General Relativity and Quantum Cosmology
Mind the second gap: The impact of gaps on noise and signal parameter inference
Ollie Burke, Federico Pozzoli, Martina Muratore et al. (+1 more)
Gravitational-wave data is never analysed without some conditioning: filtering and tapering act multiplicatively on the noise, destroying the stationarity on which the Whittle likelihood — the backbone of nearly all gravitational-wave inference — rests. The problem is particularly evident for LISA, where gaps are expected to overlap almost all signals and the noise must be estimated jointly with those astrophysical signals. We provide an analytical and numerical framework to assess the impact of noise mis-modelling when signal and noise parameters are inferred jointly in the presence of gaps. From a Fisher-
matrix formalism verified against
Bayesian inference, we obtain closed forms for the model uncertainties, their maximum-likelihood estimates and the true scatter in the latter, for various approximations to the likelihood. The Fisher-based linear formalism is extended through the Godambe–White
curvature to the non-linear regime that severe mis-modelling produces. We survey gap families from long, well-tapered interruptions to short, high-rate ones, injecting massive black-hole binaries. Except in the case of frequent gaps, we show that the windowed covariance is well approximated by its leading diagonal — the window convolved with the power spectral density — for the estimation of both signal and noise parameters. By omitting the convolution, the signal sector remains unbiased but the noise parameters, in particular the optical-metrology noise which is dominant at high frequency, is displaced by over an order of magnitude in power. At the highest glitch rates the diagonal approximation stays accurate yet loses an order of magnitude in precision. To remedy this, we propose an exact time-domain likelihood of the surviving samples which can be efficiently (and accurately solved) via preconditioned conjugate gradient methods.
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All authors Ollie Burke, Federico Pozzoli, Martina Muratore, Jonathan R. Gair
Combinatorics
2-colouring shift-chains
Zak Smith
A shift-chain is an $ r $-uniform hypergraph $ \mathcal{H} $ on vertex set $ [n] $ with the property that, for any two edges $ \{ e_1, \ldots, e_r \} $ and $ \{ f_1, \ldots, f_r \} $ with $ e_1 < \cdots < e_r $ and $ f_1 < \cdots < f_r $, either $ e_i \le f_i $ for all $ i \in [r] $ or $ f_i \le e_i $ for all $ i \in [r] $. It is known that all shift-chains are properly vertex-colourable with three colours (that is, such that no edge is monochromatic), which is optimal for $ r \in \{ 2, 3 \} $. It was asked by Pálvölgyi in 2010 whether all shift-chains of sufficiently large uniformity are properly $ 2 $-colourable. We answer this question in a strong form, proving that in fact all shift-chains of uniformity at least $ 4 $ are properly $ 2 $-colourable. The colouring is obtained via a natural
algorithm with linear running time.
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Number Theory
On the infinite sum of reciprocals of the fourth powers of balancing numbers
Subhasis Panda, Aditya Kumar Dash and Utkal Keshari Dutta
In this note, we study the infinite reciprocal sum $\sum_{k=n}^{\infty}1/B_k^4$ involving the fourth powers of balancing numbers $B_n$. We show that, for every $n\geq2$, \begin{equation*} \left\lfloor \left( \sum_{k=n}^{\infty}\frac{1}{B_k^4} \right)^{-1} \right\rfloor = B_n^4-B_{n-1}^4 -\left\lceil\frac{B_{2n-1}}{280}\right\rceil +\varepsilon_n, \end{equation*} where $\varepsilon_n=1$ if $n\equiv1\pmod{12}$ and $\varepsilon_n=0$ otherwise. This result extends the corresponding reciprocal-sum result for Fibonacci numbers due to Hwang, Park and Song to balancing numbers.
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Statistical Methodology
Two Conformal Constructions for Adaptive Within-Document AI-Text Screening
Marco Mandap, Jerahmeel Hipolito, Arcel Galvez et al. (+4 more)
We study false-alert control when screening for text generated by artificial intelligence (AI). The screening procedure selects document prefixes and detectors from observed evidence and may stop before exhausting its inspection budget. We give two finite-sample constructions under document-level exchangeability between human calibration documents and a new null document, with no restriction on dependence among
tokens within a document. Construction A registers a finite family of prefix-detector scores and allocates a false-alert budget across their conformal ranks. A union bound protects any executed subset of that family. Construction B calibrates the complete-path maximum of a development-fixed adaptive policy. Each partial-path maximum is bounded by the complete maximum, so a terminal conformal rank protects early stopping without splitting the error budget. We prove marginal control of any false alert across the permitted inspection path and derive necessary calibration counts for rejection. We also state oracle testing, distribution-shift, and independent-audit bounds with their additional assumptions. Both constructions protect stopping within their specified scope; neither proof constructs an e-process or justifies multiplying conformal ranks. Detection power and computational savings remain questions for empirical evaluation.
