arXiv subjects

Akash Yadav

Publications and source records attributed to Akash Yadav.

14 recordsLinked to original sources

arXiv2026

Finite-Sum Realization of Archimedean Asai and Exterior-Square $L$-Factors

We prove that the archimedean Asai $L$-factor attached to an irreducible generic representation of $\operatorname{GL}_n(\mathbb{C})$ can be expressed as a finite sum of Flicker local zeta integrals. For an archimedean local field $F$, we also prove that the exterior-square $L$-factor attached to an irreducible generic representation of $\operatorname{GL}_m(F)$ can be expressed as a finite sum of Jacquet--Shalika local zeta integrals.

math.NT↗

arXiv2026

Relativistic Signatures of Dark Matter Equations of State in Static Spherically Symmetric Spacetimes

We study how three physically motivated dark matter equations of state alter the spacetime geometry of static, spherically symmetric black holes in General Relativity. The models considered are anisotropic perfect fluid dark matter (PFDM), isotropic constant-$\omega$ dark matter, and Bose-Einstein condensate (BEC) dark matter with a polytropic equation of state (EoS). For each model, we derive the Einstein field equations and solve for the metric function analytically in the PFDM and constant-$\omega$ cases, and numerically via the Tolman-Oppenheimer-Volkoff equations for BEC dark matter. We then compute the key strong gravity observables: event horizon radius, photon sphere radius, black hole shadow radius, innermost stable circular orbit (ISCO), and circular orbital velocity profiles. The shadow radii obtained for each model are compared against the Event Horizon Telescope constraints to place bounds on the dark matter parameters. Physical viability is assessed through the null, weak, dominant, and strong energy conditions, along with causality requirements on the sound speed. Our results show that PFDM produces near Schwarzschild geometry with mild anisotropic corrections, the constant-$\omega$ model is strongly restricted by causality to $0 \leq \omega \leq 1$, and BEC dark matter generates smooth, bounded deviations governed by the bosonic self-interaction parameter K. Taken together, these findings show that strong gravity observables can serve as practical tools for distinguishing between competing dark matter models through their geometric imprints on black hole space times.

gr-qc↗

arXiv2026

Exceptional poles of archimedean Rankin-Selberg L-functions for principal series representations of GL(n,R)

We prove that for any pair of irreducible principal series representations $(\pi_1,\pi_2)$ of $\operatorname{GL}_n(\mathbb{R})$ in general position, the notions of exceptional pole of type 1 and type 2 coincide. Using this identification, we express the Rankin--Selberg $L$-function $L(s,\pi_1\times\pi_2)$ in terms of the exceptional $L$-factors attached to the irreducible constituents of the derivatives of $\pi_1$ and $\pi_2$.

math.NT↗

arXiv2026

Calibrating Scientific Foundation Models with Inference-Time Stochastic Attention

Transformer-based scientific foundation models are increasingly deployed in high-stakes settings, but current architectures give deterministic outputs and provide limited support for calibrated predictive uncertainty. We propose Stochastic Attention, a sample average lightweight inference-time modification that randomizes attention by replacing softmax weights with normalized multinomial samples controlled by a single concentration parameter, and produces predictive ensembles without retraining. To set this parameter, we introduce a calibration objective that matches the stochastic attention output with the target, yielding an efficient univariate post-hoc tuning problem. We evaluate this mechanism on scientific foundation models for weather and time-series forecasting, as well as several regression tasks. Across benchmarks against uncertainty-aware baselines, we find that Sample Average Stochastic Attention achieves the strongest native calibration and the sharpest prediction intervals at comparable calibration, with adaptation costs nearly three orders of magnitude lower than the next-best baseline.

cs.LG↗

arXiv2025

Nonparametric Stochastic Subspaces via the Bootstrap for Characterizing Model Error

