PLENARY SPEAKERS

Abstract: Will be provided soon.

Abstract: In this presentation, I will provide a comprehensive overview of deterministic asset pricing models. I will introduce asset flow differential equations as a framework for modeling a single-asset market consisting of a group of investors and subsequently extend this approach to a two-asset market system. The derivation of these models is based on the assumption of a finite supply of assets, as opposed to unbounded arbitrage opportunities, and incorporates investment strategies driven by either price momentum (trend-following) or valuation-based considerations.

2010 AMS Subject Clasifications: 91B25, 91B50, 91G99

Keywords: Ordinary differential equations for asset pricing, price dynamics, asset flow, dynamical system approach to mathematical finance.

REFERENCES

G. Caginalp, G.B. Ermentrout, Numerical studies of differential equation related to theoritical financial markets, Appl. Math. Lett., 4, 35-38, (1991).
H. Bulut, H. Merdan, D. Swigon, Asset price dynamics for a two-asset market system, Chaos 29, 023114 (2019).
H. Merdan, G. Caginalp, W. C. Troy, Bifurcation analysis a single-group asset flow model, Quarterly Applied Mathematics, Quart. Appl. Math. 74, 275-296, (2016).
H. Merdan, M. Alisen, A mathematical model for asset pricing, Applied Mathematics and Computation, 218, 1449-1456, (2011).
G. Caginalp, H. Merdan, Asset price dynamics with heterogeneous groups, Physica D, 225, 43-54, (2007).
G. Caginalp, Nonlinear price evolution, Quart. Appl. Math., 63, 715-720, (2005).
G. Caginalp, D. Balenovich, Asset flow and momentum: deterministic and stochastic equations, Phil. Trans. R. Soc. Lond. A, 357, 2119-2133, (1999).

Abstract: Will be provided soon

Abstract: The speech will introduce the concept of Generative Artificial Intelligence (GenAI) having with the utilities and risks and emphasizing its role in leveraging mathematical models to innovate and solve problems; discuss recent advancements in GenAI technologies, focusing on improvements in model architectures and notable examples like GPT-3 and AlphaFold; explore the fundamental mathematical concepts behind GenAI, including probability, statistics, and their application in various GenAI architectures; highlight GenAI’s contributions to solving complex mathematical problems and its ability to generate new mathematical data for research; address the technical challenges such as model bias and overfitting, alongside the ethical concerns of GenAI deployment; encourage further interdisciplinary research between mathematicians and GenAI experts; and summarize the potential of GenAI in mathematics and its practical applications, ending with a look at future trends in the field.

Abstract: Will be provided soon…

Abstract: This talk will explore the challenge of solving algebraic equations over finite fields. This fundamental problem is growing in significance due to its critical applications in coding theory and cryptography. Addressing this problem from theoretical and practical perspectives is essential for advancing these fields.

Traditionally, research has focused on determining the number of solutions for specific equations rather than explicitly deriving all possible solutions. While this approach has sufficed to particular applications in cryptographic function theory, a deeper understanding is necessary to achieve more comprehensive results. Expanding the toolkit for solving equations over finite fields will provide valuable resources for theorists, cryptographers, and coding theorists.

We will begin by outlining our primary motivations before highlighting significant recent advancements in solving key algebraic equations over finite fields. We will then discuss the underlying methodologies and mathematical concepts that drive these developments and their impact on symmetric cryptography and coding theory.

