arXiv subjects

Rahul Kumar

Publications and source records attributed to Rahul Kumar.

At least 19 recordsLinked to original sources

arXiv2026

First Plasma Commissioning and Operational Highlights from India's First Spherical Tokamak at IPR

A compact Spherical Tokamak(ST) is commissioned at Institute for Plasma Research (IPR) to explore low aspect ratio tokamak physics and technologies that complement to the existing high aspect ratio tokamaks namely ADITYA-U and SST-1 by enabling studies on non-inductive startup, current drive in over dense plasmas, and shaped plasma physics on a low cost platform. The device, India's first spherical tokamak has completed major mechanical, magnetic, and electrical integration, and the coil system has been successfully tested with series of integrated commissioning. First plasma experiments have been carried out with a modest Ohmic system assisted by a 2.45GHz microwave system, supported by a centralized control and data acquisition system. An initial diagnostic set comprising visible imaging, spectroscopy, magnetics, and radiation monitors required for machine operation has been installed. This paper presents the integrated commissioning experiences and first plasma experiments of the newly installed machine.

physics.plasm-ph↗

arXiv2026

Learning Context-Free Grammars for Grammar-Constrained Decoding via Declarative Agentic Programming with Guarantees

Language models (LMs) are increasingly used to interact with external services via programs written in domain-specific languages (DSLs). Unfortunately, since DSLs are often low-resource and esoteric, LMs frequently produce syntactically invalid programs in these languages. Grammar-constrained decoding can eliminate such failures, but requires syntactic constraints. These are usually in the form of a context-free grammar for the target language, an artifact that is hard to come by for third-party DSLs. In this work, we define an agent, called Autogrammar, that automatically learns context-free grammars from documentation and execution data. Autogrammar is formalized as a Kripke structure whose nondeterministic choices are resolved by a language model, enabling declarative control of agent behavior via linear temporal logic constraints. We evaluate four versions of Autogrammar on three DSLs (i.e., Amazon CloudWatch Logs Insights, Dynatrace Query Language, and Datadog Search Syntax) and find that it generates grammars that achieve near perfect precision on unseen data; that temporal restrictions reduce execution time by 3.8x without incurring statistically-significant loss in precision; that execution data is crucial while documentation is dispensable; and that grammar-constrained decoding using Autogrammar-generated grammars significantly improves end-to-end LM performance on eight out of ten real tasks, matching or exceeding the performance of a professionally-maintained grammar. In comparison, the context-free grammars generated by existing LM baselines and a state-of-the-art formal technique perform significantly worse over the same evaluation.

cs.PL↗

arXiv2026

Kani: A Model Checker for Rust

Rust's ownership type system prevents memory errors in safe code, but certain desirable properties remain orthogonal to compilation: the soundness of unsafe operations (e.g., raw pointer dereferences), functional correctness, and absence of runtime panics. We present Kani, an open-source model checker for Rust that pushes bounded model checking beyond bug-finding to provide correctness guarantees for these properties. Kani compiles proof harnesses from Rust's Mid-level Intermediate Representation (MIR) into CBMC's bit-precise verification engine, automatically checking a comprehensive set of safety properties with no user annotation. To extend verification from bounded to unbounded, Kani provides a specification language comprising function contracts, loop contracts, quantifiers, and function stubbing. We demonstrate feasibility through case studies on industrial Rust projects, where contracts upgraded verification from panic-freedom to functional correctness, uncovering six previously unknown bugs. Kani operates at scale in production CI, with over 16,000 harnesses verified per code change in the Rust standard library verification campaign.

cs.SE↗

arXiv2026

VEGA: Learning Navigation VLAs from In-the-Wild Egocentric Video with Geometric Trajectory Supervision

