Papers

Generating and predicting spatiotemporal physical fields from scarce measurements is challenging, as observations are insufficient to characterize a distribution over complete fields. This limits conventional data-driven diffusion models that rely on full-field datasets. We introduce PhysDEM, a physics-defined diffusion framework that combines governing equations with spatially sparse observations to generate multiple plausible fields. First, we construct a Gibbs target by reweighting a measurement-conditioned Gaussian reference with PDE residual energy. Second, we derive an exact conditional-mean identity that reduces denoising to supervised learning of the standardized energy-induced mean correction. Third, a physics-displacement probability flow cancels Gaussian reference terms and enables amortized sampling with changing measurements through Gaussian conditioning, without retraining. Experiments on synthetic PDE systems and real-world-informed applications demonstrate that PhysDEM supports coherent field recovery and efficient sampling while maintaining stable diagnostics under tested noise levels, illustrating its practical value for field assessment. To our knowledge, PhysDEM is the first physics-defined diffusion model enabling amortized spatiotemporal field inference without preassembled full-field datasets.

Category-level object pose estimation (COPE), capable of generalizing to intra-class unknown objects, has become a core technique for robotic 3D scene understanding. However, existing COPE methods still require labor-intensive recollection of real-world training data for novel object categories, which limits their scalability in practical applications. This paper aims to achieve synthetic-to-real (Syn2Real) generalized COPE, where a model is trained solely on rendered synthetic data and directly generalized to real-world deployments. The central challenge lies in the significant domain gap between synthetic and real-world data, particularly in texture appearance. To address this, we aim to enhance domain generalization by learning domain-invariant representations that capture semantic commonalities among objects within the same category. We introduce 2D and 3D semantic consistency constraints to reduce the sensitivity of feature encoders to domain-specific features. In addition, we propose an end-to-end pose regression framework that performs 2D-3D cross consistency learning, leveraging dense cross-modality fusion to further refine pose estimation. Since simplicity and effectiveness are essential for real-world robotic deployment, our model operates exclusively on global features, yielding a highly lightweight and efficient architecture. Extensive experiments on the REAL275 and Wild6D benchmarks, as well as real-world robotic manipulation scenes, show superior Syn2Real generalization performance of our paradigm. Code and demos are released at https://paperreview99.github.io/GenCOPE/.

The discovery of spin-density-wave (SDW) order in bilayer nickelates has intensified interest in its interplay with superconductivity. Unlike cuprates, where doping rapidly suppresses the Néel temperature, the SDW transition temperature ($T_{\mathrm{SDW}}$) in bilayer nickelates is robust against oxygen annealing and even increases under pressure. Here, we combine oxygen annealing with isovalent rare-earth ($A$-site) substitution to effectively apply $c$-axis uniaxial pressure, realizing superconducting bilayer nickelate films with $T_{\mathrm{SDW}}$ suppressed from 150 K to 70 K. Notably, while SDW order is weakened but remains, a second charge-like anisotropy order is completely eliminated in the superconducting state. Polarization-resolved O $K$-edge X-ray absorption and electronic structure calculations show that strengthened interlayer coupling reconstructs the Fermi surface and weakens the SDW. These findings, consistent with a spin-spinless stripe ground state, provide new insight into the mechanism of density wave formation and their interplay with superconductivity.

Decentralized agent economies increasingly build a single task from protocols that were designed and secured separately. This creates a simple problem: a workflow can look correct at each step and still produce the wrong outcome. For example, a correct escrow may release payment on an authorized approval that provides little evidence that the delivered work actually satisfied the task. We systematize this problem across the full lifecycle of an agent task. Our study organizes security and economic requirements into 17 property families over six stages, with receipt soundness and completeness assessed separately. We examine 12 systems and standards, five reusable mechanism families, and four classical baselines. We introduce guarantee closure, a task-relative criterion for determining whether guarantees established at one stage remain available and constrain the later decisions that depend on them. We apply the criterion to controlled and native workflows, covering 840 matched executions and an exhaustive 11,648-case check over a finite objective-task domain. Our results expose recurring failures between verification and settlement, where conforming work can remain unaccepted or valid evidence can be ignored. Public records and model judgments further distinguish recorded approval from evidence of task conformance, while economic analysis identifies the report, penalty, and shared-error assumptions behind these guarantees. These findings show where end-to-end guarantees fail and what must be repaired to preserve them across the workflow.

