Papers

Distributed quantum processors could scale variational algorithms beyond single devices, but circuit depth, communication overhead, and noise limit their performance. We compare ladder, mixed-canonical, and brick-wall realizations of matrix-product-state (MPS) pretraining with matched per-layer two-qubit-block resources. Despite comparable ideal variational quantum eigensolver performance and gradient scales, the shallower brick-wall architecture reduces circuit duration, idle-time decoherence, and zero-noise-extrapolation (ZNE) overhead, yielding superior noisy and ZNE-assisted performance. We then extend MPS-pretrained circuits to modular processors with one communication qubit per quantum processing unit (QPU); a nearest-neighbor QPU-path schedule keeps the per-layer depth constant as QPUs are added. Distributed circuits whose inter-QPU links realize long-range interactions of the target Hamiltonian match or outperform the single-processor brick-wall under noise when communication idle time is short compared with the coherence time. These results establish hardware-aware co-design of tensor-network pretraining, circuit scheduling, and communication topology as a principle for variational quantum computation on noisy modular hardware.

Illusory matches between distinct yet visually similar 3D surfaces–doppelgangers–remain a fundamental obstacle for large-scale, in-the-wild 3D reconstruction and visual localization. Prior work mitigates this issue with pairwise classifiers, but this design limits multi-view contextual reasoning and incurs O(n^2) inference complexity for downstream structure-from-motion (SfM). We present MVDG, a scalable multi-view disambiguation framework built on the 3D foundation model VGGT, which jointly reasons over an arbitrary number of multiview images. By incorporating 3D-aware multi-view features, our method reduces dependence on pairwise comparisons by encoding and decoding views in a single pass. We further observe that direct multi-view fine-tuning of VGGT can be unstable under noisy supervision; motivated by label ambiguity in Doppelgangers, we construct a pseudo-pairwise training set from AerialMegaDepth and show that fine-tuning on sampled subsets yields stable optimization and strong generalization to held-out scenes. Finally, because full SfM evaluation (even with faster pipelines such as GLOMAP) remains expensive, we process a pseudo-pairwise dataset for efficient validation; we derive a predictive relationship between regular SfM metrics and the classification accuracy on this pseudo-pairwise test. Experiments show that our method achieves comparable pairwise accuracy while improving both SfM accuracy and inference speed over baselines.

End-to-end research agents can now produce complete scientific papers, yet manuscript claims often diverge from executed experiments. This gap is structural: research state, failure histories, and claim-evidence alignment are not maintained as persistent, verifiable state across long-horizon pipelines. We present YouRA (Your Research Agent), an architecture for stateful, evidence-traceable autonomous research. YouRA preserves research state, execution evidence, and failure history across the research trajectory by integrating three components: a Verification State Architecture (VSA) that tracks hypotheses, gates, and evidence pointers; an Independent Controller that turns state and reflection records into lifecycle, recovery, and debate/review control while separating control from execution; and Stateful Reflection that logs failures as structured lessons and routes recovery through bounded repair, redesign, or reset. On MLR-Bench's predefined ten-task end-to-end subset, YouRA improves over both MLR-Agent and AI Scientist V2 on scalar Overall across all three matched backbones. An automated diagnostic using MLR-Bench's hallucination taxonomy reports intersection/union counts for four fact-based failure types, and data-provenance diagnostic shows more real-data-based outputs. Ablating each of the four components (the VSA, the Independent Controller, MCP tool access, and reflection-guided recovery) supports their separable contributions. Removing either core-state component drops YouRA below the full system. Code: https://github.com/PrayPrey/Your-Research-Agent.

A post-hoc out-of-distribution (OOD) detector reads the activations of a trained classifier and returns a score. It fits that score on in-distribution data, and the benchmarks that evaluate it supply a second piece of OOD data for the fitting itself. Some detectors tune a constant on it. Others fit a direction in feature space or train a flexible combiner and report the number that it reaches as the gain that is still available. Every such fit is validated on held-out samples of the same OOD dataset. That check rules out memorizing individual images. It says nothing about a fit that has instead learned which dataset it is looking at, and a direction that recognizes one OOD dataset rather than novelty passes it perfectly. The detector that a practitioner installs meets OOD data from a source that nobody fitted it on, so the difference decides what the reported number is worth. We measure it by holding out the whole OOD dataset rather than a sample of it, and we call that gap the inflation. We read it across a range of combiners on ImageNet and CIFAR-100 backbones. Most of the gain that the usual protocol reports turns out to be dataset identity rather than novelty. The size of the fit does not move what survives, so the effect is not ordinary overfitting. The share depends instead on whether the input exposes class identity, and two controls that vary that property alone separate the inflation on every backbone of both benchmarks. A closed form accounts for the effect and computes it from the fitting rows, so a practitioner can tell which fits will inflate without running the hold-out protocol. One of these fits survives, namely the single constant that the field already picks on a designated validation dataset. Anything above it reports a gain that the hold-out protocol does not return, and on one benchmark what survives falls while what is reported climbs.