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All authors Marco Mandap, Jerahmeel Hipolito, Arcel Galvez, Charlie Margaret Balagtas, Michael Joshua Buluran, Jeff Roel Durmiendo, Rizzette E. Lopez
Machine Learning
BeatGraph: Self-Supervised Heartbeat Graphs for Infant ECG Representations from the Home Environment
Mohammad Nur Hossain Khan, M. S. Krafczyk, Beverly G. Bolster et al. (+3 more)
Electrocardiogram (ECG) foundation models typically tokenize the signal into fixed-length patches that ignore cardiac structure, so a patch may split a heartbeat and the number of beats in each patch shifts with heart rate. This matters most for infants, whose heart rates are higher and whose ECG differs from the adult, clinic-recorded 12-lead data these models are built on. A model for infant ECG should therefore reason about heartbeats directly rather than recover them from arbitrary patches. We propose BeatGraph, which makes the heartbeat its unit of representation, modeling each 30-second window as a graph of beats. A shared beat encoder embeds each heartbeat from its waveform and inter-beat intervals, a
Transformer with positional encoding orders the beats in time, and residual graph
attention layers relate every beat to every other before
attention pooling yields a window
embedding. We pretrain BeatGraph on our new corpus of unlabeled infant recordings by predicting masked-beat
embeddings, then fine-tune it for each task. One backbone supports sleep-wake detection, infant-state classification, activity-source identification (infant- or caregiver-initiated movement), and affect recognition, improving macro-F1 over the strongest baseline on each task by 0.076 to 0.158. It also transfers across age groups, reaching 0.892 AUROC on the ZZU-pECG pediatric
benchmark (ages 0 to 14), within 0.001 of the best published self-supervised ECG model, and matching that model under linear evaluation on the adult PTB-XL
benchmark despite infant-only pretraining. Finally, to our knowledge, we release the first public infant ECG corpus collected in homes, classrooms, and laboratory settings with state and affect labels. It contains 3,408 hours of single-channel ECG from 143 infants aged 3 to 11 months, with unlabeled pretraining data,
benchmark tasks, and subject-level splits.
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All authors Mohammad Nur Hossain Khan, M. S. Krafczyk, Beverly G. Bolster, Nancy McElwain, Mark A. Hasegawa-Johnson, Bashima Islam
Materials Science
Unconventional magnetoelastic behavior in Al rich CoFeAl Films with inverse Heusler like local order for flexible spintronics
Rupalipriyadarsini Chhatoi, Anuroopa Behatha, Swayang Priya Mahanta et al. (+6 more)
Strain engineering of
magnetic properties offers a promising route toward flexible spintronic applications. Here, we report an unconventional magnetoelastic response in Al rich Co Fe Al thin films on flexible substrates using strain dependent magneto optical Kerr effect microscopy and magnetometry measurements. While the films exhibit a conventional positive magnetostriction coefficient, consistent with standard in plane easy axis rotation under stress, their saturation magnetization increases under compressive strain and decreases under tensile strain. First principles calculations reveal that this unconventional response originates from a strain induced competition between exchange splitting and
crystal field effects in an inverse Heusler like local environment created by Al enrichment. This leads to a highly sensitive, sublattice dependent
magnetic state, consistent with a strain induced reconfiguration of Co and Fe moments. Our results demonstrate that local compositional tuning can fundamentally alter magnetoelastic behavior, establishing strain controlled sublattice compensation as a route toward programmable
magnetic functionality in flexible spintronic systems.
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All authors Rupalipriyadarsini Chhatoi, Anuroopa Behatha, Swayang Priya Mahanta, Shubhransu Sahoo, Soubhagya Dash, Bhuvneshwari Sharma, Abhisek Mishra Esita Pandey, Satadeep Bhattacharjee, Subhankar Bedanta
Artificial Intelligence
A Flow Matching Framework for Neural Representational Dissimilarity
Zeyuan Ye and Xue-Xin Wei
Neural representational dissimilarity quantifies differences between neural response distributions, and is essential for comparing neural codes across stimuli,
brain areas, tasks, and models. Commonly used distance metrics involve different assumptions and are estimated with separate methods. Here, we show that a variety of distance metrics can be unified under a flow matching framework developed in deep generative models. That is, these distances arise as Jeffreys divergences under different velocity constraints. We find that flow matching has advantages for estimating distances involving complicated distributions and continuous variables. Furthermore, this framework enables the design of new distance metrics in a principled way. Together, flow matching provides a unified approach for understanding, estimating, and designing neural representational dissimilarity metrics.
