Papers

We determine exactly how harmonic sums, taken over integers with a given number of occurrences of a fixed block of digits, depend on that number of occurrences. Language factorizations, combined with stochastic radix expansions, relate these harmonic sums to the iteration of an operator whose eigenvectors are the Lebesgue measure and distributional derivatives of singular measures. The dual picture is given by a Riesz basis of eigenpolynomials in a suitable Hardy space. The resulting modal expansion admits a natural interpretation as a block-directed Euler-Maclaurin formula interpolating between Euler-Maclaurin and Taylor expansions.

In order to circumvent that no universal set of gates can be achieved on a given quantum error-correcting codes, additional gates can be performed through magic state injection. This however requires to have access to high fidelity magic state, which can be obtained by the distillation of low quality states to fewer higher quality ones. In this paper, we provide a family of distillation protocols able to produce diagonal states at every level of the Clifford hierarchy. This family is obtained recursively using code doubling techniques and leveraging qubit recycling, the fact that some idle qubits of the protocols can be measured and re-used. At a given level of the Clifford hierarchy, we show that the protocols we derive can be performed at arbitrary high distance on a fix number of logical qubits. This family recovers many known efficient protocols, and uncovers new ones, such as a $111 \to 1$ protocol for $|T\rangle$ state distillation at distance $7$, which are the most compact in term of volume. Finally, we discuss possible extension of this framework for distillation protocols producing more than one output state.

Multi-hop question answering requires combining information from multiple documents to answer complex questions. These systems have grown increasingly capable, yet when they fail, the error is typically attributed to not finding the right documents. Whether this holds at the level of individual reasoning steps remains largely unexamined. We investigate this across three standard multi-hop QA benchmarks and find that failures decompose into two distinct modes: retrieval failures, where the needed passage was not retrieved, and extraction failures, where the passage was retrieved but the needed fact could not be extracted - a phenomenon we term the fact-grounding gap. Extraction failures account for nearly half of all per-hop deficiencies and are invisible to standard retrieval metrics. They remain unresolved by every retrieval intervention we test, establishing a ceiling for retrieval-only improvements. The gap's severity varies across benchmarks and question types, but extraction failures appear on every dataset we measure. Our findings reveal that retrieval failures and extraction failures are fundamentally different bottlenecks requiring different solutions - a distinction absent from current evaluation practice.

Learning flexible motor primitives is a hallmark of skilled motor control. Recent neuroscience theory proposes that motor primitives may be implemented as low-rank perturbations of a shared recurrent network, but leaves open how such a system is learned. We translate this principle into a novel architecture for learning motor skills end-to-end: a shared recurrent core modulated by a bank of residual adapters, each selected by a discrete latent code. Trained on closed-loop biomechanical control, the adapters develop emergent low-rank perturbations of the recurrent dynamics despite no architectural rank constraint, placing task representations in disparate subspaces of the shared core network. A simple high-level policy over the learned options, optimized while the whole network is frozen, sequences the low-rank adapters to produce novel out-of-distribution movements. We demonstrate the ability to generalize to novel motor sequences within the closed-loop control setting, improving on the generalization error of a task-input-conditioned multitask baseline by upto order of magnitude.

In this paper, we study the notion of $\mathcal{I}$$^{st}$-convergence of sequences of real numbers which is an extension work of $\mathcal{I}$$^*$-convergence on real sequences. We also define the convergence field of $\mathcal{I}$$^{st}$-convergence and $\mathcal{I}$$^{st}$-limit points and we discuss some properties related to these notions.

