Papers

Reinforcement learning (RL) has emerged as a promising approach for placement optimization, particularly when combined with graph neural networks (GNNs) that capture circuit connectivity. However, most learning-based placement approaches focus on floorplanning, macro placement, or global placement, while detailed placement refinement remains relatively unexplored. In this paper, we present GPlaceRL, an open-source graph reinforcement learning framework for detailed placement refinement. GPlaceRL represents legalized placements as graphs and provides a modular environment for studying graph encoders, policy architectures, reward formulations, and local placement actions. To demonstrate the capabilities of GPlaceRL, we conduct a systematic evaluation of proximal policy optimization (PPO) policies with graph attention network (GAT) encoders in a per-design optimization setting. Across five placement benchmarks, the best greedy evaluation results achieve HPWL improvements ranging from $3.27\%$ to $32.87\%$. The results highlight the importance of compact GAT architectures and flexible local action spaces for placement optimization. Overall, GPlaceRL provides a reproducible and extensible framework for systematic research on RL-based detailed placement refinement.

For residually finite groups, we study the automorphism and normalizer groups of odometers and their symbolic extensions: Toeplitz subshifts. In relation to orbit equivalence theory, we show that two continuous orbit equivalent $G$-odometers have commensurable normalizers when $G=\mathbb{Z}^d$, but that this result fails for other nilpotent groups $G$. The automorphism and normalizer groups of any Toeplitz subshift embed into those of its underlying odometer; despite this constraint, they exhibit considerable flexibility. For instance, we exhibit examples of low-complexity $G$-Toeplitz subshifts whose centralizer is isomorphic to $G$ (or, at the other extreme, restricted to its center) yet whose normalizer group is as large as possible.

Heterogeneous multi-robot path planning is a well-studied problem in which agents with disparate kinematic and dynamic models must coordinate to achieve shared objectives. These formulations, however, treat all agents as robotic-their cost models are mechanical and their traversability is sensor-derived. In human-robot teaming, the human partner remains relegated to command and supervisory roles rather than being modeled as a physical co-navigator with distinct mobility constraints and dynamic energy reserves. This work investigates joint path planning for a two-agent human-UGV team in search-and-rescue casualty retrieval scenarios. We model the human agent using the Pandolf-Santee metabolic cost model with fatigue-modulated speed, and the UGV using a rolling-resistance energy model with terrain-dependent speed limits. By exploiting the complementary traversability of each agent-the human's ability to traverse dense vegetation and shallow water versus the UGV's superior speed on open terrain and roads-we optimize casualty transfer locations, termed switch points, to minimize total mission time. Evaluated across multiple synthetic 1km2 environments with procedurally generated elevation and land-cover data, the optimized strategy reduces mean mission time by 5.3% relative to a human-only baseline and by 7.0% relative to a naive human-UGV strategy without switch point optimization, while reducing human energy expenditure by 17.8% relative to baseline. Notably, the naive strategy reduces human energy expenditure by a larger margin (22.4%) but incurs a 2% increase in mission time relative to baseline, illustrating that switch point optimization is necessary to realize time savings from human-UGV teaming.

We present boundary conditions for the quasiclassical Green's functions describing spin active interfaces between two materials, at least one of which is in the diffusive regime. These boundary conditions are developed with the help of the action formalism, and provide clean and easily tractable expressions. We connect our expressions to previous literature in limiting cases and describe normal transport, magneto-resistance transport and spin-precession through the bound ary. By using the Keldysh-Nambu-spin formalism, our equations are valid both in the normal and superconducting state. The construction through the action formalism also allows us to derive the corresponding full counting statistics for charge currents, thermal currents and spin currents. We use this boundary condition to consider the anomalous proximity effect, and to study the Josephson coupling between triplet and spin-split superconductors through a magnetic interface. We find an analytic expression for the zero bias conductance in junctions with a p-wave superconductor and a spin-filter, and show how it depends on the relative orientation of the exchange field and d-vector. For Josephson junctions, we show that, in agreement with time-reversal symmetry, the conditions on the relative orientations of the spins in the materials for the appearance of anomalous Josephson currents, are distinctly different for two spin-split superconductors and a spin-split superconductor with a triplet superconductor. Moreover, we show that the anomalous Josephson currents are only accompanied by a diode effect if both transparencies for spin up and down are nonzero and distinct.