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Cosmology and Nongalactic Astrophysics
A derived evolution of dark energy from cosmic inhomogeneity confronted with baryon acoustic oscillations and type Ia supernovae
Jacky David Yang and Hans-Otto Carmesin
The volume dynamics of space is a framework in which the possibility that matter can be unevenly distributed enters the expansion dynamics directly. It yields a
redshift-dependent effective Hubble constant and dark-energy density parameter from the Planck parameters alone. We derive the expansion history $H(z)$ of the framework and show that it is flat $\Lambda$CDM with the cosmological constant replaced by a dark-energy density that grows by 31 percent toward the present, with an effective equation of state $w(0) = -1.21$ approaching $-1$ at high
redshift and a present-day age of 13.52 Gyr, 0.3 Gyr younger than in the homogeneous limit. We confront it with the DESI DR2
baryon acoustic oscillations and the Pantheon+ type Ia
supernovae, with the Hubble constant, the sound horizon and the
supernova absolute magnitude free, so that only the shape of $H(z)$ is tested. Relative to $\Lambda$CDM the prediction is disfavored by $\Delta\chi^2 = 65$ with one parameter fewer. A free matter density reduces this to $\Delta\chi^2 = 42$, because each probe alone accommodates the model only with incompatible matter densities (0.35 from the oscillations, 0.54 from the
supernovae). Their combination bounds the heterogeneity amplitude to $\sigma_8 < 0.14$ at 95 percent confidence, against the Planck input 0.81; the best fit of the heterogeneous model is its homogeneous limit, flat $\Lambda$CDM. At the leading order currently evaluated, the heterogeneous contribution cannot account for the Hubble tension, and it acts opposite to the
evolution of dark energy that current distance data favor.
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Functional Analysis
Quotients of $L_1$ by subsequences of the Haar system have cotype 2
Stephen Dilworth, Denka Kutzarova, Mikhail Ostrovskii et al. (+1 more)
Let $Y$ be the closed linear span of a subsequence of the Haar system in $L_1$. We prove that the quotient space $L_1/Y$ has cotype~$2$. This result implies that transportation cost spaces on diamond graphs have cotype $2$.
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All authors Stephen Dilworth, Denka Kutzarova, Mikhail Ostrovskii, Thomas Speckhofer
Quantum Physics
Sipser-Spielman meets Dijkgraaf-Witten: non-Abelian qLDPC codes via twisted sheaf gauge theory and almost-constant-overhead magic state fountain
Guanyu Zhu, Shi Jie Samuel Tan, Ryohei Kobayashi et al. (+1 more)
Sipser-Spielman codes and Dijkgraaf-Witten twisted gauge theories are among the most profound ideas in the last few decades in the areas of computer science and mathematical physics respectively. This work unifies them in the same framework using the
language of sheaf
cohomology, and produces a new framework of twisted sheaf gauge theories describing a class of
quantum low-density parity-check (qLDPC) codes with non-Abelian $D_4$ topological order. The corresponding twisted Clifford-stabilizer qLDPC code can be obtained from gauging a new type of 0-form sub-complex
symmetry from a qLDPC code defined on a general sheaf complex, and can be interpreted as a topological defect network of non-Abelian $D_4$ patches glued together with proper gapped interfaces. As an application, one can use this to realize a magic state fountain via the gauging measurement of the addressable logical CZ gates as 0-form subcomplex
symmetries in a 2D hypergraph-product (HGP) sheaf code. This includes a scheme of subdividing an arbitrary constant-rate 2D HGP code with parameters $[[n,\Theta(n), \Omega(n^{1/2})]]$ into a
quantum sheaf code which allows preparation of $\Theta(n^{1/2})$ logical CZ magic states in parallel, equivalent to the recent
geometric construction using the code-to-
manifold mapping in (arXiv:2601.06736). Moreover, using the recent sheaf complex and algebraic code constructions by Golowich-Tamo-Zhu (arXiv:2609.27801) with parameters $[[n,\Theta(n^{1-\epsilon}), \Omega(n^{(1-\epsilon)/2})]]$ for arbitrary small $\epsilon$, one can prepare $\Theta(n^{1-\epsilon})$ CZ magic states in parallel and hence achieve an almost-constant magic rate.
