these inequalities on the Euclidean space, for the Lebesgue and the Gaussian measures, and discuss their differences in terms of moments and stability. We give new and direct proofs, as well as examples and discuss the stability of a logarithmic uncertainty principle. Although we do not cover all aspects of the topic, we hope to contribute to establishing the state of the art.}, author = {Brigati, Giovanni and Dolbeault, Jean and Simonov, Nikita}, issn = {2730-9657}, journal = {La Matematica}, publisher = {Springer Nature}, title = {{Logarithmic Sobolev Inequalities: A review on stability and instability results}}, doi = {10.1007/s44007-025-00180-y}, volume = {5}, year = {2026}, } @article{21275, abstract = {DNA methylation is a primary layer of epigenetic modification that plays a pivotal role in the regulation of development, aging, and cancer. The concurrent activity of opposing enzymes that mediate DNA methylation and demethylation gives rise to a biochemical cycle and active turnover of DNA methylation. While the ensuing biochemical oscillations have been implicated in the regulation of cell differentiation, their functional role and spatiotemporal dynamics are unknown. In this work, we demonstrate that chromatin-mediated coupling between these local biochemical cycles can lead to the emergence of phase-locked domains, regions of locally synchronized turnover activity, whose coarsening is arrested by genomic heterogeneity. We introduce a minimal model based on stochastic oscillators with constrained long-range and nonreciprocal interactions, shaped by the local chromatin organization. Through a combination of analytical theory and stochastic simulations, we predict both the degree of synchronization and the typical size of emergent phase-locked domains. We qualitatively test these predictions using single-cell sequencing data. Our results show that DNA methylation turnover exhibits surprisingly rich spatiotemporal patterns that may be used by cells to control cell differentiation.}, author = {Olmeda, Fabrizio and Gupta, Misha and Bektas, Onurcan and Rulands, Steffen}, issn = {2835-8279}, journal = {PRX Life}, publisher = {American Physical Society}, title = {{Spatiotemporal patterns of active epigenetic turnover}}, doi = {10.1103/89bj-79g5}, volume = {4}, year = {2026}, } @article{21344, abstract = {Tropospheric ozone has the potential to become an increasingly pressing public health issue in Bogotá, Colombia, due to rising concentrations across the city driven by complex interactions among emissions, meteorology, and urban structure. This study presents a comprehensive spatiotemporal analysis of ozone levels from 2013 to 2023 and assesses the associated health burden using mortality data from the same period. Results reveal a consistent upward trend in ozone concentrations, particularly in northern, western, and southern localities, with seasonal peaks linked to biomass burning and photochemical conditions. Mortality analysis, based on the Global Exposure Mortality Model, estimates that 18.3% of all deaths among individuals aged 25 and older are attributable to long-term ozone exposure. The highest burdens are found in densely populated and socioeconomically vulnerable areas such as Kennedy, Suba, and Ciudad Bolívar, with the elderly being the most affected. Building on these findings, we developed a machine learning prediction model for ozone using a convolutional merge with a long-short term memory network architecture trained on air quality and meteorological variables. The model demonstrated strong predictive performance (mean Rho=0.86, RMSE=3.5 μg/m3) across monitoring stations (17 with at least 35000 data points), supporting its potential application in real-time early warning systems across Bogotá. This integrated approach highlights the importance of localized air quality management, combining epidemiological assessment with predictive modeling. The findings underscore the urgency of implementing region-specific mitigation strategies and improving monitoring infrastructure to reduce health risks from ozone exposure in Bogotá’s rapidly growing urban environment.