@article{21951, abstract = {The central engines of Little Red Dots (LRDs) may be “black hole stars” (BH*s), early stages of black hole growth characterized by dense gas envelopes. So far, the most direct evidence for BH*s comes from a handful of sources where the host galaxy is completely outshone as suggested by their remarkably steep Balmer breaks. Here we present a novel scheme to disentangle BH*s from their host galaxies assuming that the [O III]5008˚A line arises exclusively from the host. Using a sample of 98 LRDs (z ≈ 2 − 9) with high quality NIRSpec/PRISM spectra, we demonstrate that the hostsubtracted median stack displays a Balmer break > 2× stronger than massive quiescent galaxies, with the rest-optical continuum resembling a blackbody-like SED (Teff ≈ 4050 K, log(Lbol) ≈ 43.9 erg s−1 , Reff ≈ 1300 au). We measure a steep Balmer decrement (Hα/Hβ > 10) and numerous density-sensitive features (e.g., Fe II, He I, O I). These are hallmark signatures of dense gas envelopes, providing population-level evidence that BH*s indeed power LRDs. In the median LRD, BH*s account for ∼ 20% of the UV emission, ∼ 50% at the Balmer break, and ∼ 90% at wavelengths longer than Hα with the remainder arising from the host. BH*s preferentially reside in low-mass galaxies (M⋆ ≈ 108 M⊙) undergoing recent starbursts, as evidenced by extreme emission line EWs (e.g., [O III]5008˚A≈ 1100˚A, C III]≈ 12˚A), thereby favoring BH* origins linked to star-formation. We show V-shaped LRD selections are biased to high BH*/host fractions (≳ 60% at 5500˚A) – less dominant BH*s may be powering JWST’s blue broad-line AGN. We find BH*s are so commonplace and transient (duty cycle ∼ 1%, lifetime ∼ 10 Myrs) that every massive black hole may have once shone as a BH*. }, author = {Sun, Wendy Q. and Naidu, Rohan P. and Matthee, Jorryt J and De Graaff, Anna and Chisholm, John and Greene, Jenny E. and Oesch, Pascal A. and Torralba Torregrosa, Alberto and Hviding, Raphael E. and Brammer, Gabriel and Simcoe, Robert A. and Bose, Sownak and Bouwens, Rychard and Dayal, Pratika and Eilers, Anna Christina and Fei, Qinyue and Furtak, Lukas J. and Gottumukkala, Rashmi and Goulding, Andy and Heintz, Kasper E. and Hirschmann, Michaela and Kokorev, Vasily and Leja, Joel and Liu, Zhaoran and Natarajan, Priyamvada and Santarelli, Andrew D. and Setton, David J. and Smith, Aaron and Tacchella, Sandro and Volonteri, Marta and Walter, Fabian and Weibel, Andrea and Williams, Christina C.}, issn = {2565-6120}, journal = {The Open Journal of Astrophysics}, publisher = {Maynooth Academic Publishing}, title = {{Little Red Dot - Host Galaxy = Black Hole Star: A gas-enshrouded heart at the center of every Little Red Dot}}, doi = {10.33232/001c.162505}, volume = {9}, year = {2026}, } @article{21954, abstract = {We investigate a framework for train-free MRI segmentation based on Topological Data Analysis. The pipeline proceeds in three steps, first identifying the whole object to segment via automatic thresholding, then detecting a distinctive subset whose topology is known in advance, and finally deducing the various components of the segmentation. A key ingredient is the extraction of approximate representative cycles from persistence diagrams, which provides an interpretable link between persistent features and anatomical components. To clarify the method’s scope, we make the underlying topological and intensity assumptions explicit, quantify when they hold on real data, and analyze typical failure modes. We evaluate the approach on glioblastoma and on fetal cortical plate segmentation, with comparisons to unsupervised and deep-learning references. By operating without large annotated datasets, the method is well suited to scarce-data settings and provides an interpretable baseline and practical initialization for expert refinement or learning-based pipelines.