@phdthesis{21393, abstract = {This thesis documents a voyage towards truth and beauty via formal verification of theorems. To this end, we develop libraries in Lean 4 that present definitions and results from diverse areas of MathematiCS (i.e., Mathematics and Computer Science). The aim is to create code that is understandable, believable, useful, and elegant. The code should stand for itself as much as possible without a need for documentation; however, this text redundantly documents our code artifacts and provides additional context that isn’t present in the code. This thesis is written for readers who know Lean 4 but are not familiar with any of the topics presented. We manifest truth and beauty in three formalized areas of MathematiCS. We formalize general grammars in Lean 4 and use grammars to show closure of the class of type-0 languages under four operations; union, reversal, concatenation, and the Kleene star. Our second stop is the theory of optimization. Farkas established that a system of linear inequalities has a solution if and only if we cannot obtain a contradiction by taking a linear combination of the inequalities. We state and formally prove several Farkas-like theorems over linearly ordered fields in Lean 4. Furthermore, we extend duality theory to the case when some coefficients are allowed to take “infinite values”. Additionally, we develop the basics of the theory of optimization in terms of the framework called General-Valued Constraint Satisfaction Problems, and we prove that, if a Rational-Valued Constraint Satisfaction Problem template has symmetric fractional polymorphisms of all arities, then its basic LP relaxation is tight. Our third stop is matroid theory. Seymour’s decomposition theorem is a hallmark result in matroid theory, presenting a structural characterization of the class of regular matroids. We aim to formally verify Seymour’s theorem in Lean 4. First, we build a library for working with totally unimodular matrices. We define binary matroids and their standard representations, and we prove that they form a matroid in the sense how Mathlib defines matroids. We define regular matroids to be matroids for which there exists a full representation rational matrix that is totally unimodular, and we prove that all regular matroids are binary. We define 1-sum, 2-sum, and 3 sum of binary matroids as specific ways to compose their standard representation matrices. We prove that the 1-sum, the 2-sum, and the 3-sum of regular matroids are a regular matroid, which concludes the composition direction of the Seymour’s theorem. The (more difficult) decomposition direction remains unproved. In the pursuit of truth, we focus on identifying the trusted code in each project and presenting it faithfully. We emphasize the readability and believability of definitions rather than choosing definitions that are easier to work with. In search for beauty, we focus on the philosophical framework of Roger Scruton, who emphasizes that beauty is not a mere decoration but, most importantly, beauty is the means for shaping our place in the world and a source of redemption, where it can be viewed as a substitute for religion.}, author = {Dvorak, Martin}, isbn = {978-3-99078-074-9}, issn = {2663-337X}, pages = {160}, publisher = {Institute of Science and Technology Austria}, title = {{Pursuit of truth and beauty in Lean 4 : Formally verified theory of grammars, optimization, matroids}}, doi = {10.15479/AT-ISTA-21393}, year = {2026}, } @article{21501, abstract = {Kinetically constrained models were originally introduced to capture slow relaxation in glassy systems, where dynamics are hindered by local constraints instead of energy barriers. Their quantum counterparts have recently drawn attention for exhibiting highly degenerate eigenstates at zero energy—known as zero modes—stemming from chiral symmetry. Yet, the structure and implications of these zero modes remain poorly understood. In this work, we focus on the properties of the zero mode subspace in quantum kinetically constrained models with a U(1) particle-conservation symmetry. We use the U(1) East, which lacks inversion symmetry, and the inversion-symmetric U(1) East-West models to illustrate our two main results. First, we observe that the simultaneous presence of constraints and chiral symmetry generally leads to a parametric increase in the number of zero modes due to the fragmentation of the many-body Hilbert space into disconnected sectors. Second, we generalize the concept of compact localized states from single-particle physics and introduce the notion of collective bound states, a special kind of nonergodic eigenstates that are robust to enlarging the