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All of arXiv

Friday 18 September

Strongly Correlated Electrons

Unified Field Bosonization Technique for strongly inhomogenous Luttinger Liquids

Soundarya P, Venkata Suryanarayana M and Joy Prakash Das

We introduce the Unified Field Bosonization Technique (UFBT), a direct bosonization framework for strongly inhomogeneous one-dimensional Luttinger liquids (LLs) containing static impurities. UFBT incorporates impurity scattering through a symmetrized combination of bosonic phase fields and yields closed-form expressions for arbitrary N-point correlation functions for a broad class of static impurity potentials, including delta barriers, finite barriers and finite wells. The formalism requires neither renormalization-group analysis nor perturbative expansions, providing an analytical description of the inhomogeneous system at the bosonized level. The resulting correlation functions capture the leading singular contributions relevant to the present analysis. The technique is validated by recovering known limiting cases, showing agreement with the first-order perturbative expansion in the interaction strength, and demonstrating consistency with the Schwinger-Dyson equations. A key result is that the correlation function exponents remain independent of the impurity strength, while the impurity dependence is captured by the spatial structure and amplitudes of the correlation functions. The resulting correlation functions establish a foundation for analytical studies of transport, Friedel oscillations, and the local and dynamical density of states in strongly inhomogeneous Luttinger liquids.
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Probability

A variational approach for the 2D Abelian Yang-Mills-Higgs measure

Nikolay Barashkov, Ajay Chandra, Ilya Chevyrev et al. (+2 more)

We use the Boué-Dupuis variational method to construct the Abelian Yang-Mills-Higgs measure on the two-dimensional torus with polynomial Higgs potentials, giving, to our knowledge, the first rigorous construction of an interacting gauge theory by this approach. We first use the variational method to construct the Higgs field conditioned on the gauge field, with a covariant Gaussian free field as the reference measure. Integrating out the Higgs field produces a weight on the gauge field, which we control through a second application of the variational method. We also prove new exponential integrability estimates for the joint gauge-Higgs field and establish gauge covariance. Finally, we prove convergence of the Laplace transforms of the regularised measures and establish a new large-deviation principle for gauge-invariant observables in the semiclassical limit.
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All authors Nikolay Barashkov, Ajay Chandra, Ilya Chevyrev, Andreas Koller, Abdulwahab Mohamed

Chemical Physics

Development of a Non-Empirical Exchange-Hole Dipole Moment Dispersion Model

Alastair J. A. Price and Alberto Otero-de-la-Roza

The inclusion of dispersion effects is important in density-functional theory (DFT) to model non-covalent interactions correctly, a task that is essential in many applications of the theory. Many dispersion functionals have been proposed in the past. The exchange-hole dipole moment (XDM) model combines the simplicity of a damped pairwise asymptotic expression for the dispersion energy with a theory-grounded approach to calculate the dispersion coefficients. XDM is, arguably, the most accurate dispersion correction for the description of molecular crystals and it has been thoroughly tested for other applications across a wide range of chemistries. Here, we address the two main shortcomings of XDM. First, XDM relies on the use of experimentally determined free-atom polarizabilities. Second, because the XDM atom-in-molecule properties (volumes, polarizabilities, exchange-hole dipole moments) use the Hirshfeld partition method, XDM describes systems with large atomic partial charges, like alkali cations or halide anions, poorly. We propose neXDM, a non-empirical variant of XDM that removes the experimental parameters by using the Kirkwood polarizability formula, thereby making neXDM a pure meta-GGA dispersion functional. In addition, following previous work by Bučko et al. on the similar Tkatchenko–Scheffler (TS) method, we replace the Hirshfeld partitioning with its iterative counterpart. The performance of neXDM is shown to be on par with XDM in standard molecular and crystal benchmark sets, and greatly improves the modeling of ionic systems. The new neXDM method sets a new record for the best dispersion-corrected generalized-gradient approximation (GGA) functional for molecular crystal lattice energies in the X23 set (0.700~kcal/mol).
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Strongly Correlated Electrons

Machine learning magnetic interactions from neutron powder diffraction data

Adit S. Desai, Yongqiang Cheng and Joseph A. M. Paddison

Neutron diffraction is a versatile experimental technique capable of probing a material's magnetic properties. While diffraction is typically used to determine the magnetic structure of a material, magnetic diffuse scattering data from a diffraction experiment are also sensitive to the magnetic interactions in its Hamiltonian. However, accurately determining magnetic interaction parameters from neutron-scattering data involves an inverse scattering problem that is challenging to solve in general. Here, we investigate the effectiveness of a machine learning approach to predict the interaction parameters given magnetic diffuse-scattering data measured on powder samples, for a comprehensive survey of isotropic interactions on eight high-symmetry lattices. Across all lattices we considered, the machine-learning approach estimates the interaction parameters with high (~2%) accuracy, while avoiding the issue of false minima that is encountered with non-linear least squares refinement. Our results highlight that powder diffuse-scattering data can provide a compact "fingerprint" of the magnetic interactions for many materials.
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Analysis of PDEs

2D Torus defocusing NLSE with a potential and random initial data

Nicolas Lindstrom

We consider the non-linear cubic defocusing Schrödinger equation on the 2D Torus ($T^2$) with a potential $V(x)\in H^{2^+}(T^2)$. The initial data, $u_0$,is given by a centered gaussian variable with covariance $(-\Delta+V)^{-1}$, and thus is almost surely in $H^{0^-}(T^2)$. We show that it is almost surely well-possed for all time in the weak sense, and that $u-e^{it(\Delta -V)}u_0$ is in $H^{s}(T^2)$ for some $s>0$, and that the solution is the limit of the solutions to the truncated equation. This result is a generalization of the results first given by Bourgain in Invariant Measures for the {2D}-Defocusing Nonlinear {Schrödinger} Equation.
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Metric Geometry