Goniopolar metals exhibit opposite thermoelectric polarities along different crystallographic directions, enabling zero-field transverse thermoelectricity but offering few means for external control. Here we show that a spatially structured Laguerre–Gaussian vector potential can programmably reconstruct the goniopolar phase space of NaSn$_2$As$_2$. First-principles-derived Wannier transport with bond-dependent Peierls coupling reveals two OAM-dependent spatial scaling laws: the radial response follows the Laguerre–Gaussian radius $r_{\max}\propto\sqrt{|\ell|}$, while calculations for $|\ell|=2$–5 yield a dominant angular harmonic $m_{\mathrm{dom}}=2|\ell|$, encoding the optical winding in a frequency-doubled thermoelectric response. Increasing $|\ell|$ simultaneously reconstructs pre-existing goniopolar windows, enhancing a representative window by approximately 17% at $|\ell|=5$. By contrast, reversing $\ell$ at fixed polarization produces only a small correction that approximately interchanges upon polarization reversal. Energy-resolved transport reveals that the structured field redistributes in-plane and cross-plane electronic velocities, shifting the directional Seebeck-zero boundaries that define the goniopolar state. These results establish vortex position and OAM magnitude as programmable control coordinates for goniopolar thermoelectricity.

Video Anomaly Detection (VAD) aims to temporally localize abnormal events in videos. Most existing approaches rely on dataset-specific training and curated annotations, limiting generalization in open-set scenarios. Recent zero-shot methods based on Large Vision- Language Models (LVLMs) alleviate this dependency but often lack temporal continuity and structured reasoning. We propose Cog-VADU, a fully training-free framework that reformulates VAD as a sequential cognitive reasoning task. Cog-VADU introduces Chain-of- Anomaly Detection Thought Prompting (CoADTP), which unrolls an LVLM into a recurrent reasoning chain across video segments. By propagating structured rationales over time, the model maintains implicit temporal memory, enabling robust discrimination between com- plex anomalies and high-motion normal activities. To improve reliability, we further design a cross-modal re-ranking stage that aligns textual rationales with visual embeddings, enforcing semantic consistency and temporal coherence for refined and stable predictions. Extensive experiments on multiple public VAD benchmarks demonstrate that Cog-VADU achieves competitive zero-shot performance. Moreover, cross-model evaluations show that CoADTP consistently enhances reasoning-based anomaly detection in a model-agnostic manner, pro- viding interpretable and generalizable anomaly understanding for real-world applications.

We study three recurrent double sequences whose colored diagrams encode mirrored versions of the finite-ordinal construction. Two sequences use three letters and realize variants with two and three initial symbols. A four-letter sequence realizes the von Neumann construction from one initial symbol. For each sequence we describe its cells explicitly and identify the ordered nesting of its rectangles. For four letters, we distinguish ordinary and virtual boxes and prove their assembly rules. The proofs proceed by induction along antidiagonals. For the constructions with one and three initial symbols, we reduce the recurrence to finite sets of local configurations and verify those sets by computer. We derive formulas for the numbers of nested boxes, including arithmetic-term representations, and we prove that none of the three sequences is $k$-automatic for any integer $k \geq 2$.