An important and unresolved problem in the physical sciences is explaining the predictions made by neural networks. Several explainable artificial intelligence (XAI) methods have been proposed to address this problem, including gradient XAI, Integrated Gradients, and GradientSHAP. We evaluate the baseline XAI methods according to four scores: sensitivity (XAI patterns strongly affect predictions), attribution (XAI patterns reproduce the change in prediction relative to a baseline), robustness (XAI patterns remain stable for nearby inputs), and coherence (XAI patterns are spatially smooth). We also introduce a new method, average gradient outer product (AGOP) XAI, that uses global gradient information to identify an important direction for a specific input. We apply XAI to neural network predictions of the El Niño-Southern Oscillation (ENSO) based on data from the Zebiak-Cane model. AGOP XAI achieves the highest attribution, robustness, and coherence scores in the architecture and lead-time comparisons reported here. Its sensitivity is surpassed by gradient XAI, which is maximally sensitive by definition. Beyond diagnosing neural-network behavior, AGOP XAI can generate candidate hypotheses about physical mechanisms. The method highlights an equatorial thermocline-depth signal consistent with recharge oscillator physics, together with a southeastern-Pacific lobe that may be specific to the Zebiak-Cane model. Finally, we test the physical relevance of AGOP using optimized perturbations that move the Zebiak-Cane model along AGOP explanation coordinates. Such perturbations can suppress the selected extreme events or, from a near-neutral ensemble, generate strong El Niño or La Niña events 10 months later.

We consider a cavity quantum electrodynamics (CQED) setup where an ensemble of spin-1 atoms driven by a classical field interacts with two driven cavity field modes. We show that the two sub-systems - the atoms and the two-mode cavity field, exhibit limit-cycle or quantum synchronization depending on the cavity drive strengths and other system parameters. In order to visualize the limit cycle and synchronization in the field, we introduce generalized two-mode field Husimi-Q function using SU(2) coherent states. For atomic spin states, we make use of spin-1 Husimi-Q function to visualize the same. We further corroborate the occurrence of field synchronization and limit cycle by analyzing $U(1)$ symmetry breaking, Wigner quasi-probability distribution, coherence properties of reduced field density matrix. Our results reveal intriguing interplay between the limit-cycle and quantum synchronization behavior, highlighting emergent quantum phenomena in driven dissipative interacting quantum systems. Additionally, we calculate Wehrl mutual information between the two modes and find that the field synchronization and Wehrl mutual information are mutually exclusive. Our study would be important to extract quantum advantages in quantum metrology using coupled atom-cavity systems.

Spacecraft rendezvous and proximity operations (RPO) are currently planned through an expertise-intensive process in which engineers translate high-level operational intent into safe, dynamically feasible trajectories, creating a bottleneck to scalable operations. Large language model (LLM)-based agents could offer an intuitive interface for this process, although their outputs are not inherently grounded in orbital dynamics, operational constraints, or the structure of admissible spacecraft maneuvers. To exploit their semantic reasoning while ensuring the generated plan's physical validity, this paper presents a hierarchical framework for spacecraft task-and-motion planning (TAMP) that grounds LLM reasoning in a graph of reusable behaviors and domain-specific planning modules. Within this framework, a pretrained LLM maps a natural-language command to a partial mission specification. The associated planners then resolve unspecified decisions within the admissible operational space. Finally, trajectory optimization converts the completed mission specification into a dynamically feasible trajectory. Numerical experiments demonstrate that this architecture substantially improves intent recovery over direct LLM generation, achieving 98% exact recovery of partial mission specifications across all evaluated splits when backed by frontier LLMs. Additional test-time-compute experiments show that, for a compact 9B model, verifier-guided revision increases exact recovery from 75% to 88%, while broader behavior-plan search independently improves selection among admissible trajectory realizations. Overall, these results establish a scalable and auditable foundation for language-driven agentic planning of spacecraft RPO.

