arXiv subjects
Publications and source records attributed to Sourav Ghosh.
We prove uniqueness of tangent flows for mean curvature flow with free boundary at singularities modeled on half-cylindrical self-shrinkers. More precisely, if a tangent flow is of the form $\mathbb{S}^{n-k} \times \mathbb{R}^k_+$ or $\mathbb{S}^{n-k}_+ \times \mathbb{R}^k $, then it is unique. This provides the free-boundary analogue of the uniqueness theory for cylindrical singularities.
The microstructural stability of nickel-based superalloys critically depends on the morphology and evolution of $\gamma'$-precipitates, which is governed by elastic and interfacial anisotropies at the atomic scale. Here, we present a novel quantitative multiscale framework that, for the first time, directly incorporates atomistically computed interface energy anisotropy into mesoscale phase-field simulations to elucidate morphological selection and instability in the Ni--Al system. We employ density functional theory (DFT) to accurately predict the orientation-dependent $\gamma/\gamma'$ interface energies for key crystallographic planes. A rigorous analytic mapping is then developed to systematically reduce the three-dimensional (3D) interface anisotropy landscape to the two-dimensional (2D) simulation plane. This enables quantitative transfer of DFT-informed anisotropy parameters into a continuum phase-field model that also accounts for elastic inhomogeneity and eigenstrain. Our simulations demonstrate that the explicit inclusion of DFT-based interface energy anisotropy fundamentally alters precipitate morphological evolution, robustly suppressing instability and faceting phenomena otherwise promoted by supersaturation and elastic effects. The framework bridges atomic- to mesoscale modeling, enabling predictive control of precipitate shapes and providing new insights into the interplay of elastic and interfacial contributions in Ni-based superalloys. This approach paves the way for quantitative microstructural design in advanced high-temperature alloys via first-principles-guided multiscale simulation.
We establish a dynamic generalization of Nevanlinna-Pick interpolation for functions invariant under the action of a finite Blaschke product $f$, reducing global bounded holomorphic extension on orbit spaces to structured block-kernel positivity. Furthermore, we demonstrate that membership in $H^\infty(\mathbb{D})$ is universally detectable via deformations by any finite Blaschke product. These results are proved via an underlying operator-theoretic lifting framework for covariant operator pairs in the spirit of Sarason. Finally, in the setting of non-commutative function theory, we show that despite the universal validity of the matrix-valued von Neumann inequality over the free polydisk, Arveson-type complete spectral set representations break down for non-commutative inner varieties.
Automatic singing quality assessment (SQA) requires evaluating lyrical correctness and musical fidelity while handling expressive variations. However, existing systems largely rely on either acoustic cues or lyric transcriptions exclusively, limiting holistic performance evaluation. Furthermore, their integration is non-trivial due to challenges in robust singing transcription amid melisma, vibrato, and tempo elasticity. To this end, we propose MusicJudge, a modality-guided framework for automated SQA that performs block-aligned multimodal analysis by coupling lyric correctness with pitch-rhythm fidelity. It detects semantically meaningful lyric blocks using multi-signal matching that integrates semantic embeddings, lexical similarity, and phonetic alignment. To improve singing audio transcription, we introduce Modality-Guided LoRA for ASR fine-tuning. Experiments across datasets demonstrate strong agreement with human expert judgments and validate the generalizability of MusicJudge.
To minimize privacy concerns and inference latency on edge devices like smartphones, lightweight on-device models remain important for end-user applications. Many of these applications involve natural language classification, but deploying multiple specialized models creates a memory footprint challenge. We investigate: Can a single lightweight architecture solve multiple Speech-Adjacent (SA) classification tasks through reduction to a nuanced text similarity formulation? We propose AnySimLite, a lightweight similarity encoder that combines word-level and character-level channels. Together with a dataset transformation strategy, we evaluate AnySimLite across multiple SA classification tasks and show that it consistently achieves state-of-the-art (SOTA) or SOTA-competitive performance in few-shot settings while maintaining a low memory footprint. Even in the worst case, the performance drop remains below 7% while using $<\frac{1}{250}^{\mathrm{th}}$ of the model size of the SOTA qLLaMA_LoRA-7B baseline.
