Papers

We study Fourier decay of natural invariant measures for real analytic skew products $T(x,y)=(f(x),g(x,y))$ on $\mathbb{S}^1 \times [-1,1]$, where $f$ is expanding and $0<|\partial_y g(x,y)|<1$. Let $\mathcal S$ denote the associated solenoidal attractor. We prove a dichotomy: either $\mathcal S$ is a single horizontal graph, or both the SRB measure and the measure of maximal entropy have polynomial Fourier decay. No transversality assumption is imposed.

A qKZ-type discrete flat connection with multiplicative step $p$ has monodromy operators when $p$ is a root of unity. The monodromy operators are commuting endomorphisms of the connection. We construct their eigensections and eigenvalues. The construction is based on the presentation of the discrete flat connection as a discrete Gauss-Manin connection.

Traditional theoretical treatments of ferroelectricity do not straightforwardly extend to sliding ferroelectrics, which are increasingly-studied layered materials where a switchable electrical polarization is controlled by two-dimensional relative motion of the stacked layers. Therefore, in-depth analyses of the underlying processes which dictate their polarization behavior remain challenging. In this paper, we present a comprehensive approach for identifying the symmetry-adapted microscopic parameters which are responsible for driving the emergence of this polarization. First, we outline our approach, which appeals to group theory arguments and the distortion of Wannier orbital densities to connect macroscopic symmetries to the microscopic electronic distortions which dictate the appearance of ferroelectricity. Then, we illustrate this process by using density functional theory to apply our strategy to honeycomb bilayer systems, including hexagonal boron nitride. In this way, we find that combinations of dipole-like and quadrupole-like distortions of lone pair electron orbitals control electronic reorganization, and by extension, ferroelectricity in such systems.

Face swapping and face compositing pipelines routinely produce a face that is geometrically well aligned but photometrically implausible: the donor face carries flat, near-frontal studio illumination while the host body and background carry directional scene light. Most existing remedies re-synthesise the face through colour transfer, neural relighting, or inverse rendering, and therefore risk altering identity, skin tone, and texture. We present a conservative alternative: geometry-driven form-shadow injection. The pipeline never repaints the face. It estimates a per-pixel gain field $g\in[g_{\min},1]$ from a rasterised 3D face proxy and multiplies it channel-uniformly onto linear RGB, so the operator can only darken and cannot shift chromaticity. A dense landmark mesh is rasterised into a depth buffer, from which we derive surface normals, a cavity term, and screen-space cast shadows. Key-light direction is estimated from host-side cues (body, background, hair halo); on-face cues are downweighted because they recover the donor's lighting. Shadow magnitude is not matched to the host: it is set by a three-parameter transfer $(\tau,\sigma,g_{\min})$. The shading field is divided by its 75th percentile over skin, then gated, scaled, clamped, smoothed, and re-clipped inside a feathered, skin-gated face mask. On an analytic face heightfield, the default $(\tau,\sigma,g_{\min})=(0.90,0.45,0.82)$ modifies 56.5% of face pixels with mean gain 0.938 (0.890 on modified pixels) and drives 3.4% of pixels to the floor. Hue invariance is a corollary of the operator. We analyse the transfer in closed form, ablate its parameters, and discuss failure modes of a monotone, darkening-only formulation, including double-shadowing of non-flat donors.

Knot Floer homology associates to a knot in $S^3$ a bigraded chain complex over $\mathbb{F}[W,Z]$, from which many classical and concordance invariants can be extracted. Recent work shows that this algebraic object can equivalently be represented by a decorated immersed multicurve in a marked surface. This survey explains the immersed curve interpretation of knot Floer homology, aided by many examples, and shows how several invariants arising from the knot Floer complex can be extracted from the corresponding immersed curves. The decorated multicurve associated to a knot has a distinguished curve component $\gamma_0$ and a distinguished connected component $\Gamma_0$, both of which are concordance invariants of the knot. We pay particular attention to these components and various numerical concordance invariants that can be extracted from them. We introduce new generalizations of the $V_s$ invariants, and we give a new curve-based description of the Upsilon invariant by showing that it is determined by generalized $V_s$ invariants.

