arXiv subjects

Sourav Das

Publications and source records attributed to Sourav Das.

At least 19 recordsLinked to original sources

arXiv2026

Infinitesimal Deformations of Generalized Parabolic Hitchin Pairs

We develop the infinitesimal deformation theory of generalized parabolic Hitchin pairs (GPHs) on irreducible nodal curves. For any GPH $(E,\phi,F(E))$ we associate an explicit three-term deformation complex $\mathcal{C}_{(E_\bullet,\phi)}$ whose first hypercohomology $\mathbb{H}^1(\mathcal{C}_{(E_\bullet,\phi)})$ parameterizes first-order deformations. As the main application, we prove that the coarse moduli space $\mathcal{M}_{\mathrm{GPH}}$ of $1$-stable generalized parabolic Hitchin pairs of rank $n$ and degree $d$ with $\gcd(n,d)=1$ is a local complete intersection, smooth in codimension one, and hence a normal variety. We further show that this moduli space carries a natural Poisson structure.

math.AG↗

arXiv2026

Weil's Theorem for Logarithmic Connections on Irreducible Nodal Curves

We establish an analogue of Andr\'e Weil's classical theorem for irreducible nodal curves. Let $X_0$ be an irreducible projective nodal curve. We prove that an indecomposable vector bundle or torsion-free coherent sheaf $E$ on $X_0$ admits a holomorphic logarithmic connection $\nabla\colon E\to E\otimes\omega_{X_0}$ with respect to the dualizing sheaf if and only if $\deg E=0$. Moreover, when $\deg E=0$, such a connection can be chosen so that the induced logarithmic connection on the normalization has scalar residues $\lambda\cdot I$ at one preimage of the node and $-\lambda\cdot I$ at the other, for some $\lambda\in\mathbb{C}$. Explicit one-parameter families of flat connections are constructed on the irreducible rational nodal cubic curve as an illustration.

math.AG↗

arXiv2026

Extreme values and logarithm laws for toral translations

We study extreme values of normalized $r$-th nearest neighbour distance functions in inhomogeneous Diophantine approximation, proving Weibull and Fr\'echet limit laws when the shift satisfies a natural Diophantine condition. Using these extreme value laws we prove corresponding logarithm laws for these functions. Our approach is based on homogeneous dynamics. The key input is to adapt the Poisson approximation strategy of Bj\"{o}rklund and Gorodnik (arXiv:2201.05116) combined with an effective multiple equidistribution result, which we deduce using results of Str\"{o}mbergsson (arXiv:1309.6103) and of Bj\"{o}rklund and Gorodnik (arXiv:2105.05468).

math.NT↗

arXiv2026

Can We Optimize the Performance-Carbon Emission Break-Even Point?: The Quest for Greener LLMs

The carbon footprint of any deployed Large Language Model (LLM) accumulates during inference, where repeated use of the model substantially exceeds the one-time cost of fine-tuning. Yet most efficiency interventions target either pre-training scale or post-hoc compression. We ask whether folding a calibrated, differentiable energy surrogate into the fine-tuning objective can produce inference behavior that gains task accuracy at zero or near-zero carbon cost, a break-even configuration. We propose a joint loss mechanism with a per-model carbon-emission parameter, a linear surrogate over parameter norm, FLOP proxy, and a memory proxy, fit from on-hardware energy profiling. We fine-tune three architecturally distinct families: Gemma-2 2B, Llama-3.1 8B, and Qwen-2.5 14B, and evaluate inference F1 and CO$_2$ emissions on three MMLU subjects: abstract algebra, philosophy, and formal logic. We discover from several outcomes that the carbon term behaves as either harmful interference or beneficial regularization depending on the task structure. We position calibrated carbon-aware fine-tuning as a lightweight, drop-in regularizer with a non-empty but model and task-dependent break-even region. This is an ongoing work, and we will release our codebase soon.

cs.CL↗

arXiv2026

CP-preserving channels

Completely positive (CP) matrices are ubiquitous in modern science and technology with applications in optimization, graph theory, and quantum entanglement. Recently, Johnston \emph{et al.} [Linear Algebra and its Applications, 2022] have cast CP matrices into the framework of quantum resource theories, where CP states serve as free states and CP-preserving channels act as free operations. This work addresses several questions raised in their work. Specifically, we provide the necessary and sufficient conditions of CP-preserving channels in small dimensions, which are necessary in higher dimensions, and discuss the resource quantification via the trace distance of non-negativity. By constructing an explicit counterexample, we demonstrate that the trace-distance measure of non-negativity violates strong monotonicity. We also provide an alternative proof that every CPDNN channel $\Phi:\MM_n\to \MM_2$ is CPCP. Additionally, we show that any unital CPDNN map $\Phi:\MM_2\to \MM_n$ is also CPCP.