Wild test-time adaptation (WTTA) updates a source model online under small test batches, concurrent distribution shifts, and time-varying class imbalance. Most WTTA methods derive their adaptation signals, including predictive uncertainty, sample reliability, and local feature geometry, from the model being adapted. When the source model is unreliable under shift, these signals can reinforce its own errors, forming a self-referential loop. We introduce MASA (Multimodal-LLM-Anchored Semantic Adaptation), which complements model-internal evidence with structured semantic descriptions from a frozen multimodal large language model (MLLM). To limit inference cost, MASA queries the MLLM only for a small set of diverse, reliability-ranked anchors. The resulting descriptions capture the object family and nuisance factors such as style, viewpoint, and occlusion. MASA encodes these descriptions, propagates them to neighboring test samples, and stores the resulting visual-semantic information in an online prototype memory. Descriptor-aware retrieval from this memory provides an auxiliary target for lightweight adaptation of normalization-affine parameters. We evaluate MASA on the WTTA ImageNet-C benchmark under limited-batch, mixed-domain, and imbalanced-label-shift settings with ResNet and ViT backbones.

Sparse-view 3D scene reconstruction with 3D Gaussian Splatting (3DGS) is inherently underconstrained. Plausible renderings can also coexist with erroneous Gaussian geometry, as errors in positions or depths may be concealed by opacity, scale, and appearance; we term this failure mode Geometry Cheating. Existing regularization methods constrain geometry but remain limited to observed views, while video-diffusion-based methods complete unseen views yet mainly use them as RGB pseudo-supervision, underusing motion and temporal priors and lacking explicit geometry supervision. We present Bi-FlowGS, which uses optical flow to bridge generative view completion and Gaussian geometry regularization. Our plug-and-play Video-to-Geometry Flow Distillation (V2G) distills temporal correspondence priors from restored videos into Gaussian geometry to alleviate Geometry Cheating. Conversely, Geometry-to-Video Flow-Guided Restoration (G2V) uses the current 3DGS geometry to guide temporally consistent video restoration, providing more reliable generative supervision. Together, V2G and G2V form an implicit bidirectional co-refinement process, enabling restored videos and the optimized 3DGS scene to iteratively improve each other. Experiments demonstrate improved rendering quality and geometric consistency across wide-baseline and unbounded 360{\deg} benchmarks.

In the present work, we study the radiative decays of the $P$-wave $D\bar{D}^*$ molecular state $G_0$ with $I^G(J^{PC})=0^+(0^{-+})$ using a phenomenological Lagrangian approach. The molecular coupling is fixed by the compositeness condition with a Gaussian form factor. The partial widths for $G_0\to \gamma\gamma$, $\gamma J/\psi$, $\gamma \psi(2S)$, $\gamma h_c$, $\gamma \rho$, and $\gamma \omega$ are evaluated. Our results show that the two-photon and $\gamma h_c$ channels are highly suppressed, while $\gamma J/\psi$, $\gamma \psi(2S)$, and $\gamma \rho$ are of the order of a few keV, and $\gamma \omega$ reaches several tens of keV, making it the dominant radiative mode. The ratios $\Gamma(G_0 \to \gamma \psi(2S))/\Gamma(G_0 \to \gamma J/\psi)$ and $\Gamma(G_0 \to \gamma \omega)/\Gamma(G_0 \to \gamma \rho)$ are predicted to be $1-2.6$ and $3.4-5.4$, respectively, with mild parameter dependence. We also compare with hadronic decays and find that the total radiative decay width is lower than the hadronic decay widths by about one order of magnitude. We propose searching for $G_0$ in the sequential decay $Y(4230)\to \gamma G_0 \to \gamma\omega J/\psi$, which is accessible to further experimental measurements by the BESIII, Belle II and LHCb Collaborations.

