Papers

In the present article the self-contained derivation of main formulas of the inverse eigenvalue problem for the Sturm-Liouville operator is given on the base of its discrete approximation and the subsequent transition to the limit of the continuum coordinate. In doing so, we adhere to Tikhonov concept, where the discrete approximation is performed as a regularization of the ill-posed operator problem. While the continuum limit for the three-diagonal matrix Hamiltonian is impossible as such, following the Tikhonov procedure leads not to a limit for the potential matrix itself, but rather for a certain combination of the matrix elements, and this limit is precisely the desired potential in the continuum case.

Impact-echo testing is a nondestructive testing method used to detect internal defects in concrete structures. However, boundary reflections, structured interference, and measurement noise can produce complex Fourier amplitude spectra, making defect classification difficult. We constructed a two-dimensional frequency–amplitude persistence image (FA-PI) from the Fourier amplitude spectrum. Using a fixed parameterization of exact multi-parameter persistent homology, each retained Fourier component is represented with frequency-bin location as one coordinate and amplitude as the other, and Gaussian kernels are then applied in this two-dimensional space. This construction has a direct analytical connection to the corresponding one-dimensional Gaussian-smoothed Fourier amplitude spectrum. FA-PI was evaluated on an experimental backfill-void dataset and a public bridge-deck impact-echo dataset, and compared with raw and Gaussian-smoothed Fourier amplitude spectra using a linear classifier with a Softmax output and identical signal-level data splits. The evaluation included original signals and signals corrupted by Gaussian noise, sinusoidal interference, or mixed noise, with matching noise types and signal-to-noise ratios during training, validation, and testing. Performance was assessed using accuracy and macro-averaged precision, recall, and F1-score. Across the two datasets, FA-PI consistently outperformed the raw and Gaussian-smoothed Fourier baselines in the noisy-condition summaries. These findings indicate that representing Fourier spectral components in a two-dimensional frequency–amplitude space can improve impact-echo defect classification beyond frequency-axis smoothing alone.

We study quantum communication, entanglement distribution, and secret-key generation through multimode bosonic loss and fading channels, assisted by local quantum operations and two-way classical communication. Using sector teleportation, we determine the exact two-way quantum and secret-key capacities of multimode pure-loss channels under a mean photon-number constraint, allowing arbitrary adaptive quantum protocols. We extend these results to continuous frequency-dependent loss under a power constraint and identify the optimal allocation of photons among optical modes. For constant loss over an unlimited bandwidth, we obtain a closed-form capacity proportional to the square root of power. For randomly varying loss, we determine exact finite-energy capacities when the channel realization is publicly revealed, distinguishing knowledge before and after transmission. When fading remains unobserved, we derive capacity bounds and explicit formulas for an on/off channel. We also establish strong-converse bounds, with exact thresholds for the deterministic loss models considered here, observed fading, and unobserved fading with finitely many possible transmissivities. Under mean energy constraints, these thresholds generally exceed the corresponding finite-energy capacities. These results guide energy allocation and provide benchmarks for energy-constrained optical quantum communication with multimode signals and variable loss.

Manufacturers often need to characterize a new material, process, or product before enough operating data are available to train reliable predictive models for this new, target domain. Existing manufacturing operations contain potentially useful knowledge to accelerate this characterization, but indiscriminate reuse of data from existing source domains can cause negative transfer in learning of the new, target domain when the manufacturing domains differ sufficiently. This work proposes a reinforcement-learning method for selective knowledge transfer, where its reward scores each opportunity to transfer against supervised alternatives, so negative transfer is avoided and controlled during forward prediction instead of being diagnosed afterwards. Given limited data from a new target domain, the learned policy chooses among predictors based on individual source operations, subsets of the sources, or the supervised alternatives: fully pooled sources, or target data alone. A validation gate deploys the transferred prediction only when it improves upon the supervised alternatives. The method is designed for learning variables supporting carbon accounting, as well as performance and quality outcomes. We demonstrate the approach by quantifying the embodied greenhouse-gas emissions of parts produced via material-extrusion additive manufacturing, using data from 729 experiments spanning five materials: ABS, PETG, TPU, PLA, and recycled PLA. The response combines measured fabrication electricity with polymer-specific cradle-to-gate production factors, while 22 material, process, and toolpath features characterize each experiment. In leave-one-material-out evaluation, this method achieves a mean test RMSE of 5.2 g CO2e per part, 20.00% lower than target-only training (32.5% lower when only 5-10% of the target training data are available) and 10.30% lower than indiscriminate source-target pooling.