Many self-supervised methods for training foundation models at the Large Hadron Collider (LHC) rely on data augmentations to encourage the model to embed events into a representation space invariant to certain physical or detector symmetries. A common challenge arises from the large freedom in choosing a proper set of augmentations on which downstream performance depends. The implementation of augmentations involves either modifying existing events, potentially breaking the event fidelity, or simulating more event variants, which is computationally intensive. In this work, we present a data-driven method of pairing events by their similarity via the energy mover's distance (EMD), which measures how similar two events are in terms of the work required to transform one into the other. With this approach, distinct events are sampled and matched by their similarity to serve as views for learning invariance, keeping the physics content of each event intact without handcrafted distortions. We demonstrate this augmentation-free pairing method by pre-training on QCD jets via self-distillation and show that it can yield semantic jet embeddings with downstream discrimination power comparable to or better than an augmentation-based baseline.

Space-based photometry has detected solar-like oscillations in thousands of stars, whose global seismic parameters yield stellar properties via the asteroseismic scaling relations. Because these relations systematically overestimate red-giant masses and radii empirical calibration is required. Double-lined eclipsing binaries hosting oscillating red giants provide precise dynamical masses and radii without external calibration, making them ideal benchmarks. We present KIC 8129189 and KIC 10920813, two Kepler eclipsing binaries containing less-evolved oscillating red giants, as new benchmarks that extend the calibration sample toward smaller radii. We measured radial velocities from high-resolution spectra, extracted global asteroseismic parameters from Kepler light curves, and modeled the binaries with JKTEBOP and PHOEBE-2 using both full light curves and selected eclipse sets, adopting benchmark masses and radii from the envelope of tested model/data configurations. We then fit correction factors $f_{\Delta\nu}$ and $f_{\nu_{max}}$ to the underlying $\Delta\nu$-density and $\nu_{max}$-surface-gravity relations. We obtain $M_{RG}=1.413 \pm 0.037 M_\odot$ and $R_{RG}=4.296 \pm 0.061 R_\odot$ for KIC 8129189, and $M_{RG}=1.383 \pm 0.022 M_\odot$ and $R_{RG}=5.914 \pm 0.043 R_\odot$ for KIC 10920813. The adopted 15-star calibration gives $f_{\Delta\nu}=0.9777 \pm 0.0048$ and $f_{\nu_{max}}=1.024 \pm 0.008$, corresponding to $C_M=0.850 \pm 0.020$ and $C_R=0.9333 \pm 0.0090$. Neither correction factor depends significantly on radius, nor does $f_{\nu_{max}}$ depend on metallicity; model-based $f_{\Delta\nu}$ values are systematically lower than the dynamically derived ones. Both systems agree with the correction from previous benchmarks, showing that continued expansion of the eclipsing-binary sample is essential for testing the scaling relations across evolutionary stage.

Most molecular transitions occur on time scales far beyond direct molecular dynamics simulations. The committor, the probability that a configuration reaches a product state before a reactant state, is a central kinetic statistic, providing a mechanism-independent reaction coordinate and a foundation for transition path theory and the calculation of rates. This review surveys modern approaches for estimating the committor and related kinetic statistics from molecular simulations, with an emphasis on self-supervised methods that learn solutions of their defining dynamical equations rather than relying on labeled shooting data. We develop a common operator viewpoint connecting generator-based partial differential equations, variational principles, Markov state models, dynamical Galerkin approximation, and neural networks. Empirical and theoretical evidence points to the efficiency of these methods. We provide theoretical and practical guidance for realizing their full potential in applications, including strategies for treating non-Markovian effects and for sampling. We conclude by identifying opportunities for further research, including connections to reinforcement learning and generative modeling.

The generalized switch is a highly flexible queueing model, covering multiclass, multiserver, and multiresource queueing systems as well as a wide variety of stochastic networks. Although many scheduling policies have been developed for this model, they almost entirely address unknown job duration settings. How to optimally use known job durations in the generalized switch has remained open. Moreover, optimizing mean response time remains open in both settings. We introduce the first policy to guarantee heavy-traffic optimal mean response time in the generalized switch, our Smallest Equalizing Bucket (SEB) policy. The key challenge in designing an optimal scheduling policy is that we must simultaneously prioritize small jobs and also minimize resource waste, all while fitting within the generalized switch's service options. SEB overcomes this challenge by grouping jobs into duration-based buckets and enforcing an "equalizing" service structure that keeps each bucket balanced while still prioritizing the smallest jobs. We prove SEB's heavy-traffic optimality. Simulations further confirm the effectiveness of SEB-inspired heuristics.