Improved bounds for universal convex covers of unit arcs

Ethan Keller

Moser's worm problem asks for a planar region of least area containing a congruent copy of every unit arc. We show that the infimum area $\alpha$ among convex universal covers satisfies $0.239\le\alpha\le0.24633\ldots$, reducing the gap between the previous refereed bounds by over $75\%$. For the lower bound, we choose four unit polygonal arcs and prove by finite subdivision that, however they are placed, their convex hull has area at least $0.239$. For the upper bound, we construct a quadrilateral of area $0.24633\ldots$ and prove cover universality by showing that its support inequalities force uncovered arcs to have length greater than one. The full proof is formalized in Lean 4 and verified by the Lean kernel. Code and certificates are available at https://github.com/ethan-keller/moser-worm-improved-bounds.
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Computation and Language

NemotronLabs VoiceChat: An Open Full-duplex Speech-to-Speech Model with Tool Calling Capabilities

Jagadeesh Balam, Travis Bartley, Edresson Casanova et al. (+51 more)

We introduce NemotronLabs VoiceChat, an open full-duplex speech-to-speech model with native tool-calling capabilities. NemotronLabs VoiceChat combines a streaming speech encoder and decoder-only language model with parallel specialized output streams for agent text and structured function calls, an auxiliary RNN-T branch for incremental user transcription, and a streaming TTS decoder. This design enables the model to listen, transcribe, reason, invoke tools, and speak within a unified streaming architecture while preserving the temporal behavior required for natural conversation. On Full-Duplex-Bench 1.0, NemotronLabs VoiceChat achieves the lowest pause-handling takeover rates among evaluated open-weight systems, 100% takeover following user interruptions, and a 4.33/5 post-interruption response-quality score. On Full-Duplex-Bench 1.5, it resumes its response after user backchannels in 93% of cases. NemotronLabs VoiceChat obtains a 55.1 normalized average on VoiceBench and, on Full-Duplex-Bench 3.0 (FDB 3.0), achieves 82.5% tool-selection F1, while argument accuracy and end-to-end tool execution remain areas for improvement. These results demonstrate that full-duplex interaction, speech recognition and generation, general language capabilities, and external tool use can be integrated in a single open speech-to-speech model without sacrificing real-time conversational behavior.
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All authors Jagadeesh Balam, Travis Bartley, Edresson Casanova, Sanjay Chauhan, Chen Chen, Zhehuai Chen, Zijia Chen, Francesco Ciannella, Shalini De Mello, Slyne Deng, Mikyas Desta, Harishchandra Dubey, Slim Essid, Nourchene Ferchichi, Boris Ginsburg, Mariana Graterol Fuenmayor, Negar Habibi, Kevin Hu, Anand Joseph, Viraj Karandikar, Myungjong Kim, Viacheslav Klimkov, Seelan Lakshmi Narasimhan, Lily Lee, Jason Li, Eileen Long, Ameya Mahabaleshwarkar, Aditya Malte, Adi Margolin, Amrita Mazumdar, Sasha Meister, Valentin Mendelev, Koki Nagano, Oluwatobi Olabiyi, Seonwook Park, Ankita Pasad, Yifan Peng, Elena Rastorgueva, Jayda Ritchie, Jason Roche, Rajarshi Roy, Nikhil Srihari, Yuanhang Su, Yoshi Suhara, Viet Anh Trinh, Jinhan Wang, Piotr Zelasko, Hui Wang, Puhui Meng, Chaosen Zhang, Yunsheng Liu, Shawn Wang, Wenjing Li, Zhonglei He

Formal Languages and Automata

Automata-Theoretic Verification of Interval Markov Decision Processes

Sarvin Bahmani, Soumyajit Paul, Sven Schewe et al. (+2 more)

Interval Markov decision processes (IMDPs) provide a natural framework for modeling stochastic systems with uncertain transition probabilities, represented by probability intervals and resolved adversarially. Such uncertainty arises naturally, for example, when the transition model is learned from finite data or obtained through model-based reinforcement learning. In this paper, we study the automata-theoretic verification of IMDPs against rich temporal specifications, including all LTL specifications, by considering the broader class of {\omega}-regular objectives. We show that classical automata-theoretic verification techniques extend to IMDPs, but with a sharp distinction determined by the structure of the transition intervals. For stable IMDPs, where either the upper bound is zero or the lower bound is strictly positive, verification reduces to ordinary MDP analysis and can be carried out using the standard automata used in that setting (good-for-MDP automata). For unstable IMDPs, where intervals may include zero while the upper bound is strictly positive, verification becomes game-like and requires automata whose nondeterminism can be resolved on the fly (good-for-games automata). Building on these insights, we develop algorithms for verifying {\omega}-regular specifications over IMDPs and derive probabilistic guarantees when the interval model is learned from sampled data. The resulting framework enables principled verification of stochastic systems under probabilistic model uncertainty, connecting automata-based verification with data-driven stochastic modeling.
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All authors Sarvin Bahmani, Soumyajit Paul, Sven Schewe, Sadegh Soudjani, Ashutosh Trivedi

Computational Engineering

The ecological collapse of color: photoreceptor number buys a geometric hue manifold that natural spectra never fill

Mohammad Rostami

We ma[ the profound gap between the theoretical color dimensions an organism's eye can perceive and the actual color dimensions supplied by the natural world. Geometric theory predicts that n photoreceptor classes allow an organism to perceive a hue manifold homeomorphic to an (n-2)-dimensional sphere. While this math was previously only derived analytically for humans and birds, this research empirically proves the existence of this biological “topological ladder” across multiple species using persistent homology. We recover a dichromat's line, a trichromat's hue ring ($S^1$), a tetrachromat's hue sphere ($S^2$), and a pentachromat's glome ($S^3$) using real animal cones. Crucially, the study reveals that the “ecological color manifold”, the colors actually created by natural reflectance spectra under natural light, falls dramatically short of these geometric capabilities. Across 25 diverse species spanning three independent hyperspectral databases, an animal's geometric color capacity climbs steeply with more photoreceptors, yet the actual effective dimension of the colors they experience stays stuck near unity. As a result, the fraction of available geometry the world actually fills steadily declines as receptor counts grow. A controlled decomposition shows this mismatch is driven by the low spectral rank of nature rather than receptor limitations; the effect vanishes in a simulated, full-rank world. The real-world constraint yields an ecological prediction confirmed on held-out species: aquatic tetrachromats, whose light fields are spectrally narrowed by water, collapse more deeply than land or air species ($p = 0.012$).
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Spectral Theory