Video generation models are increasingly being explored as world simulators for embodied planning and learning. To do so effectively, these models must not only generate visually appealing frames, but also predict how environments dynamically evolve when executing goal-directed actions. While evaluating these capabilities is crucial, existing benchmarks focus mainly on single short actions or step-by-step instructions. This leaves multi-step physical reasoning underexplored, especially in egocentric video generation that requires planning to simulate proper execution to accomplish high-level goals by carrying out multiple real-world manipulations. We introduce Ego2Act, a goal-directed benchmark featuring 2,640 videos from 110 real-world tasks across day-to-day settings, varying object clutter and multi-step complexity. Given an initial scene image and a high-level goal, Ego2Act evaluates whether video generation models can produce realistic egocentric videos of a hand manipulating objects to carry out the task. To support scalable evaluation, we also introduce Ego2ActJudge, a reference-free evaluation pipeline that achieves better task completion and physics plausibility evaluation alignment with human consensus compared to relevant baselines. Our findings reveal that models' generated simulations often skip or partially execute steps, leaving later steps missing dependent states, which leads to unfulfilled goal. Furthermore, models consistently fail at fine-grained physical dynamics, particularly during complex object manipulation and persistent world modeling. We hope Ego2Act provides a rigorous testbed for advancing video models toward physically plausible, goal-directed simulation.

Let $Q$ be a translation invariant indefinite quadratic form in $8$ variables. Let $\mathcal{P}$ be the set of all primes. Let $\mathcal{A}\subset\mathcal{P}\cap\{1,\dots,X\}$. By developing the recent work of Green, we prove that subject to a mild condition on the form $Q$ there exist pairwise distinct primes $p_{1},\dots,p_{8}\in \mathcal{A}$ satisfying $Q(p_{1},\dots,p_{8})=0$ provided that \[\frac{|\mathcal{A}|}{X/\log X}\gg_{Q}(\log\log X)^{-c}\] for some absolute constant $c>0$.

We conduct a numerical study of a generalization of the Blume-Capel model in which the crystal field $D_i$, which controls the local vacancy density, is site dependent rather than uniform. We employ Markov Chain Monte Carlo to compute the shifted phase transition line $T_c$ as a function of the width $\sigma$ of a gaussian distribution $P(D_i) \sim \exp( -(D_i - \bar{D})^2/2 \sigma^2)$ at fixed $\bar{D}$. We characterize how the presence of this on-site Gaussian disorder reduces $T_c$ across the second order transition line, and discuss how our results suggest that $T_c$ remains finite even at large values of $\sigma$. We also determine the effects of disorder on the tricritical point of the conventional, uniform, Blume-Capel model, finding that it significantly suppresses the first-order phase transition, eliminating it entirely at large values of $\sigma$.

Spintronic terahertz (THz) emitters based on ferromagnet/heavy-metal heterostructures provide efficient broadband sources of THz radiation, yet the microscopic relation between ultrafast spin transport and charge redistribution remains incompletely understood. Here, we employ time-dependent density functional theory to resolve the coupled charge, spin, and magnetization dynamics of Co/Pt and Co/W bilayers in real time and space. Despite qualitatively similar interlayer spin-current dynamics, the two heterostructures exhibit markedly different interlayer charge transfer: Co/Pt shows a relatively small and partially reversed transfer from Pt to Co, whereas Co/W exhibits a larger and persistent transfer from Co to W. We trace these differences to the material-dependent ground-state electronic structure and the spin- and orbital-resolved phase space accessible to photoexcited carriers. Spin-resolved dynamics further reveal coexisting spin-orbit-mediated redistribution and optically induced intersite spin transfer, including a delayed minority-spin transfer from the heavy metal to Co common to both systems. While net electronic spin angular momentum is transferred between the layers, we find no corresponding net transfer of electronic orbital angular momentum. In Co/W, the persistent redistribution of electronic density from interstitial to atom-centered states additionally provides strong evidence for light-induced electronic localization. These results demonstrate that ultrafast spin transport does not uniquely determine charge or angular-momentum redistribution in spintronic THz emitters, which instead depends critically on the material-specific electronic phase space.

