arXiv subjects

Sumit Kumar

Publications and source records attributed to Sumit Kumar.

At least 19 recordsLinked to original sources

arXiv2026

Physics-Informed Identification of Tensegrity Prestress across Taut-Slack Transitions

Prestress governs the stability, stiffness, and dynamic behavior of tensegrity structures, but it is not directly observable from sparse structural measurements, and it may decrease during service life. Under strong excitation, the cables may slacken and the dynamics become nonsmooth. Existing identification methods are limited to the taut regime, and physics-informed networks for tensegrities solve only the forward problem of predicting the response from known member parameters. This study formulates the inverse problem. Neural networks are trained on the equation-of-motion residual in constrained Cartesian coordinates, where the mass matrix is constant and the force densities enter linearly. The force densities, damping, and axial stiffness are trainable parameters, and the tension-only cable law is kept. A Fisher-information analysis shows, before inversion, which member parameters a record can determine. The method is tested on simulated planar tensegrity frames with up to five modules and a three-dimensional prism, and on measured records of a biomimetic leg and a full-scale tensegrity simplex. On the one-module frame, the identifiable force densities are recovered within 1.5% from noisy accelerations at half the free coordinates, on records with and without taut-slack transitions. Records with transitions determine members that taut records leave undetermined. On the five-module frame, a 16-cable two-span bridge, the median force-density error rises moderately, to 4.2%. On measured records, an identified spring stiffness is within 0.1% of its independently measured value on average, and the identified simplex prestress at 13 levels agrees with its cable force transducers to 2.9% root-mean-square.

cs.LG↗

arXiv2026

Runtime Control for AI Agents: Closing the Evaluation--Execution Gap in Operational Workflows

Language-model agents increasingly participate in operational workflows where approvals, binds, and payments create commitments. An approval valid when issued may no longer authorize execution after relevant facts, evidence, policy, or authority change. We call this the evaluation--execution gap. We specify a state-bound runtime assurance layer that separates probabilistic measurement from deterministic adjudication, binds an execution allowance to the decision-relevant basis of an approval, invalidates that allowance after relevant logged changes, and rechecks admissibility at dispatch. This distinguishes the continued validity of a prior approval from a current-state policy check. We describe eight failure modes, an assurance model, a reference architecture, and prospective interventions with retrospective remediation. In a scripted 42-case replay, the state-bound configuration identifies 15 later-invalidated approvals that a deliberately non-re-evaluating point-in-time comparator does not revisit; it holds 14 affected actions before dispatch and compensates one landed effect. These results illustrate behavior under the stipulated policies and event orders, not superiority over dispatch-time enforcement designs or production effectiveness. Under explicit interception, ingestion, dependency, and serialization assumptions, the model establishes dispatch-time validity within the registered execution surface.

cs.AI↗

arXiv2026

Kadison-Kastler Distance and Interior Angle for Masas: Connections with Entropy and Probabilistic Index

We study the Kadison--Kastler distance and the interior angle between masas in finite-dimensional matrix algebras. In $\mathbb{M}_2(\mathbb{C})$, we obtain an explicit formula for the Kadison--Kastler distance between two masas and show that every value in $[0,1]$ is attained by $\mathrm{d}_{\textrm{KK}}(Δ,uΔu^*)$. We further prove that the distance attains its maximal value precisely when the relative unitary is a Hadamard unitary. In addition, for every $v$ in the groupoid normaliser of $Δ$, the Kadison--Kastler distance between $Δ$ and $vΔv^*$ assumes either its minimal or maximal possible value. We also establish the identity \[ \mathrm{d}_{\textrm{KK}}(\mathcal{A},\mathcal{B})=\sinα(\mathcal{A},\mathcal{B}) \] for any two intermediate subalgebras $\mathbb{C}\subsetneq\mathcal{A},\mathcal{B}\subsetneq\mathbb{M}_2(\mathbb{C})$. Most notably, for any unitaries $u,v\in\mathbb{M}_2(\mathbb{C})$, we establish the equivalence of maximal Kadison--Kastler distance, maximal interior angle, maximal Connes--Størmer modified entropy, and minimal Popa probabilistic index: \[ \mathrm{d}_{\textrm{KK}}(uΔu^*,vΔv^*)=1 \iff h(uΔu^*,vΔv^*)=\log 2 \iff α(uΔu^*,vΔv^*)=\fracπ{2} \iff λ(uΔu^*,vΔv^*)=\frac{1}{2}. \] For general $\mathbb{M}_n(\mathbb{C})$, we prove a unitary invariance property for the interior angle and derive an explicit formula for the angle between arbitrary masas of the form $uΔ^{(n)}u^*$ and $vΔ^{(n)}v^*$. As a consequence, the interior angle is $\fracπ{2}$ precisely when the relative unitary $u^*v$ is a Hadamard unitary. Finally, we show that every value in $\left[0,\fracπ{2}\right]$ is attained as the interior angle between a pair of masas in $\mathbb{M}_n(\mathbb{C})$.