system size. We formulate sufficient criteria for their existence, arguing that the degenerate zero mode subspace plays a central role, and demonstrate bound states in both example models and in a two-dimensional model, the U(1) North-East, and in the pairflip model, a system without particle conservation. Our results motivate a systematic study of bound states and their relation to ergodicity breaking, transport, and other properties of quantum kinetically constrained models. }, author = {Nicolau Jimenez, Eulalia and Ljubotina, Marko and Serbyn, Maksym}, issn = {2691-3399}, journal = {PRX Quantum}, publisher = {American Physical Society}, title = {{Fragmentation, zero modes, and collective bound states in constrained models}}, doi = {10.1103/sl79-1xgb}, volume = {7}, year = {2026}, } @article{21503, abstract = {Currently, pharmacogenetics relies on partially annotated star alleles, leaving novel variants and complex haplotypes uninterpretable. Computational scoring frameworks could overcome these limitations. Here, we comprehensively evaluated the ability of existing (CADD, FATHMM-XF, PROVEAN, MutationAssessor, SIFT, PhyloP100, APF, APF2) and novel (PharmGScore and PharmMLScore) variant effect predictors to assess pharmacogenetic alleles in multiple scenarios. Altogether we analyzed 541 PharmVar alleles, high‑throughput CYP2C9 and CYP2C19 mutational maps, and 200 642 UK Biobank exomes linked with health records containing antidepressant treatment outcomes. Many evaluated tools, especially ensemble frameworks, matched or exceeded star allele classifications (ROC‑AUC up to 0.85 for allele definitions, 0.95 in vitro; TPR up to 0.99 for exomes) and accurately predicted severe antidepressant adverse events for carriers of deleterious variants in CYP2C19 (OR 1.20–1.35). Our findings show that computational predictors deliver star allele accuracy while overcoming their limitations. With additional validation, computational tools could enhance clinical decision frameworks by enabling continuous scoring, incorporating previously unknown variants, and providing genome-wide applicability.}, author = {Hajto, Jacek and Piechota, Marcin and Krätschmer, Ilse and Konowalska, Paula and Boyle, Gabriel E. and Fowler, Douglas M. and Borczyk, Malgorzata and Korostynski, Michal}, issn = {1473-1150}, journal = {Pharmacogenomics Journal}, number = {2}, publisher = {Springer Nature}, title = {{Computational variant predictors for pharmacogenomics: From evaluation of single alleles to assessment of adverse drug reactions to antidepressants}}, doi = {10.1038/s41397-026-00399-0}, volume = {26}, year = {2026}, } @article{21509, abstract = {Chromatin remodeling complexes mobilize nucleosomes and promote transcription factor (TF) binding. Using ensemble and single-molecule assays combined with cryo-electron microscopy (cryo-EM), we studied the interaction between pioneer TFs OCT4–SOX2 and the human BRG1/BRM-associated factor (BAF) complex on nucleosomes. BAF engages TF-bound substrates in two orientations, placing OCT4–SOX2 at either the remodeler ENTRY or EXIT site. At the ENTRY site, OCT4–SOX2 initially coexists with BAF without structural interference. However, continued DNA translocation is expected to cause collisions with bound TFs, which can trigger remodeling direction reversals or may induce TF dissociation. To accommodate TFs at the EXIT site, BAF undergoes structural rearrangements, and ensemble assays reveal a nucleosome subpopulation translocating away from TF-binding sites. Moreover, single-molecule experiments show that nucleosome-bound BAF frequently changes remodeling direction, and we identify an ADP-bound remodeler conformation as a potential intermediate. Together, these findings reveal key aspects of the conformational dynamics and remodeling outcomes underlying BAF processing of TF-bound nucleosomes.}, author = {Weiss, Joscha and Vecchia, Luca and Domjan, David and Cavadini, Simone and Sabantsev, Anton and Kempf, Georg and Pathare, Ganesh R. and Brackmann, Klaus and Michael, Alicia and Kater, Lukas and Hietter-Pfeiffer, Eric and Haddawi, Mina and Kuber, Urja P. and Mühlhäusser, Sandra and Grand, Ralph S. and Stadler, Michael B. and Deindl, Sebastian and Thomä, Nicolas H.