City-scale 3D surface reconstruction from multiview images for downstream 3D simulation, poses highly challenging problems due to the scale and complexity of urban scenes. Existing city-scale 3D reconstruction methods based on NeRF, Gaussian Splatting etc. often fail to recover 3D meshes ready for simulation due to incomplete/missing geometry and irregular, noisy surfaces. Scaling existing small-scale 3D reconstruction methods to arbitrarily large urban scenes is highly infeasible due to their computational complexity. We present City-Mesh3R, a scalable framework for reconstructing watertight surface meshes directly from large unordered image collections. Unlike recent methods which use global sparse SfM point-cloud initialization followed by a distributed 3D dense reconstruction of large-scale scenes, our method follows an end-to-end images-to-mesh 3D reconstruction approach using a divide-and-conquer strategy. The sparse city map is reconstructed via topological image clustering, cluster-wise independent sparse SfM and map merging, without need for exhaustive image feature matching. Then this map is partitioned spatially to perform geometry-aware camera selection, followed by dense surface reconstruction and surface refinement using curvature-aware adaptive vertex density remeshing. These partition meshes are then stitched together to produce the global mesh of the city. The proposed end-to-end framework is evaluated on city-scale reconstruction datasets. As demonstrated by our qualitative and quantitative results, our proposed method yields high-fidelity watertight 3D meshes with regular geometry, capturing fine surface details, and is suitable for scaling to arbitrarily large scenes owing to the end-to-end processing in a distributed setting.
In this article, we conduct a comprehensive study of weighted Sobolev spaces with logarithmic weights, orginially introduced by Calanchi and Ruf to analyze the sharp exponential integrability of radial functions belonging to these spaces. By exploring the connection between these logarithmically weighted energies and the Leray energy, we expand the framework to incorporate non-radial functions. More precisely, we establish optimal exponential integrability for general functions in the spirit of optimal Leray-Trudinger inequalities established by Di Blasio, Pisante and Psaradakis. Furthermore, we prove sharp versions of these inequalities when restricted to radial functions. Notably, the inequalities presented here are fundamentally different in nature from those of Calanchi and Ruf, for which the non-radial extension fails to hold.
We consider the rescaled flow associated with a mean curvature flow that develops a compact singularity of multiplicity one. We prove that the ``decay order'' of such a rescaled flow is uniformly bounded. As a consequence, we prove a unique continuation result.
In this note, we develop a parallel theory of the classical Sz.-Nagy--Foias dilation and model theory for a single contraction operator in the setting of pairs of \em{{$q$-commuting}} contraction operators for a unimodular complex number $q$.
The only non-compact linearly stable singularity models for mean curvature flow are cylindrical, as shown by Colding-Minicozzi. The uniqueness of blowups at singularities modeled on cylinders was established by Colding-Minicozzi. They also proved rigidity results for cylindrical singularities in their earlier work. In this paper, we develop a different approach inspired by Sz\'ekelyhidi to study cylindrical singularities and prove uniqueness and rigidity results.
Due to rapid advancements in technology, datasets are available from various domains. In order to carry out more relevant and appropriate analysis, it is often necessary to project the dataset into a higher or lower dimensional space based on requirement. Projecting the data in a higher-dimensional space helps in unfolding intricate patterns, enhancing the performance of the underlying models. On the other hand, dimensionality reduction is helpful in denoising data while capturing maximal information, as well as reducing execution time and memory.In this context, it is not always statistically evident whether the transformed embedding retains the local and global structure of the original data. Most of the existing metrics that are used for comparing the local and global shape of the embedding against the original one are highly expensive in terms of time and space complexity. In order to address this issue, the objective of this study is to formulate a novel metric, called Clustering guided METric (CMET), for quantifying embedding quality. It is effective to serve the purpose of quantitative comparison between an embedding and the original data. CMET consists of two scores, viz., CMET_L and CMET_G, that measure the degree of local and global shape preservation capability, respectively. The efficacy of CMET has been demonstrated on a wide variety of datasets, including four synthetic, two biological, and two image datasets. Results reflect the favorable performance of CMET against the state-of-the-art methods. Capability to handle both small and large data, low algorithmic complexity, better and stable performance across all kinds of data, and different choices of hyper-parameters feature CMET as a reliable metric.
