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Arun Kumar

Publications and source records attributed to Arun Kumar.

At least 37 records · Page 2Linked to original sources
arXiv2025

Probing Loop Quantum Gravity black holes through gravitational lensing

We investigate strong gravitational lensing by a charged loop quantum gravity (LQG) black hole obtained through the polymerisation scheme of Borges \textit{et al.} \cite{Borges:2023fog}. These effective geometries replace the Reissner--Nordström singularity with a symmetric transition surface and admit an extremal, cold remnant determined by the minimal area gap in LQG. In turn, we derive the null geodesic equations, investigate the photon effective potential, and obtain expressions for the photon-sphere radius and critical impact parameter. We compute the weak-field deflection angle and Einstein ring size, highlighting the deviations induced by the polymerisation parameter and the Barbero--Immirzi parameter. In the strong-field regime, we compute the strong deflection coefficients $(\bar{a},\bar{b})$ and evaluate the lensing observables $θ_\infty$, $s$, and $r_{\rm mag}$. Unlike the Reissner--Nordström case, the LQG corrections enhance the deflection angle and increase the angular separation of relativistic images, with deviations growing as the geometry approaches the LQG remnant limit. We further compute the corresponding observables for Sgr~A* and M87*, finding that the quantum-gravity modifications lie within the potential sensitivity of next-generation VLBI facilities. For M87*, the angular separation $s\in(0.05712,0.19123)\,μ\text{as}$, while it is $s\in(0.07595,0.25426)\,μ\text{as}$ for Sgr A*. The relative flux ratio is found to lie in the range, $r_{\rm mag}\in(4.49272,5.96397)$. Our analysis demonstrates that LQG-induced corrections leave characteristic strong and weak-lensing imprints, offering a promising observational pathway to probe quantum gravity using near-future high-resolution observations.

gr-qc↗
arXiv2025

The First Mathematical Model for Elk Wolf Interaction in Yellowstone National Park Using the E-SINDy Algorithm

In this study, we investigate the prey predator dynamics of the elk wolf system in northern Yellowstone National Park, USA, using a data driven modeling approach. We used yearly population data for elk and wolves from 1995 to 2022 to construct a mathematical model using a sparse regression modeling framework. To the best of our knowledge, no previous work has applied this framework to capture elk wolf interactions over this time period. Our modeling pipeline integrates Gaussian process regression for data smoothing, sparse identification of nonlinear dynamics for model discovery, and model selection techniques to identify the most suitable mathematical representation. The resulting model is analyzed for its nonlinear dynamics with ecologically meaningful parameters. Stability and bifurcation analyzes are then performed to understand the systems qualitative behavior. A saddle node bifurcation identifies parameter ranges where both species can coexist, while regions outside this range may lead to the extinction of one or both populations. Hopf and saddle node bifurcations together delineate zones of stable co existence, periodic oscillations, and extinction scenarios. Furthermore, co dimension two bifurcations, including Bogdanov Takens and cusp bifurcations, are explored by varying two parameters simultaneously. Ecologically, these bifurcations reflect the complex interplay between wolf pressure and elk defence mechanisms, such as grouping or herd behavior. They suggested that small changes in ecological parameters can lead to sudden shifts in population outcomes ranging from stable co existence to extinction or oscillatory cycles.

math.DS↗
arXiv2025

Structured Relational Representations

Invariant representations are core to representation learning, yet a central challenge remains: uncovering invariants that are stable and transferable without suppressing task-relevant signals. This raises fundamental questions, requiring further inquiry, about the appropriate level of abstraction at which such invariants should be defined and which aspects of a system they should characterize. Interpretation of the environment relies on abstract knowledge structures to make sense of the current state, which leads to interactions, essential drivers of learning and knowledge acquisition. Interpretation operates at the level of higher-order relational knowledge; hence, we propose that invariant structures must be where knowledge resides, specifically as partitions defined by the closure of relational paths within an abstract knowledge space. These partitions serve as the core invariant representations, forming the structural substrate where knowledge is stored and learning occurs. On the other hand, inter-partition connectors enable the deployment of these knowledge partitions encoding task-relevant transitions. Thus, invariant partitions provide the foundational primitives of structured representation. We formalize the computational foundations for structured relational representations of the invariant partitions based on closed semiring, a relational algebraic structure.