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All authors Guanyu Zhu, Shi Jie Samuel Tan, Ryohei Kobayashi, Po-Shen Hsin
Networking
Can You Check That? The Checkability Boundary for Local LLM Network Automation
Maleeha Masood and Momina Nofal
Sending every network-automation input to a third-party frontier LLM exports sensitive artifacts such as production configurations,
topologies, and logs. Querying small
language models (SLMs) locally avoids this egress, but SLM outputs can be error-prone for direct use. This work introduces checkability as a criterion for determining which tasks are suitable for local inference. A task is checkable when it exposes a cheap, deterministic test - an intrinsic check - that rejects outputs violating a necessary correctness condition. We instantiate this idea in Touchstone, a local-first pipeline that uses seven off-the-shelf SLMs (1-8B parameters) to generate candidates, uses task-specific intrinsic checks to reject responses, and escalates unresolved inputs to a frontier LLM. On conflict detection and intent translation tasks, Touchstone reaches 98.6% and 93.8% end-to-end accuracy while escalating only 16% and 17% of inputs, respectively. On TeleQnA, a knowledge-only control that has no task-specific intrinsic checks, Touchstone is unable to match the accuracy of the frontier baseline. Our results support a simple deployment rule: keep inference local when task semantics support precise, low-cost checks; escalate the rest.
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Machine Learning
NEXT: Physics-Informed Neuro-Spectral Exponential Time Differencing Architectures
Márcio Marques, Leonardo Mendonça, Leonardo M. Moreira et al. (+6 more)
Physics-Informed Neural Networks (PINNs) build neural representations of time-dependent PDE solutions, naturally incorporating physics knowledge and observational data, which makes them well suited to both forward and inverse PDE problems. PINNs, however, are known to suffer from spectral bias and lack of causality. Neuro-Spectral Architectures (NeuSA), a recently proposed alternative to PINNs, mitigate both issues, but their numerical integration becomes unstable for stiff differential equations arising in many relevant physical problems. This study proposes Neuro-Spectral Exponential Time Differencing Architectures (NEXT), which combines the spectral representation of the PDE solution in NeuSA with high-order exponential integrators. Within this approach, the linear stiff part of the vector field induced by the PDE is integrated exactly through
matrix exponentials, while the possibly nonlinear remainder is modeled by a neural network. The effectiveness of NEXT is verified through
benchmark experiments on a set of stiff PDEs, in which NEXT is stable and accurate while NeuSA diverges numerically. It is also shown that NEXT can be applied to inverse problems, where the model has to learn unknown parameters or boundary conditions from sparse data. All code used in this work is publicly available at: https://github.com/marcioh2m/next.git .
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All authors Márcio Marques, Leonardo Mendonça, Leonardo M. Moreira, Christian Júnior de Oliveira, Vitor Balestro, Tiago Novello, Daniel Yukimura, Pavel Petrov, Lucas Nissenbaum
Differential Geometry
Anchor Radicals and Metric Rigidity in $n$-Lie–Rinehart Algebras
Irmely Gladesh Mabanza Nsiloulou and Basile Guy Richard Bossoto
For an $n$-Lie–Rinehart
algebra, $n>2$, the anchor is defined on $\Aext{n-1}L$, so its kernel does not determine a distinguished submodule of $L$. We introduce the anchor radical $\Rad(\rho)\subset L$ and prove that it is an adjoint-stable ideal on which the bracket is $A$-multilinear. We then derive an explicit obstruction to the $A$-linearity of metric compatibility in fundamental directions. This obstruction vanishes on $\Rad(\rho)$, whereas a strongly nondegenerate compatible metric on all of $L$ forces the anchor to vanish. These results lead to a natural notion of orthogonal structure on the anchor radical. For anchors induced by Nambu tensors, the radical is identified with the cotangent annihilator of the tensor.
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Combinatorics
How large can $B_n$- and $D_n$-friezes be?
Florian Ito Sprung
We pin down the largest entries possible in positive integral friezes of types $D_n$ for $n\geq 4$ and $B_n$ for $n\geq 2$, addressing a
conjecture of Robin Zhang. For type $D_n$, the sharp upper bound is $F_nF_{n+1}-1$, and for type $B_n$, it is $F_{n+1}F_{n+2}-1$, where $F_k$ are the Virahanka–Fibonacci numbers.