math.FA↗

arXiv2026

Distances Between von Neumann Subalgebras: Spin Models, Commuting Squares, and Free Group Factors

We investigate the relative position of von Neumann subalgebras through the Mashood--Taylor ($\mathrm{d}_{\mathrm{MT}}$) and Kadison--Kastler ($\mathrm{d}_{\mathrm{KK}}$) distances and the interior angle. For each $n\in\mathbb{N}$, we show that the hyperfinite $\mathrm{II}_1$-factor $\mathscr{R}$ contains an uncountable family of pairwise distinct regular $n\times n$ spin model subfactors. In particular, this yields a continuous family $(\mathscr{R}_{\mathsf{H}_α})_{α\in[0,π)}$ of $2\times2$ spin model subfactors which, equipped with $\mathrm{d}_{\mathrm{MT}}$, is homeomorphic to the circle group $\mathbb{T}$ and admits a natural topological group structure. We further establish \[ \mathrm{d}_{\mathrm{MT}}(\mathscr{R}_{\mathsf{H}_α},\mathscr{R}_{\mathsf{H}_β}) =\vert\sin(α-β)\vert. \] We prove that two such spin model subfactors form a commuting square over their intersection if and only if they are maximally distant. More generally, commuting squares of $\mathrm{II}_1$-factors, under natural index conditions, force maximal distance, yielding $\mathrm{d}_{\mathrm{KK}}=1=\mathrm{d}_{\mathrm{MT}}$. We also show that diffuse subalgebras which are orthogonal in the sense of Popa are maximally distant. In contrast, no two members of the above spin model family are Popa-orthogonal. Nevertheless, maximal distance between two such subfactors implies that their interior angle over the intersection is $π/2$, highlighting the distinction between angle orthogonality and Popa orthogonality. Finally, in $L(\mathbb{F}_2)=L(\langle a,b\rangle)$, for $u\in L(\langle b\rangle)$, we obtain \[ \mathrm{d}_{\mathrm{MT}}(L(\langle a\rangle),uL(\langle a\rangle)u^*) =\sqrt{1-\vertτ(u)\vert^4}, \] and construct maximally distant masas not arising from subgroups of $\mathbb{F}_2$.

math.OA↗

arXiv2026

Benchmarking Neural Defend ARCAS 1B: A Foundational Multimodal Deepfake Detection Model

AI-generated imagery evolves faster than benchmark-specific detector evaluations, making a single score an incomplete account of generalization. This paper evaluates Neural Defend ARCAS 1B across benchmark families without benchmark-specific parameter updates. We retain native aggregation and supplement it with record-level measures, coverage accounting, and subgroup diagnostics. Each Results subsection identifies the release and evaluation population, reports the official metric, and describes observed error patterns. A combined analysis synthesizes shared patterns while preserving the distinction between native and pooled quantities. Cross-paper comparisons are restricted to aligned evidence; differences in release, population, preprocessing, training, or benchmark exposure are context rather than rank. The findings characterize performance on evaluated records, not universal reliability, calibration, attribution, or future adaptive attacks. By keeping benchmark-native outcomes distinct from pooled summaries, the study makes test-population, class-balance, and missing-record-coverage differences visible. It supports interpretation of detector results in research, platform-safety, and forensic-review settings, foregrounding traceable protocol conditions over claims or leaderboard comparisons.

