Python for Mathematical Thinking

Pradeep Singh Pradeep Singh 0001 National Institute of Technology, Raipur, India http://www.nitrr.ac.in/viewdetails.php?q=cs.psingh https://nitrr.irins.org/profile/112668 https://scholar.google.com/citations?user=Pg36s_QAAAAJ https://orcid.org/0000-0002-2806-8432 Pradeep Singh 0002 Indian Institute of Technology (IIT) Delhi, Department of Electrical Engineering, India https://orcid.org/0000-0003-4494-4436 Pradeep Singh 0003 University of Hong Kong, Faculty of Dentistry, Hong Kong https://orcid.org/0000-0003-2975-1003 Pradeep Singh 0004 Panjab University, Institute of Engineering and Technology, Chandigarh, India https://orcid.org/0000-0003-2864-3262 Pradeep Singh Balasubramanian Raman Python for Mathematical Thinking Springer 2026 1-481 978-981-95-4079-2 https://doi.org/10.1007/978-981-95-4080-8

Pradeep Singh Shradhdha Agrawal Balasubramanian Raman Phase-modulated permutation reservoirs for robust biomedical time-series forecasting. 109460 2026 116 Biomed. Signal Process. Control. https://doi.org/10.1016/j.bspc.2026.109460 db/journals/bspc/bspc116.html#SinghAR26 streams/journals/bspc

Anushka Joshi Pradeep Singh Balasubramanian Raman Scalable multiscale echo state reservoirs with dendritic readouts for intelligent earthquake early warning systems. 2026 111161 135 Comput. Electr. Eng. https://doi.org/10.1016/j.compeleceng.2026.111161 db/journals/cee/cee135.html#JoshiSR26 streams/journals/cee

Pradeep Singh Kanishk Sharma Balasubramanian Raman Adaptive group-weighted convolutions: Enhancing equivariant networks via learnable symmetry importance maps. 132689 2026 671 Neurocomputing https://doi.org/10.1016/j.neucom.2026.132689 db/journals/ijon/ijon671.html#SinghSR26 streams/journals/ijon

Pradeep Singh Shradhdha Agrawal Shreyas Rajesh Dahale Sutirtha Ghosh Balasubramanian Raman Hierarchical fractal reservoirs: Unsupervised multiscale symbolic graphs for long-horizon prediction of chaotic flows. 2026 133603 684 Neurocomputing https://doi.org/10.1016/j.neucom.2026.133603 db/journals/ijon/ijon684.html#SinghADGR26 streams/journals/ijon

Pradeep Singh Balasubramanian Raman Semantic spherical mixup: geometry-aware data augmentation in latent manifolds for parameter-efficient language model adaptation. 2026 December 103 68 Knowl. Inf. Syst. 1 https://doi.org/10.1007/s10115-026-02719-z db/journals/kais/kais68.html#SinghR26 streams/journals/kais

Pradeep Singh Balasubramanian Raman Thalamocortical burst gating enables event-locked memory. 114947 2026 333 Knowl. Based Syst. https://doi.org/10.1016/j.knosys.2025.114947 db/journals/kbs/kbs333.html#SinghR26 streams/journals/kbs

Pradeep Singh Ashutosh Kumar Sutirtha Ghosh Balasubramanian Raman Topologically informed echo state networks via poincaré return maps for chaotic time-series. 2026 109264 204 Neural Networks https://doi.org/10.1016/j.neunet.2026.109264 db/journals/nn/nn204.html#SinghKGR26 streams/journals/nn

Arti Jain Pradeep Singh ADC-Net: a deep attention-based framework for preserving fine image details in denoising. 2026 117594 146 Signal Process. Image Commun. https://doi.org/10.1016/j.image.2026.117594 db/journals/spic/spic146.html#JainS26 streams/journals/spic

Junjie Zhao Jingyi Liang Zhenyang Cai Jiaming Zhang Zhenwei Wen Shuzhi Deng Wenjing Yi Chunfeng Luo Hexian Zhang Junying Chen Tianrui Liu Zhuhui Bai Zixu Zhang Pradeep Singh Xiang Liu Jianquan Li Nhan L. Tran Falk Schwendicke Zuolin Jin Lijian Jin Liangyi Chen Wei-Fa Yang Benyou Wang Junwen Wang Shan Jiang GlobalDentBench: A Multinational Benchmark for Evaluating LLM Clinical Reasoning in Dentistry with Expert Calibration. 2026 May abs/2605.24636 CoRR https://doi.org/10.48550/arXiv.2605.24636 db/journals/corr/corr2605.html#abs-2605-24636 streams/journals/corr