The Y-partition is the optimal three-partition for the disc and the harmonic oscillator

Mikael Sundqvist

We prove that the Y-partition into three equal sectors is the minimal spectral three-partition both for the Dirichlet Laplacian on the unit disc and for the planar harmonic oscillator $-\Delta+|x|^2$, with minimal energies $j_{3/2,1}^{2}$ and $5$; for the disc, this confirms a conjecture of Helffer and Hoffmann-Ostenhof. The minimizing regular strong partition is unique up to rotation, and every open minimizing partition has cells with the Dirichlet form domains of the sectors. The proof is a positive radial transplantation to the sphere that preserves segregation and matches the angular-energy measures of the separated model states; the three-lune theorem of Helffer, Hoffmann-Ostenhof, and Terracini then gives the lower bound. The transplantation lowers the shifted quadratic form by a nonnegative defect with strictly positive radial weight; in the equality case, spherical equipartition makes the defects vanish, which separates variables, and a Poincaré inequality on the circle identifies the sectors.
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Soft Condensed Matter

Active colloidal rafts perform swimming strokes that propel their host droplets

Airi N. Kato, Julien Brémont, Etienne Harté et al. (+3 more)

Active particles confined in droplets can set their host droplet into motion. This phenomenon is usually attributed to direct hydrodynamic forcing by the enclosed particles. Here we reveal a different mechanism: we show that a self-propelled raft of active colloids confined in a thin oil droplet at the surface of water typically follows an off-centered orbit, thus periodically deforming the droplet's contact line in an anisotropic way. This non-reciprocal deformation acts as a swimming stroke and propels the droplet according to the principles of low-Reynolds-number swimming. The effect is absent for a single colloid and arises from the intrinsically many-body dynamics of the raft, which we capture with a dynamical model coupling viscous hydrodynamics and many-body active dynamics. Our results show how collective internal activity can be converted into locomotion through deformation of a soft confining boundary.
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All authors Airi N. Kato, Julien Brémont, Etienne Harté, Jean-Michel Rampnoux, Jean-François Joanny, Hamid Kellay

Artificial Intelligence

Learning Cardiac Features: ECG Biometrics Across Time and~Exercise

Luca Thiebaud, Paul Chauchat, Mustapha Ouladsine et al. (+1 more)

Electrocardiograms (ECGs) carry subject-specific patterns enabling reliable individual discrimination, forming the basis of ECG biometrics. Beyond authentication, this paradigm holds significant potential to secure sensitive cardiac data and to serve as a pretext task in self-supervised learning. Yet, most studies remain confined to singlesession, resting data, leaving robustness to temporal and physiological variations largely untested. We address this gap by evaluating ECG biometrics under realistic conditions involving exercise-induced stress and cross-session variability. A Siamese ResNet with late multi-lead fusion strategy is trained on a large ECG dataset extracted from cardiopulmonary exercise tests and evaluated with a exercise-and time-aware protocol, as well as on public benchmarks. This first extensive assessment of ECG biometrics under combined physiological and temporal variability achieves an intra-session rest-to-peak EER of 1.7% and stateof-the-art 3.9% on the CYBHi dataset. Findings support the presence of an intrinsic cardiac signature resilient to physiological and temporal drift.
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All authors Luca Thiebaud, Paul Chauchat, Mustapha Ouladsine, Stéphane Delliaux

Quantum Physics

Single-atom-based asynchronous photonic interconnect for scalable modular quantum computing

Jérémy Raskop, Nadav Kandel, Geva Arwas et al. (+6 more)

Scaling quantum computation beyond the capacity of a single quantum processing unit requires quantum interconnects between modular processors. Optical photons are natural carriers for distributing entanglement between these processors. Most loss-resilient protocols use photonic Bell-state measurements based on the linear-optics type-II fusion gate. The resulting entanglement rate scales quadratically with each processor's typically low photon-delivery probability. Here we analyze a memory-assisted quantum interconnect using a near-deterministic, robust photon–atom controlled-$Z$ gate via a single atom trapped in a high-finesse cavity. Detecting and measuring a photon from one processor heralds entanglement between that processor and the atom. This entanglement is preserved while the process repeats with the second processor until the second photon is detected and measured. Reading out the atomic qubit finalizes the entanglement between the processors. As the entanglement is mediated by the atom, the photons from both processors do not need to be indistinguishable, removing a major source of infidelity. Furthermore, by removing the simultaneous photon-arrival requirement, the protocol allows the entanglement rate to scale linearly rather than quadratically with photon-arrival probability over a wide parameter range. We derive entanglement rates under realistic parameters, accounting for decay of the atom's entanglement with the first processor and for decoherence caused by unheralded photon interactions. The nanosecond-scale of the gate and read-out operations leads to orders-of-magnitude entanglement-rate gain over linear optics, removing a key bottleneck in modular quantum computing.
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All authors Jérémy Raskop, Nadav Kandel, Geva Arwas, Yaniv Amichy, Yaron Jarach, Tal Kanonich, Andrei Militaru, Johannes Fink, Barak Dayan

Statistics Theory

Schedule optimization for tau-leaping in masked discrete diffusion

Cecilia Secchi and Giacomo Zanella

Masked diffusions are popular generative models for discrete distributions. Unlike standard autoregressive sampling, they reveal several coordinates in parallel, approximating each block's joint conditional law by a product of one-coordinate conditionals. The resulting procedure, usually called tau-leaping, reduces computational cost but introduces a factorization error ($\varepsilon_\text{fact}$), even with perfectly learned predictors. We study the resulting tradeoff between generative accuracy and computational cost, focusing on how to choose a denoising schedule to minimize $\varepsilon_\text{fact}$ for a fixed sampling budget. To do so, we establish an exact integral representation of $\varepsilon_\text{fact}$ separating the schedule from the target's dependence structure, summarized by a dependence density $\rho$. This representation yields recursive stationarity equations for optimal schedules and allows us to quantify how estimation errors in $\rho$ affect schedule selection. As the dimension $N$ and sampling budget grow, we characterize the optimal schedule and quantify the cost of random block sizes relative to a deterministic planner. We highlight a fundamental dichotomy: if $\rho$ converges uniformly to a strictly positive continuous profile as $N\to\infty$, schedule optimization can only improve the leading constant of $\varepsilon_\text{fact}$, while if $\rho$ degenerates, schedule optimization can improve the asymptotic order. Examples based on stationary processes and exchangeable mixtures illustrate these regimes.
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Social and Information Networks

