Quantum Physics
An Exact Operator Formulation of Statistical Quasiparticle Theory for Nonlinear System-Bath Coupling
Yu Su and Yao Wang
We develop an operator formulation of statistical quasiparticle theory for open
quantum systems with nonlinear system-bath coupling, extending beyond the linear coupling setting of the standard Gaussian influence functional formulation. For Gaussian baths, the statistical quasiparticles, termed dissipatons, are explicitly constructed as collective operators in the thermofield bath space. Our construction provides a microscopic operator basis for the dissipaton
algebra and generates hierarchical equations of motion directly from the Liouville equation. Nonlinear interactions are incorporated through a recursive generalized Wick's
theorem, enabling automatic generation of hierarchical equations for
polynomial couplings. The resulting framework connects explicit bath operator representations to nonperturbative, non-Markovian dynamics and unifies the treatment of linear and nonlinear system-bath interactions.
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Statistical Mechanics
Random-matrix and transport frequencies in eigenstate spectral functions
Kadir Çeven, Rohit Patil, Marcos Rigol et al. (+1 more)
The fact that generic isolated many-body
quantum systems thermalize is understood using the eigenstate thermalization hypothesis (ETH). In recent years, there has been much interest in the behavior of the ETH spectral functions, which characterize the smooth dependence of the variance of the off-diagonal
matrix elements of observables on the associated energy and frequency, and whose low-frequency part contains information about the long-time dynamics. In finite systems described by the ETH, the spectral functions are expected to exhibit plateaus below a characteristic frequency $\omega^{}_{\mathrm{ETH}}$. In this regime, the statistics of the
matrix elements of observables are expected to be described by random
matrix theory. Related frequencies that have been studied in the literature are $\omega^{}_{\mathrm{SFF}}$, which controls the onset of random-
matrix behavior in the spectral form factor, and the transport frequencies $\omega^{}_{\mathrm{tr}}$, which are derived from transport coefficients. However, a direct quantitative comparison of these frequencies is lacking. Using exact diagonalization, we conduct such a comparison for the spectral functions of current operators in clean and disordered
quantum spin ladders with diffusive energy and
spin transport. We find clear evidence for the expected low-frequency plateaus in the ETH spectral functions. For the accessible system sizes, $\omega^{}_{\mathrm{SFF}}$ is consistent with the extent of the plateaus, while the transport frequencies are systematically larger and lie in the nonuniversal regime of the spectral functions. Our findings highlight the need to better understand the origin of these quantitative differences.
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All authors Kadir Çeven, Rohit Patil, Marcos Rigol, Fabian Heidrich-Meisner
Functional Analysis
On absolutely Cesàro bounded operators
Arafat Abbar, Loris Arnold and Clément Coine
We study $p$-absolutely Cesàro bounded operators, with particular emphasis on self-improvement, weighted shifts, and linear dynamics. Our first main result shows that, for $1<p<\infty$, every positive absolutely Cesàro bounded operator on $L^p(\Omega)$ is automatically $p$-absolutely Cesàro bounded. We then characterize $q$-absolute Cesàro boundedness of backward shifts on weighted $\ell^p$-spaces for $q\geq p$ and use this characterization to construct examples exhibiting a wide range of possible growth rates of the powers. In the dynamical direction, we obtain new obstructions to absolute and strong Cesàro boundedness; in particular, no strongly Cesàro bounded operator on a nonzero
Banach space is chaotic or upper frequently hypercyclic. We also introduce Cesàro ratio-boundedness and compare it with absolute Cesàro boundedness. Finally, a general Baire-category principle yields a genericity
theorem for the failure of $p$-absolute Cesàro boundedness.
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Analysis of PDEs
The Boltzmann-BGK model with nontrivial collision frequency near vacuum
Sungsu Park and Seok-Bae Yun
We study the Cauchy problem for the Boltzmann-BGK model in the three-dimensional whole space with nontrivial collision frequency $\nu(f)=\rho^\alpha T^{\beta}$, where $\alpha\in(1/3,1]$, $\beta\in[0,1]$, and $3\alpha+2\beta\geq 2$. Existing well-posedness results for such models have largely been confined to near-
equilibrium regimes and stationary problems. For nonnegative initial data with finite mass and energy that are sufficiently small in suitable
polynomial-weighted $L^{\infty}$ norms, we establish global existence and uniqueness of mild solutions near
vacuum. No uniform positive lower bound on the macroscopic density or temperature is imposed. The analysis relies on two complementary mechanisms. First, a phase-space weight invariant along free-transport characteristics yields dispersive estimates for the collision frequency and the gain term. The resulting time-integrable decay controls the nonlinear growth and closes the global weighted estimates. Second, we establish a Lipschitz estimate for the relaxation operator in a weighted $L^1$ space controlling mass and energy, with a Lipschitz constant depending only on weighted upper bounds for the distribution functions. The relaxation operator $\nu\mathcal{M}$ has a more favorable structure for Lipschitz estimates than the local Maxwellian $\mathcal{M}$ alone: the collision frequency compensates for the singular dependence on the macroscopic fields, allowing us to establish Lipschitz continuity without uniform positive lower bounds for the density or temperature. Together, these estimates yield a unique global mild solution with uniform weighted bounds.
