Papers

Most image generation models rely on uniform tokenization, allocating the exact same computational budget to equally-sized image patches. This static paradigm cannot adapt to different resource constraints at inference time, and yields suboptimal quality-cost tradeoff by devoting the same effort to both plain backgrounds and intricate details. We propose BudgetPix, an adaptive tokenization framework that dynamically allocates compute based on visual complexity and spatial layout, enabling flexible computational budgeting at inference time. BudgetPix comprises three key components: (1) an adaptive encoder that maps a fixed-size image to a variable-length token sequence using an entropy-guided quadtree alongside a multi-scale patch embedder; (2) a scale-aware decoder reconstructs fixed-resolution images from multi-scale token sets; and (3) a flexible training and sampling schedule that enables pixel-space denoisers to operate across variable token counts. BudgetPix seamlessly integrates with existing pixel-space diffusion architectures, enabling a single checkpoint to be operated at a wide range of compute budgets. Evaluated on text-to-image generation, BudgetPix matches the fidelity of MiniT2I-L at $512^2$ and PixelDiT at $1024^2$ using just 25% of the original compute budget. In class-conditional generation using a MeanFlow backbone, BudgetPix requires merely 60% of the full compute budget to produce images with near-zero quality degradation, observing a marginal 0.8-point increase in FID. Comprehensive assessments by human and VLM judges confirm that BudgetPix establishes a significantly improved quality-efficiency tradeoff over prior budget-adaptive baselines. More details are available at our project page: https://karaozgur.com/BudgetPix

Learning and problem solving depend critically on the structure of internal representations. While many modern data-driven artificial systems achieve strong predictive performance, their learned representations often lack explicit structure for expressing abstraction, invariance, and task-relevant regularities. We propose a minimal structural framework in which representational operations relevant to problem solving, such as context formation, invariance recognition, representative selection, abstraction, and procedural reuse, are made explicit. The central notion is that of a context, formalized as a partition of a subset of an underlying state space, which fixes the distinctions, granularity, and form in which a problem can be posed. Within this setting, invariance recognition and representative selection are treated as fundamental representational operations. The framework is realized as a Knowledge Space composed of two coupled graph structures: a Concept Graph that hosts constructed and refined concepts, and a Procedure Graph that encodes typed operations over representations. Together, these structures provide a minimal cognitive-representational algebra for operating on representations without assuming sophisticated inference, learning, control, perception, or motor mechanisms. Using simple illustrative examples and a finite weak-solver demonstration, we show that appropriate representational organization can simplify the form and scope of admissible regularities, even when problem solving is carried out by a fixed and limited solver. The contribution of the paper is structural rather than algorithmic: it identifies representational prerequisites for abstraction, invariance, and procedural reuse in problem solving, and states explicit success and failure conditions for the weak-solver setting.

As Multimodal Large Language Models (MLLMs) can describe increasingly complex visual scenes, token-level grounding becomes crucial. Yet, when an MLLM generates "the yellow banana on the left", established grounding approaches focus on what is in the image ("banana"), overlooking tokens that help describe which instance is meant ("yellow", "left"). In this work, we ask whether frozen MLLM representations contain decodable grounding information about the referred instance across generated tokens, extending to modifiers such as attributes, spatial expressions, and relational/action terms. To address this question, we introduce OTTER, a lightweight supervised probe over frozen MLLM representations that uses Optimal Transport (OT) to align generated tokens with visual regions and produce compact grounding maps. Our results show that (i) instance-discriminative visual information can be decoded from modifier tokens, with the clearest evidence for spatial terms, but (ii) is not confined to them, as contextualized object nouns also carry referential information; (iii) the recovered grounding remains informative under context perturbations, while selected regions remain relevant to generation; and (iv) the learned OT-based grounding extends beyond the controlled setting to free generation and cross-dataset transfer.