The nonparametric maximum likelihood estimator (NPMLE) of a Gaussian location mixture maximizes the likelihood over the infinite-dimensional space of mixing distributions. The maximizing mixing distribution can be nonunique, and the classical bound on its number of atoms grows linearly with the sample size $n$. We show that a vanishingly small random perturbation of the likelihood yields exact polylogarithmic sparsity. The resulting randomly reweighted NPMLE maximizes a weighted likelihood whose independent weights, taken to be Gamma in our analysis, concentrate around one as $n$ grows. With high probability, it is unique, has $O\{(\log n/\log\log n)^d+\log n\}$ atoms in dimension $d$, nearly maximizes the ordinary likelihood, and estimates the mixture density at a Hellinger rate that is parametric up to logarithmic factors. This sparsity holds for the estimator itself, not for an approximation of it, and requires no support penalty. The proof rests on an effective-dimension principle for positive kernel mixtures: low-dimensional variation of the fitted values controls the support of every extreme point of the set of maximizers. Numerical illustrations verify that the reweighted NPMLE has Hellinger risk and support size comparable to those of the ordinary NPMLE.

We characterize admissible BLD remetrizations of branched self-covers of spheres by linear local contractibility of their canonical pullback length metrics. A relative homology obstruction involving the total degree of an inverse image component yields uniform porosity of branch values. Explicit degree-two cusp covers of $\mathbb S^n$, $n\ge3$, have uniformly porous branch values of Hausdorff dimension $n-2$ but admit no compatible Ahlfors $n$-regular, linearly locally contractible BLD source metric. Short homologically essential loops provide the obstruction, showing that porosity is necessary but insufficient for admissibility. We also prove quasisymmetric invariance and sharp degree dependence of porosity for sphere-to-sphere covers in dimension two.

Peptides occupy a particularly challenging regime of biomolecular dynamics. Short peptides lack a stable folded core and populate broad conformational ensembles, while cyclization adds ring closure, non-local residue coupling, and stereochemical diversity. Deep generative models have made remarkable progress in emulating molecular-dynamics trajectories directly, yet each is trained on windows cut at a fixed interval and therefore observes the process at a fixed temporal resolution. More fundamentally, none takes that interval as an input, so the physical time a window spans is never represented, leaving the sparse frames on which a peptide crosses between metastable states difficult to learn. Here, we introduce PepTIDE, a multi-scale temporal framework for peptide trajectory generation. The stride of each training window is drawn from a continuous range, so one model observes the same dynamics at many temporal resolutions, and an Adaptive Physical-Time Embedding encodes the relative interval of a window together with the absolute time of each frame, making the shared velocity field interval-aware. All frames are generated jointly through a stochastic-interpolant flow, and pair-aware invariant point attention captures the geometry and topology of both linear and cyclic peptides. On PepMD and a 50-system cyclic-peptide benchmark, PepTIDE reaches state-of-the-art distribution agreement and structural validity. Read in temporal order, its trajectories recover these sparse transition frames and reproduce inter-state fluxes more faithfully, confirming that modeling multiple temporal scales is what makes these rare events accessible.

Active metasurfaces are a promising platform for spatial light modulators (SLMs) in applications such as holography, beam shaping, and light detection and ranging (LiDAR), as they enable dynamic control over the amplitude and phase of light at subwavelength scales. Among these, transmissive metasurfaces offer a compact alternative to conventional SLMs, since they allow monolithic integration with chip-scale light sources. While independent amplitude and phase modulation have been previously demonstrated in active reflective metasurfaces, this important milestone has not been achieved in transmission due to the inherent challenges in designing active transmissive metasurfaces. Here, we theoretically demonstrate an active transmissive metasurface that enables independent amplitude and phase modulation in the mid-infrared. The proposed metasurface consists of high-Q cuboid germanium (Ge) Mie resonators integrated with graphene stripes. Utilizing the intraband and interband transitions of graphene, electrostatic gating enables modulation of the transmittance from near 0% to 5% at one spectral frequency and achieves 281{\deg} phase-only modulation at another frequency in the same device. To achieve both types of modulation at the same operating wavelength, we use the thermo-optic effect of Ge as a global tuning mechanism to spectrally align the resonant frequencies, enabling both transmittance and phase-only modulation at different base temperatures. The proposed dual-mechanism architecture achieves transmittance modulation efficiency of ~100% and 282{\deg} phase-only modulation. Finally, we demonstrate the efficacy of phase-only modulation by individually addressing each unit cell to realize a beam-steering device with relative diffraction efficiencies over 90%. Our individually addressable active metasurface opens a route toward compact, dynamically reconfigurable metaphotonic devices.