Vision-language models (VLMs) that segment from language must pass the location of the referent to a pixel decoder. The dominant interface compresses it into the hidden state of a single [SEG] token, a d-dimensional vector with no spatial index, and leaves the decoder, which never sees the expression, to recover the referent's extent. We show that the VLM already computes a better signal: the [SEG] token's attention over the image tokens, which is defined on the patch grid by construction. Probing a frozen segmentation VLM, we find that this attention yields 18 to 22 more gIoU than the [SEG] hidden state when read by the same probe, that it gains nothing from the image where the hidden state does, and that it is concentrated in the late layers. Building on these findings, we introduce AttnSeg, which replaces the [SEG] embedding with this attention as the decoder's prompt. A learned, signed combination of the attention heads forms a dense spatial prompt, and an attention-guidance objective supervises it directly. A two-stage recipe first trains the VLM to localize without the decoder, then trains the decoder to refine, within the budget of standard fine-tuning. Applied to Sa2VA, AttnSeg improves ReasonSeg by 6.4 gIoU and GS-Eval by 10.2 at 4B (4.2 and 9.6 over the same model fine-tuned on the same data), and by 8.8 and 11.3 at 14B. The gains reach 13 to 18 gIoU on object parts, multiple objects, and single objects, where the referent must be singled out, and are negligible on stuff regions, which the decoder already recovers unaided. Code and models are available at https://eslambakr.github.io/attseg_project_page/

Wilms tumor (WT) is a heterogeneous pediatric renal malignancy. Invasive procedures to establish histology prior to pre operative treatment are not recommended by the International Society of Pediatric (SIOP) Oncology Renal Tumor Study Group, yet different tissue components are associated with different responses to therapy (SIOP Umbrella protocol). Intravoxel incoherent motion (IVIM) magnetic resonance imaging (MRI) may improve subtype differentiation before surgery as a noninvasive radiographic biomarker by capturing both diffusion and perfusion characteristics, as opposed to the conventionally used apparent diffusion coefficient (ADC). The objective of this study is to evaluate the discriminative performance of IVIM MRI in differentiating WT subtypes. IVIM provides quantitative parameters that disentangle the diffusion coefficient (D), incoherent blood flow (pseudodiffusion Dstar) and perfusion fraction (f). This retrospective study included thirthy children with WT. Standardized 1.5T MRI with 10 b value diffusion weighted imaging (DWI) was performed. IVIM parameters were estimated using a selfsupervised implicit neural representations network and were correlated with histopathology via a patient specific 3D printed cutting guide. Statistical analyses included mixed models, receiver operating curve analysis, and logistic regression. Thirty lesions were MRI histopathology correlated on slice level. Significant subtype differences were observed for Dstar stromal versus epithelial (p = 0.024), regressive tumors (p = 0.031) and mixed WT tumors (p = 0.043). ADC showed no significant subtype differences. Direct MRI histopathology correlation enabled differentiation between stromal subtype and epithelial, mixed and regressive subtype on macroscopic slice level using Dstar.