Rashi Chauhan Karnati Mohan Pradeep Singh Fused multi-level attention features with a constraint fusion network for colorectal tissue classification using histopathological images. 110296 2025 124 Comput. Electr. Eng. https://doi.org/10.1016/j.compeleceng.2025.110296 db/journals/cee/cee124.html#ChauhanMS25 streams/journals/cee

Anushka Joshi Pradeep Singh Balasubramanian Raman IsoMapGen: Framework for early prediction of peak ground acceleration using tripartite feature extraction and gated attention model. 105849 2025 196 Comput. Geosci. https://doi.org/10.1016/j.cageo.2024.105849 db/journals/gandc/gandc196.html#JoshiSR25 streams/journals/gandc

Pradeep Singh Shreyas Rajesh Dahale Yash Shruti Gupta Balasubramanian Raman Brain-lateralized reservoirs: Neuro-anatomically constrained echo state networks for chaotic and physiological signals. 114735 2025 331 Knowl. Based Syst. https://doi.org/10.1016/j.knosys.2025.114735 db/journals/kbs/kbs331.html#SinghDYGR25 streams/journals/kbs

Pradeep Singh Mehak Sharma Anupriya Dey Balasubramanian Raman Frozen in Time: Parameter-Efficient Time Series Transformers via Reservoir-Induced Feature Expansion and Fixed Random Dynamics. 2283-2290 2025 ECAI https://doi.org/10.3233/FAIA251071 conf/ecai/2025 db/conf/ecai/ecai2025.html#SinghSDR25 Pradeep Singh Sutirtha Ghosh Ashutosh Kumar Balasubramanian Hrishit B. Pa Raman HypER: Hyperbolic Echo State Networks for Capturing Stretch-and-Fold Dynamics in Chaotic Flows. 3186-3193 2025 ECAI https://doi.org/10.3233/FAIA251184 conf/ecai/2025 db/conf/ecai/ecai2025.html#SinghGKR25

Arti Jain Pradeep Singh Training-free Quantum-Inspired Image Edge Extraction Method. 2025 January abs/2501.18929 CoRR https://doi.org/10.48550/arXiv.2501.18929 db/journals/corr/corr2501.html#abs-2501-18929 streams/journals/corr

Pradeep Singh Ashutosh Kumar Sutirtha Ghosh Hrishit B. P Balasubramanian Raman Dynamics and Computational Principles of Echo State Networks: A Mathematical Perspective. 2025 April abs/2504.11757 CoRR https://doi.org/10.48550/arXiv.2504.11757 db/journals/corr/corr2504.html#abs-2504-11757 streams/journals/corr

Pradeep Singh Lavanya Sankaranarayanan Balasubramanian Raman Contraction, Criticality, and Capacity: A Dynamical-Systems Perspective on Echo-State Networks. 2025 July abs/2507.18467 CoRR https://doi.org/10.48550/arXiv.2507.18467 db/journals/corr/corr2507.html#abs-2507-18467 streams/journals/corr

Pradeep Singh Mehak Sharma Anupriya Dey Balasubramanian Raman Frozen in Time: Parameter-Efficient Time Series Transformers via Reservoir-Induced Feature Expansion and Fixed Random Dynamics. 2025 August abs/2508.18130 CoRR https://doi.org/10.48550/arXiv.2508.18130 db/journals/corr/corr2508.html#abs-2508-18130 streams/journals/corr

Pradeep Singh Sutirtha Ghosh Ashutosh Kumar Hrishit B. P Balasubramanian Raman HypER: Hyperbolic Echo State Networks for Capturing Stretch-and-Fold Dynamics in Chaotic Flows. 2025 August abs/2508.18196 CoRR https://doi.org/10.48550/arXiv.2508.18196 db/journals/corr/corr2508.html#abs-2508-18196 streams/journals/corr

Pradeep Singh Balasubramanian Raman Echo State Networks as State-Space Models: A Systems Perspective. 2025 September abs/2509.04422 CoRR https://doi.org/10.48550/arXiv.2509.04422 db/journals/corr/corr2509.html#abs-2509-04422 streams/journals/corr