In this work, we study bipartiteness and expansion testing, two canonical problems in graph property testing in the bounded-degree model through the lens of quantum query complexity. In the classical setting, it is known that $\widetilde{\Theta}(\sqrt{N})$ queries are necessary and sufficient for both these testing problems (Goldreich and Ron, 1999, 2000 & 2002), where $N$ denotes the number of vertices of the input graph. Due to their significance, (Ambainis, Childs, and Liu, 2011) initiated the study of these problems in the quantum setting and designed quantum algorithms for bipartiteness and expansion testing that perform $\widetilde{O}(N^{1/3})$ queries, showing a polynomial speedup. They also proved that $\widetilde{\Omega}(N^{1/4})$ queries are necessary for expansion testing, but the possibility of an exponential quantum advantage for bipartiteness testing remained open. Despite significant effort, there has been no improvement in these results in the last decade and a half. In this work, we prove essentially tight $\widetilde{\Omega}(N^{1/3})$ quantum query lower bounds for both bipartiteness and expansion testing, thereby completely characterizing the quantum query complexity of these problems up to polylogarithmic factors. While our proofs use the polynomial method similarly to Ambainis, Childs, and Liu, we use intermediate problems that we relate to the main problems via reductions, and perform a more precise analysis of the resulting polynomials, leading to the near-optimal lower bounds.

Adaptive model search is path dependent: once a challenger is adopted, it becomes the reference from which later candidates are generated. A statistically unsupported replacement can therefore alter hypotheses that have not yet been proposed. We introduce Evidence-Gated Research (EGR), a statistical adoption layer for moving-incumbent search. EGR freezes each challenger before decision evidence is revealed, builds anytime-valid evidence across a predeclared set of environments, routes evidence predictably toward unresolved components, composes a persistent candidate e-value, and passes that e-value to an online controller. Under explicit conditional-validity and predictability conditions, the resulting procedure controls false discovery rate for the declared all-environment adoption target even though earlier adoptions change later challengers. In a 5,000-trajectory closed-loop benchmark, development-only e-LOND attains persistent FDR 0.621, whereas no persistent false-adoption path is observed for the audited EGR variants in that finite run. In matched replay over 600 challenger–incumbent pairs, Stagewise EGR preserves fixed-anytime alternative crossing decisions while using 56.1% less decision evidence at the representative threshold. A three-environment public-data study and a 40,000-sample controlled neural benchmark reproduce the evidence-efficiency pattern. These results identify model replacement as a distinct statistical control point in adaptive model development.

Cooperative 3D tracking must integrate complementary observations across agents and time while maintaining consistent identities. When evidence integration and identity inheritance share a matching decision, errors arising from cross-view appearance differences and spatial misalignment can compromise both feature fusion and track continuity. We propose FFBL-Coop, a fuse first, bind later framework that separates instance admission from identity management. Confidence-ranked Slot Admission (CSA) allocates cooperative queries to available ego slots using confidence and spatial proximity. Unified Representation Aggregation (URA) uses cooperative semantic features and aligned anchors to guide ego-feature retrieval, refining the augmented query bank within a shared transformer decoder. After refinement, Cooperative-Priority Identity Anchoring (CPIA) combines learned association with persistent mappings to establish accepted identity assignments across frames. A shared codebook reduces transmitted payload while retaining AP and AMOTA close to the uncompressed variant. FFBL-Coop achieves AMOTA/AP of 0.611/0.548 on V2X-Seq and 0.688/0.653 on Griffin-25M. Code will be released.

Topological Data Analysis (TDA) offers novel methods for understanding temporal dynamics in complex systems, yet its application in information systems design faces a fundamental challenge: how should systems present analytical outputs when interpretation frameworks are still developing? This paper reports on the development of TopoLA, a dashboard system applying Zigzag Persistent Homology to learning management system data, and proposes three early design principles for interpretation support in emerging analytics: (1) separation of objective measurement from contextual interpretation, (2) graduated disclosure from metrics through patterns to reflective prompts, and (3) explicit acknowledgment of methodological uncertainty. The system implements a modular three-stage pipeline–feature extraction, topological computation, and interpretation support–enabling extension to additional analytical methods. This work contributes to information systems research by articulating preliminary design knowledge for systems that must communicate analytical insights from methods lacking established interpretation norms–a challenge increasingly common as novel computational techniques enter applied domains.

