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Abhishek

Publications and source records attributed to Abhishek.

At least 19 recordsLinked to original sources
arXiv2026

Variation of Iwasawa Invariants for Ordinary Representations

Let $K$ be a number field and $p$ be an odd prime. Greenberg introduced a natural topology on the space of all $\mathbb{Z}_p$-extensions of $K$ and established several boundedness results for the classical Iwasawa invariants. We extend this framework to compare the Iwasawa invariants of Selmer groups attached to an ordinary $p$-adic representation across $\mathbb{Z}_p$-extensions lying in a Greenberg neighbourhood in the sense of Greenberg. We also establish analogous results for the fine Selmer groups. Finally, in a neighbourhood of the cyclotomic $\mathbb{Z}_p$-extension, we provide evidence for the expected connection between the characteristic ideal of the Selmer group and the conjectural $p$-adic $L$-function introduced by Disegni.

math.NT↗
arXiv2026

Exploring the limits of high-energy proton-pion separation in granular calorimeters

Highly granular calorimeters provide detailed information about hadronic-shower development that may enable particle identification beyond their conventional role in energy measurement. We investigate how well this information can distinguish protons from positively charged pions and how the achievable discrimination depends on detector segmentation and particle energy. The study uses Geant4 simulations of isolated particles with energies from 10 to 100 GeV in a homogeneous lead-tungstate calorimeter. A Deep Sets model operating directly on cell positions and detected energy and time outperforms a boosted decision tree based on reconstructed shower observables. With cells measuring $3 \times 3 \times 6$ mm$^3$, Deep Sets achieves an accuracy of 93.8% at 10 GeV, decreasing to 67.2% at 100 GeV. Shower topology is independently informative, deposited energy provides the largest additional contribution, and timing supplies complementary information. Coarser segmentation reduces discrimination, with performance more sensitive to longitudinal than transverse granularity. These results provide an encouraging benchmark for calorimeter-based hadron identification and motivate its inclusion among the optimization targets for future highly granular calorimeters.

hep-ex↗
arXiv2026

A Formal Hierarchical Architecture for Agentic Orchestration with Stack-Based Execution and Lazy Discovery

The rapid expansion of capabilities in Large Language Model (LLM) agents has exposed a critical architectural bottleneck: when agents are given access to a flat, monolithic registry of tools, the model must evaluate hundreds or thousands of options simultaneously. This leads to decision-space explosion, context window saturation, and degraded routing accuracy. To address these limitations, this paper presents a hierarchical, skill-based architecture for agentic orchestration. Capabilities are organized as a rooted tree where internal nodes make routing decisions and leaf nodes execute deterministic tasks. The runtime enforces a single-step execution loop governed by a Last-In-First-Out (LIFO) stack, giving the agent a form of memory akin to a Pushdown Automaton, therefore enabling it to track nested execution contexts and resume deterministically from any depth. Capability discovery follows a manifest-driven, lazy-loading protocol: only the immediate children of the active node are loaded, so memory and prompt costs scale with the explored path rather than the global registry. By replacing global memory with localized stack frames, the architecture prevents outputs from one execution branch from leaking into another, establishing the isolation guarantees required for deployment in regulated enterprise environments. We also discuss UPI Help, an AI-powered digital payments support product, as a motivating production deployment context. We provide a mathematical formalization of the orchestration state, detailed algorithmic analysis of the execution loop, and controlled benchmarks comparing flat and hierarchical routing under increasing tool catalogs, multi-step workflow pressure, and visible schema-token exposure per LLM call.

cs.AI↗
arXiv2026

On the existence results for $m$-Harmonic equation with critical Choquard Nonlinearity

This article established the existence results for the $m$-harmonic equation involving critical Choquard nonlinearity and subcritical perturbation. We first explore the minimizers of the $m$-harmonic operator with the critical Choquard equation. Then, using these minimizers, we establish delicate estimates to show the energy below the threshold level, which helps to recover the compactness. Further, we prove the existence of a nontrivial solution for our problem with different kinds of local and nonlocal subcritical perturbations. To the best of our knowledge, this is the first article dealing with the polyharmonic equation and critical Choquard type nonlinearity. The results obtained are even new for $m\geq 2$.

