arXiv subjects

Partha Pratim Roy

Publications and source records attributed to Partha Pratim Roy.

At least 19 recordsLinked to original sources

arXiv2026

Sharp Bohr and Bohr-Rogosinski inequalities involving area measure for close-to-convex harmonic mappings

In this article, we investigate refined and generalized versions of the Bohr and Bohr--Rogosinski inequalities for a normalized subclass $\mathcal{P}_{\mathcal{H}}^{0}(α)$ ($0 \le α< 1$) of univalent close-to-convex harmonic mappings $f = h + \overline{g}$ defined on the open unit disk $\mathbb{D} \subset \mathbb{C}$. By incorporating non-negative monotone increasing functions associated with the planar area integral $S_r/π$ of the image domain $f(\mathbb{D}_r)$, we establish new sharp Bohr-type inequalities expressed in terms of the Euclidean distance $d(f(0), \partial f(\mathbb{D}))$. Furthermore, we establish sharp Bohr--Rogosinski-type inequalities involving powers of the modulus of the mapping $|f(z)|^p$ ($p \ge 1$). All associated radii are proven to be sharp, and extremal functions realizing the equality cases are explicitly identified. As applications, our results generalize and unify several well-known classical and recent theorems in geometric function theory.

math.CV↗

arXiv2026

What Does the Brain See? Multiview Neural Representations to Demystify the Brain-Visual Alignment

Zero-shot visual decoding from electroencephalography (EEG) aims to infer visual semantics from non-invasive neural recordings, but remains challenging due to the low signal-to-noise ratio, non-stationarity, and limited spatial resolution of EEG. Existing EEG-vision alignment methods often rely on holistic EEG embeddings, which can obscure the complementary temporal, spectral, and spatial structure underlying visual perception. We introduce a unified multiview EEG representation learning framework for aligning brain responses with visual semantic embeddings. Our method builds an EEG encoder that jointly models three complementary views: input-conditioned state-space temporal dynamics, learnable wavelet-based spectral decomposition for sample-adaptive frequency modeling, and attention-modulated graph learning for structured electrode interactions. The resulting multiview EEG embeddings are fused and aligned with pretrained visual representations in a shared semantic space using contrastive learning with EEG-specific regularization, enabling 200-way zero-shot visual classification. Experiments on THINGS-EEG benchmark show that our method achieves state-of-the-art performance, with 54.8% Top-1 and 85.6% Top-5 accuracy in the within-subject setting and 15.3% Top-1 and 45.4% Top-5 accuracy in the cross-subject setting. We further present the first systematic cross-session EEG-image decoding evaluation, achieving 40.8% Top-1 and 78.0% Top-5 accuracy. These results suggest that explicitly modeling multiview neural structure improves both semantic alignment and generalization in EEG-based visual decoding.

cs.CV↗

arXiv2026

The Bohr Phenomenon for Close-to-Convex Harmonic Mappings

The classical Bohr inequality states that if $f(z)=\sum_{n=0}^{\infty} a_n z^n$ is analytic and $|f(z)|<1$ in the unit disk $\mathbb{D}$, then $\sum_{n=0}^{\infty} |a_n| r^n \le 1$ for $|z|=r \le 1/3$, where $1/3$ is sharp. Extending this to harmonic mappings $f=h+\overline{g}$ is central in geometric function theory due to the co-analytic part $g$. This paper establishes sharp Bohr-type inequalities for two classes of sense-preserving close-to-convex harmonic mappings. Let $\mathcal{H}_0$ be the class of harmonic mappings $f=h+\overline{g}$ in $\mathbb{D}$ normalized by $h(0)=g(0)=h'(0)-1=g'(0)=0$. We introduce: \[ \mathcal{P}_{\mathcal{H}_0}(M) := \{ f \in \mathcal{H}_0 : \text{Re}(zh''(z)) > -M + |zg''(z)|, \; z \in \mathbb{D}, \; M > 0 \} \] \[ \mathcal{W}_{\mathcal{H}_0}(α,β) := \{ f \in \mathcal{H}_0 : \text{Re}(h'(z) + αzh''(z) - β) > |g'(z) + αzg''(z)|, \; z \in \mathbb{D} \} \] where $α\ge 0$, $β< 1$. We prove generalized Bohr inequalities by replacing the basis $\{r^n\}$ with non-negative continuous functions $\{φ_n(r)\}$. The results are proved using sharp coefficient bounds and growth theorems, providing new insights into the Bohr phenomenon for harmonic mappings and subclasses defined by differential inequalities.