In this paper, we study the number of points of $\mathbb{Z}$-schemes $X$ of finite type over the finite rings $\mathbb{Z}/p^m\mathbb{Z}$ for positive integers $m$ and prime numbers $p$. Motivated by Igusa's conjecture for exponential sums and the Lang-Weil estimate, we establish an estimate of $X(\mathbb{Z}/p^m\mathbb{Z})$ in terms of $m$, $X(\mathbb{Z}/p^{m-1}\mathbb{Z})$ and poles of the $p$-adic Igusa local zeta function of $X$ uniformly in $m\geq 2$ and $p$. Our estimate might be viewed as an inductive version for counting points of schemes over finite rings of the Lang-Weil estimate. Our estimate agrees with the expected bound of Igusa's conjecture for exponential sums if $X_{\mathbb{Q}}$ is not a locally complete intersection having only rational singularities. This can be regarded as an analogous version of the estimate of exponential sums modulo powers of primes of polynomials with non-rational singularities given by Cluckers, Mustaţǎ and the author in 2019. In the case that $X_{\mathbb{Q}}$ is a locally complete intersection having only rational singularities, our estimate is very close to the expected bound of Igusa's conjecture for exponential sums. To prove our estimate, beside using the usual tools such as resolutions of singularities and Denef's formula for Igusa local zeta functions, we also use the Hermit interpolation formula to study the numerators of Igusa local zeta functions. By the same method, we are able to approach Igusa's conjecture for exponential sums in the case of rational singularities. Lastly, to have further applications of our result in the future, we study heavily on $p$-adic analysis to give an upper bound of the real parts of non-trivial poles of Igusa local zeta functions in terms of suitable generalized log canonical thresholds.

Two integer partitions $t$-intersect if they have at least $t$ common parts, counted with multiplicity. We study the largest $t$-intersecting families of integer partitions of $n$ into exactly $k$ positive parts. The canonical $t$-star consists of the partitions containing at least $t$ ones. Applying Kupavskii's weak-spread theorem, we prove that this star is largest whenever $n\ge Ak^3$, for every fixed $A>24$ and all sufficiently large $k$, uniformly over $1\le t<k$. We also give counterexamples to Borg's conjecture at every intersection scale: for all sufficiently large $k$ and for every $1\le t\le \lceil k/4\rceil$, we describe $t$-intersecting families on integer partitions of $n=\lfloor tk^2/3\rfloor$ into $k$ parts which are strictly larger than the corresponding canonical stars. Moreover we present a family of counterexamples to Borg's conjectures about largest $t$-intersecting families of integer partitions of $n$ without restricting the number of parts.

Autonomous driving systems have become a central focus of intelligent transportation research, with End-to-End Learning and Modular Architectures offering two prominent design paradigms for their implementation. E2E Learning uses deep learning algorithms to map raw sensory inputs directly to driving actuators, providing a streamlined and adaptable solution. while Modular Architectures employ a pipeline-based approach, dividing the system into distinct subsystems for perception, cognition, planning, and control. This paper presents a comprehensive comparative analysis of these paradigms, focusing on their strengths, limitations, and trade-offs to provide insights into their suitability for various autonomous driving applications. The study evaluates key factors such as interpretability, scalability, robustness, and real-world applicability. While End-to-End Learning emphasizes simplicity and adaptability in dynamic environments, it lacks transparency and is highly dependent on large datasets. Conversely, Modular Architectures offer superior interpretability and task-specific optimization, but face challenges related to integration complexity and scalability. To address these limitations, hybrid approaches that combine the strengths of both paradigms have emerged, offering a promising direction for overcoming these challenges. Beyond this comparative synthesis, following work proposes a Four-Dimensional Architecture Selection Framework, comprising twelve binary criteria across safety, operating environment, data/computational resources, and deployment context, and validate it against ten published autonomous driving systems, correctly recommending 7/10 deployed architectures. This work synthesizes existing literature to highlight key trade-offs between the paradigms and identifies hybrid architectures as a promising direction for future research.