Abstract: Mathematical modeling is acknowledged to contribute to the comprehension of the way neurological and virological diseases progress while being able to tackle their dynamic and complex mechanisms including subtle attributes and patterns. Utmost attention is to be paid not to compromise accuracy, specificity and reliability to achieve informed decisions, precise and personalized health interventions and accurate diagnosis based on precise classifications by the incorporation of fractal-fractional methods, wavelets, Hidden Markov modeling, and quantum machine learning methods among other applicable ones. Amid these challenges and affordances, quantum Artificial Intelligence (AI) provides the merging of the quantum computing strength with AI, and thus, quantum computing is likely to supercharge the capabilities of AI as a result of removing limitations due to complexity, data size and the time period it takes to solve problems.  Quantum computation as a computational paradigm with quantum computers is capable of solving selected problems via the exploitation of quantum effects such as entanglement and interference. Belonging to the computational complexity theory, quantum complexity theory helps one address complexity classes defined within the use of quantum computers as a computational model governed by quantum mechanics. Quantum   computers are operated on short pulses of light, ensuring practicality owing to the speeding up the computer operations in which the data are converted into quantum bits rather than being directly stored. This kind of storage can be applied to different domains including medicine, neurology, biology, virology, neurovirology, virus biology, healthcare, public health, and so on. All of these benefits point toward quantum supremacy to solve a problem that would not be possible to be solved by classical computers within a reasonable period of time. In the case of the human brain, a heterogeneous medium made up of tissues with cells having various patterns, shapes and sizes distributed across an extra-cellular space along with the numerous synapses forming complex neural networks, an in-depth and accuracy-oriented probing along with the computing of patterns and signatures in individual cells as well as neurons are required. While the human brain is known to excel in pattern recognition, adaptability and parallel processing, quantum computers and computing provide substantial computational power for conducting specific tasks.  Accordingly, the way fractal and multifractional-based predictive optimization model has ensured the classification of subtypes of stroke. Another outcome is the computational complexity modeling of the micro–macrostructural brain tissues with diffusion Magnetic Resonance Imaging MRI signal processing and neuronal multi-components, which has been achieved by means of fractional calculus operators, Bloch–Torrey partial differential equation and Artificial Neural Networks (ANNs). Besides these models, Hidden Markov model and multifractal method within the framework of predictive quantization complexity models has been able to provide for the differential prognosis and differentiation of the subgroups concerning multiple sclerosis (MS). In addition and related to these modes of modeling, methods and techniques, theory of complexity and complex systems with their origins is to be briefly discussed.  Taken together, quantum computing and AI within the foundational characteristics of mathematical modeling with advanced applications provide a framework for the solution of real-life problems towards achieving efficiency and saving time. Furthermore, fractal-fractional and wavelet methods, to cite a few, can be employed for characterizing complex and dynamic patterns in various domains so that specificity, regularity, self-similarity and significant attributes can be detected, which could offer facilitating functions for physicians and clinicians while follow-up procedures, treatment regimens and precision medicine can be efficiently managed so that the life quality of the patients can be maintained.

Keywords: Mathematical neurology; Medical virology; Neurovirology; Virus biology; Quantum computing; Quantum AI; Computational complexity; Quantum complexity theory; ANN; Diffusion MRI signal processing; Wavelet transform modulus maxima; Fractals; Fractional calculus operators; Bloch–Torrey PDE; Hidden Markov.

References:

[1] Karaca, Y. (2025), Mathematical Modeling of Human Hepatitis Medical Virology-based Multifractal Wavelet Analysis by Quantum SVM Computing, Paul Shapshak et al. (Eds): Global Virology V: 21st Century Vaccines and Viruses, Springer.

[2] Karaca, Y. (2023). Fractional calculus operators–Bloch–Torrey partial differential equation–artificial neural networks–computational complexity modeling of the micro–macrostructural brain tissues with diffusion MRI signal processing and neuronal multi-components. Fractals, 31(10), 2340204.

[3] Karaca, Y., Baleanu, D., & Karabudak, R. (2022). Hidden Markov model and multifractal method-based predictive quantization complexity models vis-á-vis the differential prognosis and differentiation of multiple sclerosis’ subgroups. Knowledge-Based Systems, 246, 108694.

[4] Karaca, Y. (2022). Theory of complexity, origin and complex systems. In Multi-Chaos, Fractal and Multi-fractional Artificial Intelligence of Different Complex Systems (pp. 9-20). Academic Press.