Natural Language Autoencoders (NLAs) are proposed as oversight tools for language models: an Activation Verbaliser (AV) writes an English explanation of an activation vector, and an Activation Reconstructor (AR) maps the explanation back to a vector. Their value for oversight depends on a human monitor being able to tell a true account of an activation from a false one, given the Av's explanation. We formalise NLA training and NLA oversight deployment as two different referential games from Emergent Communication: training is a generative referential game, while oversight is a discriminative, multi-modal, partially-observable referential game played over a many-to-many relation between the monitored language model's activations and the accounts that are true of them. The gap between the two games predicts that AV's explanations will identify which activation they describe without discriminating its true account from closely matched false ones, since training never asks explanations to rule anything out. Using the NLA's own AR as a maximally-sympathetic surrogate monitor model, we experimentally confirm this theoretical insight on one released checkpoint: true accounts beat accounts of other activations in all 320 comparisons, but beat fluent rivals differing in a single claim only 60.2% of the time (std.err. 6.7%, chance at 50%, $n = 35$). A meaning-preserving rewrite by an uninvolved model costs only 2.1% of the distance to another activation's account, so the failure is not due to the NLA pair having developed private conventions in the AV's explanations. Our rival accounts test only transcript-level truths, which the monitored language model's conversation settles, so these results bound the easiest case and leave claims about the monitored model's own processing untested. We state conjectures that would make both results consequences of the framework.

Code-switching (CS), the alternation between languages within an utterance, is common in multilingual speech but underrepresented in pretraining corpora. Increasing CS coverage requires finding relevant utterances in large speech collections so that they can be included in training data. One way to find such utterances is to transcribe the speech and detect language alternation in the text, but this depends on obtaining accurate multilingual transcriptions. We propose a lightweight method that detects CS directly from speech. It uses frame-level language information in pretrained speech encoders to determine whether both languages are present within an utterance. Specifically, we identify language-selective hidden-state dimensions using monolingual recordings and aggregate their frame-level activations into a CS prediction. With a small CS set used to tune a decision rule, we show that the Whisper-small encoder achieves a mean F1 of $0.798$ across 14 language pairs in CS-FLEURS, compared with $0.776$ for a CNN and $0.751$ for a HuBERT linear baseline trained for monolingual language identification. Our findings suggest that pretrained speech encoders already encode the information needed to identify CS utterances, and they provide a lightweight tool for building more representative multilingual corpora.

A transformer trained on sequences whose source parameters are drawn afresh each time can learn only what the sequences share: the source family and its prior. The Bayesian predictor that knows both, which we call informed Bayes, is the unique minimizer of the training loss and is computable from the family alone; we use it as a quantitative, falsifiable reference. Where earlier work compared transformers with Bayes on sources whose contexts can be learned independently, we build Markov sources with up to 64 symbols in which observations in one context inform prediction in another: product sources with known or hidden encodings, transition rows sharing an unknown base law and depth, and a mixture of three families. Our main result is that informed Bayes predicts, from the family and prior alone, how a trained transformer behaves in four tests that go beyond the learning curve: the loss that remains under a source outside the training family (predicted 2.237 bits, measured 2.309), the doubling of the extra loss when two independent components change rather than one (0.345 predicted, 0.350 measured), the benefit of other contexts when a token appears for the first time, and the depth at which copying an earlier continuation starts to pay. On the learning curves themselves, small transformers match informed Bayes when the shared structure is visible in the tokens, and hidden structure needs more layers and training, with gaps below 0.01 bits per token for the largest models. We explain why the imitation is possible and where it must fail: informed Bayes decomposes into sufficient statistics that attention selects and accumulates and an estimator, fixed by the prior, that the feed-forward network learns; training pays the complexity of informed Bayes under the architecture's prior, and finite-memory universal prediction bounds how closely a bounded network can reach it.

The rapid advancement of image-to-text extraction systems and large language models (LLMs) poses new challenges for educational assessment by making assignment materials easy to transcribe and solve with minimal human effort. To address this problem, we present AIRRI (Artificial Intelligence Resilient Reading Interface), a framework for generating machine-resistant educational content, a dataset of higher-education assignments for evaluation, and an initial evaluation of the human readability of AIRRI machine-resistant text designs. AIRRI employs two categories of machine-resistance techniques. First, AIRRI applies image transformations including character spacing, word spacing, line spacing, character opacity variation, stripe overlays, and image noise. Second, AIRRI applies decision-based adversarial attacks: RayS, SurFree, and ADBA. We evaluate AIRRI against three image-to-text systems: Tesseract, EasyOCR, and the transformer-based GOT-OCR2 model. Our results show that AIRRI substantially degrades automated text extraction performance. AIRRI increased character error rates for EasyOCR (6.9% to 55.9%), Tesseract (2.3% to 100.0%), and GOT-OCR2 (30.7% to 48.1%). Word error rates increased for EasyOCR (24.9% to 96.7%) and Tesseract (10.7% to 100.0%). Among the evaluated decision-based attacks, ADBA consistently produced the largest degradation in image-to-text performance, while RayS and SurFree produced more moderate reductions. EasyOCR and Tesseract were generally more susceptible to both image-based and adversarial perturbations than the transformer-based GOT-OCR2 model. Our findings suggest that AIRRI can significantly reduce the reliability of image-to-text-to-LLM workflows, increasing the effort required for AI-assisted assignment completion.