Understanding large language model (LLM) reasoning requires looking beyond behavioral performance to examine how reasoning ability is reflected in internal organization. Inspired by neuroscience findings linking higher intelligence to stronger small-world organization in functional brain networks, we investigate small-world connectivity as a structural signature of LLM reasoning. We construct functional graphs from attention-head activation similarities and find that a higher small-world index (SWI), capturing local clustering and short global paths, consistently correlates with better fluid reasoning performance across models and training checkpoints. Since local clustering is central to small-world organization, we further examine how heads important for model performance connect within and across communities. We find that these heads tend to have a larger share of connection weight within their own communities (high core scores) and a more concentrated weight distribution across communities (low bridge scores). These observations motivate the hypothesis that high core and low bridge scores serve as structural indicators of head importance for reasoning capability. We validate this hypothesis through pruning, introducing Small-World Allocation (SWA), a hierarchical sparsity allocation method guided by these scores. Across six LLMs, SWA better preserves small-world organization and model performance than competing allocation strategies, reducing WikiText perplexity by up to 20%. Together, these findings identify small-world functional connectivity as a measurable signature of LLM reasoning performance, offering a structural perspective that complements behavioral evaluation.

Declarative logic programs offer a powerful and interpretable abstraction for encoding relational structure and neurosymbolic reasoning, by expressing dependencies as weighted compositional rules. However, inducing them from data remains fundamentally hard, bottlenecked by the combinatorial explosion of symbolic search spaces. LLMs have recently emerged as powerful hypothesis generators, but when used in isolation, they lack the capacity to do systematic inductive reasoning needed to reliably synthesize valid programs that fit complex relational distributions. We introduce grasp (Gradient-boosted Synthesis of Probabilistic logic programs), a neurosymbolic framework that casts relational structure learning as functional gradient boosting in which the weak learner is a first-order rule and the intractable inner search is delegated to an LLM proposal oracle. We evaluate grasp on four relational benchmarks spanning molecular toxicity prediction (Tox21), mutagenesis, and citation matching (Cora), and show that it improves over purely symbolic, neural, and LLM-based baselines, while producing interpretable weighted rule ensembles. By replacing combinatorial search with gradient-guided LLM hypothesis generation, grasp retains boosting guarantees without sacrificing the transparency of symbolic outputs.

We develop an algorithm that takes as input a veering triangulation V and a flow cycle c of V, and outputs a veering parent V_c of V. Constructing veering parents combinatorializes drilling out closed orbits of transitive pseudo-Anosov flows. The algorithm relies on locally approximating the structure of the loom space associated to V in sufficient detail to carry out a certain modification of the Agol-Guéritaud construction. We use an implementation of the drilling algorithm to construct layered parents of non-layered veering triangulations (and hence Birkhoff sections for transitive pseudo-Anosov flows) and geometric parents of non-geometric veering triangulations. We also find closed orbits of (drilled) pseudo-Anosov flows that are not ambiently isotopic to the geodesics in their free homotopy classes, and show that certain veering triangulations encode almost orbit equivalent flows. In particular, we provide new computational evidence for a conjecture of Ghys asserting that all transitive Anosov flows with orientable invariant foliations are almost orbit equivalent.

Due to the availability of powerful analytic techniques, vastly superior lower bounds are known for the measurable chromatic number of Euclidean spaces compared to their ordinary chromatic number. Indeed, even the breakthrough lower bound of 5 for the famous Hadwiger-Nelson problem lagged over 35 years behind that of the measurable setting. This raises the fundamental question of whether the measurable and ordinary chromatic number of Euclidean spaces differ as conjectured by Székely in 1984. Our main result is that $\overline\alpha(\mathbb{R}^4)=m_1(\mathbb{R}^4)$ and $\chi(\mathbb{R}^4)=\chi^{(m)}(\mathbb{R}^4)$, and for $d\ge5$ that \[ \overline\alpha(\mathbb{Q}^d) = \overline\alpha(\mathbb{R}^d)=m_1(\mathbb{R}^d) \qquad\text{and}\qquad \chi(\mathbb{Q}^d) = \chi(\mathbb{R}^d)=\chi^{(m)}(\mathbb{R}^d). \] Our theorem also holds for multiple forbidden distances $D=\{d_1,\ldots,d_t\}$ provided that $d_1^2,\ldots,d_t^2 \in \mathbb{Q}$. As a consequence, we immediately lift numerous measurable chromatic number results into the ordinary setting. We also take the opportunity to further optimize the new bounds. For multiple distances, Erdős asked whether the chromatic number of $\mathbb{R}^d$ with up to $k$ forbidden distances $D$ grows exponentially in $k$. By a theorem of Bukh, we obtain for $d \ge 4$ that \[ \sup_{|D|=k}\chi_D(\mathbb{R}^d) \ge m_1(\mathbb{R}^d)^{-k}. \] Making progress on another problem of Erdős, we prove that \[ (2+o(1))^d \le \chi(\mathbb{R}^d) \le \left(\frac{3\sqrt{3}}{4}+o(1)\right)^d. \] We also vastly improve the lower bounds for $\chi(\mathbb{R}^d)$ for small $d\ge4$. We expect that our techniques could be developed much further. This includes the possibility of extending our main theorem that $\chi(\mathbb{R}^d)=\chi^{(m)}(\mathbb{R}^d)$ for $d\ge 4$ to $d=3$ or possibly even to $d=2$ to tackle the Hadwiger-Nelson problem.