Eigenstate thermalization fixes the smooth energy-resolved envelope of few-body observables but not the microscopic overlap statistics that realize it. In the multi-resolvent hierarchy, this missing information appears in a two-resolvent fluctuation sector. We solve that sector exactly in a tractable benchmark, random free fermions, obtaining a non-Porter-Thomas intensity hierarchy, a structured channel-distance covariance, and an exact overlap kernel that closes the two-resolvent covariance. We then reconstruct the same sector without using its exact solution: a projected self-consistency scheme fixes the irreducible vertex through independently computable projections, while unconstrained residuals identify the sectors missed by a minimal ansatz and are completed exactly by a finite-size Weingarten evaluation, without fitting. For interacting deformations, we prove a model-independent moment identity showing that the deep-plane coefficients are fixed by Hamiltonian-moment covariances. This yields an exact rigidity law: pair-hopping interactions freeze the sector, dense perturbations add only an isotropic layer, and density-density interactions produce an explicit polynomial deformation in channel geometry. By contrast, the bulk sector requires the interacting eigenstate-overlap kernel and exhibits a logarithmically divergent perturbative response. The fluctuation sector therefore splits into a rigid moment-determined part and an intrinsically nonperturbative eigenstate-resolved part.

Binding energies of molecules on ice mantles are important to understand the evolution of molecular complexity in molecular clouds. They are often computed using density functional theory (DFT) calculations, typically on either small amorphous ice clusters or crystalline slabs. Since these calculations require an accurate description of the electronic structure, hybrid functionals with dispersion corrections, basis set superposition error corrections and zero point energy corrections are typically employed. This, however, comes at a high computational cost, so most often small ice clusters are considered, frequently containing no more than twenty water molecules or so. While several recent studies have explored binding energy distributions, the effect of finite cluster size remains insufficiently quantified. To address this gap, we perform DFT calculations using six different functionals, on ice clusters containing 10 to 100 H2O molecules, separating the direct electronic effect of cluster truncation from the geometry-relaxation effects. As probe molecules, we use CO, CO2 and NH3. These calculations demonstrate that, irrespective of the molecule and functional used, interaction energies only start to converge from thirty to forty water molecules onwards. The dispersion energy flattens out earlier, whereas induction and polarisation effects require larger clusters to stabilise, particularly at structurally confined (cavity) sites. We conclude that ice cluster sizes of at least 30-40 water molecules are needed to obtain reliable binding energies, and that cluster size is as important as the choice of the functional.

Soft and continuum robots enable manipulation through distributed body deformation and contact, yet translating language and visual context into executable whole-body actuation remains a fundamental challenge. We present SWIM, a framework that maps an initial RGB observation and a language instruction to a complete actuation-command sequence. Its vision-language-action (VLA) policy, SWIM-VLA, combines a diffusion action head with Visual Soft Proprioception (VSP) through a shared representation of RGB observations, language instructions, and tendon states. The diffusion head models conditional distributions of expert command chunks, while VSP supervises ordered body-anchor predictions using simulation ground truth, encouraging the representation to retain body geometry when learning from limited demonstrations. Embodied mechanical intelligence supports physical execution of command sequences generated through iterative virtual rollout from evolving simulated observations, with intrinsic compliance providing local contact adaptation without online policy queries. We evaluate SWIM on packing, reaching, and grasping on a planar tendon-driven soft robot, with grasping targets anchored. In simulation, SWIM-VLA achieves success rates of 100%, 96%, and 88%, respectively, outperforming an adapted OpenVLA-OFT baseline and controlled ablations. On hardware, SWIM achieves success rates of 100%, 80%, and 75%, compared with 75%, 40%, and 25% for direct online deployment of the same policy checkpoint.

The Thom-Levine theorem is a classical method for proving the triviality of deformations by integrating suitable vector fields. In this note, we show that the converse of this criterion does not hold in the bi-Lipschitz category. More precisely, we give an example of a smooth one-parameter deformation of a real function germ in two variables which is bi-Lipschitz trivial but not strongly bi-Lipschitz trivial. The central germ has an isolated critical point, though it is not finitely determined.