Capillary forces are commonly regarded as an energetically closed channel in multiphase turbulence, redistributing kinetic energy across scales without net gain or loss. Here we show that this picture breaks down in bubble-laden turbulence when short-range near-contact interactions are active. A spectral analysis of the kinetic-energy budget reveals that the cumulative capillary power does not vanish at statistical stationarity, but instead retains a finite negative residual. This apparent imbalance is exactly compensated by the work of short-range repulsive forces, which is negligible at large and intermediate scales and becomes positive only at small scales. Near-contact interactions therefore open a distinct small-scale pathway in the interfacial energy transfer, rather than acting as a mere regularization of unresolved thin films. The proper scale-by-scale description is thus an extended interfacial transfer, combining capillary and near-contact work, rather than a purely capillary one.

Achieving robotic-assisted string assembly has been a longstanding objective in superconducting cavity pro-duction to improve precision, repeatability, and through-put while reducing operator-dependent variability. At Fermilab, robotic systems have been successfully deployed for the installation of individual components on SSR2 cavities inside a cleanroom environment. The single-cavity installations validated the feasibility of robotic techniques and provided confidence to extend automation to the assembly of a full prototype cavity string. Leveraging lessons learned from earlier operations, the robotic system was adapted for the string assembly. This work describes the robotic-assisted assembly process in detail, including alignment strategies for coupler flanges, torque control for bellows connections, and mitigation of particulate generation in cleanroom conditions. Performance metrics of the cryomodule are presented, together with an analysis of improvements needed for robotic assembly. The effort also represents a broader R&D initiative at Fermilab to the long-term goal of scalable SRF cryomodule production.

The McEliece cryptosystem based on algebraic geometry codes has been proposed as a way to reduce the key size of code-based cryptography, but several structural attacks have demonstrated the vulnerability of particular families of algebraic geometry codes. Despite this, until recently, there remained schemes and parameter sets that were not vulnerable to any known attack. We propose a new structural attack with “hints” that applies to elliptic codes with arbitrary effective divisors. In particular, we prove that, given the elliptic curve, the public generator matrix, and three points from the evaluation divisor, the entire divisor can be recovered in polynomial time, independently of the number of errors used in the cryptosystem. The attack requires $\mathcal{O}(k^2n^2+|\mathcal{E}(\mathbb{F}_q)|+n)$ operations in $\mathbb{F}_q$ and succeeds with overwhelming probability, after which the second divisor is recovered in $\mathcal{O}\!\left(k^2n^2 + (|\mathcal{E}(\mathbb{F}_q)|-n)n^2\right)$ operations. We further propose an optimized version of the attack that requires no additional information at all. Exploiting the action of the automorphisms of the curve, the three known points are replaced by the enumeration of a single pair of field elements, which yields an equivalent key on the given public curve in $\mathcal{O}\!\left(k^2n^2 + q^2 + (|\mathcal{E}(\mathbb{F}_q)|-n)n^2\right)$ operations on average.

High-resolution land use and land cover (LULC) products derived from Sentinel-2 imagery are widely used for environmental monitoring and land management, yet their performance can vary across regions with complex ecological gradients and heterogeneous surface conditions. In Quebec, these limitations motivated the development of a provincial 10-m land-cover product, the COTQ, designed to support annual monitoring of land occupation and soil artificialisation. This study presents a systematic evaluation of the COTQ product relative to three global 10-m LULC datasets: ESA WorldCover, ESRI LandCover, and Google DynamicWorld. This paper does not introduce a new mapping methodology but focuses on analysing the behaviour and consistency of the COTQ using complementary evaluation approaches. All products are harmonized under a common legend and compared using structural indicators (object-size distributions, shape complexity, Adjusted Rand Index, and Intersection over Union), spectral separability metrics derived from Sentinel-2 reflectance data, and a targeted photo-interpretation of disagreement areas. The analysis is conducted over eight Sentinel-2 tiles selected to represent the main bioclimatic domains of Québec, from temperate and boreal forests to northern tundra environments. The results show that the COTQ exhibits structural and spectral characteristics most similar to ESA WorldCover among the reference global products, while revealing systematic differences linked to class definitions and thematic priorities, particularly for urban areas, wetlands, and rocky or cryptogamic surfaces. This multi-criteria evaluation provides an objective characterization of the COTQ product and clarifies its relative positioning with respect to existing global land-cover datasets for operational land monitoring in Québec.