cs.CR↗

arXiv2026

Compositional Policy Violations: When Step-Level Compliance Fails In Agentic AI Workflows

Agentic workflows now make consequential decisions in regulated settings, and the governance placed around them is almost entirely step-scoped: input-output classifiers, per turn rails, and span-level evaluators. The policies organizations actually hold, such as referral thresholds, authority limits, and review requirements, are properties of the whole execution rather than of any one step. This mismatch admits a failure mode we call a Compositional Policy Violation (CPV): every individual step passes its own check while the composed execution violates the governing policy. A predicate over a single step cannot evaluate a property that step does not determine, so no improvement in the accuracy of the step-scoped monitors detects this class. We define CPVs as the failure of step-level compliance to compose, and present a taxonomy of four types: Authority Creep, Threshold Laundering, Cumulative Sum Violation, and Context Collapse. We show that the correct repair for each class is dictated by where the guarded quantity mutates. We then introduce a provenance-aware runtime architecture that evaluates policies over complete execution traces, recomputing guarded quantities from raw provenance rather than the pipeline's derived representation.

cs.AI↗

arXiv2026

$TCP_α$: Margin-Controlled Confidence estimation for reliable Music Information Retrieval

Deep neural networks are often overconfident, assigning high confidence even to incorrect predictions. Consequently, users lack a reliable signal for deciding when a prediction can be trusted. Post-hoc confidence estimation addresses this by training a lightweight auxiliary head over a frozen classifier. Existing targets, however, suffer from inherent ambiguity: they assign overlapping confidence values to correct and incorrect predictions, while errors near the decision boundary receive confidence scores indistinguishable from correct predictions. In this work, we propose $TCP_α$, a novel confidence target that resolves these limitations by introducing a margin-controlled penalty for misclassified samples. We prove that $TCP_α$ guarantees complete separation between the target values of correct and incorrect predictions, with a separation margin that is independent of the number of classes and increases monotonically with the penalty parameter. Since accurate classifiers naturally produce very few errors, learning these targets results in a severely imbalanced regression problem. We therefore present a systematic study of training strategies for learning under this imbalance and identify an effective training configuration through extensive ablation studies. We evaluate the proposed approach on rāga identification, investigate its robustness under domain shift, and further validate it on frame-wise ornamentation detection without modifying the selected configuration. Across all settings, $TCP_α$ consistently outperforms existing confidence targets for failure prediction. Rejecting only the least-confident 8\% of predictions improves the base model's macro-F1 from 0.89 to 0.98, while fine-tuning the confidence head with only 5\% labeled samples from a new corpus effectively restores performance under domain shift.

eess.AS↗

arXiv2026

Shaping SHAPE - A spectro-polarimeter onboard Chandrayaan-3 to observe Earth as an Exoplanet

Spectro-polarimetry of HAbitable Planet Earth (SHAPE) is an experimental instrument onboard the Propulsion Module (Orbiter) of the Chandrayaan-3 mission, designed to perform disc-integrated spectro-polarimetric observations of Earth from lunar and highly elliptical Earth orbits. SHAPE is a compact, lightweight spectro-polarimeter comprising three subsystems: the Electro-Optical Detector System (EODS)-Optics, EODS-Electronics, and Radio Frequency Source (RFS). An Acousto-Optic Tunable Filter (AOTF), driven by an in-house-developed 80$-$135 MHz RF source, provides spectral filtering in the near-infrared (NIR) wavelength range of 1.0$-$1.7 $μ$m and produces two narrow-band beams with mutually perpendicular linear polarization states. The instrument optics, with a field of view of approximately 2.6°, focus the two beams onto InGaAs detectors. A spectral resolution of 2$-$4 nm is achieved using in-house-designed low-noise front-end electronics. The instrument also incorporates processing and power electronics for signal processing, detector biasing, and subsystem control. We present the overall instrument design, results from pre-launch ground-based testing, and in-orbit operational performance. The current configuration enables SHAPE to measure disc-integrated signatures of Earth over a range of phase angles, providing a test bed for characterizing Earth-like exoplanets and benchmarking future exoplanet observations.

astro-ph.IM↗

arXiv2026

A Complete Characterization of Cartan Inclusions of Finite Dimensional $C^*$-algebras

