Tag: Mathematics
Ana Carpio, Mathematics, Innovative Researcher Award
Prof. Dr. Ana Carpio: Professor of Applied Mathematics at Universidad Complutense de Madrid, Spain
Article Details
The article “Hierarchical topological clustering and meaningful outliers” by Ana Carpio & Gema Duro was published in Soft Computing on 07 February 2026. It presents a mathematical and computational framework that integrates topological data analysis with hierarchical clustering to detect clusters of any shape and identify meaningful outliers in datasets. The approach is demonstrated using MATLAB on datasets from diverse domains, including biological, physical, and economic data.
Novelty
The work introduces a hierarchical topological clustering (HTC) algorithm that combines persistence-based topological analysis with clustering, a method not found in traditional algorithms like K-means, K-medoids, or DBSCAN. Its novelty lies in enabling multiscale clustering of arbitrary shapes while providing a mathematically grounded method to quantify cluster stability and identify significant outliers.
Impact
The algorithm has the potential to transform how researchers analyze complex, high-dimensional data where conventional clustering fails. By accurately identifying clusters and meaningful outliers, it can impact fields such as genomics, image analysis, swarm robotics, and economic modeling. Its robustness to noise also enhances the reliability of insights drawn from real-world datasets.
Originality
The approach is original because it integrates persistent homology from topological data analysis into a hierarchical clustering framework. Unlike other methods, it does not rely on pre-set parameters or assume convexity of clusters. The identification of “meaningful outliers” adds a layer of interpretability uncommon in standard clustering techniques.
Experimental Rigor
The authors validate the algorithm across multiple datasets of moderate size, employing different distance measures (Euclidean, Wasserstein, Fermat). MATLAB simulations demonstrate its ability to detect both complex cluster structures and significant outliers. However, large-scale computational benchmarking and comparisons with state-of-the-art topological clustering methods could further strengthen rigor.
Sustainability Impact
By efficiently identifying key data patterns and reducing misclassification, the method may indirectly support sustainable decision-making, for example, in resource allocation, disease diagnosis, and trade analysis, where misinterpretation of data can lead to resource waste or inefficiency. Its computational efficiency also reduces unnecessary computational load compared to repeated parameter tuning in traditional clustering methods.
Applicability
The HTC algorithm is highly applicable across domains requiring nuanced data analysis. Its ability to handle non-convex clusters, hierarchical structures, and meaningful outliers makes it suitable for bioinformatics, materials science, social network analysis, economic modeling, robotics, and image compression. The flexibility in distance metrics further broadens its applicability across varied datasets.
Research Portfolio
Ana Carpio is a Professor of Applied Mathematics at the Universidad Complutense de Madrid, specializing in numerical analysis and its applications to physical and biological systems. She has built an international reputation for bridging rigorous mathematical theory with real-world problems in fluid dynamics, biomedicine, and complex systems modeling. Throughout her career, she has supervised numerous Ph.D. students, led interdisciplinary research projects, and collaborated with top institutions worldwide.
Online Profile
Carpio maintains a verified academic profile at UCM and a personal homepage detailing her research, publications, collaborations, and ongoing projects. Her work is widely cited, with over 3,600 total citations, an h-index of 35, and an i10-index of 91, reflecting her substantial impact in applied mathematics. Her profile highlights both theoretical contributions and practical applications, emphasizing the relevance of mathematics to engineering, biology, and computational science.
Education
Carpio earned her B.S. and M.S. in Mathematics (Numerical Analysis) from Universidad Politécnica de Valencia in 1988. She completed her DEA d’Analyse Numérique at Université Pierre et Marie Curie (Paris VI) in 1989 and obtained her Ph.D. in Mathematics in 1993 under the supervision of A. Haraux, focusing on numerical methods for partial differential equations. In 2004, she earned her Habilitation as Full Professor of Applied Mathematics from the MEC, Spain, marking her qualification for senior academic leadership.