Approximate multipliers can reduce hardware area and energy consumption in Deep Neural Network (DNN) inference; however, they introduce computational errors. Assessing the accuracy of numerous approximate multiplier designs across diverse DNN models and large-scale datasets remains challenging due to prohibitive evaluation times. This overhead primarily stems from the slow emulation of approximate multiplier behavior using look-up tables (LUTs) on CPU and GPU platforms. Moreover, the resulting accuracy degradation must be carefully quantified and, if necessary, mitigated (e.g., through retraining), further increasing the overall evaluation cost. To address these challenges, we propose FAME, an FPGA-based platform for evaluating approximate multipliers. The platform exploits the reconfigurable logic of Field-Programmable Gate Arrays (FPGAs) to implement approximate multipliers directly in hardware, eliminating the need for LUT-based emulation on CPU/GPU platforms and thereby enabling efficient DNN inference while significantly reducing evaluation time on large datasets. Furthermore, we introduce a pattern-guided DNN retraining technique to mitigate accuracy degradation induced by approximate multipliers. Specifically, retraining is guided by multiplier-specific patterns to effectively recover potential accuracy losses. We evaluate FAME using two DNN models, ResNet-18 and MobileNetV2, on the ImageNet dataset across 27 approximate multipliers. During inference, our approach achieves up to a 3.47x speedup in approximate multiplier evaluation compared to prior LUT-based emulation methods. Furthermore, the proposed retraining technique improves accuracy by up to 65.5% over existing retraining approaches for the evaluated multipliers. The code is publicly available at: https://github.com/gicLAB/FAME

We present the RMSTAR (RECONS M STAR) catalog, a 25 pc volume-limited and effectively volume-complete sample of the nearest 3352 M dwarf systems and their 305 wide stellar and 9 brown dwarf companions. RMSTAR has been created using only results from Gaia Data Releases 3 (GDR3) and 2 (GDR2), Hipparcos, and ground-based discoveries of M dwarf systems that are not available in the space-based results. The wide companions are identified using only results from GDR3 and GDR2, and have separations $\rho\ge0.''46$. There are 291 primaries with stellar companions, yielding a multiplicity rate of 8.68$\pm$0.49% for these widely separated systems, with a rate of 6.86$\pm$0.44% for projected separations $s\geq30$ au, where the sample of stellar companions is complete except perhaps for a few fringe cases. It is shown that the rate of stellar companions increases from the search limit of 30,000 au down to separations of 30 au, with a large set of companions to be characterized at closer separations in future work. We determine luminosity and mass functions for all stellar red dwarfs and their wide secondaries, finding that the luminosity function displays a classic turnover at $M_G\sim11$, whereas the mass function is described by an exponential function that rises from 0.60 M$_{\odot}$ to the end of the stellar main sequence at 0.075 M$_{\odot}$. We assess the large population of close, unresolved companions to M dwarfs by analyzing several Gaia parameters, identifying 1089 (30%) individual sources as having at least one of these elevated unresolved companion indication parameters.

Recent Vision-Language-Action (VLA) models for autonomous driving have incorporated world modeling by predicting future driving scenes alongside driving actions, demonstrating strong planning performance. Future driving scenes are utilized as dense supervision, encouraging the policy to learn rich internal representations useful for planning. However, these World-Modeling VLAs rely on explicit future generation to learn such representations, thereby introducing two key limitations: additional training burden and inference latency. To address these limitations, we propose RAF-VLA (Representation Alignment with the Future), a VLA-based autonomous driving framework that shapes planning-relevant internal representations through direct guidance from future-frame representations. RAF-VLA employs Future-Aligned Supervised Fine-Tuning, in which a straightforward regularization aligns the policy's hidden states with future-frame representations obtained from a pretrained world encoder while learning driving actions. This simple alignment allows RAF-VLA to avoid the training burden and inference latency associated with future generation. Extensive experiments on the NAVSIM benchmark show that RAF-VLA achieves competitive planning performance against state-of-the-art VLA planners with substantially fewer training samples seen. Moreover, RAF-VLA incurs only 3.8% training overhead and a negligible 1 ms inference overhead.

