@misc{21145, abstract = {Protein conformational energy landscapes are shaped not only by intramolecular interactions but also by their environment. In protein crystals and protein-protein complexes, intermolecular contacts alter this energy landscape, but the exact nature of this alteration is difficult to decipher. Understanding how the crystal lattice affects protein dynamics is crucial for crystallography-based studies of motion, yet its influence on collective motions remains unclear. Aromatic ring flips in the hydrophobic core represent sensitive probes of such dynamics. Here, we compare the kinetics of aromatic ring flips in the protein GB1 in crystals, in complex with its binding partner IgG, and in solution, combining advanced isotope labeling with quantitative NMR methods. We show that rings in the core flip nearly a thousand times less frequently in crystals than in solution. Enhanced-sampling molecular dynamics simulations, based on a new crystal structure, reproduce these elevated barriers and reveal how the crystal restrains motions. }, author = {Becker, Lea Marie and Schanda, Paul and Chipot, Christophe}, publisher = {Institute of Science and Technology Austria}, title = {{Additional Data for "Aromatic Ring Flips Reveal Reshaping of Protein Dynamics in Crystals and Complexes"}}, doi = {10.15479/AT-ISTA-21145}, year = {2026}, } @article{22613, abstract = {A phase plate has long been sought in transmission electron microscopy (TEM) to maximize the image contrast of weakly-scattering objects like biomolecules. The laser phase plate (LPP) has recently demonstrated that an amplified, focused laser standing wave reliably phase shifts the electron beam, achieving phase-contrast TEM. Building on the single-beam LPP, here we introduce the crossed laser phase plate (XLPP): two laser standing waves which intersect in the diffraction plane. We present a theoretical model for the XLPP inside the microscope and show that, relative to the original LPP, it increases information transfer at low spatial frequencies while suppressing ghost images formed by Kapitza-Dirac diffraction. We also present a simple acquisition scheme, enabled by the XLPP, which further suppresses ghosts. Finally, we discuss practical considerations of XLPP design and show experimental results from a prototype. The results of this study chart the course for future developments of LPP hardware.}, author = {Petrov, Petar N and Zhang, Jessie T. and Axelrod, Jeremy J. and Olshin, Pavel K. and Müller, Holger}, issn = {2041-1723}, journal = {Nature Communications}, publisher = {Springer Nature}, title = {{Crossed laser phase plates for transmission electron microscopy}}, doi = {10.1038/s41467-026-74060-6}, volume = {17}, year = {2026}, } @article{22365, abstract = {Phase plates can, in principle, overcome the poor image contrast in cryo–electron microscopy (cryo-EM) and the resulting limits on the structural reconstruction of small proteins. However, previous designs have been unstable and compromised the high-resolution signal and have thus been unable to surpass results achieved by standard cryo-EM. Here, we show that the laser phase plate (LPP), installed in a modern, custom Titan Krios microscope, enhances the resolution in single-particle reconstruction of small proteins by improving specimen-motion correction and recovery of information from the early frames, as well as particle visualization, three-dimensional classification, and alignment. These advances use standard defocus ranges and reconstruction procedures but open the door to LPP-tailored protocols, offering further improvements by leveraging the LPP demonstrated here.}, author = {Petrov, Petar N and Zhang, Jessie T. and Remis, Jonathan and Axelrod, Jeremy J. and Cheng, Hang and Cooper, Eric S. and Hicklin, Ian K. and Sandhaus, Shahar and Schnurr, Cooper and Glaeser, Robert M. and Müller, Holger}, issn = {1095-9203}, journal = {Science}, number = {6807}, pages = {195--196}, publisher = {AAAS}, title = {{Laser phase plate improves structure determination of small proteins by cryo-EM}}, doi = {10.1126/science.aeh0665}, volume = {393}, year = {2026}, } @article{22443, abstract = {Society faces increasingly severe flood hazards, intensifying demand for flood early warning systems (FEWS) that deliver accurate and actionable information. However, most existing FEWS remain prediction‐centric, treating decision‐making as a downstream consumer of hazard forecasts while offering limited support for uncertainty interpretation, risk communication, and real‐world response. This Perspective presents a vision and blueprint for a novel inland FEWS‐decision‐making (FEWS‐DM) framework that repositions decision‐making as an equal partner in the forecasting process—not a