Research Focus
Her research centers on the development and application of mathematical models and numerical methods to complex systems, with a focus on physical and biological phenomena. She works on partial differential equations, fluid dynamics, and microbiome interactions, integrating computational tools to solve problems in biomedicine and industry. Her interdisciplinary approach emphasizes both theoretical rigor and the translation of mathematics into actionable scientific and technological solutions.
Experience
Carpio’s professional experience spans multiple institutions and countries. She began as a predoctoral researcher at Université Pierre et Marie Curie, followed by assistant and associate professorships at UCM, and postdoctoral research at Oxford. She has held visiting scholar and researcher positions at Stanford, Harvard, NYU Courant Institute, Institut Henri Poincaré, the University of Iceland, and the Fields Institute. Currently, she is Professor of Applied Mathematics at UCM and directs the Research Group on Mathematics Applied to Physical and Biological Systems.
Research Timeline & Activities
Her research timeline reflects a continuous evolution from foundational numerical analysis in the late 1980s and 1990s to interdisciplinary applications in fluid dynamics, biomedicine, and computational modeling from 2005 onward. She has led projects that connect mathematics with industrial, environmental, and health-related applications, and has collaborated with international research centers and institutes. Her activities include supervising graduate students, organizing workshops, and contributing to collaborative scientific networks.
Awards & Honors
Carpio has received multiple awards recognizing both her research excellence and innovative contributions. She won the Best Ph.D. Thesis Award at UCM in 1993, the SEMA Prize for Young Researchers in 1998, a mention from the Madrid-MIT Vision Program for innovative ideas in biomedicine in 2013, and a winning project in the Repsol Inspire Program in 2013. These honors reflect her sustained impact in applied mathematics and her leadership in interdisciplinary research initiatives.
Prof. Dr. Ana Carpio the Innovative Researcher Award based:
1. Pioneering Research in Applied Mathematics
Prof. Carpio has consistently developed novel mathematical frameworks that bridge theory and practice. Her work on hierarchical topological clustering exemplifies her ability to translate advanced mathematical concepts, such as persistent homology, into actionable tools for data analysis across biology, economics, and engineering. This demonstrates a forward-thinking, innovative approach in applied mathematics.
2. Interdisciplinary Impact
Her research seamlessly integrates mathematics with biomedicine, fluid dynamics, microbiome studies, and complex systems modeling. By tackling real-world problems with rigorous mathematical methods, she has created solutions that cross traditional disciplinary boundaries, exemplifying innovation through interdisciplinary application.
3. Methodological Originality and Novelty
The hierarchical topological clustering algorithm she co-developed introduces new ways to detect non-convex clusters and meaningful outliers. This method addresses limitations of conventional clustering techniques, showing her strength in creating original, high-impact methodologies that advance both theoretical and practical aspects of data science.
4. Global Academic Leadership and Collaboration
Carpio’s career demonstrates international leadership and collaboration, with research positions and partnerships at top institutions like Stanford, Harvard, NYU, Institut Henri Poincaré, and the Fields Institute. Her ability to lead interdisciplinary projects and mentor future scientists reflects her innovative influence on global research networks.
5. Sustained Excellence and Recognition
Her numerous awards—Best Ph.D. Thesis, SEMA Prize, Madrid-MIT Vision Program recognition, and Repsol Inspire Program winner—highlight her sustained excellence and innovation. Coupled with an h-index of 35 and over 3,600 citations, this underscores her impact as a researcher whose innovations have both academic and societal relevance.
Protected: Swati Goyal, Mathematics, Best Innovator Award
Prashant Pandey, Mathematics, Emerging Researcher Award
Asst. Prof. Prashant Pandey: Assistant professor at Amity University Ranchi Jharkhand, India
Title/Designation: Asst. Prof
Name: Prashant Pandey
Current Role/Designation: Assistant Professor
Organization/Institution: Amity University Ranchi, Jharkhand
Country: India
Subject Track: Mathematics
Award Category: Emerging Researcher Award
Prashant Kumar Pandey is an applied mathematician and researcher with expertise in numerical analysis, scientific computing, and high-order methods for partial differential equations. He specializes in the development of non-oscillatory and entropy-stable numerical schemes for hyperbolic conservation laws, with growing interests in machine-learning-assisted numerical methods. He completed his PhD in Applied Mathematics from SRM Institute of Science and Technology, where his work addressed robustness, accuracy, and stability in advanced computational schemes.