We show, under a certain assumption, that the Cheeger constant of a connected Cayley graphon is bounded from above in terms of its bipartiteness ratio, and also in terms of the gap between the top of the spectrum of its Laplacian and $2$. Using this result, we prove that if a connected Cayley graphon $C(G,\gamma)$ is bipartite, then there exists an index two subgroup $H$ of $G$ that avoids the support of $\gamma$.

Robot manipulation models primarily reason from 2D observations while acting in the 3D physical world. To bridge this gap, recent work has augmented robot data with geometric priors such as depth, point clouds, and 3D trajectories, while renderable 3D Gaussian representations provide another promising form of 3D supervision. However, 3DGS representation is designed mainly for photometric fidelity and may not preserve real-world metric scale, particularly when the supplied camera extrinsics are unreliable. We study the effect of extrinsic reliability and pose conditioning on feed-forward 3DGS, and propose a calibration-aware pipeline that anchors reconstructed scenes to the robot's metric workspace. Our experiments show that pose conditioning improves novel-view fidelity, while its geometric benefit depends on the reliability of the injected extrinsics. Using this pipeline, we present a renderable, metric-pose-anchored dataset with scene-level reliability information for robot manipulation research. Our dataset is available at https://huggingface.co/datasets/wonguen/3DROID

Heterogeneous high–performance computing architectures expose numerical algorithms to perturbations arising from the non–associativity of floating–point arithmetic. In Large–Eddy Simulation (LES), similar numerical effects may become relevant when they affect the filter–width entering the subgrid scale (SGS) model. This work investigates this mechanism for the least–squares (LSQ) based filter–width formulation, focusing on how floating–point effects are generated, transmitted, and coupled with the resolved flow. We show that, for fixed resolved kinematics, the LSQ filter–width is logarithmically non-expansive but not strictly contractive with respect to perturbations of the mesh metrics. Consequently, small disturbances may be transmitted with little attenuation through strongly directional filter-width responses. To mitigate this sensitivity, we introduce a scalar max–min compression of the directional mesh scales together with a bounded modulation based on the resolved velocity gradient. The resulting formulation reroutes floating–point perturbations through the filter-width operator, improving robustness while preserving the flow–dependent character of the original LSQ construction. The framework is assessed on heterogeneous CPU and GPU architectures for flow past a circular cylinder at Re=3900 and the Taylor–Green vortex at Re=1600. In the former, nearly one–to–one transmission of relative metric disturbances can become relevant when the transmitted perturbations interact with shear-layer transition. By contrast, on orthogonal Taylor–Green vortex grids, the accumulation pathway is structurally absent and no comparable macroscopic response develops. These results suggest floating–point sensitivity matters for LES filter–width formulations in heterogeneous computing environments.

Equipping artificial agents with spatial intelligence requires a comprehensive generative prior over the dynamic 3D world. We propose World Motion Models (WMMs) that capture "what was, is, and will be where across time" via sparse SE(3) pose trajectories. WMMs are built on the observation that elements of dynamic scenes can be well approximated by a set of rigid SE(3) trajectories, a minimal yet expressive primitive for 4D modeling. This representation unifies articulated objects, human bodies, hand-object interactions, piecewise-rigid scene dynamics, camera motion, and even robot states and actions into a single shared space. Given this representation, we cast the joint distribution of these entities as a flexible sequence modeling problem, utilizing flow-matching with per-token noise levels. Coupled with a context token mechanism for non-sequential conditioning, this formulation supports any-to-any marginal conditioning across an arbitrary number of entities and time steps. Tasks such as future prediction, motion infilling, model-predictive control, inverse kinematics, cross-embodiment retargeting, and policy learning all reduce to the application of different masks over the same network. Experiments on 6 diverse applications of 3D vision and robotics demonstrate the versatility and flexibility of WMMs with strong performance.

