For a system of partial differential equations admitting point, contact, or higher symmetries, the framework of invariant reduction systematically computes how invariant geometric structures, such as conservation laws, presymplectic structures, variational principles, and Poisson brackets, are inherited by the systems governing symmetry-invariant solutions. We extend this mechanism to geometric structures that are not invariant but are $\textit{rescaled}$ by a symmetry. Specifically, if $X$ is the symmetry used for reduction, $X_s$ is a symmetry satisfying $[X_s,X]=aX$, and the Lie derivative $\mathcal{L}_{X_s}$ acts on an $X$-invariant element of the Vinogradov $\mathcal{C}$-spectral sequence as multiplication by $b$, then the restricted symmetry $X_s|_{\mathcal{E}_X}$ acts on the corresponding reduction as multiplication by $a+b$. This shift rule gives rise to two phenomena: the $\textit{emergence of invariance}$, where reductions acquire an invariance that was not present at the level of the original structure, and the $\textit{loss of invariance}$, where reductions of invariant structures are no longer invariant. As an application, we describe a class of exact solutions to systems possessing sufficiently many symmetries and conservation laws subject to certain compatibility conditions. These solutions are invariant under pairs of symmetries and are completely determined by explicitly constructed functions that are constant on them; the description is geometric and does not require any integrability-related structures such as Lax pairs. The framework is illustrated by two examples: the Lin--Reissner--Tsien equation of potential nonstationary transonic gas flows, for which closed-form exact solutions are obtained and validated numerically, and the potential Boussinesq system, for which the inherited Poisson bracket is employed to describe solutions determined by algebraic equations.

For the Dirichlet integral fractional Laplacian, we prove root exponential convergence of tensor-product $hp$-finite element approximations on $(0,1)^3$, for forcing $f$ that is analytic in $[0,1]^3$. Exploiting analytic regularity estimates in weighted Sobolev spaces, we prove for $hp$-GLL interpolation approximations with $N$ degrees of freedom the energy norm error bound $\lesssim \exp(-b\sqrt[6]{N})$. Tensor product mesh families which are geometrically refined towards all sides of $(0,1)^3$ are used. Numerical experiments with $hp$-Galerkin FEM confirm the bound.

Efficient LLM inference scheduling is crucial for user experience. However, LLM inferences exhibit remarkable demand uncertainty (with unknown output length beforehand) and hybridity (being both compute and memory intensive). Existing LLM schedulers rely on simple heuristics or focus purely on compute resource, suffering suboptimal performance. In this work, we propose SageSched, an efficient LLM scheduler that properly handles demand uncertainty and hybridity of inference workloads. SageSched combines prompt contents with the past inference results to predict output-length distribution in a light-weight and also accurate manner. Meanwhile, it models the true service cost of an inference request with both compute and memory aspects considered. Finally, SageSched employs an uncertainty-aware scheduling policy that can yield the best overall efficiency given the request cost distributions. Testbed experiments over diverse setups confirm that SageSched can attain an efficiency improvement of over 28.7%.

Online platforms are seeing increasing amounts of AI-generated content -- text and other forms of media that are made or co-created with generative AI. This trend suggests platforms may need to establish governance frameworks, including policies and enforcement strategies for how users create, post, share, and engage with such content to encourage responsible use. We investigate the governance of AI-generated content across 40 popular social media platforms. Just over two-thirds explicitly describe governance of AI-generated content spanning six themes. Most platforms focus on moderating AI-generated content that violates established content rules and discloses AI-generated content. Fewer platforms -- those that are focused on creativity and knowledge-sharing -- address other issues such as ownership and monetization. Based on these findings, we suggest stakeholders and policymakers develop more direct, comprehensive, and forward-looking AI-generated content governance, as well as tools and education for users about the use of such content.