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Physics and Society
Collective impact of opinion formation on agent-based epidemic dynamics
Andrea Bondesan, Riccardo Vecchio, Chiara Barbati et al. (+3 more)
Epidemic spread and collective opinion formation are tightly coupled processes: individual beliefs about the severity of an outbreak and the value of protective measures shape behavior, while the evolving epidemic itself reshapes public sentiment through risk perception. We propose an
agent-based framework that couples opinion dynamics with a compartmental epidemic model, in which each
agent carries both a health status and a continuous opinion variable describing adherence to protective measures. Opinion
evolution is driven by binary interactions among
agents and by an exogenous background field that reflects the current state of the epidemic, while the disease transmission rate depends explicitly on the opinions of interacting
agents. Using methods of statistical mechanics, we characterize the resulting macroscopic system for the compartmental mass fractions and mean opinions in both far-from-
equilibrium and close-to-
equilibrium regimes. The calibration shows that incorporating behavioral opinion dynamics substantially improves the interpretation of epidemic
evolution. In particular, the inferred risk perception function evolves consistently with the observed epidemic burden, indicating that behavioral adaptation can explain part of the temporal variation that would otherwise be absorbed into time-dependent transmission parameters. Our results illustrate how integrating opinion heterogeneity in kinetic epidemic models offers quantitative insights into the feedback between behavior and disease spread.
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All authors Andrea Bondesan, Riccardo Vecchio, Chiara Barbati, Jonathan Franceschi, Anna Odone, Mattia Zanella
Combinatorics
Discounted Hitting Domination on Graphs with Submodularity, Complexity and Exact Algorithms
Julian D. Allagan, Kevin Pereyra and William A. Massey
On a network with a fixed set of verified sources, discounted averaging induces an
equilibrium support $h_i^S=\mathbb{E}_i[\lambda^{T_S}]$, the discounted probability that a random walk reaches $S$ before attenuation. We define the discounted hitting domination number $\delta_{\lambda,\tau}(G)$ as the minimum number of sources required to guarantee $h_i^S\ge\tau$ at every vertex. Although this potential is known through penalized and group hitting probabilities, the associated minimum-cardinality uniform-coverage problem appears to be new. Aggregate support is monotone submodular, while the uniform-floor problem is an exact submodular-cover problem. Moreover, if $\lambda^{r+1}<\tau\le\left(\frac{\lambda}{\Delta}\right)^r$, then $\delta_{\lambda,\tau}(G)$ equals the distance-$r$ domination number. This yields NP-completeness and APX-completeness at $(\lambda,\tau)=(1/4,1/14)$ on graphs of maximum degree three. For spiders, we obtain an exact finite-state characterization and a
polynomial-time
algorithm for every fixed rational pair $(\lambda,\tau)$, and show that the branching vertex need not belong to a minimum source set. Finally, an exact mixed-integer linear formulation certifies optimal placements on a real network and a synthetic graph and demonstrates substantial differences from degree, closeness, and classical domination.
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Accelerator Physics
Generation of 10-TW Attosecond X-Ray Pulses in a Free Electron Laser
E.A.Schneidmiller, S.Serkez, I.Zagorodnov et al. (+35 more)
Attosecond pulses provide direct access to electron dynamics in atoms, molecules, and solids on their natural timescales. While table-top sources have achieved attosecond pulse durations at moderate intensities, extending attosecond science to high peak powers in the x-ray regime requires free-electron
lasers (FELs). Here we report the generation of soft-x-ray pulses with a duration of $\sim\!100$ as and peak power on the order of 10 TW at the European XFEL. The unprecedented combination of pulse duration and peak power is enabled by operation of a soft-x-ray undulator at high electron energy together with five-stage bunch compression, producing ultrahigh peak currents. These millijoule-level attosecond x-ray pulses establish a new regime for attosecond science.