For a prime power $q\geq2$ and an integer $m\geq2$, let $PG(m,q)$ denote the $m-$dimensional projective hypergraph over the finite field $\mathbb{F}_q$. Employing the $\mathsf{L}^p-$method and using the incidence structure, we establish the Turán density of $PG(m,q)$ \begin{equation*} \pi(PG(m,q))\leq\begin{cases} \left(1-\frac{1}{q+1}\right)^{\frac{1}{q}} & \text{ if } m=2, \left(1-\frac{1}{(q+1)|E(PG(m-1,q))|}\right)^{\frac{1}{1+q^{m-1}}} & \text{ if } m\geq3. \end{cases} \end{equation*} The previously known upper bound on its Turán density was $1-\binom{q^m}{q}^{-1}$. As a consequence of our estimate, this upper bound is improved for each prime power $q\geq3$ and for each dimension index $m\geq2$. For a positive integer $t$, let $B_{t}[PG(2,q)]$ be the $(q+1)-$graph formed by taking $t$ copies of the $PG(2,q)$ that shares a common edge. Using the $\mathsf{L}^p-$method, we establish that the upper bound of the Turán density of $B_{t}[PG(2,q)]$ is $\left(1-\frac{1}{q+1}\right)^{\frac{1}{qt}}$.

Vision-language-action (VLA) policies have demonstrated impressive capabilities in generalizable robotic manipulation, but their deployment in the real world remains challenging due to potential collisions involving different parts of the robot, manipulated objects, and the surrounding environment. Existing inference-time VLA safety frameworks typically rely on simplified end-effector-centered representations that do not explicitly model the full articulated robot and attached-object geometry. In this paper, we present WBAG, a safety framework that models the robot's whole-body and grasp-dependent attached geometry. WBAG constructs a grasp-conditioned safe set that adapts the protected geometry as objects are grasped, then converts this evolving geometry into differentiable CBF constraints that minimally modify the VLA's six-dimensional operational-space action for collision avoidance across robot, scene, and attached geometry. On the SafeLIBERO benchmark, a variant of LIBERO augmented with obstacles for safety evaluation, WBAG achieves the best overall safety and safe task success among the evaluated methods under a scene-level safety evaluator that monitors all eligible non-task objects, reaching 97.38% aggregate Scene Safety and 59.38% Safe Success. Project page: https://samuelzhen.com/projects/wbag

Dialectal machine translation remains challenging due to limited data and strong linguistic variation not captured by standard benchmarks, which often assume standardized and well-edited text. We study Polish-Silesian MT using neural and rule-based systems, evaluating on SiLTT - a new Pol-Szl testset, alongside established BOUQuET and FLORES benchmarks. Results show our rule-based system is consistently strongest on SiLTT and BOUQuET datasets and that TranslateGemma fine-tuned on a curated dataset improves over strong neural baselines but does not surpass the rule-based system in dialectal settings. We release SiLTT and our best neural model to support further research.

Implicit full waveform inversion (IFWI) reparameterizes the velocity model with a neural network, but it suffers from spectral bias and requires many iterations to converge. Multi-resolution hash encoding uses a learnable feature grid to recover high wavenumber details at multiscales and provides strong local representations. However, activating all resolution levels from the start of the inversion introduces high wavenumber components, which can exacerbate cycle skipping. In this paper, we propose a coarse-to-fine IFWI (C2F-IFWI) that activates the multi-resolution hash levels progressively rather than all at once. Specifically, only a few coarse base levels are kept active at initialization, while the remaining levels are introduced progressively. A frozen hash level contributes no gradient until it is activated, so the coarse levels resolve the long-wavelength background before the finer levels are introduced regardless of the frequency range of the data. A continuous activation index increases with iterations and determines how many levels are active at any point in training. Each newly admitted level is then faded in gradually through a smooth weighting rather than switched on abruptly, which keeps the optimization stable during transition. This scheme allows model capacity to grow synchronously with wavenumber without adding any additional trainable parameters and with negligible computational overhead. Experiments on the synthetic Overthrust and BP 2004 models and on the Viking marine field dataset show that, compared with the all-resolution hash baseline, the coarse-to-fine scheme converges faster, attains higher accuracy, and is markedly more robust to the choice of initial model and to strong data noise.