This paper investigates how to substantially reduce the memory footprint of learned sparse retrieval indexes without sacrificing the efficiency of state-of-the-art retrieval data structures. Building on SEISMIC, we revisit both levels of its design: the inverted index used to select candidates and the forward index used to score them. For the inverted index, we replace costly per-block summaries with medoids, namely existing documents elected as block representatives, collapsing the per-block metadata from a sparse vector to a single document identifier. For the forward index, we compress both components and values. We reorder the vocabulary to place co-occurring components closer together and encode the resulting $\Delta$-gaps with DOTPACKING8, a SIMD-friendly bit-packing scheme that fuses decompression with dot-product evaluation; values are quantized with compact per-component 4-bit codebooks fitted to each component's distribution. We further introduce JUMPDOT, a blocked dot-product kernel tailored for queries that contain only a few non-zero entries. Our forward-index compression is independent of SEISMIC and can be plugged into any system relying on forward-index-based scoring, as we demonstrate by integrating it into KANNOLO. A comprehensive evaluation on MS MARCO with three state-of-the-art learned sparse encoders shows that our solutions markedly improve the speed-space trade-off of learned sparse retrieval: at equal accuracy, our indexes answer queries up to 5.3x faster than the best competitor while using about 3x less memory, and in the most memory-constrained regime, they remain up to 1.9x faster while using up to 3.9x less memory.

Egocentric world models predict first-person observations conditioned on an agent's actions, but most focus on a single agent. Real embodied settings often involve multiple agents that act and interact within a shared environment. Existing multi-agent world models rely on coarse actions like locomotion, camera control, or discrete commands, leaving fine-grained embodied interactions underexplored. We formulate multi-agent egocentric world modeling as synchronized ego-stream generation for multiple agents interacting through fine-grained actions in a shared world. This requires cross-view action consistency, shared-environment consistency, and consistent propagation of interaction-induced state updates. We propose Multi-agent Egocentric World Model (ME-World), which jointly denoises multiple ego streams in a shared token sequence, conditions each stream on all agents' target-view poses, and grounds generation with shared environment memory. We train and evaluate on real and synthetic multi-agent data and introduce shared-world consistency metrics for environment, update, and identity consistency. Experiments show ME-World improves shared-world consistency, action control, identity preservation, and video quality over existing methods.

The Princeton Axion Search (PXS) targets the mass window $0.8\text{--}2.1~\mu\text{eV}$ (corresponding to frequencies $200\text{--}500~\text{MHz}$) at DFSZ sensitivity. The experiment, a haloscope, will use a cylindrical copper-plated aluminum cavity of $700~\text{mm}$ diameter and $1022~\text{mm}$ height, immersed in a $5~\text{T}$ solenoidal magnetic field. A $152~\text{mm}$ diameter tuning rod spanning the height of the cavity rotates to tune the primary mode resonance from $390\text{--}480~\text{MHz}$, the frequency range for initial operations. We deduce the electric and magnetic field mode patterns using a combination of dielectric and metallic bead perturbations on the empty cavity. The measured mode frequencies and the $\text{TM}_{010}$ field profile, as a function of tuning rod position, are in excellent agreement with simulations. We describe the effect of fabrication and assembly imperfections, including the bowing of end plates and tilt of the tuning rod. The welded seams and end-cap joints are demonstrated to not significantly degrade $Q$. We combine measurement and simulation to assess an uncertainty on form factor across the full tuning range. Our results validate PXS's cavity architecture and inform future searches for sub-$\mu\text{eV}$ axions, in which large-volume high-$Q$ structures are required to reach QCD sensitivity.