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Chemical Physics
Composition-Dependent Self-Diffusion Coefficients in Liquid Mixtures from Hybrid Machine Learning
Jens Wagner, Thomas Specht, Hans Hasse et al. (+1 more)
Self-
diffusion coefficients are key descriptors of molecular mobility, yet experimental data remain scarce, highlighting the need for reliable prediction methods. In previous work, we introduced the hybrid Enhanced Stokes-Einstein (ESE) model, which advanced the state of the art in the physically consistent prediction of self-
diffusion coefficients of solutes at infinite dilution in pure solvents by integrating the Stokes-Einstein equation with machine learning (ML). Here, we extend this approach to concentration-dependent self-
diffusion coefficients and multicomponent solvents with HADES. This hybrid architecture leverages a deep-set neural network to connect pure-component and mixture prediction within a single framework. HADES predicts self-
diffusion coefficients in
liquid mixtures with any number of components at any composition and temperature. The only required inputs are SMILES-encoded molecular structures of the components and the pure-component viscosities, making the method broadly applicable. Trained and evaluated on a comprehensive
dataset of 2526 data points for 600 systems, HADES significantly outperforms
benchmark prediction methods. The trained model and its source code are fully disclosed, and the application is available via an interactive website https://ml-prop.mv.rptu.de/.
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All authors Jens Wagner, Thomas Specht, Hans Hasse, Fabian Jirasek
Logic in Computer Science
Aligning HOL-Light and Rocq libraries formally
Frédéric Blanqui and Antoine Gontard
We report on our efforts to translate HOL-Light
theorems on HOL-Light types/functions into Rocq
theorems on Rocq types/functions. To this end, we developed in Rocq tactics to automate the proofs required for replacing a HOL-Light inductive type or recursive function definition by an equivalent but more idiomatic one in Rocq. We also explain how we replaced the definition of real numbers, as well as a number of mathematical notions like Rn spaces and the definition of limit, hence providing to Rocq users many definitions and
theorems in logic and analysis that had not been formalized in Rocq before.
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Differential Geometry
Kähler-Einstein cone metrics and parabolic bundles
Martin de Borbon
Let $X$ be a compact Kähler
manifold, let $D=\sum_iD_i$ be a simple normal crossing divisor, and fix $\beta_i\in(0,1)$. We introduce a
parabolic structure $TX_*$ on $TX$, given along each $D_i$ by the filtration $0\subset TD_i\subset TX|_{D_i}$ with weight $w_i=1-\beta_i$ on the normal quotient. If $X\setminus D$ carries a Kähler–Einstein metric $\omega$ with cone angle $2\pi\beta_i$ along $D_i$, we show that $TX_*$ is
parabolic polystable with respect to $[\omega]$. When the Einstein constant $\lambda$ is non-zero, we introduce
parabolic structures on the Tian extension ($\lambda>0$) and on Simpson's canonical
Higgs bundle ($\lambda<0$), and prove that these are polystable too. Combined with the Bogomolov–Gieseker inequality for
parabolic bundles, this yields a Miyaoka–Yau inequality for these pairs.
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Atomic Physics
Vector Measurements Using Integrated Radio Frequency Atomic Magnetometers
Ayse Marasli, Thomas W. Kornack, D. Casey Oware et al. (+1 more)
We demonstrate reconstruction of three-dimensional
radio-frequency (RF)
magnetic-field vectors using a pair of integrated RF atomic magnetometers operated with orthogonal bias-field orientations. A theoretical and experimental analysis identifies a phase-ambiguity dead band that limits reconstruction when the two sensor responses become nearly identical. Measurements performed in an unshielded laboratory environment demonstrate accurate reconstruction of RF
magnetic-field orientations and validate the predicted dependence of reconstruction accuracy on signal imbalance. These results establish integrated RF atomic magnetometers as a compact and sensitive platform for directional RF
magnetic-field sensing, particularly at low frequencies, and provide a foundation for portable source-localization and field-mapping applications.