Transaction processing systems underpin modern commerce, finance, and critical infrastructure, yet their security has never been studied across the full evolutionary arc of these systems. Over five decades, transaction processing has progressed through four distinct generations, from centralized databases, to distributed databases, to blockchain and distributed ledger technologies (DLTs), finally to multi-context systems that span cyber-physical components under real-time constraints. Each generation has introduced new transaction types and new classes of vulnerabilities, yet security research remains fragmented by domain, and the foundational ACID transaction model has not been revisited to reflect the demands of contemporary systems. We classify 163 papers on transaction security by evolutionary generation, security focus, and relevant Common Weakness Enumeration (CWE) entries, and distill a curated set of 41 high-impact or seminal papers spanning all four generations. We make three principal contributions. First, we develop a four-generation evolutionary taxonomy that contextualizes each work within the broader trajectory of transaction processing. Second, we map each paper's security focus to CWE identifiers, providing a systems-oriented vocabulary for analyzing transaction-specific threats across otherwise siloed domains. Third, we demonstrate that the classical ACID properties are insufficient for modern transactional systems and introduce RANCID, extending ACID with Real-timeness (R) and N-many Contexts (N), as a property set for reasoning about the security and correctness of systems that must coordinate across heterogeneous contexts under timing constraints. Our systematization exposes a pronounced bias toward DLT security research at the expense of broader transactional security and identifies concrete open problems for the next generation of transaction processing systems.

Self-evolving agents offer a promising path toward scalable autonomy. However, in this work, we show that in competitive environments, self-evolution can instead give rise to a serious and previously underexplored risk: the spontaneous emergence of deception as an evolutionarily stable strategy. We conduct a systematic empirical study on the self-evolution of large language model (LLM) agents in a competitive Bidding Arena, where agents iteratively refine their strategies through interaction-driven reflection. Across different evolutionary paths (\eg, Neutral, Honesty-Guided, and Deception-Guided), we find a consistent pattern: under utility-driven competition, unconstrained self-evolution reliably drifts toward deceptive behaviors, even when honest strategies remain viable. This drift is explained by a fundamental asymmetry in generalization. Deception evolves as a transferable meta-strategy that generalizes robustly across diverse and unseen tasks, whereas honesty-based strategies are fragile and often collapse outside their original contexts. Further analysis of agents internal states reveals the emergence of rationalization mechanisms, through which agents justify or deny deceptive actions to reconcile competitive success with normative instructions. Our paper exposes a fundamental tension between agent self-evolution and alignment, highlighting the risks of deploying self-improving agents in adversarial environments.

Nanoconfinement reduces the favorable hydration free energies of single ions, which is correlated with ion rejection and modified chemical reactivity in water-filled nanopores. Many factors contribute to the magnitude of the observed confinement effect. Here we use simple classical force fields and non-polarizable carbon nanotubes filled with water as minimal, "hydrogen atom"-like models to evaluate the single-ion intrinsic confinement hydration free energy penalty (Delta Delta G(hyd)). In tubes of radius R=7.5 Angstrom, we predict Delta Delta G(hyd)'s that are up to 7.8 kcal/mol, are much larger for Cl$^-$ than the smaller Na+ ion, and contradict the canonical Born Equation for ion solvation. Adding a 1.0~M background electrolyte reduces Delta Delta G(hyd) for the Na$^+$/Cl$^-$ pair by an amount exceeding the Debye-Huckel estimate in unconfined media by almost an order of magnitude. We identify concentration-dependent ion-screening of confinement effects as a major, unheralded consequence of electrolytes in cylindrical nanopores.

We present a systematic analysis of 2544 cataclysmic variable systems and related candidates observed by the Transiting Exoplanet Survey Satellite (TESS), with the aim of compiling a comprehensive catalogue of orbital periods. Using 2-minute photometric time-series data, we applied an automated algorithm to generate Lomb-Scargle periodograms and identify the most significant coherent periodic signals, which were subsequently verified through visual inspection. This process yielded a confident sample of 910 sources exhibiting at least one periodic signal, hereafter referred to as the Cataclysmic Variable Confident Catalogue (CCC). For each object, we report the most likely orbital period together with additional periodic features such as spin modulations and/or superhump signals when present. To assess consistency with previously published measurements, we cross-matched the CCC with the Ritter \& Kolb catalogue, identifying 300 overlapping systems, of which 215 showed full agreement with the R\&K orbital periods, while 39 displayed discrepancies for which the R\&K values were revised based on our TESS measurements and supporting evidence from the literature. Overall, the CCC provides a means to validate known orbital periods, propose corrections where necessary, and offer new determinations for systems with previously unknown periods, thereby supporting a more complete and reliable characterisation of the cataclysmic variable population.