We show that the numbers of colourings of a link by all finite quandles is equivalent, as an invariant of links, to the profinite completion of the peripheral system. This allows us to reformulate the classical question of the completeness of the former invariant in terms of profinite rigidity. We also develop some profinite quandle theory, and we show that a topological quandle is profinite if and only if it is compact and totally discontinuous and its group of inner automorphism is relatively compact in its homeomorphism group.

Graph neural networks (GNNs) are the standard tool for node representation learning and are increasingly used in high-stakes settings. Their message-passing backbone, however, can amplify topological bias, raising fairness concerns. We study group fairness at the level of downstream predictions for node classification, link prediction, and node regression, and bound the demographic parity gap for an arbitrary number of sensitive groups. Our node classification bound is provably no looser than the closest prior result. For link prediction, ours is the first bound on the parity gap of the deployed sigmoid-activated prediction rather than a pre-activation proxy, and for node regression we provide the first such bound. Across all three tasks, the analysis identifies two distinct sources of bias: the separation between group means and the within-group covariance of the final representations. Building on this insight, we embed fairness into propagation itself by augmenting the convex smoothing problem underlying APPNP with a convex group-mean constraint and a within-group covariance regularizer. Unfolding projected gradient descent on this problem yields FairProp, whose layers pair a propagation step with a closed-form projection and which provably converges linearly to the unique fair optimum. Experiments on three tasks show that FairProp, even with exact group-mean equalization alone, provides a strong inductive bias that achieves excellent fairness-utility trade-offs against strong baselines.

We investigate the longitudinal momentum distributions (LMDs) of the deuteron using a relativistic deuteron wave function derived from a realistic nucleon-nucleon (NN) interaction within the light-front framework. By convoluting the deuteron LMDs with the nucleon parton distribution functions (PDFs), we analyze the unpolarized, longitudinally polarized, and tensor-polarized structure functions of the deuteron. In addition, we also study the EMC effect in the weakly bound deuteron through the structure function ratio $F_{2}^{D}/(F_{2}^{p}+F_{2}^{n})$, which deviates from unity due to nuclear binding and Fermi motion effects.

We prove that deciding whether a graph has lettericity at most k is NP-complete, even for four-colorable comparability graphs. Our reduction maps a bipartite graph G to the graph obtained from its incidence graph by inflating each vertex by a clique or an independent set of three vertices. The lettericity of this graph is determined by the numbers of vertices and edges of G and the greatest number of edge-disjoint paths on four vertices in G. Teypaz and Rapine showed that deciding whether the edges of a bipartite graph can be partitioned into paths on four vertices is NP-complete.

As AI agents increasingly tackle complex repository-level coding tasks, distributing work across multiple agents is a natural way to scale beyond the capabilities of a single agent. To coordinate their interdependent work, these agents share findings and agree on interfaces between modules. However, exchanged information often serves only as context, leaving individual agents to interpret it and incorporate it into subsequent work. Consequently, shared findings may go unused and deviations from interface agreements may go undetected, undermining the reliability and efficiency of collaboration. This motivates moving part of the coordination responsibility from individual agents to the execution harness. To make shared information actionable during execution, we introduce the Artifact-Exclusive Communication Protocol (AECP). AECP requires agents to communicate exclusively through structured artifacts and specifies how the harness processes them. The harness supplies findings when agents access relevant code, screens implementations for mismatches with recorded interface commitments, and requires affected agents to revisit revised agreements. These coordination steps become part of harness execution rather than actions that agents must initiate from prior messages. Across Doc2Repo, NL2Repo, and CodeProjectEval, using closed- and open-source models including Opus-4.8 and DeepSeek-V4-Flash, AECP improves average test pass rate by 28.2% and reduces average wall time by 16.5% relative to an agent team using free-form inter-agent messages. Artifact-exclusive communication also blocks the relay of malicious instructions between agents, reducing how often they reach other agents from 95% to 0% and how often those agents act on them from 40% to 0%.