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All authors Ayse Marasli, Thomas W. Kornack, D. Casey Oware, Karen L. Sauer
Computer Vision
Applications of Neural Cellular Automata: State of the Art, Challenges and Opportunities
Nick Lemke, Niklas Ihm, John Kalkhof et al. (+11 more)
Neural Cellular Automata (NCAs) are a new type of neural network architecture which enable accurate and robust inference at extremely small model sizes. Recently, NCAs have advanced to become interesting low-resource alternatives to convolution- and
attention-based architectures for various tasks such as image analysis, synthetic image generation, and simulation. The rapid development and increased research interest necessitate a comprehensive review of the emerging technology. This review provides an overview of the fundamentals of NCAs, applications to medical imaging, as well as insights into the state of the art. We analyze recent modifications to the originally proposed NCA architecture with respect to their efficiency and accuracy. Furthermore, we review practical applications in real-world scenarios with a focus on medical image analysis,
segmentation, classification, registration, depth estimation, and image synthesis. Finally, we identify several advantages of NCAs, research gaps, and conclude with an analysis of future opportunities for NCAs in medical applications in confined settings or areas that have particular demands for robustness or efficient data processing.
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All authors Nick Lemke, Niklas Ihm, John Kalkhof, Mirko Konstantin, Henry J. Krumb, Daniel M. Lang, Ehsan Pajouheshagar, Ario Sadafi, Arjan Kuijper, Karim Lekadir, Marco Lorenzi, Carsten Marr, Julia A. Schnabel, Anirban Mukhopadhyay
Logic in Computer Science
Formal Verification of Proofs from Automated Theorem Provers for Higher-Order Logic
Melanie Taprogge, Frédéric Blanqui and Alexander Steen
We identify common challenges and requirements for verifying proofs from automated
theorem provers in the Dedukti logical framework and develop a general methodology for deriving encodings of calculus rules and proof steps, including clausification. We then apply this methodology to the EP calculus for higher-order logic and integrate it into the automated
theorem prover Leo-III. The resulting prototype reconstructs about 80% of generated proof steps automatically, making Leo-III the first higher-order automated
theorem prover to support independently checkable proof reconstruction and providing a basis for cross-system reuse. The implementation uncovered several bugs in Leo-III.
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Game Theory
Polyhedral Methods for Cooperative Games: Small Lifts and Hard Faces
Michel Grabisch and. Hans Raj Tiwary
We study the computational complexity of fundamental algorithmic problems – membership testing, separation, valid-inequality testing, and linear optimization – over polytopes and cones arising from cooperative games (also known as pseudo-Boolean functions). A central obstacle in the study of such problems is that a general cooperative game on $n$ players requires $2^n$ values, so the input size is $2^n$ for a game with $n$ players, making these computational tasks theoretically trivial. Restricting to $k$-additive games reduces the input size to $O(n^k)$, making such games a natural target for meaningful questions about the existence of efficient
algorithms. On the positive side, we give an explicit extended formulation of size $O(n^k)$ for the core of $k$-additive $k$-monotone games, allowing all four problems to be solved by a single
polynomial-size linear program – in particular, circumventing the ellipsoid method that is needed when building from earlier tractability results of Deng and Papadimitriou, or of Edmonds. For the cone of $k$-additive $(k{-}1)$-monotone games, we give a complete characterization of its extreme rays and derive the same $O(n^k)$ bound on extension complexity, yielding a geometry-based proof and generalization of a result of Billionnet and Minoux. On the negative side, we show that for $l \leq k-2$ the cone of $k$-additive $l$-monotone games is computationally intractable: membership testing is not in NP (unless NP\,=\,coNP), valid-inequality testing is NP-complete, and extension complexity is at least $1.5^n$. Our hardness results yield, as a special case, a result of Crama and of Gallo and Simone. Furthermore, our hardness results also explain the lack of any good characterization of the extreme rays of the cone of $k$-additive $(k{-}2)$-monotone games.
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Information Theory
Deterministic Smoothed MAP Detection for High-Dimensional MIMO Systems
Vitor Tucci Ramos, Stephane Senecal and Sheng Yang
We propose a deterministic smoothed maximum a posteriori (SMAP) framework for high-dimensional multiple-input multiple-output (
MIMO) detection. The discrete constellation prior is approximated by an i.i.d. Gaussian mixture, yielding a differentiable MAP objective that retains the constellation structure while enabling continuous optimization. Unlike sampling-based approaches, SMAP formulates detection as a deterministic optimization problem and can be initialized by the output of an arbitrary detector, allowing it to operate either as a standalone detector or as a refinement stage. For hard detection, we introduce SMAP-KR, which complements the continuous solution with a local $K_R$-neighbor search evaluated according to the original maximum-likelihood metric. Annealed continuation improves robustness for higher-order constellations, while a two-neighbor approximation reduces the cost of evaluating the mixture prior. We further develop a soft-output SMAP method in which a local Gaussian approximation based on the
curvature of the smoothed posterior provides symbol probabilities and bit log-likelihood ratios without posterior sampling or explicit counterhypothesis lists. Numerical results for critically loaded MU-
MIMO systems show that SMAP-KR provides an increasingly favorable performance-complexity tradeoff as the system dimension grows and can also effectively refine the output of existing detectors. For coded transmission, soft SMAP provides substantial block-error-rate gains over both LMMSE- and K-best-based soft detection.
