arXiv subjects

Gaurav Kumar

Publications and source records attributed to Gaurav Kumar.

At least 37 records · Page 2Linked to original sources

arXiv2025

Iterations of Meromorphic Functions involving Sine

In this article, the dynamics of a one-parameter family of functions $f_λ(z) = \frac{\sin{z}}{z^2 + λ},$ $λ>0$, are studied. It shows the existence of parameters $0< λ_{1}< λ_{2}$ such that bifurcations occur at $λ_1$ and $λ_2$ for $f_λ$. It is proved that the Fatou set $\mathcal{F}(f_λ)$ is the union of basins of attraction in the complex plane for $λ\in (λ_1, λ_2) \cup (λ_2, \infty)$. Further, every Fatou component of $f_λ$ is simply connected for $λ\geq λ_1$. The boundary of the Fatou set $\mathcal{F}(f_λ)$ is the Julia set $\mathcal{J}(f_λ)$ in the extended complex plane for $λ> 1$. Interestingly, it is found that $f_λ$ has only one completely invariant Fatou component, say $U_λ$ such that $\mathcal{F}(f_λ) = U_λ$ for $λ>λ_2$. Moreover, the characterization of the Julia set of $f_λ$ is seen for $λ\in (λ_1, \infty)\setminus \{λ_2\}$.

math.DS↗

arXiv2025

Composable NLP Workflows for BERT-based Ranking and QA System

There has been a lot of progress towards building NLP models that scale to multiple tasks. However, real-world systems contain multiple components and it is tedious to handle cross-task interaction with varying levels of text granularity. In this work, we built an end-to-end Ranking and Question-Answering (QA) system using Forte, a toolkit that makes composable NLP pipelines. We utilized state-of-the-art deep learning models such as BERT, RoBERTa in our pipeline, evaluated the performance on MS-MARCO and Covid-19 datasets using metrics such as BLUE, MRR, F1 and compared the results of ranking and QA systems with their corresponding benchmark results. The modular nature of our pipeline and low latency of reranker makes it easy to build complex NLP applications easily.

cs.CL↗

arXiv2024

Do Voters Get the Information They Want? Understanding Authentic Voter FAQs in the US and How to Improve for Informed Electoral Participation

Accurate information is crucial for democracy as it empowers voters to make informed decisions about their representatives and keeping them accountable. In the US, state election commissions (SECs), often required by law, are the primary providers of Frequently Asked Questions (FAQs) to voters, and secondary sources like non-profits such as League of Women Voters (LWV) try to complement their information shortfall. However, surprisingly, to the best of our knowledge, there is neither a single source with comprehensive FAQs nor a study analyzing the data at national level to identify current practices and ways to improve the status quo. This paper addresses it by providing the {\bf first dataset on Voter FAQs covering all the US states}. Second, we introduce metrics for FAQ information quality (FIQ) with respect to questions, answers, and answers to corresponding questions. Third, we use FIQs to analyze US FAQs to identify leading, mainstream and lagging content practices and corresponding states. Finally, we identify what states across the spectrum can do to improve FAQ quality and thus, the overall information ecosystem. Across all 50 U.S. states, 12% were identified as leaders and 8% as laggards for FIQS\textsubscript{voter}, while 14% were leaders and 12% laggards for FIQS\textsubscript{developer}.

cs.CY↗

arXiv2024

Machine learning framework to predict the performance of lipid nanoparticles for nucleic acid delivery