Channel state information (CSI) prediction has emerged as a promising approach for mitigating channel aging in wireless communication systems. Recently, generative models have been employed to develop CSI prediction frameworks capable of modeling the uncertainty in future channel realizations. However, the high computational complexity and inference latency of these models remain major obstacles to their practical deployment. To address these challenges, this paper focuses on a class of one-step generative models, namely MeanFlow models, in which inference requires only a single neural function evaluation (NFE), significantly reducing computational cost and latency. To alleviate the difficulty of generating CSI directly from noise, we introduce a channel-informed prior that initializes the generation process from an informative estimate of the future channel rather than pure Gaussian noise. Incorporating this channel-informed prior substantially improves both point prediction accuracy and uncertainty calibration. Furthermore, we compare the proposed MeanFlow-based CSI prediction framework with a recent diffusion-based approach. The results demonstrate that MeanFlow achieves comparable point prediction accuracy while producing better-calibrated CSI predictions with only a single NFE.

We derive a thermodynamic uncertainty relation for work in an open quantum system driven by a time-dependent protocol and subject to repeated projective energy measurements. The protocol is represented by a sequence of protocol quenches separated by finite-time Lindblad evolution, so that work is accumulated at the quenches while dissipation occurs between them. The resulting work statistics obey the Gallavotti-Cohen symmetry to give rise to the Crooks and Jarzynski fluctuation relations. By perturbing the dissipative dynamics and combining the Cramér–Rao inequality with the quantum Fisher information, we obtain $\mathrm{Var}\,W/[\tau\partial_\tau\langle W\rangle]^2\ge 1/F\ge\max(1/A,2/E)$, where $\langle W\rangle$ is the work expectation value, $\mathrm{Var}\,W$ is the variance of work, $F$ is the Fisher information, $A$ is the dynamical activity, $E$ is the dimensionless entropy production, and $\tau$ is the switching time interval between quenches. The two thermodynamic bounds follow from two independent perturbations that generate the same response of the work statistics. We illustrate the relation for a dissipative two-level system under square-wave and sinusoidal driving and show that the tighter thermodynamic bound can depend on the driving protocol and switching time scale.

Even exact knowledge of the Markov generator at one environmental condition does not determine how that generator changes with the environment unless additional reaction-structure information is supplied. We establish this non-identifiability for mass-action reaction networks driven by a chemostatted species. Distinct chemical embeddings can share the same generator and path law at a reference concentration u0 while differing in how the chemostat enters individual reaction channels. Changing integer chemostat reactant molecularities and rescaling the corresponding kinetic constants preserves all propensities at u0 . This ambiguity already occurs for low-molecularity elementary reactions: a one-species birth–death example has identical path measures at the reference condition but dimensionless stationary sensitivities one and zero. Single-condition data can therefore determine the observed Markov dynamics at u0 without determining their parametric response. As an illustration of the complementary role of prior chemical structure, we also show that a known stoichiometric integral coordinate imposes a conditional zero-frequency identity within the linear-noise approximation.

Structural nonlinearity is the emergence of nonlinear input-output transformations from purely linear processes. In optics, this arises from the multiple interactions of light with input data. Current implementations achieve either a finite number of interactions, or partial modulation of the optical field. In this study, we present an architecture that combines both arbitrarily many interactions and full modulation. Our design consists of a Fabry-Pérot cavity, where one mirror is replaced by a spatial light modulator on which data is displayed. We develop an analytical model from which we derive closed-form expressions for the main metrics of nonlinearity, and find good agreement with experiment. Our analysis extends beyond the present implementation and reveals relationships that are independent of a specific physical system, providing a basis for a unified description of structural nonlinearity, and a first-principles design guide for machine learning applications.