We study the quasinormal-mode and quasibound-state spectra of a massless scalar field in weakly magnetized Ernst–Schwarzschild spacetime. In the separated $O(B_0^2)$ regime, the Klein–Gordon equation reduces to a radial confluent-Heun equation. We construct an endpoint-selected spectral Wronskian directly from the canonical confluent-Heun recurrence and its regular-to-irregular connection limit. Quasinormal modes and quasibound states are then obtained as zeros of the same analytic spectral function on the radiative and bound sheets, respectively, providing a unified treatment of the two spectral sectors within the separated weak-field problem. The resulting QNM and QBS frequencies agree with independent weak-field Ernst and massive-Schwarzschild benchmarks available in the literature. We further show, for representative cases, that the frequencies selected by the local Heun-series termination relation examined here do not satisfy the endpoint-selected quasibound-state condition. The construction therefore provides a direct horizon-to-infinity spectral condition for both radiative and bound states within the weak-field Ernst problem.

Reconstructing the mass of a heavy resonance from its decay products with missing energy is one of the central tasks that directly determine the sensitivity in new physics searches at collider experiments. Supervised learning approaches to this problem often struggle to generalize well due to the presence of various systematic uncertainties and distribution shifts. Exhausting all possible variations in the labeled data can be very compute-intensive, while a failure of the model to generalize can corrupt the reconstructed resonance widths that are critical in peak-hunting analyses. In this work, following the foundation model paradigm, we use a self-supervised approach to pre-train a transformer encoder with VICReg to learn an embedding invariant to various corruptions, then fine-tune it for mass regression on a heavy resonance with masses ranging from 2.5 to 6.5 TeV and a SUSY-like cascade decay into an eleven-body final state. We show that the pre-trained model reconstructs sharper resonance peaks and has a more stable performance under various realistic corruptions, compared to a supervised model of the same architecture trained on the same augmented data from scratch.

Most modern lattice QCD calculations take the masses of the light quarks to be degenerate, setting $m_u=m_d$, a choice that, while not physical, increases computational efficiency and lowers the complexity of simulations and analysis. For many observables, the systematic error associated with this simplification is expected to be negligible, as $\Delta m_{ud}=m_d-m_u$ is significantly below the QCD scale. So far lattice studies have examined the role of strong isospin breaking (SIB) in hadron mass splittings, but SIB effects in thermodynamic observables have only been studied in terms of the crossover temperature with unphysically heavy quarks. Motivated by the recent observation of an unexpectedly large ratio between the abundances of charged versus neutral kaons in heavy-ion collision experiments, we investigate the effects of SIB in QCD thermodynamics by computing observables for three non-degenerate flavors ($N_f=1+1+1$) with physical quark masses using dynamical improved staggered fermions. In particular, we investigate the difference between the $u$- and $d$-quark condensates and extract the pseudocritical temperature, the equation of state, and conserved-charge fluctuations, comparing results to standard $N_f=2+1$ simulations.

We investigate the dynamics of entanglement asymmetry in periodically driven two-dimensional conformal field theories with a global U$(1)$ symmetry, using a dynamical-system description based on iterated conformal maps, in particular Möbius maps. Starting from a symmetry-breaking excited state prepared by a local operator insertion, we show that a broad range of nonequilibrium phenomena, including local symmetry restoration, the quantum Mpemba effect, and its inverse, admit a simple geometric description in terms of the invariant data of the conformal map. We explicitly demonstrate this using Möbius maps, for which the invariant structure is described by the conjugacy classes. In particular, the dynamics of entanglement asymmetry is determined by the relative positions of the state-preparing operator insertion, the subsystem, and the fixed points, yielding distinct patterns of growth, decay, oscillation, and saturation. We further argue that this geometric picture extends to general holomorphic maps, establishing the conformal-map dynamics as a natural framework for organizing the phenomenology of entanglement asymmetry in periodically driven two-dimensional conformal field theories.