cs.LG↗
arXiv2025

Probing Lorentz Symmetry Violation through Lensing Observables of Rotating Black Holes

We find a Kerr-like black hole solution-a rotating Bumblebee black hole (RBBH) with a Lorentz-violating parameter $\ell$ and examine the strong lensing by it. The parameter $\ell$ changes the event horizon radius and photon sphere, resulting in a different lensing signature compared to the Kerr black hole of general relativity. Using the strong deflection limit formalism, we compute key observables such as the angular positions of relativistic images, their separation, magnification, and time delays for supermassive black holes Sgr A* and M87*. Our results show that the parameter $\ell$ has a profound influence on these observables, with $\ell > 0$ suppressing and $\ell < 0$ increasing the deflection angle compared to the Kerr case. We compare RBBH observables with those of Kerr black holes, using Sgr A* and M87* as lenses to observe the effect of the Lorentz symmetry-breaking parameter $\ell$. For Sgr A*, the angular position $θ_\infty$ in $\in~(18.25-33.3)~μas$, while for M87* $\in~(13.71-25.02)~μas$. The angular separation $s$, for supermassive black holes (SMBHs) Sgr A* and M87*, differs significantly, with values ranging $\in~(0.005-0.81)~μas$ for Sgr A* and $\in~(0.003-0.6)~μas$ for M87*. The relative magnitude $r_{\text{mag}}$ $\in~(3.04-8.15)~μas$. We also compared the time delays between the relativistic images in the SMBHs and found that RBBH can be quantitatively distinguished from Kerr black holes. Our analysis concludes that, within the 1$σ$ region, a significant portion of the parameter space agrees with the EHT results of M87* and Sgr A*. This demonstrates the feasibility of utilizing strong gravitational lensing to identify Lorentz symmetry violations in extreme gravity regimes. Weak lensing analysis and Einstein ring observations provide further constraints, producing an upper bound of $\ell \lesssim \mathcal{O}(10^{-6})$.

gr-qc↗
arXiv2025

Lyapunov Exponent Approach to Phase Structure of Schwarzschild AdS Black Holes Surrounded by a Cloud of Strings

We investigate Schwarzschild black holes in anti-de Sitter (AdS) spacetimes surrounded by a cloud of strings (BH-AdS-CoS), incorporating both electric- and magnetic-like components of the string bi-vector. Thermodynamically, these systems exhibit small/intermediate/large black hole phases with first- and second-order transitions governed by the string parameter $c_0$. Dynamically, we probe the phase structure using Lyapunov exponents $λ$ from unstable circular geodesics. For massless particles ($δ= 0$), analytical expressions $λ$ reveal multivalued behavior in first-order transition regimes ($c_0 < c_{\text{cri}}$), with branches mapping to thermodynamic phases ($λ_{\text{SBH}}, λ_{\text{IBH}}, λ_{\text{LBH}}$). The discontinuity $Δλ= λ_{\text{SBH}} - λ_{\text{LBH}}$ at $T_p$ follows mean-field scaling: $Δλ/ λ_{\text{cri}} \propto (T_\text{cri} - T)^{1/2} \quad (β= 1/2)$. For massive particles ($δ= 1$), numerical computation of timelike geodesics confirms $λ$ as an order parameter, with critical exponent $β= 1/2$ universally. Key distinctions emerge: $λ\to 1$ asymptotically for photons, while $λ\to 0$ in the significant black hole phase for massive particles due to vanishing unstable orbits. The transition of $λ$ from multivalued to single-valued at $c_0 = c_{\text{cri}}$ establishes it as a universal dynamical probe of black hole criticality. The universal critical exponent of 1/2 for \(Δλ\) further reinforces the analogy with conventional thermodynamic systems. Our results confirm a direct connection between the thermodynamic phase structure of BH-AdS-CoS and the dynamics of test particles, with the Lyapunov exponent emerging as a sensitive diagnostic of black hole criticality.

gr-qc↗
arXiv2025

Effect of Signal Quantization on Performance Measures of a 1st Order One Dimensional Differential Microphone Array