We present an optimal tester for support size that determines whether an unknown probability distribution is supported on $n$ elements or $\varepsilon$-far away (in total variation distance) with sample complexity $\Theta(\frac{n}{\varepsilon\log(n)})$, improving the prior best $O(\frac{n}{\varepsilon\log(n)} \log(\min\{\frac{1}{\varepsilon}, n\}))$ due to Ferreira Pinto Jr. and Harms (STOC 2025). As a generalization, we provide a pretty good lower bound on support size.

The valence-bond-glass state of the 4d^1 double perovskite Ba2YMoO6 combines Mo^5+ singlets with residual paramagnetic "orphan" spins whose coupling is hard to reach with bulk probes. We probe them by electron paramagnetic resonance of a dilute Gd^3+ ion on the Y^3+ site via broadband coplanar-waveguide transmission at 5 K. The isostructural nonmagnetic niobate Ba2YNbO6, doped with the same Gd^3+ probe, is a fixed-lattice control. The Gd^3+ linewidth nearly doubles in the magnetic host. Dipolar coupling to the sparse orphans is nearly an order of magnitude too weak; the excess is instead reproduced by a transferred f-d superexchange of J ~ 0.2 K, so the width is a static measure of orphan-spin coupling. The half-field (Delta m_S = +/-2) satellite collapses in the magnetic host, a dynamical dephasing channel, while the unchanged g-factor marks a zero-mean random internal field. Together the two channels probe the coupling and dynamics of valence-bond-glass orphan spins.

Modern attack surfaces are inherently dynamic. Vulnerabilities emerge over time and they remain exposed to exploit until defenders discover and patch them. Artificial intelligence (AI) amplifies these dynamics by accelerating both offensive and defensive processes, making modern cybersecurity increasingly a competition among interacting time scales and resources. We capture this competition using a queue of branching processes that couples vulnerability discovery and resource-constrained patching with the evolving attacker population targeting each vulnerability. Our primary risk metric is the cumulative number of exploits a vulnerability experiences before it is patched. We derive the expected cumulative number of exploits under birth-death-immigration (BDI) and rise-decay (RD) models of attacker activity. Under a BDI model of attacker activity, we identify a phase transition: the expected cumulative number of exploits is finite only when attacker growth remains below both the vulnerability discovery rate and the effective patching rate. Across both attacker models, increasing the exploit rate does not necessarily increase the expected number of exploits because faster attacker departure can sufficiently limit the active attacker population. Finally, we show that equal proportional AI amplification of offensive and defensive capabilities need not preserve security: accelerating both sides can shift the defensive bottleneck and move the system into an unbounded-risk regime.

We show by explicit counterexample that the Becker–Gottlieb transfer cannot be made functorial. A different counterexample using rational homotopy theory was discovered concurrently by the third author and Robin Stoll.