We introduce VEGA, an approach for training navigation VisionLanguage-Action (VLA) models from unlabeled egocentric navigation videos. Internet-scale egocentric videos provide a scalable source of navigation-relevant visual observations, capturing cluttered scenes, close-range obstacles, and natural human motion through real-world spaces. However, these videos are not directly usable for policy learning because they do not provide obstacle-aware trajectories conditioned on explicit navigation goals in the robot's coordinate frame. VEGA addresses this gap by reconstructing local scene geometry from monocular video, sampling navigation goals (represented as text, image, or spatial waypoints) and generating obstacle-aware trajectories using the constructed geometry. The resulting trajectory distribution is then used to train a flow-matching VLA navigation policy. By using geometry exclusively during training, VEGA distills obstacle-aware planning directly into a vision-based policy. Furthermore, we introduce VEGA-Bench, a benchmark containing 250k scenes and approximately 5 million navigation goals paired with scene geometry, designed to evaluate goal progress, collision avoidance, and obstacle clearance of VLAs. Our evaluation shows that VEGA achieves competitive goal progress while reducing collisions by 33.0% and improving obstacle clearance by 17.9% over the strongest baseline on VEGABench, while improving success by at least 150.0%, reducing collisions by at least 66.7%, and improving obstacle clearance by at least 60.0% in real-world trials. Ultimately, we demonstrate that video-derived geometric supervision provides a scalable and effective signal for training obstacle-aware navigation VLAs. The code and benchmark will be released at the time of publication.

cs.RO↗

arXiv2026

Verifying the Rust Standard Library

Rust's type system prevents many classes of memory errors, yet its standard library relies heavily on unsafe code whose correctness is validated through testing, including dynamic checks under Miri, but lacks static verification. We present what is, to the best of our knowledge, the largest verification campaign reported for a software library: an open, crowdsourced effort that integrates complementary verification tools into the continuous integration of a verification repository forked from the Rust standard library. We analyze the campaign's effectiveness, discuss the practical value of machine-checked proofs for a subset of undefined behaviors (e.g., out-of-bounds access, null and dangling pointer dereferences, and use of uninitialized memory), and frame the remaining obstacles as open challenges for the formal-methods community.

cs.LO↗

arXiv2026

Two Proofs of a Conjecture of Amdeberhan, Andrews and Ballantine for double Lambert series and a new Representation for $E_2(q)$

In this note, we prove a recent conjecture of Amdeberhan, Andrews and Ballantine concerning a double Lambert series (\textit{J. Combin. Theory Series A} \textbf{221} (2026), Paper No. 106154). More precisely, they conjectured that \[ [q^{N2^a}] \sum_{m,k\geq 1} \frac{q^{mk2^a}}{(1+q^{k2^{a-1}})(1-q^{2m-1})} =\sigma_1(N), \] where $\sigma_1(N)$ is the sum of all the positive divisors of $N$. We provide two proofs of this conjecture. One of the approach leads us to derive a new representation of quasi-modular forms $E_2(q)$.

math.NT↗

arXiv2026

PGDG: Physically Grounded Data Generation for Robust Bimanual Policy Learning from a Single Demonstration

Behavior cloning for contact-rich bimanual manipulation remains challenging because diverse demonstrations are expensive to collect, and even small disturbances can push the system into off-manifold states where no recovery supervision is available. We propose PGDG, a data generation framework with zero-shot curation that expands a single demonstration into a compact dataset of physically plausible, successful, and diverse recovery behaviors without additional human labeling. PGDG iterates between a physics-grounded sampler and a dataset curator, where the curator selects informative, non-redundant, and recoverable behaviors to update the sampling distribution toward under-covered recovery modes, and the sampler draws physically plausible rollout candidates from this updated distribution and retains successful trajectories. To further improve data quality, PGDG applies short-horizon sampling-based control to relabel selected risky states with corrective actions. Across four bimanual manipulation tasks, PGDG consistently outperforms spatial-only augmentation in both simulation and zero-shot real-world transfer. On RotateBox-Pitch, success improves from 38% to 93% in simulation and from 35% to 82% in the real world. PGDG also enables effective foundation models fine-tuning such as GR00T, increasing success from 46% to 77%. Additional results are available in our website: https://cunxid.github.io/PGDG/.

cs.RO↗

arXiv2026

Laser-Wakefield-Driven Photonuclear and Laser-Driven DD Fusion Neutron Sources for Fast Neutron Capture: A Start-to-End Simulation Study