math.CV↗

arXiv2026

HeartBeatAI: An Interpretable and Robust Deep Learning Framework for Multi-Label ECG Arrhythmia Detection

While Deep Learning (DL) enhances automated electrocardiogram (ECG) analysis, clinical deployment is hindered by class imbalance and the generalization gap. This paper presents HeartBeatAI, a deep learning framework combining domain generalization, multi-scale feature aggregation, and clinical explainability for robust 12-lead ECG classification. Moving beyond image-based paradigms, HeartBeatAI integrates a Squeeze-and-Excitation (SE) ResNet to isolate diagnostic leads alongside a Multi-Layer Concentration Pipeline to capture macro-rhythm and micro-morphological anomalies. To mitigate domain shift, the framework employs MixStyle regularization and Label Smoothing. Rigorous benchmarking across four large-scale datasets using intra-source and Leave-One-Domain-Out (LODO) protocols demonstrates high performance (98% Macro F1-score) under intra-source conditions. However, LODO evaluations reveal significant degradation in detecting rare anomalies, highlighting a persistent challenge in cross-institutional deployment.

cs.AI↗

arXiv2026

Moduli difference of initial inverse logarithmic coefficients for starlike and convex functions

Let $\mathcal{A}$ denote the class of functions $f$ that are analytic in the open unit disk $\mathbb{D}$ and satisfy the normalization conditions $f(0) = 0$ and $f'(0) = 1$. This paper investigates the inverse logarithmic coefficients $Γ_n$, which are defined by the expansion $\log(f^{-1}(w)/w) = 2\sum_{n=1}^{\infty} Γ_n w^n$. We establish sharp upper and lower bounds for the difference of the moduli of the first two inverse logarithmic coefficients, $|Γ_2| - |Γ_1|$, for several significant subclasses of univalent functions. Specifically, we derive sharp estimates for functions belonging to the class of starlike functions with respect to symmetric points ($\mathcal{S}_S^*$), convex functions with respect to symmetric points ($\mathcal{K}_S$), and functions associated with the lune domain ($\mathcal{S}_{\leftmoon}^*$ and $\mathcal{C}_{\leftmoon}$). The results are obtained by employing subordination techniques and utilizing sharp estimates for the coefficients of Schwarz functions. In each case, the extremal functions that attain these bounds are explicitly identified. Our findings provide further insights into the geometric properties of inverse mappings and extend recent research on coefficient functionals in geometric function theory.

math.CV↗

arXiv2026

Modified TSception for Analyzing Driver Drowsiness and Mental Workload from EEG

Driver drowsiness is a leading cause of traffic accidents, necessitating real-time, reliable detection systems to ensure road safety. This study proposes a Modified TSception architecture for robust assessment of driver fatigue and mental workload using Electroencephalography (EEG). The model introduces a five-layer hierarchical temporal refinement strategy to capture multi-scale brain dynamics, surpassing the original TSception's three-layer approach. Key innovations include the use of Adaptive Average Pooling (ADP) for structural flexibility across varying EEG dimensions and a two-stage fusion mechanism to optimize spatiotemporal feature integration for improved stability. Evaluated on the SEED-VIG dataset, the Modified TSception achieves 83.46% accuracy, comparable to the original model (83.15%), but with a significantly reduced confidence interval (0.24 vs. 0.36), indicating better performance stability. The architecture's generalizability was further validated on the STEW mental workload dataset, achieving state-of-the-art accuracies of 95.93% and 95.35% for 2-class and 3-class classification, respectively. These results show that the proposed modifications improve consistency and cross-task generalizability, making the model a reliable framework for EEG-based safety monitoring.

cs.HC↗

arXiv2025

Enhancing EEG Signal-Based Emotion Recognition with Synthetic Data: Diffusion Model Approach

Emotions are crucial in human life, influencing perceptions, relationships, behaviour, and choices. Emotion recognition using Electroencephalography (EEG) in the Brain-Computer Interface (BCI) domain presents significant challenges, particularly the need for extensive datasets. This study aims to generate synthetic EEG samples similar to real samples but distinct by augmenting noise to a conditional denoising diffusion probabilistic model, thus addressing the prevalent issue of data scarcity in EEG research. The proposed method is tested on the DEAP and SADT datasets, showcasing up to 5.6% improvement in classification accuracy when using synthetic data with DEAP and similar positive results with SADT. This is higher compared to the traditional Generative Adversarial Network (GAN) based and Denoising Diffusion Probabilistic Model (DDPM) based approaches. This study further evaluates the effectiveness of state-of-the-art classifiers on EEG data, employing both real and synthetic data with varying noise levels, and utilizes t-SNE and SHAP for detailed analysis and interpretability. The proposed diffusion-based approach for EEG data generation appears promising in refining the accuracy of emotion recognition systems and marks a notable contribution to EEG-based emotion recognition.