Online Profiles
Since 2020, Prashant Kumar Pandey’s research work has received 9 total citations, with an h-index of 2, reflecting the growing visibility and scholarly impact of his contributions in applied mathematics, numerical analysis, and entropy-stable computational schemes.
Education
He earned his PhD in Applied Mathematics (2018–2024) from SRM Institute of Science and Technology, Kanchipuram, with a doctoral thesis focused on efficient and robust construction of non-oscillatory and entropy-stable schemes. Prior to this, he completed an MSc in Mathematics from IIT Madras in 2013, gaining strong analytical and computational training, and a BSc (Hons.) in Mathematics from Banaras Hindu University in 2010, establishing a solid foundation in pure and applied mathematics.
Research Focus
His research interests center on high-order finite difference and finite volume methods for hyperbolic conservation laws, including ENO and WENO reconstructions, entropy-stable discretizations, and shock-capturing techniques. He also works on integrating machine learning approaches—such as classification and regression neural networks—into numerical schemes to enhance adaptivity, accuracy, and computational efficiency in simulations involving discontinuities.
Experience
He has accumulated experience in both teaching and research roles, having served as a lecturer in mathematics at Meerut Institute of Engineering and Technology and as a JEE (Main) mathematics trainer at reputed integrated institutions in Karnataka and Tamil Nadu. Alongside teaching, he has extensive research experience gained during his doctoral tenure, involving numerical modeling, algorithm development, scientific programming, and collaborative research in applied mathematics.
Research Timeline & Activities
Since December 2017, he has been actively engaged in doctoral and postdoctoral-level research activities at SRM Institute of Science and Technology. His research timeline includes developing novel numerical schemes, publishing in SCI-indexed journals, presenting research at national and international conferences, participating in workshops on conservation laws and numerical methods, and collaborating with researchers on interdisciplinary projects combining numerical analysis and machine learning.
Awards & Honors
He has demonstrated strong academic performance at the national level by qualifying the IIT-JAM Mathematics examination with an All India Rank of 120 in 2011 and successfully qualifying the GATE examination in Mathematics in 2013. These achievements reflect his solid theoretical background and competitive standing among mathematics graduates in India.
Top Noted Publication
His top noted publications include Q1 and Q2 SCI-indexed journal articles in Applied Mathematics and Computation, Computational and Applied Mathematics, Physica Scripta, and Soft Computing. Among these, his 2023 article in Applied Mathematics and Computation on sign-stable arbitrary high-order reconstructions for entropy-stable schemes stands out for its methodological rigor and impact in the field of numerical methods for conservation laws.