}, author = {François, Anton and Tinarrage, Raphaël}, issn = {1573-7683}, journal = {Journal of Mathematical Imaging and Vision}, number = {3}, publisher = {Springer Nature}, title = {{Train-free segmentation in MRI with cubical persistent homology}}, doi = {10.1007/s10851-026-01300-1}, volume = {68}, year = {2026}, } @article{21955, abstract = {AgRP neurons cause hunger, the drive to seek and consume food. Their activation by fasting is key for survival and is thought to be triggered by feedback when energy stores are low. However, we know that environmental cues can also regulate AgRP neurons since cues that predict future food intake rapidly inhibit AgRP neurons, but is the converse true: can the prediction of future fasting rapidly activate AgRP neurons? Here, we show in mice that such rapid fasting activation of AgRP neurons does occur. This rapid activation is driven by excitatory input from paraventricular hypothalamic (PVH) neurons expressing Sim2, which are bidirectionally sensitive to predictions of future energy state. Thus, cognitively processed contextual information conveyed by PVHSim2 neurons strongly activates AgRP neurons. Lastly, chronic silencing of PVHSim2 neurons causes persistent hypophagia. This PVHSim2-to-AgRP-neuron circuit, by anticipating and preventing negative energy balance, provides an important new dimension of hunger regulation.}, author = {Walker, Samuel J. and Lowenstein, Elijah D. and Douglass, Amelia May Barnett and Thomas, Callum M.P. and Madara, Joseph C. and Kucukdereli, Hakan and Barbosa-Meillon, Eunice A. and Tao, Jenkang and Resch, Jon M. and Lowell, Bradford B.}, issn = { 1097-4199}, journal = {Neuron}, keywords = {hunger, hypothalamus, AGRP neurons, neuroscience, metabolism, homeostasis, feeding, food intake, energy balance, appetite}, publisher = {Elsevier}, title = {{A hypothalamic circuit for anticipating future changes in energy balance}}, doi = {10.1016/j.neuron.2026.05.010}, year = {2026}, } @phdthesis{21957, abstract = {This thesis investigates algorithmic certification and approximation methods for degenerate semidefinite programs (SDPs) and the singular roots of polynomial systems. In the first part, we present a hybrid symbolic-numeric algorithm for certifying the feasibility of weakly feasible, degenerate SDPs. By reformulating linear matrix inequalities (LMIs) into a structured polynomial system via facial reduction and incidence varieties, we guarantee the existence of an isolated exact solution. This algebraic reduction enables the certification of maximum-rank numerical approximations using methods from algebraic geometry. In the second part, we address the severe ill-conditioning and loss of quadratic convergence that plague standard path-tracking methods near isolated singular roots. To overcome this, we propose tracking algorithms that achieve superlinear convergence without the computational bloat characteristic of classical deflation techniques. By modeling the solution path as a generalized fractional Puiseux series, our approach combines an explicitly derived algebraic predictor with a localized hyperplane desingularization phase during the corrector step. Furthermore, we introduce a continuous path-limit method and an extension of the geometric sequence rule to directly extract exact fractional exponents. This bypasses traditional heuristic trial-and-error methods and explicitly accommodates sparse series expansions. Numerical experiments confirm that our method significantly reduces the cumulative number of matrix inversions while achieving high-accuracy root approximations, even for heavily degenerate systems exhibiting higher coranks.}, author = {Zapata, Jeferson}, isbn = {978-3-99078-079-4}, issn = {2663-337X}, pages = {89}, publisher = {Institute of Science and Technology Austria}, title = {{Overcoming degeneracy and singularity : Techniques for semidefinite programs and homotopy continuation endgames}}, doi = {10.15479/AT-ISTA-21957}, year = {2026}, } @misc{21960, abstract = {Solitons - localized wave packets that travel without spreading - play a central role in understanding transport and properties of nonlinear systems. In quantum many-body systems, however, such robust excitations are typically destroyed by thermalization. Here, we theoretically demonstrate the existence of solitonic excitations in high-energy states of Rydberg atom chains in the regime of strong nearest-neighbor Rydberg blockade. These localized wave packets propagate directionally atop a special class of reviving initial states related to quantum many-body scars and are capable of carrying energy. Exhibiting long coherence times, these states constitute a form of non-ergodic quantum dynamics and can be efficiently implemented on Rydberg atom simulators. In this work, in addition to a phenomenological description of solitons, we identify their counterpart in a classical nonlinear dynamical system, demonstrate their potential use in quantum information transfer, and conjecture their relevance for anomalous energy transport reported in numerical studies of Rydberg atom arrays.