Active Galactic Nuclei (AGN) feedback plays a key role in galaxy evolution. Highly ionized outflows, detected in X-ray absorption, are a promising candidate for quasar-mode feedback. We present a new Bayesian analysis of 0.65 Ms of Chandra High Energy Transmission Gratings (HETG) observations of MCG-6-30-15 from 2000 and 2004. Our approach detects new wind components, improving estimates of outflow demographics and impact. These include a hot ultra-fast outflow (UFO; 0.08c), recently confirmed by XRISM but seen in HETG for the first time, which has the power to potentially influence its host galaxy. We also detect the first potentially collisionally ionized absorbers in this source, a physical process typically not considered in previous analyses, but potentially important for wind impact and demographics. The warm absorber complex is resolved in unprecedented detail, uncovering evidence of a correlation between outflow velocity and ionization, constraining its geometry. We also confirm the presence of dust in the wind, clearly distinguishing it from the cold ISM components, which may impact wind acceleration. Our work highlights the power of applying new methods to deep, legacy HETG datasets, and the limitations of current atomic databases when considering OIV, V, and VI K-shell transitions. Furthermore, our work establishes a baseline for decade-scale outflow variability for new observations with XRISM and NewAthena in the future.

Digital trace data provide rich measures of behavior in everyday settings, but the research ecosystem supporting their collection is constrained by declining platform API access and a historical reliance on publicly observable data. Participant-mediated data donation offers a complementary approach in which individuals contribute selected portions of their own digital histories to research. Such data can include longitudinal and non-public behavior, span multiple platforms and modalities, and be linked to independently collected study measures, enabling study designs that are difficult to implement using public social media data alone. These opportunities also introduce methodological challenges around participant control, data minimization, heterogeneous platform exports, privacy, and governance, particularly when semantic or multimodal content is necessary to study the construct of interest. We present CANDOR (Collecting and Analyzing Networked Data for Open Research), an end-to-end infrastructure for participant-mediated collection and governance of sensitive digital trace data. CANDOR supports participant-directed selection of platforms, data types, and temporal ranges; modular platform- and modality-specific parsing and de-identification; linkage to independent study measures; and protected processing, storage, and access. We derive design requirements for this class of research and compare CANDOR with existing data donation infrastructures, identifying how different approaches support participant control, data minimization, scientifically necessary data richness, study-design flexibility, and governance. Together, this work provides a methodological and infrastructural framework for using participant-contributed digital traces in behavioral research, particularly when the data needed to address a scientific question are longitudinal, non-public, multimodal, or sensitive.

Lipid nanoparticles (LNPs) have transformed RNA medicine, yet their clinical utility remains constrained by predominant hepatic accumulation after systemic administration. Redirecting LNPs to extrahepatic tissues requires understanding of how lipid chemistry and formulation composition jointly govern in vivo biodistribution. Here, we develop an interpretable machine learning framework to predict hepatic versus extrahepatic LNP accumulation and identify molecular design rules for extrahepatic RNA delivery. A literature-derived dataset of 476 intravenous LNP formulations was curated from 81 studies, integrating formulation composition, lipid chemical structures, and IVIS-based biodistribution profiles. Standardized SMILES representations of ionizable lipids, helper lipids, sterols, PEGylated or polymer-conjugated lipids, additional lipids, and polymer repeat units were converted into RDKit Expert descriptors and combined with formulation-level variables to generate an 808-dimensional feature representation. Logistic regression, random forest, and XGBoost achieved ROC-AUC values of 0.839, 0.866, and 0.874, respectively. SHAP-based interpretation and consensus feature ranking revealed that ionizable-lipid descriptors dominate biodistribution prediction, while formulation composition, particularly ionizable lipid, sterol, and PEGylated/polymer-conjugated lipid fractions, contributes substantially. The top 20 consensus features retained nearly all predictive information in tree-based models. The most informative features implicated electrotopological surface properties, charge- and hydrophobicity-weighted surface areas, molecular topology, and amide/alkyl structural motifs as drivers of extrahepatic accumulation. This study establishes an interpretable, data-driven strategy for decoding LNP biodistribution and provides actionable design principles for engineering LNPs beyond the liver.

In this paper, we study logarithmic Donaldson-Thomas invariants for local log Calabi-Yau $4$-folds with simple normal crossing divisors. Using the family version of shifted Lagrangian classes announced by Khan-Kinjo-Park-Safronov, we construct relative and family logarithmic $\mathsf{DT}_4$-theories for logarithmic Hilbert schemes of curves, and prove a degeneration formula. For logarithmic Hilbert schemes of points, we construct virtual classes and prove a degeneration formula in Chow groups; in particular, it is independent of shifted Lagrangian classes. Finally, combining our degeneration formula with logarithmic cobordism, we explicitly compute the zero-dimensional logarithmic $\mathsf{DT}_4$-invariants for local surface snc pairs.