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Machine Learning
Taking a Second Look: Correcting Sea Ice Forecasts with Sparse Observations
Tianshuo Zhang, Xianglei Xing, Aowen Yang et al. (+4 more)
Sea ice forecasts are issued several days ahead, allowing errors to accumulate while new, often sparse sea ice concentration (SIC) observations become available. We find that fixed-propagation errors concentrate near structured, high-gradient ice edges, whereas homogeneous interiors require limited propagation, suggesting that propagation distance should be state dependent. We therefore introduce ECHO (Evidence-guided Correction with Heterogeneous prOpagation), where ECHO-Scale adapts propagation distance while preserving correction geometry, and ECHO-Delta learns a bounded residual around fixed propagation. Across all 96 standard evaluation settings spanning diverse priors, observation times, sparsity levels, geometries, and noise conditions, both outperform fixed propagation. ECHO-Delta achieves the best average accuracy, while ECHO-Scale is more robust to geometry shifts. Code is available at https://github.com/yingtian22/TAKING-A-SECOND-LOOK.
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All authors Tianshuo Zhang, Xianglei Xing, Aowen Yang, Jia Gao, Wenzhe Zhai, Shanshan Liu, Chengtao Cai
Statistics Applications
Overcoming Model Misspecification in Bayesian Inference of Molecular Signalling Networks
Yinghan Li, Heishiro Kanagawa, Francesca Romana Crucinio et al. (+2 more)
Bayesian inference of molecular signalling networks usually relies on tractability of the marginal likelihood, enabling the set of possible networks to be efficiently explored. As such, linear models with independent errors and conjugate priors are routinely used. However, the dynamics of molecular signalling are nonlinear, and relevant confounders are often unobserved; failure to account for these complexities will almost certainly lead to over-confident inferences in the standard
Bayesian framework. To confront this reality, we develop a post-
Bayesian approach to inference of molecular signalling networks, guided by the principle that uncertainty should not vanish when the statistical model is misspecified, even in the infinite-data limit. Technically, we extend the predictively-oriented (PrO) posterior of McLatchie et al. (2025) to the setting of latent variable models, empirically investigating the properties of PrO posteriors in the challenging network inference context.
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All authors Yinghan Li, Heishiro Kanagawa, Francesca Romana Crucinio, Matthew A. Fisher, Chris. J. Oates
Astrophysics of Galaxies
LATED: JWST integral field spectroscopy of a galaxy caught in chemical infancy at $z=4.8$ behind Abell 2744
Mingyu Li, Roberto Maiolino, Zheng Cai et al. (+26 more)
When Population III (Pop III)
star formation ended remains an open question. LATED-1 is an intrinsically faint ($M_\mathrm{UV}=-16.15$) Ly$\alpha$ emitter at $z=4.80$ revealed by VLT/MUSE behind the
lensing cluster Abell 2744 ($z=0.308$). Before any spectroscopic
metallicity constraints, it was identified as an extremely metal-poor or metal-free
galaxy candidate from JWST imaging by LATED, our novel photometric selection framework. Here we present serendipitous JWST/NIRSpec PRISM integral-field spectroscopy of this target. The spectrum reveals Ly$\alpha$, H$\beta$, and H$\alpha$ at 7.0, 5.6, and 17.7$\sigma$, as well as tentative detections of [O III]$\lambda\lambda4959,5007$ at 2.9$\sigma$, and yields $R3=\mathrm{[O\,III]\lambda5007/H\beta}=0.59^{+0.27}_{-0.21}$, upholding the earlier LATED photometric prediction of $R3<1.54$ ($2\sigma$ limit). The canonical JWST-based strong-line calibration, extrapolated to low
metallicity, implies $\log (O/H)=6.45^{+0.17}_{-0.19}$, or $Z/Z_\odot=0.58_{-0.20}^{+0.28}\%$, placing LATED-1 among the most metal-poor
galaxies known. Its modest magnification ($\mu=2.80$) leaves the intrinsic properties insensitive to the lens model. LATED-1 is therefore a
dwarf galaxy caught in the earliest state of chemical enrichment, and a compelling target for testing whether Pop III
star formation can persist to $z<5$. The result demonstrates that photometric selection, especially through the LATED methodology, can reach below one per cent
solar metallicity to identify Pop III
galaxy candidates for spectroscopic follow-up.