In practical systems, recorded analog signals must be digitized for processing, introducing quantization as a critical aspect of data acquisition. While prior studies have examined quantization effects in various signal processing contexts, its impact on differential microphone arrays (DMAs), particularly in one-dimensional (1D) first-order configurations, remains unexplored. This paper investigates the influence of signal quantization on the performance of first-order 1D-DMAs across various beampatterns. An analytical expression for quantized beamformed output for a first-order 1D-DMA has been formulated. The effect of signal quantization has been studied on array performance measures such as the Beampattern, Directivity Factor (DF), Front-to-Back Ratio (FBR), and suppression depth at null points (SDN). Simulation results reveal that the beampattern shape remains structurally invariant across quantization bit depths, with quantization primarily affecting SDN. DF and FBR remain constant with the varying number of quantization bits. Additionally, SDN is shown to be frequency-independent, however, it increases with increasing quantization bit depths, enhancing interference suppression. The study also examines the effect of steering nulls across the azimuthal range, showing that SDN degrades as the null moves closer to the source look direction (0 degree), indicating reduced interference suppression.

eess.SP↗
arXiv2025

Nano-silica based Aqueous Colloidal Gels as Eco-friendly Thixotropic Lubricant

The environmental risks posed by traditional oil and grease-based lubricants can be significantly mitigated by adopting water-based alternatives engineered with superior rheological performance. In this work, we present a fundamentally new and environmentally sustainable aqueous thixotropic colloidal gel of silica nanoparticles formed in the presence of NaCl. We conducted a systematic and detailed investigation of their rheological and tribological characteristics. The tribological performance was evaluated against dry and water-lubricated conditions for steel-steel interface. Our experiments demonstrate that the tribological performance of the formulated nanoparticle gel can be optimized by tuning its rheological properties. A combination of super-low friction and negligible wear was observed. The friction coefficient reduced by up to 97.46% (from 0.63 to 0.016) compared to dry sliding, and by 97.04% (from 0.541 to 0.016) compared to water lubrication. Similarly, the specific wear rate decreased by up to 99.62% and 96.10% under dry conditions and water lubrication respectively. This performance is attributed to a thixotropic, chemically robust gel formed via van der Waals interactions between silica flocs, enabling self-repairing properties, continuous tribo-film formation, and a nano-bearing effect from silica nanoparticles. These attributes enable the gel to maintain and regain its structure during periods of non-shear while also forming a thin film with sufficiently low viscosity to slip into the interfacial contact zone and continuously replenish it with lubricant.

cond-mat.soft↗
arXiv2025

Analysis of Null Related Beampattern Measures and Signal Quantization Effects for Linear Differential Microphone Arrays

A differential microphone array (DMA) offers enhanced capabilities to obtain sharp nulls at the cost of relatively broad peaks in the beam power pattern. This can be used for applications that require nullification or attenuation of interfering sources. To the best of our knowledge, the existing literature lacks measures that directly assess the efficacy of nulls, and null-related measures have not been investigated in the context of differential microphone arrays (DMAs). This paper offers new insights about the utility of DMAs by proposing measures that characterize the nulls in their beam power patterns. We investigate the performance of differential beamformers by presenting and evaluating null-related measures namely null depth (ND) and Null Width (NW) as a function of depth level relative to the beam power pattern maxima. A study of signal quantization effects due to data acquisition for 1st, 2nd and 3rd order linear DMAs and for different beampatterns i.e. dipole, cardioid, hypercardioid and supercardioid is presented. An analytical expression for the quantized beamformed output for any general $ N^{th} $ order DMA is formulated. Simulation results of the variation of ND with number of quantization bits and the variation of NW as a function of depth are also presented and inferences are drawn. Lab experiments are conducted in a fully anechoic room to support the simulation results. The measured beampattern exhibits a pronounced null depth, confirming the effectiveness of the experimental setup.

eess.SP↗
arXiv2025

The Cambridge Report on Database Research

On October 19 and 20, 2023, the authors of this report convened in Cambridge, MA, to discuss the state of the database research field, its recent accomplishments and ongoing challenges, and future directions for research and community engagement. This gathering continues a long standing tradition in the database community, dating back to the late 1980s, in which researchers meet roughly every five years to produce a forward looking report. This report summarizes the key takeaways from our discussions. We begin with a retrospective on the academic, open source, and commercial successes of the community over the past five years. We then turn to future opportunities, with a focus on core data systems, particularly in the context of cloud computing and emerging hardware, as well as on the growing impact of data science, data governance, and generative AI. This document is not intended as an exhaustive survey of all technical challenges or industry innovations in the field. Rather, it reflects the perspectives of senior community members on the most pressing challenges and promising opportunities ahead.