Lipid nanoparticles (LNPs) are highly effective carriers for gene therapies, including mRNA and siRNA delivery, due to their ability to transport nucleic acids across biological membranes, low cytotoxicity, improved pharmacokinetics, and scalability. A typical approach to formulate LNPs is to establish a quantitative structure-activity relationship (QSAR) between their compositions and in vitro/in vivo activities which allows for the prediction of activity based on molecular structure. However, developing QSAR for LNPs can be challenging due to the complexity of multi-component formulations, interactions with biological membranes, and stability in physiological environments. To address these challenges, we developed a machine learning framework to predict the activity and cell viability of LNPs for nucleic acid delivery. We curated data from 6,398 LNP formulations in the literature, applied nine featurization techniques to extract chemical information, and trained five machine learning models for binary and multiclass classification. Our binary models achieved over 90% accuracy, while the multiclass models reached over 95% accuracy. Our results demonstrated that molecular descriptors, particularly when used with random forest and gradient boosting models, provided the most accurate predictions. Our findings also emphasized the need for large training datasets and comprehensive LNP composition details, such as constituent structures, molar ratios, nucleic acid types, and dosages, to enhance predictive performance.

q-bio.BM↗

arXiv2024

The Rogers-Ramanujan dissection of a theta function

Page 27 of Ramanujan's Lost Notebook contains a beautiful identity which not only gives, as a special case, a famous modular relation between the Rogers-Ramanujan functions $G(q)$ and $H(q)$ but also a relation between two fifth order mock theta functions and $G(q)$ and $H(q)$. We generalize Ramanujan's relation with the help of a parameter $s$ to get an infinite family of such identities. Our result shows that a theta function can always be ``dissected'' as a finite sum of products of generalized Rogers-Ramanujan functions. Several well-known results are shown to be consequences of our theorem, for example, a generalization of the Jacobi triple product identity and Andrews' relation between two of his generalized third order mock theta functions. We give enough evidence, through asymptotic analysis as well as by other means, to show that the identities we get from our main result for $s>2$ transcend the modular world and hence look difficult to be written in the form of a modular relation. Using asymptotic analysis, we also offer a clinching evidence that explains how Ramanujan may have arrived at his generalized modular relation.

math.NT↗

arXiv2024

Dominant balance-based adaptive mesh refinement for incompressible fluid flows

This work introduces a novel adaptive mesh refinement (AMR) method that utilizes dominant balance analysis (DBA) for efficient and accurate grid adaptation in computational fluid dynamics (CFD) simulations. The proposed method leverages a Gaussian mixture model (GMM) to classify grid cells into active and passive regions based on the dominant physical interactions in the equation space. Unlike traditional AMR strategies, this approach does not rely on heuristic-based sensors or user-defined parameters, providing a fully automated and problem-independent framework for AMR. Applied to the incompressible Navier-Stokes equations for unsteady flow past a cylinder, the DBA-based AMR method achieves comparable accuracy to high-resolution grids while reducing computational costs by up to 70%. The validation highlights the method's effectiveness in capturing complex flow features while minimizing grid cells, directing computational resources toward regions with the most critical dynamics. This modular and scalable strategy is adaptable to a range of applications, presenting a promising tool for efficient high-fidelity simulations in CFD and other multiphysics domains.

physics.flu-dyn↗

arXiv2024

An aeroacoustic mechanism to explain universal behavior in hypersonic wake flow oscillations

Recent experimental studies reveal that the near-wake region of a circular cylinder at hypersonic Mach numbers exhibits self-sustained flow oscillations. The oscillation frequency was found to have a universal behavior. Experimental observations suggest an aeroacoustic feedback loop to be the driving mechanism of oscillations. An analytical aeroacoustic model which predicts the experimentally observed frequencies and explains the universal behavior is presented here. The model provides physical insights and informs of flow regimes where deviations from universal behavior are to be expected.

physics.flu-dyn↗

arXiv2024

CFAT: Unleashing TriangularWindows for Image Super-resolution

Transformer-based models have revolutionized the field of image super-resolution (SR) by harnessing their inherent ability to capture complex contextual features. The overlapping rectangular shifted window technique used in transformer architecture nowadays is a common practice in super-resolution models to improve the quality and robustness of image upscaling. However, it suffers from distortion at the boundaries and has limited unique shifting modes. To overcome these weaknesses, we propose a non-overlapping triangular window technique that synchronously works with the rectangular one to mitigate boundary-level distortion and allows the model to access more unique sifting modes. In this paper, we propose a Composite Fusion Attention Transformer (CFAT) that incorporates triangular-rectangular window-based local attention with a channel-based global attention technique in image super-resolution. As a result, CFAT enables attention mechanisms to be activated on more image pixels and captures long-range, multi-scale features to improve SR performance. The extensive experimental results and ablation study demonstrate the effectiveness of CFAT in the SR domain. Our proposed model shows a significant 0.7 dB performance improvement over other state-of-the-art SR architectures.