cs.HC↗

arXiv2025

Bohr-Rogosinski Inequalities for bounded analytic functions

In this article, we analyze refined and improved versions of the classical Bohr inequality for the function class $\mathcal{B}$, which consists of analytic self-mappings defined on the unit disk $\mathbb{D}$. We improve the Bohr-Rogosinski inequality for the class $\mathcal{B}$ of analytic self-maps by incorporating the area measure of sub-disks $\mathbb{D}_r$ in $\mathbb{D}$.

math.CV↗

arXiv2025

Handwritten Text Recognition for Low Resource Languages

Despite considerable progress in handwritten text recognition, paragraph-level handwritten text recognition, especially in low-resource languages, such as Hindi, Urdu and similar scripts, remains a challenging problem. These languages, often lacking comprehensive linguistic resources, require special attention to develop robust systems for accurate optical character recognition (OCR). This paper introduces BharatOCR, a novel segmentation-free paragraph-level handwritten Hindi and Urdu text recognition. We propose a ViT-Transformer Decoder-LM architecture for handwritten text recognition, where a Vision Transformer (ViT) extracts visual features, a Transformer decoder generates text sequences, and a pre-trained language model (LM) refines the output to improve accuracy, fluency, and coherence. Our model utilizes a Data-efficient Image Transformer (DeiT) model proposed for masked image modeling in this research work. In addition, we adopt a RoBERTa architecture optimized for masked language modeling (MLM) to enhance the linguistic comprehension and generative capabilities of the proposed model. The transformer decoder generates text sequences from visual embeddings. This model is designed to iteratively process a paragraph image line by line, called implicit line segmentation. The proposed model was evaluated using our custom dataset ('Parimal Urdu') and ('Parimal Hindi'), introduced in this research work, as well as two public datasets. The proposed model achieved benchmark results in the NUST-UHWR, PUCIT-OUHL, and Parimal-Urdu datasets, achieving character recognition rates of 96.24%, 92.05%, and 94.80%, respectively. The model also provided benchmark results using the Hindi dataset achieving a character recognition rate of 80.64%. The results obtained from our proposed model indicated that it outperformed several state-of-the-art Urdu text recognition methods.

cs.CV↗

arXiv2025

Quasiconformal Extension of Meromorphic Functions with High-Order Poles

In this paper, we study the class ${Σ^{(m)}(p)}$ of meromorphic univalent functions $f$ in $\mathbb{D}$ with a pole of order ${m \geq 1}$ at $p \in (0,1)$, admitting a $k$-quasiconformal extension ($0 \leq k < 1$) to $\widehat{\mathbb{C}}$. Using the Area Theorem and convolution methods, we establish a generalized area-type inequality and derive explicit analytic membership conditions for $Σ^{(m)}(p)$. We also extend the convolution theorem to a modified Hadamard product of $m$ functions, $f_j \in Σ^{(m)}_{k_j}(p)$, determining sufficient conditions for the product to be in ${Σ^{(m)}_α(p)}$, with $α$ defined by $k_j$ and $p$. Further results include a sufficient criterion for sense-preserving harmonic mappings on convex domains to admit quasiconformal extensions, and the sharp Schwarzian norm for $f \in Σ_k(p)$ (the $m=1$ case). These findings improve upon existing results of [{\em Proc. Amer. Math. Soc.}, {144}(6) (2016), 2593--2601].

math.CV↗

arXiv2025

A Unified Study of Bohr's Inequality for analytic and harmonic mappings on the Unit Disk

We investigate improved forms of the Bohr inequality, using the quantity $S_r/π$, for analytic selfmaps in class $\mathcal{B}$ of $\mathbb{D}$, where $S_r$ is the area measure of $\mathbb{D}_r$. We then generalize the inequality for harmonic mappings ($\mathcal{P}^0_{\mathcal{H}}(M)$ and $\mathcal{W}^0_{\mathcal{H}}(α)$ of the form $f = h + \overline{g}$) by introducing a sequence $\{φ_n(r)\}_{n=0}^\infty$ of differentiable, increasing functions on $[0, 1)$. The Hurwitz Lerch Zeta function is utilized for some consequences, and all results are shown to be sharp.

