arXiv subjects

Saurabh Verma

Publications and source records attributed to Saurabh Verma.

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

Testing Exponential $f(R)$ Gravity with CMB, DESI-DR2, and Supernova Data

One of the most popular competitors to the CDM paradigm as an explanation for the late-time acceleration of the universe is the modification of general relativity (GR), with models such as $f(R)$ gravity among the main motivations. In this study, we consider an exponential $f(R)$ gravity model as a possible extensions of the GR. The extra scalar degrees of freedom and their effects on the cosmic expansion and structure formation are continuously considered in this scenario. By combining the PPS, BBN, CC, DESI-DR2, and CMB datasets, we imposed limitations on this model. We performed a detailed statistical analysis of the free model parameter $b$ together with the standard cosmological parameters. Our analysis yields values of $H_0$ that are slightly lower than those obtained in $\Lambda$CDM, indicating no significant relaxation of the $H_0$ tension. In contrast, the model predicts systematically higher values of $S_8$, leading to a moderate alleviation of the $S_8$ tension by up to $\sim 1.2\sigma$ when late-time datasets are included. Overall, these results demonstrate that although the considered $f(R)$ gravity model does not resolve all cosmological tensions simultaneously, it provides a consistent improvement in the description of large-scale structure formation.

gr-qc↗

arXiv2026

LLM Prompt Duel Optimizer: Efficient Label-Free Prompt Optimization

Large language models (LLMs) are highly sensitive to prompts, but most automatic prompt optimization (APO) methods assume access to ground-truth references (e.g., labeled validation data) that are costly to obtain. We propose the Prompt Duel Optimizer (PDO), a sample-efficient framework for label-free prompt optimization based on pairwise preference feedback from an LLM judge. PDO casts prompt selection as a dueling-bandit problem and combines (i) Double Thompson Sampling to prioritize informative comparisons under a fixed judge budget, with (ii) top-performer guided mutation to expand the candidate pool while pruning weak prompts. Experiments on BIG-bench Hard (BBH) and MS MARCO show that PDO consistently identifies stronger prompts than label-free baselines, while offering favorable quality--cost trade-offs under constrained comparison budgets.

cs.CL↗

arXiv2026

Some remarks on the exponential separation and dimension preserving approximation for sets and measures

In the dimension theory of sets and measures, a recent breakthrough happened due to Hochman, who introduced the exponential separation condition (ESC) and proved the Hausdorff dimension result for invariant sets and measures generated by similarities on the real line. Following this groundbreaking work, we make a modest contribution by weakening the condition. Further, we define the modified ESC using the convex hull of the attractor and show that for homogeneous self-similar IFS on $\mathbb{R},$ both definitions coincide. We also define some sets in the class of all nonempty compact sets using the Assouad and Hausdorff dimensions and subsets of measures in the space of Borel probability measures on $\mathbb{R}^m$ using the $L^q$ dimension and the Rajchman property, and prove their density in the respective spaces.

math.DS↗

arXiv2026

Alleviating the Hubble Tension with Logarithmic Dark Energy: Constraints on the $w_{log}$CDM Model

Observational constraints are considered on a $w_{log}$CDM model of the dark energy equation of state, $w_{d}(z) = w_{0} + w_{a}\left( \frac{\ln(2+z)}{1+z} - \ln 2 \right)$, using the most recent cosmological datasets including DESI Baryon Acoustic Oscillation (BAO) measurements, Big Bang Nucleosynthesis (BBN) priors, Cosmic Chronometer (CC) observations, and Pantheon Plus (PPS) Type Ia supernovae. From the combined DESI BAO+BBN+CC+PPS dataset, we obtain $H_0 = 71.02 \pm 0.66~\text{kms}^{-1}\text{Mpc}^{-1}$, $Ω_m = 0.2863 \pm 0.0080,$ $w_0 = -0.875 \pm 0.066,$ $w_a = -0.69^{+0.37}_{-0.32},$ at the 68\% and 95\% confidence levels, indicating a preference for phantom dark energy with mild evidence for temporal evolution. The Hubble constant obtained from our model is closer to the local SH0ES measurement than the standard $Λ$CDM prediction, partially easing the Hubble tension. We perform extensive parameter-space exploration revealing correlations between $w_0$, $w_a$, and $H_0$, showing that dynamical dark energy models can fit higher values of the Hubble constant. The reconstructed deceleration parameter $q(z)$ shows the transition from deceleration to acceleration at $z \sim 0.6$--$0.7$, while the equation-of-state reconstruction remains consistent with a cosmological constant across the observed redshift range. A model comparison using information criteria indicates that the $w_{log}$CDM model remains statistically competitive with $Λ$CDM.