passive recipient of its outputs. The framework is built on three tightly coupled, co‐evolving thrusts: Physical Science (T1), which advances flood prediction with quantified uncertainty informed by decision relevance; Human Science (T2), which incorporates psychology, behavior, and cultural and institutional context; and Decision Science (T3), which unifies physical predictions and human factors through principled, utility‐based decision support with end‐to‐end uncertainty management. Rather than treating T1 as a solved problem, FEWS‐DM recognizes that forecast development itself must be shaped by decision needs through continuous bidirectional feedback. We identify key scientific, behavioral, and operational challenges limiting such integration and discuss the enabling role of AI, while emphasizing human‐centered design and community feedback as essential for building trust and improving flood risk management.}, author = {Tran, Vinh Ngoc and Huan, Xun and Antar, Anindya Das and Banovic, Nikola and Bednar, Jeff H. and Bergt, Shannon Marie and Cheng, Chen and Dominguez, Francina and Fatichi, Simone and Gonzalez, Richard and Gray, Kevin and Jewett, Brian and Kim, Jongho and Le, Phong V.V. and Lu, Dan and Prabhudesai, Snehal and Putri, Deffi and Rath, Sudhansu and Sargsyan, Khachik and Whitaker, Sarah H. and Wright, Daniel B. and Xu, Donghui and Ziker, John P. and Ivanov, Valeriy Y.}, issn = {2328-4277}, journal = {Earth's Future}, number = {6}, publisher = {American Geophysical Union}, title = {{Reimagining how flood warnings can inform decision‐making and community actions}}, doi = {10.1029/2026ef008857}, volume = {14}, year = {2026}, } @article{21381, abstract = {The lack of long-range electrostatics is a key limitation of modern machine learning interatomic potentials (MLIPs), hindering reliable applications to interfaces, charge-transfer reactions, polar and ionic materials, and biomolecules. In this Perspective, we distill two design principles behind the Latent Ewald Summation framework, which can capture long-range interactions, charges, and electrical response just by learning from standard energy and force training data: (i) use a Coulomb functional form with environment-dependent charges to capture electrostatic interactions, and (ii) avoid explicit training on ambiguous density functional theory partial charges. When both principles are satisfied, substantial flexibility remains: essentially any short-range MLIP can be augmented; charge equilibration schemes can be added when desired; dipoles and Born effective charges can be inferred or fine-tuned; and charge/spin-state embeddings or tensorial targets can be further incorporated. We also discuss current limitations and open challenges. Together, these minimal, physics-guided design rules suggest that incorporating long-range electrostatics into MLIPs is simpler and perhaps more broadly applicable than is commonly assumed.}, author = {Kim, Dongjin and Cheng, Bingqing}, issn = {1089-7690}, journal = {The Journal of Chemical Physics}, number = {6}, publisher = {AIP Publishing}, title = {{Long-range electrostatics for machine learning interatomic potentials is easier than we thought}}, doi = {10.1063/5.0316886}, volume = {164}, year = {2026}, } @article{22441, abstract = {Warming impacts both net primary production (NPP) and soil organic carbon (SOC) decomposition, and consequently, SOC storage. However, the role of warming in regulating SOC storage remains debated. Here, we leverage literature data of warming experiments and a mechanistic model to explore SOC responses to warming by partitioning the effects of air and soil warming. Both the literature data and numerical model show that air and soil warming play distinct roles in regulating SOC storage, with insignificant SOC responses under air warming and negative responses to soil warming. Soil warming decreases SOC storage because of temperature-driven increases in decomposition rate. Air warming effects on SOC are more complex. In some cases, air warming can lead to a lower NPP and higher decomposition rate. In others, air warming can stimulate NPP and enhance soil moisture depletion that inhibits SOC decomposition. Once the latter mechanisms dominate, SOC storage increases with air warming.