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All authors E.A.Schneidmiller, S.Serkez, I.Zagorodnov, N.Gerasimova, M.Scholz, N.Golubeva, M.Guetg, G.Geloni, S.Karabekyan, F.Sottocorona, A.Trebushinin, G.Perosa, S.Tomin, F.Mayet, Th.Maltezopoulos, J.Gruenert, J.Laksman, H.Ahmadi Rashtabadi, T.M.Baumann, R.Boll, F.Calegari, G.Catacchio, S.Dold, D.E.Ferreira de Lima, L.Funke, W.Helml, M.Ilchen, T.Mazza, M.Meyer, T.Mullins, M.Robinson, S.Savio, K.Scharei, Ph.Schmidt, A.Thiel, S.Usenko, L.Wuelfing, W.Decking
Materials Science
Structural prediction of B$_{18}$Y$_{2}$ cluster: A Machine-Learning-Assisted Basin-Hopping Study
Peter Ludwig Rodríguez-Kessler
The structural and optical properties of the doubly yttrium-doped boron cluster B$_{18}$Y$_2$ have been systematically investigated using density functional theory calculations. The lowest-energy structure was identified through extensive basin-hopping searches accelerated by a pre-trained MACE machine-learning potential and subsequently refined and validated at the DFT level. The resulting global-minimum structure adopts a double-ring geometry, consisting of two fused B$_9$ rings stabilized by yttrium atoms positioned above and below the boron framework. Vibrational frequency calculations confirm the dynamical stability of the optimized structure, while the calculated infrared and UV–Vis spectra provide characteristic signatures of the Y–B interactions and the electronic structure of the boron framework. These results demonstrate how yttrium doping can stabilize unusual double-ring boron architectures and highlight the effectiveness of machine-learning-assisted basin-hopping searches for exploring the complex potential-energy landscapes of doped boron clusters.
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Number Theory
Computing the Iwasawa $\mu$-Invariants for Elliptic Curves over $\mathbb{Z}_2$-Extensions
Zichao Lin and Mulun Yin
Let $E$ be an
elliptic curve defined over rational numbers. Further assume $E$ has good ordinary reduction at $p=2$ and $E[4]$ is reducible as a $G_\mathbb{Q}$-representation. In this paper, we offer sufficient and necessary computational criteria for the algebraic Iwasawa $\mu$-invariant over the cyclotomic $\mathbb{Z}_2$-extension of rational number to be $0$, $1$ or $\geq 2$. We also show that
elliptic curves with isomorphic mod-$4$ representations have algebraic $\mu$-invariant equal to $0$ if one of the curves does.
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Machine Learning
HySTAR: Anchored Hypergraphs for Stable Credit Assignment in Cooperative Multi-Agent Reinforcement Learning
Xinglong Luo, Yuding Zhang, Yuheng Kuang et al. (+5 more)
Cooperative multi-
agent reinforcement learning under partial observability and shared rewards requires assigning team outcomes to individual
agents and high-order coalitions. A MAPPO-style critic compresses joint behavior into one global value, while critics that dynamically reconstruct the grouping
topology change the mapping from
agents and coalitions to value components as interactions or active
agents evolve. We refer to this inconsistency as structural target drift. We introduce HySTAR, a MAPPO-based framework that separates adaptive representation learning from a temporally consistent high-order value-decomposition basis. HySTAR anchors an overlapping sparse hypergraph as a uniformly covered decomposition scaffold, uses a spatiotemporal encoder to represent physical and task-dependent interactions, and combines temporal and structural relevance to construct
agent-specific advantages. Experiments on SMAC, GRF, Traffic Junction, and MPE demonstrate consistent improvements over MAPPO-style, value-factorization, and dynamic-grouping baselines. On the hardest SMAC settings, HySTAR achieves relative gains of 16.7% over MAPPO and 15.6% over HYGMA, ranks first on all six GRF scenarios, reduces Traffic Junction convergence epochs by up to 40.2% relative to MAGIC, and obtains the highest MPE episode rewards. Controlled
topology,
agent-death, neighborhood, and parameter analyses support the benefit of anchoring the decomposition scaffold while adapting the propagated representations.
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All authors Xinglong Luo, Yuding Zhang, Yuheng Kuang, Shuxuan Yuan, Zhenni Zeng, Weiqiang Zhu, Zhenhai Ji, Zhengning Wang
General Relativity and Quantum Cosmology
Spectral Invariance for Black-Hole Differential Observables
Vedant Subhash
We study first-order differential quantities built from solutions of second-order black-hole wave equations. These quantities can satisfy new differential equations that contain extra singular points, even when the original physical solutions remain regular. We show that an isolated zero of the transformation determinant can produce such an apparent singularity, but it does not by itself create a new resonance or quasinormal-mode frequency. We then study the corresponding Green functions and show that the physical transformed response has the same spectral poles as the original problem, provided that the transformation does not become globally degenerate. For the Regge–Wheeler and Zerilli equations, this means that ordinary turning points can appear as singular points of the derivative equation without changing the nonzero-frequency quasinormal-mode spectrum. The zero-frequency case is different and must be studied separately.