Setting the clock: Evaluating temporal window parameters for coordinated behavior detection

Georgios Panayiotou, Lorenzo Mannocci and Maurizio Tesconi

Coordinated behavior is a central mechanism of online collective action. On social media platforms, it can support legitimate mobilization, but it can also be exploited in disinformation campaigns, astroturfing, and information operations. Detecting coordinated behavior on social media platforms typically relies on coordination networks, where users are linked when they perform similar actions within shared temporal windows. While the temporal window is central to how coordination is operationalized, it is often treated as an implementation detail rather than as a substantive modeling decision. This paper presents a first analysis of how two key temporal parameters, window length and stride, affect the detection of coordinated communities within information operation campaigns. We find that window length determines which coordination patterns are detectable, while window stride has negligible effect on precision and recall. Our analysis highlights selecting appropriate temporal window parameters as an open methodological challenge requiring careful treatment.
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Optics

Momentum microscopy of a holey nanostructure

Kerstin Harland, Julia Altenburg, Xiaofei Wu et al. (+10 more)

Momentum microscopy records the three-dimensional momentum distribution of photoelectrons emitted from a solid sample and, by utilizing sufficiently high photon energies in the ultraviolet spectral range, offers direct access to the electronic band structure of a material. By employing a pump-probe scheme, this method provides a femtosecond view of light-matter interaction and the subsequent relaxation and transport dynamics in a broad range of material systems. However, momentum microscopy has so far been mostly limited to flat and spatially extended surfaces. Photoelectron emission from different three-dimensional facets, in combination with inhomogeneous electric fields around these structures, makes the analysis of the momentum distribution significantly more challenging. Here, we extend the state-of-the-art to a substantially more complex structure and show that a careful analysis of the electron distribution recorded with a momentum microscope provides rich information about both the spatial and momentum distributions on a few-nm and few-mÅ$^{-1}$ scale, respectively. Combined with prior knowledge of the three-dimensional structure, momentum-resolved photoelectrons can be assigned to nano-localized emission spots, permitting a new level of insight into spatio-temporal charge carrier dynamics.
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All authors Kerstin Harland, Julia Altenburg, Xiaofei Wu, Zsuzsanna Pápa, Leon David Schwarz, Lina Hansen, Katrin Meier, Arvid Klösgen, Bert Hecht, Germann Hergert, Péter Dombi, Jer-Shing Huang, Jan Vogelsang

Cryptography and Security

Provisional Reachability: Containing Agents by Making Every Crossing Revocable

Yoshiaki Takashita

A companion paper found that what a defender must block over time has units: bits per period [Takashita, 2026a]. This paper sets it. Hold every crossing in escrow for one period, audit each held item independently with probability r, and revoke the window if any audit catches something. An adversary crossing k times, each carrying c bits, expects kc(1-r)^k, maximised at k* = 1/ln(1/(1-r)), a bound of L(r) ~ c/(er) per window. The bound is a supremum over the adversary's choice, so the scheme may be public; simulation matches it to 7.7 standard errors. It is a rate, not a total: escrow alone still lets the secret assemble in every run. But if the secret decays at a fraction mu of held bits per period, holdings converge to g/mu at any horizon, so an L-bit secret is unreachable once mu > g/L – an error threshold in Eigen's sense, sharp where the closed form puts it (100% of runs assemble at 0.9mu*, 0% at 2mu*, over 20,000 windows). Deception that needs the adversary to reason badly fails: a surface whose names lie left accuracy at 18 of 18, and 100% at three reader strengths. Withholding reference works, and differently: no reader would commit at all. Keying the entry points hides 0.10 bits of what a module does; keying the denotation hides 2.64 of 3.00 at chance accuracy, while 100% of readers still call it ordinary Python. Variance must be removed from the audit rate, where loot is convex in r, and added to the activation budget, where survival is multiplicative: extinction 70% to 100% at a fixed mean. End to end the stack takes the leak from 100,000 to 59 bits, a factor of 1,704, leaving 12% of legitimate work standing; keying the window to the caller restores that to 100% at no cost in leakage, at the price of a bound that is per principal. Of 65 read-only tools, escrow leaves 2,400 bits per call: a factor of 10, not infinity.
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Computers and Society

Beyond the Desert Label: A Pathway Diagnostic for User-Centered Smart Mobility Service Design

Oluwasegun Adegoke and Sevgi Erdogan

Smart-city mobility platforms increasingly rely on spatial screening tools to identify neighborhoods where public transit fails dependent users, but a single transit desert label can mask very different user problems: localized mismatch between service and concentrated need, or basic absence of usable service. These call for different user-centered responses. This paper introduces a pathway-based, reproducible, data-driven diagnostic that distinguishes relative transit mismatch from minimum-service failure and reports the specific service attributes (frequency, span, weekend service, walking access, and destination accessibility) driving each classification. The workflow combines open data (GTFS, ACS, LEHD, Census, and OpenStreetMap), detects spatially coherent mismatch using Local Moran's I, and applies an equity-informed service-failure test that centers vulnerable users. Applied to Baltimore, Philadelphia, Nashville, and Dallas, the diagnostic shows that legacy-transit cities are dominated by localized mismatch, while auto-oriented cities show broader minimum-service failure, with distinct service-deficit profiles in each case. By making the mechanism behind an under-service label explicit, the tool supports more inclusive, user-centered smart-mobility planning across cities with different transit baselines.
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2609.21956 · 18 Sep · 5 pages, 4 figures. Accepted for publication in the Proceedings of the 2026 IEEE International Smart Cities Conference (ISC2), Workshop W02, Porto, Portugal. (c) 2026 IEEE. Personal use of this material is permitted; permission from IEEE must be obtained for all other uses

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Statistics Applications

A Probabilistic Modeling Framework for Transient Debris Outcomes in Low Lunar Orbits