Predictive Vision-Language-Action (VLA) models aim to improve robotic manipulation via future observation or world dynamics forecasting. However, existing approaches often fail to realize this potential and underperform direct action prediction models. We argue that these limitations stem from modality misalignment between observations and actions, together with joint optimization conflicts that drive learning away from an action-centric objective. To this end, we introduce ATI-VLA, an Action-Centric Predictive Vision-Language-Action framework via Actionable Alignment Then Adaptive Injection. Specifically, it follows a two-step design: 1) Actionable Representation Alignment via a Shared Codebook. It aligns predictive observation and action representations by mapping both modalities into a shared discrete latent space via a unified codebook, making predictive observation latents readily usable for action generation and mitigating modality misalignment. 2) Action-Centric Adaptive Injection of Predictive Latents. Building upon this, it then injects predictive observation latents into action decoding as explicit predictive priors via a lightweight adaptive side-path, enabling adaptive predictive guidance under a single action-centric objective. Extensive experiments on both simulation and real-world robotic tasks demonstrate that ATI-VLA achieves state-of-the-art performance with faster convergence.

We develop Toeplitz infinite GMRES for solving large sparse analytic parameterized systems $A(s)x(s)=z$ at many parameter values. Our method exploits a block upper triangular Toeplitz structure in the companion Krylov sequence to construct the Arnoldi process and recover solution approximations without storing full Arnoldi vectors. We derive incremental recurrences requiring $\mathcal{O}(np^2+p^3)$ arithmetic and $\mathcal{O}(np+p^2)$ storage for $p$ Arnoldi steps, excluding factorization setup and assuming linear-cost coefficient actions and triangular solves. A dynamic generator-refreshing strategy addresses cancellation in this basic recurrence. Moreover, we show that the Arnoldi basis can be simply represented using one block row and a nilpotent matrix. For $A(s)$ admitting a split form, we further use this structure to develop an implicitly rebased method. A residual lower bound for square-summable Taylor coefficients explains the effect of scaling outside the unit disk. Theoretical analysis and numerical experiments illustrate the computational efficiency of the proposed methods.

Sampling from discrete, unnormalized distributions without access to data is a challenging problem. Neural samplers offer a promising approach by training generative models from density evaluations directly. However, existing discrete neural samplers are prone to mode collapse, come without convergence guarantees when trained via fixed-point iterations, and are often tied to a specific reference process such as masked or uniform diffusion. In this work, we introduce Discrete Gibbs Iterative Neural Sampler, a fixed-point neural sampler that addresses these limitations, enabling efficient, scalable learning, substantially reducing mode collapse in practice. Besides masked diffusion, the framework also extends to transport between arbitrary distributions. DIG-IN mitigates mode collapse on Ising and Potts models and scales to amortized sampling with up to 2,500 sites, recovers alloy phase diagrams, and learns to sample biomolecular Boltzmann distributions from energy alone. Its transport formulation accurately estimates solvation and conformational free energies. As a maximum-entropy RL policy, DIG-IN outperforms the Gaussian, diffusion, and flow policies we compare against across 20 continuous-control tasks.

Asynchronous online learning offers temporal flexibility at a structural cost: learning communities tend to fragment rather than cohere. $\beta_0$, the number of disconnected behavioral clusters from Zigzag Persistent Homology, serves as a cohort-level indicator of this structure. Two questions remained unverified at scale: (1) does apparent $\beta_0$ convergence reflect genuine behavioral alignment or learner dropout? and (2) do assessment deadlines produce reproducible fragmentation-convergence cycles? We address both across all 22 OULAD courses (N > 22,000; 857 week-pairs). Changes in $\beta_0$ strongly co-vary with active learner changes (pooled r = 0.387; median per-course r_delta = 0.459, 20/22 courses), identifying $\beta_0$ as a participation-sensitive indicator: $\beta_0$ and active learner counts co-respond to deadline events rather than one causing the other. Deadlines produced fragmentation in 82.6% of assessments and the full Fragment First, Converge Later (FFCL) cycle in 60.2%. 3-phase analysis confirmed structural fragmentation as the dominant long-term trajectory (90.9% of courses), moderated by curriculum structure. These findings establish $\beta_0$ as a participation-sensitive structural indicator with direct implications for AI-augmented learning analytics design.