}, author = {Bustos, Daniela and Garcia, Diana and Rojas, Nestor Y. and Lopez-Barrera, Ellie A. and Peña-Rincon, Carlos and Casallas Garcia, Alejandro}, issn = {2509-9434}, journal = {Earth Systems and Environment}, publisher = {Springer Nature}, title = {{Ozone trends and mortality risk: The growing need for machine learning predictions in Bogotá, Colombia}}, doi = {10.1007/s41748-026-01052-3}, year = {2026}, } @article{21657, abstract = {We compare three global kilometer-scale models (ICON, IFS and NICAM) to clarify the advantages and challenges of high-resolution global weather and climate modeling, using different approaches to represent convection, from fully parameterized to fully explicit. Our analysis focuses on tropical precipitation characteristics spanning a wide range of spatio-temporal scales—including the diurnal cycle, extreme precipitation, convective organization, and the Madden-Julian Oscillation (MJO)—along with interactions between convection and the thermodynamic environment. All three models commonly show weaker convective organization with smaller precipitation cells than observed, though the strength of the bias varies by model. This diversity is introduced by differences in the representation of (a) convective initiation affected by the convective sensitivity to moisture and (b) tropospheric moistening associated with deep convection. Models with stronger thermodynamic-convection coupling increase environmental moisture near convection, thereby enhancing convective organization. This has important upscale effects on the MJO; while IFS and NICAM capture its eastward propagation well, ICON has difficulty reproducing it. The amplitudes and phases of precipitation diurnal cycles over land show much greater disagreement among the models than over ocean, influenced by how convection is initiated. Biases in rain evaporation and cold pool formation hinder the propagation of mesoscale convection, leading to errors such as the misrepresentation of nocturnal convection moving off the coast of Sumatra in IFS and ICON. These results highlight the importance of thermodynamic-convection coupling in realistically simulating tropical convection across scales. To improve this coupling, kilometer-scale models require better representation of the interaction between resolved convection and three-dimensional turbulent mixing.}, author = {Takasuka, Daisuke and Becker, Tobias and Bao, Jiawei}, issn = {1942-2466}, journal = {Journal of Advances in Modeling Earth Systems}, number = {3}, publisher = {Wiley}, title = {{Precipitation characteristics and thermodynamic-convection coupling in global kilometer-scale simulations}}, doi = {10.1029/2025MS005343}, volume = {18}, year = {2026}, } @article{21661, abstract = {Model checking undiscounted reachability and expected-reward properties on Markov decision processes (MDPs) are key for the verification of systems that act under uncertainty. Popular algorithms are policy iteration and variants of value iteration; in tool competitions, most participants rely on the latter. These algorithms generally need worst-case exponential time. However, the problem can equally be formulated as a linear programme, solvable in polynomial time. In this paper, we give a detailed overview of today’s state-of-the-art algorithms for MDP model checking with a focus on performance and correctness. We highlight their fundamental differences, and describe various optimizations and implementation variants. We experimentally compare floating-point and exact-arithmetic implementations of all algorithms on three benchmark sets using two probabilistic model checkers. Our results show that (optimistic) value iteration is a sensible default, but other algorithms are preferable in specific settings. This paper thereby provides a guide for MDP verification practitioners—tool builders and users alike.}, author = {Hartmanns, Arnd and Junges, Sebastian and Quatmann, Tim and Weininger, Maximilian}, issn = {1433-2787}, journal = {International Journal on Software Tools for Technology Transfer}, keywords = {Quantitative model checking, Markov decision process, Linear programming, Value iteration, Policy iteration}, publisher = {Springer Nature}, title = {{The revised practitioner’s guide to MDP model checking algorithms}}, doi = {10.1007/s10009-026-00848-y}, year = {2026}, } @article{21755, abstract = {Tropical shallow clouds are a major source of uncertainty in Earth's climate sensitivity, especially through their spatial arrangement, which global climate models do not represent. Efforts to understand their organization have partly relied on classifying observed scenes, identifying four patterns as archetypal regimes. Here we analyze geostationary satellite imagery of the western tropical Atlantic using the L‐function, a tool based on point pattern theory that quantifies cloud organization across spatial scales. Classical examples of the four patterns show distinct L‐function fingerprints, revealing their characteristic clustering and regularity scales and aiding physical interpretation. Yet, when evaluating many scenes at fixed spatial scales, the L‐function distribution lacks the distinct modes expected from discrete regimes. This is corroborated by analyses of other organization indices employing diverse approaches, from inter‐cloud nearest‐neighbor distances to fractal analysis. Implications for the parameterization of mesoscale cloud organization in climate models are discussed.