Reliable forward uncertainty quantification in engineering requires methods that account for aleatory and epistemic uncertainties. In many applications, epistemic effects arising from uncertain parameters and model form dominate prediction error and strongly influence engineering decisions. Because distinguishing and representing each source separately is often infeasible, their combined effect is typically analyzed using a unified model-error framework. Model error directly affects model credibility and predictive reliability; yet its characterization remains challenging. To address this need, we introduce a bootstrap-based stochastic subspace model for characterizing model error in the stochastic reduced-order modeling framework. Given a snapshot matrix of state vectors, the method leverages the empirical data distribution to induce a sampling distribution over principal subspaces for reduced order modeling. The resulting stochastic model enables improved characterization of model error in computational mechanics compared with existing approaches. The method offers several advantages: (1) it is assumption-free and leverages the empirical data distribution; (2) it enforces linear constraints (such as boundary conditions) by construction; (3) it requires only one hyperparameter, significantly simplifying the training process; and (4) its algorithm is straightforward to implement. We evaluate the method's performance against existing approaches using numerical examples in computational mechanics and structural dynamics.

cs.CE↗

arXiv2025

Bayesian Optimization under Uncertainty for Training a Scale Parameter in Stochastic Models

Hyperparameter tuning is a challenging problem especially when the system itself involves uncertainty. Due to noisy function evaluations, optimization under uncertainty can be computationally expensive. In this paper, we present a novel Bayesian optimization framework tailored for hyperparameter tuning under uncertainty, with a focus on optimizing a scale- or precision-type parameter in stochastic models. The proposed method employs a statistical surrogate for the underlying random variable, enabling analytical evaluation of the expectation operator. Moreover, we derive a closed-form expression for the optimizer of the random acquisition function, which significantly reduces computational cost per iteration. Compared with a conventional one-dimensional Monte Carlo-based optimization scheme, the proposed approach requires 40 times fewer data points, resulting in up to a 40-fold reduction in computational cost. We demonstrate the effectiveness of the proposed method through two numerical examples in computational engineering.

cs.LG↗

arXiv2025

Reheating study of Mexican-Hat-type Potentials

We study reheating in Mexican Hat type potentials, emphasizing the role of the post-inflationary equation-of-state parameter($\overline{\omega }_{\text{re}}$) in shaping observable predictions. By exploring the allowed range of $\overline{\omega }_{\text{re}}$, we derive reheating temperature, e-fold counts, and inflationary observables, showing that the conventional Mexican Hat model satisfies Planck18+BK18+BAO constraints on $n_s$ and r. The analysis underscores reheating as a critical link between theoretical potentials and CMB data. In addition, the holographic Mexican Hat realization is examined as a benchmark, with our results mapping its phenomenological boundaries. This work illustrates how reheating studies sharpen constraints and guide refinements of unified inflationary scenarios.

astro-ph.CO↗

arXiv2025

Stochastic Subspace via Probabilistic Principal Component Analysis for Characterizing Model Error

This paper proposes a probabilistic model of subspaces based on the probabilistic principal component analysis (PCA). Given a sample of vectors in the embedding space -- commonly known as a snapshot matrix -- this method uses quantities derived from the probabilistic PCA to construct distributions of the sample matrix, as well as the principal subspaces. It is applicable to projection-based reduced-order modeling methods, such as proper orthogonal decomposition and related model reduction methods. The stochastic subspace thus constructed can be used, for example, to characterize model-form uncertainty in computational mechanics. The proposed method has multiple desirable properties: (1) it is naturally justified by the probabilistic PCA and has analytic forms for the induced random matrix models; (2) it satisfies linear constraints, such as boundary conditions of all kinds, by default; (3) it has only one hyperparameter, which significantly simplifies training; and (4) its algorithm is very easy to implement. We demonstrate the performance of the proposed method via several numerical examples in computational mechanics and structural dynamics.

cs.CE↗

arXiv2025

Differential Machine Learning for Time Series Prediction

Accurate time series prediction is challenging due to the inherent nonlinearity and sensitivity to initial conditions. We propose a novel approach that enhances neural network predictions through differential learning, which involves training models on both the original time series and its differential series. Specifically, we develop a differential long short-term memory (Diff-LSTM) network that uses a shared LSTM cell to simultaneously process both data streams, effectively capturing intrinsic patterns and temporal dynamics. Evaluated on the Mackey-Glass, Lorenz, and R\"ossler chaotic time series, as well as a real-world financial dataset from ACI Worldwide Inc., our results demonstrate that the Diff- LSTM network outperforms prevalent models such as recurrent neural networks, convolutional neural networks, and bidirectional and encoder-decoder LSTM networks in both short-term and long-term predictions. This framework offers a promising solution for enhancing time series prediction, even when comprehensive knowledge of the underlying dynamics of the time series is not fully available.