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All authors Mingyu Li, Roberto Maiolino, Zheng Cai, Hannah Übler, Boyuan Liu, Qiao Duan, Fuyan Bian, Sijia Cai, Francesco D'Eugenio, Eiichi Egami, Bjorn H. C. Emonts, Xiaohui Fan, Yuki Isobe, Lucy R. Ivey, Xihan Ji, Gareth C. Jones, Maria Koller, Xiaojing Lin, Christopher C. Lovell, Kimihiko Nakajima, Masami Ouchi, Robert G. Pascalau, J. Xavier Prochaska, Jan Scholtz, Fengwu Sun, Sandro Tacchella, Yunjing Wu, Fujiang Yu, Zijian Zhang
Astrophysics of Galaxies
LATED: Ly$\alpha$-anchored photometric selection of candidate metal-free and extremely metal-poor star formation from the end of reionisation to cosmic noon
Mingyu Li, Zheng Cai, Roberto Maiolino et al. (+24 more)
Cosmological simulations allow a low-level tail of Population III (Pop III)
star formation to persist to $z=2-6$. Spectroscopic confirmation is expensive, so an efficient photometric pre-selection is needed. We present LATED (Lyman-Alpha
Tomography of Extremely Metal-poor Domains), which selects metal-free and extremely metal-poor candidates from a Ly$\alpha$-emitter parent sample using strong-line diagnostics. The method requires three bands and two colours, $x=m_{\rm OIII}-m_{{\rm H}\alpha}$ and $y=m_{{\rm H}\alpha}-m_{\rm cont}$, which trace oxygen abundance and the H$\alpha$ equivalent width, respectively. Requiring that the filters simultaneously contain [O III]+H$\beta$ and H$\alpha$, together with a Ly$\alpha$ parent selection, defines five windows spanning $z=1.92-6.60$ (four JWST/NIRCam, one Roman/WFI). The criteria, $x\geq x_{\rm min}(z)$ and $y\leq y_{\rm max}(z)$, are set by the per-
redshift extrema of a forward-modelled Pop III template locus. Ordinary metal-enriched
star-forming and AGN templates fall outside the selection region, and possible contaminants such as little red dots are flagged by their multi-band colours. To check contamination empirically, we apply LATED to 1126 JADES spectroscopic
galaxies, and no source is selected in the four NIRCam windows. We release a Python package which converts the same photometry into R3=[O III]/H$\beta$ as a measurement or upper limit, reproducing JADES spectroscopy with small 0.12 dex scatter. Applied to 85 archival MUSE Ly$\alpha$ emitters in Abell 2744, LATED recovers the confirmed extremely metal-poor
galaxy AMORE6 and reveals three new candidates at $z=3-5$. Photometry alone cannot establish a metal-free nature. LATED delivers prioritised candidates for spectroscopic follow-up, providing a scalable route toward a systematic census of late-time Pop III
star formation.
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All authors Mingyu Li, Zheng Cai, Roberto Maiolino, Fuyan Bian, Sijia Cai, Francesco D'Eugenio, Qiao Duan, Eiichi Egami, Xiaohui Fan, Yuki Isobe, Xihan Ji, Gareth C. Jones, Maria Koller, Xiaojing Lin, Boyuan Liu, Christopher C. Lovell, Kimihiko Nakajima, Masami Ouchi, Robert G. Pascalau, Zijin Su, Jan Scholtz, Fengwu Sun, Sandro Tacchella, Hannah Übler, Yunjing Wu, Fujiang Yu, Zijian Zhang
Dynamical Systems
Complete classification of algebraically primitive Teichmüller curves in $\Omega\mathcal{M}_g(g-1,g-1)^{\mathrm{hyp}}$
Myeongjae Lee
We give a complete classification of algebraically primitive Teichmüller curves in $\Omega\mathcal M_g(g-1,g-1)^{\mathrm{hyp}}$ for $g>2$. These curves are precisely those generated by the Veech $2p$-gons, where $p=2g+1$ is
prime.
