arXiv subjects

Ayan Chatterjee

Publications and source records attributed to Ayan Chatterjee.

At least 19 recordsLinked to original sources

arXiv2026

Reconstructing $f(R)$ gravity from generalized entropies: exact Lagrangians

Generalized horizon entropies are widely used as theoretical modifications of the Bekenstein-Hawking area law, but through the Wald construction they may also encode modifications of the underlying gravitational dynamics. We reconstruct metric $f(R)$ gravity from prescribed entropy-area relations and show that the procedure is intrinsically branch dependent through the required area-curvature map. On the maximally symmetric branch, where $A=48\pi/R$ exactly, the reconstruction reduces to a single quadrature and can be performed non-perturbatively. We obtain closed-form Lagrangians for several generalized entropies and show that an entropy term $a~S_{BH}^{q}$ generates a curvature term proportional to $R^{2-q}$. In particular, Kaniadakis entropy produces a $1/R$ correction, while logarithmic entropy generates an $R^2\ln R$ term. We further derive a branch-independent criterion, $\partial_{R}^{2} f=(ds/dR)d(S/s)/ds$, relating Dolgov-Kawasaki stability directly to the entropy functional, together with $m_{\rm sc}^2=S'(s)/(3f_{RR})$ on the maximally symmetric branch. Comparison with the fixed-mass Schwarzschild-de Sitter branch reveals different reconstructed Lagrangians and reversed stability properties. Finally, the weak-isolated-horizon boost charge reproduces the original generalized entropy. These results establish a direct non-perturbative link between generalized horizon thermodynamics and modified gravitational dynamics.

gr-qc↗

arXiv2026

Hawking radiation from black holes in 2+1 dimensions

The paper develops a model to understand the effective quantum geometry of a black hole horizon and the emission of Hawking spectrum in $2+1$ dimensions. Using the algebra of Hamiltonian charges on the horizon, we establish that one should view the black hole horizon as formed out of quantised lengths of elementary quanta of value $8\pi \ell_{P}\, n$, where $n\in \mathbb{N}$, and $\ell_{P}$ is the Planck length. We determine the black hole entropy using this equidistant length spectrum in the microcanonical ensemble and show that its value is close to the Bekenstein-Hawking entropy. To evaluate the Hawking spectrum, we note that, to an observer near the black hole horizon, the entropy (or length of horizon cross-section) is related to the black hole energy. Hence, one may develop a formulation of length ensemble (similar to the area canonical ensemble of Krasnov) from which the black body spectrum may be obtained directly. This local observer perceives a Hawking spectrum whose temperature is modified by the Tolman factor.

gr-qc↗

arXiv2026

Non-Minimally Coupled Scalar Field, Area Quantization and Black Hole Entropy

The enumeration of black hole entropy in candidate theories of quantum gravity utilises the quantum properties of microstates residing on the black hole horizon. For example, in Loop Quantum Gravity, the computation of entropy is based on the spectrum of area operator, and one determines the possible number of area mirocrostates corresponding to a given classical horizon area. In this paper, we derive the eigenspectrum of the horizon area operator for rotating/non-rotating black holes in a gravitational theory non-minimally coupled to scalar fields. Using the weak isolated horizon formalism, we show that the spectrum of area operator follows unambiguously from the algebra of horizon symmetry. More precisely, from the quantum mechanical point of view, the horizon geometry must be naturally discrete, a conclusion which is arrived at directly, without the need for any particular theory of quantum gravity. The area spectrum depends on the Barbero-Immirzi parameter as well as the value of scalar field on horizon. The area spectrum is equidistant, which is consistent with the Bekenstein-Mukhanov proposal and gives rise to black hole entropy and their quantum corrections.

gr-qc↗

arXiv2025

Evaporation of Primordial Black Holes in a Thermal Universe: A Thermofield Dynamics Approach

We investigate the impact of a finite temperature environment on the Hawking radiation from black holes (BHs), with particular focus on Kerr BHs immersed in a cosmological thermal bath. The emitted particles from BHs interact with the thermal background and thermalize, leading to a modification in the Hawking radiation spectrum. By employing the methods of Thermofield Dynamics (TFD), a real time formalism of thermal quantum field theory, we derive the modified occupation numbers of the Hawking spectrum for asymptotically flat spacetimes like the Schwarzschild and the Kerr geometries. These corrections depend on the interplay between the BH temperature and the ambient bath temperature. We apply this formalism in the early universe reheating background scenario arising after inflation and demonstrate that the thermal correction to Hawking spectrum enhances the evaporation rate of primordial black holes (PBHs). As a result, the lifetime of PBH shortens compared to the zero temperature vacuum and leads to interesting cosmological consequences.