We give a complete characterization of Cartan inclusions of finite dimensional $C^*$-algebras in terms of their inclusion matrices. More precisely, for a unital inclusion $\mathcal{B}\subseteq\mathcal{A}$ with inclusion matrix $Λ=(Λ_{ij})$, where Cartan means that $\mathcal{B}$ is a \emph{generalised Cartan subalgebra} of $\mathcal{A}$ in the sense of Exel, we prove that the inclusion is Cartan if and only if \[ \sum_i Λ_{ij}\leq 1 \] for every $j$. We call matrices satisfying this condition \emph{multiplicity free}. Thus, our characterization provides a purely combinatorial criterion for determining when a finite dimensional inclusion is Cartan. We further prove that every Cartan inclusion admits a unique conditional expectation from $\mathcal{A}$ onto $\mathcal{B}$. Conversely, we show that, for unital inclusions of finite dimensional $C^*$-algebras, the uniqueness of the conditional expectation is sufficient for the inclusion to be Cartan. Consequently, a unital inclusion $\mathcal{B}\subseteq\mathcal{A}$ of finite dimensional $C^*$-algebras is Cartan if and only if there exists a unique conditional expectation from $\mathcal{A}$ onto $\mathcal{B}$.

math.OA↗

arXiv2026

A Complete Characterization of Regular Inclusions of Finite Dimensional $C^*$-algebras

We give a complete characterization of regular (in the sense of Kumjian and Renault) unital inclusions of finite-dimensional $C^*$-algebras. For subalgebras $\bigoplus_j( \mathbb{M}_{d_j}(\mathbb{C}) \otimes \mathbb{I}_{p_j})$ of $\mathbb{M}_n(\mathbb{C})$, we show that regularity depends only on equality of the multiplicities $p_j$, while unitary regularity---characterized recently by the first author and Silambarasan---additionally requires equality of the $d_j$; we recover the latter via a streamlined alternative proof. Extending this to inclusions of arbitrary finite-dimensional $C^*$-algebras, encoded by an inclusion matrix $Λ$, we show that regularity is equivalent to an explicit row/column condition on $Λ$---coinciding with the normalizer matrix introduced by the first author and Silambarasan ---so that the device used there to detect unitary regularity is shown to characterize regularity in general; unitary regularity is recovered by a further dimension-equality condition.

math.OA↗

arXiv2026

Cyber security of OT networks: A tutorial, survey of attacks and overview of current state of defense tools, protocols, & challenges

The convergence of Operational Technology (OT) and Information Technology (IT) under Industry~4.0 has widened the cyber-attack surface of critical infrastructure across manufacturing, energy, transportation, water, and healthcare. This survey synthesizes OT/IT cybersecurity along four axes. First, we taxonomize \emph{attack vectors} that traverse the IT--OT boundary, separating IT-side initial access (phishing, exploits, supply-chain compromise, exposed remote access) from OT-side propagation and impact (insecure protocols, weak authentication, firmware tampering, control-logic manipulation). Second, we review \emph{defensive technologies} -- signature-based intrusion detection, AI/ML anomaly detection, Zero Trust Architecture, blockchain-based event logging, digital twins, and OT-aware Security Operations Centers -- and identify remaining \emph{gaps}: OT-specific patch management, dataset scarcity for ML, IoMT segmentation, and the absence of consistent resilience metrics. Third, we compile a cross-validated \emph{historical record} of 69 high-impact incidents spanning 2010--2025, from Stuxnet to Jaguar Land Rover, and quantify their \emph{commercial effects} sector by sector using figures sourced from SEC filings, government post-incident reviews, and primary regulatory disclosures. Fourth, we map the \emph{regulatory landscape}: NIST Cybersecurity Framework2.0 and SP~800-82~Rev.~3, IEC~62443, the EU NIS2 Directive, DORA, the Cyber Resilience Act, NERC~CIP, and healthcare-specific regimes (IEC-80001-1, FDA, NIST-SP-1800-8). A sectoral deep-dive on healthcare illustrates the IT--OT convergence threat model under high-consequence conditions. The result is a single, source-traceable reference on where OT/IT cybersecurity stands, what the historical record costs defenders who lag, and where investment yields the highest marginal return on resilience.