quant-ph↗

arXiv2026

ProbeScale: Probing Analysis to Optimize Neural Scaling Laws for Efficient Small Language Model Inference

Small Language Models (SLMs) offer a balance between capability and computational feasibility. Neural scaling laws inform their optimal training, suggesting that they possess rich internal representations that scale with their size. However, deploying even these SLMs can be challenging under strict resource constraints. Language model probing provides methods for analyzing the linguistic knowledge encoded in a model's internals. We propose ProbScale, a framework that unifies insights from scaling laws and probing to identify parameter-efficient subnetworks within pre-trained SLMs. ProbScale utilizes the high-quality representations of well-scaled SLMs and uses task-specific probes to mathematically quantify the relevance of each layer for target downstream capabilities. This allows selecting subnetworks that optimally trade off performance against parameter size. We formulate the subnetwork selection as finding a layer subset maximizing aggregated, task-weighted probe performance under a parameter budget. Experiments on representative SLMs such as RoBERTa-Large and T5-Base demonstrate that ProbScale identifies subnetworks achieving significant parameter reduction, from 5 to 10 times, while maintaining high performance (95% to 98% of the original SLMs) on targeted tasks, outperforming heuristic baselines.

cs.CL↗

arXiv2026

Bayesian fuzzy optimization using fuzzy Gaussian process

In many real-life problems, decision-making gets complicated due to dual sources of uncertainty, known as randomness and fuzziness or imprecision, which can be challenging for traditional optimization methods. Most of the existing fuzzy optimization techniques that optimize fuzzy-valued objective functions ignore fuzziness, while the probabilistic optimization techniques ignore randomness. To handle this dual source of uncertainty, Kwakernaak introduced the concept of a fuzzy random variable as ``random variables whose values are not real, but fuzzy numbers". This work aims to derive a theoretical background for the Gaussian fuzzy process and fuzzy acquisition functions, which will be used to develop a novel \emph{Bayesian fuzzy optimization} (BFO) technique that optimizes a fuzzy-values objective function. Based on fuzzy random variables, the Gaussian fuzzy process is developed, which is used as a prior belief about the fuzzy-valued objective function in the BFO. Fuzzy acquisition functions are defined to act as a guide for the search process of BFO with the help of posterior fuzzy mean and fuzzy variance. The proposed method demonstrated effective performance in both fuzzy mean-variance portfolio allocation and Indian temperature data analysis, showing robust predictive accuracy and adaptability. The proposed method can have broader applications in various fields like healthcare, material science, agriculture, etc.

math.GM↗

arXiv2026

MTRBO: Multiple trust-region based Bayesian optimization

Bayesian Optimization (BO) is a popular framework for optimizing black-box functions. Despite its effectiveness, BO is often inefficient for high-dimensional problems due to the exponential growth of the search space, heterogeneity of the objective function, and low sampling budget. To overcome these issues, this work proposes a multiple trust region-based Bayesian optimization technique(MTRBO). A trust region is a localized region within which an optimization model is trusted to approximate the objective function accurately. Assuming a Gaussian process (GP) as a prior belief about the objective function and based on the posterior mean and variance functions, the method adaptively exploits near the promising current solution inside a trust region. Also explores the most uncertain region in the search space inside another trust region. The theoretical global convergence property of the proposed method is established. Then the work is benchmarked against other state-of-the-art trust-region-based Bayesian optimization algorithms, demonstrating superior performance on a variety of non-convex and high-dimensional test functions. The proposed method outperforms others in terms of solution quality within the sampling budget (the number of function evaluations). The proposed method is applied to the portfolio optimization problem to verify its applicability in real-world scenarios.

math.OC↗

arXiv2026

Effective multi-equidistribution for translates of unipotent flows and Central limit theorems in inhomogeneous Diophantine approximation