Let $Z_N$ be the partition function of the Sherrington-Kirkpatrick model at inverse temperature $\beta>1$. Replica theory (Kondor near the critical temperature, Parisi and Rizzo at all temperatures) predicts that the probability that $N^{-1}\log Z_N$ exceeds its typical value by $\delta$ decays like $\exp(-Na\delta^{6/5})$ with an explicit $a$; Aronow and Lopatto recently proved bounds of this order. The exponent is the Legendre transform of the Parisi problem constrained to carry an atom $\theta$ at zero. We show that the constrained minimum exceeds the equilibrium free energy by $c_\beta\theta^5(1+o(1))$, where $c_\beta=\frac{9}{640}\beta^3\rho_\beta(0)^{-3}$ and $\rho_\beta(0)>0$ is the density at zero of the Parisi measure. With the fractional-moment formula this gives the exponent $\frac56(6c_\beta)^{-1/5}\delta^{6/5}(1+o(1))$ as $N\to\infty$ and then $\delta\to0$. The constrained minimizer has a marginal first positive contact, to leading order at $3\theta/(2\rho_\beta(0))$ with an atom $\theta/2$. This plateau calculus applies to every mixture with $\xi'''(0)=0$ whose Parisi measure accumulates at zero; a small field $h$ opens a gap of order $|h|^{2/3}$, and an atom of the Parisi measure at zero, present in every pure $p$-spin model with $p\ge3$, makes the rate leave zero linearly. Near criticality the constant tends to Kondor's value $9/5120$ and the marginal regime ends at a de Almeida-Thouless threshold. For the Sherrington-Kirkpatrick model at every $\beta>1$, a finite-step curvature inequality from an unrefereed preprint shows that every constrained minimizer either has an interval of positive contacts, all marginal, or has exactly two atoms, and that the marginal regime ends at a unique de Almeida-Thouless threshold $\theta_c(\beta)$. The laws at every $\beta>1$ use that the Parisi measure accumulates at zero, a theorem of Lopatto also proved in earlier work of the author.

KV caches are a major bottleneck in long-context inference and long-form generation with large language models. Existing training-free eviction policies largely rely on proxy importance signals, such as attention mass, to decide which past tokens to retain. We argue that cache compression should instead preserve the predictive behavior of the full-cache model, retaining entries whose removal would substantially change the model's output distribution. We propose Behavior-Preserving KV Cache Compression, a training-free framework that scores candidate evictions by estimating the compressed-cache logits induced by their removal and evaluating the resulting KL to the full-cache next-token distribution. Using pre-eviction forward statistics, the method avoids running separate masked forward passes for each candidate. Across diverse architectures and both prefill-time and generation-time compression, our method delivers substantial gains in downstream task quality over lightweight attention-based heuristics at matched retained-KV budgets, with the largest gains under aggressive compression. It achieves these gains with additional compression-time computation while retaining an end-to-end speedup over full-cache inference in our evaluated settings.

Sound morphing, generating intermediate sounds that transition from one sonic identity to another, can be a powerful tool for musical sound design. Existing diffusion-based morphing approaches entangle temporal structure and timbral identity, offering no mechanism to hold one fixed while transforming the other. We present smorph, a training-free guidance framework that preserves how a sound behaves over time while transforming what the sound is, allowing users to morph, for instance from brass to strings at a fixed pitch. We demonstrate across three morphing modes: prompt-to-prompt, audio-to-prompt, and audio-to-audio. Evaluations across diverse datasets show that smorph effectively produces smooth morph trajectories while substantially improving temporal-structure and source preservation over baselines, albeit with more conservative target-ward transformation in some settings. In an exploratory case study, musicians found smorph trajectories to be expressive and playable, suggesting structural anchoring can serve as a productive constraint for instrumental interaction.

We report an implementation of continuous-wave (CW) vacuum-ultraviolet (VUV) generation at 148.4 nm by single-pass second-harmonic generation of 296.8 nm light in strontium tetraborate (SBO). At an incident fundamental power of approximately 580~mW, we estimate a VUV output power of approximately 1.7 nW at the crystal exit. The crystal is grown by the top-seeded solution growth method and operated in a helium-filled chamber. The quadratic power dependence observed under vacuum, together with its strong suppression in air, supports the identification of the generated second harmonic. We further characterize the dependence of the VUV signal on beam position, incidence angle, polarization, and crystal temperature, providing practical guidance for SBO-based CW VUV sources for nuclear spectroscopy and clock applications.