Machine Learning
Overlay\_dx - Automating forecasting evaluation
Long Ngo, Mohammed Amine Chamli, Jonathan Rivalan et al. (+1 more)
Traditional evaluation metrics provides numerical values but often lack comprehensibility, hindering effective differentiation of model performances. Our work addresses this challenge by introducing overlay\_dx, a novel evaluation metric measuring the performance of time series prediction models. Overlay\_dx is a visual metric that represents the percentage of predictions falling within a confidence interval around actual values. Additionally, once evaluation results are plotted, overlay\_dx computes the area under the overlay curve, providing a quantitative measure of
alignment between predicted and actual values across different thresholds and predictions. Through extensive experiments, we demonstrate that our approach offers a unified evaluation framework that combines both visual and numerical assessments, enabling improved model comparison and providing valuable insights for further research and optimization efforts in time series prediction.
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All authors Long Ngo, Mohammed Amine Chamli, Jonathan Rivalan, Thomas Jaillon
Mesoscale and Nanoscale Physics
Corbino-Enhanced Supersonic Acoustic-Emission Threshold in a GaAs Two-Dimensional Electron System
A. D. Levin, A. S. Jaroshevich, Z. D. Kvon et al. (+5 more)
We report nonlinear differential-resistance measurements in a high-mobility GaAs/AlGaAs two-dimensional electron system patterned in a Corbino geometry. At zero
magnetic field, $R_{\mathrm{diff}}(I_{dc})$ exhibits a pronounced polarity-selective threshold peak on the negative-current branch, gradually suppressed by a perpendicular
magnetic field. We interpret the Corbino anomaly as a local Cherenkov-like threshold for acoustic
phonon emission, enabled by the radial current concentration $j_r(r)=I/(2\pi r)$, which drives the local electron velocity above the sound velocity in a region adjacent to the inner contact. The polarity selectivity is attributed to Peltier heating and cooling, which modify the local thermal and boundary conditions near the contact, rather than to the kinematic threshold itself. Our results identify the Corbino geometry as a sensitive platform for probing local nonequilibrium electron–
phonon processes in a high-mobility electron system within an independently established hydrodynamic-crossover regime and suggest that the inner Corbino contact can act as a geometry-defined source for supersonic acoustic emission.
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All authors A. D. Levin, A. S. Jaroshevich, Z. D. Kvon, V. A. Chitta, M. S. Aksenov, D. V. Dmitriev, A. K. Bakarov, G. M. Gusev
Algebraic Geometry
Untwisting the twisted character variety via a stacky curve
Anna Borri
Given a smooth projective curve $X$ over $\mathbb{C}$, we show that the twisted character variety of $X$ is equivalent to a component of the character variety of a stacky curve $\mathcal{X}$, constructed by adding an orbifold point to $X$. This allows to interpret the non abelian Hodge correspondence in degree $d$ over $X$ as a statement about the geometry of the Hodge
moduli space of $\lambda$-connections on $\mathcal{X}$. Following Shende's approach (see arXiv:1411.4975), we exploit this interpretation to compute the weights of the tautological classes on the
cohomology of the twisted character variety, by replacing $\mathcal{X}$ with a simplicial scheme $\Delta_{\mathcal{X}}$ obtained from a triangulation.
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Systems and Control
Optimal Allocation of Grid-Forming Frequency Shaping Control
Zhaomin Lyu, Ding Zhang and Yan Jiang
Various inverter-based control strategies have been proposed to improve frequency security for power systems with high renewable penetration. Among them, the grid-forming frequency shaping control is particularly promising due to its ability to shape the post-contingency aggregate system frequency dynamics into first-order with prescribed rate of change of frequency (RoCoF) and steady-state frequency deviation. Moreover, the shaped aggregate dynamics depends on the harmonic sum of all inverter transfer functions rather than on their distribution. In light of this, here we explore how to allocate shaping control resources to minimize the transient control effort needed to achieve ideal coherent dynamics. We formulate it as a constrained optimization problem by tackling two main difficulties. First, we make the squared $\mathcal{H}_2$ norm legitimate quantification of transient control cost under step power imbalances through a system transformation. Second, we simplify the $s$-domain constraint for Nadir elimination into a standard constraint that is easy to implement in optimization. The resulting non-convex optimization problem can be solved by existing successive convexification method. The effectiveness of the allocation has been verified on the modified Icelandic Power Network test case.
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High Energy Physics (Theory)
The Gaiotto-Kim Trace Formula and Line Defects
Sungjoon Kim and Spencer Stubbs
We study the insertion of 4d half-BPS line defects into the trace formula proposed by Gaiotto and Kim, which computes the ellipsoid partition function of the 3d topological
quantum field theory (TQFT) arising from a 4d $\mathcal{N}=2$ superconformal field theory. This yields a homomorphism to 3d Wilson loops, preserving the fusion
algebra of the 4d defects. We also present a systematic
algorithm for determining the simple objects of a 3d TQFT in terms of Wilson loops in the UV 3d $\mathcal{N}=2$ abelian Chern-Simons-matter theory. Utilizing supersymmetric localization, we characterize the modular $S$- and $T$-
matrices of the TQFT. We apply our
algorithm to various 3d TQFTs arising from the trace formula with higher-power monodromy of the $(A_1,G)$ Argyres-Douglas theories.