In this paper, we prove a central limit theorem for inhomogeneous Diophantine approximation with a fixed shift, provided the shift is non-Liouville. This generalizes earlier work of Dolgopyat, Fayad, and Vinogradov~\cite{DFV}. This is achieved by translating the problem to one involving flows on homogeneous spaces. In this latter setting, we establish an effective multi-equidistribution result for diagonal translates of unipotent flows. This result is obtained by combining a recent result of Kim~\cite{Kim2024} with the height function construction of Shi~\cite{Shi20}. The central limit theorem is then deduced using the method of Bj\"orklund and Gorodnik~\cite{BG}.

math.NT↗

arXiv2026

Cosmology-Independent Constraints on the Etherington Relation and SNeIa Absolute Magnitude Evolution from DESI-DR2

We carry out a test of the fundamental Etherington relation (cosmic distance duality relation) which relates the luminosity distance $D_{\rm L}$ and angular diameter distance $D_{\rm A}$ in metric theories of gravity. We use the latest measurements of the angular diameter distance as a function of redshift from the Dark Energy Spectroscopic Instrument Data Release 2 (DESI-DR2) and the luminosity distance from a variety of compilations of Supernovae of Type Ia (SNeIa). Our results indicate that these measurements are statistically consistent with the Etherington relation. In addition to providing a confirmation of the underlying assumptions of the Etherington relation, i.e., the metric nature of gravity, Lorentz invariance and photon number conservation, our results are also a stringent test of any residual systematic effects. We interpret the absence of evidence of any deviation from this relation to constrain the evolution of the absolute magnitude of SNeIa to $dM/dz = 0.07 \pm 0.07$ over and above the systematics that are already accounted for in the SNeIa analyses. We discuss how the Etherington relation can be used to constrain systematic parameters in the analyses of dynamical dark energy using geometric probes, to make it more robust against systematic effects.

astro-ph.CO↗

arXiv2026

A new class of coherent states involving Fox-Wright functions and their generalization in the bicomplex framework

In this work, an extensive class of coherent states is introduced by taking the Fox Wright function as the normalization function. It is demonstrated that these states satisfy the key requirements of continuity, normalizability and resolution of unity. Furthermore, coherent states associated with the continuous spectrum are obtained through a discrete to continuous limiting procedure. Moreover, FW generalized multi parameter nu function is introduced and shown to act as the normalization function for the Fox Wright coherent states in the continuous spectrum. Later the Fox Wright function with bicomplex arguments has been introduced and its existence has been investigated. Bicomplex Fox Wright coherent states are also developed for the discrete spectrum based on this new function and their properties are analyzed. Subsequently, the results regarding Fox Wright coherent states are generalized to the bicomplex setting. In addition, a bicomplex FW generalized multi-parameter nu function is defined to demonstrate that it provides the normalization for these states in the continuous spectrum.

quant-ph↗

arXiv2026

MUSEQuBES: Probing Anisotropies in Gas and Metal Distributions in the Circumgalactic Medium

We investigate the azimuthal dependence of HI and OVI-bearing gas in the circumgalactic medium (CGM) of 113 isolated galaxies in the redshift range $0.12<z<0.75$, including 91 new measurements from the MUSE Quasar-fields Blind Emitters Survey (MUSEQuBES). Of these, measurements for 46 galaxies lie within the virial radius ($R_{\rm vir}$), including 36 non-face-on systems for which azimuthal angle ($\phi$) measurements are robust. The HI covering fraction (k_HI) within $R_{\rm vir}$ of low-mass ($7<\log(M/M_{\odot})\leq 9$) galaxies, for a threshold column density of ${\rm log}_{10}(N(HI)/{\rm cm}^{-2})=14.5$, exhibits an enhancement along both the disk plane ($\phi\lesssim20^{\circ}$) and in the polar direction ($\phi\gtrsim70^{\circ}$). In contrast, such a bimodal distribution is not observed for higher mass galaxies ($9<\log(M/M_{\odot})\leq 11.3$). Similarly, the OVI covering fraction (k_OVI), for a threshold of ${\rm log}_{10}(N(OVI)/{\rm cm}^{-2})=14.0$, shows a tentative enhancement along both the projected major and minor axes for low-mass galaxies. In contrast, \OVI-bearing gas around higher-mass galaxies appears more uniformly distributed, with no significant azimuthal dependence. Finally, using the halo circular-velocity-normalized pixel-velocity two-point correlation function (TPCF), we find that OVI absorbers are kinematically narrower along the disk plane compared to the polar directions of the host galaxies with similar stellar mass distributions. The observed isotropic distribution of OVI in high-mass halos suggests that its spatial distribution is governed by global halo properties; however, the OVI kinematics retain memory of the site of origin.