Traditional energy forecasting solutions rely on task-specific supervision and energy asset representations, limiting transferability and the ability to capture general temporal dynamics across heterogeneous assets. We address this by proposing a distributed Joint Embedding Predictive Architecture (JEPA) for self-supervised learning from heterogeneous energy time-series. The framework predicts latent representations of masked temporal segments while integrating temporal observations and contextual information within a shared embedding space. To prevent representation collapse, training combines a latent-space predictive objective with covariance and temporal variance regularization. The evaluation was conducted on energy consumption and generation datasets under data-degradation scenarios and compared with a Transformer forecasting baseline. The learned representations remained stable (cosine similarity $\approx 0.98$; effective rank 185-235). JEPA achieved performance comparable to a Transformer on building energy data, higher $R^2$ in 3/5 consumer clusters, and outperformed the baseline on 9/10 unseen PVs ($R^2$=0.73-0.88 vs. <0.45), while showing greater robustness to missing data.

Companion to arXiv:2609.10614, which built a physics judge that classifies the gap symmetry of a superconductor candidate from its structure and showed that generation in the wire families re-finds the known canon. Here the judge is applied end to end to the single compound that survived its own screen. From 58 iron-pnictide compositions in the electronic window of BaFe$_2$As$_2$ absent from the Materials Project, a zero-cost literature-and-stability screen leaves one with no bulk synthesis and no band-structure, magnetic or pairing calculation: NaFeP (111-type, P4/nmm, Fe$^{2+}$ d$^6$, arsenic-free). The judge, refined with an explicit Stoner gate and a frame-independent symmetry reader, returns a paramagnetic DFT ground state and an s$\pm$ gap: a clean sign reversal between the hole cylinders at Gamma and the electron sheets at the zone corner, at nesting vector (1/2,1/2,1/2), in every basis and cell tried. Whether the gap is nodeless is where the instrument is tested. The phosphorus height (1.16 Å) lies below the empirical threshold of about 1.33 Åseparating nodal from nodeless pnictides, so the structural rule calls NaFeP nodal. The sealed verdict on a metal-only basis said nodeless; a d+p basis that passes the same gates puts the inner hole cylinder at the node threshold (min|g|/max|g| = 0.07-0.10), and a scan of the phosphorus height reproduces, inside one compound, the ingredients of the height rule: a third hole pocket, a switch of the nesting vector to (1/2,1/2,0), a monotonic approach to the Stoner instability, and near-degeneracy of s$\pm$ and d channels beyond 1.33 Å. The prediction we stand behind is the d+p reading: an s$\pm$ superconductor with a near-nodal inner hole sheet, on the LiFeP side of the rule, with the disagreement between bases reported, not resolved by choice. No Tc is asserted; the discriminating measurement, nodal or nodeless, is stated in advance.

Let $F=F(X)$ be a free group of finite rank, with palindromic length taken with respect to the fixed basis $X$. We embed $F$ as the index-two subgroup of the universal Coxeter group $W=F\rtimes_\theta\langle t\mid t^2=1\rangle$, where $\theta(x)=x^{-1}$ for $x\in X$, and prove $\mathrm{pl}(g)=\min{\ell_T(g),\ell_T(gt)}$. Dyer's deletion theorem then identifies reflection length with the minimum number of unmatched positions in a noncrossing equal-label partial matching on a reduced Coxeter word. This gives an $O(n^3)$-time, $O(n^2)$-space algorithm for palindromic length, together with recovery of an optimal palindromic factorization. The matching model also gives a structural characterization. For every ordered full binary tree with $k$ leaves we define a literal word template whose leaves are palindromes and whose internal vertices carry arbitrary words. A reduced word $w$ represents an element of palindromic length at most $k$ if and only if $w$ is a literal instance of one of these templates. Hence the $C_{k-1}$ ordered binary-tree shapes give a complete finite family for each fixed $k$. For $k=4$ the five templates are exactly the five forms proposed by Frid, proving the completeness of that list. A companion Lean 4 development verifies the four-palindrome classification end to end for every finite rank, including the ordinary reduced-word formulation and the literal five-form conclusion.