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Sign stable arbitrary high order reconstructions for constructing non-oscillatory entropy stable schemes
P. K. Pandey, R. K. Dubey, Applied Mathematics and Computation, Vol. 454, Article 128099, 2023 — Cited by 4 -
High-resolution WENO schemes using local variation-based smoothness indicator
P. K. Pandey, F. Ismail, R. K. Dubey, Computational and Applied Mathematics, 41(5), 208, 2022 — Cited by 3 -
Learning numerical viscosity using artificial neural regression network
R. K. Dubey, A. Gupta, V. K. Jayswal, P. K. Pandey, International Conference on Computational Sciences: Modelling, Computing and Simulation, 2020 — Cited by 2 -
An efficient scaling of WENO-JS weights for accuracy preserving and higher resolution schemes
P. K. Pandey, R. K. Dubey, Physica Scripta, 98(8), 085247, 2023 -
ENO classification and regression neural networks for numerical approximation of discontinuous flow problems
V. K. Jayswal, P. K. Pandey, Soft Computing, 2024 -
Efficient diffusion for high order non-oscillatory entropy stable schemes
A. Sahu, P. K. Pandey, R. K. Dubey, Applied Mathematics and Computation, Vol. 518, Article 129901, 2026
Strengths for the Emerging Researcher Award
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Strong Research Foundation in High-Impact Areas
Dr. Prashant Kumar Pandey has developed a solid research foundation in applied mathematics, particularly in numerical analysis of hyperbolic conservation laws. His work on non-oscillatory and entropy-stable schemes addresses fundamental challenges of stability, accuracy, and robustness, making his research highly relevant to both theoretical and computational mathematics. -
Publications in Reputed SCI Journals
He has published multiple research articles in well-regarded Q1 and Q2 SCI-indexed journals such as Applied Mathematics and Computation, Computational and Applied Mathematics, Physica Scripta, and Soft Computing. These publications demonstrate his ability to produce high-quality, peer-reviewed research early in his academic career, a key indicator of an emerging researcher. -
Interdisciplinary Integration of Machine Learning and Numerics
A notable strength of his research profile is the integration of machine learning techniques—such as classification and regression neural networks—into classical numerical schemes. This interdisciplinary approach enhances adaptivity and performance in numerical simulations and reflects innovation at the intersection of applied mathematics and artificial intelligence. -
Growing Research Impact and Visibility
Since 2020, his work has accumulated citations with an h-index of 2, indicating increasing recognition within the research community. His most cited works in Applied Mathematics and Computation and Computational and Applied Mathematics highlight the relevance and applicability of his contributions to ongoing research in numerical methods. -
Commitment to Academic Growth and Research Leadership
As an Assistant Professor at Amity University Ranchi, he actively balances teaching with research, contributing to curriculum delivery while continuing scholarly output. His consistent engagement in conferences, workshops, collaborations, and future-oriented research projects reflects strong potential for long-term academic leadership and recognition as an emerging researcher.
Protected: Thandra Jithendra, Mathematics, Best Researcher Award
Protected: Arsen Shutovskyi, Mathematics, Best Innovator Award
Protected: Oleksiy Dovgoshey, Mathematics, Innovative Researcher Award
Protected: Lyudmila Kovalchuk, Mathematics, Best Innovator Award
Protected: Danish Malik, Mathematics, Best Innovator Award
Surath Ghosh, Mathematics, Best Researcher Award
Dr. Surath Ghosh: Assistant Professor at Vellore Institute of Technology – Chennai Campus, India
Dr. Surath Ghosh is an accomplished academic and researcher currently serving as an Assistant Professor at the Department of Mathematics, Vellore Institute of Technology (VIT), Chennai, India. He specializes in fractional calculus, numerical analysis, and mathematical modeling. After completing his Ph.D. in Mathematics from the National Institute of Technology Jamshedpur (NIT Jamshedpur) in 2022, his research has focused on developing new numerical methods and analytical techniques to solve complex fractional-order differential equations that arise in diverse fields, such as mathematical physics, population dynamics, and bio-mathematics. Dr. Ghosh has a passion for using advanced computational techniques to solve real-world problems and has published extensively in high-impact journals.
Online Profiles
Dr. Surath Ghosh’s academic work has garnered significant attention and recognition in the research community. As of now, his published papers have accumulated 463 citations, with a notable h-index of 8, indicating that at least 8 of his papers have each been cited 8 or more times. His i10-index stands at 6, meaning that 6 of his publications have received 10 or more citations each. These metrics highlight the growing impact of his work in the fields of fractional calculus, numerical analysis, and applied mathematics.
Education
Dr. Ghosh’s academic journey is marked by a strong foundation in both pure and applied mathematics. He completed his Ph.D. in Mathematics at NIT Jamshedpur in 2022, with a dissertation focusing on Numerical and Analytical Solutions of Fractional Models of Mathematical Physics with New Operators. Prior to his Ph.D., he earned an M.Tech. in Computer Science & Data Processing from IIT Kharagpur (2018), followed by an M.Sc. in Mathematics from Visva Bharati University (2015). He completed his B.Sc. in Mathematics from the University of Burdwan in 2013, where he developed a keen interest in advanced mathematical modeling and computational methods.