math.CV↗

arXiv2025

Feature Reweighting for EEG-based Motor Imagery Classification

Classification of motor imagery (MI) using non-invasive electroencephalographic (EEG) signals is a critical objective as it is used to predict the intention of limb movements of a subject. In recent research, convolutional neural network (CNN) based methods have been widely utilized for MI-EEG classification. The challenges of training neural networks for MI-EEG signals classification include low signal-to-noise ratio, non-stationarity, non-linearity, and high complexity of EEG signals. The features computed by CNN-based networks on the highly noisy MI-EEG signals contain irrelevant information. Subsequently, the feature maps of the CNN-based network computed from the noisy and irrelevant features contain irrelevant information. Thus, many non-contributing features often mislead the neural network training and degrade the classification performance. Hence, a novel feature reweighting approach is proposed to address this issue. The proposed method gives a noise reduction mechanism named feature reweighting module that suppresses irrelevant temporal and channel feature maps. The feature reweighting module of the proposed method generates scores that reweight the feature maps to reduce the impact of irrelevant information. Experimental results show that the proposed method significantly improved the classification of MI-EEG signals of Physionet EEG-MMIDB and BCI Competition IV 2a datasets by a margin of 9.34% and 3.82%, respectively, compared to the state-of-the-art methods.

cs.LG↗

arXiv2025

Position and Rotation Invariant Sign Language Recognition from 3D Kinect Data with Recurrent Neural Networks

Sign language is a gesture-based symbolic communication medium among speech and hearing impaired people. It also serves as a communication bridge between non-impaired and impaired populations. Unfortunately, in most situations, a non-impaired person is not well conversant in such symbolic languages restricting the natural information flow between these two categories. Therefore, an automated translation mechanism that seamlessly translates sign language into natural language can be highly advantageous. In this paper, we attempt to perform recognition of 30 basic Indian sign gestures. Gestures are represented as temporal sequences of 3D maps (RGB + depth), each consisting of 3D coordinates of 20 body joints captured by the Kinect sensor. A recurrent neural network (RNN) is employed as the classifier. To improve the classifier's performance, we use geometric transformation for the alignment correction of depth frames. In our experiments, the model achieves 84.81% accuracy.

cs.CV↗

arXiv2025

MECASA: Motor Execution Classification using Additive Self-Attention for Hybrid EEG-fNIRS Data

Motor execution, a fundamental aspect of human behavior, has been extensively studied using BCI technologies. EEG and fNIRS have been utilized to provide valuable insights, but their individual limitations have hindered performance. This study investigates the effectiveness of fusing electroencephalography (EEG) and functional near-infrared spectroscopy (fNIRS) data for classifying rest versus task states in a motor execution paradigm. Using the SMR Hybrid BCI dataset, this work compares unimodal (EEG and fNIRS) classifiers with a multimodal fusion approach. It proposes Motor Execution using Convolutional Additive Self-Attention Mechanisms (MECASA), a novel architecture leveraging convolutional operations and self-attention to capture complex patterns in multimodal data. MECASA, built upon the CAS-ViT architecture, employs a computationally efficient, convolutional-based self-attention module (CASA), a hybrid block design, and a dedicated fusion network to combine features from separate EEG and fNIRS processing streams. Experimental results demonstrate that MECASA consistently outperforms established methods across all modalities (EEG, fNIRS, and fused), with fusion consistently improving accuracy compared to single-modality approaches. fNIRS generally achieved higher accuracy than EEG alone. Ablation studies revealed optimal configurations for MECASA, with embedding dimensions of 64-128 providing the best performance for EEG data and OD128 (upsampled optical density) yielding superior results for fNIRS data. This work highlights the potential of deep learning, specifically MECASA, to enhance EEG-fNIRS fusion for BCI applications.

cs.HC↗

arXiv2024

EEG-Based Mental Imagery Task Adaptation via Ensemble of Weight-Decomposed Low-Rank Adapters

Electroencephalography (EEG) is widely researched for neural decoding in Brain Computer Interfaces (BCIs) as it is non-invasive, portable, and economical. However, EEG signals suffer from inter- and intra-subject variability, leading to poor performance. Recent technological advancements have led to deep learning (DL) models that have achieved high performance in various fields. However, such large models are compute- and resource-intensive and are a bottleneck for real-time neural decoding. Data distribution shift can be handled with the help of domain adaptation techniques of transfer learning (fine-tuning) and adversarial training that requires model parameter updates according to the target domain. One such recent technique is Parameter-efficient fine-tuning (PEFT), which requires only a small fraction of the total trainable parameters compared to fine-tuning the whole model. Therefore, we explored PEFT methods for adapting EEG-based mental imagery tasks. We considered two mental imagery tasks: speech imagery and motor imagery, as both of these tasks are instrumental in post-stroke neuro-rehabilitation. We proposed a novel ensemble of weight-decomposed low-rank adaptation methods, EDoRA, for parameter-efficient mental imagery task adaptation through EEG signal classification. The performance of the proposed PEFT method is validated on two publicly available datasets, one speech imagery, and the other motor imagery dataset. In extensive experiments and analysis, the proposed method has performed better than full fine-tune and state-of-the-art PEFT methods for mental imagery EEG classification.