hep-th↗

arXiv2025

Laws of black hole mechanics in the Einstein-Gauss-Bonnet theory

We extend the isolated horizon formalism to include rotating black holes arising in five dimensional Einstein-Gauss-Bonnet (EGB) theory of gravity, and derive the laws of black hole mechanics. This result allows us to show that the first law of black hole mechanics is modified, due to the Gauss-Bonnet term, so as to include corrections to (i) the area of horizon cross-sections and, to (ii) the expression of horizon angular momentum. Once these modifications are included, the Hamiltonian generates an evolution on the space of solutions of the EGB theory admitting isolated horizon as an internal boundary, the consequence of which is the first law of black hole mechanics. These boundary conditions may help in the search for exact solutions describing rotating black holes in this theory.

gr-qc↗

arXiv2025

Gravitational collapse of matter fields in de Sitter spacetimes

In this paper, we discuss the spherically symmetric gravitational collapse of matter fields in the de Sitter universe. The energy-momentum tensor of the matter field is assumed to admit a wide variety including dust, perfect fluids with equations of state, fluids with tangential and radial pressure, and with bulk and shear viscosity. Under different initial conditions imposed on the velocity and the density profiles, and by combining the results from exact analytical methods with those obtained from numerical techniques, we track the formation and evolution of spherical marginally trapped spheres as the matter suffers continual gravitational collapse. We show that the quasilocal formalism of trapped surfaces provides an ideal framework to study the evolution of horizons. More precisely, black hole and cosmological horizons may be viewed as the time development of marginally trapped surfaces.

gr-qc↗

arXiv2025

Spherical trapped surfaces in n-dimensional general relativity

In this paper, we examine gravitational collapse of matter fields in $n$-dimensional general relativity. The matter energy-momentum tensor under consideration includes dust, perfect fluids with equations of state and matter admitting bulk and shear viscosity. By adjusting various parameters of the matter energy-momentum tensor, we determine the trapped region and spherical marginally trapped surfaces in homogeneous and inhomogeneous models of collapse. We show that, as expected, the time development of marginally trapped tube is intricately related to the initial velocity and density profiles of the collapsing matter configuration. This study clarifies the role of initial data in the formation of spacetime singularity during gravitational collapse and implies that, under generic conditions on the matter profiles, the central spacetime singularity is always covered by a horizon.

gr-qc↗

arXiv2025

Gravitational collapse in pure Gauss- Bonnet theory

In this paper, we study the gravitational collapse of matter fields, which include dust, perfect fluids as well as fluids admitting bulk and shear viscosity. The initial conditions on these matter fields have been kept to be quite general: the initial velocity profile of the matter is taken to include both the bound and the marginally bound models, while the density profile of the initial matter configuration is assumed to have physically admissible portrayal, and smooth falloffs. We determine, under these general conditions, the time of formation of the central singularity and the formation and evolution of black hole horizons, depicted here in terms of quasilocal marginally trapped surfaces. Our study shows that under these general conditions, the central singularity remains hidden from the asymptotic observer.

gr-qc↗

arXiv2025

Transfer Learning for Temporal Link Prediction

Link prediction on graphs has applications spanning from recommender systems to drug discovery. Temporal link prediction (TLP) refers to predicting future links in a temporally evolving graph and adds additional complexity related to the dynamic nature of graphs. State-of-the-art TLP models incorporate memory modules alongside graph neural networks to learn both the temporal mechanisms of incoming nodes and the evolving graph topology. However, memory modules only store information about nodes seen at train time, and hence such models cannot be directly transferred to entirely new graphs at test time and deployment. In this work, we study a new transfer learning task for temporal link prediction, and develop transfer-effective methods for memory-laden models. Specifically, motivated by work showing the informativeness of structural signals for the TLP task, we augment a structural mapping module to the existing TLP model architectures, which learns a mapping from graph structural (topological) features to memory embeddings. Our work paves the way for a memory-free foundation model for TLP.

cs.LG↗

arXiv2025

Black holes in thermal bath live shorter: implications for primordial black holes