The completeness properties of spaces of immersed curves endowed with Sobolev-type reparametrization-invariant Riemannian metrics have been studied extensively in recent years. Whereas constant-coefficient metrics of large enough order on the space of closed curves are known to be complete, this is not the case for open curves. In this work, we characterize the metric completion of the space of real-valued immersed open curves with respect to these metrics. We show that the set of additional limit points in the completion is homeomorphic to $H^n$-diffeomorphisms of a closed interval. This result answers a question of the structure of the completion, posed in (Bauer et al., Ann. Sc. Norm. Super. Pisa Cl. Sci. (2023)), in the negative, and suggests a more refined conjecture on the structure in the case of multi-dimensional ambient space.

Dynamic Image Graph Construction (DIGC) is the primary performance bottleneck in FPGA acceleration of Vision Graph Neural Networks (ViGs), reconstructing graph connectivity at every layer through irregular, memory-intensive computation. Existing FPGA accelerators optimize DIGC but still execute it unconditionally, making repeated graph reconstruction a persistent source of latency and energy consumption. We propose the SpecReuse algorithm, which computes compact spectral descriptors of intermediate features and reuses previously constructed graphs when descriptor drift remains below a calibrated threshold. We further present the SpecReuse accelerator, an FPGA architecture that realizes graph reuse through lightweight hardware for spectral descriptor extraction and reuse control while remaining compatible with existing graph-construction accelerators. Experimental results demonstrate up to a $2.69\times$ speedup in end-to-end inference and approximately 58–65% lower energy per inference with negligible FPGA resource overhead and minimal loss in classification accuracy.

We study an infinite-horizon stochastic control problem for the optimal exploitation of an exhaustible resource with unknown total reserves. Information is generated both endogenously through continued extraction without depletion and exogenously through an external information flow. This interaction makes the natural problem non-Markovian and time-inconsistent. We show that it nevertheless admits an equivalent time-consistent formulation with the same optimal controls. The associated value function is characterized as the unique viscosity solution of a stochastic Hamilton–Jacobi equation with random coefficients. We prove comparison on the infinite horizon through a Snell-envelope-based strict-contact argument and establish uniqueness by an independent Brownian regularization and a BSDE correction, avoiding piecewise Markovian approximations. Finally, we identify the deterministic benchmark and show that, under persistent reserve uncertainty, the rescaled stochastic value function converges to a pathwise deterministic control problem, with the long-run optimal extraction rate determined by the asymptotic hazard rate of the limiting reserve distribution.

We show that microscopically inversion-asymmetric, permeable active fluid membranes are statistically flat and effectively inversion-symmetric at large scales. Their fluctuations are governed by an asymptotically exact linear hydrodynamic equation giving orientational long-range order and positional quasi-long-range order. At intermediate scales, their dynamics is described by a Kardar-Parisi-Zhang equation with spatially long-range noise, producing rough membranes with short-range translational and long-range orientational order described by exactly known scaling exponents. Active stresses can destabilize the membrane at long wavelengths, while sufficiently strong active permeation flow can drive finite-wavevector instabilities and pattern formation. These results reveal a novel activity-driven route to the destruction of flat fluid membranes.

By applying recent estimates on the number of integer solutions of ternary quadratic forms in boxes due to Browning and Heath-Brown, we obtain new estimates for the number of lattice points close to a curve. This leads to a new result on the distribution of squarefull numbers in short intervals.

Real-world robotic disassembly requires long-horizon execution, where robots must perform ordered sequences of manipulation tasks across multiple parts within a single scene. Multiple valid task goals and diverse assembly configurations make it difficult for imitation policies to infer the intended skill from raw observations alone, particularly when training data cannot cover the combinatorial diversity of real-world configurations and part geometries. We show that incorporating task context through language alleviates these challenges by providing explicit structure for skill selection and associating language-specified tasks with their corresponding manipulation targets in the visual scene. The proposed framework combines hierarchical task selection with task-context-aware imitation learning to ground language instructions in spatial visual representations for robotic disassembly. The resulting framework generalizes across diverse connector geometries and assembly configurations without requiring explicit object annotations. Our method improves end-to-end task success by 35 percentage points over the baseline diffusion policy and by 75 percentage points over the previous task-context-aware baseline.