}, author = {Biagioli, Giovanni and Mandorli, Giulio and Freischem, Lilli Johanna and Casallas Garcia, Alejandro and Tompkins, Adrian Mark}, issn = {1944-8007}, journal = {Geophysical Research Letters}, number = {8}, publisher = {Wiley}, title = {{Spatial patterns of shallow clouds: Challenging the concept of defined regimes}}, doi = {10.1029/2025gl119921}, volume = {53}, year = {2026}, } @article{21760, abstract = {3I/ATLAS is the third interstellar object discovered to date, following 1I/‘Oumuamua and 2I/Borisov. Its unusually high excess velocity and active cometary nature make it a key probe of the Galactic population of icy planetesimals. Understanding its origin requires its past trajectory through the Galaxy to be traced and the possible role of stellar encounters to be assessed, both as a potential origin and a perturber to its orbit. We integrated the orbit of 3I/ATLAS backward in time for 10 Myr, together with a sample of Gaia DR3 stars with high-quality astrometry and radial velocities, to identify close passages within 2 pc. We identify 93 nominal encounters, 62 of which are significant at the 2σ level. However, none of these encounters produced any meaningful perturbation. The strongest perturber Gaia DR3 6863591389529611264 at 0.30 pc and with a relative velocity of 35 km s−1, imparted only a velocity change of ∣Δv∣ ≃ 5 × 10−4 km s−1 to the orbit of 3I/ATLAS. Our results indicate that no stellar flybys within the past 10 Myr and 500 pc contained in Gaia DR3 can account for the present trajectory of 3I/ATLAS or be associated with its origin. We further show that 3I/ATLAS is kinematically consistent with a thin-disk population, despite its large peculiar velocity.}, author = {Pérez-Couto, X. and Torres Rodriguez, Santiago and Villaver, E. and Mustill, A. J. and Manteiga, M.}, issn = {1538-4357}, journal = {The Astrophysical Journal}, number = {2}, publisher = {IOP Publishing}, title = {{3I/ATLAS: In search of the witnesses to its voyage}}, doi = {10.3847/1538-4357/ae56ff}, volume = {1001}, year = {2026}, } @article{21884, abstract = {We show that a randomly perturbed digraph, where we start with a dense digraph Dα and add a small number of random edges to it, will typically contain a fixed orientation of a bounded-degree spanning tree. This answers a question posed by Araujo, Balogh, Krueger, Piga and Treglown and generalizes the corresponding result for randomly perturbed graphs by Krivelevich, Kwan and Sudakov. More specifically, we prove that there exists a constant c=c(α,Δ) such that if T is an oriented tree with maximum degree Δ and Dα is an n-vertex digraph with minimum semidegree αn, then the graph obtained by adding cn uniformly random edges to Dα will contain T with high probability.}, author = {Morawski, Patryk and Petrova, Kalina H}, issn = {1077-8926}, journal = {Electronic Journal of Combinatorics}, number = {2}, publisher = {Electronic Journal of Combinatorics}, title = {{Randomly perturbed digraphs also have bounded-degree spanning trees}}, doi = {10.37236/13316}, volume = {33}, year = {2026}, } @article{20422, abstract = {We show that if n is odd and p>=Clog n/n, then with high probability Hamilton cycles in G(n,p) span its cycle space. More generally, we show this holds for a class of graphs satisfying certain natural pseudorandom properties. The proof is based on a novel idea of parity-switchers, which can be thought of as analogues of absorbers in the context of cycle spaces. As another application of our method, we show that Hamilton cycles in a near-Dirac graph G, that is, a graph G with odd n vertices and minimum degree n/2+C for sufficiently large constant C, span its cycle space. }, author = {Christoph, Micha and Nenadov, Rajko and Petrova, Kalina H}, issn = {1096-0902}, journal = {Journal of Combinatorial Theory