cs.CR↗

arXiv2026

Simulating Unified Tensor Resharding in heterogeneous AI systems

State-of-the-art AI training simulators assume homogeneous compute and network infrastructure. However, real-world training infrastructure is becoming increasingly heterogeneous since: (a) Model architectures such as multimodal and MoE exploit heterogeneity to improve device utilization, (b) Public cloud platforms often provide limited availability of homogeneous hardware due to fast hardware evolution, and (c) Large enterprises frequently deploy geographically distributed infrastructure that is both diverse and heterogeneous. In this paper, we present Xsim, a heterogeneity-aware simulator for distributed LLM training. Xsim supports: (i) Load balancing through non-uniform workload partitioning across heterogeneous device groups, (ii) Heterogeneity-aware collective communication via customized ring construction and chunk partitioning, (iii) Reusable heterogeneity-aware abstractions for emerging pipeline-parallel algorithms and non-uniform tensor resharding technique, (iv) Flexible input abstractions for specifying deployment plans with custom device groups and custom device-to-parallelism mappings, and (v) Pluggable integration with NS-3 and htsim, allowing users to trade off simulation fidelity for performance and scalability. Our evaluation demonstrates that Xsim accurately predicts training time for real-world heterogeneous deployments, with an error of less than 5% across most heterogeneous data-parallel/tensor-parallel configurations and around 2% error with pipeline-parallel communication modeling. We expose actionable metrics such as pipeline bubble time and straggler waiting time.

cs.DC↗

arXiv2026

Mitigating Systematic Errors in Parameter Estimation of Binary Black Hole Mergers in O1-O3 LIGO-Virgo Data

Systematic errors in the parameter estimation (PE) of gravitational wave (GW) mergers can arise from various sources, including waveform systematics, noise mischaracterization, data analysis artifacts, and other unknown factors. In this study, we analyze selected events from the first three observing runs of the LIGO-Virgo-KAGRA (LVK) collaboration. We choose events that have been flagged in various studies as potentially affected by systematic errors. Here, we reanalyze these events using a couple of parametric models developed in previous work that incorporate uncertainties in both the phase and amplitude of the GW waveform. In this data-driven approach, we apply sufficiently broad priors on the uncertainty parameters to account for potential systematic errors. Our findings show that the proposed method effectively reduces systematic errors, even those arising from data artifacts, such as glitches occurring near a signal and the deglitching process in GW frame files. Similarly, inconsistent results from different waveform models become much more consistent in our framework. One noteworthy event we examine is GW191109\_010717, which is particularly interesting due to its anti-aligned spin properties. We report that, within our framework, the event still exhibits anti-aligned spin characteristics, but the inference results become consistent across raw and deglitched frame files, as well as across the waveform models used for this event (IMRPhenomXPHM, IMRPhenomXO4a, and NRSur7dq4). A similar trend is observed for the event GW200129\_065458, which previously yielded a high, but inconsistent precession parameter among different waveform models. In contrast, we observe a non-zero and consistent value of $χ_{p}=0.60^{+0.31}_{-0.33}, 0.58^{+0.30}_{-0.29}$ and $0.56^{+0.31}_{-0.28}$ for the IMRPhenomXPHM, IMRPhenomXO4a, and NRSur7dq4 waveform models, respectively.

astro-ph.HE↗

arXiv2026

Second moment of $\textrm{GL(3)} \times \textrm{GL(2)}$ $L$--functions

For $M_1$ and $ M_2$ two distinct primes, let $ H_k^\star(M_1M_2, ψ)$ denote the set of primitive newforms of level $M_1M_2$, weight $k\geq 3$ and Nebentypus $ψ$ of conductor $M_1$. Let $π$ be a fixed $SL(3, \mathbb{Z})$ Hecke cusp form. We prove a Lindelöf--consistent upper bound for the second moment \[ \mathop{ \sum_{\substack{ψ(M_1) \\ ψ(-1)=(-1)^k }}} \sideset{}{^h}\sum_{f \in H_k^{\star}(M_1M_2,ψ)} |L(1/2, π\times f)|^2 \ll_{π,ε} M_1^{1+ε}\] in the range $M_2\leq M_1^{1+ε}$.