[5] Karaca, Y., Moonis, M., & Baleanu, D. (2020). Fractal and multifractional-based predictive optimization model for stroke subtypes’ classification. Chaos, Solitons & Fractals, 136, 109820.

Abstract: The talk addresses basic principles in fractional modeling related to problems merging in nonlocal continua such as heat, mass, and momentum transfer, applied rheology, and other dynamic hereditary models. Two approaches have been considered: the constitutive approach based on fading memory and thermodynamic consistency and formalistic fractionalization. The analysis stresses the attention on the correct model build-up when kernels of various types, dictated by the relaxation behavior of the physical process modeled, have to be applied and their physical and mathematical adequacies.

Abstract: Will be provided soon.

Abstract: Will be provided soon.

Abstract: A partial Caputo fractional model blends classical and Riemann-Liouville terms in epidemiology and sociology. The Riemann-Liouville component introduces non-Markovian behavior, lowering transition hazard risk over time. This model generalizes standard Caputo models by combining fractional and classical terms. We prove well-posedness through fixed-point theory, with results on existence, uniqueness, and continuity. Fractional power-series solutions follow a Cauchy-Kovalevskaya-type theorem, and uniqueness relies on Gronwall- and Nagumo-like methods. Linear equations show global existence, series solutions, and stability via Mikusiński calculus. We discuss applications, stochastic extensions, and open conjectures.

Abstract: Will be provided soon.

Abstract: Understanding animal decision-making is a fundamental challenge in cognitive science and artificial intelligence. This study explores the cognitive mechanisms underlying decision-making in T-maze environments by integrating computational modeling with machine learning techniques. Specifically, it investigates the binary decision-making process in T-mazes, where animals choose between two paths based on prior experiences and environmental cues. A mathematical model is developed to capture and analyze the decision-making behavior of fish, providing theoretical insights into their cognitive processes. Additionally, advanced machine learning algorithms are employed to classify and predict behavioral patterns in zebrafish and rats. By combining cognitive models with data-driven approaches, this study achieves high predictive accuracy, demonstrating the potential of hybrid methodologies in decoding animal cognition. The findings contribute to a deeper understanding of cognitive learning mechanisms in non-human species and highlight the synergy between mathematical modeling and artificial intelligence in behavioral research.

Abstract: Physiological systems are inherently nonlinear and complex, often exhibiting chaotic behavior that reflects both healthy adaptability and disease states [1-2]. Understanding and modeling these complex dynamics through artificial intelligence (AI) and data science offer new opportunities for predictive and personalized medicine [3]. By combining machine learning, deep learning, and nonlinear dynamics analysis, it becomes possible to detect early disease biomarkers, refine risk assessment models, and develop targeted treatment strategies [3-5]. Medical robotics plays a crucial role in converting this predictive information into intelligent and adaptive interventions. Robotic systems, equipped with AI-driven analytics, can process chaotic biomedical signals in real time to improve surgical precision, personalize rehabilitation protocols, and automate patient monitoring [6]. In medical imaging and diagnostics, robot-assisted tools control advanced pattern recognition techniques to detect refined pathological changes, improving early disease detection [7]. By combining chaos theory, AI, and robotics, this interdisciplinary approach covers the way for a new era of responsive, patient-centered healthcare. This convergence not only improves predictive capabilities, but also enables autonomous decision-making in real time, promoting more accurate, efficient, and personalized medical care in the context of Health 5.0 [3,8].