Reinforcement learning with verifiable rewards (RLVR) has substantially improved the mathematical reasoning capabilities of large language models. Recent work introduces search into RLVR rollouts to increase trajectory diversity, but diversity alone does not ensure that the search-induced rollout policy improves upon the current policy. To address this gap, we propose APIVIS, a training-time framework that adapts finite-budget Gumbel search to chunk-level mathematical reasoning. APIVIS combines direct and searched responses within each rollout group, allowing improvements found by search to produce informative relative rewards. It further applies selective supervision to search-improved tokens, preserving a learning signal when uniform group rewards render GRPO ineffective. We show that exact value-guided selection improves the expected verifier reward at each searched state and that this guarantee extends to the complete rollout policy, with a corresponding approximate guarantee under bounded value-estimation error. Experiments on widely recognized mathematical reasoning benchmarks and different model scales demonstrate substantial improvements over competitive search-based methods, validating the effectiveness of APIVIS.

Machine-learning Network Intrusion Detection Systems (IDS) depend on substantial labeled datasets and task-specific training, whereas Large Language Models (LLMs) detection can analyze flow records directly but incurs higher inference cost and latency, with less constrained outputs. This paper presents JEV-IDS, an open experimental general NIDS based on the Jev System One Model (SOM) to detect zero day intrusions Under label scarcity. JEV-IDS serializes one flow per request and asks JEV two questions: a binary attack probability and a finite-choice traffic category. Our results show that, at k=1, JEV was 4.8 times faster and 3.8 times cheaper than GPT-5.6 Luna, with 1.5 times higher novel-attack recall; it also produced 15 times fewer false alarms than a low-data Random Forest. Across 5,400 decisions on a 300-flow NSL-KDD pilot split, JEV achieved F1-Score 0.859, precision 0.941, recall 0.790, and novel-attack recall 0.838. Increasing k to 2 reduced its F1-Score to 0.839.

Upon binding to transposable elements seeded DNA, initiator transcription factors are poised to activate the hybrid assembly pathways (HAP) of endogenous multiprotein complexes (EMC) by iteratively engaging protein-protein interaction (PPI) cascade and creating cell type-specific pools of protein dimers. Here, molecular features and inferred biological functions of PPI cascade constituents were elucidated within the context of cell type-specific intracellular protein monomer pools documented in the Human Protein Atlas (HPA) of 154 human cell types. The following key features of the molecular architecture and functional performance of the 4 families of PPI cascade constituents were documented within the HPA contexts of intracellular proteomes: a) the ubiquitous expression and balanced representation; c) the universal availability and engagements; d) constitutive {invariant) and cell type-specific assembly profiles of EMCs. The biological relevance of the PPI cascades is demonstrated by cell-type-resolved multiprotein complex-engagement analysis across the HPA of human body, which faithfully recovers without supervision the intrinsic lineage structures of EMCs and lineage-specific master-regulator multiprotein assemblies. PPI cascade constituents have the capacity to generate 51,830 protein dimers within the proteome availability contexts of 154 types of human cells. Present analyses revealed critical impacts of the persistence of proteinopathy proteins that may cause the damage to the PPI cascade performance by sequestering 44 synaptic proteins. The sequestration of synaptic proteins withdraws structural-functional components of synapses suggesting a mechanism contributing to the pathogenesis of neurodegeneration. Conversely, reconstitution of availability of defined synaptic structural proteins appears to restore stoichiometry and recovers the lost assembly of synaptic protein dimers.