physics.gen-ph↗

arXiv2026

Observational Constraints and Geometric Diagnostics of Barboza-Alcaniz and Logarithmic Dark Energy Parametrizations

This study investigates and compares two prominent two-dimensional dark energy (DE) parameterizations: Barboza-Alcaniz (BA) and Logarithmic forms by comparing them with a comprehensive set of observational data comprising Type Ia Supernovae (SNe Ia) from the Pantheon compilation, Baryon Acoustic Oscillations (DESI BAO), and Cosmic Chronometers (CC). The primary objective was to explore the constraining power and cosmological implications of each parameterization in light of the current data. After formulating the theoretical framework and background equations governing cosmic expansion, we employ Markov Chain Monte Carlo (MCMC) techniques using the emcee Python package to constrain the free parameters of each model. The best-fit values for parameters $ω_0$, $ω_a$, and $H_0$ were extracted for each model using individual and combined datasets. The results include confidence contours at the levels $1σ$ and $2σ$. Our findings demonstrate that both parameterizations are consistent with observational data, with logarithmic parameterization showing slightly better constraints in terms of parameter evolution. Furthermore, we employed a statefinder diagnostic to analyze the geometric behavior of the models, providing an effective distinction between the two DE scenarios. This study contributes to a deeper understanding of DE evolution and its constraints in light of current cosmological data.

physics.gen-ph↗

arXiv2026

Weaker quantization dimension results for self-similar measures

In this paper, we investigate the quantization dimension of self-similar measures, particularly when the IFS does not satisfy the separation condition, but the sub-IFS at some level satisfies the separation condition. Further, we study the approximation of the space of Borel probability measures $\mathcal{P}(\mathbb{R}^m)$ with respect to the geometric mean error, i.e., the quantization dimension of order zero.

math.DS↗

arXiv2025

Set-Valued Fractal Approximation for Countable Data Sets

Fractal geometry deals mainly with irregularity and captures the complexity of a structure or phenomenon. In this article, we focus on the approximation of set-valued functions using modern machinery on the subject of fractal geometry. We first provide a construction of fractal functions for countable data sets and use these functions in the approximation and study of set-valued mappings. We also show the existence and uniqueness of an invariant Borel measure supported on the graph of a set-valued fractal function. In addition, we obtain some effective bounds on the dimensions of the constructed set-valued fractal functions.

math.FA↗

arXiv2025

Some results on Lower Assouad and quantization dimensions

In this paper, we first show that the collection of all subsets of $ \mathbb{R} $ having lower dimension $ γ\in [0,1] $ is dense in $ Π(\mathbb{R}) $, the space of compact subsets of $ \mathbb{R} $. Furthermore, we show that the set of Borel probability measures with lower dimension $ β\in [0, m] $ is dense in $ Ω(\mathbb{R}^m) $, the space of Borel probability measures on $ \mathbb{R}^m $. We also prove that the quantization and the lower dimension of a measure $ \vartheta $ coincide with those of the convolution of $ \vartheta $ with a finite combination of Dirac measures. In the end, we compute the lower dimension of the invariant measure associated with the product IFS.