Continual learning must balance the learning of new knowledge with the retention of previously learned knowledge to incrementally learn tasks from a data stream without catastrophic forgetting. While leveraging pretrained models has significantly advanced continual learning, existing methods exhibit a scalability bottleneck when trained sequentially on many tasks, suffering from performance degradation due to inter-task interference and loss of plasticity. Inspired by evidence that sparse fine-tuning achieves performance comparable to full fine-tuning, this paper presents a novel sparsity-driven continual learning framework. Our continual learning method, termed CLARE, operates in two stages: it first identifies a sparse, task-critical parameter mask via a sparsity-inducing objective, then performs mask-constrained fine-tuning by only optimizing parameters selected by the mask. This two-stage sparse adapter mechanism enables all tasks to be accumulated within a shared adapter space while reducing destructive interference across tasks. Extensive experiments demonstrate the scalability of CLARE. On the long task-sequence benchmark Omnibenchmark-1k, CLARE outperforms strong baselines in final accuracy by a large margin, e.g, improving EASE by 4.64% and 13.34% after learning 100 tasks, respectively.

Empirical mass-radius relations have long been used in exoplanetology to study planet demographics and to predict masses and radii for objects where only one of these is known. Inferred transitions between planet classes can also provide empirical evidence in support of theory. However, mass-radius relations fitted in two-dimensions can be complicated when additional factors influence the planetary parameters, as is the case with the radius inflation of giant planets. In this work, we present an empirical mass-radius relation derived by fitting a broken power-law to a cleaned PlanetS sample from which inflated giants have been removed. We find that when inflated giants are excluded, the preferred model contains three breakpoints and four segments, showing the emergence of a distinct Saturnian regime between $54\pm3~{\rm M_\oplus} <M< 258\pm11~{\rm M_\oplus}$. In this regime, planets are still growing but at a lower rate than the Neptunian regime, consistent with the onset of gravitational self-compression. We also update the irradiation threshold for giant planet inflation, $S_{\rm thr}=99~\rm S_\oplus$ ($1.3~\rm ergs\,s^{-1}\,cm^{-2}$); below $S_{\rm thr}$, 90% of giant planets have a radius excess $\Delta \log{R}<2\sigma$.

Disc evolution dictates the time for planet formation providing the raw material to build the planets' cores. Dynamical stellar masses derived from the kinematics of the gas in discs provide constraints on the ages of very young stars, offering a powerful approach to studying disc evolution and the epoch of giant-planet formation. We investigated a sample of 33 solar-type stars with bright protoplanetary discs and ages between 1 and 9\,Myr. We modeled the spectral energy distributions and ALMA dust continuum images simultaneously to constrain the stellar radius and effective temperature, accretion rate, disc dust mass, the radii of the inner and outer disc regions (roughly separated at the ice line), and the maximum grain size in the inner disc. Combining the stellar masses and radii with stellar evolutionary models, we derived individual stellar ages. We found that the accretion rate and the dust mass of the inner disc evolve with time. The dust mass of the inner disc correlates with the observed accretion rates for stars younger than 2\, Myr. A depletion of centimetre-sized grains in the inner disc is observed in more than half of the analysed stars with ages between 2 and 5\, Myr indicating the action of a mechanism that inhibits the inward drift of large grains, potentially associated with the progressive growth of giant-planet cores more massive than 30 \MEarth, although the exact mass threshold remains uncertain. In addition, three discs exhibiting strong asymmetries in their ALMA continuum emission are associated with stars with ages of $\sim$2\, Myr. The results provide observational indications of significant changes in the dust distribution during the epoch when giant planets may be forming.

Adaptive-Optics assisted astronomical imaging and satellite imaging from the ground share many commonalities but have also specificities. In particular satellites are non-stationary objects in terms of both shape and flux, encouraging relatively short exposure times. Besides, very short exposures freeze the turbulence and preserve high spatial frequency information in speckles, but at the cost of a low image SNR, which complicates the post-processing. Conversely, long exposures lead to speckle-less images where some high frequency information is lost. In this communication, we propose a method for determining the exposure time that optimizes the image quality after post-processing. In particular, we focus on the reduction of the jitter effects – induced by atmospheric tip-tilt residues, vibrations and object non stationarity – which may dramatically reduce the image quality when imaging satellites. Our model takes into account the object type and flux, the residual aberrations power spectral density and the noise level.