math.AP↗
arXiv2026

A Multi-Fidelity Convolutional Autoencoder-Transfer Learning Framework for Guided-Wave-Based Damage Diagnosis Using Large Simulated and Limited Experimental Datasets

Guided wave-based structural health monitoring (GWSHM) with onboard transducers offers significant potential for the early diagnosis of damage in engineering structures. However, the practical deployment of deep learning models is often hindered by the limited availability of labelled experimental data and the high computational cost of generating large-scale high-fidelity simulation datasets. This study presents a multifidelity transfer learning framework that integrates lightweight physics-based simulations, convolutional autoencoder (CAE)-based deep feature learning, a feed-forward neural network, and limited experimental measurements for accurate damage localisation and sizing in plate-like structures instrumented with piezoelectric transducers. A computationally efficient one-dimensional time-domain spectral element model is employed to generate a large synthetic dataset for pretraining, while transfer learning adapts the model to experimental domains using only a small amount of labelled data. The CAE-based transfer learning framework significantly outperforms its CNN-based counterpart in damage localisation accuracy. The model achieves excellent predictive performance with $R^2$ scores exceeding 0.93 for damage localisation and 0.99 for damage sizing. Its generalisation capability is demonstrated on previously unseen data, showing high prediction accuracy for damage scenarios not represented during pretraining or fine-tuning. The results establish the proposed framework as an accurate, computationally efficient, and practically viable solution for real-world GWSHM applications.

cs.LG↗
arXiv2026

Modular $S_4$ Scotogenic Model with Flavored Resonant Leptogenesis

We construct a radiative neutrino mass model that combines the scotogenic mechanism with modular $S_4$ flavour symmetry. The entire lepton flavour structure is governed by holomorphic modular forms of a single complex modulus $\tau$, eliminating the need for flavon fields. Beyond the Standard Model, the particle content consists of two right-handed Majorana fermions assigned to the $S_4$ doublet representation and an inert scalar doublet odd under a $\mathbb{Z}_2$ parity. Neutrino masses emerge at one loop through the scotogenic mechanism, and the lightest $\mathbb{Z}_2$-odd state serves as a dark matter candidate. A comprehensive scan of the parameter space demonstrates consistency with all five neutrino oscillation observables at the $3\sigma$ level. Having exactly two right-handed neutrinos forces the light neutrino mass matrix to rank two, leaving one neutrino massless and selecting normal ordering as the only viable option. The framework predicts a total neutrino mass in the narrow window $\Sigma m_\nu \simeq 0.059$--$0.06\,\mathrm{eV}$, well within current cosmological bounds, and an effective Majorana mass $m_{\beta\beta} \simeq (1.3$--$3.5)\times 10^{-3}\,\mathrm{eV}$ relevant for neutrinoless double beta decay searches. The modular structure of the right-handed Majorana mass matrix intrinsically produces a quasi-degenerate heavy neutrino spectrum, enabling flavoured resonant leptogenesis at $M_1 \sim 10^5\,\mathrm{GeV}$ without any fine-tuning. Integration of the full three-flavour Boltzmann equations confirms that the observed baryon asymmetry is reproduced, establishing that neutrino masses, leptonic mixing, and the baryon asymmetry of the Universe all find a common explanation within this framework.

hep-ph↗
arXiv2026

Iwasawa invariants of Bertolini--Darmon theta elements

In this article we study the Iwasawa invariants of Bertolini--Darmon theta elements in the anticyclotomic $\mathbb{Z}_p$-extension of an imaginary quadratic field $K$ for weight two modular forms $f\in S_2(\Gamma_0(N))$. We cover both the cases of ordinary and non-ordinary reduction at a prime $p$. Our results extend the known results of Pollack--Weston and Gajek-Leonard--Lei in the cyclotomic setting.

math.NT↗
arXiv2026

Graph-Structured Number-Conserving Variational Quantum Eigensolver for Fermionic Pairing Hamiltonians