For Vertex Cover, a minimal blocking set of a graph $G$ is an inclusion-wise minimal vertex set contained in no minimum vertex cover of $G$. Bougeret et al. [SIDMA 2022] showed that, for all minor-closed graph classes $\mathcal{G}$, Vertex Cover has a polynomial kernel parameterized by the distance to $\mathcal{G}$ if and only if $\mathcal{G}$ has bounded minimal blocking sets. In this work, we explore how far this connection between minimal blocking sets and kernelization extends to $\mathcal{F}$-Minor Deletion parameterized by the deletion distance to $\mathcal{G}$. A minimal $\mathcal{F}$-blocking set of $G$ is a minimal vertex set not contained in any optimal $\mathcal{F}$-Minor Deletion solution of $G$. For connected families $\mathcal{F}$, we show that if some graph class $\mathcal{G}$ closed under disjoint union has unbounded minimal $\mathcal{F}$-blocking sets, then $\mathcal{F}$-Minor Deletion parameterized by the deletion distance to $\mathcal{G}$ has no polynomial kernel. This generalizes a result of Hols et al. [SIDMA 2022] for Vertex Cover. We then show that this criterion does not capture all kernelization lower bounds for $\mathcal{F}$-Minor Deletion, even for minor-closed graph classes. Motivated by the work of Dekker and Jansen [Discrete Appl. Math. 2024], we study the more general notion of extended $\mathcal{F}$-blocking sets and the kernelization lower bounds they yield. For every fixed integer $\eta\geq 1$, Pw-$\eta$ Deletion is the problem of deleting at most $k$ vertices to reduce the pathwidth to at most $\eta$. We show that it has no polynomial kernel parameterized by the distance to graphs with pathwidth at most $\eta+1$. Moreover, for connected families $\mathcal{F}$, we show that $\mathcal{F}$-Minor Deletion parameterized by the distance to graphs with pathwidth at most $\max_{F\in\mathcal{F}} pw(F)+1$ has no polynomial kernel.

We prove that the Becker-Gottlieb transfer is not functorial, even on rational cohomology. More precisely, for any even $n \ge 4$, we construct a fibration $f \colon X \to S^{n+1}$ with fiber $S^2 \vee S^n$, and an oriented $S^1$-bundle $g \colon Y \to X$ such that the transfer of $f \circ g$ is non-trivial on rational cohomology. Since the transfer of an oriented $S^1$-bundle vanishes, this implies that the transfer of $f \circ g$ and the composite of the transfers of $f$ and $g$ induce different maps on rational cohomology and are thus not homotopic. The proof that the transfer of $f \circ g$ is non-trivial uses the rational models for the Becker–Gottlieb and THH transfers obtained in previous work of the authors. In the appendix, we provide a second, more involved, proof that relies on constructing explicit $C_\infty$-algebra models for odd spherical fibrations (including circle bundles), which might be of independent interest. Concurrently, another counterexample (of very different flavor) was found by Georg Lehner, Cary Malkiewich, and the first author.

We consider the problem of estimating the expectation of a function (observable) with respect to a high-dimensional probability distribution, under the assumption that a low-dimensional collective variable map captures all the directions of slow mixing for the distribution. More precisely, under the assumption that the fibers of the collective variable map satisfy a log-Sobolev inequality, we establish non-asymptotic relative-error guarantees for this problem using the eigenvector method for umbrella sampling (EMUS). Our analysis applies to both log-Lipschitz observables and indicator of convex sets, and gives complexity bounds that are polynomial in regularity parameters and inverse relative accuracy, and exponential in the dimension of the collective variable space. As a relative error guarantee, our bounds apply to rare event estimation. We consider Gaussian biasing windows defined on a low-dimensional collective variable space and analyze a modified sparse matrix version of EMUS. The bounds quantify the effect of the map through mixing of the conditional distribution and fluctuation of the observable along the fibers.

We study the imaginary part of the holographic timelike entanglement entropy (HTEE) in a charged asymptotically AdS$_5$ black-hole background whose dual field theory exhibits a critical point in the presence of a chemical potential $\mu$ and temperature $T$. Identifying the imaginary part of the HTEE with the imaginary part of the pseudoentropy, we derive an analytical expression for this quantity and investigate its behavior on the stable and unstable thermodynamic branches. We find that the imaginary HTEE vanishes in the uncharged limit and is induced entirely by a nonzero chemical potential, signaling the emergence of quantum coherence between the initial and final states. As the dimensionless ratio $\mu/T$ approaches its critical value, we obtain an inverse-square-root divergence in the derivative of the imaginary HTEE and extract the critical exponent $\theta_I = 1/2$ analytically. We further show that the same exponent governs the temperature response at fixed chemical potential. Our results establish the imaginary part of the HTEE as a non-local quantum-information probe of criticality in strongly coupled systems, and they imply that the initial and final states become maximally coherent at the critical point.