}, issn = {1097-2765}, journal = {Molecular Cell}, number = {4}, pages = {625--639.e8}, publisher = {Elsevier}, title = {{The human BAF chromatin remodeler processes nucleosomes bound by pioneer transcription factors OCT4–SOX2}}, doi = {10.1016/j.molcel.2026.01.021}, volume = {86}, year = {2026}, } @article{21483, abstract = {Embryogenesis in the model plant Arabidopsis thaliana provides a framework for understanding how cell polarity and patterning coordinate with hormonal signalling to establish the plant body plan. Following fertilisation, the zygote divides asymmetrically to generate apical and basal lineages, establishing the apical–basal axis that defines future shoot and root poles. Genetic and molecular analyses of classical mutants including gnom, monopteros (mp), bodenlos (bdl) and topless revealed that localised auxin biosynthesis, directional transport and downstream transcriptional responses are central to apical–basal axis establishment and organ initiation. The main components of this regulation are polarly localised PIN auxin transporters and downstream modules involving MONOPTEROS and WUSCHEL-RELATED HOMEOBOX transcription factors. Advances in microscopy have transformed the study of Arabidopsis embryogenesis: fluorescence-compatible clearing reagents and three-dimensional reconstructions now permit quantitative analyses of cell geometry, division orientation, and cytoskeletal dynamics. Live ovule imaging setups with confocal laser scanning and multiphoton microscopes enable real-time observation of embryo development, while laser-assisted cell ablation can be used to probe cell-to-cell communication and fate plasticity. Together, these methodological breakthroughs position Arabidopsis embryos as a prime model for dissecting the chemical and biophysical cues that shape plant development.}, author = {Babic, David and Zupunski, Milan and Friml, Jiří}, issn = {1469-8137}, journal = {New Phytologist}, publisher = {Wiley}, title = {{Imaging and genetic toolbox to study Arabidopsis embryogenesis}}, doi = {10.1111/nph.71072}, year = {2026}, } @article{21502, abstract = {The mammalian brain stores glucose, the main circulating energy substrate, as glycogen. In rodents, the cerebellum contains relatively high glycogen levels, yet its cellular and subcellular distribution remains poorly defined. Using monoclonal antibodies against glycogen, we examined its distribution in the mouse cerebellar cortex. Glycogen was predominantly localized to Bergmann glia (BG) processes in the molecular layer and was also detected in Purkinje cells (PCs), the principal cerebellar neurons. To assess the functional significance of cerebellar glycogen, we analyzed behavior in mice lacking glycogen synthase 1 (Gys1) in BG or PCs using a floxed Gys1 line. Gys1 deficiency in either PCs or GFAP-positive cells reduced anxiety-like behavior, whereas combined deletion caused PC degeneration and ataxia. These findings reveal a critical role for glycogen metabolism in both astrocytes and neurons in cerebellar function.}, author = {Akther, Sonam and Lee, Ashley Bomin and Konno, Ayumu and Asiminas, Antonis and Vittani, Marta and Mishima, Tsuneko and Hirai, Hirokazu and Meehan, Claire Francesca and Duran, Jordi and Guinovart, Joan and Ashida, Hitoshi and Morita, Tsuyoshi and Baba, Otto and Shigemoto, Ryuichi and Nedergaard, Maiken and Hirase, Hajime}, issn = {2589-0042}, journal = {iScience}, number = {4}, publisher = {Elsevier}, title = {{Distribution and functional significance of rodent cerebellar glycogen}}, doi = {10.1016/j.isci.2026.115192}, volume = {29}, 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}, publisher = {World Scientific Publishing}, title = {{From kinetic theory to AI: A rediscovery of high-dimensional divergences and their properties}}, doi = {10.1142/S0218202526410010}, year = {2026}, } @article{20865, abstract = {We prove the convergence of a modified Jordan–Kinderlehrer–Otto scheme to a solution to the Fokker–Planck equation in Ω e R^d with general—strictly positive and temporally constant—Dirichlet boundary conditions. We work under mild assumptions on the domain, the drift, and the initial datum. In the special case where Ω is an interval in R1, we prove that such a solution is a gradient flow—curve of maximal slope—within a suitable space of measures, endowed with a modified Wasserstein distance. Our discrete scheme and modified distance draw inspiration from contributions by A. Figalli and N. Gigli [J. Math. Pures Appl. 94, (2010), pp. 107–130], and J. Morales [J. Math. Pures Appl. 112, (2018), pp. 41–88] on an optimal-transport approach to evolution equations with Dirichlet boundary conditions. Similarly to these works, we allow the mass to flow from/to the boundary ∂Ω throughout the evolution. However, our leading idea is to also keep track of the mass at the boundary by working with measures defined on the whole closure Ω . The driving functional is a modification of the classical relative entropy that also makes use of the information at the boundary. As an intermediate result, when Ω is an interval in R1, we find a formula for the descending slope of this geodesically nonconvex functional.