Series B}, pages = {254--267}, publisher = {Elsevier}, title = {{The Hamilton space of pseudorandom graphs}}, doi = {10.1016/j.jctb.2025.09.002}, volume = {176}, year = {2026}, } @article{20482, abstract = {In his study of graph codes, Alon introduced the concept of the odd-Ramsey number of a family of graphs H in Kn, defined as the minimum number of colours needed to colour the edges of K so that every copy of a graph H E H intersects some colour class in an odd number of edges. In this paper, we focus on complete bipartite graphs. First, we completely resolve the problem when H is the family of all spanning complete bipartite graphs on n vertices. We then focus on its subfamilies, that is, {Kt,n-t : t E T} for a fixed set of integers T c [[n/2]]. We prove that the odd-Ramsey problem is equivalent to determining the maximum dimension of a linear binary code avoiding codewords of given weights, and leverage known results from coding theory to deduce asymptotically tight bounds in our setting. We conclude with bounds for the odd-Ramsey numbers of fixed (that is, non-spanning) complete bipartite subgraphs.}, author = {Boyadzhiyska, Simona and Das, Shagnik and Lesgourgues, Thomas and Petrova, Kalina H}, issn = {0195-6698}, journal = {European Journal of Combinatorics}, publisher = {Elsevier}, title = {{Odd-Ramsey numbers of complete bipartite graphs}}, doi = {10.1016/j.ejc.2025.104235}, volume = {131}, year = {2026}, } @article{22247, abstract = {A linearly ordered (LO) k-colouring of a hypergraph is a colouring of its vertices with colours 1, …, k such that each edge contains a unique maximal colour. Deciding whether an input hypergraph admits LO k-colouring with a fixed number of colours is NP-complete (and in the special case of graphs, LO colouring coincides with the usual graph colouring). Here, we investigate the complexity of approximating the “linearly ordered chromatic number” of a hypergraph. We prove that the following promise problem is NP-complete: Given a 3-uniform hypergraph, distinguish between the case that it is LO 3-colourable, and the case that it is not even LO 4-colourable. We prove this result by a combination of algebraic, topological, and combinatorial methods, building on and extending a topological approach for studying approximate graph colouring introduced by Krokhin, Opršal, Wrochna, and Živný (2023).}, author = {Filakovský, Marek and Nakajima, Tamio Vesa and Opršal, Jakub and Tasinato, Gianluca and Wagner, Uli}, issn = {1942-3462}, journal = {ACM Transactions on Computation Theory}, keywords = {Constraint satisfaction problem, hypergraph colouring, promise problem, topological methods}, number = {2}, publisher = {Association for Computing Machinery}, title = {{Hardness of linearly ordered 4-colouring of 3-colourable 3-uniform hypergraphs}}, doi = {10.1145/3779121}, volume = {18}, year = {2026}, } @article{21385, abstract = {We prove that the average size of a mixed character sum (math. formular) (for a suitable smooth function w) is on the order of √x for all irrational real θ satisfying a weak Diophantine condition, where χ is drawn from the family of Dirichlet characters modulo a large prime r and where x 6 r. In contrast, it was proved by Harper that the average size is o(√x) for rational θ. Certain quadratic Diophantine equations play a key role in the present paper. }, author = {Wang, Victor and Xu, Max}, issn = {1473-7124}, journal = {Proceedings of the Royal Society of Edinburgh: Section A Mathematics}, pages = {1--15}, publisher = {Cambridge University Press}, title = {{Average sizes of mixed character sums}}, doi = {10.1017/prm.2026.10123}, year = {2026}, } @article{17437, abstract = {We prove that the zero-fiber of the moment map of a totally negative quiver has rational singularities. Our proof consists in generalizing dimension bounds on jet spaces of this fiber, which were introduced by Budur. We also transfer the rational singularities property to other moduli spaces of objects in 2-Calabi-Yau categories, based on recent work of Davison. This has interesting arithmetic applications on quiver moment maps and moduli spaces of objects in 2-Calabi-Yau categories. First, we generalize results of Wyss on the asymptotic behaviour of counts of jets of quiver moment maps over finite fields. Moreover, we interpret the limit of counts of jets on a given moduli space as its p-adic volume under a canonical measure analogous to the measure built by Carocci, Orecchia and Wyss on certain moduli spaces of coherent sheaves.