Simulating strongly correlated fermionic pairing in the presence of rotational and pair-breaking fields requires deep quantum circuits. We present a graph-structured variational quantum eigensolver whose pair-transfer and single-excitation rotations follow the nonzero pairing and one-body mixing edges of the Hamiltonian. The circuit conserves particle number exactly and uses one parameter per retained edge. We benchmark one layer against exact fixed-number diagonalization for 1500, $M=8$ Hamiltonians represented by 16 qubits. Its mean energy error rises from 0.86 keV without one-body driving to 691 keV at the strongest drive; the one-layer circuit loses accuracy as pair breaking strengthens. In a matched eight-qubit comparison, the graph circuit reaches the 0.42 keV high-drive error of a pair-plus-all-singles circuit with 8 instead of 34 parameters. Fixed-number Adaptive Derivative-Assembled Pseudo-Trotter VQE reaches 0.056 keV with 304 decomposed controlled-NOT gates and iterative pool screening, while a 52-parameter, single-repetition unitary coupled-cluster singles-and-doubles circuit gives 17.6 keV with 2752 such gates. At a separate twelve-qubit point, a second graph layer reduces the high-drive error from 378 to 35 keV. Across the exact grid, an off-diagonal pair-coherence scale tracks the leading pair-density eigenvalue, condensate fraction, and interaction energy. Cranked zirconium Hamiltonians provide the benchmark instances and tune the strength of one-body pair breaking.

quant-ph↗
arXiv2026

Asymmetric dark matter from leptogenesis in type-III seesaw framework with modular $S_4$ symmetry

We present a unified framework for neutrino masses, baryogenesis, and dark matter based on a modular $S_4$ symmetry combined with a type-III seesaw mechanism. All Yukawa couplings, CP phases, and flavor textures originate from a single complex modulus $\tau$, whose vacuum expectation value controls both visible and dark sector dynamics. The same modular parameter fixes the neutrino mass matrix, determines the CP asymmetries driving resonant leptogenesis, and correlates the resulting baryon and dark matter abundances. A detailed numerical analysis shows that the model reproduces all neutrino oscillation data within the $3\sigma$ NuFIT~5.2 (2024) ranges for normal ordering, predicting $\delta_{\rm CP} \simeq \pm (150^\circ-180^\circ)$, $\sum m_\nu\simeq(0.06-0.08)~\mathrm{eV}$, and an effective Majorana mass $m_{\beta\beta} \simeq (8 - 18)\times 10^{-3}~\mathrm{eV}$, testable in next-generation neutrinoless double-beta decay experiments. The same modular Yukawas yield resonantly enhanced CP asymmetries $|\epsilon_{L,\chi}| \sim 10^{-9}-10^{-6}$ at $M_\Sigma \sim 10^{7}~\mathrm{GeV}$, successfully generating the observed baryon asymmetry $\eta_B\simeq6\times10^{-10}$ and dark relic density $\Omega_\chi h^2\simeq0.12$ without additional free parameters. The predicted correlation $\Omega_\chi/\Omega_B\simeq5.4$ fixes the dark matter mass to $m_\chi\simeq0.1-2~\mathrm{GeV}$, consistent with all current constraints. This framework therefore realizes a fully predictive baryon$-$dark matter co-genesis, where the geometry of the modular symmetry links the origin of flavor, CP violation, and the cosmic matter asymmetry.

hep-ph↗
arXiv2025

Resonant leptogenesis in inverse see-saw framework with modular $S_4$ symmetry

We introduce a lepton mass generation and flavor mixing model, realized through a (2,3) inverse seesaw structure based on modular \( S_4 \) symmetry. The model employs modular forms to construct the lepton Yukawa couplings, significantly simplifying the framework by reducing redundant parameters. A detailed numerical analysis demonstrates consistency with current neutrino oscillation data, yielding specific outputs for the mixing angles and CP-violating phases. The Dirac CP phase is predicted to lie near $\delta_{\rm CP} \approx \pm 90^\circ$, corresponding to near-maximal leptonic CP violation. The total neutrino mass lies within $\sum m_\nu \approx 0.0587\text{--}0.0924$ eV, and the effective Majorana mass $|m_{ee}| \approx (0.002\text{--}0.02)$ eV, within reach of upcoming neutrinoless double beta decay experiments such as nEXO and AMoRE-II. The model also remains consistent with current bounds on charged lepton flavor violating processes from MEG and BaBar. We further explore resonant leptogenesis enabled by quasi-degenerate heavy neutrino states and show that the observed baryon asymmetry of the universe can be successfully generated in this scenario. The combined treatment of low-energy observables and high-scale baryogenesis demonstrates the predictivity and testability of the modular \( S_4 \)-based ISS(2,3) framework.