Hawking radiation from a non-extremal black hole is known to be approximately Planckian. The thermal spectrum receives multiple corrections including greybody factors and due to kinematical restrictions on the infrared and ultraviolet frequencies. We show that another significant correction to the spectrum arises if the black hole is assumed to live in a thermal bath and the emitted radiation gets thermalised at the bath temperature. This modification reshapes the thermal spectrum, and leads to appreciable deviation from standard results including modification in the decay rate of black holes. We argue that this altered decay rate has significance for cosmology and, in a realistic setting, show that it alters the life time of primordial black holes (PBHs) in the early universe. In particular, the very light PBHs formed right after the end of inflation decay faster which may have interesting phenomenological implications.

hep-th↗

arXiv2024

Generating Human Understandable Explanations for Node Embeddings

Node embedding algorithms produce low-dimensional latent representations of nodes in a graph. These embeddings are often used for downstream tasks, such as node classification and link prediction. In this paper, we investigate the following two questions: (Q1) Can we explain each embedding dimension with human-understandable graph features (e.g. degree, clustering coefficient and PageRank). (Q2) How can we modify existing node embedding algorithms to produce embeddings that can be easily explained by human-understandable graph features? We find that the answer to Q1 is yes and introduce a new framework called XM (short for eXplain eMbedding) to answer Q2. A key aspect of XM involves minimizing the nuclear norm of the generated explanations. We show that by minimizing the nuclear norm, we minimize the lower bound on the entropy of the generated explanations. We test XM on a variety of real-world graphs and show that XM not only preserves the performance of existing node embedding methods, but also enhances their explainability.

cs.LG↗

arXiv2023

Effects of electromagnetic field on a radiating star

In this paper we study the shear free spherical symmetric gravitational collapse of charged radiating star. All the physical quantities including pressure, density are regular. Energy conditions are satisfied throughout the interior of the matter configuration. The luminosity is time independent and mass is radiated linearly. The causal and non causal temperature remains greater than that of the uncharged collapsing scenario.

gr-qc↗

arXiv2023

GRASP: Accelerating Shortest Path Attacks via Graph Attention

Recent advances in machine learning (ML) have shown promise in aiding and accelerating classical combinatorial optimization algorithms. ML-based speed ups that aim to learn in an end to end manner (i.e., directly output the solution) tend to trade off run time with solution quality. Therefore, solutions that are able to accelerate existing solvers while maintaining their performance guarantees, are of great interest. We consider an APX-hard problem, where an adversary aims to attack shortest paths in a graph by removing the minimum number of edges. We propose the GRASP algorithm: Graph Attention Accelerated Shortest Path Attack, an ML aided optimization algorithm that achieves run times up to 10x faster, while maintaining the quality of solution generated. GRASP uses a graph attention network to identify a smaller subgraph containing the combinatorial solution, thus effectively reducing the input problem size. Additionally, we demonstrate how careful representation of the input graph, including node features that correlate well with the optimization task, can highlight important structure in the optimization solution.

cs.LG↗

arXiv2023

Disentangling Node Attributes from Graph Topology for Improved Generalizability in Link Prediction

Link prediction is a crucial task in graph machine learning with diverse applications. We explore the interplay between node attributes and graph topology and demonstrate that incorporating pre-trained node attributes improves the generalization power of link prediction models. Our proposed method, UPNA (Unsupervised Pre-training of Node Attributes), solves the inductive link prediction problem by learning a function that takes a pair of node attributes and predicts the probability of an edge, as opposed to Graph Neural Networks (GNN), which can be prone to topological shortcuts in graphs with power-law degree distribution. In this manner, UPNA learns a significant part of the latent graph generation mechanism since the learned function can be used to add incoming nodes to a growing graph. By leveraging pre-trained node attributes, we overcome observational bias and make meaningful predictions about unobserved nodes, surpassing state-of-the-art performance (3X to 34X improvement on benchmark datasets). UPNA can be applied to various pairwise learning tasks and integrated with existing link prediction models to enhance their generalizability and bolster graph generative models.