}, author = {Quattrocchi, Filippo}, issn = {1432-0835}, journal = {Calculus of Variations and Partial Differential Equations}, number = {1}, publisher = {Springer Nature}, title = {{Variational structures for the Fokker-Planck equation with general Dirichlet boundary conditions}}, doi = {10.1007/s00526-025-03193-1}, volume = {65}, year = {2026}, } @article{21658, abstract = {Dipolar (ℓ = 1) mixed modes have revealed a surprisingly weak differential rotation between the core and the envelope of evolved solar-like stars. Quadrupolar (ℓ = 2) mixed modes also contain information regarding internal dynamics but are very rarely characterised due to their low amplitude and the challenging identification of adjacent or overlapping rotationally split multiplets affected by near-degeneracy effects. We aim to extend the broadly used asymptotic seismic diagnostics beyond ℓ = 1 mixed modes by developing an analogue asymptotic description of ℓ = 2 mixed modes while explicitly accounting for near-degeneracy effects that distort their rotational multiplets. We have derived a new asymptotic formulation of near-degenerate mixed ℓ = 2 modes that describes off-diagonal terms representing the interaction between modes of adjacent radial orders. This formalism, expressed directly in the mixed-mode basis, provides analytical expressions for the near-degeneracy effects. We implemented the formalism within a global Bayesian mode-fitting framework for a direct fit of all ℓ = 0, 1, 2 modes in the power spectrum density. We were able to asymptotically model the asymmetric rotational splitting present in various radial orders of ℓ = 2 modes observed in young red giant stars without the need for any numerical stellar modelling. We applied our formalism to the Kepler target KIC 7341231, and it yielded core and envelope rotation rates consistent with previous numerical modelling while providing improved constraints from the global and model-independent approach. We also characterised the new target, KIC 8179973, measuring its rotation rate and mixed-mode parameters for the first time. As our framework relies on a direct global fit, it allows for much better precision on the asteroseismic parameters and rotation rate estimates than standard methods, yielding better constraints for rotation inversions. We have placed the first observational constraints on the asymptotic ℓ = 2 mixed-mode parameters (ΔΠ2, q2, and εg, 2), thus paving the way towards the use of asymptotic seismology beyond ℓ = 1 mixed modes.}, author = {Liagre, Bastien Raymond Bernard and Desai, Aayush A and Einramhof, Lukas and Bugnet, Lisa Annabelle}, issn = {1432-0746}, journal = {Astronomy and Astrophysics}, publisher = {EDP Sciences}, title = {{Near-degeneracy effects in quadrupolar mixed modes: From an asymptotic description to data fitting}}, doi = {10.1051/0004-6361/202558023}, volume = {707}, 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{21659, abstract = {The recent detection of solar equatorial Rossby waves has renewed interest in the study of gravito-inertial waves propagating in the convective envelope of solar-type stars. In particular, the ability of these envelope gravito-inertial modes to couple with those trapped in the radiative interior could open up new opportunities for probing the deep-layer dynamics of solar-type stars. The possibility for such a coupling to occur is particularly favoured among pre-main-sequence (PMS) solar-type stars. Indeed, due to the contraction of the protostellar object, they are able to reach high rotation frequencies before nuclear reactions are ignited and magnetic braking becomes the driving mechanism for their rotational evolution. In this work, we studied the coupling between the envelope inertial waves and the radiative interior g modes in PMS stars, focussing on the case of prograde dipolar modes. We considered the cases of 0.5 M⊙ and 1 M⊙ PMS models, each with three different scenarios of rotational evolution. We show that for stars that have formed with a sufficient amount of angular momentum, this coupling can occur in frequency ranges that are accessible to space-borne photometry, creating inertial dips in the period spacing pattern. Using an asymptotic analysis, we characterised the shape of these inertial dips to show that they depend on rotation and on the stiffness of the convective-radiative interface.}, author = {Breton, S. N. and Pezzotti, C. and Mathis, S. and Bugnet, Lisa Annabelle and Di Mauro, M. P. and Joergensen, J. and Zwintz, K. and Lanza, A. F.