We prove the 2143-3421 case of Burstein's conjecture on the distribution of descent-top sets by constructing an explicit bijection between the two avoidance classes. The bijection also preserves the pinnacle set and reverses the left-to-right order of the pinnacle values. We combine an involution on maximum Cartesian trees with exchanges of the final entries of maximal decreasing runs. On an intermediate avoidance class, we prove that the exchange procedures terminate and that the output in each direction is independent of the choices made. This gives an explicit inverse. Restricting the bijection to Dumont permutations of the first kind proves the conjecture of Burstein and Jones that 2143 and 3421 are Wilf-equivalent on this class

Structured electronic health records (EHRs) contain a patient's clinical trajectory as a sequence of clinical codes. Answering clinical questions from such records requires both the context of the whole trajectory and the specific events that support the answer. We introduce GLoC-EHR, a multimodal language model that reads a contextual encoding of the record through a fixed-size global memory of the trajectory and a local memory of selected events. The model learns to generate hospital-course summaries from the global memory and descriptions of masked concepts from the local memory, aligning both with clinical text. It is then trained to cite evidence before answering, through rationale fine-tuning followed by group relative policy optimization (GRPO) with rewards for correct answers and record-supported evidence. On three MIMIC-IV outcome tasks, GLoC-EHR attains the highest macro AUROC among the compared models when it answers directly, whereas zero-shot LLMs reading the serialized record fall far behind. With evidence-cited reasoning, it stays close to its direct multi-task counterpart in macro AUROC, and the evidence terms of the objective reduce unsupported evidence at a similar macro AUROC. The local memory adds distinct supported findings, particularly under strict matching, without a detectable change in macro AUROC. Without retraining, GLoC-EHR transfers to EHRSHOT on par with EHR-BERT and answers two unseen laboratory questions better than zero-shot prompting of its own backbone.

We study the $\rm{PGL}_2$ skein algebras of small surfaces, focusing on the closed torus and the once-punctured torus. We provide explicit finite presentations by generators and relations for the $\rm{PGL}_2$ skein algebra of the torus and once-punctured torus, analogous to those of Bullock and Przytycki for the Kauffman bracket skein algebras. We give explicit bases of the $\rm{PGL}_2$ skein algebras of the torus and once-punctured torus and describe the multiplicative structure of the basis for the torus, analogous to the product-to-sum formula of Frohman and Gelca. We twist the basis for the torus to obtain one with structure constants in $\mathbb{N}[q,q^{-1}].$ We compute the kernels of natural maps between the $\rm{PGL}_2$ and Kauffman bracket skein algebras associated to the once-punctured torus and closed torus. We compute the center of the $\rm{PGL}_2$ skein algebra of the torus, which depends on the specialization of the quantum parameter $q.$

The task of learning the Hamiltonian interactions governing a quantum system, given samples of its thermal (or 'Gibbs') states, is a foundational question at the intersection of quantum learning theory and many-body physics. In this paper, we draw connections to the quantum Gibbs sampling literature to introduce a natural learning algorithm we call the stationarity test: which simply "guesses" the Hamiltonian, and measures the rate-of-change of local observables, under the associated detailed-balanced quantum Markov chain [CKG23]. We leverage the stationarity test to address the following applications: 1. To give the first learning algorithm for the underlying interaction graph, i.e. structure learning, of lattice Hamiltonians at all temperatures, given copies of their Gibbs states. 2. To give the first learning algorithm for the coefficients of a lattice Hamiltonian, given only copies of its thermal metastable states, modeled as the "local minima" of the free energy. 3. In addition, we present a refinement to the recent area law for thermal metastable states [BCV25], which holds in the thermodynamic limit. Our learning algorithms are rigorous, time-efficient, and nearly sample-optimal in system size and accuracy. At a technical level, our arguments are based on new approximate locality and convexity properties for the quantum Fisher information of these Gibbs sampling algorithms.

Recursive self-improvement (RSI) allows agents to carry useful changes across generations. Maintaining safety across these generations involves both preventing unsafe behavior from persisting and enabling recovery when failures occur. We study these challenges through a controlled testbed of stateful authorization tasks, where fixed LLM editors optimize executable agent components and independent traces record their effects. Paired interventions separate which revisions pass validation, which program continues running, and which program the editor revises next. After a new authorization dependency invalidates previously tested optimizations, historical scores preserve the same unsafe programs in 22 of 48 framework histories despite a correct alternative in every affected archive. Refreshing scores restores correctness on the original suite, with residual failures on independently composed tests. Failures also persist under an unchanged contract when all proposals are rejected and the failed incumbent remains active. Starting from shared failures, editing the initial implementation instead of the failed one improves recovery, although the advantage varies across editors. Full validation and validated rollback end with fully correct programs in the core trajectory study while retaining over 43% deployment savings. Preserving agent safety requires checking what will run under current conditions and choosing which implementation to edit next.