}, author = {Vernet, Tanguy}, issn = {1531-586X}, journal = {Transformation Groups}, pages = {1047--1083}, publisher = {Springer Nature}, title = {{Rational singularities for moment maps of totally negative quivers}}, doi = {10.1007/s00031-024-09873-0}, volume = {31}, year = {2026}, } @article{20590, abstract = {Moist convection is a fundamental process occurring in the Earth's atmosphere. It plays a central role in the weather and climate of the Tropics, where, to first order, the heating of the atmosphere by convection is in balance with the cooling of the atmosphere by the emission of radiation to outer space. In this study, we use a cloud-resolving model in radiative–convective equilibrium with an imposed constant rate of radiative cooling and study the response of moist convection to varying this rate of radiative cooling. In particular, we study two types of simulation: varying air temperature (VAT) simulations, where the air temperature is allowed to adjust to the imposed radiative cooling, and constant air temperature (CAT) simulations, where the surface temperature is tuned to ensure that the atmospheric temperature profile in the domain is constant. We recover the previously known result that, in response to increasing radiative cooling, the area of convection expands rapidly, while the intensity of convection does not change. We find that this response is explained by the increased boundary-layer variability in simulations with greater radiative cooling, which compensates for the decreasing temperature by adding a larger initial velocity close to the cloud base. We also propose a fundamental scaling of the non-dimensional cumulus mass flux in moist convection, which is robust across models of different complexity. We aim to bridge the gap between highly idealised prototypes of moist convection, such as the “Rainy–Bénard convection” introduced by Vallis et al., and comprehensive cloud-resolving models.}, author = {Agasthya, Lokahith N and Muller, Caroline J}, issn = {1477-870X}, journal = {Quarterly Journal of the Royal Meteorological Society}, number = {775}, publisher = {Wiley}, title = {{Moist convection and radiative cooling: Dynamical response and scaling}}, doi = {10.1002/qj.70044}, volume = {152}, year = {2026}, } @article{20655, abstract = {Traits that affect organismal fitness are often highly genetically variable. This genetic variation is vital for populations to adapt to their environments, but it is also surprising given that nature – after all – ‘selects’ the best genotypes at the expense of those that fall short. Explaining the extensive genetic variation of fitness‐related traits is thus a longstanding puzzle in evolutionary biology, with cascading implications for ecology, conservation, and human health. Balancing selection – an umbrella term for scenarios in which natural selection maintains genetic variation – is a century‐old explanation to resolve this puzzle that has gained recent momentum from genome‐scale methods for detecting it. Yet evaluating whether balancing selection can, in fact, resolve the puzzle is challenging, given the logistical constraints of distinguishing balancing selection from alternative hypotheses and the daunting collection of theoretical models that formally underpin this debate. Here, we track the development of balancing selection theory over the last century and provide an accessible review of this rich collection of models. We first outline the range of biological scenarios that can generate balancing selection. We then examine how fundamental features of genetic systems – non‐random mating between individuals, ploidy levels, genetic drift, linkage, and genetic architectures of traits – have been progressively incorporated into the theory. We end by linking these theoretical predictions to ongoing empirical efforts to understand the evolutionary processes that explain genetic variation.