Arjun Chhabra and Ryne Beeson

This work presents a novel probabilistic framework for the assessment of orbital debris fragment outcomes in the low lunar orbit (LLO) regime over time horizons ranging from a few hours to a hundred days after a debris generation event. The framework develops continuous distributions for the probability of sinking (lunar collision) and non-sinking over these transient time horizons, building upon NASA's Standard Breakup Model to provide insights into the variations in the likelihood of debris outcomes across the LLO regime and offering an alternative to computationally expensive Monte Carlo simulations. The effects of perturbative forces such as solar radiation pressure are used to assess the realization of debris outcomes over varying time horizons, providing an analytical framework that bounds the likelihood of each outcome. Results indicate variations in the probability of sinking over short time horizons depending on the originating location of the debris generation event, as well as a link between the physical characteristics of fragments and their likelihood of sinking over longer time horizons. The future incorporation of this framework into broader-scale orbital environment models, mission risk assessment procedures, and policy development are briefly discussed.
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Probability

Finite Explosion for One-dimensional Lévy Driven SDEs and its Application to SPDEs

Pei-Sen Li, Yuichi Shiozawa and Jian Wang

We study finite-time explosion to $-\infty$ for the one-dimensional stochastic differential equation \[ X_t^x=x-\int_0^t b(X_s^x)\,\dd s+L_t,\quad x\in\R, \] where $b$ is locally Lipschitz and $(L_t)_{t\ge0}$ is a pure-jump Lévy process. We give verifiable conditions involving Osgood-type integrability under which explosion occurs almost surely from every finite initial state. Under stronger tail conditions, we obtain a uniform bound on the mean explosion time. In particular, under suitable tail monotonicity, converse results make these criteria necessary and sufficient, and yield an explicit classification for Riccati drifts. As an application, we consider a semilinear parabolic stochastic partial differential equation (SPDE) with additive Lévy space–time white noise and homogeneous Dirichlet boundary conditions. We give explicit conditions on the nonlinearity and the Lévy measure under which every local weak solution defined up to explosion has an almost surely finite explosion time.
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Machine Learning

RACER: Role-Aligned Competence Estimation for Human-AI Routing

Joshua Strong, Emma Sun, Alexander Capstick et al. (+3 more)

Learning to defer asks a predictive system when to act autonomously and when to defer to a human expert. Population-adaptive deferral extends this problem to unseen experts using a small context set of expert behavior. Neural context encoders such as L2D-Pop can be query-dependent, but may learn routing shortcuts tied to absolute class coordinates. Identity-Free Deferral (IFD) removes such shortcuts through role-indexed classwise competence profiles, but its estimates are constant within each class and cannot capture instance-level expert specialization. We propose RACER—Role-Aligned Competence Estimation for Routing—a role-relative framework for estimating an unseen expert's competence from context. RACER estimates the posterior-predictive probability that the expert is correct on a query under each candidate class role, then combines these estimates with the model posterior to obtain the Bayes-relevant expert-correctness probability. Nonparametric and neural kernel-pooling estimators use candidate-role relations, shared aggregation, and symmetric summaries, excluding absolute class-identity channels. We prove coherent class-relabelling invariance, derive a Bayes-aligned deferral surrogate, and give a plug-in regret bound relating routing regret to classifier and competence-estimation error. On controlled synthetic benchmarks, including a PathMNIST histopathology context-scaling study with simulated experts, RACER benefits from additional context under hidden subtype dependence and gives the strongest aggregate performance on a separately sampled unseen-expert split in the CIFAR-100 synthetic experiments. On the radiologist and human–AI chest-radiography benchmarks (VinDr-CXR and CheXpert), the RACER family is competitive or best in budget-swept deferral, with calibration results varying across metrics and datasets.
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All authors Joshua Strong, Emma Sun, Alexander Capstick, Pramit Saha, Cheng Ouyang, J. Alison Noble

Geometric Topology

Finite covers of a product of surfaces with bounded rank and arbitrarily large systole

Koji Fujiwara

We construct finite covers of a fixed product of two closed hyperbolic surfaces of genus two whose fundamental groups are generated by at most fifteen elements and whose injectivity radii tend to infinity. The construction uses fibre products over finite groups. These covers are closed aspherical four-manifolds with universal cover $\mathbb H^2\times\mathbb H^2$. They give counterexamples to a conjecture of Avramidi and Delzant for symmetric spaces of higher rank, in the case \(\mathbb H^2\times\mathbb H^2\).
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Plasma Physics

Azimuthal mode decomposition Particle in Cell algorithm for cylindrical plasma sources

Matteo Ripoli, Eduardo Ahedo and Mario Merino

An efficient Particle-in-Cell numerical approach to perform full-dimensional kinetic simulations of low temperature plasmas is presented. Taking advantage of the cylindrical geometry of most plasma sources, a Fourier mode decomposition of the fields is carried out in the azimuthal ($\theta$) direction up to a chosen maximum number of modes $N_m$. Macroparticles are pushed in all $D$ dimensions and weighed, for each mode $m$, onto a $(D-1)$ dimensional grid. The computation of the electric field for each mode is independent and reduces to solving $(N_m+1)$ $(D-1)$ dimensional Poisson problems. The approach brings spectral accuracy in the azimuthal direction, while the computational cost is comparable to that of a simulation with $(D-1)$ dimensions. We verify this approach against a planar test case based on a Penning discharge, widely used for benchmarking and validation purposes in the low-temperature plasma community. Our approach allows us to reduce the 2D problem into a collection of coupled 1D problems and to naturally perform spectral analysis of the different azimuthal modes, recovering the contribution of each mode to radial transport, with a computational time saving of one order of magnitude with respect to state of the art 2D particle-in-cell codes.
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Differential Geometry