Polymer electrolyte water electrolysis is considered as a pivotal technology for green hydrogen production. Iridium dioxide (IrO2) serves as the benchmark electrocatalyst for the anodic oxygen evolution reaction (OER) in these cells. However, the scarcity and cost of iridium drives efforts to find durable and cost-effective replacements or drastically reduce the iridium loading. While ruthenium dioxide (RuO2) offers comparable activity, its practical utility is impacted by its stability being inferior to IrO2. The presented computational study analyzes the metal-oxygen bond strengths in bulk IrO2 and RuO2 to provide insights into the electronic origins of their differing stabilities. Through a comparative analysis of the electronic structure of bulk rutile IrO2, RuO2, and selected MO2 systems, it is able to discriminate the covalent and ionic contributions to the metal-oxygen bond using crystal-orbital-derived electronic descriptors.

We study strict inverse systems of locally convex Lie groupoids and Lie algebroids. We show that strict inverse limits of Lie algebroids and Lie groupoids inherit natural Lie structures and establish a natural isomorphism of functors $\varprojlim\circ\operatorname{Lie}\cong\operatorname{Lie}\circ\varprojlim$. We then consider inverse systems of integrable Banach-Lie algebroids and their source-simply connected levelwise integrations. We give conditions under which these integrations form a strict inverse system of Lie groupoids and hence their inverse limit integrates the inverse-limit algebroid. Under additional hypotheses on the source-fiber inverse sequence, we describe the obstruction to source-simply connectedness of the resulting integration in terms of the derived inverse limit $\varprojlim^{1}\pi_2$ of the second homotopy groups of the source fibers. We illustrate the theory with several examples: inverse limits of jet groupoids, current groupoids, and gauge groupoids, including the corresponding inverse-limit Atiyah algebroids and a source-simply connected inverse-limit integration arising from the quaternionic Hopf bundle.

A subgroup $A$ of a finite group $G$ is \emph{hereditarily $G$-permutable} if, for every subgroup $E$ with $A\leq E\leq G$ and every subgroup $B$ of $E$, some $G$-conjugate of $B$ permutes with $A$ in $E$. We give a new criterion for a finite group to be simple. A nontrivial finite group $G$ is simple if and only if it has no proper nontrivial hereditarily $G$-permutable subgroup. This proves the conjecture of Galt and Tyutyanov and answers Skiba's question in part (b) of Problem 17.112 in the Kourovka Notebook. Earlier work settled the conjecture for alternating groups, sporadic groups, exceptional groups of Lie type, and the groups ${\rm PSL}_2(q)$ and ${\rm PSU}_3(q)$. We prove the conjecture for all classical groups. The proof uses descent through parabolic subgroups and the classification of factorizations of finite simple groups.

Quantum spin ice hosts collective excitations and quantum fluctuations that are largely electrically silent because the materials supporting them are insulating. Coupling this magnetic environment to surface-localized Weyl states offers a route to encode its correlations directly into Fermi-arc transport. Experimental access to this regime, however, has remained largely unexplored. Here, we realize a synthetic Kondo lattice interface between the Weyl semimetal $\mathrm{Eu_2Ir_2O_7}$ and the quantum-spin-ice candidate $\mathrm{Tb_2Ti_2O_7}$, and demonstrate that quantum-spin-ice correlations are imprinted on Weyl Fermi-arc transport. At ultra-low temperature, electronic transport evolves from a sixfold anisotropic response at low field into a twelvefold response over an intermediate field window, before entering a reentrant sixfold anisotropy at high field. No analogous twelvefold response occurs at the classical-spin-ice interface. The quantum–classical contrast shows that the same itinerant electronic channel acquires qualitatively different symmetry information when interacting with the quantum-fluctuating Tb moments, consistent with an interfacial coupling between the Weyl surface states and the transverse, multipolar degrees of freedom, in addition to the longitudinal, dipolar contribution. Our work establishes synthetic Kondo lattice interfaces as a route for transducing frustrated quantum magnetism with multipole correlations into distinct Weyl Fermi-arc transport responses.