Robotic manipulation of labware is difficult when transparent or reflective objects must be identified and localized. Coded planar fiducials are a practical retrofit: easy to print, they leave the marked face flat and graspable. Yet a single planar tag is least reliable in near-frontal views, where perspective cues fade. Non-planar geometries restore those cues but intrude on the flat face that a parallel-jaw gripper must contact. Our idea is to tilt multiple tags within one compact footprint, so that each tag is seen at a non-frontal angle even when the marker faces the camera. We propose the quARtet marker, a 3D-printable fiducial embodying this idea: all detected corners of its four tilted AprilTags enter one Perspective-n-Point solve, and a shared configuration defines the fabricated geometry and the detector model. Because tilting consumes flat area, its three layouts trade pose-estimation consistency against graspability. In robot-referenced, same-setup fixed-camera experiments, all three layouts reduced the mean frontal orientation error from 2.18 degree for a single planar tag to 0.24-0.47 degree and the root-mean-square position error from 1.50 to 0.17-0.20 mm. A robot-mounted-camera pose-hold test confirmed this separation under closed-loop visual feedback. In swing-down trials under identical conditions, the two layouts with flat contact strips retained the object, whereas the layout without flat strips slipped about a hundred times more than a single planar tag. For the tested conditions, the results support a rule: the layout without flat strips when pose-estimation consistency dominates, a layout with flat strips when the marked face must remain graspable.

We give a randomized polynomial-time algorithm that colors any promised $3$-colorable graph on $n$ vertices with $\smash{O(n^{4/23}) = O(n^{0.17391\ldots})}$ colors, improving on the recent bounds of $O(n^{0.19539})$ by Bansal, Huang, and Lee and Narang and Tang who obtained $O(n^{(13-\sqrt{97})/18+\epsilon})=O(n^{0.17506\dots + \epsilon})$ colors for every fixed $\smash{\epsilon>0}$. To prove our result, we start from a fixed-level semidefinite relaxation, where we use a finite-depth recursion on Gaussian covers. Fixing a root vertex, we group vertices by correlation with the root vector. Here, each step extends a cover of directions by one edge and transfers it to a successor group. Our key analytic ingredient is a variance bound for Gaussian maxima: for a maximum of $m\geq 2$ centered linear forms with coefficient norms at most $r$, mean $\mu$, and variance $v$, we prove $v\leq r^2-\mu^2/(2\log m)$ using Chen's Gaussian convexity theorem. Together with a variance-scale lower-tail estimate, this controls the threshold loss at each extension, which shows that root-conditioned vector colorings can either extract a large independent set from a group or bound its size, forcing a contradiction after constantly many steps. The resulting sparse-case guarantee combines with the dense progress bound of Kawarabayashi, Thorup, and Yoneda, and the recursion's numerical inequalities are verified via rational interval arithmetic.

Ion transport controls the macroscopic performance of solid electrolytes, battery electrodes, ion-selective membranes, electrolysis ceramics, mixed conductors, porous sorbents, and biological channels. In each case, ion transport is determined by structural characteristics, namely the available diffusion pathways and the specific bottleneck atoms that limit the ionic jumps. These are intrinsic properties of the crystalline framework, whereas temperature, carrier concentration, and correlated motion govern the transport rate. Ab initio molecular dynamics (AIMD) resolves the mechanism directly but is too costly for materials screening, and most surrogate models give only a single transport number. Here we present a calibration-free method for determining the mechanism, based on Topo-Spectral Percolation Descriptors (TSPD). TSPD obtains the transport mechanism from a single static structure in seconds. It constructs a periodic migration network whose edge barriers are computed from physics-based energetics. We then analyze the barrier-threshold topology of this network and the spectrum of its barrier-weighted graph Laplacian. To establish its validity for computational solid-state ionics, we test TSPD against AIMD ion densities and neutron diffraction data for eight materials, including cathodes and solid electrolytes, whose transport ranges from one- to three-dimensional. TSPD reproduces the established mechanism in every case and correctly identifies structures in which geometric openness does not imply viable ion percolation. The method is most informative for pathway-limited, direction-dependent transport, and it complements full dynamical simulations for strongly cooperative or nearly isotropic transport.