We quantize, in the homogeneous temporal gauge, both the electric and the magnetic Carrollian Yang-Mills theories with SU(N) gauge symmetry in the fundamental representation. We use the BRST method implemented in the path integral. We show that in the first case all the interaction vertices vanish, thus, giving a free theory. In the magnetic case, there are no loop contributions to the Green functions of the elementary fields –i.e., Green functions not involving composite operators– and the only connected parts of such Green functions with a dependence on the coupling constant are the tree level contributions to the three and four point functions of the field $\xi_i$. We also show that in the magnetic case the Green functions involving only Wilson loops are trivial and not so in the electric case.

Non-clashing teaching minimizes teaching complexity among models satisfying the Goldman–Mathias collusion-avoidance criterion. While the Vapnik–Chervonenkis dimension (VCdim) measures the complexity of learning from samples, non-clashing teaching dimension (NCTD) measures the number of examples required when a teacher can select them. Whether NCTD is always bounded above by VCdim remains a fundamental open question in learning theory. In this paper, we investigate this question for the concept classes of closed neighborhoods in planar graphs. We prove a tight upper bound of two on their NCTD, thereby establishing the conjectured inequality for this family. For the positive variant NCTD+, in which teaching sets contain only positive examples, we obtain a tight upper bound of four. Finally, we show that deciding whether either NCTD+ or NCTD is at most one is NP-complete, even for concept classes of closed neighborhoods in planar graphs. In particular, despite the upper bound of two on NCTD for such classes, distinguishing between NCTD values of one and two remains NP-hard.

The rational exponents conjecture of Erdős and Simonovits asserts that for every rational $r\in [1,2]$ there exists a graph $H$ such that $\mathrm{ex}(n,H)=\Theta(n^r)$. We present a proof of this conjecture claimed by Epoch AI, explaining how it builds upon ideas and methods developed by many researchers.

We introduce PULSUS, a direct frequency-domain framework for multidimensional spectroscopy of open quantum systems beyond the impulsive rotating-wave approximation. Coherence-frequency intervals are represented through Liouvillian resolvents, while finite Gaussian pulses are incorporated through operator-valued functions of the field-free Liouvillian. This enables direct evaluation on Cartesian grids or arbitrary spectral coordinates while retaining molecular evolution during the pulse envelopes and, when required, the complete light–matter interaction. The implementation is validated against analytical and independent time-domain benchmarks and supports targeted spectral sampling that reduces the number of evaluated coordinates when the response is spectrally localized. A controlled hierarchy of finite-pulse, rotating-wave, short-pulse, and impulsive models separates the errors introduced by each approximation. For a coupled electronic dimer, the total impulsive-RWA error is nonmonotonic in pulse duration: an intermediate regime provides the highest accuracy, whereas ultrashort pulses expose coupling-enabled beyond-RWA pathways and longer pulses develop substantial finite-pulse corrections. These results show that the impulsive and rotating-wave approximations cannot be assumed to improve simultaneously and should be tested when quantitatively interpreting multidimensional spectra. PULSUS provides a direct frequency-domain framework for carrying out that comparison.

Current recipes for robot learning require massive amounts of robot demonstrations to obtain robust and adaptive policies. In this work, we introduce Steertuning, a system that enables robots to learn new tasks in new environments from 5 human demonstrations in under 5 Steertuning consists of two parts. (1) We pretrain a 400M-parameter diffusion policy on our egocentric human dataset, which consists of 100 hours of densely annotated random interactions. This pretraining makes Steertuning robust to background differences and enables spatial and object generalization when deployed on new tasks. (2) Given 5 demonstrations of a new task, we finetune our model for only 2 minutes (2000 training updates) and steer the policy's actions during reverse sampling using the demonstration whose observation is closest to that of the deployment environment. Together with a carefully designed data processing pipeline for embodiment transfer, this enables Steertuning to achieve a 71% success rate across 12 tasks in 12 new environments, ranging from lab settings to kitchens in new homes. The entire process, from data collection for a new task to robot policy deployment, takes less than 5 minutes. Our full dataset, model weights, codebase, and robot videos will be made available at our website: https://steertuning.github.io.