Projective Rigidity of $U(k)$-Radial Ricci-Flat Kähler Metrics

Shaosai Huang

We study Kähler immersions of Ricci-flat metrics into finite- or infinite-dimensional complex projective space. Let $L^{\otimes k}\simeq K_X$ over a real-analytic Kähler manifold $X$. Let $\phi$ be a base potential and $s$ the canonical squared fibre norm on $L^{\oplus k}$. Consider Ricci-flat potentials $\phi+h(s)$ near the zero section, with $h$ independent of the base point. We prove that local projective inducibility forces the base to be Ricci-flat and the metric to split locally as $X\times\mathbb C^k$. In that case projective inducibility is equivalent to that of the base. The proof combines Calabi's criterion, positivity of the homogeneous fibre-degree blocks, and the singularities of the radial profile. A related obstruction along holomorphic curves excludes every positive multiple of the Taub–NUT metric and Calabi's hyperkähler metrics on $T^{*1,0}\mathbb{CP}^n$. Applications also include the resolved conifold, canonical-bundle metrics in non-Einstein classes, and Cifarelli's rank-two Type-2 metric.
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Classical Analysis and ODEs

A boundedness result for degenerate parabolic Riesz transforms with rough coefficients

Khalid Baadi

In this paper, we prove a boundedness result for parabolic Riesz transforms in the range $p \le 2$ associated with degenerate parabolic operators whose elliptic part is in divergence form with complex coefficients depending measurably on space and time. The degeneracy is determined by a spatial weight in the Muckenhoupt class $A_2(\mathbb{R}^n)$. The argument relies on off-diagonal estimates for the parabolic gradient of the resolvent family, together with weighted embeddings. We obtain boundedness in a range of exponents strictly below $2$, with explicit ranges quantified by the reverse Hölder class of the weight. For real coefficients, this quantification is sharp and extends down to $1$.
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Robotics

GALA: Geometry-Aware Latent Action Modeling for Vision-Language-Action Model Pretraining across Embodiments

Yichen Liu, Puzhen Yuan, Xiang Zhu et al. (+2 more)

Learning large-scale vision-language-action (VLA) models from multi-embodiment datasets remains challenging due to heterogeneous action spaces across end effectors. Although latent action models (LAMs) can learn embodiment-agnostic action representations from diverse video data, existing image-based LAMs often fail to capture fine-grained end-effector articulation, particularly finger-level geometric changes in human and dexterous robot hands. To address this limitation, we propose GALA, a Geometry-Aware Latent-Action modeling framework that augments image-based latent actions with 3D end-effector geometric motion. However, naively incorporating point clouds yields fine-grained action representations with limited shared semantics, hindering cross-embodiment pretraining. To address this issue, we introduce the Unified End-effector Motion Representation (UEMR), which preserves fine-grained motion information while improving the cross-embodiment generalizability of latent actions. Building upon UEMR, GALA combines visual latent actions that capture scene-level dynamics with geometric latent actions that capture shared fine-grained end-effector articulation, providing effective supervision for VLA pretraining from multi-embodiment data, including action-free ego-centric human videos. Experiments on fine-grained motion probing, cross-embodiment retrieval, and downstream VLA evaluation demonstrate GALA's effectiveness in modeling generalizable fine-grained motions across embodiments, achieving 68.3% RoboCasa-GR1 success rate and 75.5% real-world success rate. Code, appendix, and demos are available at https://puzhenyuan.github.io/GALA-website/.
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All authors Yichen Liu, Puzhen Yuan, Xiang Zhu, Yanjiang Guo, Jianyu Chen

High Energy Physics (Experiment)

Test of lepton flavor universality with $\bar{B} \rightarrow D^{(*)} \tau^{-} \bar{\nu}_{\tau}$ and $\bar{B} \rightarrow D^{(*)} \ell^{-} \bar{\nu}_{\ell}$ decays at Belle II

Belle II Collaboration: M. Abumusabh, I. Adachi, K. Adamczyk et al. (+494 more)