Ionization profile monitors (IPM) are used in many accelerator laboratories around the world for non-destructive profile measurements of high-energy particle beams. They have been used in nearly all the synchrotrons built at Fermilab and are presently used in the Main Injector (MI), Recycler (RR), and Booster. This paper will present the current status of the design of a new pair of IPMs to be installed in the Integrable Optics Test Accelerator (IOTA), an experimental proton storage ring with a beam energy of 2.5 MeV. The design incorporates aspects of several IPMs previously or currently used at FNAL. Similar to the Booster IPM, ions are collected rather than electrons, thus requiring no external magnetic field. To increase the signal, each IPM uses two microchannel plates in the chevron configuration as is done in the MI/RR IPMs, and due to the ring's ultrahigh vacuum conditions, the local vacuum pressure is increased with a calibrated leak, akin to the former Tevatron IPMs, to increase the ionization yield per bunch. Data acquisition includes upgraded preamplifiers and leveraging of the digitizer design of the beam position monitor system already in use at IOTA. In addition to the mechanical and electronic designs, simulation results of the effects of the electric fields and injected gas on the circulating beam will also be presented.

Autonomous wheel-loader control requires joint reasoning over task semantics, egocentric vision, proprioception, and 3D scene geometry. We present sensVLA, a Vision-Language-Action (VLA) architecture that combines a Qwen3-2B Vision-Language Model (VLM) with a fully trainable transformer action expert trained by flow-matching velocity regression. sensVLA routes Bird's-Eye-View (BEV) features, extracted from fused front and rear lidar, directly to the action expert through a dedicated cross-attention pathway, while the VLM consumes front and rear RGB views to provide task-conditioned semantic context. This design decouples spatial grounding from linguistic reasoning while preserving interaction between both streams at decision time. The expert predicts six action dimensions: longitudinal velocity, steering, body-frame displacement, arm rate, and bucket rate. On a real-world dataset from a wheel loader, sensVLA reaches aggregate per-step parity with a strong camera-only baseline and reduces longitudinal velocity RMSE by 28% and displacement error by 9% on loading centric scenarios. It also degrades 29% less when the camera stream is corrupted or removed, evidencing that explicit spatial grounding improves accuracy and fault-tolerance for heavy equipment autonomy.

We give new bounds for list sizes of random linear codes at capacity, max loads of linear hash functions, and Furstenberg sets, over every finite field $\mathbb{F}_q$. 1. Random linear codes over $\mathbb{F}_q$ with rate $1 - H_q(p) - \epsilon$ are $(p, O(q H_q(p)/\epsilon))$-list decodable with high probability for all values of $p, q, \epsilon$, including the high error regime. This nearly matches the list size lower bound of $H_q(p)/\epsilon$ due to Guruswami, Li, Mosheiff, Resch, Silas, and Wootters [IEEE Trans. Inf. Theory 2022]. Our bound is the first uniform improvement for $q > 2$ since Guruswami, Håstad, and Kopparty [STOC 2010]. 2. Linear hash functions over $\mathbb{F}_q$ hashing $n$ balls to $n$ bins achieve maximum load $O(q \ln \ln q / {\ln q}) \cdot \ln n / {\ln \ln n}$, both in expectation and with probability $1-o(1)$. This nearly matches the lower bound of $\ln n / {\ln \ln n}$. Previously, only a polylogarithmic upper bound was known for $q > 2$, due to Alon, Dietzfelbinger, Miltersen, Petrank, and Tardos [J. ACM 1999]. We reduce list decodability and linear hashing to strong Furstenberg set lower bounds, which we prove using a new polynomial method of multiplicity gaps. While previous polynomial methods analyze a set $S$ by studying polynomials that vanish on it, we consider polynomials that vanish everywhere, but with higher multiplicity inside $S$ than outside.