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Theoretical Economics
Prior-Free Delegation
Terrence McGovern, Jan Benedikt Napp and Wenjun Zheng
We consider a robust delegation problem in which the principal does not know the distribution from which the underlying state is drawn. The principal can choose a general randomized mechanism and maximizes her worst-case expected payoff over all state distributions. Our main result characterizes the robustly optimal mechanism. The mechanism has up to three regions: (i) accommodation, where the
agent's ideal action is taken, (ii) calibrated randomization, where each type receives a distinct lottery, and (iii) pooling, where all types receive the same lottery. We then extend our model to a multidimensional setting in which preferences are additively separable and satisfy a cross-dimensional
symmetry condition, and show that delegating separately across dimensions is robustly optimal.
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Quantum Physics
Quantum-HPC Workflows Across Multiple Quantum Computing Platforms: Two Case Studies
Philipp Seitz, Miwako Tsuji, John Children et al. (+5 more)
We describe the
Quantum-HPC hybrid system comprising the supercomputer Fugaku, the QPUs Quantinuum Reimei and ibm_kobe, and the Tierkreis hybrid workflow software. We present two demonstrations of the system at work. In the first, we compute the excited states of a biomolecular system using Fugaku and Reimei (simulator) to handle classical and
quantum parts of the workflow respectively. In the second, Fugaku coordinates Reimei and ibm_kobe working together in a combined VQE + QPE workflow to compute the ground state energy of a simple system.
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All authors Philipp Seitz, Miwako Tsuji, John Children, Yuta Kikuchi, Riku Masui, Juan Pedersen, Kentaro Yamamoto, Ross Duncan
Number Theory
On Conjectures of $\mu$-Invariant for Selmer Groups at $p=2$
Zichao Lin and Mulun Yin
Let $E$ be an
elliptic curve define over $\mathbb{Q}$. Further assume $E$ has good ordinary reduction at $p=2$. In this article, we prove Greenberg's
conjecture on the value of the algebraic Iwasawa $\mu$-invariant when $E$ has a rational isogeny of degree 2, and obtain a sharp absolute upper bound of the $2$-adic $\mu$-invariants for all such curves. We also prove the vanishing of the algebraic $\mu$-invariant of the fine Selmer group introduced by Coates and Sujatha at $p=2$.
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Statistics Theory
Bi-invariant Geodesic Regression: Existence, Uniqueness, and Convergence
Martin Hanik and Christoph von Tycowicz
Bi-invariant geodesic regression generalizes linear regression to Lie groups. Its main feature is that it respects the
symmetries of the group so that the resulting
estimator is independent of arbitrary choices such as a reference frame. However, the local existence and uniqueness of the underlying
estimator have not been shown until now. Furthermore, the convergence properties of the proposed
algorithm for computing the
estimator are not known. In this work, we investigate these questions. We prove that, locally, a unique
estimator exists and give explicit bounds on the size of this neighborhood. We also show that the proposed iterative
algorithm converges linearly to this
estimator.
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Sound
TinyAudio: Compact and Efficient Text-to-Audio Generation for Low-Resource Deployment
Junxi Liu, Xiquan Li, Wenhao Guan et al. (+5 more)
Text-to-audio (TTA) generation has advanced rapidly in generation quality and instruction following. However, representative systems often require around a billion parameters, limiting deployment on resource-constrained devices. This paper introduces TinyAudio, a compact flow-matching-based TTA model for low-resource deployment. At its core, TinyAudio uses TA-DiT, a 35M single-stream flow-matching
Transformer. TinyAudio also includes TA-CLAP, a 32M audio-aligned text encoder, and TA-VAE, whose 20M decoder reconstructs 44.1 kHz audio from compressed latents. TinyAudio has only 87M parameters in total, over 90% fewer than representative billion-parameter pipelines, and uses 0.48 GB peak GPU
memory. TinyAudio achieves competitive generation quality on AudioCaps and TTA-Bench. We further introduce TinyAudio-MF, a MeanFlow-accelerated model that enables real-time generation with a four-core CPU quota. Our results demonstrate a practical quality-footprint trade-off for low-resource TTA deployment.