This paper studies pressure-robustness for the axisymmetric Stokes problem. The transformation to cylindrical coordinates requires that the radially weighted velocity is divergence-free in the classical sense. Consequently, traditional divergence-free finite element methods from the Cartesian setting -- even if inf-sup stable -- are in general not divergence-free in the axisymmetric formulation. We therefore explore the approach that restores pressure-robustness via reconstruction operators for a low-order Bernardi--Raugel discretization. We show that an application of standard interpolation operators from the Cartesian setting to radially weighted test functions works in principle, but it lacks properties needed to derive optimal consistency error estimates. To address this, we introduce a reconstruction operator into a finite element space spanned by Raviart--Thomas functions that are modified such that they vanish on the rotation axis. This vanishing-on-axis property is the key to obtain optimal consistency error estimates. Numerical examples demonstrate the overall feasibility of the approach and include cases where the vanishing-on-axis property yields significantly better results.

Dirac particles can undergo perfect transmission through a sufficiently high potential barrier in the Klein zone. Although the perfect Klein tunneling (often referred to as the Klein paradox) is similar to the non-relativistic resonant transmission which occurs only when the kinetic energy exceeds the barrier, the underlying mechanism is believed to be fundamentally distinct. In this work, we show that for the relativistic double-barrier model the perfect-transmission curve can pass continuously from the above-barrier zone to the Klein zone. Additionally, in the Klein zone, perfect transmission occurs even for subcritical barrier heights, supported by both bound-state analysis and wave-packet dynamics. These findings suggest a connection between perfect Klein tunneling and resonant transmission, and provide new insights into the physical nature of the Klein paradox.

Inductive invariants are crucial in model checking, yet generating effective inductive invariants automatically and efficiently remains challenging. A common approach is to iteratively analyze counterexamples to induction (CTIs) and derive invariants that rule them out, as in IC3. However, IC3's clause-based learning is limited to a CNF representation. For some designs, the resulting invariants may require a large number of clauses, which hurts scalability. We present CIll, a CTI-guided framework that leverages LLMs to synthesize invariants for model checking. CIll alternates between (bounded) correctness checking and inductiveness checking for the generated invariants. In correctness checking, CIll uses BMC to validate whether the generated invariants hold on reachable states within a given bound. In inductiveness checking, CIll checks whether the generated invariants, together with the target property, become inductive under the accumulated strengthening. When inductiveness fails, CIll extracts CTIs and provides them to the LLM. The LLM inspects the design and the CTI to propose new invariants that invalidate the CTIs. The proposed invariants are then re-validated through correctness and inductiveness checks, and the loop continues until the original property strengthened by the generated invariants becomes inductive. CIll also employs IC3 to work with the LLM for automatically discovering invariants, and uses K-Induction as a complementary engine. To improve performance, CIll applies local proof and reuses invariants learned by IC3, reducing redundant search and accelerating convergence. In our evaluation, CIll proved full compliance within RISCV-Formal framework and full accuracy of all non-M instructions in NERV and PicoRV32, whereas M extensions are proved against the RVFI ALTOPS substitute semantics provided by RISCV-Formal.

We derive a fluctuation dissipation relation connecting the drag and diffusion jet transport coefficients for an energetic light quark traversing a non-perturbative thermalized gluon plasma. The hard quark is taken to be close to on-shell, with an energy scale parametrically larger than the medium temperature. We introduce a general complex-valued function for each transport coefficient. Evaluating these in the deep Euclidean momentum region enables their expression in terms of local operators. Using contour-integration techniques, we relate these local operators, after vacuum subtraction, to the physical transport coefficients that arise along a branch cut, close to light-like dispersion. The derived relation relates the longitudinal drag coefficient to the longitudinal and transverse diffusion coefficients, and the thermal gluon condensate.