Research Focus
Dr. Ghosh’s research interests are primarily centered around fractional calculus and its applications in solving complex mathematical models. His work involves using fractional operators to model physical and biological systems more accurately, taking into account memory effects and non-local phenomena. He also focuses on the development of robust numerical methods such as spectral methods and wavelet-based techniques for solving fractional-order differential equations, which have broad applications in nonlinear dynamics, population biology, and fluid dynamics. Additionally, Dr. Ghosh explores computational techniques in theoretical computer science, further bridging the gap between mathematics and technology.
Experience
Dr. Ghosh has rich academic and research experience across multiple institutions. Before joining VIT Chennai in 2022, he served as an Assistant Professor at JECRC University, Jaipur (2021-2022). He also worked as a Senior Research Fellow and Junior Research Fellow at NIT Jamshedpur, where he contributed significantly to research on fractional calculus and mathematical modeling. Dr. Ghosh has also been a Teaching Assistant at IIT Kharagpur, where he assisted in undergraduate-level courses, such as C Programming Lab. His diverse teaching roles across various levels and courses have allowed him to develop a comprehensive understanding of both theoretical and applied mathematics.
Research Timeline & Activities
Dr. Ghosh’s research journey began during his M.Tech. studies at IIT Kharagpur, where he worked on mining frequent patterns in transactional databases. Following his transition to NIT Jamshedpur for his Ph.D., his focus shifted toward fractional calculus and its numerical solutions. His research has spanned a wide range of topics, including heat equations, population dynamics, and the modeling of physical phenomena using fractional differential equations. Dr. Ghosh’s research timeline also includes active participation in workshops, conferences, and training programs, both as a participant and presenter. Notable conferences include the International Conference on Mathematical Analysis & Applications (2020) and International Conference on Mathematical Modelling, Applied Analysis, and Computation (2021).
Awards & Honors
Dr. Ghosh has received numerous accolades throughout his academic career. Notable honors include a GATE fellowship in 2015 and a prestigious government scholarship for higher education. His paper on the analysis of heat equations, published in Mathematical Methods in the Applied Sciences, was recognized as a Top Cited Article for 2020-2021. His contributions to the field of fractional calculus and applied mathematics have earned him widespread recognition, and his research has been featured in high-impact journals. He has also been a recipient of several fellowships and grants for his research projects.
Top Noted Publication
One of Dr. Ghosh’s top publications is “An analysis for heat equations arising in diffusion process using new Yang-Abdel-Aty Cattani fractional operator”, published in Mathematical Methods in the Applied Sciences (SCI, Q2, Impact Factor – 1.8). This work was selected as a Top Cited Article for the 2020-2021 period, highlighting its significance in advancing the study of fractional operators in diffusion processes. This paper demonstrates the application of fractional calculus in understanding complex diffusion dynamics, and its recognition attests to its impact within the mathematical sciences community. Dr. Ghosh has authored or co-authored multiple other impactful publications in journals such as Numerical Methods for Partial Differential Equations, Applied Numerical Mathematics, and International Journal of Applied and Computational Mathematics.