eess.SP↗

arXiv2024

Neural Networks Meet Neural Activity: Utilizing EEG for Mental Workload Estimation

Electroencephalography (EEG) offers non-invasive, real-time mental workload assessment, which is crucial in high-stakes domains like aviation and medicine and for advancing brain-computer interface (BCI) technologies. This study introduces a customized ConvNeXt architecture, a powerful convolutional neural network, specifically adapted for EEG analysis. ConvNeXt addresses traditional EEG challenges like high dimensionality, noise, and variability, enhancing the precision of mental workload classification. Using the STEW dataset, the proposed ConvNeXt model is evaluated alongside SVM, EEGNet, and TSception on binary (No vs SIMKAP task) and ternary (SIMKAP multitask) class mental workload tasks. Results demonstrated that ConvNeXt significantly outperformed the other models, achieving accuracies of 95.76% for binary and 95.11% for multi-class classification. This demonstrates ConvNeXt's resilience and efficiency for EEG data analysis, establishing new standards for mental workload evaluation. These findings represent a considerable advancement in EEG-based mental workload estimation, laying the foundation for future improvements in cognitive state measurements. This has broad implications for safety, efficiency, and user experience across various scenarios. Integrating powerful neural networks such as ConvNeXt is a critical step forward in non-invasive cognitive monitoring.

cs.HC↗

arXiv2024

Awake at the Wheel: Enhancing Automotive Safety through EEG-Based Fatigue Detection

Driver fatigue detection is increasingly recognized as critical for enhancing road safety. This study introduces a method for detecting driver fatigue using the SEED-VIG dataset, a well-established benchmark in EEG-based vigilance analysis. By employing advanced pattern recognition technologies, including machine learning and deep neural networks, EEG signals are meticulously analyzed to discern patterns indicative of fatigue. This methodology combines feature extraction with a classification framework to improve the accuracy of fatigue detection. The proposed NLMDA-Net reached an impressive accuracy of 83.71% in detecting fatigue from EEG signals by incorporating two novel attention modules designed specifically for EEG signals, the channel and depth attention modules. NLMDA-Net effectively integrate features from multiple dimensions, resulting in improved classification performance. This success stems from integrating temporal convolutions and attention mechanisms, which effectively interpret EEG data. Designed to capture both temporal and spatial characteristics of EEG signals, deep learning classifiers have proven superior to traditional methods. The results of this study reveal a substantial enhancement in detection rates over existing models, highlighting the efficacy of the proposed approach for practical applications. The implications of this research are profound, extending beyond academic realms to inform the development of more sophisticated driver assistance systems. Incorporating this fatigue detection algorithm into these systems could significantly reduce fatigue-related incidents on the road, thus fostering safer driving conditions. This paper provides an exhaustive analysis of the dataset, methods employed, results obtained, and the potential real-world applications of the findings, aiming to contribute significantly to advancements in automotive safety.

cs.HC↗

arXiv2024

DrowzEE-G-Mamba: Leveraging EEG and State Space Models for Driver Drowsiness Detection

Driver drowsiness is identified as a critical factor in road accidents, necessitating robust detection systems to enhance road safety. This study proposes a driver drowsiness detection system, DrowzEE-G-Mamba, that combines Electroencephalography (EEG) with State Space Models (SSMs). EEG data, known for its sensitivity to alertness, is used to model driver state transitions between alert and drowsy. Compared to traditional methods, DrowzEE-G-Mamba achieves significantly improved detection rates and reduced false positives. Notably, it achieves a peak accuracy of 83.24% on the SEED-VIG dataset, surpassing existing techniques. The system maintains high accuracy across varying complexities, making it suitable for real-time applications with limited resources. This robustness is attributed to the combination of channel-split, channel-concatenation, and channel-shuffle operations within the architecture, optimizing information flow from EEG data. Additionally, the integration of convolutional layers and SSMs facilitates comprehensive analysis, capturing both local features and long-range dependencies in the EEG signals. These findings suggest the potential of DrowzEE-G-Mamba for enhancing road safety through accurate drowsiness detection. It also paves the way for developing powerful SSM-based AI algorithms in Brain-Computer Interface applications.

cs.HC↗