eess.IV↗

arXiv2024

Quantum-Based Salp Swarm Algorithm Driven Design Optimization of Savonius Wind Turbine-Cylindrical Deflector System

Savonius turbines, prominent in small-scale wind turbine applications operating under low-speed conditions, encounter limitations due to opposing torque on the returning blade, impeding high efficiency. A viable solution involves mitigating this retarding torque by directing incoming airflow through a cylindrical deflector. However, such flow control is highly contingent upon the location and size of the cylindrical deflector, and its angular velocity. This study introduces a novel design optimization framework tailored for enhancing the turbine-deflector system's performance. Leveraging surrogate models for computational efficiency, six different models were assessed, with Kriging selected for subsequent analysis based on its superior performance at approximating the relation between design parameters and objective function. The training data for the surrogate model and the flow field data around the system were obtained through Unsteady Reynolds-Averaged Navier Stokes (URANS) simulations using a sliding mesh technique. An in-house code for the Quantum-based Salp Swarm Optimization (QSSO) algorithm was then employed to obtain design parameters corresponding to the peak power coefficient (Cp) for the stationary deflector-turbine system. Additionally, the QSSO algorithm was quantitatively compared with nine other competing algorithms. The optimized stationary deflector-turbine system showed an improvement of 26.94% in Cp at Tip Speed Ratio (TSR) of 0.9 compared to the baseline case. Further investigation into the effect of deflector rotational velocity ($ω_d$) revealed significant improvements: 40.98% and 11.33% enhancement at $ω_d$ = 3 rad/s, and 51.23% and 19.42% at $ω_d$ = 40 rad/s, compared to configurations without a deflector and with the optimized stationary deflector, respectively at a TSR of 0.9.

physics.flu-dyn↗

arXiv2024

InterroGate: Learning to Share, Specialize, and Prune Representations for Multi-task Learning

Jointly learning multiple tasks with a unified model can improve accuracy and data efficiency, but it faces the challenge of task interference, where optimizing one task objective may inadvertently compromise the performance of another. A solution to mitigate this issue is to allocate task-specific parameters, free from interference, on top of shared features. However, manually designing such architectures is cumbersome, as practitioners need to balance between the overall performance across all tasks and the higher computational cost induced by the newly added parameters. In this work, we propose \textit{InterroGate}, a novel multi-task learning (MTL) architecture designed to mitigate task interference while optimizing inference computational efficiency. We employ a learnable gating mechanism to automatically balance the shared and task-specific representations while preserving the performance of all tasks. Crucially, the patterns of parameter sharing and specialization dynamically learned during training, become fixed at inference, resulting in a static, optimized MTL architecture. Through extensive empirical evaluations, we demonstrate SoTA results on three MTL benchmarks using convolutional as well as transformer-based backbones on CelebA, NYUD-v2, and PASCAL-Context.

cs.LG↗

arXiv2024

Predicting Rubisco:Linker Condensation from Titration in the Dilute Phase

The condensation of Rubisco holoenzymes and linker proteins into 'pyrenoids', a crucial super-charger of photosynthesis in algae, is qualitatively understood in terms of 'sticker-and-spacer' theory. We derive semi-analytical partition sums for small Rubisco:linker aggregates, which enable the calculation of both dilute-phase titration curves and dimerisation diagrams. By fitting the titration curves to Surface Plasmon Resonance and Single-Molecule Fluorescence Microscopy data, we extract the molecular properties needed to predict dimerisation diagrams. We use these to estimate typical concentrations for condensation, and successfully compare these to microscopy observations.