}, author = {Luo, Zhaoyang and Ren, Jianning and Fatichi, Simone}, issn = {2662-4435}, journal = {Communications Earth & Environment}, publisher = {Springer Nature}, title = {{Air and soil warming have different effects on soil organic carbon storage}}, doi = {10.1038/s43247-026-03367-5}, volume = {7}, year = {2026}, } @article{22528, abstract = {Quantification of the impact of environmental stress on terrestrial vegetation photosynthesis is crucial for our understanding of the global carbon cycle, particularly under a changing climate. Vegetation responses to environmental stress manifest first as plant physiological changes, and at later stages through changes in canopy structure. Here we leverage CO2 and water flux data from 103 eddy covariance towers and satellite thermal images to assess whether current satellite reconstructions of solar-induced chlorophyll fluorescence capture these plant mechanisms. After removing seasonality using standardized anomalies (z-scores), we found that the relationship between tower-observed gross primary productivity and fluorescence reconstructions considerably weakened across a wide range of biomes. This loss of correlation results from a decoupling between stomatal responses and the physiological emission yield (ΦF) of fluorescence reconstructions during soil and atmospheric dry periods. The consequence is that productivity derived from fluorescence reconstructions will be progressively overestimated as dry conditions persist.}, author = {Zhao, Jiacheng and Paschalis, Athanasios and Gentine, Pierre and Feng, Zhaozhong and Fatichi, Simone}, issn = {2662-4435}, journal = {Communications Earth & Environment}, publisher = {Springer Nature}, title = {{Limited capability of current satellite solar-induced chlorophyll fluorescence reconstructions to capture stomatal responses to environmental stresses}}, doi = {10.1038/s43247-025-03035-0}, volume = {7}, year = {2026}, } @article{22663, abstract = {The detection of strong, large-scale magnetic fields at the surfaces of the oldest white dwarfs might point toward a hidden internal magnetic field slowly rising to the surface. In addition, strong magnetic fields have recently been measured through asteroseismology in the radiative interiors of red giant stars, the progenitors of white dwarfs. To investigate the potential connection between these observations, we revisited the fossil field framework using asteroseismic detections to constrain the strength of such magnetic fields as red giants evolve into the white dwarf stage. We assumed that the magnetic field was either created during the core convection on the main sequence or that it fills the radiative interior as the star evolves on the red giant branch. From these initial conditions, we evolved the magnetic flux, allowing for magnetic diffusion along the evolution of a modeled 1.5 M⊙ star. We find that measured field strengths in red giants attributed to the hydrogen-burning shell are compatible with the field amplitudes and emergence timescales of magnetized white dwarfs. On the contrary, magnetic fields generated solely from a convective-core dynamo on the main sequence and detectable on the red giant branch would be buried too deep in the star and would not match the breakout timescales or the field strengths of magnetic white dwarfs. Therefore, for us to connect magnetic fields observed along the late evolution of stars via a fossil field we would need to find a broadly magnetized internal radiative zone on the red giant branch.}, author = {Einramhof, Lukas and Bugnet, Lisa Annabelle and Calcaferro, L. M. and Barrault, Lucas and Das, S. B.}, issn = {1432-0746}, journal = {Astronomy & Astrophysics}, publisher = {EDP Sciences}, title = {{Magneto-archeology of white dwarfs}}, doi = {10.1051/0004-6361/202659069}, volume = {708}, year = {2026}, } @article{22648, abstract = {Bifurcation characterizes the qualitative changes in parameterized dynamical systems and is one of the major topics in the field. In this work, we study combinatorial bifurcations within the framework of combinatorial dynamical systems—a young but already well-established theory. We introduce the Conley–Morse persistence barcode, a compact algebraic descriptor of combinatorial bifurcations. This barcode captures structural changes in a dynamical system at the level of Morse decompositions and provides a characterization of the nature of observed transitions in terms of the Conley index. The construction of the Conley–Morse persistence barcode builds upon ideas from topological persistence. Specifically, we consider a persistence module obtained from the Conley index of invariant sets indexed over a poset. Using gentle algebras, we prove that this module decomposes into simple intervals (bars) and compute them by adapting the zigzag persistence algorithm to our purpose.