Forest managers need timely stand-level information to support operational planning, particularly in mixed-species, structurally heterogeneous forests facing climate-related disturbance. Model-based estimation combines sparse field data with remotely sensed predictors to estimate growing stock volume (GSV) for small areas. While uncrewed aerial vehicle laser scanning (ULS) offers flexible, high-resolution LiDAR acquisition, its advantages over conventional airborne laser scanning (ALS) remain unclear. We compared publicly available ALS and newly acquired ULS data using Bayesian change-of-support models to estimate GSV in a mixed-species forest in north-eastern Germany. We evaluated distributional LiDAR metrics and spatial random effects. ULS consistently outperformed ALS, achieving cross-validated RMSPEs of 68.5 m^3/ha and 79.5 m3/ha, respectively-a 13.8 % reduction in prediction error. Distributional metrics improved ULS models more strongly, reducing RMSPE by up to 10.1 %; spatial effects provided only minor gains at substantially higher computational cost. ULS also produced lower uncertainty in latent stand-mean GSV estimates. The ULS advantage may reflect both finer-scale canopy information and closer temporal alignment with field measurements. Timely, information rich LiDAR may therefore be more valuable for stand-level GSV estimation than increasingly complex spatial models. Temporally matched ALS-ULS comparisons are needed to isolate platform effects.

DRAM continues to limit the performance, energy efficiency, and robustness of modern systems. Many prior works propose DRAM techniques that support in-DRAM computation, improve memory access latency and parallelism, and enhance DRAM maintenance and reliability. However, adopting each new technique requires repeated modifications to the rigid DRAM interface and memory controller, hindering its deployment. Our goal is to reduce these repeated modifications. We observe that the DRAM commands and memory controller structures of many DRAM techniques are similar. Our key idea is to use these similarities to compose a set of primitives for implementing diverse DRAM techniques. We propose Terracotta, a new framework with two flexible components: (i) custom command extensions that let DRAM vendors define new commands within a single, standardized interface, and (ii) a programmable memory controller that system designers can program to support new DRAM techniques post-silicon. Together, these enable deployment by configuring the memory controller instead of modifying the interface and controller. We design Terracotta for a DDR5-based system and evaluate its performance, energy, and hardware complexity. For four DRAM techniques from four distinct domains (processing-using-DRAM, low-cost DRAM maintenance, subarray-level parallelism, and latency reduction), Terracotta retains almost all of the performance benefits (>96%) of custom implementations. A Terracotta-based composition of two techniques outperforms the Terracotta-based implementation of each technique alone, demonstrating the benefits of adding techniques without repeated interface and controller modifications. Terracotta incurs low DRAM energy (0.6-3.2%), area (0.03%), and power (0.56%) overheads in a high-end server-grade processor. Terracotta's source code is freely available at https://github.com/CMU-SAFARI/Terracotta.

A Direct Numerical Simulation (DNS) investigates transonic flow over a NACA0012 airfoil coupled with single-DOF structural dynamics. Analysis is performed for angle of attack ({\alpha}) 8{\deg} with varying reduced velocity (U*) from 2 to 8, reduced mass (m*) 5.0, Reynolds number (Re_\infty) of 3 \times 10^6, and Mach number (M_\infty) 0.8. The speed of sound in air is calculated as a = sqrt({\gamma}RT_\infty). It is noted that the magnitude of the aerodynamic loads and moments increased with higher reduced velocity. The Fast Fourier Transform (FFT) of the moment coefficient (C_M) in the fixed-airfoil condition is carried out to extract the non-dimensional dominant frequency, referred to as the Strouhal number (St), along with the coupled oscillation frequency of the airfoil (Stc). The FFT analysis for the stationary case at {\alpha} = 8{\deg} yields a value of St = 1.3161. The presence of high-frequency components indicates the onset of instability associated with shock-boundary layer interaction. The computed values of the coupled oscillation frequency (Stc ) are 0.0762 and 0.1716 for the cases with angle of attack (AoA) 8{\deg} and reduced velocities U* = 2.0 and 8.0, respectively. The corresponding natural aeroelastic frequencies (Stn) are taken as 1/U*, yielding values of 0.5 and 0.125. It is observed that for U* = 2, the coupled frequency (Stc) aligns with the subharmonic of shock-buffet frequency, indicating flow-dominated dynamics. In contrast, for U* = 8, Stc coincides with the natural pitching frequency, indicating a dominant influence of the structural mode. Pressure fluctuation contours are examined to analyze the characteristics of acoustic radiation. Vorticity and schlieren visualizations are employed to identify the nature of vortex structures, the strength of the shock, and its spatial location, respectively.