cond-mat.soft↗

arXiv2024

A model for frequency scaling of flow oscillations in high-speed double cones

Coherent small-amplitude unsteadiness of the shock wave and the separation region over a canonical double cone flow, termed in literature as oscillation-type unsteadiness, is experimentally studied at Mach 6. The double cone model is defined by three non-dimensional geometric parameters: fore- and aft-cone angles ($θ_1$ and $θ_2$), and ratio of the conical slant lengths ($Λ$). Previous studies of oscillations have been qualitative in nature, and mostly restricted to a special case of the cone model with fixed $θ_1 = 0^\circ$ and $θ_2 = 90^\circ$ (referred to as the spike-cylinder model), where $Λ$ becomes the sole governing parameter. In the present effort we investigate the self-sustained flow oscillations in the $θ_1$-$Λ$ parameter space for fixed $θ_2 = 90^\circ$ using time-resolved schlieren visualization. The experiments reveal two distinct sub-types of oscillations, characterized by the motion (or lack thereof) of the separation point on the fore-cone surface. The global time scale associated with flow oscillation is extracted using spectral proper orthogonal decomposition. The non-dimensional frequency (Strouhal number) of oscillation is seen to exhibit distinct scaling for the two oscillation sub-types. The relationship observed between the local flow properties, instability of the shear layer, and geometric constraints on the flow suggests that an aeroacoustic feedback mechanism sustains the oscillations. Based on this insight, a simple model with no empiricism is developed for the Strouhal number. The model predictions are found to match well with experimental measurements. The model provides helpful physical insight into the nature of the self-sustained flow oscillations over a double cone at high-speeds.

physics.flu-dyn↗

arXiv2023

Stabilizing two-dimensional turbulent Kolmogorov flow via selective modification of inviscid invariants

We stabilize two-dimensional turbulent Kolmogorov flow by selectively altering the time rate of change of inviscid invariants (energy and enstrophy) of the flow. This method has earlier been demonstrated to modify the two-dimensional unforced decaying turbulent flow to reach steady states. However, Kolmogorov flow exhibits flow unsteadiness over a range of spatial and temporal scales which are driven by constant external forcing at wave number $k_f$. The energy injected at scale ($k \approx k_f$) is distributed to large ($k > k_f$) and small ($k < k_f$) wave numbers through interactions of different scales called direct and inverse energy cascading, respectively. The selective modification strategy autonomously identifies additional forcing inputs into the governing equations which results in the transformation of Kolmogorov flow into a non-trivial steady state. We demonstrate that this method is highly effective in altering the inverse energy cascading, a particularly intricate challenge in fluid dynamics. Intriguingly, we have also found that the steady states achieved through this approach resemble an invariant solution of the original Kolmogorov flow, highlighting the potential significance of our method.

physics.flu-dyn↗

arXiv2023

A Novel Framework for Optimizing Gurney Flaps using RBF Neural Network and Cuckoo Search Algorithm

Enhancing aerodynamic efficiency is vital for optimizing aircraft performance and operational effectiveness. It enables greater speeds and reduced fuel consumption, leading to lower operating costs. Hence, the implementation of Gurney flaps represents a promising avenue for improving airfoil aerodynamics. The optimization of Gurney flaps holds considerable ramifications for improving the lift and stall characteristics of airfoils in aircraft and wind turbine blade designs. The efficacy of implementing Gurney flaps hinges significantly on its design parameters, namely, flap height and mounting angle. This study attempts to optimize these parameters using a design optimization framework, which incorporates training a Radial Basis Function surrogate model based on CFD data from two-dimensional (2D) Reynolds-Averaged Navier-Stokes (RANS) simulations. The Cuckoo Search algorithm is then employed to obtain the optimal design parameters and compared with other competing optimization algorithms. The optimized Gurney flap configuration shows a notable improvement of 10.28% in Cl/Cd, with a flap height of 1.9%c and a flap mounting angle of -58 degrees. The study highlights the effectiveness of the proposed design optimization framework and furnishes valuable insights into optimizing Gurney flap parameters. The comparison of metaheuristic algorithms serves to enhance the study's contribution to Gurney flap design optimization.