cs.DB↗
arXiv2024

European Option Pricing in Regime Switching Framework via Physics-Informed Residual Learning

In this article, we employ physics-informed residual learning (PIRL) and propose a pricing method for European options under a regime-switching framework, where closed-form solutions are not available. We demonstrate that the proposed approach serves an efficient alternative to competing pricing techniques for regime-switching models in the literature. Specifically, we demonstrate that PIRLs eliminate the need for retraining and become nearly instantaneous once trained, thus, offering an efficient and flexible tool for pricing options across a broad range of specifications and parameters.

q-fin.CP↗
arXiv2024

Unseen Object Reasoning with Shared Appearance Cues

This paper introduces an innovative approach to open world recognition (OWR), where we leverage knowledge acquired from known objects to address the recognition of previously unseen objects. The traditional method of object modeling relies on supervised learning with strict closed-set assumptions, presupposing that objects encountered during inference are already known at the training phase. However, this assumption proves inadequate for real-world scenarios due to the impracticality of accounting for the immense diversity of objects. Our hypothesis posits that object appearances can be represented as collections of "shareable" mid-level features, arranged in constellations to form object instances. By adopting this framework, we can efficiently dissect and represent both known and unknown objects in terms of their appearance cues. Our paper introduces a straightforward yet elegant method for modeling novel or unseen objects, utilizing established appearance cues and accounting for inherent uncertainties. This representation not only enables the detection of out-of-distribution objects or novel categories among unseen objects but also facilitates a deeper level of reasoning, empowering the identification of the superclass to which an unknown instance belongs. This novel approach holds promise for advancing open world recognition in diverse applications.

cs.CV↗
arXiv2024

Freezing of short-range ordered antiferromagnetic clusters in the CrFeTi$_2$O$_7$ system

We report on the CrFeTi$_2$O$_7$ (CFTO) system using a combination of x-ray diffraction, dc magnetization, ac susceptibility, specific heat and neutron diffraction measurements. CFTO is seen to crystallize in a monoclinic $P21/a$ symmetry. It shows a glassy freezing at $T{_f}$ ~ 22 K, characterized by the observation of bifurcation between ZFC and FC $χ$ (T) curves, frequency dispersion across $T{_f}$ in ac susceptibility, appearance of non-zero remanent magnetization and coercivity below $T{_f}$, very slow relaxation of iso-thermal remanent magnetization with time and a linear temperature dependence of magnetic contribution to specific heat $C{_m}$ below $T{_f}$. The microscopic neutron diffraction analysis of CFTO not only confirms the absence of long-range antiferromagnetic ordering but also exhibits diffuse scattering due to the presence of shortrange ordered antiferromagnetically correlated spin clusters.

cond-mat.str-el↗
arXiv2023

Saturn: An Optimized Data System for Large Model Deep Learning Workloads

Large language models such as GPT-3 & ChatGPT have transformed deep learning (DL), powering applications that have captured the public's imagination. These models are rapidly being adopted across domains for analytics on various modalities, often by finetuning pre-trained base models. Such models need multiple GPUs due to both their size and computational load, driving the development of a bevy of "model parallelism" techniques & tools. Navigating such parallelism choices, however, is a new burden for end users of DL such as data scientists, domain scientists, etc. who may lack the necessary systems knowhow. The need for model selection, which leads to many models to train due to hyper-parameter tuning or layer-wise finetuning, compounds the situation with two more burdens: resource apportioning and scheduling. In this work, we tackle these three burdens for DL users in a unified manner by formalizing them as a joint problem that we call SPASE: Select a Parallelism, Allocate resources, and SchedulE. We propose a new information system architecture to tackle the SPASE problem holistically, representing a key step toward enabling wider adoption of large DL models. We devise an extensible template for existing parallelism schemes and combine it with an automated empirical profiler for runtime estimation. We then formulate SPASE as an MILP. We find that direct use of an MILP-solver is significantly more effective than several baseline heuristics. We optimize the system runtime further with an introspective scheduling approach. We implement all these techniques into a new data system we call Saturn. Experiments with benchmark DL workloads show that Saturn achieves 39-49% lower model selection runtimes than typical current DL practice.