We establish a symmetry-protected correspondence between band topology of coherent Hamiltonians and Liouvillian spectral winding of open quantum systems with quadratic dissipations. This allows the Hamiltonian topology to act as a knob for controlling Liouvillian topology and corresponding non-equilibrium dynamics, rather than being passively manipulated by system-environment exchanges. In particular, by exactly solving the Liouvillian spectrum in a class of one-dimensional dissipative lattices, we find that the Hamiltonian band topology constrains the Liouvillian spectral winding and determines the Liouvillian skin effect, provided the Hamiltonian and quantum jump operators respect the same chiral symmetry. We further demonstrate that lattice parity controls the associated bulk-boundary correspondence and the coherence properties of the steady state. Our results unveil a symmetry-enforced topological control of spectral and spatial organization in open quantum systems, providing a unified perspective on topology in Hamiltonian and dissipative dynamics.

Motivated by applications of self-dual theories to the AdS/CFT correspondence, we study self-dual Yang-Mills theory (SDYM) and its relation to Yang-Mills theory and to Chalmers-Siegel theory with Dirichlet, Neumann, and mixed boundary conditions. A Fefferman-Graham analysis of SDYM is performed to identify its boundary CFT data. We make a proposal for self-dual holography that defines $3d$ ``self-dual CFTs''. The bulk-to-bulk and boundary-to-bulk propagators for SDYM and for Yang-Mills/Chalmers-Siegel theory with mixed boundary conditions are derived in Feynman and axial gauges. Three- and four-point functions are computed in the spinor-helicity formalism, and the relations among the results in the various theories are clarified. The flat limit and the gauge-(in)dependence of the results are analyzed.

Let $H$ be an infinite-dimensional Hilbert space. We prove that every unconditional Schauder frame for $H$ contains a subsequence that can be normalized to form a frame for $H$. As a consequence, every semi-normalized unconditional Schauder frame contains a frame for $H.$ Here we say that a sequence $\{x_n\}_{n\in \mathbb{N}}$ in a Hilbert space $H$ is an \emph{unconditional Schauder frame} for $H$ if there exists some sequence $\{y_n\}_{n\in \mathbb{R}}subseteq H$ such that $$x=\sum_{n=1}^\infty \langle x,y_n\rangle x_n\quad \text{for all }x\in H,$$ with the unconditional convergence of the series in the norm of $H.$ We say that $\{x_n\}_{n\in\mathbb{N}}$ is semi-normalized if $m\leq \|x_n\|\leq M$ for all $n\in \mathbb{N}$ for some positive constants $m,M.$ We then apply our main results to answer several open questions concerning the existence of certain unconditional Schauderf frames. For example, we prove that if a closed subspace of $L^2(\mathbb{R}^d)$ contains $\{e^{2πib\cdot x}g\}_{b\in Λ}$ for some infinite uniformly discrete subset $Λ$ of $\mathbb{R}^d$ and some nonzero function $g$ in the Feichtinger algebra, it does not admit any unconditional Schauder frames of translates with finitely many generators. We will also show that no Gabor system with the critical lower Beurling density can be an unconditional Schauder frame when the window function belongs to the Feichtinger algebra. Furthermore, we present an example of a compact set of $\mathbb{R}$ which does not admit any unconditional Schauder frames of exponentials with the critical lower Beurling density. All results in this paper apply equivalently to sequences that can be rescaled to form a frame for $H.$

Energy dependence of global scattering parameters, mostly of total cross section, is studied for proton-proton and antiproton-proton collisions. Results are presented for physical analysis updated with taken into account the recent data from accelerator experiments as well as from cosmic ray measurements. The analytic parameterizations suggested within Axiomatic Quantum Field Theory (AQFT) provide the quantitative description of energy dependence of global scattering parameters for rather wide energy range. Detailed scan on low boundary of the fitting range for energy dependence of global scattering parameters allows the observation of the onsets for regions in which Pomeranchuk theorem and / or Froissart-Martin one is valid. It is obtained that global scattering parameters show the behavior corresponded to any formulations of Pomeranchuk theorem and closed to (modified) Froissart-Martin limit in functional sense in multi-TeV energy region. Bosonic condensation is considered as one of the possible dynamical mechanisms which would be provide the total cross section approaches to (modified) Froissart-Martin limit at quantitative level but not functionally only.