Transforming static images into interactive experiences remains a challenging task in computer vision. Tackling this challenge holds the potential to elevate mobile user experiences, notably through interactive and AR/VR applications. Current approaches aim to achieve this either using pre-recorded video responses or requiring multi-view images as input. In this paper, we present PhysID, that streamlines the creation of physics-based interactive dynamics from a single-view image by leveraging large generative models for 3D mesh generation and physical property prediction. This significantly reduces the expertise required for engineering-intensive tasks like 3D modeling and intrinsic property calibration, enabling the process to be scaled with minimal manual intervention. We integrate an on-device physics-based engine for physically plausible real-time rendering with user interactions. PhysID represents a leap forward in mobile-based interactive dynamics, offering real-time, non-deterministic interactions and user-personalization with efficient on-device memory consumption. Experiments evaluate the zero-shot capabilities of various Multimodal Large Language Models (MLLMs) on diverse tasks and the performance of 3D reconstruction models. These results demonstrate the cohesive functioning of all modules within the end-to-end framework, contributing to its effectiveness.
Rapid spread of false images and videos on online platforms is an emerging problem. Anyone may add, delete, clone or modify people and entities from an image using various editing software which are readily available. This generates false and misleading proof to hide the crime. Now-a-days, these false and counterfeit images and videos are flooding on the internet. These spread false information. Many methods are available in literature for detecting those counterfeit contents but new methods of counterfeiting are also evolving. Generative Adversarial Networks (GAN) are observed to be one effective method as it modifies the context and definition of images producing plausible results via image-to-image translation. This work uses an independent discriminant network that can identify GAN generated image or video. A discriminant network has been created using a convolutional neural network based on InceptionResNetV2. The article also proposes a platform where users can detect forged images and videos. This proposed work has the potential to help the forensics domain to detect counterfeit videos and hidden criminal evidence towards the identification of criminal activities.
Let $L_t$ be a zero Maslov Lagrangian mean curvature flow in $\mathbb{C}^2.$ We show that if the mean curvature stays uniformly bounded along the flow, then the tangent flow at a singular point is unique i.e. the limit of the parabolic rescalings does not depend on the chosen sequence of rescalings.
We study the inequality of citations received for different publications of various researchers and Nobel laureates in Physics, Chemistry, Medicine and Economics using Google Scholar data from 2012 to 2024. Citation distributions are found to be highly unequal, with even greater disparity among Nobel laureates. Measures of inequality, such as the Gini and Kolkata indices, emerge as useful indicators for distinguishing Nobel laureates from others. Such high inequality corresponds to growing critical fluctuations, suggesting that excellence aligns with an imminent (self-organized dynamical) critical point. Additionally, Nobel laureates exhibit systematically lower values of the Tsallis--Pareto parameter \( b \) and Shannon entropy, indicating more structured citation distributions. We also analyze the inequality in Olympic medal tallies across countries and find similar levels of disparity. Our results suggest that inequality measures can serve as proxies for competitiveness and excellence.
In this survey article we discuss about possible generalizations of Anosov representations in the affine setting and their consequences.
The main goal of this article is to generalize Mess' work and using results from Labourie--Wentworth, Potrie--Sambarino and Smilga, to show that inside Hitchin representations, infinitesimal deformations of Fuchsian representations of a cocompact surface group do not act properly along the directions corresponding to the sum of a mixed odd differential and a $2m$-differential for any $1\leq m \leq \lfloor\frac{n}{2}\rfloor$. In the process, we introduce affine versions of cross ratios and triple ratios. We introduce Margulis invariants and relate them with affine crossratios and infinitesimal Jordan projections. We obtain a general equivalent criterion for existence of proper affine actions in terms of the structure of the Margulis invariant spectra. Also, using a stability argument we show the existence of proper affine actions of non-abelian free groups whose linear part is a Hitchin representation.
Object rearrangement in a multi-room setup should produce a reasonable plan that reduces the agent's overall travel and the number of steps. Recent state-of-the-art methods fail to produce such plans because they rely on explicit exploration for discovering unseen objects due to partial observability and a heuristic planner to sequence the actions for rearrangement. This paper proposes a novel hierarchical task planner to efficiently plan a sequence of actions to discover unseen objects and rearrange misplaced objects within an untidy house to achieve a desired tidy state. The proposed method introduces several novel techniques, including (i) a method for discovering unseen objects using commonsense knowledge from large language models, (ii) a collision resolution and buffer prediction method based on Cross-Entropy Method to handle blocked goal and swap cases, (iii) a directed spatial graph-based state space for scalability, and (iv) deep reinforcement learning (RL) for producing an efficient planner. The planner interleaves the discovery of unseen objects and rearrangement to minimize the number of steps taken and overall traversal of the agent. The paper also presents new metrics and a benchmark dataset called MoPOR to evaluate the effectiveness of the rearrangement planning in a multi-room setting. The experimental results demonstrate that the proposed method effectively addresses the multi-room rearrangement problem.