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Combinatorics
On splitting properties of the stability problem with integer choice functions
Alexander V. Karzanov
We consider the integer version of Alkan–Gale's model on stability in a two-sided
market, called the stable generalized allocation one. It is given by a triple $(G,b,C)$, where $G=(V,E)$ is a finite bipartite graph with nonnegative integer capacities $b(e)\in{\mathbb Z}_+$ of edges $e\in E$, and for each vertex (“
agent”) $v\in V$, the preferences on the set $E_v$ of its incident edges depend on a choice function $C_v$. The latter acts on the set of vectors in ${\mathbb Z}_+^{E_v}$ bounded by the capacities and obeys the standard axioms of substitutability and size monotonicity. Alkan–Gale's prominent
theorem implies that the stability problem in this case always has a stable solution $x\in{\mathbb Z}_+^E$ and, moreover, the set ${\cal S}_{G,b,C}$ of these solutions (“stable generalized allocations”) forms a distributive
lattice. However, this
lattice is rather intricate to construct and work with, and we wonder whether it can be represented via a “simpler” stability model. Answering this issue, we arrange a sort of splitting techniques to embed ${\cal S}_{G,b,C}$, as a sublattice, in the
lattice of stable matchings and, more compactly, in the
lattice of stable allocations (as in Baiou–Balinski's stability model). This generalizes Fleiner's result on a detachment in the special case with all-unit capacities. Keywords: stable marriage, stable allocation, choice function, rotation, distributive
lattice, poset representation
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Representation Theory
One-periodic category of twisted complexes, Cohen-Macaulay modules and differential modules
Joseph Winspeare
In this paper, we give an $A_\infty$-enhancement of the triangulated orbit category $(\mathcal{T}/[1])_{tr}$ when $\mathcal{T}$ is an algebraic triangulated category. We then use this enhancement to give a description of $(\text{per}(A)/[1])_{tr}$ in terms of differential modules and Cohen-Macaulay modules when $A$ is a finite dimensional $\mathbb{Z}$-graded
algebra of finite global dimension.
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Machine Learning
Universal Multi-Modal Traceformer: Integrating Heterogeneous Context for Process Event Prediction
Fabian Spaeh, Jingxing Fang, Shandian Zhe et al. (+1 more)
Event logs arise in a wide range of real-world processes, capturing not only event activities and timestamps but also multi-modal contextual information. Existing event-sequence models, including many temporal point process approaches, primarily model event activities and timestamps while overlooking heterogeneous context, such as numerical measurements, categorical attributes, textual descriptions, and metadata associated with individual events and entire traces. In this paper, we propose Universal Multi-Modal Traceformer (UMT), a unified framework for incorporating heterogeneous process context into next-event prediction. Built on a
Transformer backbone, UMT introduces a universal feature encoder that maps diverse feature types into a shared representation space and handles contextual information at both the event and trace levels. UMT further develops a per-event Perceiver module that dynamically weights contextual features and adaptively integrates them into event-
token representations. To accommodate the heavy-tailed and potentially multi-modal distribution of inter-arrival times, UMT represents each interval at multiple temporal scales and jointly predicts the corresponding scale-specific quantities. Experiments on 13 real-world event logs show that UMT improves both next-event activity and time prediction over existing approaches.
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All authors Fabian Spaeh, Jingxing Fang, Shandian Zhe, Bin Shen
Differential Geometry
Geometric quantizazion and TYCZ coefficients of HyperKähler 4-manifolds
Simone Cristofori
In this paper we study conditions for the existence of a
geometric quantization of a complete hyperKähler four
manifold with an effective tri–
Hamiltonian circle action and we show that the vanishing of the third coefficient $a_3$ associated to these metrics is equivalent to flatness.
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Commutative Algebra
Descent along flat composed with radicalization
Mohsen Asgharzadeh
We study the following general situation. Let $R\to S$ be a finite flat morphism of regular rings of zero (resp.
prime) mixed or (equi)-characteristic. For $P\in Spec R$, put $A=R/P, C=S/PS,$ and $B=S/\sqrt{PS}=C_{\mathrm{red}}.$ The basic question is whether a property of $B$ forces the same property of $A$. The main point is that ordinary finite-flat descent applies naturally to $A\to C$, whereas the passage $C\to C_{\mathrm{red}}$ may (not) destroy nilpotent information.