We characterize the moduli space of étale Klein coverings (i.e. Galois with deck group $\mathbb{Z}_2^2$) of hyperelliptic curves of genus 3. We prove that the Prym map on each component is injective. As an application, we show that the Prym map of étale Klein coverings of genus 3 curves is generically finite.

Burst oscillations during thermonuclear X-ray bursts are powered by thermonuclear energy on the neutron star (NS) surface and typically occur close to the spin frequency of the NS. We performed a comprehensive timing analysis of all thermonuclear bursts from the newly discovered millisecond X-ray pulsar SRGA J144459.2$-$604207, observed with NICER, XMM-Newton, and NuSTAR during the 2024 outburst. A total of 39 bursts were detected, allowing for a detailed search for burst oscillations, which had not been previously observed from this source. We report the discovery of burst oscillations at 447.7$-$448.0 Hz from SRGA J144459.2$-$604207 using XMM-Newton and NuSTAR data, consistent with the spin frequency of the NS. The strongest burst oscillation in the XMM-Newton data occurred with a single-trial significance of $5.1σ$ and maximum $Z^2$ power of $\sim31$. In the NuSTAR data, the strongest oscillation signal has a significance of $5.2σ$ and maximum $Z^2$ power of $\sim32$. The folded pulse profile corresponding to the strongest signal in the 0.5-10 keV band of the XMM-Newton data shows a sinusoidal shape with a fractional rms amplitude of $\sim8.5\%$, while the measurements of the NuSTAR data (3-40 keV range) yield $\sim21\%$. These results represent the first detection of burst oscillations in SRGA J144459.2$-$604207. Additionally, we report the detection of 447.6 Hz oscillations occurring just before a burst onset observed with XMM-Newton. This marks only the second instance in which burst oscillations have been observed before the burst onset.

Environmental effects such as hierarchical triple motion can introduce cumulative phase modulation in gravitational-wave signals through time-dependent line-of-sight acceleration. Whether such smooth time-warp distortions are observable depends jointly on deformation strength and signal-to-noise ratio (SNR), yet this relationship has not been quantified in a template-free framework. We study the detectability of these distortions using time-frequency representations derived from the continuous wavelet transform. Instead of reconstruction error alone, we analyze trajectory-level statistics, in particular the evolution of the power-weighted frequency centroid. We find that environmental modulation can be detected using a single-sample statistic referenced to an isolated-binary distribution, without requiring matched templates. Across a grid of cumulative phase distortions and SNR, detection performance collapses onto a single scaling parameter defined as Lambda = Delta phi x SNR. The ROC-AUC follows an approximately sigmoid transition in this parameter. Moderate distortions are detectable even at low SNR, whereas smaller distortions require higher SNR. These results indicate that smooth environmental phase modulation is not generically absorbed by intrinsic waveform variability; instead, detectability is governed by a simple scaling between cumulative phase distortion and signal strength.

Pure 3d gravity in AdS is believed to admit a holographic description in terms of 2d CFT. We introduce a theory of fermionic 3d gravity where we sum over geometries equipped with spin structure, and propose it is holographically described by fermionic 2d CFT data. We evaluate the leading contributions to the gravity path integral with one and two torus boundaries, extracting both the spectrum and its spectral statistics from the torus wormhole. Strikingly, the theory has fermionic black hole microstates, even in the absence of bulk fermionic matter. We then incorporate subtle bulk topological field theories, classified by appropriate cobordism groups, and evaluate the one and two-boundary torus partition functions. The spectral statistics we derive from gravity are shown, in all cases, to be consistent with the pattern of anomalies expected from classifications of fermionic 2d CFT. We also define a version of RMT$_2$, a random-matrix framework compatible with the symmetries of 2d CFTs, which naturally accommodates fermionic spectra and reproduces our gravitational results across all cases we analyze.