}, issn = {1432-0746}, journal = {Astronomy & Astrophysics}, publisher = {Wiley}, title = {{Core-envelope coupling of gravito-inertial waves in pre-main-sequence solar-type stars}}, doi = {10.1051/0004-6361/202659309}, volume = {707}, year = {2026}, } @article{21660, abstract = {Kapitza-Dirac scattering, the diffraction of matter waves from a standing light field, is widely utilized in ultracold gases, but its behavior in the strongly interacting regime is an open question. Here, we develop a numerically exact two-body description of Kapitza-Dirac scattering for two contact-interacting atoms in a one-dimensional harmonic trap subjected to a pulsed optical lattice, enabling us to obtain the numerically exact dynamics. We map how interaction strength, lattice depth, lattice wave number, and pulse duration reshape the diffraction pattern, leading to an interaction-dependent population redistribution in real and momentum space. By comparing the exact dynamics to an impulsive sudden-approximation description, we delineate the parameter regimes where it remains accurate and those, notably at strong attraction and small lattice wave number, where it fails. Our results provide a controlled few-body benchmark for interacting Kapitza-Dirac scattering and quantitative guidance for Kapitza-Dirac-based probes of ultracold atomic systems.}, author = {Becker, A. and Koutentakis, Georgios and Schmelcher, P.}, issn = {2643-1564}, journal = {Physical Review Research}, publisher = {American Physical Society}, title = {{Two-body Kapitza-Dirac scattering of one-dimensional ultracold atoms}}, doi = {10.1103/rdsn-stlq}, volume = {8}, 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}, } @phdthesis{20964, author = {Vladimirtsev, Dmitrii}, issn = {2791-4585}, pages = {22}, publisher = {Institute of Science and Technology Austria}, title = {{Armadillo repeat only proteins are master regulators of plant cyclic-nucleotide gated channels}}, doi = {10.15479/AT-ISTA-20964}, year = {2026}, } @phdthesis{21198, abstract = {In recent years there has been a massive increase in the amount of data generated in a decentralized manner. Ever more powerful edge devices, such as smartphones, have become ubiquitous in most societies on earth. Through text typed, photos taken and apps used, these devices, which we refer to as clients, generate enormous amounts of high quality and complex data. Moreover, the nature of these devices means the data they generate is often sensitive and privacy concerns prevent it being gathered and stored in a central location. This presents a challenge to the modern machine learning paradigm that requires central access to large amounts of data. Federated learning (FL) has emerged as one of the answers to this problem. Rather than bringing the data to the model, FL sends the model to the data. Model training takes place on device, with periodically synchronized updates, allowing data to remain locally stored. While this approach offers significant privacy advantages it comes with its own set of unique challenges. These include: data heterogeneity, the notion that different devices generate data in distinct ways which can negatively impact training dynamics; systems heterogeneity, meaning that different devices may have differing hardware specifications; high communication costs, which are induced by the repeated transferring of models over the network and low device computational power, which limits the use of larger models on device. In this thesis we present a range of methods for federated learning. We focus primarily on the challenge of data heterogeneity, though the methods presented are designed to be well adapted to the other challenges of a federated setting, such as the constraints of limited compute and communication overhead. We first present a method for explicitly modeling client data heterogeneity. The approach formulates clients as samples from a certain probability distribution and infers the parameters of this distribution from the available training clients. This learned distribution then represents the heterogeneity present among the clients and can be sampled from in order to create new simulated clients that are similar to the real clients we have observed so far. Following this we present two methods for directly dealing with data heterogeneity through personalization. Highly heterogeneous client data distributions can mean that learning a single global model becomes suboptimal, and some form of personalization of models to each individual client is required. Our approaches are based around hypernetworks, which we use to generate personalized model parameters without the need for additional training or finetuning. In the first approach we focus on generating full parameterizations of client models using learned embeddings of client data and labels, with a hypernetwork located on the central server. In the second approach we address the more challenging scenario where we want to generate a personalized model for a client without any label information. The hypernetwork is trained to generate a low dimensional representation of a client’s personalized model parameters, allowing it to be transferred to and run on the client devices. In our final presented method, we change our focus and rather than aim to directly address the challenge of data heterogeneity, we instead ensure we are unaffected by it. This is done in the context of k-means clustering and we present a method for federated clustering with a focus on added privacy guarantees.