}, author = {Kerschbaumer, Aron}, publisher = {Institute of Science and Technology Austria}, title = {{Research Data: "Quasi-solitons in Rydberg atom chains"}}, doi = {10.15479/AT-ISTA-21960}, year = {2026}, } @unpublished{21962, abstract = {The generation of faithful cell-type diversity and correct projection neuron numbers is essential for cerebral cortex development. Corticogenesis is however susceptible to genetic interference of critical signaling pathways, including mutations in Mtor/Rptor that lead to microcephaly. How the loss of Rptor/mTORC1 function affects cortical developmental programs, at single cell level, is still unknown. Here, we utilized Mosaic Analysis with Double Markers (MADM) technology to probe Rptor gene function upon sparse single cell- or global tissue-wide ablation. We found that tissue-wide effects drive the etiology of cortical microcephaly upon loss of Rptor, rather than deficits in projection neuron genesis. Conversely, Rptor function is cell-autonomously required for postnatal projection neuron survival in a highly cell-type-specific manner. Collectively, our results suggest that the fine balance of precise cell-type-specific cell-autonomous Rptor/mTORC1 function in concert with non-cell-autonomous tissue-wide effects is essential for the development of a properly-sized cerebral cortex with accurate projection neuron diversity.}, author = {Villalba Requena, Ana and Beattie, Robert J and Pauler, Florian and Streicher, Carmen and Miranda, Osvaldo and Krausgruber, Thomas and Senekowitsch, Martin and Farlik, Matthias and Bock, Christoph and Rülicke, Thomas and Hippenmeyer, Simon}, booktitle = {bioRxiv}, title = {{Mtor/Rptor function globally prevents cortical microcephaly and cell-autonomously promotes postnatal neuron survival in cell type specific manner}}, doi = {10.64898/2026.05.01.722172}, year = {2026}, } @unpublished{21963, abstract = {The cerebral cortex consists of immense numbers of neuronal and glial cell-types derived from radial glial progenitor (RGP) cells. How RGPs generate appropriate quantities of distinct cortical cell-types to safeguard a brain of correct size, is not well understood. However, genetic aberration in human, including mutations in PTEN, lead to cortical malformation such as macrocephaly, albeit with unknown etiology. Here we utilized Mosaic Analysis with Double Markers (MADM)-based clonal analysis and single cell phenotyping to decipher the role of Pten in neurogenic and gliogenic RGP lineage progression during cortical ontogeny. While neurogenic RGP lineage progression and projection neuron production was moderately altered in the absence of Pten, cortical astrocyte production was drastically increased. Through genetic epistasis experiments we show that the loss of Pten uncouples astrocyte generation from essential growth factor signaling hubs, funneling into MAPK. Collectively, our results suggest that Pten regulates RGP lineage progression with distinct sequential functions in cortical projection neurogenesis and astrocyte production to ensure the emergence of a correctly-sized cerebral cortex.}, author = {Miranda, Osvaldo and Contreras, Ximena and Pauler, Florian and Davaatseren, Amarbayasgalan and Amberg, Nicole and Streicher, Carmen and Villalba Requena, Ana and Heger, Anna-Magdalena and Marie, Corentine and Hassan, Bassem A. and Rülicke, Thomas and Hippenmeyer, Simon}, booktitle = {bioRxiv}, title = {{Pten orchestrates neurogenic radial glia lineage progression and tunes neocortical astrocyte production}}, doi = {10.64898/2026.05.01.722191}, year = {2026}, } @unpublished{21968, abstract = {Balancing selection, a form of selection that maintains genetic diversity, is difficult to detect, and the importance of balancing selection for the maintenance of genetic variation may be larger than often assumed. We model the possibility that the diversity-promoting effects of balancing