We study regularity of bounded weak solutions to complex Monge-Ampère equations on compact Hermitian manifolds with right-hand side possibly decreasing in the unknown. Our proof relies on the domination principle and a priori estimates, partially motivated by the Monge-Ampère eigenvalue problem. Our main result roughly says that any bounded solution is smooth in the regular locus of the data. When the right-hand side is strictly positive and smooth, we recover known results by Nie, Ko lodziej-Nguyen for the Hermitian case and Székelyhidi-Tosatti for the Kähler case, which rely on the regularizing property of the Kähler-Ricci flow.

We address the challenge of accurate 3D object reconstruction from multi-view images in Gaussian Splatting. Existing object-level 3DGS methods reconstruct the entire scene rather than directly optimizing the target object, even when only the target object is needed, which incurs substantial computational overhead. They also rely on 2D segmentation masks to associate Gaussians with objects, but these masks are often inconsistent across views. Such inconsistencies corrupt Gaussian optimization and produce incorrectly supervised Gaussians that degrade object reconstruction fidelity. To overcome these limitations, we propose MaRO-GS, a 3DGS framework that directly optimizes target-object Gaussians from object-masked multi-view images and remains robust to inconsistent supervision. For reliable supervision, mask-reliability view filtering excludes unreliable views. Object-supported Gaussian density control suppresses Gaussians irrelevant to the target object and prevents background densification, while Silhouette-aligned Object Loss maintains object-focused optimization. Extensive experiments across diverse datasets demonstrate that MaRO-GS improves PSNR, segmentation accuracy, and computational efficiency, with the largest PSNR gain of 2.05 dB on the small-object LERF-Mask dataset.

In this paper we give an analytic proof of the Two-point Chowla conjecture for the truncated Möbius function $\mu_M$ for the function field case in the fixed $q$ setting. We reformulate the problem into studying the distribution of $(\omega_M,\omega_M\circ T_a)$. Thus we develop a uniform bivariate Erdős-Kac theorem in terms of the characteristic function for small pair of real numbers $(u,v)$ via the Kubilius model. For this purpose we also develop and employ the pure Brun sieve for polynomials in this paper.

The large $D$ membrane paradigm provides a perturbative, non-gravitational description of black hole dynamics. While the local second law of thermodynamics has been established for neutral membranes, the explicit determination of the local entropy production in the charged large $D$ membrane paradigm remains an open problem. In this paper, we compute the subleading-order correction to the divergence of the membrane velocity for a charged black hole in a flat background. Using the non-affine null Raychaudhuri equation and the Einstein-Maxwell equation at the physical event horizon, we relate the horizon expansion to the auxiliary membrane kinematics. We demonstrate that the membrane velocity produces a non-negative divergence at the first non-vanishing order in the membrane worldvolume, which is driven by two quadratic forms: the membrane shear and an additional term arising from the Maxwell field. Using this result, we subsequently construct the corresponding membrane entropy current and establish the non-negativity of its divergence through this order, thereby establishing the local second law for the charged large $D$ membrane paradigm.