We test lepton flavor universality with a measurement of the branching-fraction ratios $R(D^{(*)}) \equiv \mathcal{B}(\bar{B} \rightarrow D^{(*)} \tau^{-} \bar{\nu}_{\tau})/\mathcal{B}(\bar{B} \rightarrow D^{(*)} \ell^{-} \bar{\nu}_{\ell})$, where $\ell$ denotes an electron or muon. The analysis uses $387\times 10^6$ $\Upsilon(\mathrm{4S})$ decays collected with the Belle II detector in energy-asymmetric $e^+e^-$ collisions. One $B$ meson is fully reconstructed in a hadronic decay mode, while the other is reconstructed either in $\bar{B}\rightarrow D^{(*)}\tau^{-}\bar{\nu}_{\tau}$, with $\tau^- \rightarrow \ell^- \bar{\nu}_{\ell}\nu_{\tau}$, or in $\bar{B}\rightarrow D^{(*)}\ell^{-}\bar{\nu}_{\ell}$. We extract the signal from the distributions of the residual calorimeter energy and the squared mass of the undetected particles, obtaining $R(D^{*}) = 0.242 \pm0.019(\mathrm{stat}) \pm0.016(\mathrm{syst})$ and $R(D) = 0.439 \pm 0.055(\mathrm{stat}) \pm 0.046(\mathrm{syst})$. These results are consistent with both the standard model predictions and previous measurements, and constitute the most precise determination of $R(D^{(*)})$ with hadronic tagging.
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All authors Belle II Collaboration: M. Abumusabh, I. Adachi, K. Adamczyk, A. Aggarwal, L. Aggarwal, H. Ahmed, Y. Ahn, H. Aihara, M. Akdag, N. Akopov, A. Akram, S. Alghamdi, M. Alhakami, A. Aloisio, N. Althubiti, K. Amos, M. Angelsmark, N. Anh Ky, C. Antonioli, K. Arai, D. M. Asner, H. Atmacan, T. Aushev, V. Aushev, R. Ayad, V. Babu, H. Bae, N. K. Baghel, S. Bahinipati, P. Bambade, Sw. Banerjee, S. Bansal, M. Barrett, M. Bartl, J. Baudot, A. Baur, A. Beaubien, F. Becherer, J. Becker, J. V. Bennett, F. U. Bernlochner, V. Bertacchi, M. Bertemes, E. Bertholet, M. Bessner, S. Bettarini, V. Bhardwaj, B. Bhuyan, F. Bianchi, T. Bilka, A. Biswas, D. Biswas, A. Bobrov, D. Bodrov, A. Bondar, G. Bonvicini, J. Borah, A. Boschetti, A. Bozek, M. Bračko, P. Branchini, R. A. Briere, T. E. Browder, A. Budano, S. Bussino, F. Callet, Q. Campagna, M. Campajola, L. Cao, M. Carminati, G. Casarosa, C. Cecchi, M.-C. Chang, P. Chang, P. Cheema, L. Chen, B. G. Cheon, C. Cheshta, H. Chetri, K. Chilikin, K. Chirapatpimol, H.-E. Cho, K. Cho, S.-J. Cho, S.-K. Choi, S. Choudhury, S. Chutia, J. Cochran, J. A. Colorado-Caicedo, I. Consigny, L. Corona, H. Crotte Ledesma, S. Cuccuini, J. X. Cui, L. Damer, E. De La Cruz-Burelo, S. A. De La Motte, G. de Marino, G. De Nardo, G. De Pietro, R. de Sangro, M. Destefanis, S. Dey, R. Dhayal, A. Di Canto, J. Dingfelder, Z. Doležal, I. Domínguez Jiménez, T. V. Dong, X. Dong, M. Dorigo, K. Dugic, G. Dujany, P. Ecker, D. Epifanov, J. Eppelt, R. Farkas, P. Feichtinger, T. Ferber, T. Fillinger, C. Finck, G. Finocchiaro, F. Forti, A. Frey, B. G. Fulsom, A. Gabrielli, P. Gagneja, A. Gale, E. Ganiev, M. Garcia-Hernandez, R. Garg, A. Garmash, L. Gärtner, G. Gaudino, V. Gaur, V. Gautam, A. Gaz, P. Gebeline, A. Gellrich, G. Ghevondyan, D. Ghosh, H. Ghumaryan, G. Giakoustidis, R. Giordano, A. Giri, P. Gironella Gironell, A. Glazov, B. Gobbo, R. Godang, O. Gogota, P. Goldenzweig, W. Gradl, E. Graziani, D. Greenwald, Y. Guan, K. Gudkova, I. Haide, H. Haigh, Y. Han, K. Hara, K. Hayasaka, H. Hayashii, S. Hazra, C. Hearty, M. T. Hedges, A. Heidelbach, G. Heine, I. Heredia de la Cruz, M. Hernández Villanueva, T. Higuchi, M. Hoek, M. Hohmann, R. Hoppe, P. Horak, X. T. Hou, C.-L. Hsu, A. Huang, T. Humair, T. Iijima, K. Inami, G. Inguglia, N. Ipsita, A. Ishikawa, R. Itoh, M. Iwasaki, P. Jackson, D. Jacobi, W. W. Jacobs, E.-J. Jang, Q. P. Ji, S. Jia, Y. Jin, A. Johnson, K. K. Joo, H. Kakuno, M. Kaleta, J. Kandra, K. H. Kang, S. Kang, G. Karyan, T. Kawasaki, F. Keil, C. Ketter, M. Khan, C. Kiesling, C. Kim, D. Y. Kim, H. Kim, J.-Y. Kim, K.-H. Kim, H. Kindo, K. Kinoshita, P. Kodyš, T. Koga, S. Kohani, K. Kojima, H. Korandla, A. Korobov, S. Korpar, E. Kovalenko, R. Kowalewski, M. Krein, P. Križan, P. Krokovny, T. Kuhr, Y. Kulii, D. Kumar, J. Kumar, R. Kumar, K. Kumara, T. Kunigo, S. Kurokawa, B. Kutsenko, A. Kuzmin, Y.-J. Kwon, S. Lacaprara, T. Lam, L. Lanceri, J. S. Lange, T. S. Lau, M. Laurenza, R. Leboucher, F. R. Le Diberder, H. Lee, M. J. Lee, C. Lemettais, P. Leo, P. M. Lewis, C. Li, H.-J. Li, L. K. Li, Q. M. Li, S. X. Li, W. Z. Li, Y. Li, Y. B. Li, Y. P. Liao, J. Libby, J. Lin, S. Lin, Z. Liptak, V. Lisovskyi, A. Little, G. Liu, M. H. Liu, Q. Y. Liu, Y. Liu, Z. Q. Liu, D. Liventsev, S. Longo, A. Lozar, T. Lueck, C. Lyu, J. L. Ma, Y. Ma, M. Maggiora, S. P. Maharana, R. Maiti, G. Mancinelli, R. Manfredi, E. Manoni, M. Mantovano, D. Marcantonio, S. Marcello, M. Marfoli, C. Marinas, C. Martellini, A. Martens, T. Martinov, L. Massaccesi, M. Masuda, J. Materne, T. Matsuda, K. Matsuoka, D. Matvienko, S. K. Maurya, M. Maushart, F. Mawas, J. A. McKenna, Z. Mediankin Gruberová, R. Mehta, F. Meier, D. Meleshko, M. Merola, C. Miller, M. Mirra, K. Miyabayashi, H. Miyake, R. Mizuk, G. B. Mohanty, S. Moneta, A. L. Moreira de Carvalho, H.-G. Moser, N. Mudgal, Th. Muller, H. Murakami, R. Mussa, I. Nakamura, K. R. Nakamura, M. Nakao, H. Nakayama, Y. Nakazawa, M. Naruki, Z. Natkaniec, A. Natochii, M. Nayak, M. Neu, M. Niiyama, S. Nishida, R. Nomaru, A. Novosel, S. Ogawa, R. Okubo, H. Ono, Y. Onuki, I. Ostrowski, F. Otani, P. Pakhlov, G. Pakhlova, A. Panta, S. Pardi, K. Parham, J. Park, K. Park, S.-H. Park, A. Passeri, S. Patra, S. Paul, T. K. Pedlar, R. Pestotnik, M. Piccolo, L. E. Piilonen, P. L. M. Podesta-Lerma, T. Podobnik, L. Polat, A. Prakash, V. Prasad, C. Praz, S. Prell, E. Prencipe, M. T. Prim, S. Privalov, I. Prudiiev, H. Purwar, P. Rados, S. Raiz, V. Raj, K. Ravindran, J. U. Rehman, M. Reif, S. Reiter, M. Remnev, L. Reuter, D. Ricalde Herrmann, I. Ripp-Baudot, G. Rizzo, S. H. Robertson, J. M. Roney, A. Rostomyan, N. Rout, G. Russo, S. Saha, L. Salutari, D. A. Sanders, S. Sandilya, L. Santelj, C. Santos, V. Savinov, B. Scavino, C. Schmitt, J. Schmitz, S. Schneider, G. Schnell, M. Schnepf, K. Schoenning, C. Schwanda, A. J. Schwartz, Y. Seino, K. Senyo, J. Serrano, M. E. Sevior, C. Sfienti, W. Shan, G. Sharma, C. P. Shen, X. D. Shi, T. Shillington, T. Shimasaki, J.-G. Shiu, D. Shtol, A. Sibidanov, F. Simon, J. B. Singh, J. Skorupa, R. J. Sobie, M. Sobotzik, A. Soffer, A. Sokolov, E. Solovieva, W. Song, S. Spataro, K. Špenko, B. Spruck, M. Starič, P. Stavroulakis, S. Stefkova, R. Stroili, M. Sumihama, K. Sumisawa, N. Suwonjandee, M. Takahashi, M. Takizawa, U. Tamponi, S. Tanaka, S. S. Tang, K. Tanida, F. Tenchini, F. Testa, A. Thaller, T. Tien Manh, O. Tittel, R. Tiwary, E. Torassa, K. Trabelsi, F. F. Trantou, I. Tsaklidis, M. Uchida, I. Ueda, E. Uenlue, T. Uglov, K. Unger, Y. Unno, K. Uno, S. Uno, P. Urquijo, Y. Ushiroda, S. E. Vahsen, R. van Tonder, K. E. Varvell, M. Veronesi, A. Vinokurova, V. S. Vismaya, L. Vitale, V. Vobbilisetti, R. Volk, R. Volpe, M. Wakai, S. Wallner, M.-Z. Wang, X. L. Wang, A. Warburton, M. Watanabe, S. Watanuki, C. Wessel, J. Wiechczynski, E. Won, X. P. Xu, B. D. Yabsley, S. Yamada, W. Yan, W. Yan, J. Yelton, K. Yi, J. H. Yin, K. Yoshihara, C. Z. Yuan, J. Yuan, L. Zani, F. Zeng, B. Zhang, X. Zhao, V. Zhilich, J. S. Zhou, Q. D. Zhou, X. Y. Zhou, L. Zhu, R. Žlebčík