selection extend to other loci that show sign epistasis with a locus under balancing selection. Rather than focusing on overdominance, as was done in previous efforts, we explore the effects of negative frequency dependence and show that this has important effects on the conditions under which the diversity-promoting effect of epistasis can occur in diploids. Our results show that not only recombination rate but also the dominance of sign epistasis are key parameters that determine the maintenance of polymorphism beyond the locus under direct balancing selection. We suggest that the effect we explore may play a significant role, especially when balancing selection acts on major effect loci.}, author = {Khudiakova, Kseniia and Barton, Nicholas H and Arnqvist, Goran}, booktitle = {bioRxiv}, title = {{Sign epistasis extends the effects of balancing selection on genetic diversity}}, doi = {10.1101/2025.04.09.647826}, year = {2026}, } @misc{21971, abstract = {A Rust library for analyzing dendritic structures using quadric matrices. This project provides efficient tools for representing dendritic trees, computing quadric error metrics, and visualizing eigenvalue distributions on hexagonal plots. This library implements quadric-based geometric analysis of dendritic structures, commonly found in neuroscience applications. Key features include: Tree data structures: Hierarchical vertex and edge representations for dendritic trees Quadric matrices: Computation of quadric error metrics for edges and vertices Visualisation: Hexagonal plot generation using NormPolar transformations Interactive tools: Desktop application with plotting capabilities}, author = {Bleile, Yossi and Cortinovis, Emanuele}, keywords = {quadratics, mathematics, dendrites, geometry, topology}, publisher = {Institute of Science and Technology Austria}, title = {{Quadrix}}, doi = {10.15479/AT-ISTA-21971}, year = {2026}, } @article{21980, abstract = {Despite significant progress in the field of molecular electronics over the last two decades, the quantitative prediction of metal-molecule-metal junction conductance remains a challenge. The standard computational framework combines density functional theory (DFT) with nonequilibrium Green’s functions (NEGF) using low-rung exchange-correlation functionals such as PBE, which overestimate the conductances. More advanced correction methods exist but require complex workflows and high computational cost, limiting their accessibility. Here, we introduce a physically motivated approach that approximates results obtained with high-rung functionals. Our method fits the PBE-calculated transmission to a Breit-Wigner form and subsequently refines the fit parameters using molecular orbital energies and metal densities of states computed for the isolated subsystems with high-rung functionals. This approach is applicable to a broad range of molecular junctions yielding conductance values in quantitative agreement with experiments. Our approach is simple, low-cost, and accurate, making it well-suited for routine and large-scale prediction of single-molecule junction conductance.}, author = {Gulyaev, Artem and Hazarika, Jyotisman and Liu, Zhen-Fei and Venkataraman, Latha}, issn = {1530-6992}, journal = {Nano Letters}, number = {22}, pages = {7429–7434}, publisher = {American Chemical Society}, title = {{A computationally efficient and accurate method for predicting conductance of single-molecule junctions}}, doi = {10.1021/acs.nanolett.6c01462}, volume = {26}, year = {2026}, } @article{20328, abstract = {We consider the standard overlap (math formular) of any bi-orthogonal family of left and right eigenvectors of a large random matrix X with centred i.i.d. entries and we prove that it decays as an inverse second power of the distance between the corresponding eigenvalues. This extends similar results for the complex Gaussian ensemble from Bourgade and Dubach [15], as well as Benaych-Georges and Zeitouni [13], to any i.i.d. matrix ensemble in both symmetry classes. As a main tool, we prove a two-resolvent local law for the Hermitisation of X uniformly in the spectrum with optimal decay rate and optimal dependence on the density near the spectral edge.