Closed-loop evaluation of end-to-end driving requires continuous rollouts that reveal how earlier decisions affect subsequent driving. However, existing benchmarks evaluate only short segments and fail to capture later consequences. Ambiguous directional commands also obscure the intended navigation objective. We introduce Odyssey, a closed-loop benchmark for long-horizon driving comprising 100 scenarios, each reconstructed from a 100-second nuPlan driving log to preserve the context of navigation maneuvers and traffic interactions. To provide a consistent navigation objective, Odyssey replaces directional commands with explicit standard-definition (SD) map routes that specify which roads to follow, while sensor-based planning determines local driving actions. Throughout these rollouts, diffusion-based refinement of 3DGS-rendered images reduces rendering artifacts along the ego trajectory. To assess how effectively planners follow these routes and prepare for upcoming maneuvers, we introduce SD Route Compliance and Pre-Lane Change Score. These assessments are complemented by RouteDS, which extends the Driving Score with penalties for SD-route deviations and failed lane preparation. We adapt state-of-the-art planners, including vision-language-action (VLA) models, and evaluate their navigation performance using these metrics. Odyssey highlights open questions in route representation and integration for E2E driving. Benchmark code and adapted baselines will be released publicly.

Modern graph generative models typically operate directly in the discrete graph space, explicitly generating node and edge variables, which can become costly as graphs grow. In this paper, we perform generation explicitly on latent representations of entire graphs obtained from a pretrained Variational Autoencoder with high reconstruction fidelity. The generated representations, obtained through flow matching, are then decoded only at the final step. Across molecular benchmarks of increasing size, our approach achieves strong validity and FCD while offering a favorable quality-efficiency trade-off compared with state-of-the-art explicit graph generative models. One of the main advantages of this formulation is that the graph representation only needs to be learned once, after which the same one can be reused across multiple generative objectives without retraining. We demonstrate generation guided by molecular properties and further introduce validity-aware generation though a classifier learned directly in latent space. All code will be made available upon acceptance.

Understanding phase stability and navigating vast compositional spaces in multicomponent solids remain central challenges in solid-state chemistry. Here, we develop a quantum spectral thermodynamic framework connecting interaction-induced phonon spectral broadening to free energy, alongside an uncertainty-guided active-learning workflow that explores 7.7 million high-entropy ceramic configurations at density-functional-theory fidelity, achieving a $10^5$-fold acceleration. We show that phonon self-energy effects arising from chemical disorder provide an intrinsic vibrational contribution to thermodynamic stabilization beyond ideal configurational entropy, compensating unfavorable mixing enthalpies and suppressing phase separation. Across the chemical space, we uncover a robust ~12 at.% solute threshold separating strengthening and softening regimes, associated with the filling of metal-carbon antibonding states. Chemical disorder further enables an unusual combination of high-temperature mechanical stiffness and low thermal conductivity, together with anomalous temperature-dependent lattice heat transport. This work establishes a quantum spectral foundation for connecting many-body interactions to thermodynamics and phase stability, while providing a scalable framework for exploring previously inaccessible multicomponent chemical spaces.

Let $(M^n,g_0)$ be a closed hyperbolic manifold, $n\geq3$. We compute the Hessian of volume entropy at $g_0$ under the constraint $Sc_g=-n(n-1)$ and express it as a quadratic form on transverse-traceless symmetric two-tensors. In dimension three, the Hessian is negative definite, and every sufficiently $C^\infty$-close metric with $Sc_g\geq-6$ has entropy at most $2$, with equality precisely for pullbacks of $g_0$. In dimensions $n\geq4$, a universal spectral threshold determines the Hessian sign. Nonzero trace-free Codazzi tensors give positive directions, and hyperbolic bending provides smooth constrained entropy saddles in every such dimension.

Pretrained speech representations are increasingly used for depression detection, but selecting the best encoder layer on the same data used for evaluation biases reported performance. On DAIC-WOZ, with repeated nested cross-validation across five deep encoder families, naive best-of-25-layer probing inflates AUC by up to $0.09$. On shuffled labels over the real latent representations, naive best-of-25 still reaches AUC $0.59$ versus $0.50$ under nested selection, and this bias grows with the number of probed layers and with smaller samples, isolating selection, not signal, as the cause. The effect replicates on a second clinical corpus and language (Androids, Italian). Under leakage-free selection, a fair comparison across representation families identifies a compact, task-aligned affect–prosody model as competitive with substantially more complex SSL, deep-learning, audio-LLM, and codec-based approaches, while using $\sim\!10^{3}\times$ fewer trainable downstream parameters. Extending the analysis to individual PHQ-8 symptoms shows that the same selection bias persists at this finer-grained level. We argue nested model-selection protocols should be standard when probing encoder layer representations on small clinical speech datasets.