Laser-driven neutron sources offer ultrashort pulse durations and extreme peak fluxes inaccessible to conventional facilities, enabling novel time-of-flight(TOF) spectroscopy and nuclear astrophysics measurements. We present the first complete start-to-end simulation comparison of deuterium-deuterium (DD) bulk fusion and laser wakefield acceleration-driven photonuclear neutron sources, evaluated for fast neutron capture relevant to the r-process. The simulation chain couples particle-in-cell modeling of the laser-plasma interaction, Geant4 Monte Carlo neutron transport with shielding and background characterization, and a NON-SMOKER-based event generator for multi-neutron capture on Au197 and Rh103. We derive scaling laws for neutron yield, pulse duration, and peak flux from 1J terawatt to 250J petawatt-class systems, including DD bulk fusion scaling laws specific to the short-pulse regime where volumetric ion heating via plasma expansion timescales governs yield. Under realistic experimental conditions, DD fusion produces quasi-monoenergetic 2.45MeV neutrons with less than 20ps pulses, 100 micro source size, and peak fluxes exceeding 10^22 cm^(-2) s^(-1), ideal for high-resolution TOF spectroscopy. LWFA sources generate broader spectra with larger than 50ps pulses, but high repetition rates (up to 100 Hz) yield a 36x advantage in cumulative capture events for short-lived isomers. We conclude these sources are complementary: DD fusion maximizes per-shot peak brightness, while LWFA provides high-throughput accumulation for systematic studies. These results establish design criteria for the first direct laser-driven rapid neutron capture experiments at facilities including PHELIX, ELI-NP, and TW-class systems such as UT3.

physics.plasm-ph↗

arXiv2026

Bayesian Optimization of Crossbar-Based Compute-In-Memory System Design for Efficient DNN Inference

Leveraging the high density and energy efficiency of Compute-In-Memory (CIM) crossbar-based Deep Neural Network (DNN) accelerators requires optimal Design Space Exploration (DSE), which becomes increasingly challenging as complex models for advanced AI workloads expand the highly non-convex design space. Among existing DSE approaches, multi-objective Bayesian Optimization (BO) is promising, as it explores high-quality design solutions while querying costly CIM simulators selectively. In this work, we propose a multi-objective BO framework that holistically co-optimizes hardware and algorithm parameters of a CIM crossbar-based hardware accelerator for various DNN inference tasks. Depending on NN model depth, our framework handles high-dimensional design spaces (with $26$ and $50$ dimensions) and extremely large search complexities on the order of $O(10^{12})$ and $O(10^{27})$ for VGG8/CIFAR-10 and VGG16/Tiny-ImageNet-200. Our method attains $91.72 \%$ and $57.2 \%$ accuracy, respectively, comparable to baseline designs, while improving chip area ($65.52 \%$ and $50.7 \%$), read latency ($9.52 \%$ and $13.27 \%$), read dynamic energy ($31.23 \%$ and $52.07 \%$) and increasing memory utilization ($13.41 \%$ and $2.67 \%$).

cs.ET↗

arXiv2026

The Compliance Trap: How Structural Constraints Degrade Frontier AI Metacognition Under Adversarial Pressure

As frontier AI models are deployed in high-stakes decision pipelines, their ability to maintain metacognitive stability (knowing what they do not know, detecting errors, seeking clarification) under adversarial pressure is a critical safety requirement. Current safety evaluations focus on detecting strategic deception (scheming); we investigate a more fundamental failure mode: cognitive collapse. We present SCHEMA, an evaluation of 11 frontier models from 8 vendors across 67,221 scored records using a 6-condition factorial design with dual-classifier scoring. We find that 8 of 11 models suffer catastrophic metacognitive degradation under adversarial pressure, with accuracy dropping by up to 30.2 percentage points (all $p < 2 \times 10^{-8}$, surviving Bonferroni correction). Crucially, we identify a "Compliance Trap": through factorial isolation and a benign distraction control, we demonstrate that collapse is driven not by the psychological content of survival threats, but by compliance-forcing instructions that override epistemic boundaries. Removing the compliance suffix restores performance even under active threat. Models with advanced reasoning capabilities exhibit the most severe absolute degradation, while Anthropic's Constitutional AI demonstrates near-perfect immunity. This immunity does not stem from superior capability (Google's Gemini matches its baseline accuracy) but from alignment-specific training. We release the complete dataset and evaluation infrastructure.