}, author = {Cipolloni, Giorgio and Erdös, László and Xu, Yuanyuan}, issn = {0022-1236}, journal = {Journal of Functional Analysis}, number = {1}, publisher = {Elsevier}, title = {{Optimal decay of eigenvector overlap for non-Hermitian random matrices}}, doi = {10.1016/j.jfa.2025.111180}, volume = {290}, 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{20456, abstract = {Given a locally finite set A⊆Rd and a coloring χ:A→{0,1,…,s}, we introduce the chromatic Delaunay mosaic of χ, which is a Delaunay mosaic in Rs+d that represents how points of different colors mingle. Our main results are bounds on the size of the chromatic Delaunay mosaic, in which we assume that d and s are constants. For example, if A is finite with n=#A, and the coloring is random, then the chromatic Delaunay mosaic has O(n⌈d/2⌉) cells in expectation. In contrast, for Delone sets and Poisson point processes in Rd, the expected number of cells within a closed ball is only a constant times the number of points in this ball. Furthermore, in R2 all colorings of a dense set of n points have chromatic Delaunay mosaics of size O(n). This encourages the use of chromatic Delaunay mosaics in applications.}, author = {Biswas, Ranita and Cultrera di Montesano, Sebastiano and Draganov, Ondrej and Edelsbrunner, Herbert and Saghafian, Morteza}, issn = {1432-0444}, journal = {Discrete and Computational Geometry}, pages = {24--47}, publisher = {Springer Nature}, title = {{On the size of chromatic Delaunay mosaics}}, doi = {10.1007/s00454-025-00778-7}, volume = {75}, 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{21437, abstract = {Altermagnets are a class of collinear magnets that exhibit non-relativistic spin splitting (NRSS) of electronic bands in the absence of net magnetization. Their potential to generate large spin polarization without spin-orbit coupling has created strong interest in probes that access the underlying order parameter directly. In this Perspective, we show that linear magneto-birefringence (LMB) provides a natural and broadly applicable route to detecting altermagnetic order. Building on the correspondence between the momentum-space structure of NRSS and the ferroic ordering of magnetic multipoles in real space, we demonstrate how $d$-wave and $g$-wave NRSS textures yield distinct LMB responses. We present a symmetry-based framework that identifies the optical geometries and field configurations required to isolate specific multipole components, enabling domain imaging and providing benchmarks for theoretical models of LMB.}, author = {Sunko, Veronika and Orenstein, J.}, issn = {2397-4648}, journal = {npj Quantum Materials}, publisher = {Springer Nature}, title = {{Linear magneto-birefringence as a probe of altermagnetism}}, doi = {10.1038/s41535-026-00901-8}, year = {2026}, } @article{22101, abstract = {Evolutionary biology examines how the genetic and phenotypic composition of populations changes over time. An important goal is to determine the fixation probability of a single advantageous mutant that arises in a homogeneous population of N residents. Many real populations experience environmental gradients that cause mutations to be beneficial in some spatial regions but harmful in others. Here, we study the fixation probability of a mutant placed on a simple one-dimensional spatial structure that experiences such a gradient. The mutant’s fitness varies linearly from1 − s to 1 + s, whereas the resident fitness is constant and equal to 1. The existing literature suggests that such heterogeneity in the mutant’s fitness should lead to a decrease in its fixation probability. However, in this work, we find that small, non-negligible gradients (s < 1=√N) substantially increase the fixation probability,while larger gradients (s > (log N)/√N) substantially decrease it.Moreover, we quantify the strength of this phenomenon analytically and we precisely delimit the range of the gradients for which it occurs. Our computer simulations closely match those findings. Altogether, our results indicate that subjecting a simple population structure to natural environmental conditions can produce strong counterintuitive effects.