The Canadian Hydrogen Intensity Mapping Experiment (CHIME) has published its second catalog of 3,641 fast radio bursts (FRBs). While this sample includes 981 bursts from 83 repeating sources, only 2.3% of CHIME FRBs are observed to repeat. This raises the question of whether the FRB population truly consists of a single repeating population or includes a distinct subpopulation of one-off sources. We apply Simulation Based Inference (SBI), a likelihood-free machine learning framework, to model the CHIME/FRB Catalog 2 dataset, testing eight FRB population models, half of which include a subpopulation of truly one-off sources. The current catalog strongly and decisively favors models including such a subpopulation, with the best-fitting model combining a log-normal burst rate distribution, a Poissonian wait-time distribution, and a one-off subpopulation. This preference is corroborated by an independent random forest classifier and by the ability of one-off models to naturally reproduce the hyperactive repeating sources present in the catalog without having been trained on them. We place upper limits on the potentially observable CHIME/FRB population of 36,000 repeating sources and 19 one-off sources per day in the CHIME sky. Models with a one-off subpopulation naturally account for the hyperactive repeating sources present in the catalog without having been trained on them, providing an independent consistency check on our results. We predict the repeater percentage will fall below 2% in the next five years, eventually declining to ~0.5% as the sample saturates with one-off detections.

We construct Schauder bases of $L^p(\mathbb{R})$ with significant structural constraints on their elements. First, we construct non-negative Schauder bases of $L^p(\mathbb{R})$ for every $1 \leq p < \infty$. Although such bases cannot be unconditional, their basis constants can be made arbitrarily close to one. By duality, we also obtain bases with positive biorthogonal functionals and the same bounds for all $1\leq p<\infty$. Finally, we prove that $L^p(\mathbb{R})$ admits a Schauder basis consisting of translates of a single function for every $2\le p<\infty$. The generating function $f$ can be chosen to be the restriction to $\mathbb{R}$ of an entire function. For $p>2$, the translation parameters can be chosen from any prescribed unbounded subset of $\mathbb{R}$, a conclusion that fails for $p=2$.

Long-term infrastructure investment often requires choosing between an established technology and a capital-intensive alternative that gains value as demand matures. For electric vehicle (EV) charging, this trade-off is between incumbent stationary charging technology and emerging dynamic wireless charging (DWC). DWC could fundamentally alter transportation electrification by enabling high-throughput charging in motion and reducing reliance on large onboard batteries; however, its high upfront cost makes the timing and location of deployment critical. Overcommitting to stationary charging stations (SCS) risks technological lock-in and forgoing the benefits of DWC, whereas premature DWC deployment can strand capital in underutilized corridors. Through a joint investment assessment framework coupling DWC, SCS, and supporting grid infrastructure across nearly 49,000 miles of the US Interstate freight network, we find that higher utilization and longer project lifetimes rapidly shift investment toward DWC, whose share rises sharply from 48% at a project lifetime of 30 years to 100% at 32 years. Contiguous DWC segments can share grid connections, enabling them to provide over six times the rated charging capacity of SCS while requiring 46% less investment in new distribution-grid infrastructure. We also find that a combined DWC and SCS portfolio reaches a maximum lifetime value of USD 60 billion, 63% above the case with only SCS. We further identify specific traffic demand, construction, and grid access conditions that shape where each technology becomes advantageous, yielding actionable thresholds for SCS and DWC deployment that directly inform long-term EV charging infrastructure investment and policy.