}, author = {Scott, Jonathan A}, issn = {2663-337X}, pages = {158}, publisher = {Institute of Science and Technology Austria}, title = {{Data heterogeneity and personalization in federated learning}}, doi = {10.15479/AT-ISTA-21198}, year = {2026}, } @phdthesis{21021, abstract = {This thesis examines how geometry and topology intersect in the representation, transformation, and analysis of complex shapes. It considers how continuous manifolds relate to their discrete analogues, how topological structures evolve in persistence vineyards, and how tools from topological data analysis can illuminate problems in mathematical physics. Central to this exploration is the question of how structure, both geometric and topological, persists or changes under approximation, sampling, or deformation. The work develops new approaches to skeletal and grid-based representations of surfaces, reveals the full expressive capacity of persistence vineyards, and applies topological methods to the longstanding problem of equilibria in electrostatic fields. These threads braid together into a broader understanding of how topology and geometry inform one another across theory, computation, and application.}, author = {Fillmore, Christopher D}, issn = {2663-337X}, pages = {122}, publisher = {Institute of Science and Technology Austria}, title = {{Braiding geometry and topology to study shapes and data}}, doi = {10.15479/AT-ISTA-21021}, year = {2026}, } @unpublished{21051, abstract = {In this work, we introduce and study what we believe is an intriguing and, to the best of our knowledge, previously unknown connection between two areas in computational topology, topological data analysis (TDA) and knot theory. Given a function from a topological space to $\mathbb{R}$, TDA provides tools to simplify and study the importance of topological features: in particular, the $l^{th}$-dimensional persistence diagram encodes the $l$-homology in the sublevel set as the function value increases as a set of points in the plane. Given a continuous one-parameter family of such functions, we can combine the persistence diagrams into an object known as a vineyard, which track the evolution of points in the persistence diagram. If we further restrict that family of functions to be periodic, we identify the two ends of the vineyard, yielding a closed vineyard. This allows the study of monodromy, which in this context means that following the family of functions for a period permutes the set of points in a non-trivial way. In this work, given a link and value $l$, we construct a topological space and periodic family of functions such that the closed $l$-vineyard contains this link. This shows that vineyards are topologically as rich as one could possibly hope. Importantly, it has at least two immediate consequences: First, monodromy of any periodicity can occur in a $l$-vineyard, answering a variant of a question by [Arya et al 2024]. To exhibit this, we also reformulate monodromy in a more geometric way, which may be of interest in itself. Second, distinguishing vineyards is likely to be difficult given the known difficulty of knot and link recognition, which have strong connections to many NP-hard problems.}, author = { Chambers, Erin and Fillmore, Christopher D and Stephenson, Elizabeth R and Wintraecken, Mathijs}, booktitle = {arXiv}, title = {{Braiding vineyards}}, doi = {10.48550/ARXIV.2504.11203}, year = {2026}, } @article{21726, abstract = {Quantum control of the many-body wavefunction is a central challenge in quantum materials research, as it could yield a precise control knob to manipulate emergent phenomena. Floquet engineering, the coherent dressing of quantum states with periodic non-resonant optical fields, has become an important strategy for quantum control. Most applications to solid-state systems have targeted weakly interacting or single-ion states, leaving the manipulation of many-body wavefunctions largely unexplored. Here we use Floquet engineering to achieve quantum control of a strongly correlated Hubbard exciton in the one-dimensional Mott insulator Sr2CuO3. A non-resonant mid-infrared optical field coherently dresses the exciton wavefunction, driving its rotation between bright and dark states. We use resonant third-harmonic generation to quantify ultrafast π/2 rotations on the Bloch sphere spanned by these exciton states. Our work advances the quest towards programmable control of correlated states and exciton-based quantum sensing.