physics.flu-dyn↗

arXiv2023

Optimizing Data Augmentation Policy Through Random Unidimensional Search

It is no secret amongst deep learning researchers that finding the optimal data augmentation strategy during training can mean the difference between state-of-the-art performance and a run-of-the-mill result. To that end, the community has seen many efforts to automate the process of finding the perfect augmentation procedure for any task at hand. Unfortunately, even recent cutting-edge methods bring massive computational overhead, requiring as many as 100 full model trainings to settle on an ideal configuration. We show how to achieve equivalent performance using just 6 trainings with Random Unidimensional Augmentation. Source code is available at https://github.com/fastestimator/RUA/tree/v1.0

cs.LG↗

arXiv2023

To Raise or Not To Raise: The Autonomous Learning Rate Question

There is a parameter ubiquitous throughout the deep learning world: learning rate. There is likewise a ubiquitous question: what should that learning rate be? The true answer to this question is often tedious and time consuming to obtain, and a great deal of arcane knowledge has accumulated in recent years over how to pick and modify learning rates to achieve optimal training performance. Moreover, the long hours spent carefully crafting the perfect learning rate can come to nothing the moment your network architecture, optimizer, dataset, or initial conditions change ever so slightly. But it need not be this way. We propose a new answer to the great learning rate question: the Autonomous Learning Rate Controller. Find it at https://github.com/fastestimator/ARC/tree/v2.0

cs.LG↗

arXiv2023

On $θ$-Hurewicz and $α$-Hurewicz Topological spaces

In this paper, we introduced $α$-Hurewicz $\&$ $θ$-Hurewicz properties in a topological space $X$ and investigated their relationship with other selective covering properties. We have shown that for an extremally disconnected semi-regular spaces, the properties: Hurewicz, semi-Hurewicz, $α$-Hurewicz, $θ$-Hurewicz, almost-Hurewicz, nearly Hurewicz and midly Hurewicz are equivalent. We have also proved that for an extremally disconnected space X, every finite power of X has $θ$-Hurewicz property if and only if X has the selection principle $U_{fin}(θ$-$Ω, θ$-$Ω)$. The preservation under several types of mappings of $α$-Hurewicz and $θ$-Hurewicz properties are also discussed. Also, we showed that, if $X$ is a mildly Hurewicz subspace of $ ω^ω$, than $X$ is bounded.

math.GN↗

arXiv2022

Low-threshold, highly stable colloidal quantum dot short-wave infrared laser enabled by suppression of trap-assisted Auger recombination

Pb-chalcogenide colloidal quantum dots (CQDs) are attractive materials to be used as tuneable laser media across the infrared spectrum. However, excessive nonradiative Auger recombination due to the presence of trap states outcompetes light amplification by rapidly annihilating the exciton population, leading to high gain thresholds. Here, we employ a binary blend of CQDs and ZnO nanocrystals in order to passivate the in-gap trap states of PbS-CQD gain medium. Using transient absorption, we measure a five-fold increase in Auger lifetime demonstrating the suppression of trap-assisted Auger recombination. By doing so, we achieve a two-fold reduction in amplified spontaneous emission (ASE) threshold. Finally, by integrating our proposed binary blend to a DFB resonator, we demonstrate single-mode lasing emission at 1650 nm with a linewidth of 1.23 nm (0.62 meV), operating at a low lasing threshold of ~385 μJ.cm-2. The Auger suppression in this system has allowed to achieve unprecedented lasing emission stability for a CQD laser with recorded continuous operation of 5 hours at room temperature and ambient conditions.

physics.optics↗