math.DS↗

arXiv2025

Dimension Of Inhomogeneous Sub-Self-Similar Sets

In this paper, we introduce the concept of Inhomogeneous sub-self-similar (ISSS) sets, building upon the foundations laid by Falconer (Trans. Amer. Math. Soc. 347 (1995) 3121-3129) in the study of sub-self-similar sets and drawing inspiration from Barnsley's work on inhomogeneous self-similar sets (Proc. Roy. Soc. London Ser. A 399 (1985), no. 1817, 24). We explore a range of examples of ISSS sets and elucidate a method to construct ISSS sets. We also investigate the upper and lower box dimensions of ISSS sets and discuss the continuity of the Hausdorff dimension.

math.DS↗

arXiv2025

Barnsley-Navascués fractal operators on Banach spaces on the Sierpiński gasket

In this article, we define fractal operators motivated by the works of Barnsley and Navascués on various function spaces such as energy space, Lebesgue space, and oscillation space on the well-known fractal domain Sierpiński gasket. We further explore the properties of these operators from the perspectives of operator and approximation theory.

math.FA↗

arXiv2025

Testing $f(T)$ Gravity with Cosmological Observations: Confronting the Hubble Tension and Implications for the Late-Time Universe

In recent years, modifications to General Relativity (GR) have been explored to address cosmological observations, particularly in the context of late-time cosmic acceleration. Among these, modifications based on the Teleparallel Equivalent of General Relativity (TEGR), particularly $f(T)$ gravity, have gained significant attention. In this work, we investigate the scalar perturbations in $f(T)$ gravity, focusing on how these perturbations modify the Poisson and lensing equations and how they impact cosmological observables. By incorporating observational data from cosmic chromatometers, Big Bang nucleosynthesis, the DESI BAO survey, and Type Ia Supernovae (SNe Ia), we derive constraints on the parameters of the $f(T)$ power-law model. Our results suggest that $f(T)$ gravity can effectively alleviate some of the tensions observed in the standard $Λ$CDM model, including the Hubble constant ($H_0$) discrepancy. Furthermore, the evolution of the supernova luminosity and its dependence on the gravitational constant are considered to refine the measurement of cosmological parameters. The model's ability to address the $H_0$ tension is critically examined, and we find that $f(T)$ gravity offers a viable alternative to the standard model. The work concludes by comparing the fits of the $f(T)$ gravity model to the $Λ$CDM model using various information criteria, revealing key insights into the viability of modified gravity in contemporary cosmology.

astro-ph.CO↗

arXiv2025

Quantization for a condensation system

For a given $r \in (0, +\infty)$, the quantization dimension of order $r$, if it exists, denoted by $D_r(μ)$, represents the rate at which the $n$th quantization error of order $r$ approaches to zero as the number of elements $n$ in an optimal set of $n$-means for $μ$ tends to infinity. If $D_r(μ)$ does not exist, we define $\underline{D}_r(μ)$ and $\overline{D}_r(μ)$ as the lower and the upper quantization dimensions of $μ$ of order $r$, respectively. In this paper, we investigate the quantization dimension of the condensation measure $μ$ associated with a condensation system $(\{S_j\}_{j=1}^N, (p_j)_{j=0}^N, ν).$ We provide two examples: one where $ν$ is an infinite discrete distribution on $\mathbb{R}$, and one where $ν$ is a uniform distribution on $\mathbb{R}$. For both the discrete and uniform distributions $ν$, we determine the optimal sets of $n$-means, and calculate the quantization dimensions of condensation measures $μ$, and show that the $D_r(μ)$-dimensional quantization coefficients do not exist. Moreover, we demonstrate that the lower and upper quantization coefficients are finite and positive.

math.DS↗

arXiv2025

Dimension preserving set-valued approximation and decomposition via metric sum

In the literature, the Minkowski-sum and the metric-sum of compact sets are highlighted. While the first is associative, the latter is not. But the major drawback of the Minkowski combination is that, by increasing the number of summands, this leads to convexification. The present article is uncovered in two folds: The initial segment presents a novel approach to approximate a continuous set-valued function with compact images via a fractal approach using the metric linear combination of sets. The other segment contains the dimension analysis of the distance set of graph of set-valued function and solving the celebrated distance set conjecture. In the end, a decomposition of any continuous convex compact set-valued function is exhibited that preserves the Hausdorff dimension, so this will serve as a method for dealing with complicated set-valued functions.