}, author = {Baykusheva, Denitsa Rangelova and Carmichael, Deven and Weber, Clara S. and Lu, I. Te and Glerean, Filippo and Meng, Tepie and De Oliveira, Pedro B.M. and Homes, Christopher C. and Zaliznyak, Igor A. and Gu, G. D. and Dean, Mark P.M. and Rubio, Angel and Kennes, Dante M. and Claassen, Martin and Mitrano, Matteo}, issn = {1476-4660}, journal = {Nature Materials}, publisher = {Springer Nature}, title = {{Quantum control of Hubbard excitons}}, doi = {10.1038/s41563-026-02517-6}, year = {2026}, } @article{21725, abstract = {The initial–final mass relation (IFMR) links a star’s birth mass to the mass of its white dwarf (WD) remnant, providing key constraints on stellar evolution. Open clusters offer the most straightforward way to empirically determine the IFMR, as their well-defined ages allow for direct progenitor lifetime estimates. We construct the most comprehensive open cluster WD IFMR to date by combining new spectroscopy of 22 WDs with an extensive literature review of WDs with strong cluster associations. To minimize systematics, we restrict our analysis to spectroscopically confirmed hydrogen-atmosphere (DA) WDs consistent with single-stellar origins. We separately analyze a subset with reliable Gaia-based astrometric membership assessments, as well as a full sample that adds WDs with strong cluster associations whose membership cannot be reliably assessed with Gaia. The Gaia-based sample includes 69 spectroscopically confirmed DA WDs, more than doubling the sample size of previous Gaia-based open cluster IFMRs. The full sample, which includes 53 additional literature WDs, increases the total number of cluster WDs by over 50% relative to earlier works. We provide functional forms for both the Gaia-based and full-sample IFMRs. The Gaia-based result useful for Mi � 2.67 M⊙ is Mf = [0.179 0.100H (Mi 3.84 M )] × (Mi 3.84 M ) + 0.628 M , where H(x) is the Heaviside step function. Comparing our IFMR to recent literature, we identify significant deviations from best-fit IFMRs derived from both Gaia-based volume-limited samples of field WDs and double WD binaries, with the largest discrepancy occurring for initial masses of about 5 M⊙.}, author = {Miller, David R. and Caiazzo, Ilaria and Heyl, Jeremy and Richer, Harvey B. and Hollands, Mark A. and Tremblay, Pier Emmanuel and El-Badry, Kareem and Rodriguez, Antonio C. and Vanderbosch, Zachary P.}, issn = {1538-4357}, journal = {The Astrophysical Journal}, keywords = {White dwarf stars, Open star clusters, Compact objects, Stellar evolution}, number = {1}, publisher = {IOP Publishing}, title = {{The White Dwarf initial–final mass relation from open clusters in Gaia DR3}}, doi = {10.3847/1538-4357/ae18c8}, volume = {996}, year = {2026}, } @unpublished{21699, abstract = {Recent research in nanophotonics for scintillation-based imaging has demonstrated promising improvements in scintillator performance. In parallel, advances in nanophotonics have enabled wavefront control through metasurfaces, a capability that has transformed fields such as microscopy by allowing tailored control of optical propagation. This naturally raises the following question, which we address in this perspective: can wavefront-control strategies be leveraged to improve scintillation-based imaging? To answer this question, we explore nanophotonic- and metasurface-enabled wavefront control in scintillators to mitigate image blurring arising from their intrinsically diffuse light emission. While depth-of-field extension in scintillation faces fundamental limitations absent in microscopy, this approach reveals promising avenues, including stacked scintillators, selective spatial-frequency enhancement, and X-ray energy-dependent imaging. These results clarify the key distinctions in adapting wavefront engineering to scintillation and its potential to enable tailored detection strategies.}, author = {Chen, Joshua and Vaidya, Sachin and Pajovic, Simo and Choi, Seou and Michaels, William and Louis Martin-Monier, Louis Martin-Monier and Hu, Juejun and Cogswell, Carol and Roques-Carmes, Charles and Soljačić, Marin}, booktitle = {arXiv}, title = {{Wavefront engineering for scintillation-based imaging}}, doi = {10.48550/arXiv.2601.09830}, year = {2026}, }