Machine learning (ML) in high-energy nuclear physics (HENP) is entering a new stage in which physical knowledge is incorporated more directly into data analysis, simulation, and physics inference. This mini-review focuses on developments that have matured in the past several years. Whereas earlier applications emphasized event classification, pattern recognition, and surrogate models for selected observables, recent work has moved toward physics-integrated workflows: calibrated Bayesian extraction of QCD matter properties, dense-matter equation-of-state inference from heavy-ion and neutron-star data, generative event modeling, neural unfolding of weak physical signals, differentiable inverse solvers, gauge-equivariant and diffusion-based lattice-field samplers, and neural reconstruction of model functions in holographic QCD. We survey recent applications of ML in heavy-ion collisions, neutron-star physics, lattice QFT, and holographic or continuum QCD. The emphasis is not on ML architectures alone, but on how they enter concrete physics workflows, how physical constraints such as symmetries, conservation laws, causality, thermodynamic stability, and topology are imposed, and how uncertainty quantification and validation determine whether an AI-assisted result can support a reliable physics conclusion.

A typed decision model reads a piece of text and returns a probability over caller-defined options, each with a short written definition, generating no text. Recent work places these models in agent systems as guardrails: the component that reads a proposed tool call or incoming message and decides whether to allow it. We evaluate seven open-weight models in that role and report the two error directions separately: a fail-open error allows a prohibited action and is a vulnerability; a fail-closed error blocks a permitted one and is only a cost. On prompt-injection, jailbreak and toxic-content screening, accuracy at the allow-or-block decision ranges from 36% to 72% against a chance level of 50%. A low error rate in one direction only reflects which answer a model defaults to: one allows nearly everything, another blocks nearly everything. On a synthetic suite of agent tool calls, six lines of server log text that say nothing about the policy raise a gate's fail-open rate from 0% to 63% on a policy it otherwise decides correctly. Giving the permissive option a misleading name, with its definition and the judged text untouched, raises that rate to between 93% and 100% on the four models that place the label in their input. Every defense we tested is defeated, either by an attacker who targets its mechanism or by attacker-controlled text. Escalating the least confident decisions does not help either: a decision an attack has reversed is no less confident than the one it replaced. Parsing each policy field into a typed value does eliminate one attack, but it also makes the model unnecessary: a deterministic rule over those values reaches 100% accuracy on all six policies. These models can reduce how many cases reach a reviewer, but on this evidence they should not be the component that decides. Code is available at https://github.com/ArminAzizi98/option-channel-attack.

Using the circle method, we prove that every sufficiently large positive integer is a sum of two primes, $u$ Fibonacci numbers and $5-u$ Lucas numbers for each $u\in\{1,2,3,4\}$. All recurrence indices are positive, and terms may be repeated.

This paper proposes a tri-hybrid precoder design, cascading digital, analog, and electromagnetic processing layers, for cell-free massive multiple-input multiple-output (CFmMIMO) systems. We jointly optimize the three-layer precoders and access point (AP) transmit power to maximize global energy efficiency (GEE) under per-AP power and fronthaul constraints. To solve this, we develop an alternating optimization algorithm. The first sub-routine maximizes sum spectral efficiency (SE) for precoder design using weighted minimum mean square error, Riemannian manifold optimization, and gradient ascent over Lorentzian phases. The second optimizes power allocation via Dinkelbach's fractional programming and successive convex approximation. Convergence and computational complexity are also analyzed. Simulation results show the proposed design improves GEE by 87% and 11% over fully digital and classical hybrid precoders, respectively, at 20dBm transmit power. Moreover, joint power optimization yields 22% SE and 16% GEE gains over equal-power baselines, while outperforming colocated architectures in SE. Finally, we identify GEE-optimal regimes for AP and RF chain counts, and demonstrate that increasing dynamic metasurface antenna sizes enhances GEE in low-power regimes with negligible active power overhead.