}, author = {Ruzicka, Filip and Zwoinska, Martyna K. and Goedert, Debora and Kokko, Hanna and Li Richter, Xiang‐Yi and Moodie, Iain R. and Nilén, Sofie and Olito, Colin and Svensson, Erik I. and Czuppon, Peter and Connallon, Tim}, issn = {1469-185X}, journal = {Biological Reviews}, keywords = {evolutionary theory, population genetics, balancing selection, heterozygote advantage, trade-offs, negative frequency-dependent selection, fitness variation, mathematical modelling}, number = {2}, publisher = {Wiley}, title = {{A century of theories of balancing selection}}, doi = {10.1111/brv.70103}, volume = {101}, year = {2026}, } @article{21217, abstract = {This study investigates the mechanisms driving clustered convection and the breakdown of the Intertropical Convergence Zone (ITCZ) over the Western Pacific Warm Pool using high‐resolution cloud‐resolving simulations and machine‐learning sensitivity experiments. Results show that ITCZ breakdown episodes, marked by spatially homogeneous convection and weakened meridional moisture gradients, are triggered primarily by anomalous moisture advection linked to the equatorial Rossby‐wave activity. While large‐scale moisture advection regulates the background convective state strongly, it is the surface and low‐level meridional winds that dominate transitions between clustered and random convection. Simulations demonstrate that moisture alone can sustain convective clustering, but breakdown episodes are more persistent and widespread when coupled with southerly meridional advection. These findings confirm that wave‐driven advection acts as a regulatory mechanism, periodically disrupting convective clustering and reshaping the meridional moisture gradient. This modulation of organization by wave‐induced breakdown events is critical for understanding tropical convection variability and its implications for the climate system.}, author = {Casallas Garcia, Alejandro and Mark Tompkins, Adrian and Muller, Caroline J}, issn = {1477-870X}, journal = {Quarterly Journal of the Royal Meteorological Society}, number = {777}, publisher = {Wiley}, title = {{Moisture and wind effects of Rossby waves on Western Pacific Intertropical Convergence Zone breakdown events}}, doi = {10.1002/qj.70131}, volume = {152}, year = {2026}, } @article{21504, abstract = {Selecting an appropriate divergence measure is a critical aspect of machine learning, as it directly impacts model performance. Among the most widely used, we find the Kullback–Leibler (KL) divergence, originally introduced in kinetic theory as a measure of relative entropy between probability distributions. Just as in machine learning, the ability to quantify the proximity of probability distributions plays a central role in kinetic theory. In this paper, we present a comparative review of divergence measures rooted in kinetic theory, highlighting their theoretical foundations and exploring their potential applications in machine learning and artificial intelligence.}, author = {Auricchio, Gennaro and Brigati, Giovanni and Giudici, Paolo and Toscani, Giuseppe}, issn = {1793-6314}, journal = {Mathematical Models and Methods in Applied Sciences}, number = {6}, pages = {1185--1233}, publisher = {World Scientific Publishing}, title = {{From kinetic theory to AI: A rediscovery of high-dimensional divergences and their properties}}, doi = {10.1142/S0218202526410010}, volume = {36}, year = {2026}, } @article{21849, abstract = {The development of complex tissues relies on the precise assignment of cell identity. At the molecular scale, this process depends on the deposition of epigenetic modifications—such as methylation—that are regulated by complex biochemical networks and occur at specific regions on the DNA and chromatin. Here we show that despite the complexity of epigenetic regulation, dynamical scaling and self-similarity of DNA methylation marks emerge in embryonic development. Drawing on single-cell multi-omics experiments, super-resolution microscopy and statistical physics, we demonstrate that these phenomena originate in dynamical feedback between DNA methylation and the formation of nanoscale dynamic chromatin aggregates. These nanoscale processes lead to genome-wide increase in DNA methylation marks following a power law and self-similar correlation functions. Using this framework, we identify methylation patterns that precede gene expression changes in embryonic symmetry breaking. Our work identifies linear sequencing measurements as a laboratory to study mesoscopic biophysical processes in vivo.}, author = {Olmeda, Fabrizio and Lohoff, Tim and Kafetzopoulos, Ioannis and Clark, Stephen J. and Benson, Laura and Santos, Fatima and Krueger, Felix and Walker, Simon and Reik, Wolf and Rulands, Steffen}, issn = {1745-2481}, journal = {Nature Physics}, pages = {931--940}, publisher = {Springer Nature}, title = {{Scaling and self-similarity in the formation of the embryonic epigenome}}, doi = {10.1038/s41567-026-03263-x}, volume = {22}, year = {2026}, }