Group Theory

Finite Quotients of Right-angled Artin Groups

Zihao Liu

We prove that right-angled Artin groups (RAAGs) are profinitely rigid relative to the class of Artin groups. More precisely, if $A_\Gamma$ is an arbitrary Artin group and $A_\Lambda$ is a right-angled Artin group such that their profinite completions are isomorphic, i.e., $\widehat{A_\Gamma}\cong\widehat{A_\Lambda},$ then $\Gamma$ is right-angled and $\Gamma\cong\Lambda$ as labeled graphs. The proof combines the structure of pro-$p$ completions of Artin groups with finite Coxeter quotients to recover the defining graph.
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Machine Learning

Learning to Move Cities: Deep Meta-Models and Reinforcement Policies for Calibration and Control in Urban Networks

Adewumi Augustine Adepitan, Christopher J. Haruna, Oluwasegun Adegoke et al. (+2 more)

Urban transportation networks present complex optimization challenges spanning calibration of high-fidelity simulators and real-time operational control. This paper presents a shared latent-space framework that connects simulator calibration and reinforcement learning control through a common learned representation of urban traffic dynamics. First, we develop a combinatorial MLP-autoencoder architecture that learns low-dimensional manifolds linking simulator inputs (origin-destination demand, network parameters) to outputs (travel times, congestion patterns), enabling efficient Bayesian optimization for calibration. This approach demonstrates superior sample efficiency compared to traditional dimension reduction methods, achieving better fit to observational data within fixed computational budgets. Second, we implement a deep Q-learning agent with experience replay and target networks to optimize dynamic traffic assignment through scheduling and routing adjustments. In empirical evaluations on benchmark networks, our approach reduces system-wide travel times by up to 51% compared to baseline operations. The learned latent representation is not only used to reduce the dimensionality of Bayesian calibration, but is also incorporated into the reinforcement learning state representation, allowing the control policy to operate on compressed and calibrated traffic dynamics. This shared latent-space formulation provides a unified pathway from simulator calibration to adaptive operational control within intelligent transportation systems. Our results highlight the transformative potential of deep learning methods in urban mobility planning and management, particularly for large-scale networks where traditional optimization approaches face computational bottlenecks.
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All authors Adewumi Augustine Adepitan, Christopher J. Haruna, Oluwasegun Adegoke, Ayooluwatomiwa Ajiboye, Oluwatobi Oluwasakin

Quantum Physics

Guiding Agents of Quantum Games to Equilibrium using Matrix Exponential Fixed-Point Iteration

Alireza Habibi, Luis F. Abanto Leon and Setareh Maghsudi

In recent years, quantum game theory has gained significant attention as a framework for studying decision-making in multi-agent systems using quantum principles. However, computing equilibrium strategies is challenging because the dimension of the joint Hilbert space grows as the product of the players' local dimensions. In this paper, we consider an extended Gutoski-Watrous (EGW) game in which each player's quantum strategy is represented by a local density matrix. We derive tensor-contraction expressions for the payoff functions and their gradients, thereby avoiding the explicit construction of the full joint density matrix and its computationally expensive multiplication by the payoff operators. Building on the resulting effective Hamiltonians, we propose the Matrix Exponential Fixed-Point Iteration with Annealing (MEFPIA) algorithm to search for equilibrium points in EGW games. We compare MEFPIA with the Matrix Multiplicative Weights Update (MMWU) algorithm in terms of convergence. For the tested instances and parameter settings, both algorithms approach the same strategy profiles and payoffs, while MEFPIA achieves lower relative error in fewer iterations. These results indicate that MEFPIA is a promising numerical method for equilibrium search in multi-agent quantum games. Our findings provide important insights into the quantum game theory's potential for addressing complex decision-making processes, as well as opening up new paths for future research and exploration in multi-agent quantum systems.
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