cs.LG↗

arXiv2022

Quality Assurance in MLOps Setting: An Industrial Perspective

Today, machine learning (ML) is widely used in industry to provide the core functionality of production systems. However, it is practically always used in production systems as part of a larger end-to-end software system that is made up of several other components in addition to the ML model. Due to production demand and time constraints, automated software engineering practices are highly applicable. The increased use of automated ML software engineering practices in industries such as manufacturing and utilities requires an automated Quality Assurance (QA) approach as an integral part of ML software. Here, QA helps reduce risk by offering an objective perspective on the software task. Although conventional software engineering has automated tools for QA data analysis for data-driven ML, the use of QA practices for ML in operation (MLOps) is lacking. This paper examines the QA challenges that arise in industrial MLOps and conceptualizes modular strategies to deal with data integrity and Data Quality (DQ). The paper is accompanied by real industrial use-cases from industrial partners. The paper also presents several challenges that may serve as a basis for future studies.

cs.SE↗

arXiv2022

Deterministic Random Walk Model in NetLogo and the Identification of Asymmetric Saturation Time in Random Graph

Interactive programming environments are powerful tools for promoting innovative network thinking, teaching science of complexity, and exploring emergent phenomena. This paper reports on our recent development of the deterministic random walk model in NetLogo, a leading platform for computational thinking, eco-system thinking, and multi-agent cross-platform programming environment. The deterministic random walk is foundational to modeling dynamical processes on complex networks. Inspired by the temporal visualizations offered in NetLogo, we investigated the relationship between network topology and diffusion saturation time for the deterministic random walk model. Our analysis uncovers that in Erd\H{o}s-R\'{e}nyi graphs, the saturation time exhibits an asymmetric pattern with a considerable probability of occurrence. This behavior occurs when the hubs, defined as nodes with relatively higher number of connections, emerge in Erd\H{o}s-R\'{e}nyi graphs. Yet, our analysis yields that the hubs in Barab\'{a}si-Albert model stabilize the the convergence time of the deterministic random walk model. These findings strongly suggest that depending on the dynamical process running on complex networks, complementing characteristics other than the degree need to be taken into account for considering a node as a hub. We have made our development open-source, available to the public at no cost at https://github.com/bravandi/NetLogo-Dynamical-Processes.

cs.MA↗

arXiv2022

MultiViz: A Gephi Plugin for Scalable Visualization of Multi-Layer Networks

The process of visually presenting networks is an effective way to understand entity relationships within the networks since it reveals the overall structure and topology of the network. Real networks are extremely difficult to visualize due to their immense complexity, which includes vast amounts of data, several types of interactions, various subsystems and several levels of connectivity as well as changes over time. This paper introduces the "MultiViz Plugin," a plugin for gephi, an open-source software tool for graph visualization and modification, in order to to visualize complex networks in a multi-layer manner. A collection of settings are availabe through the plugin to transform an existing network into a multi-layered network. The plugin supports several layout algorithms and lets user to choose which property of the network to be used as the layer. The goal of the study is to give the user complete control over how the network is visualized in a multi-layer fashion. We demonstrate the ability of the plugin to visualize multi-layer data using a real-life complex multi-layer datasets.

cs.SI↗

arXiv2022

Testing of Machine Learning Models with Limited Samples: An Industrial Vacuum Pumping Application

There is often a scarcity of training data for machine learning (ML) classification and regression models in industrial production, especially for time-consuming or sparsely run manufacturing processes. A majority of the limited ground-truth data is used for training, while a handful of samples are left for testing. Here, the number of test samples is inadequate to properly evaluate the robustness of the ML models under test for classification and regression. Furthermore, the output of these ML models may be inaccurate or even fail if the input data differ from the expected. This is the case for ML models used in the Electroslag Remelting (ESR) process in the refined steel industry to predict the pressure in a vacuum chamber. A vacuum pumping event that occurs once a workday generates a few hundred samples in a year of pumping for training and testing. In the absence of adequate training and test samples, this paper first presents a method to generate a fresh set of augmented samples based on vacuum pumping principles. Based on the generated augmented samples, three test scenarios and one test oracle are presented to assess the robustness of an ML model used for production on an industrial scale. Experiments are conducted with real industrial production data obtained from Uddeholms AB steel company. The evaluations indicate that Ensemble and Neural Network are the most robust when trained on augmented data using the proposed testing strategy. The evaluation also demonstrates the proposed method's effectiveness in checking and improving ML algorithms' robustness in such situations. The work improves software testing's state-of-the-art robustness testing in similar settings. Finally, the paper presents an MLOps implementation of the proposed approach for real-time ML model prediction and action on the edge node and automated continuous delivery of ML software from the cloud.

cs.SE↗