math.NT↗

arXiv2026

Automatic Detection and Analysis of Singing Mistakes for Music Pedagogy

The advancement of machine learning in audio analysis has opened new possibilities for technology-enhanced music education. This paper introduces a framework for automatic singing mistake detection in the context of music pedagogy, supported by a newly curated dataset. The dataset comprises synchronized teacher learner vocal recordings, with annotations marking different types of mistakes made by learners. Using this dataset, we develop different deep learning models for mistake detection and benchmark them. To compare the efficacy of mistake detection systems, a new evaluation methodology is proposed. Experiments indicate that the proposed learning-based methods are superior to rule-based methods. A systematic study of errors and a cross-teacher study reveal insights into music pedagogy that can be utilised for various music applications. This work sets out new directions of research in music pedagogy. The codes and dataset are publicly available.

eess.AS↗

arXiv2026

The Orchestration of Multi-Agent Systems: Architectures, Protocols, and Enterprise Adoption

Orchestrated multi-agent systems represent the next stage in the evolution of artificial intelligence, where autonomous agents collaborate through structured coordination and communication to achieve complex, shared objectives. This paper consolidates and formalizes the technical composition of such systems, presenting a unified architectural framework that integrates planning, policy enforcement, state management, and quality operations into a coherent orchestration layer. Another primary contribution of this work is the in-depth technical delineation of two complementary communication protocols - the Model Context Protocol, which standardizes how agents access external tools and contextual data, and the Agent2Agent protocol, which governs peer coordination, negotiation, and delegation. Together, these protocols establish an interoperable communication substrate that enables scalable, auditable, and policy-compliant reasoning across distributed agent collectives. Beyond protocol design, the paper details how orchestration logic, governance frameworks, and observability mechanisms collectively sustain system coherence, transparency, and accountability. By synthesizing these elements into a cohesive technical blueprint, this paper provides comprehensive treatments of orchestrated multi-agent systems - bridging conceptual architectures with implementation-ready design principles for enterprise-scale AI ecosystems.

cs.MA↗

arXiv2026

Probing Cosmic Expansion and Early Universe with Einstein Telescope

Over the next two decades, gravitational-wave (GW) observations are expected to evolve from a discovery-driven endeavour into a precision tool for astrophysics, cosmology, and fundamental physics. Current second-generation ground-based detectors have established the existence of compact-binary mergers and enabled GW multi-messenger astronomy, but they remain limited in sensitivity, redshift reach, frequency coverage, and duty cycle. These limitations prevent them from addressing many fundamental open questions in cosmology. By the 2040s, wide-field electromagnetic surveys will have mapped the luminous Universe with unprecedented depth and accuracy. Nevertheless, key problems including the nature of dark matter, the physical origin of cosmic acceleration, the properties of gravity on cosmological scales, and the physical conditions of the earliest moments after the Big Bang will remain only partially constrained by electromagnetic observations alone. Progress on these fronts requires access to physical processes and epochs that do not emit light. Gravitational waves provide a unique and complementary observational channel: they propagate over cosmological distances largely unaffected by intervening matter, probe extreme astrophysical environments, and respond directly to the geometry of spacetime. In this context, next-generation GW observatories such as the Einstein Telescope (ET) will be transformative for European astronomy. Operating at sensitivities and frequencies beyond existing detectors, ET will observe binary black holes and neutron stars out to previously inaccessible redshifts, enable continuous high signal-to-noise monitoring of compact sources, and detect gravitational-wave backgrounds of astrophysical and cosmological origin. Together with space-based detectors, ET will play a central role in advancing our understanding of cosmic evolution and fundamental physics.

astro-ph.CO↗

arXiv2026

On stability of distance under some tensor products and some calculations

We prove that the Kadison-Kastler and Christensen distances are stable under the Banach space injective tensor product (resp., the Banach space projective tensor product) of a Banach space with any unital commutative $C^*$-algebra (resp., of a $C^*$-algebra with any unital $C^*$-algebra). Apart from these stability results, we make some explicit calculations of the Kadison-Kastler, Christensen and Mashood-Taylor distances between certain subalgebras of some crossed-product operator algebras.

math.OA↗