math.DS↗

arXiv2025

Quantization dimension for a generalized inhomogeneous bi-Lipschitz iterated function system

For a given $r\in (0, +\infty)$, the quantization dimension of order $r$, if it exists, denoted by $D_r(\mu)$, of a Borel probability measure $\mu$ on ${\mathbb R}^d$ represents the speed how fast the $n$th quantization error of order $r$ approaches to zero as the number of elements $n$ in an optimal set of $n$-means for $\mu$ tends to infinity. If $D_r(\mu)$ does not exists, we call $\underline D_r(\mu)$ and $\overline D_r(\mu)$, the lower and upper quantization dimensions of $\mu$ of order $r$. In this paper, we estimate the quantization dimension of condensation measures associated with condensation systems $(\{f_i\}_{i=1}^N, (p_i)_{i=0}^N, \nu)$, where the mappings $f_i$ are bi-Lipschitz and the measure $\nu$ is an image measure of an ergodic measure with bounded distortion supported on a conformal set. In addition, we determine the optimal quantization for an infinite discrete distribution, and give an example which shows that the quantization dimension of a Borel probability measure can be positive with zero quantization coefficient.

math.DS↗

arXiv2024

Proactive Detection and Calibration of Seasonal Advertisements with Multimodal Large Language Models

A myriad of factors affect large scale ads delivery systems and influence both user experience and revenue. One such factor is proactive detection and calibration of seasonal advertisements to help with increasing conversion and user satisfaction. In this paper, we present Proactive Detection and Calibration of Seasonal Advertisements (PDCaSA), a research problem that is of interest for the ads ranking and recommendation community, both in the industrial setting as well as in research. Our paper provides detailed guidelines from various angles of this problem tested in, and motivated by a large-scale industrial ads ranking system. We share our findings including the clear statement of the problem and its motivation rooted in real-world systems, evaluation metrics, and sheds lights to the existing challenges, lessons learned, and best practices of data annotation and machine learning modeling to tackle this problem. Lastly, we present a conclusive solution we took during this research exploration: to detect seasonality, we leveraged Multimodal LLMs (MLMs) which on our in-house benchmark achieved 0.97 top F1 score. Based on our findings, we envision MLMs as a teacher for knowledge distillation, a machine labeler, and a part of the ensembled and tiered seasonality detection system, which can empower ads ranking systems with enriched seasonal information.

cs.IR↗

arXiv2024

Construction of Fractal Functions Using Kannan Mappings and Smoothness Analysis

Let T be a self-map on a metric space (X, d). Then T is called the Kannan map if there exists α, 0 < α< 1/2, such that d(T(x), T(y)) <= α[d(x, T(x)) + d(y, T(y))], for all x, y in X. This paper aims to introduce a new method to construct fractal functions using Kannan mappings. First, we give the rigorous construction of fractal functions with the help of the Kannan iterated function system (IFS). We also show the existence of a Borel probability measure supported on the attractor of the Kannan IFS satisfying the strong separation condition. Moreover, we study the smoothness of the constructed fractal functions. We end the paper with some examples and graphical illustrations.

math.DS↗

arXiv2023

Algorithm Selection for Deep Active Learning with Imbalanced Datasets

Label efficiency has become an increasingly important objective in deep learning applications. Active learning aims to reduce the number of labeled examples needed to train deep networks, but the empirical performance of active learning algorithms can vary dramatically across datasets and applications. It is difficult to know in advance which active learning strategy will perform well or best in a given application. To address this, we propose the first adaptive algorithm selection strategy for deep active learning. For any unlabeled dataset, our (meta) algorithm TAILOR (Thompson ActIve Learning algORithm selection) iteratively and adaptively chooses among a set of candidate active learning algorithms. TAILOR uses novel reward functions aimed at gathering class-balanced examples. Extensive experiments in multi-class and multi-label applications demonstrate TAILOR's effectiveness in achieving accuracy comparable or better than that of the best of the candidate algorithms. Our implementation of TAILOR is open-sourced at https://github.com/jifanz/TAILOR.

cs.LG↗