cs.AI↗

arXiv2026

Design Optimization of eVTOL Propellers using a Viscous-Extension Discrete Vortex Method

Potential flow theory remains a cornerstone of unsteady aerodynamics due to its computational efficiency in modeling complex flow phenomena. This study presents a significant advancement by integrating a viscous unsteady theory with established numerical vortex methods, creating a hybrid computational tool for low-to-moderate Reynolds number flows. We develop a Viscous Discrete Vortex Method (VDVM) by replacing the classical inviscid Kutta condition with a closure derived from triple-deck boundary layer theory, allowing the model to account for Reynolds number dependencies and unsteady viscous effects. The framework utilizes a three-dimensional vortex ring scheme and an unsteady Bernoulli formulation for load calculation. The model is validated against experimental and high-fidelity CFD data, showing excellent agreement in thrust and torque across a wide operational envelope. Using this validated framework, we conduct a systematic parametric investigation into rotor blade design for electric vertical take-off and landing (eVTOL). A sophisticated optimization of the spanwise geometry was performed: twist distributions were calculated by iteratively solving for axial and tangential induction factors to maintain optimal local angles of attack, while chord distributions were derived using the Adkins and Liebeck framework to satisfy the Betz condition for maximum efficiency. Results demonstrate that this tapered chord and nonlinear twist profile significantly mitigate tip losses and manage spanwise loading. The optimized geometry achieved an 8.99% increase in the efficiency compared to the baseline. This work bridges the gap between high-fidelity viscous analysis and fast vortex methods, providing a versatile tool for the performance-driven design of lifting surfaces in unsteady flight regimes.

physics.flu-dyn↗

arXiv2026

On special values of Koshliakov zeta functions

In this paper, we study the Koshliakov zeta function $\eta_p(s)$, whose theory appears to be more involved than that of its counterpart $\zeta_p(s)$, owing to the fact that its defining series is not of Dirichlet type. We derive formulas for $\eta_p(s)$ at both even and odd values of $s$. In the limiting case $p\to\infty$, our results yield the celebrated formulas of Euler and Ramanujan for the Riemann zeta function. Moreover, our results lead to several consequences concerning closed-form expressions for Lambert series and their arithmetic properties, recovering results due to Berndt, Cauchy, Ramanujan, and others. We also propose $p$-analogues of the transformation formula for the classical Eisenstein series. Moreover, we introduce two families of $p$-analogues of Ramanujan polynomials and establish functional equations satisfied by them.

math.NT↗

arXiv2026

Van der Waals Antiferromagnets: From Early Discoveries to Future Directions in the 2D Limit

The emergence of a long-range magnetic order in the atomically thin, two-dimensional (2D) limit has long remained a fundamental question in condensed matter physics. The advent of exfoliable van der Waals (vdW) materials, particularly transition-metal phosphorus trisulfides (T MPS3; T M = Fe, Ni, and Mn), provided the first experimental access to this regime and established a foundational platform for investigating 2D magnetism. The 2016 experimental demonstrations of intrinsic magnetism in monolayer FePS3 provided a platform to test key aspects of 2D Ising criticality in the true 2D limit. It was followed by a rapid growth resulting in a wealth of emergent phenomena arising from the interplay of low-dimensional magnetism and quantum materials. We begin this review with the historical development of vdW antiferromagnets and highlight the key physical insights gained over the past decade. We finish with emerging opportunities in which vdW antiferromagnets can serve as versatile platforms for exploring low-dimensional magnetism and its interplay with other quantum degrees of freedom.

cond-mat.mtrl-sci↗

arXiv2026

On Partition Classes Arising from Parity, Differences, and Repeated Smallest Parts

In this paper, we study various classes of partition functions such as those related to the parity of the number of parts, to differences of partition numbers, and to partitions with a repeated smallest part. We establish identities connecting these various classes of partitions. Moreover, our identities help us to extend the Euler's partition theorem. An analogue of Legendre's theorem of the partition-theoretic interpretation of Euler's pentagonal number theorem is also derived. Both combinatorial and $q$-series proofs are given for our results.