Hessian structure on a manifold is a geometric structure consisting of a pair $(\nabla,g)$ of an affine connection $\nabla$ and a Riemannian metric $g$ satisfying certain compatibility conditions. It is also known as a dually flat structure in information geometry. Hessian geometry is considered to be a real analogue of Kähler geometry; in particular, Hessian sectional curvature corresponds to holomorphic sectional curvature in Kähler geometry. The standard models of Hessian manifolds with constant Hessian sectional curvature were classified by Furuhata and Kurose (2013) in the nonpositive curvature case, whereas the positive curvature case is open. In this paper, we classify the standard models in the positive curvature case. For this end, we introduce Hessian structure on quotient manifolds of Kähler manifolds equipped with suitable Hamiltonian actions of abelian Lie groups and realizing the standard models as such quotient manifolds.

Major FPGA manufacturers have incorporated bitstream encryption to protect sensitive configuration data. However, for the most widely used FPGA families, multiple attacks against unpatchable protection schemes hard-wired into the devices can bypass or fully break them, making patchable schemes desirable. In this work, we present a proof-of-concept implementation of an AMD-proposed asymmetric key encryption scheme for bitstream protection for 7-Series FPGAs, using partial reconfiguration from the Programmable Logic. We analyze the security implications and hardware overhead of this implementation. We then propose and demonstrate an optical side-channel attack that is able to recover plain-text configuration data during the dynamic reconfiguration process. This attack leverages Photon Emission Microscopy and Electro-Optical Probing to first locate and then contactlessly extract the plain-text data from the ICAP interface, which internally connects the Programmable Logic with the configuration logic. We located the ICAP buses in an AMD XC7A200T device and show that the data on it can be extracted with Electro-Optical Probing. We claim that even advanced encryption schemes utilizing Partial Reconfiguration and custom cryptographic engines are vulnerable to optical attacks, as reconfiguration is only possible via hard-wired, vulnerable configuration interfaces.

Light-pulse atom interferometry has emerged as a promising approach for developing quantum inertial and gravity sensors for real-world applications, but achieving robust operation in dynamic environments without sacrificing sensitivity remains challenging. To mitigate performance degradations resulting from vibration-induced noise and mismatches in the spatial overlap between free-falling atoms and light pulses, we demonstrate a first-of-a-kind high-data-rate, high-sensitivity grating magneto-optical trap (GMOT)-based light-pulse atom interferometer (LPAI). This system uses a compact, rugged GMOT architecture, based on an in-vacuum microfabricated grating chip and a single laser-cooling beam, to enable high-data-rate GMOT-based cold-atom generation with sub-Doppler cooling. Our GMOT-based LPAI operates at high data rates (up to 100 Hz), while simultaneously achieving both high acceleration sensitivity (550 ng/rt-Hz at 20 Hz, 1.49 ug/rt-Hz at 45 Hz, and 6.31 ug/rt-Hz at 70 Hz) and good bias stability (71 ng). This compact, rugged architecture paves the way for field-deployable quantum inertial and gravity sensors in high dynamics and for time-multiplexed, multi-axis inertial sensing.

Let $S_g$ be a closed oriented surface of genus $g$. Ivanov conjectured that if $G$ a finitely generated subgroup of $\mathrm{Mod}(S_g)$ its finite-index Frattini subgroup $\Phi_f(G)$ is nilpotent. We prove this conjecture, using recent partial results of the first author about the Andersen-Masbaum-Ueno conjecture.