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An analysis for heat equations arising in diffusion processes using the new Yang-Abdel-Aty-Cattani fractional operator
S. Kumar, S. Ghosh, B. Samet, E.F.D. Goufo
Mathematical Methods in the Applied Sciences, 43 (9), 6062-6080 (2020)
Citations: 220
This paper focuses on heat equations in the context of diffusion processes, utilizing a novel Yang-Abdel-Aty-Cattani fractional operator. It offers valuable insights into the theoretical modeling of fractional phenomena in mathematical physics. -
A fractional model for population dynamics of two interacting species using spectral and Hermite wavelets methods
S. Kumar, S. Ghosh, R. Kumar, M. Jleli
Numerical Methods for Partial Differential Equations, 37 (2), 1652-1672 (2021)
Citations: 84
This publication presents a fractional-order model for the population dynamics of two species interacting with each other. The research employs advanced wavelet methods to analyze and solve the system numerically. -
A model for describing the velocity of a particle in Brownian motion by Robotnov function-based fractional operator
S. Kumar, S. Ghosh, M.S.M. Lotayif, B. Samet
Alexandria Engineering Journal, 59 (3), 1435-1449 (2020)
Citations: 72
This paper introduces a new model using the Robotnov function-based fractional operator to describe the velocity of a particle in Brownian motion, an important area of study in statistical physics and applied mathematics. -
A fractional system of Cauchy-reaction diffusion equations by adopting Robotnov function
S. Kumar, S. Ghosh, M. Jleli, S. Araci
Numerical Methods for Partial Differential Equations, 38 (3), 470-489 (2022)
Citations: 15
This work extends the Robotnov fractional operator to solve Cauchy-reaction diffusion equations, contributing to the broader application of fractional calculus in solving complex reaction-diffusion systems. -
Spectral approximation methods for nonequilibrium transport in turbulent channel flows using fADE
S. Ghosh, S. Kundu, S. Kumar, E.E. Mahmoud
Applied Numerical Mathematics, 162, 53-66 (2021)
Citations: 14
This study develops spectral approximation techniques for modeling nonequilibrium transport in turbulent channel flows using the fractional Advection-Dispersion Equation (fADE), enhancing the modeling capabilities for complex fluid dynamics.
Strength for the Best Researcher Award
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Innovative Research in Fractional Calculus
Dr. Surath Ghosh’s expertise in fractional calculus has significantly contributed to advancing mathematical modeling techniques in various scientific disciplines. His work in introducing novel fractional operators, such as the Yang-Abdel-Aty-Cattani fractional operator and Robotnov function-based fractional operators, has expanded the theoretical framework for modeling complex phenomena such as diffusion processes, population dynamics, and Brownian motion. This innovative approach demonstrates his leadership in the field and positions him as a top researcher in fractional calculus. -
High Impact Publications and Citations
Dr. Ghosh has an impressive publication record, with multiple highly cited articles in renowned journals like Mathematical Methods in the Applied Sciences and Numerical Methods for Partial Differential Equations. His work has garnered 463 citations, and he maintains a respectable h-index of 8, signifying the broad impact of his research on the academic community. The recognition of his publication “An analysis for heat equations arising in diffusion processes” as a Top Cited Article for 2020-2021 further exemplifies his research’s influence in advancing mathematical modeling. -
Pioneering Numerical Methods for Complex Systems
A major strength of Dr. Ghosh’s research lies in the development of robust and efficient numerical methods for solving fractional-order differential equations. His application of spectral and wavelet-based methods has provided new ways to address complex models in areas like population biology, fluid dynamics, and nonlinear dynamics. This expertise is particularly relevant for solving real-world problems involving systems with memory effects, such as ecological models or turbulence in fluid flows. -
Multidisciplinary Approach and Real-World Applications
Dr. Ghosh’s research seamlessly bridges mathematics, physics, and computational science. His work on fractional models of physical phenomena, like heat diffusion and Brownian motion, is paired with practical applications in population dynamics and bio-mathematics. This multidisciplinary approach not only advances theoretical research but also addresses pressing challenges in applied sciences, making Dr. Ghosh’s contributions both academically and socially impactful. -
Recognition and Honors in Academic Community
Dr. Ghosh’s contributions to the field of fractional calculus and mathematical modeling have been widely recognized through prestigious awards and honors. These include fellowships such as the GATE fellowship, a government scholarship for higher education, and multiple research grants. His active participation in international conferences and workshops, as well as his contributions to high-impact journals, further highlight his ongoing influence and leadership in his field. His recognition as a Top Cited Author for 2020-2021 underlines the long-term value and relevance of his research.