hep-ph↗
arXiv2025

2-Selmer companion modular forms

Let $N$ be a positive integer and $K$ be a number field. Suppose that $f_1,f_2 \in S_k(\Gamma_0(N))$ are two newforms such that their residual Galois representations at $2$ are isomorphic. Let $\omega_2: G_{\mathbb Q} \rightarrow {\mathbb Z}^*_2$ be the $2$-adic cyclotomic character. Then, under suitable hypotheses, we have shown that for every quadratic character $\chi$ of $K$ and each critical twist $j$, the residual Greenberg $2$-Selmer groups of $f_1\chi\omega_2^{-j}$ and $f_2\chi\omega_2^{-j}$ over $K$ are isomorphic. This generalizes the corresponding result of Mazur-Rubin on $2$-Selmer companion elliptic curves. Conversely, if the difference of the residual Greenberg (respectively Bloch-Kato) $2$-Selmer ranks of $f_1\chi$ and $f_2\chi$ is bounded independent of every quadratic character $\chi$ of $K$, then under suitable hypotheses we have shown that the residual Galois representations at $2$ of $f_1$ and $f_2$ are isomorphic as $G_K$-modules. The corresponding result for elliptic curves was a conjecture of Mazur-Rubin, which was proved by M. Yu.

math.NT↗
arXiv2025

Low scale leptogenesis and $TM_1$ mixing in neutrinophillic two Higgs doublet model($\nu$2HDM) with S4 flavor symmetry

We study a modified version of the Standard Model that includes a scalar doublet and two right-handed neutrinos, forming the neutrinophillic two higgs doublet ($\nu\text{2HDM}$) framework. For the two Higgs-doublet vacuum expectation values satisfying $\text{v}_2 << \text{v}_1$, this model operates at a TeV scale, bringing the RHNs within experimental reach. To further enhance its predictive power, we introduce an $S_4 \times Z_4$ flavor symmetry with five flavons, resulting in mass matrices that realize the so-called Trimaximal $\text{TM}_1$ mixing scheme. The model effectively explains lepton masses and flavor mixing under the normal ordering of neutrino masses, predicting that the effective neutrino mass in 0$\nu\beta\beta$ decay lies between [4 - 5] meV, significantly lower than the sensitivity limits of current experiments. We also investigate how this framework could support low-scale leptogenesis as a natural way to explain the observed imbalance between matter and antimatter in the Universe. This work explores how neutrino physics, flavor symmetry and baryon asymmetry are connected, providing a clear framework that links theoretical predictions with experimental possibilities.

hep-ph↗
arXiv2025

Neuromorphic Readout for Hadron Calorimeters

We simulate hadrons impinging on a homogeneous lead-tungstate (PbWO4) calorimeter to investigate how the resulting light yield and its temporal structure, as detected by an array of light-sensitive sensors, can be processed by a neuromorphic computing system. Our model encodes temporal photon distributions as spike trains and employs a fully connected spiking neural network to estimate the total deposited energy, as well as the position and spatial distribution of the light emissions within the sensitive material. The extracted primitives offer valuable topological information about the shower development in the material, achieved without requiring a segmentation of the active medium. A potential nanophotonic implementation using III-V semiconductor nanowires is discussed. It can be both fast and energy efficient.