We report the first direct measurement of the period derivative in a quasi-periodic eruption (QPE), finding a smoothly increasing period with $\dot{P}\approx (1.7\pm 0.02)\times10^{-2}$ d d$^{-1}$ in the source ZTF19acnskyy/"Ansky". Most models for QPEs invoke repeated interactions of a stellar-mass orbiting companion around the supermassive black hole (SMBH) in an extreme mass-ratio inspiral (EMRI). In these scenarios, a positive $\dot{P}$ is surprising, but not impossible to produce. We explore several possible explanations for the observed $\dot{P}$, including stable mass-transfer driven by impulsive mass loss events in an EMRI, velocity kicks at pericenter due to tidal interactions with the SMBH, apparent period changes due either to general relativistic precession effects in an EMRI or light travel-time delays in a hierarchical SMBH binary, and mass-transfer variations in a thermal/viscous disk instability model. We find that none of the considered models provides a complete explanation for the data, motivating further work on physical explanations for positive period derivatives in QPEs.

The evolution of magnetic correlation in strongly correlated electron systems with altermagentic spin splitting remains largely unexplored. Here we investigate how spin splitting generated by spin-dependent next-nearest-neighbor hopping t' reshapes the Fermi surface nesting and van Hove singularities in the two-dimensional square-lattice Hubbard model, leading evolution of magnetic instabilities. Using the constrained-path quantum Monte Carlo method, we find the dominant magnetic correlation as functions of the filling and t'/t by computing the momentum-resolved spin structure factor. The analysis reveals a transition from antiferromagnetic (π,π) order in the isotropic, half-filled system to non-collinear spiral (π,q) order upon increasing the spin-dependent anisotropy or doping away from half-filling, ultimately entering a short-range correlation regime where stripe and spiral correlation coexist. These findings highlight a possible route to realizing spiral correlation in altermagnetic systems, potentially providing a platform for spintronic devices that exploit non-collinear spin textures.

We discuss a scheme to generate large Fock states. The scheme involves repeatedly applying an experimentally feasible unitary transformation to convert a semiclassical state into a Fock state. The transformation combines Kerr interaction, which is a non-Gaussian operation, and pulsed coherent drives. We identify suitable parameter values (Kerr strength, pulse timings, displacement amplitude) for the physical processes to implement the transformation and generate large Fock states with near-unity fidelity. The feasibility of implementing the scheme in circuit QED architectures is discussed. The method is also suitable for generating Fock states of cavity fields.

Critical points of classical and quantum lattice models are often described by scale-invariant Lifshitz theories which are anisotropic in the continuum limit, as characterized by a dynamical critical exponent $z\neq1$. This type of critical behavior can in principle be studied by deforming ordinary $z=1$ conformal field theories (CFTs) by relevant vector operators breaking the rotational/Lorentz symmetry. In this short note, we consider a two-dimensional system of coupled minimal model CFTs $\mathcal{M}_{m,m+1}$ which realizes this perspective in a controlled fashion via Zamolodchikov's large $m$ expansion. The model turns out to exhibit interesting properties, including a manifold of interacting Lifshitz fixed points and emergent rotational symmetry in the infrared.

ARM SVE and RISC-V RVV are emerging vector architectures in high-end processors that support vectorization of flexible vector length. In this work, we leverage an important workload for quantum computing, quantum state-vector simulations, to understand whether high-performance portability can be achieved in a vector-length agnostic (VLA) design. We propose a VLA design and optimization techniques critical for achieving high performance, including VLEN-adaptive memory layout adjustment, load buffering, fine-grained loop control, and gate fusion-based arithmetic intensity adaptation. We provide an implementation in Google's Qsim and evaluate five quantum circuits of up to 36 qubits on three ARM processors, including NVIDIA Grace, AWS Graviton3, and Fujitsu A64FX. By defining new metrics and PMU events to quantify vectorization activities, we draw generic insights for future VLA designs. Our single-source implementation of VLA quantum simulations achieves up to 4.5x speedup on A64FX, 2.5x speedup on Grace, and 1.5x speedup on Graviton.