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Robotics
What do VLM-Based Vision-Language Navigation Models Rely on: Interpreting and Steering Policy Behavior
Débora Oliveira Makowski, Samiran Gode, Abhijeet Nayak et al. (+4 more)
Modern
Vision-
Language Navigation (VLN) models rely mostly on pre-trained large
Vision-
Language Models (VLMs) to predict
navigation actions. While this fusion of
language instructions and visual observations allows
multimodal reasoning, it obscures how information is routed across modalities or what mechanisms drive
navigation decisions. Thus, it remains unclear whether VLN models ground their predictions in relevant semantic cues or can track task progress. In this work, we study the interpretability and steerability of VLN models. We use intervention-based metrics that measure how visual observations, instructions, and visual
memory causally influence
navigation decisions. Our results show that these
navigation policies are sensitive to all input modalities and do not depend on a single one. We further show that these
agents encode
navigation progress and retain semantic structure from their VLM backbones, enabling concept-level steering through internal activations. Finally, we extract activation vectors for abstract behaviors to transfer them zero-shot to out-of-distribution real-world scenarios, improving performance without additional fine-tuning.
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All authors Débora Oliveira Makowski, Samiran Gode, Abhijeet Nayak, Marco Hutter, Cordelia Schmid, Lukas Rosenberger Schmid, Wolfram Burgard
Information Theory
Single-Fragment Forensic Coding via Multidimensional Cyclically Permutable Codes
Yubo Sun, Yijun Zhang and Gennian Ge
The proliferation of 3D printing raises new security and forensic challenges, including the risk of unauthorized fabrication of untraceable firearms and other regulated items. To enable traceability, we consider single-fragment forensic coding, in which a unique identifier is embedded into a printed object and must be recoverable from any fragment containing an axis-parallel box of prescribed minimum volume and coordinatewise thickness, even in the presence of substitution errors. To address this problem, we introduce and study multidimensional cyclically permutable codes (CPCs), for which every cyclic translate uniquely determines both the original codeword and the applied translation. By applying periodic lifting to a CPC base array, every complete period contained in a fragment corresponds to an unknown cyclic translate of a codeword, thereby reducing the forensic
alignment problem to multidimensional cyclic synchronization. We establish theoretical bounds and develop explicit constructions in both the noiseless and substitution-error settings. For fixed dimension $d$ and alphabet size $q$, we obtain the optimal redundancy $d\log_q k+o(1)$ for noiseless $d$-dimensional CPCs of side length $k$. For fixed $t$, the optimal redundancy of $t$-substitution-correcting $d$-dimensional CPCs lies between $(t+1)d\log_q k+O(1)$ and $(2t+1)d\log_q k+O(1)$. For binary alphabets and $d\geq2$, an explicit robust row-anchor construction achieves $(t+1)d\log_2 k+O(\log\log k)$ redundancy, matching the optimal leading term. In the thick-fragment regime $h=cM^{1/d}$, where $M$ and $h$ lower-bound the volume and the side lengths of a box contained in the fragment, periodic lifting yields single-fragment forensic codes of rate $c^d-o(1)$. In particular, the rate approaches one when $c=1-o(1)$.
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Computation and Language
Evaluating Decision Models for Text Annotation in Computational Social Science
Hazem Ibrahim and Yasir Zaki
Computational social science increasingly relies on large
language models for text annotation, and the validity of published findings now rests on the labels generated by such models. Decision models, a new model class built for categorical question answering, answer typed questions with a choice, a probability distribution over the label set, and a confidence score rather than free text, at a small fraction of frontier inference prices. Whether their answers are accurate, and whether that stated confidence can be trusted on social science constructs, are unknown. Here, we mirror the evaluation of Ziems et al. (2024) on 18 computational social science classification tasks (7,977 items), comparing the first commercial decision model and two open-weight counterparts against 19 frontier and open-weight
language models under the same zero-shot protocol, and extending the decision-model comparison to eleven open-weight systems released in the week after it. The decision model trails the per-task best LLM on 14 of 15 evaluation tasks, with a median deficit of 11.6 macro-F1 points, at a median 44 times lower measured cost. Its confidence is better calibrated than the verbalized confidence of 16 of the 19 LLMs, yet three frontier models show lower median calibration error (0.157 against 0.066). While items above 0.9 confidence are typically labeled accurately (median accuracy 0.815), on one task, empathy in peer-support dialogues, the model reports high confidence while performing near chance. Nonetheless, our results suggest that decision models are useful as a first step in the annotation pipeline: routing low-confidence items to an LLM matches or exceeds the LLM alone at a quarter to half of its cost.
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