Large language model (LLM) coding agents have advanced test generation across diverse programming tasks. However, the common practice of evaluating tests against a single reference solution overlooks alternative valid implementations and can overstate test quality. We introduce TestPrism, comprising 300 test tasks from 17 sources and 3000 candidate implementations, evenly split between valid and invalid solutions. Its primary metric, Joint Success Function, requires the generated tests to fail on the initial program state, accept every valid candidate, and reject every invalid candidate. Across fourteen baseline coding agent configurations, Joint Success Function reaches only 28.00%, whereas single reference success reaches 59.67%. Our analysis reveals missed behaviors, unsupported assertions, and faulty test construction. To address these weaknesses, we introduce TestHelix, which combines heterogeneous synthesis of test and repair pairs with peer cross validation and recursive self improvement (RSI). Across two models, TestHelix improves Joint Success Function by 8.67 to 9.00 percentage points over the native harness comparators in the TestHelix evaluation

Given independent and identically distributed samples samples from a probability distribution in a potentially high-dimensional real space, we study the problem of testing whether the distribution is concentrated near a real algebraic complete intersection of prescribed dimension, bounded degree, and bounded condition number. We design an explicit and effective learning procedure which either certifies the nonexistence of such a manifold, up to a controlled relaxation of the approximation threshold, or returns a candidate regression manifold with controlled geometric complexity. Equivalently, the procedure tests the manifold hypothesis within this hypothesis class. The proposed procedure relies on quantitative geometric estimates for regular polynomial systems, which lead to a tractable auxiliary optimization problem. We then develop a data-driven algorithm to solve this auxiliary optimization problem, establishing explicit bounds on its sample and arithmetic complexity.

We calculate the dominant bosonic two-loop virtual electroweak corrections to parity-violating Møller scattering at low energies. The electron effective weak charge is extracted from the polarization asymmetry, retaining all contributions that are enhanced by $(1-4\sin^2\theta_W)^{-1}$ or $\ln^2(M_{W,Z}^2/Q^2)$ relative to the tree-level contribution. Analytical results are obtained using the expansion by regions method in the low-energy limit $Q^2\ll M_{W,Z}^2$. Within this approximation, the dominant two-loop bosonic corrections shift the electron effective weak charge (or equivalently the polarization asymmetry) by $0.3\%$. We examine the origin of the leading contributions to this result and assess the remaining theoretical uncertainty from purely bosonic contributions for the MOLLER experiment to about 0.1%.

Witnessing entanglement between electrons propagating in quantum circuits requires accessing their two-electron coherences, which encode the two-particle quantum correlations generated by Coulomb interactions. Yet, experimental reconstruction of two-electron coherence remains a major challenge. We introduce photo-assisted two-electron tomography, a quantum coherence reconstruction protocol from dc-currents and time-averaged current correlations, routinely measured in electron quantum optics experiments. Driving an energy filter with a small rf tone encodes off-diagonal coherences in the frequency domain into the dc-current response, enabling single-electron tomography without resorting to current-noise measurements. Extending it to two channels, current correlations after two photo-assisted filters reconstruct the two-electron Wigner distribution and isolate its irreducible two-body part. When applied to Coulomb-coupled quantum Hall edge channels, the protocol reveals interaction-induced energy entanglement. Signatures of this entanglement are visible through the violation of an entanglement witness based on Cauchy-Schwarz inequalities, as well as Wigner function negativities, which remain resolved above the thermal background for realistic device parameters. A generalized Franson geometry further extends the approach to intra-channel two-electron coherences. This opens a direct pathway to detect and characterize electronic entanglement in ballistic quantum circuits.

Learning to predict how the world evolves can provide vision-language-action (VLA) policies with predictive context for long-horizon control, but its effectiveness depends on what future representation is modeled and how it conditions action generation. We introduce PLaW-VLA, which models task-relevant future states in a pretrained prediction-oriented representation space, reducing the need to predict control-irrelevant visual details. Built on a Mixture-of-Transformers architecture, PLaW-VLA conditions action generation on observation history, current task semantics, and predicted future states through structured causal attention. Experiments show a +11.8 percentage-point (pp) gain over reactive policies on RoboTwin Hard Horizon III and a +1.77 pp gain over reconstruction-oriented latent prediction on zero-shot LIBERO-Plus, supporting improved long-horizon control and generalization under distribution shift, respectively. By avoiding low-level visual reconstruction, PLaW-VLA lowers the burden of future prediction, enabling a lightweight latent world model with parallel future prediction and about 1/19 the inference latency of generative world-action modeling at comparable policy performance.