}, author = {Dey, Tamal K. and Lipiński, Michał and Soriano Trigueros, Manuel}, issn = {1615-3383}, journal = {Foundations of Computational Mathematics}, keywords = {Multivector field, Conley index, Morse decomposition, Bifurcation, Continuation, Zigzag persistence, Persistence barcode, Gentle algebra}, publisher = {Springer}, title = {{Conley-Morse persistence barcode: A homological signature of combinatorial bifurcations}}, doi = {10.1007/s10208-026-09766-6}, year = {2026}, } @article{22677, abstract = {Study region: The Vilcanota Urubamba Basin in southern Peru includes fragile wetland ecosystems that play a key role in mountain hydrology and support grazing for Andean communities. Study focus: Mapping of wetlands variability is missing, limiting our understanding of their characteristics, seasonality and link with the cryosphere. We characterise wetland distribution, seasonality and persistence and evaluate their spatial association with glaciers and seasonal snow. Using Landsat 7 and 8 imagery, we build three-month seasonal land cover maps from 2013 to 2022 using a Random Forest classification and an Albedo Retrieval approach. New hydrological insights for the region: Wetland area decreases by 38% from the end of the wet season (October to December) to the end of the dry season (July to September). Pixel transitions indicate that wetlands primarily transform to and from agricultural and pasture lands. Highly persistent wetlands are located above 4600 m a.s.l. and closer to glaciers than less persistent wetlands. We identified three wetland seasonal drying patterns. Basins with delayed and slow dry-out wetlands were more common at higher elevations but were not always in glacierised catchments, suggesting meltwater may maintain wetlands in the early dry season. We provide the first large-scale picture of wetland seasonality, and the basis for modelling the processes that sustain wetlands in tropical high mountains.}, author = {Castro, Joshua and Fyffe, Catriona Louise and Shaw, Thomas and Miles, Evan and Potter, Emily and Hoelzle, Martin and Varghese, Vinisha and Pellicciotti, Francesca}, issn = {2214-5818}, journal = {Journal of Hydrology: Regional Studies}, publisher = {Elsevier}, title = {{Andean wetlands: Seasonal variability and their interactions with the cryosphere}}, doi = {10.1016/j.ejrh.2026.103808}, volume = {67}, year = {2026}, } @article{22675, abstract = {Tidal disruption events (TDEs) have traditionally been discovered in optical sky surveys through targeted searches of nuclear transients. However, it is expected that some TDEs will occur outside the galaxy nucleus, arising from wandering black holes (BHs) originating in galaxy mergers. Here, we present observations of TDE 2025abcr, the first optical TDE discovered in the outskirts of a host galaxy. The TDE was identified by a custom “off-nuclear” implementation of the machine learning classifier tdescore, which classifies new ZTF transients based on their lightcurves. Follow-up observations confirm that TDE 2025abcr is a TDE-H+He, occurring 9 5 (9.3 kpc projected distance) from the nucleus of a massive galaxy (M⋆ = 1011.18±0.03M⊙) with a central BH mass of 108.82±0.65M⊙. TDE 2025abcr itself was likely disrupted by a much lighter BH (106.09±0.53M⊙, as estimated with peak luminosity scaling relations). The BH was either dynamically ejected from the nucleus or lies at the center of a very faint tidally stripped dwarf galaxy undergoing a minor merger. Late-time observations of TDE 2025abcr could confirm the origin of this apparent “wandering” BH. The rate of highly offset (≳3 kpc) TDEs can be constrained to <10% of the nuclear TDE rate, but our discovery implies that many dozens of similar sources will be detected by the Vera C. Rubin Observatory each year with resolvable offsets.}, author = {Stein, Robert and Carney, Jonathan and Ward, Charlotte and Margutti, Raffaella and Hall, Xander J. and Sfaradi, Itai and Andreoni, Igor and Charalampopoulos, Panos and Chornock, Ryan and Gezari, Suvi and Mo, Geoffrey and Yao, Yuhan and Anumarlapudi, Akash and Bellm, Eric C. and Bloom, Joshua S. and Busmann, Malte and Caiazzo, Ilaria and Cenko, S. Bradley and Graham, Matthew J. and Groom, Steven L. and Gruen, Daniel and Hammerstein, Erica and Kaiser, Benjamin C. and Kasliwal, Mansi M. and O’Connor, Brendan and Palmese, Antonella and Purdum, Josiah and Rastinejad, Jillian C. and Riddle, Reed and Rusholme, Ben and Sollerman, Jesper and Somalwar, Jean J. and Veilleux, Sylvain}, issn = {2041-8213}, journal = {The Astrophysical Journal Letters}, number = {2}, publisher = {IOP Publishing}, title = {{TDE 2025abcr: A tidal disruption event in the outskirts of a massive galaxy}}, doi = {10.3847/2041-8213/ae77f3}, volume = {1006}, year = {2026}, } @article{22674, abstract = {Identification of the genomic regions that contribute to reproductive isolation and how they interact is a major goal of evolutionary genetics. Much effort has focused on locating candidate genes and potential barrier loci by scanning genomes for regions of excess differentiation (FST). An alternative, and perhaps more robust approach, is to scan for