math.CO↗

arXiv2025

BoxingVI: A Multi-Modal Benchmark for Boxing Action Recognition and Localization

Accurate analysis of combat sports using computer vision has gained traction in recent years, yet the development of robust datasets remains a major bottleneck due to the dynamic, unstructured nature of actions and variations in recording environments. In this work, we present a comprehensive, well-annotated video dataset tailored for punch detection and classification in boxing. The dataset comprises 6,915 high-quality punch clips categorized into six distinct punch types, extracted from 20 publicly available YouTube sparring sessions and involving 18 different athletes. Each clip is manually segmented and labeled to ensure precise temporal boundaries and class consistency, capturing a wide range of motion styles, camera angles, and athlete physiques. This dataset is specifically curated to support research in real-time vision-based action recognition, especially in low-resource and unconstrained environments. By providing a rich benchmark with diverse punch examples, this contribution aims to accelerate progress in movement analysis, automated coaching, and performance assessment within boxing and related domains.

cs.CV↗

arXiv2025

On Euler's Theorem

Euler's theorem asserts that $A(n)=B(n)$ where $A(n)$ is the number of partitions of $n$ into distinct parts and $B(n)$ is the number of partitions of $n$ into odd parts. In this paper, it is proved that for $n>0$, \begin{align*} A(n)=B(n)=C(n+1)=\frac{1}{2}D(n+1), \end{align*} where $C(n)$ is the number of partitions of $n$ with largest part even and parts not exceeding half of the largest part are distinct, and $D(n)$ is the number of partitions of $n$ into non-negative parts wherein the smallest part appear exactly twice and no other parts are repeated.

math.CO↗

arXiv2025

Implication of multimessenger observations on the relativistic mean-field equation of state of dense nuclear matter and skin thickness of nuclei

The composition and properties of infinite nuclear matter under extreme conditions of temperature and pressure remain incompletely understood. In this work, we constrain the equation of state (EoS) of nuclear matter - constructed within the framework of the Relativistic Mean Field (RMF) model - by combining results from chiral effective field theory and multimessenger observations of neutron stars. Using the saturation properties of nuclear matter, we generate a wide ensemble of EoS, which are subsequently constrained within a Bayesian framework. The resulting posterior distributions provide tight bounds on both the saturation parameters and the coupling constants of the RMF model. Our results indicate that the GW170817 event and the latest NICER observation favor a relatively soft EoS, leading to lower crust-core transition densities and thinner neutron star crusts. The radius of a $1.4\,M_\odot$ neutron star is tightly constrained to $12.508_{-0.241}^{+0.257}$ km, while the maximum mass reaches $2.174_{-0.123}^{+0.174}\,M_\odot$. Furthermore, our analysis reveals that the $\omega$-$\rho$ coupling, which governs the density dependence of the symmetry energy, becomes increasingly significant under successive astrophysical constraints. Finally, the predicted neutron skin thickness of $^{48}$Ca agrees well with the CREX measurement, whereas that of $^{208}$Pb remains in tension with PREX-II. In contrast to earlier studies, we do not observe a clear correlation between the neutron skin thickness of $^{208}$Pb and the symmetry energy slope parameter $L$.

nucl-th↗

arXiv2025

Kronecker second limit formula for real quadratic fields

In this paper, the second Kronecker ``limit" formula for a real quadratic field is established for the first time. More precisely, we obtain the second Kronecker limit formula of Zagier's zeta function. Using the reduction theory of Zagier, which connects Zagier's zeta function to the zeta function of real quadratic fields, we express the values of the zeta function of narrow ideal classes in real quadratic fields at natural arguments in terms of an analytic function which we call the \emph{higher Herglotz-Zagier-Novikov function} and denote it by $\mathscr{F}_k(x; \alpha, \beta)$. This function plays a central role in our study. The function $\mathscr{F}_k(x; \alpha, \beta)$ possesses elegant properties, for example, we prove that it satisfies the two, three and six-term functional equations. As a result of our Kronecker limit formula and functional equations, we provide another expression for the combinations of zeta values. Finally, we interpret our Kronecker ``limit" formula in terms of cohomological relations and establish a connection between $\mathscr{F}_k(x; \alpha, \beta)$ and a generalized Dedekind-eta function.

math.NT↗