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All authors Junxi Liu, Xiquan Li, Wenhao Guan, Yifan Duan, Zhikang Niu, Yanru Huo, Ziyang Ma, Xie Chen
Computer Vision
Structured Reasoning Agentic Framework for Interpretable Critical View of Safety Assessment
Qing Xu, Yuxiang Luo and Zhen Chen
Surgical scene understanding is critical for computer-assisted intervention, yet laparoscopic cholecystectomy remains challenged by the complex anatomy of the hepatocystic triangle and the risk of bile duct injury. Existing methods for Critical View of Safety (CVS) assessment typically treat it as a holistic prediction task, mapping visual features directly to criterion-level labels. This black-box paradigm lacks explicit
reasoning about anatomical relationships, limiting both interpretability and compositional generalization. To address this, we propose ReasonCVS, a structured
reasoning agentic framework empowered by
Vision-
Language Models (VLMs) that decomposes CVS assessment into explicit, fine-grained anatomical verification. Specifically, we devise an Anatomical Scene Graph Abstraction (ASGA) that organizes anatomical entities and their spatial relationships into a structured representation. To operationalize this, we introduce a Rationale-Aware
Reasoning Agent, powered by a Large
Language Model (LLM) fine-tuned via rationale
distillation. Functioning as a strict central decision-maker, it invokes VLM-driven Sub-criterion Verifier as a specialized perceptual tool to parse the graph and independently evaluate individual sub-criteria. Through calibrated soft
reasoning, this
agent synthesizes the tool-gathered distributed observations, yielding a final verdict alongside a traceable clinical rationale. Extensive experiments on the Endoscapes-CVS201
benchmark demonstrate that ReasonCVS achieves superior performance (68.1% mAP) over state-of-the-art while providing interpretable, criterion-level explanations for reliable
surgical assessment.
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Geometric Topology
Profinite Non-Rigidity of Arithmetic Lattices and the Kähler Property
Yukun Du, Feng Hao and Kejia Zhu
We prove that the Kählerness of a finitely presented, residually finite group is not determined by its profinite completion, which answers a question asked independently by Arapura and Libgober. In the proof, we give explicit constructions to characterize the absolute Dynkin types that admit non-isomorphic real forms of higher-rank Lie groups containing torsion-free arithmetic
lattices with isomorphic profinite completions.
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Accelerator Physics
Fabry-Pérot Resonance Shifts as a Novel Non-destructive In Situ Surface Damage Diagnostic
Gregory Blume, Colin Kirk, Sushil Poudel et al. (+6 more)
Current surface damage evaluation for nanostructured electronic devices requires specialized equipment or conditions outside the designed operating environment and cannot be used for in situ evaluation of surface damage. In this work, we developed a non-destructive method to probe the surface sublimation of a
semiconductor heterostructure which can be applied to other
semiconductor damage mechanisms. This approach employs shifts in the resonances of an optical cavity comprising the surface and an integrated distributed Bragg reflector fabricated below the
semiconductor heterostructure undergoing sublimation. We performed the demonstration of this technique under
vacuum, but surface damage effects can be observed in any operational environment either in situ or ex situ.
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All authors Gregory Blume, Colin Kirk, Sushil Poudel, John Hill, Alimohammed Kachwala, Joseph Grames, Marcy L. Stutzman, Matt Grau, Sylvain Marsillac
Statistical Mechanics
Complexity drives the symmetry breaking of temperature fluctuations
D. Rosales Herrera, M. Y. Gallegos Ruiz, A. Fernández Téllez et al. (+2 more)
Frequently, nonextensive systems are described through $q$-exponential functions, where the $q$-parameter determines how far a system is from
equilibrium. In this work, we study systems constrained to $q-1\ll1$ to describe systems near thermal
equilibrium, and derive the probability density function and temperature fluctuations. To this end, we derive the series expansion of the $q$-exponential function, yielding a perturbative series that is a superposition of gamma distributions. On the other hand, the temperature fluctuations are expressed as a superposition of Dirac delta functions and their derivatives, meaning that the bulk of the system remains at a constant temperature, while point-temperature variations emerge, marking the system's departure from thermal
equilibrium. The statistics of the temperature fluctuations exhibit a transition from a symmetric to a nonsymmetric distribution as the nonextensive parameter increases. These results provide evidence of the association between the emergence of nonextensivity and the
symmetry breaking of temperature fluctuations.
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All authors D. Rosales Herrera, M. Y. Gallegos Ruiz, A. Fernández Téllez, J. R. Alvarado García, J. E. Ramírez