genomic regions exhibiting steep clines in allele frequency across a hybrid zone. We develop a computationally efficient method for approximating cline parameters for large number of loci, and apply it to genomic data from across a hybrid zone between flower colour varieties of Antirrhinum majus (A. m. m var. pseudomajus and A. m. m var. striatum). Most steep clines are clustered in seven genomic regions, only four of which were present from FST scans between all pair-wise comparisons. Six of these regions carry previously identified loci that influence flower colour in the hybrid zone. The seventh region harbours a novel locus, RUBIA, modifying magenta intensity. Clines at RUBIA approached fixation on the magenta side of the hybrid zone, whilst remaining polymorphic on the yellow side. This polymorphism on the yellow side may reflect a smaller phenotypic effect of RUBIA in yellow compared to magenta genetic backgrounds. Our findings illustrate how whole-genome cline scans in hybrid zones can robustly detect genomic regions contributing to phenotypic differences and highlight how different reproductive barrier loci interact across the genome.}, author = {Field, David and Stankowski, Sean and Reiter, Taylor and Polechova, Jitka and Bradley, Desmond and Richardson, Daniel M. and Whibley, Annabel and Pal, Arka and Shipilina, Daria and Boell, Louis and Pickup, Melinda and Xue, Yongbiao and Coen, Enrico and Barton, Nicholas H}, issn = {1553-7404}, journal = {PLOS Genetics}, number = {7}, publisher = {Public Library of Science}, title = {{Genome-wide cline analysis identifies new locus contributing to a barrier to gene flow across an Antirrhinum hybrid zone}}, doi = {10.1371/journal.pgen.1012173}, volume = {22}, year = {2026}, } @article{22676, abstract = {We search for a population-level signature of gravitational-wave recoiling supermassive black holes: a positive correlation between dust obscuration and the magnitude of the line-of-sight velocity offset of broad emission lines relative to the host. Using the SDSS DR16 quasar catalogue, we estimate the velocity offset, $\Delta v$, as the difference between the broad H$\beta$ redshift and a noise-weighted redshift from narrow lines ([O iii] 5007, [O ii] 3728, and Ca ii 3934). We adopt the redshift-relative colour excess $\Delta (g-i)$ as a proxy for dust column density. Analysing $\sim 10^{5}$ quasars that meet basic spectral quality requirements, we find a modest but highly significant positive correlation between $|\Delta v|$ and $\Delta (g-i)$ (Spearman $r\simeq 0.12$ and Pearson $r\simeq 0.13$, with $p\ll 10^{-10}$ in both cases). The fraction of highly obscured quasars increases with $|\Delta v|$, indicating that the correlation is driven by a dust-reddened subpopulation. The result is robust to the choice of minimum $|\Delta v|$ threshold and to the line redshift estimator (peak vs. centroid). As expected, the correlation is largely absent when velocity offsets are computed between narrow emission lines. We find systematic differences between redshifted and blueshifted subsamples, which may point to residual velocity biases or additional physical effects (e.g. winds, inflows, orientation-dependent obscuration, or asymmetric broad-line regions). Recoiling massive black holes provide a natural explanation for the observed correlation, but alternative scenarios should be explored. If confirmed, this would enable population-level constraints on massive black hole merger rates, recoil dynamics, and active galactic nuclei disc properties.}, author = {Bécsy, Bence and Raffai, Peter and Haiman, Zoltán and Budai, Andor and Frei, Zsolt}, issn = {1365-2966}, journal = {Monthly Notices of the Royal Astronomical Society}, number = {4}, publisher = {Oxford University Press}, title = {{Statistical evidence for massive black hole recoils in active galactic nuclei}}, doi = {10.1093/mnras/stag1367}, volume = {550}, year = {2026}, } @phdthesis{22626, author = {Fiedler, Christine}, isbn = {978-3-99078-086-2}, issn = {2663-337X}, pages = {141}, publisher = {Institute of Science and Technology Austria}, title = {{Mechanistic insight into solution-processed p-type tin chalcogenides as a basis for designing their n-type analogs}}, doi = {10.15479/AT-ISTA-22626}, year = {2026}, } @article{22228, abstract = {In a mixed generalized linear model, the goal is to learn multiple signals from unlabeled observations: each sample comes from exactly one signal, but it is not known which one. We consider the prototypical problem of estimating two statistically independent signals in a mixed generalized linear model with Gaussian covariates. Spectral methods are a popular class of estimators which output the top two eigenvectors of a suitable data-dependent