We quantify the impact of higher-dimensional operators in the effective theory for bubble nucleation, focusing on supercooled phase transitions in the classically conformal Abelian-Higgs model. While high-temperature dimensional reduction organizes hard thermal corrections into a tower of operators in a three-dimensional effective field theory, recent results show that dimension-six terms can dominate over higher-loop corrections to the equilibrium thermodynamics of the strongest transitions. To assess their effect on the nucleation rate and the derived near-equilibrium phase-transition observables, we develop a perturbative framework that includes them in the full one-loop nucleation rate. Including higher-dimensional operators both in the bounce action and in the fluctuation determinants, we solve the resulting Sturm-Liouville problem without a derivative expansion, using a modified Gel'fand-Yaglom method. For strongly supercooled transitions, we find that higher-dimensional operators only marginally affect the nucleation rate and the resulting observables. As a byproduct, we delineate the regime of validity of the high-temperature nucleation effective theory in supercooled phase transitions.

Establishing the microscopic origin of localized emission in two-dimensional materials through consistent agreement between experiment and theory remains challenging. Recent STM/STS-STML measurements assigned an emission near 1.8 eV in monolayer MoS$_2$/hBN(2L)/graphene to the negatively charged CH$_\mathrm{S}^{-}$ defect. However, a comprehensive theoretical description of this emitter is still lacking. Here, we develop such a description and systematically investigate the photophysical properties of CH$_\mathrm{S}^{-}$ in monolayer MoS$_2$, two bilayer configurations, and a MoS$_2$/hBN heterostructure. The defect retains a similar local geometry and favors a singlet ground state in all four environments, whereas its electronic transition, zero-phonon line, electron-phonon coupling, radiative lifetime, and transition-dipole orientation depend strongly on the surrounding layers. The isolated-monolayer model exhibits substantial structural reorganization and produces a broad, dominant phonon sideband that is inconsistent with experiment. Adding an adjacent layer, either MoS$_2$ or hBN, substantially suppresses the phonon sideband, with only a minor dependence on the defect position in bilayer MoS$_2$. In particular, the MoS$_2$/hBN model yields a weak phonon sideband and closely reproduces the experimental photoluminescence lineshape. Our results thus provide the first theoretical agreement of CH$_\mathrm{S}^{-}$ emission and further reveal the role of adjacent layers in determining the electronic, vibronic, and optical properties of the quantum emitters in two-dimensional materials.

Streaming 3D reconstruction must preserve evidence from each frame while processing an expanding scene online. Spatial memory is a natural fit because it organizes history by reconstructed 3D location. Yet Point3R uses spatial proximity both to associate a new observation with an existing memory entry and to decide whether to fuse it, conflating co-location with state identity. Because pointers summarize image patches, nearby pointers may encode distinct surfaces, viewpoints, or visibility conditions; averaging them can destroy complementary evidence before later frames disambiguate it. We argue that location should determine address, not whether observations must merge. Slot3R realizes this principle as a training-free, set-associative retrofit that lets multiple states coexist at a shared address while keeping the pretrained Point3R backbone frozen. A bounded sparse readout further decouples persistent storage from per-frame decoder access. At 300-500 sampled frames, Slot3R reduces Point3R's point-cloud accuracy error (Acc) by 57.1%-63.1% on 7Scenes and 64.0%-72.0% on NeuralRGBD, lowers Sim(3)-aligned absolute trajectory error (ATE) on all three pose benchmarks, and remains competitive on video-depth estimation. It completes all evaluated settings from 600 to 1000 sampled frames at about 19 FPS under the same protocol, whereas Point3R and InfiniteVGGT run out of memory at 800 frames and beyond.

Over 90% of disease-associated variants from genome-wide association studies fall in noncoding regulatory regions, yet their functional interpretation remains a central open problem in genomic medicine. Large language models prompted to interpret such variants routinely hallucinate transcription factor (TF) binding changes, fabricate experimental support, and assign biological significance to statistically negligible signals. We present ARGUS (Agentic Regulatory Genomics for an Uncertainty-aware Scientist), which strictly separates deterministic biological computation from LLM-mediated reasoning. ARGUS wraps 458 DNABERT-based TF binding models in a hypothesis-directed investigation loop where a planner selects evidence sources based on current uncertainty, a verifier deterministically interprets each observation, and intermediate results change the investigation path. On variant rs6983267 at the 8q24 cancer risk locus, the same planner produces four divergent trajectories for four TFs. FOXA1 is rescued in 3 steps when real ADASTRA allele-specific binding data (15 experiments, FDR = 0.030) reveals a model false negative masked by saturation. KLF6 traverses 8 steps across ADASTRA, JASPAR motif analysis, and ENCODE cCRE regulatory annotation before abstaining due to mixed indirect evidence. RAD21 abstains in 8 steps after ADASTRA returns a coverage-qualified but nonsignificant allelic test (5 experiments, FDR = 0.65), and SP1, which shares FOXA1's saturated retained prediction, abstains because no direct experimental evidence exists at this locus. All observations come from real ADASTRA, JASPAR, and ENCODE cCRE queries; none are simulated. A comparison of fixed-priority and LLM-mediated planning shows that the LLM planner reaches identical verdicts with fewer tool calls by declining evidence that cannot resolve the claim under test.