While Chain-of-Thought (CoT) reasoning has been proven to be effective, it often leads to overthinking, resulting in computational overhead, inference latency, and even degraded performance in large language models (LLMs). Existing concise reasoning frameworks significantly compromise accuracy while compressing the length of output. In this paper, we propose SKIP, a self-knowledge-guided step-wise preference learning framework. Starting with lightweight fine-tuning to adjust the model's output style, SKIP introduces a carefully designed knowledge probing mechanism to guide model to output an answer at each reasoning step. Based on the correctness of intermediate steps, we construct preference data that guide the model toward more efficient and correct reasoning by leveraging DPO. Experimental results demonstrate that our method effectively improves reasoning compression while mitigating performance degradation after fine-tuning. Besides, SKIP shows strong generalization ability on out-of-distribution datasets. We further conducted ablation studies on the component parameters of our framework.

We present GANADI, a systematic approach for identifying C/C++ OSS reuse genealogies to enhance software supply chain security. Understanding OSS reuse genealogy is crucial for improving SBOM completeness and prioritizing security remediation across supply chains. Although existing approaches can identify reused compo- nents and vulnerabilities within a project, they fail to trace OSS reuse paths through intermediate projects, limiting their effectiveness in securing supply chain ecosystems. To address this limitation, GANADI constructs reuse genealogies by clustering downstream projects based on shared characteristics of origin-derived code (called pivotal functions), and then inferring reuse direction among the projects within each cluster. When applied to 20 widely reused OSS projects with over 1,500 propagation paths, GANADI achieved 84.85% precision and 95.76% recall in identifying reuse genealogies, outperforming existing approaches that achieved at most 23.21% recall. Leveraging OSS reuse genealogy for vulnerability detection, we identified 48 unpatched vulnerabilities in real-world popular C/C++ projects. Among them, 23 were patched following our responsible disclosure (including one CVE ID assigned), demonstrating the practical impact of genealogy-based vulnerability management.

During social movements, protesters need to gather with limited communication means and limited knowledge other than what they observe in their direct surroundings. We propose BeWater, a fully distributed walking protocol that achieves gathering thanks to city information like street length, number of restaurants, number of lanes, or street names. Even though using only one of these observables performs poorly, we show that combining them in more advanced tactics rapidly leads to groups of significant sizes. To do so, our work leverages OpenStreetMap data to perform experiments on several real-world cities.

Protoplanetary discs' infrared water spectra (e.g. as observed by JWST) encode information about the underlying water distribution and physical conditions. In this work, we examine and quantify the imprint of various dynamical processes (operating alone or in unison) on water abundances and emerging spectra using a new 2D model called Molecular emission Affected by Gas, Pebble, and Ice Evolution (MAGPIE). This model combines diffusion and advection for water (and associated species) and dust grains with aerodynamically decoupled pebbles, and photodissociation and a gas-phase water formation prescription. In general, we find that transport processes have a major impact on the inner disc's water content and can (re)plenish the layer above the ice reservoir which in static models is water-poor due to photodissociation. In particular, adding diffusion to a chemical model can result in strong changes in the spectrum (e.g. a flux increases of colder compared to warmer water lines) that recent work has associated with pebble drift. Adding pebble drift dramatically increases the inner disc water abundance but, surprisingly, does not readily lead to a further increase of cold water tracers as (1) efficient outward transport of water vapour is inhibited by a conveyor belt effect of incoming pebbles, and (2) the increase in hot water line fluxes overshadows smaller increases of colder lines. We conclude that dynamical processes have a significant but complex impact on water spectra. Future work should explore a range in stellar (e.g. UV irradiation) and disc properties to comprehensively understand the observed diversity of water emission.