matrix. However, despite the wide applicability, their design is still obtained via heuristic considerations, and the number of samples 𝑛 needed to guarantee recovery is superlinear in the signal dimension 𝑑. In this paper, we develop exact asymptotics on spectral methods in the challenging proportional regime in which 𝑛,𝑑 grow large and their ratio converges to a finite constant. This allows us optimize the design of the spectral method, and combine it with a simple linear estimator, to minimize the estimation error. Our characterization exploits a mix of tools from random matrices, free probability, and the theory of approximate message passing algorithms. Numerical simulations for mixed linear regression and phase retrieval demonstrate the advantage enabled by our analysis over existing designs of spectral methods.}, author = {Zhang, Yihan and Mondelli, Marco and Venkataramanan, Ramji}, issn = {2577-0187}, journal = {SIAM Journal on Mathematics of Data Science}, keywords = {spectral estimator, generalized linear models, mixed regression, high-dimensional asymptotics, random matrix theory, approximate message passing (AMP)}, number = {2}, pages = {411--439}, publisher = {SIAM}, title = {{Precise asymptotics for spectral methods in mixed generalized linear models}}, doi = {10.1137/24m1702854}, volume = {8}, year = {2026}, } @article{20585, abstract = {Motivated by applications in medical sciences, we study finite chromatic sets in Euclidean space from a topological perspective. Based on the persistent homology for images, kernels and cokernels, we design provably stable homological quantifiers that describe the geometric micro- and macro-structure of how the color classes mingle. These can be efficiently computed using chromatic variants of Delaunay and alpha complexes, and code that does these computations is provided.}, author = {Cultrera di Montesano, Sebastiano and Draganov, Ondrej and Edelsbrunner, Herbert and Saghafian, Morteza}, issn = {2639-8001}, journal = {Foundations of Data Science}, keywords = {Topological data analysis, Delaunay mosaic, alpha complex, chromatic sets, persistent homology, kernel/image/cokernel persistent homology, radius function, discrete Morse theory, exact sequences}, pages = {30--62}, publisher = {AIMS}, title = {{Chromatic alpha complexes}}, doi = {10.3934/fods.2025003}, volume = {8}, year = {2026}, } @article{21132, abstract = {We unify the variational hypocoercivity framework established by D. Albritton, S. Armstrong, J.-C. Mourrat, and M. Novack [2], with the notion of second-order lifts of reversible diffusion processes, recently introduced by A. Eberle and the second author [30]. We give an abstract, yet fully constructive, presentation of the theory, so that it can be applied to a large class of linear kinetic equations. As this hypocoercivity technique does not twist the reference norm, we can recover accurate and sharp convergence rates in various models. Among those, adaptive Langevin dynamics (ALD) is discussed in full detail and we show that for near-quadratic potentials, with suitable choices of parameters, it is a near-optimal second-order lift of the overdamped Langevin dynamics. As a further consequence, we observe that the Generalised Langevin Equation (GLE) is also a second-order lift, as the standard (kinetic) Langevin dynamics are, of the overdamped Langevin dynamics. Then, convergence of (GLE) cannot exceed ballistic speed, i.e. the square root of the rate of the overdamped regime. We illustrate this phenomenon with explicit computations in a benchmark Gaussian case.}, author = {Brigati, Giovanni and Lörler, Francis and Wang, Lihan}, issn = {1937-5077}, journal = {Kinetic and Related Models}, pages = {34--55}, publisher = {AIMS}, title = {{Hypocoercivity meets lifts}}, doi = {10.3934/krm.2025020}, volume = {20}, year = {2026}, } @article{20980, abstract = {Morse decompositions partition the flows in a vector field into equivalent structures. Given such a decomposition, one can define a further summary of its flow structure by what is called a connection matrix. These matrices, a generalization of Morse boundary operators from classical Morse theory, capture the connections made by the flows among the critical structures—such as attractors, repellers, and orbits—in a vector field. Recently, in the context of combinatorial dynamics, an efficient persistence-like algorithm to compute connection matrices has been proposed in Dey, Lipiński, Mrozek, and Slechta [SIAM J. Appl. Dyn. Syst., 23 (2024), pp. 81–97]. We show that, actually, the classical persistence algorithm with exhaustive reduction retrieves connection matrices, both simplifying the algorithm of Dey et al. and bringing the theory of persistence closer to combinatorial dynamical systems. We supplement this main result with an observation: the concept of persistence as defined for scalar fields naturally adapts to Morse decompositions whose Morse sets are filtered with a Lyapunov function. We conclude by presenting preliminary experimental results.