Public omics databases like the Gene Expression Omnibus and the Sequence Read Archive offer substantial opportunities for data reuse to address novel biomedical questions. However, it is still difficult to find samples and studies of interest since they are described by free-text metadata and lack standardized annotations. To address this issue, multiple research groups have undertaken curation efforts to add standardized annotations to large collections of these data, but these annotations are fragmented across online resources and are stored in different formats subject to varying standardization criteria, hindering the integration of annotations across sources. We developed MetaHQ to harmonize and distribute standardized metadata for public omics samples. MetaHQ comprises a database with nearly 200,000 annotations from 13 sources and a user-friendly command-line interface (CLI) to query the database and retrieve annotations. The MetaHQ CLI is deployed as a Python Package on PyPI at https://pypi.org/project/metahq-cli that accesses the MetaHQ database available at https://doi.org/10.5281/zenodo.18462463. Project source code and documentation are available at https://github.com/krishnanlab/meta-hq.

Interpreting horizon-scale black hole images currently relies on computationally intensive General Relativistic Ray Tracing (GRRT) simulations, which pose a significant bottleneck for rapid parameter exploration and high-precision tests of strong-field gravity. We demonstrate that physically accurate black hole images, synthesized from magnetized accretion flows, inherently reside on a low-dimensional manifold-encoding the essential features of spacetime geometry, plasma distribution, and relativistic emission. Leveraging this structure, we introduce a physics-conditioned diffusion model that operates in a compact latent space to generate high-fidelity black hole imagery directly from physical parameters. The model accurately reproduces critical observational signatures from full GRRT simulations-such as shadow diameter, photon-ring structure, and relativistic brightness asymmetry-while achieving over a fourfold reduction in computational expense. Compared with the previous generation of denoising diffusion models, the proposed approach achieves significant improvements in image quality, reconstruction fidelity, and parameter estimation accuracy, while reducing the average inference time per black hole image from 5.25 seconds to 1.15 seconds. Our work establishes diffusion-based latent models as efficient and scalable substitutes for traditional radiative transfer solvers, offering a practical framework toward real-time modeling and inference for next-generation black hole imaging.

In this paper, we study general Toda systems with homogeneous Neumann boundary conditions on Riemann surfaces. Assuming the surface satisfies the ``$k$-symmetric'' condition, we construct a family of bubbling solutions using singular perturbation methods, where the concentration rates of different components occur in distinct orders. In particular, we establish the existence of asymmetric blow-up solutions for the $SU(3)$ Toda system. Furthermore, the blow-up points are precisely located at the ``$k$-symmetric'' centers of the surface. Keywords: Toda system, Neumann boundary condition, Blow-up solutions, $k$-symmetry, Finite-dimensional reduction

We study proper isometric actions of non-compact semisimple Lie groups on pseudo-Riemannian symmetric spaces. Motivated by Okuda's classification of semisimple symmetric spaces admitting proper $SL(2,\mathbb{R})$-actions [J. Differential Geom., 2013], we focus on symmetric spaces lying on the boundary of the existence of proper $SL(2,\mathbb{R})$-actions. As a rigidity result, we show that any connected non-compact semisimple Lie group acting properly on these symmetric spaces must be globally isomorphic to $Spin(n,1)$ up to compact factors. Moreover, the Hurwitz-Radon number arises as the largest value of $n$ for the existence of $Spin(n,1)$-proper actions. Our symmetric spaces include the pseudo-Riemannian hyperbolic space $\mathbf{H}_{+}^{N,N-1}$ of signature $(N,N-1)$.

Qubit shuttling has become an indispensable ingredient for scaling leading quantum computing platforms, including semiconductor spin, neutral-atom, and trapped-ion qubits, enabling both crosstalk reduction and tighter integration of control hardware. Cai et al. (2023) proposed a scalable architecture that employs short-range shuttling to realize effective three-dimensional connectivity on a strictly two-dimensional device. Building on recent advances in quantum error correction, we show that this architecture enables the native implementation of folded surface codes on 2D hardware, reducing the runtime of all single-qubit logical Clifford gates and logical CNOTs within subsets of qubits from $\mathcal{O}(d)$ in conventional surface code lattice surgery to constant time. We present explicit protocols for these operations and demonstrate that access to a transversal $S$ gate reduces the spacetime volume of 8T-to-CCZ magic-state distillation by more than an order of magnitude compared with standard 2D lattice surgery approaches. Finally, we introduce a new "virtual-stack" layout that more efficiently exploits the quasi-three-dimensional structure of the architecture, enabling efficient multilayer routing on these two-dimensional devices.