We investigate parity violation searches with the 4-Point Correlation Function (4PCF) using the Quijote and Quijote-Odd halo catalogs. Specifically, we explore the auto- and cross-correlation searching methodologies that have been previously used in the Baryon Oscillation Spectroscopic Survey (BOSS) and the Dark Energy Spectroscopic Instrument (DESI) searches. Although the Quijote-Odd simulations are initialized with a parity-violating primordial trispectrum, we find no statistically detectable parity-odd signal in the halo 4PCF. Instead, we find that the halo measurements are dominated by Poisson noise. We are able to distinguish this noise-dominated behavior from the response expected for a parity-odd signal. These results clarify how parity-sensitive 4PCF statistics respond to noise in a controlled simulation setting.

We study a local stochastic volatility (LSV) model in which the variance factor follows a generalized Langevin equation (GLE) with colored noise, and past returns act on variance through a memory kernel with state-dependent amplitudes. For kernels given by finite sums of exponentials, we prove existence, uniqueness, and non-explosion under a growth condition linking the volatility map to the potential. In a one-mode family with a polynomial potential, feedback through log returns can cause explosion exactly when the squared volatility factor grows faster than the restoring force. Under structural and nondegeneracy conditions, an exact reduced Markovian state has a smooth density solving a deterministic forward equation. The Dupire conditional expectation therefore requires no stochastic partial differential equation. Under a bounded Sharpe ratio, exponential utility selects the minimal entropy martingale measure, whose premium solves a quadratic backward stochastic differential equation. Under a regularity hypothesis, which we verify in special cases with and without leverage, the premium depends only on the current state, and the squared VIX equals the expected average future local stochastic variance. Finally, a regularized calibration problem with bid–ask constraints admits a minimizer whenever a feasible point has finite objective value.

The Held–Karp bound is a linear-programming lower bound for the metric traveling salesperson problem (TSP). We approximate this bound in the multi-pass insertion-only streaming model for metrics induced by connected positive-weight graphs. For an $n$-vertex, $m$-edge graph and $0<\eps\le1/2$, the algorithm returns a $(1+\eps)$ upper approximation with high probability, using $\wtO(\eps^{-4})$ passes, $\wtO(n\eps^{-2})$ words, and $\wtO(m\eps^{-4})$ arithmetic operations per pass. We replace the changing edge-weight vector by a short history of multiplicative-weights (MWU) updates. After initialization, updates repeat until a column is removed. We store each repeated update once, with its repetition count. The record length depends on the number of columns, not updates; the argument applies to any fixed nonnegative matrix. For Held–Karp, tree-path queries recover edge weights from these records. Separate search and update thresholds allow fresh sparsifiers at successive search stages. Controlled rounding gives a bounded-precision implementation. The estimate yields a $(3/2+\eps)$ graph-metric TSP value estimate and a $(7/5+\eps)$ estimate when the input graph is unweighted. Conversely, in weighted graph streams, every one-pass $(1+\eta)$ upper approximation to Held–Karp, for fixed $0\le\eta<1$, requires quadratic space. The algorithms estimate values; they do not construct tours within these bounds.

In this paper, we propose an extremely efficient, training-free method to extract token-level reward signals directly from an existing deep reward model. Our core idea is to attribute the overall process reward to individual tokens by estimating each token's influence. This influence is defined as the change in the final macroscopic reward (e.g., the process reward) when a token is replaced with a semantically null token. Naively calculating this influence is computationally infeasible, requiring N forward passes through the PRM for an N-token sequence. We overcome this bottleneck by proposing a highly efficient gradient-based estimator. Specifically, we use a first-order Taylor approximation, which simplifies the influence calculation to the inner product of the difference between the token embedding and the null token embedding, and the gradient of the reward with respect to the token embedding. This requires only a single forward and backward pass. The resulting token-level rewards enable standard RL algorithms to perform precise credit assignment without requiring additional reward model training. Experiments on challenging reasoning benchmarks demonstrate that our method substantially improves policy optimization efficiency and enhances the generalization of LLM reasoning capabilities. Our P2T outperforms the outcome reward by +4.9% on MathVista for Qwen2.5-VL-7B-Instruct, and +11.5% on AIME24 for Qwen2.5-Math-7B. The code will be released via https://github.com/stonewst/P2T.