hep-ex↗
arXiv2025

Hadron Identification Prospects With Granular Calorimeters

In this work we consider the problem of determining the identity of hadrons at high energies based on the topology of their energy depositions in dense matter, along with the time of the interactions. Using GEANT4 simulations of a homogeneous lead tungstate calorimeter with high transverse and longitudinal segmentation, we investigated the discrimination of protons, positive pions, and positive kaons at 100 GeV. The analysis focuses on the impact of calorimeter granularity by progressively merging detector cells and extracting features like energy deposition patterns andtiming information. Two machine learning approaches, XGBoost and fully connected deep neural networks, were employed to assess the classification performance across particle pairs. The results indicate that fine segmentation improves particle discrimination, with higher granularity yielding more detailed characterization of energy showers. Additionally, the results highlight the importance of shower radius, energy fractions, and timing variables in distinguishing particle types. The XGBoost model demonstrated computational efficiency and interpretability advantages over deep learning for tabular data structures, while achieving similar classification performance. This motivates further work required to combine high- and low-level feature analysis, e.g., using convolutional and graph-based neural networks, and extending the study to a broader range of particle energies and types.

physics.ins-det↗
arXiv2025

End-to-End Detector Optimization with Diffusion models: A Case Study in Sampling Calorimeters

Recent advances in machine learning have opened new avenues for optimizing detector designs in high-energy physics, where the complex interplay of geometry, materials, and physics processes has traditionally posed a significant challenge. In this work, we introduce the $\textit{end-to-end}$ AI Detector Optimization framework (AIDO) that leverages a diffusion model as a surrogate for the full simulation and reconstruction chain, enabling gradient-based design exploration in both continuous and discrete parameter spaces. Although this framework is applicable to a broad range of detectors, we illustrate its power using the specific example of a sampling calorimeter, focusing on charged pions and photons as representative incident particles. Our results demonstrate that the diffusion model effectively captures critical performance metrics for calorimeter design, guiding the automatic search for layer arrangement and material composition that aligns with known calorimeter principles. The success of this proof-of-concept study provides a foundation for future applications of end-to-end optimization to more complex detector systems, offering a promising path toward systematically exploring the vast design space in next-generation experiments.

physics.ins-det↗
arXiv2024

A Comparison of Electronic, Dielectric, and Thermoelectric Properties of Monolayer of HfX2N4(X = Si, Ge) through First-Principles Calculations

The newly emerged two-dimensional (2D) materials family of MSi2N4, where M is a transition metal atom (i.e., Mo, W, etc.), has the potential to be named after the conventional and very popular transition metal di-chalcogenides (TMDC), which got their reputation for having bandgap tunability and high mobility. The HfSi2N4 and HfGe2N4 2D materials are members of the MSi2N4 family and possess very good figure of merit (ZT) and have high mobility, proving their suitability for thermoelectric applications. The HfSi2N4 and HfGe2N4 showed considerable ZT of 0.90 and 0.89, respectively, for p-type and 0.83 and 0.79 for n-type, at 900 K along with high mobility according to the solutions obtained after solving the Boltzmann Transport Equation (BTE). The HfGe2N4 also showed a ZT of 0.84 at 600 K and 0.68 at 300 K, which is also excellent for low-temperature operation. The bandgaps (BG) obtained for HfSi2N4 and HfGe2N4 according to the Heyd-Scuseria-Ernzerhof (HSE) approximation were 2.89 eV and 2.75 eV. The first absorption peak showed in the blue region of the visible spectrum; from this, their usefulness in visible range photodetectors can also be inferred.

cond-mat.mtrl-sci↗
arXiv2024

The TDHF code Sky3D version 1.2

The Sky3D code has been widely used to describe nuclear ground states, collective vibrational excitations, and heavy-ion collisions. The approach is based on Skyrme forces or related energy density functionals. The static and dynamic equations are solved on a three-dimensional grid, and pairing is been implemented in the BCS approximation. This updated version of the code aims to facilitate the calculation of nuclear strength functions in the regime of linear response theory, while retaining all existing functionality and use cases. The strength functions are benchmarked against available RPA codes, and the user has the freedom of choice when selecting the nature of external excitation (from monopole to hexadecapole and more). Some utility programs are also provided that calculate the strength function from the time-dependent output of the dynamic calculations of the Sky3D code.

physics.comp-ph↗