A storage code on a graph assigns a symbol to each vertex so that the symbol can be recovered from its neighbors. We prove that the binary full-parity storage codes on triangle-free coset graphs of primitive BCH codes have rate tending to one for every fixed error-correction capability of at least two. The conclusion also holds for an increasing error budget under an explicit growth condition. The proof bounds the binary rank of convolution matrices associated with polynomial maps. Low coordinate degree forces cancellation in the polynomial representing the image, and a polynomial rank bound converts this cancellation into a quantitative estimate for the storage rate. For the double-error-correcting family over $\mathbb{F}_{2^m}$, we prove that the storage deficiency is $\Theta(((1+\sqrt{5})/4)^m)$. This refinement follows from an exact Fibonacci formula for a polynomial coefficient rank and a matching exponential lower bound after finite-field evaluation.

The origin of chirality-induced spin selectivity (CISS) remains elusive, and ultrahigh spin polarization (SP) in topologically knotted molecules is unexplained. We develop a discrete geometric spin-orbit coupling (SOC) framework for molecular junctions, resolving site-specific curvature and current-partition effects beyond continuous models. For trefoil-knot molecules, it quantifies site-resolved geometric SOC, reaching $\sim$120 meV, nearly two orders of magnitude larger than intrinsic SOC of light atoms. The substrate-coupled benzene unit, carrying the largest current and remarkable geometric SOC, dominates the CISS effect. The framework quantitatively reproduces measured SP, temperature-dependent magnetoresistance (MR) and $\Delta$MR trends, establishing discrete geometric SOC as a predictive tool for CISS in topologically knotted molecules.

Let $X$ be a nonsingular Hermitian variety of even dimension over a finite field, and let $\Lambda$ be the lattice spanned by the classes of its maximal totally isotropic linear subspaces defined over the base field. By work of Dummigan, Dummigan–Tiep and Shimada, these classes span the middle cohomology, and the intersection form on the primitive part is definite, as predicted by the standard conjecture of Hodge type. We give an elementary proof, which avoids the representation theory of finite unitary groups and uses only the dual polar graph attached to the Hermitian form. It shows that the intersection form on the primitive part is an explicit positive multiple of a Euclidean inner product. The advantage of the new proof is that it also controls $\Lambda$ $p$-adically. If $X$ is defined over $\F_{q^2}$ and has dimension $2m$, every $p$-adic elementary divisor of the intersection matrix of these subspaces divides $q^m$. Consequently $q^m$ times every algebraic cycle of codimension $m$ is numerically equivalent to an integral combination of them. As a by-product, the standard conjecture of Hodge type holds for varieties finitely covered by Hermitian varieties, and the $p$-adic bound descends along finite morphisms of degree prime to $p$.

We investigate how root allometry and below-ground root competition due to root overlap affect the conditions for pattern formation in non-local scalar vegetation models. We start from a spatially explicit two-component vegetation-water system in which plants acquire soil water through their laterally extended root systems, with root allometry represented by an interaction kernel whose spatial extent increases with the above-ground biomass density. In the limit of fast water dynamics, we eliminate the water variable, resulting in a non-local scalar model for the vegetation dynamics. This reduction reveals that accounting for root overlap naturally leads to a double integral structure in the scalar model, in contrast to the single convolution term commonly used to model non-local competition for resources. For the resulting scalar model, we identify two distinct mechanisms that can drive Turing instabilities. The first instability mechanism requires root growth to outpace mortality, while the second mechanism relies on the development of competitive pressure zones, in which vegetation growth is impeded by the cumulative competitive pressure exerted by neighbouring areas with higher biomass density. Root allometry promotes the occurrence of both instability mechanisms, while root overlap inhibits the emergence of competitive pressure zones. Hence, our results show that both root allometry and root overlap are important features to consider when studying vegetation pattern formation.