cs.LG↗

arXiv2024

Non-vanishing of certain integral representations

In this paper, we prove that there exist Whittaker and Schwartz functions such that the local Flicker integrals are non-vanishing for all complex values of $s$, and the local Bump-Friedberg integrals are non-vanishing for all complex pairs $(s_1,s_2)$. As a corollary, we determine the potential locations of poles for their corresponding partial $L$-functions.

math.NT↗

arXiv2024

Disparity Driven Heterogeneous Nucleation in Finite-Size Adaptive Networks

Phase transitions are crucial in shaping the collective dynamics of a broad spectrum of natural systems across disciplines. Here, we report two distinct heterogeneous nucleation facilitating single-step and multi-step phase transitions to global synchronization in a finite-size adaptive network due to the trade-off between time scale adaptation and coupling strength disparities. Specifically, small intracluster nucleations coalesce either at the population interface or within the populations resulting in the two distinct phase transitions depending on the degree of the disparities. We find that the coupling strength disparity largely controls the nature of phase transition in the phase diagram irrespective of the adaptation disparity. We provide a mesoscopic description for the cluster dynamics using the collective coordinates approach that brilliantly captures the multicluster dynamics among the populations leading to distinct phase transitions. Further, we also deduce the upper bound for the coupling strength for the existence of two intraclusters explicitly in terms of adaptation and coupling strength disparities. These insights may have implications across domains ranging from neurological disorders to segregation dynamics in social networks.

nlin.AO↗

arXiv2024

Archimedean Distinguished Representations and Exceptional Poles

Let $F$ be an archimedean local field and let $E$ be $F\times F$ (resp. a quadratic extension of $F$). We prove that an irreducible generic (resp. nearly tempered) representation of $\operatorname{GL}_n(E)$ is $\operatorname{GL}_n(F)$ distinguished if and only if its Rankin-Selberg (resp. Asai) $L$-function has an exceptional pole of level zero at $0$. Further, we deduce a necessary condition for the ramification of such representations using the theory of weak test vectors developed by Humphries and Jo.

math.NT↗

arXiv2023

Deleterious satellite charging and possible mitigation schemes

Electrostatic charge dissipation is one of the major concerns for satellites operating in the Earth's orbits. Under energetic plasma conditions, they may acquire very high negative potential (up to 10's of kV) due to the collection of energetic plasma constituents - resulting in temporary outages and permanent damages to onboard equipment. This study proposes and discusses a couple of physics-based schemes capable of mitigating/ minimizing the excessive charging effects over satellites under extreme plasma conditions in LEO/ GEO. An estimate of charge build-up on the space objects based on the charging dynamics as a function of ambient plasma parameters has been made. Our calculations illustrate that in the absence of a significant charge dissipation mechanism, a severe charging (10's kV) in the dark/ shadowed at GEO and high latitude LEO regions. We propose that installing a suitable UV lamp and micro/nano-structuring of the surface fabric can induce an efficient dissipation mechanism and effectively prevent the surface from deleterious charging effects during satellite operation. We demonstrate that the UV illumination may maintain the satellite surface at quite a small positive potential (~ 2 V) while the surface nanofabrication sustains it at a sufficiently low negative potential (~ 10 V). Both concepts are shown to work efficiently in mitigating the potential threat of massive charging and safely performing the satellite operation.

physics.plasm-ph↗

arXiv2023

Exotic swarming dynamics of high-dimensional swarmalators

Swarmalators are oscillators that can swarm as well as sync via a dynamic balance between their spatial proximity and phase similarity. We present a generalized D-dimensional swarmalator model, which is more realistic and versatile, that captures the self-organizing behaviors of a plethora of real-world collectives. This allows for modeling complicated processes such as flocking, schooling of fish, cell sorting during embryonic development, residential segregation, and opinion dynamics in social groups. We demonstrate its versatility by capturing the manoeuvers of the school of fish and traveling waves of gene expression, both qualitatively and quantitatively, embryonic cell sorting, microrobot collectives, and various life stages of slime mold by a suitable extension of the original model to incorporate appropriate features besides a gallery of its intrinsic self-organizations for various interactions. We expect this high-dimensional model to be potentially useful in describing swarming systems in a wide range of disciplines including physics of active matter, developmental biology, sociology, and engineering.

nlin.AO↗