}, author = {Dey, Tamal K. and Haas, Andrew and Lipiński, Michał}, issn = {1536-0040}, journal = {SIAM Journal on Applied Dynamical Systems}, number = {1}, pages = {108--130}, publisher = {SIAM}, title = {{Computing a connection matrix and persistence efficiently from a morse decomposition}}, doi = {10.1137/25m1739406}, volume = {25}, year = {2026}, } @inproceedings{22405, abstract = {Computing the diameter of the intersection graphs of objects is a basic problem in computational geometry. Previous works showed that the complexity of computing the diameter mainly depends on the object types: for unit disks and squares in 2D, the problem is solvable in truly subquadratic time [Chan et al., 2025], while for other objects, including unit segments and equilateral triangles in 2D or unit balls and axis-parallel unit cubes in 3D, there is no truly subquadratic time algorithm under the Orthogonal Vector (OV) hypothesis [Bringmann et al., 2022]. We undertake a comprehensive study of computing the diameter of geometric intersection graphs for various types of objects. We discover many new irregularities, showing that the landscape is extremely nuanced: the source of hardness is a combination of the object type, the true diameter value, and how the objects intersect with each other. Our highlighted results for the 2D case include: 1) The diameter of non-degenerate, axis-aligned line segments can be computed in truly subquadratic time. Previous hardness result [Bringmann et al., 2022] for line segments applies only to degenerate instances. On the other hand, for the degenerate case, we show that a truly subquadratic time algorithm exists when the true diameter is constant. 2) An almost-linear-time algorithm for unit-square graphs of constant diameter. Previous algorithms [Duraj et al., 2024; Chan et al., 2025] rely on succinct representation assuming bounded VC-dimension; for such a strategy Ω(n^{7/4}) time is an inherent barrier. 3) An Õ(n^{4/3})-time algorithm to decide if the diameter of a unit-disk graph is at most 2. This improves upon the recent algorithm with running time Õ(n^{2-1/9}) [Chan et al., 2025]. 4) Deciding if the diameter of intersection graphs of fat triangles or line segments is at most 2 is truly subquadratic-hard under fine-grained complexity assumptions. Previous lower bounds [Bringmann et al., 2022] only hold when deciding if diameter is at most 3. Our findings are presented in a pair of papers. This paper focuses solely on the 2D case, while the companion paper is devoted to higher-dimensional cases.}, author = {Chan, Timothy M. and Chang, Hsien-Chih and Gao, Jie and Kisfaludi-Bak, Sándor and Le, Hung and Zheng, Da Wei}, booktitle = {53rd International Colloquium on Automata, Languages, and Programming}, issn = {1868-8969}, keywords = {String graphs, Fine-grained complexity, Theory of computation → Computational geometry}, location = {Egham, United Kingdom}, publisher = {Schloss Dagstuhl - Leibniz-Zentrum für Informatik}, title = {{Charting the landscape of diameter computation on geometric intersection graphs in the plane}}, doi = {10.4230/LIPICS.ICALP.2026.54}, volume = {374}, year = {2026}, } @inproceedings{22299, abstract = {The depth poset of a filtered Lefschetz complex reflects the dependencies between the cancellations of different shallow birth-death pairs. Using the fast algorithms for computing the depth poset in [Edelsbrunner et al., 2026] and for updating the persistence diagram under transpositions in [Cohen-Steiner et al., 2006], we give a complete case analysis of how transpositions of cells in the filter affect the depth poset. In addition, we present statistics on the depth poset for random point data and its sensitivity to the transpositions that occur in random straight-line homotopies.}, author = {Edelsbrunner, Herbert and Lipiński, Michał and Mrozek, Marian and Soriano Trigueros, Manuel and Zimin, Fedor}, booktitle = {42nd International Symposium on Computational Geometry}, isbn = {9783959774185}, issn = {1868-8969}, keywords = {Algebraic topology, Lefschetz complexes, persistent homology, vines and vineyards, birth-death pairs, shallow pairs, relations, partial orders, transpositions, Theory of computation → Computational geometry}, location = {New Brunswick, NJ, United States}, publisher = {Schloss Dagstuhl - Leibniz-Zentrum für Informatik}, title = {{The depth poset under transpositions in the filter}}, doi = {10.4230/LIPICS.SOCG.2026.41}, volume = {367}, year = {2026}, }