Keywords: Artificial Intelligence, Predictive Modeling, Medical Robotics, Smart Healthcare, Medical Imaging, Data Science, Healthcare Automation

• Boubaker, O. (2024). Chaos in Physiological Control Systems: Health or Disease? Chaos Theory and Applications (Vol. 6, Issue 1). https://doi.org/10.51537/chaos.1413955
• Lassoued, A., & Boubaker, O. (2020). Modeling and control in physiology. In Control Theory in Biomedical Engineering: Applications in Physiology and Medical Robotics (O. Boubaker, Ed.). https://doi.org/10.1016/B978-0-12-821350-6.00001-9
• Boubaker, O. (2025). AI and Data Science in Precision Medicine, Predictive Analytics, and Medical Practice (O. Boubaker, Ed.). Elsevier. ISBN: 9780443365546
• Boubaker, O. (2025). AI and Data Science in Medical Research (O. Boubaker, Ed.). ISBN: 9780443276385
• Boubaker, O., & Jafari, S. (2018). Recent Advances in Chaotic Systems and Synchronization: From Theory to Real World Applications. In Recent Advances in Chaotic Systems and Synchronization: From Theory to Real World Applications. https://doi.org/10.1016/C2017-0-03998-8
• Boubaker, O. (2020). Chapter 7 – Medical robotics. In O. Boubaker (Ed.), Control Theory in Biomedical Engineering (pp. 153–204). https://doi.org/10.1016/B978-0-12-821350-6.00007-X
• Boubaker, O. (2023). Medical and Healthcare Robotics: New Paradigms and Recent Advances. Elsevier. https://doi.org/10.1016/C2022-0-00158-6
• Boubaker, O. (2025). AI and Data Science in Healthcare 5.0 (O. Boubaker, Ed.). Elsevier Academic Press. ISBN: 978044336556

Biography

Pr. Olfa Boubaker is a full professor at the National Institute of Applied Sciences and Technology (INSAT) at the University of Carthage, Tunisia, where she specializes in control theory, nonlinear systems, and robotics. She holds a Ph.D. in Electrical Engineering from the National Engineering School of Tunis and a Habilitation Universitaire in Control Engineering from the National Engineering School of Sfax. Professor Boubaker has led research projects in sustainable development, including medical robotics and green energy. She is the founder / editor of the book series Medical Robots and Devices (Elsevier). Additionally, she serves as an associate editor for the journal Robotica (Cambridge University Press) and the International Journal of Advanced Robotic Systems (Sage), contributing to various scientific journals and mentoring several engineering graduates.

Abstract: In this talk, we extend the Zakharov-Rubenchik system to the fractional case by using Riesz operators of fractional order in space. We prove that the system is capable of preserving extensions of the mass, energy, momentum and two linear functionals. In a second stage, we propose a discretization to approximate the solutions of our model. In the way, we propose discrete forms of the conserved functionals, and we prove that they are also conserved in the discrete domain. We prove that the numerical scheme has second-order accuracy in both space and time. Moreover, we establish theoretically the properties of conditional stability and second-order convergence of the scheme. The numerical model was implemented computationally, and some simulations are provided in order to illustrate that the method is capable of conserving the discrete functionals and its rate of convergence. This is the first report in the literature in which a multi-conservative fractional extension of this system is proposed, and a numerical scheme to approximate its solutions is designed and fully analyzed for conservative and numerical properties. Even in the integer-order case, this is the first work which proves the approximate conservation of the momentum, and which rigorously proves the stability and the convergence of a scheme for the Zakharov-Rubenchik system.

Short biography: Prof. Dr. Jorge Eduardo Macias-Diaz obtained a PhD in Mathematics from Tulane University of Louisiana under the direction of Prof. László Fuchs (2001) and a PhD in Physics from the University of New Orleans under the supervision of Prof. Ashok Puri (2007). His academic production includes more than 200 journal articles on abstract algebra, nonlinear partial differential equations, mathematical and stochastic modeling, numerical analysis of differential equations, computer simulation of systems in physics, and fractional-order calculus. He has been in charge of various projects financed by the National Council for Science and Technology of Mexico (CONACYT). He is Associate Editor for Applied Numerical Mathematics (Elsevier), International Journal of Computer Mathematics (Taylor and Francis), Advances in Mathematical Physics (Hindawi), and Computational and Mathematical Methods (Wiley). Since 2012, he has been a regular member of the Mexican Academy of Sciences.