As technology scales to smaller nodes, increasing current densities make electromigration (EM) one of the dominant reliability challenges in on-chip interconnects. Accurate transient stress analysis is needed to identify wires susceptible to EM degradation, but applying physics-based solvers across many interconnects remains computationally expensive. This paper proposes a physics-guided transformer framework for fast EM stress prediction in multi-segment interconnect lines. The framework converts each line into geometry- and DC-aware segment tokens and uses transformer attention to capture line-level context. A lightweight query decoder then predicts stress at selected locations and time instants. The model is trained with an objective that combines normalized supervised regression, linewise relative-$L_2$ loss, and physics-guided continuity and terminal-flux terms. Experiments on IBM power grid benchmarks show that the proposed model achieves relative-$L_2$ error below 8% and reaches up to 2459.68$\times$ speedup compared with the matrix exponential~solver.

Sasakian manifolds, a subclass of contact metric manifolds, play a central role in modern differential geometry and mathematical physics, where they arise naturally in geometric mechanics, CR geometry, and supersymmetric field theories. The weak contact metric (w.c.m.) structure generalizes the contact metric structure and provides a broader framework for studying contact geometry and its applications. A fundamental problem is to understand how curvature conditions constrain the underlying contact metric structure and, in particular, how they distinguish Sasakian geometry from its weaker variants. Using the partial Ricci flow, we characterize Sasakian structure (among w.c.m. manifolds) under the $(\kappa,\mu)$-nullity condition related to curvature. For $\kappa<1$ we find conditions under which a w.c.m. manifold admits a bi-Legendrian structure, and for $\kappa=\mu=0$ establish splitting and classification results.

Our previous work [Y.~Li, D.~Xu, and Y.~Hao, Phys. Rev. Accel. Beams 28, 074001 (2025)] introduced a square-matrix method for constructing approximate invariants recursively, order by order, from the one-turn map of non-integrable Hamiltonian systems. At fourth and higher even orders, the recursive construction is intrinsically non-unique because rotationally invariant polynomials generate a null space in the corresponding homological equations. In the resonant regime, this ambiguity can lead to an incorrect description of the resonance-island topology and is therefore particularly relevant to accelerator applications that rely on stable resonance islands. In this work, we select the null-space contributions by explicitly incorporating the null-space basis vectors and determining their coefficients through an averaging procedure over a prescribed region of interest. The method is demonstrated using the Kobayashi map near a third-order resonance, extending the square-matrix construction to resonant Hamiltonian dynamics.

We construct Golod–Shafarevich towers of arithmetic surfaces over the integers. In particular, we obtain an arithmetic surface with a section and infinite geometric etale fundamental group, answering a question raised by Bost and Charles about the existence of such surfaces. Taking generic fibres gives curves over the rationals with infinite geometric etale towers in which a rational point splits completely. This answers questions posed by Ihara and by Frey, Kani and Völklein. Taking the generic fibres of the tower, we also obtain sequence of curves over the rationals whose genera goes to infinity and whose logarithmic conductors grows no more than linearly in the genera, answering a question asked by Venkatesh at PCMI in 2022. The authors worked together on this problem since 2022 and developed a general strategy. They were able to bring it to fruit only after a collaboration with GPT5.6 Sol, Fable and Aletheia a Gemini-powered internal agent developed at Google DeepMind.

We provide a complete study of the optimal control problem associated to the so-called Dyson equation, which describes the mean field evolution of the spectrum of large random matrices. We treat both the case of regular and singular terminal data. We construct admissible controls and prove the existence of optimal ones. We then proceed to give a thorough mathematical analysis of the associated Hamilton-Jacobi-Bellman equation by means of the theory of viscosity solutions in the space of measures. In particular, we characterize the value function of the optimal control problem as the unique viscosity solution to this infinite dimensional HJB equation.