Pradeep Singh Mudasani Rushikesh Bezawada Sri Sai Anurag Balasubramanian Raman The Universe Learning Itself: On the Evolution of Dynamics from the Big Bang to Machine Intelligence. 2025 December abs/2512.16515 CoRR https://doi.org/10.48550/arXiv.2512.16515 db/journals/corr/corr2512.html#abs-2512-16515 streams/journals/corr

Chehak Malhotra Mehak Gopal Akshaya Devadiga Pradeep Singh Ridam Pal Ritwik Kashyap Tavpritesh Sethi Benchmarking LLMs for Predictive Applications in the Intensive Care Units. 2025 December abs/2512.20520 CoRR https://doi.org/10.48550/arXiv.2512.20520 db/journals/corr/corr2512.html#abs-2512-20520 streams/journals/corr

Deepak Kumar Pradeep Singh Balasubramanian Raman All signals point to personality: A dual-pipeline LSTM-attention and symbolic dynamics framework for predicting personality traits from Bio-Electrical signals. 106609 2024 96 Biomed. Signal Process. Control. https://doi.org/10.1016/j.bspc.2024.106609 db/journals/bspc/bspc96.html#KumarSR24 streams/journals/bspc

Sunny Kumar Sharma Vijay Kumar Bhat Pradeep Singh On metric dimension of some planar graphs with 2n odd sided faces. 2250185:1-2250185:19 2024 January 16 Discret. Math. Algorithms Appl. 1 https://doi.org/10.1142/S1793830922501853 db/journals/dmaa/dmaa16.html#SharmaBS24

Anshul Pundhir Shivam Sagar Pradeep Singh Balasubramanian Raman Echoes of images: multi-loss network for image retrieval in vision transformers. 2037-2058 2024 July 62 Medical Biol. Eng. Comput. 7 https://doi.org/10.1007/s11517-024-03055-6 db/journals/mbec/mbec62.html#PundhirSSR24

Anushka Joshi Pradeep Singh Balasubramanian Raman A Deep Attention Model for Onsite Estimation of Earthquake Epicenter Distance and Magnitude. 1-11 2024 62 IEEE Trans. Geosci. Remote. Sens. https://doi.org/10.1109/TGRS.2024.3459425 db/journals/tgrs/tgrs62.html#JoshiSR24 streams/journals/tgrs

Deepak Kumar Pradeep Singh Ashutosh Kumar Sutirtha Ghosh Balasubramanian Raman Neuro-Emotional Mapping of Human Emotions via EEG Signals. 1-5 2024 FG https://doi.org/10.1109/FG59268.2024.10581941 conf/fgr/2024 db/conf/fgr/fg2024.html#KumarSKGR24 Rashi Chauhan Karnati Mohan Pradeep Singh Attention Based Deep Neural Network for Classification of Kidney Ailments Using CT Images. 1-5 2024 ICCCNT https://doi.org/10.1109/ICCCNT61001.2024.10723909 conf/icccnt/2024 db/conf/icccnt/icccnt2024.html#ChauhanMS24 Deepak Kumar Pradeep Singh Richa Kishore Babu Nampalle Balasubramanian Raman Integrating Physiological Signals with Dynamical Attention Networks for Personality Trait Analysis. 1-8 2024 IJCNN https://doi.org/10.1109/IJCNN60899.2024.10650662 conf/ijcnn/2024 db/conf/ijcnn/ijcnn2024.html#KumarSRNR24 streams/conf/ijcnn Deepak Kumar Surbhi Madan Pradeep Singh Abhinav Dhall Balasubramanian Raman Towards Engagement Prediction: A Cross-Modality Dual-Pipeline Approach using Visual and Audio Features. 11383-11389 2024 ACM Multimedia https://doi.org/10.1145/3664647.3688986 https://www.wikidata.org/entity/Q131177351 conf/mm/2024 db/conf/mm/mm2024.html#KumarMSDR24

Sapana Sharma Rakesh Kumar 0015 Bhavneet Singh Soodan Pradeep Singh Queuing models with customers' impatience: a survey. 523-547 2023 26 Int. J. Math. Oper. Res. 4 https://doi.org/10.1504/IJMOR.2023.135546 db/journals/ijmor/ijmor26.html#SharmaKSS23