cs.LG↗
arXiv2023

Saturn: Efficient Multi-Large-Model Deep Learning

In this paper, we propose Saturn, a new data system to improve the efficiency of multi-large-model training (e.g., during model selection/hyperparameter optimization). We first identify three key interconnected systems challenges for users building large models in this setting -- parallelism technique selection, distribution of GPUs over jobs, and scheduling. We then formalize these as a joint problem, and build a new system architecture to tackle these challenges simultaneously. Our evaluations show that our joint-optimization approach yields 39-49% lower model selection runtimes than typical current DL practice.

cs.LG↗
arXiv2023

Quasi-static remanence as a generic-feature of spin-canting in Dzyaloshinskii-Moriya Interaction driven canted-antiferromagnets

We consistently observe a unique pattern in remanence in a number of canted-antiferromagnets (AFM) and piezomagnets. A part of the remanence is $\textit{quasi-static}$ in nature and vanishes above a critical magnetic field. Present work is devoted to exploring this $\textit{quasi-static}$ remanence ($μ$) in a series of isostructural canted-AFMs and piezomagnets that possess progressively increasing Néel temperature ($T{_N}$). Comprehensive investigation of remanence as a function of $\textit{magnetic-field}$ and $\textit{time}$ in CoCO$_{3}$, NiCO$_{3}$ and MnCO$_{3}$ reveals that the magnitude of $μ$ increases with decreasing $T{_N}$, but the stability with time is higher in the samples with higher $T{_N}$. Further to this, all three carbonates exhibit a universal scaling in $μ$, which relates to the concurrent phenomenon of piezomagnetism. Overall, these data not only establish that the observation of $\textit{quasi-static}$ remanence with $\textit{counter-intuitive}$ magnetic-field dependence can serve as a foot-print for spin-canted systems, but also confirms that simple remanence measurements, using SQUID magnetometry, can provide insights about the extent of spin canting - a non trivial parameter to determine. In addition, these data suggest that the functional form of $μ$ with $\textit{magnetic-field}$ and $\textit{time}$ may hold key to isolate Dzyaloshinskii Moriya Interaction driven spin-canted systems from Single Ion Anisotropy driven ones. We also demonstrate the existence of $μ$ by tracking specific peaks in neutron diffraction data, acquired in remnant state in CoCO$_{3}$.

cond-mat.str-el↗
arXiv2023

Geometric Infinitely Divisible Autoregressive Models

In this article, we discuss some geometric infinitely divisible (gid) random variables using the Laplace exponents which are Bernstein functions and study their properties. The distributional properties and limiting behavior of the probability densities of these gid random variables at 0+ are studied. The autoregressive (AR) models with gid marginals are introduced. Further, the first order AR process is generalised to kth order AR process. We also provide the parameter estimation method based on conditional least square and method of moments for the introduced AR(1) processes.

math.ST↗
arXiv2023

Successive magnetic phase transitions with magnetoelastic and magnetodielectric coupling in the ordered triple perovskite Sr$_3$CaRu$_2$O$_9$

We report a comprehensive temperature-dependent investigation of the 1:2 ordered triple perovskite system Sr$_3$CaRu$_2$O$_9$. It crystallizes in the monoclinic structure with space group $P21/c$, consisting of corner-sharing CaO$_6$ and RuO$_6$ octahedra. Using DC magnetization and neutron diffraction measurements, we show that this system undergoes successive magnetic transitions ~190 K and ~160 K. From the analysis of the temperature-dependent neutron diffraction and dielectric data, we demonstrate two distinguishing features of the Sr$_3$CaRu$_2$O$_9$ system: (i) magnetoelastic coupling associated with the two magnetic transitions, as revealed by a change in the unit cell volume, direct Ru-Ru distance, and bond angles and (ii) magnetodielectric coupling, as revealed by the anomalies across the two magnetic transitions. The present results would add significantly to the current understanding of the triple perovskites with incipient spin-orbit coupling.

cond-mat.str-el↗