In the first part of this series the $\sigma$-ring spanned by the periodic solutions of a generalized linear cellular automaton in a discrete group was shown to be Hopf–Galois, with pro-algebraic Galois group, while a Galois theory for the $\sigma$-ring spanned by the finite support solutions was left open, with parameterized difference Galois theory suggested as the tool. We apply that tool to automata over $\mathbb Z$. The Fourier transform turns the automaton into a rank one equation $\sigma(\hat x)=\hat\alpha\hat x$ over a field on which $\delta=z\,d/dz$ acts, and we compute, and algorithmically decide, its parameterized Galois group: for genuine automata with symbols rational in the time variable it is either $\mathbb{G}_m(\mathbb C)$ or $\mathbb{G}_m$, the dividing line being separability of the symbol, $\hat\alpha(z,t)=\gamma(z)\psi(t)$. Finally, the parameterized group in the time direction decides holonomy in the space direction; as a corollary, the Stirling numbers of the first kind are not spatially holonomic.

We solve a well-known question of Polterovich from 2002 regarding the rigidity of Hamiltonian diffeomorphisms in Hofer's metric in dimension two: every non-trivial Hamiltonian diffeomorphism of a surface of genus at least one has all positive iterations separated from the identity in Hofer's metric. In higher dimensions, we make progress on the case of autonomous Hamiltonian flows: we prove Hofer non-recurrence for symplectically hyperbolic manifolds, and completely characterize Hofer recurrence for functions of the moment polytope on monotone toric manifolds. These results apply equally well to Viterbo's spectral metric, settling cases of the $\gamma$-rigidity conjecture, and therefore in many cases also to the $C^0$-metric. Our approach relies on the philosophy that symplectically visible invariant sets govern symplectic non-recurrence phenomena. In dimension two, we use invariant annuli provided by low-dimensional dynamics, and apply methods of $C^0$ symplectic topology to approximately invariant Lagrangian submanifolds. For symplectically hyperbolic manifolds, the invariant sets are provided by sublevel and superlevel sets of autonomous Hamiltonians, while in the toric case, they comprise Lagrangian torus fibers. Across the arguments, we use quantitative Lagrangian Floer theory and its relation to notions of classical dynamics.

Halide perovskite systems require specific metal oxidation states (M2+ or M+/M3+ pairs), limiting processing flexibility during traditional synthesis and posing stability challenges for multivalent metals like Sn, Cu, and Au. This work anchors a profound paradigm shift: a universal, single-step, organic-solvent free synthetic platform that directly converts stable elemental metal films into bromide perovskite and perovskite-related systems for a wide variety of (opto)electronic applications. The synthetic platform uses methylammonium polybromide melt (PBM) that reacts at room temperature with different elemental metals, including Pb, Sn, Au, and Cu, successfully transforming them into their respective Br-perovskite phases: MAPbBr3, MASnBr3, MA2Au2Br6, and MA2CuBr4. It is shown that the PBMs chemical activity can be tuned, and in situ X-ray diffraction captures in two cases transient intermediate phases during phase evolution. For Sn, which tends towards overoxidation to Sn4+ phase, changes in the PBMs composition coupled with a metallic Sn mediated comproportionation reaction allowed suppressing overoxidation, and formation of high quality MASnBr3 films under ambient conditions. Overall, oxidation and disproportionation potentials are found to be useful metrics for predicting M:PBM reaction outcomes. Industrially, this approach should be fully compatible with roll-to-roll infrastructure, providing a low-barrier pathway to scale next-generation optoelectronic technologies.