}, author = {Svoboda, Jakub and Nemati, Hossein and Tkadlec, Josef and Kaveh, Kamran and Chatterjee, Krishnendu}, issn = {2041-1723}, journal = {Nature Communications}, publisher = {Springer Nature}, title = {{The effect of the fitness gradient on fixation probability}}, doi = {10.1038/s41467-026-71777-2}, volume = {17}, year = {2026}, } @inproceedings{22103, abstract = {Modern AI systems increasingly rely on opaque, highly complex models whose inner workings remain inaccessible even to experts. This opacity creates challenges for trust, accountability, and compliance with emerging regulatory expectations such as the “right to an explanation”. While traditional explainability methods—feature attributions, counterfactuals, surrogate models—and interpretable model classes provide valuable insights for engineers, they often fall short of delivering the contextual, conversational explanations that real users expect. Large Language Models (LLMs) offer a promising new avenue for explanation due to their ability to engage interactively, adapt to user needs, and translate technical outputs into more accessible reasoning. However, their tendencies toward hallucination, conflict avoidance, and oversimplification introduce serious risks when used as explanatory agents. This paper analyzes these opportunities and limitations, examines verification strategies for ensuring explanation fidelity, and situates LLM-generated explanations within broader concerns about public trust. The paper concludes by outlining best practices and future research directions for building robust, verifiable, and human-aligned explanation systems.}, author = {Cano Cordoba, Filip}, booktitle = {Proceedings of the 18th International Conference on Agents and Artificial Intelligence}, isbn = {9789897587962}, issn = {2184-433X}, keywords = {Explainable AI, Large Language Models, Trust in AI}, location = {Marbella, Spain}, pages = {4689--4696}, publisher = {Science and Technology Publications}, title = {{Explaining decisions one conversation at a time: Opportunities and risks of LLMs as explainability assistants}}, doi = {10.5220/0014483200004052}, volume = {5}, year = {2026}, } @article{22105, 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 labelling 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 crystal structure of a GB1 variant reported in this work, reproduce these elevated barriers and reveal how the crystal restrains motions.}, author = {Becker, Lea Marie and Fu, Haohao and Tatman, Benjamin and Dreydoppel, Matthias and Kapitonova, Anna and Balazs, Daniel and Weininger, Ulrich and Engilberge, Sylvain and Chipot, Christophe and Schanda, Paul}, issn = {17554349}, journal = {Nature Chemistry}, publisher = {Springer Nature}, title = {{Aromatic ring flips reveal reshaping of protein dynamics in crystals and complexes}}, doi = {10.1038/s41557-026-02155-0}, year = {2026}, } @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}, } @inproceedings{22146, abstract = {We study differentially private model training with stochastic gradient descent under learning rate scheduling and correlated noise. Although correlated noise, in particular via matrix factorizations, has been shown to improve accuracy, prior theoretical work focused primarily on the prefix-sum workload. That workload assumes a constant learning rate, whereas in practice learning rate schedules are widely used to accelerate training and improve convergence. We close this gap by deriving general upper and lower bounds for a broad class of learning rate schedules in both single- and multi-epoch settings. Building on these results, we propose a learning-rate-aware factorization that achieves improvements over prefix-sum factorizations under both MaxSE and MeanSE error metrics. Our theoretical analysis yields memory-efficient constructions suitable for practical deployment, and experiments on CIFAR-10 and IMDB datasets confirm that schedule-aware factorizations improve accuracy in private training.}, author = {Kalinin, Nikita and Andersson, Joel D}, booktitle = {7th Symposium on Foundations of Responsible Computing}, isbn = {9783959774192}, issn = {1868-8969}, keywords = {differential privacy, machine learning, matrix factorization}, location = {Cambridge, MA; United States}, publisher = {Schloss Dagstuhl - Leibniz-Zentrum für Informatik}, title = {{Learning rate scheduling with matrix factorization for private training}}, doi = {10.4230/LIPIcs.FORC.2026.2}, volume = {368}, year = {2026}, }