astro-ph.GA↗

arXiv2025

Pulsed single-photon spectroscopy of an emitter with vibrational coupling

We analytically derive the quantum state of a single-photon pulse scattered from a single quantum two-level emitter interacting with a vibrational bath. This solution for the quadripartite system enables an information-theoretic characterization of vibrational effects in quantum light spectroscopy. We show that vibration-induced dephasing reduces the quantum Fisher information (QFI) for estimating the emitter's linewidth, largely reflecting the Franck-Condon suppression of light-matter coupling. Comparing time- and frequency-resolved photodetection, we find the latter to be more informative in estimating the emitter's linewidth for stronger vibrational coupling.

quant-ph↗

arXiv2025

Simultaneous Khintchine theorem on manifolds in positive characteristics: convergence case

We prove the convergence case of Khintchine's theorem, with general approximation functions that are not necessarily monotonic, for analytic nonplanar manifolds over local fields of positive characteristic. Our approach is based on the method of counting rational points near manifolds developed by Beresnevich and Yang. To address the scenario where the given approximating function is not monotonic, we extend our function field by adjoining an appropriate root. Additionally, in the course of the proof, we establish several new results in the geometry of numbers over function fields, which are of independent interest.

math.NT↗

arXiv2025

A survey and a result on inhomogeneous quadratic forms

We survey recent work done on the values at integer points of irrational inhomogeneous quadratic forms, namely, inhomogeneous analogues of the famous Oppenheim conjecture. We also prove that the set of such forms in two variables whose set of values at integer points avoids a given countable set not containing zero, has full Hausdorff dimension. Moreover, we consider the more refined variant of this problem, where the shift is fixed and the form is allowed to vary. The strategy is to translate the problems to homogeneous dynamics and deduce the theorems from their dynamical counterparts. While our approach is inspired by the work of Kleinbock and Weiss, the dynamical results can be deduced from more general results of An, Guan, and Kleinbock.

math.NT↗

arXiv2025

Data Integration and spatio temporal statistics can quantify relative risk of medico-legal reforms: the example of police emergency mental health responses in Queensland (Australia)

This study examined the spatial-temporal dynamics of Emergency Examination Order or Authority (EE-O/A) admissions in Far Northern Queensland (FNQ) from 2009 to 2020, using 13,035 unique police records aggregated across 83 postcodes. A two-stage modelling framework was used: Lasso was used to identify a parsimonious set of socio economic and health-service covariates, and a Conditional Autoregressive (CAR) model incorporated these predictors with structured spatial and temporal random effects. This research demonstrates that socio-economic disadvantage and service accessibility drive EE-O/A incidence, underscoring the need for targeted mental-health interventions and resource allocation in impoverished FNQ communities. Limitations include reliance on cross-sectional census data for covariates and potential ecological bias from data fusion.

stat.ME↗

arXiv2025

Optimal quantum spectroscopy using single-photon pulses

We provide the ultimate precision attainable in spectroscopy of a quantum emitter using single-photon pulses. We find the maximum for estimating the linewidth to be independent of the details of the emitter's bare Hamiltonian while that for the detunings not to be so. We also identify optimal pulse shapes attaining these precisions.

quant-ph↗

arXiv2025

On the Bessel function and $n$-dimensional Hankel transform with Bicomplex arguments and coherent states

In this work, we introduce bicomplex Bessel function and analyze its region of convergence. Important properties of the bicomplex Bessel function, such as recurrence relations, integral representations, differential relations are explored. Moreover a differential equation satisfied by the bicomplex Bessel function is established. Furthermore, we investigate bicomplex holomorphicity and discuss its asymptotic behavior. Finally, we define $n$-dimensional bicomplex Hankel transformation by using bicomplex Bessel function and show that it is an isomorphism between two suitably defined function spaces. The application of the $n$-dimensional bicomplex Hankel transform has been effectively demonstrated by solving some partial differential equations. Additionally, a new extension of coherent states is built based on the use of the bicomplex Bessel function and demonstrate that these states fulfill the conditions of normalizability, continuity and the resolution of unity.

math.CV↗