Kishore Babu Nampalle Pradeep Singh Vivek Narayan Uppala Sumit Gangwar Rajesh Singh Negi Balasubramanian Raman Transcending Grids: Point Clouds and Surface Representations Powering Neurological Processing. 2023 abs/2305.15426 CoRR https://doi.org/10.48550/arXiv.2305.15426 db/journals/corr/corr2305.html#abs-2305-15426

Pradeep Singh Kishore Babu Nampalle Vivek Narayan Uppala Balasubramanian Raman See Through the Fog: Curriculum Learning with Progressive Occlusion in Medical Imaging. 2023 abs/2306.15574 CoRR https://doi.org/10.48550/arXiv.2306.15574 db/journals/corr/corr2306.html#abs-2306-15574

Kishore Babu Nampalle Pradeep Singh Vivek Narayan Uppala Balasubramanian Raman Vision Through the Veil: Differential Privacy in Federated Learning for Medical Image Classification. 2023 abs/2306.17794 CoRR https://doi.org/10.48550/arXiv.2306.17794 db/journals/corr/corr2306.html#abs-2306-17794

Kishore Babu Nampalle Pradeep Singh Vivek Narayan Uppala Balasubramanian Raman DeepMediX: A Deep Learning-Driven Resource-Efficient Medical Diagnosis Across the Spectrum. 2023 abs/2307.00324 CoRR https://doi.org/10.48550/arXiv.2307.00324 db/journals/corr/corr2307.html#abs-2307-00324

Pradeep Singh Vijay Kumar Bhat Graph invariants of the line graph of zero divisor graph of $$\mathbb {Z}_{n}$$. 1271-1287 2022 April 68 J. Appl. Math. Comput. 2 https://doi.org/10.1007/s12190-021-01567-0 db/journals/jamc/jamc68.html#SinghB22

Pradeep Singh Vijay Kumar Bhat Adjacency matrix and Wiener index of zero divisor graph $$\varGamma (Z_n)$$. 717-732 2021 June 66 J. Appl. Math. Comput. 1-2 https://doi.org/10.1007/s12190-020-01460-2 db/journals/jamc/jamc66.html#SinghB21

Karthik Krishnamurthy Pradeep Singh Nikhil Sriraman GeoBMS: Hybrid Cloud/ On-Premise Architecture for Building Energy Optimization. 1-6 2019 GIoTS https://doi.org/10.1109/GIOTS.2019.8766402 conf/giots/2019 db/conf/giots/giots2019.html#KrishnamurthySS19 Pradeep Singh Lisa Weil Microsoft Windows for Pen Computing. 23-31 1992 conf/ifip/1992-3 IFIP Congress (3) db/conf/ifip/ifip92-3.html#SinghW92 Shradhdha Agrawal Bezawada Sri Sai Anurag Zhuhui Bai Vijay Kumar Bhat Zhenyang Cai Rashi Chauhan Junying Chen Liangyi Chen Shreyas Rajesh Dahale Shuzhi Deng Akshaya Devadiga Anupriya Dey Abhinav Dhall Sumit Gangwar Sutirtha Ghosh Mehak Gopal Shruti Gupta Arti Jain Shan Jiang Lijian Jin Zuolin Jin Anushka Joshi Ritwik Kashyap Karthik Krishnamurthy Ashutosh Kumar Deepak Kumar Rakesh Kumar 0015 Jianquan Li Jingyi Liang Tianrui Liu Xiang Liu Chunfeng Luo Surbhi Madan Chehak Malhotra Karnati Mohan Kishore Babu Nampalle Rajesh Singh Negi Hrishit B. P Ridam Pal Anshul Pundhir Balasubramanian Raman Balasubramanian Hrishit B. Pa Raman Richa Mudasani Rushikesh Shivam Sagar Lavanya Sankaranarayanan Falk Schwendicke Tavpritesh Sethi Kanishk Sharma Mehak Sharma Sapana Sharma Sunny Kumar Sharma Bhavneet Singh Soodan Nikhil Sriraman Nhan L. Tran Vivek Narayan Uppala Benyou Wang Junwen Wang Lisa Weil Zhenwei Wen Wei-Fa Yang Yash Wenjing Yi Hexian Zhang Jiaming Zhang Zixu Zhang Junjie Zhao