Special Session #1

Fractional Calculus, Neural-Neuron-Network Dynamics and Artificial Intelligence across Complex Systems
and Other Systems

 

Chairs:

Prof. Yeliz Karaca, University of Massachusetts (UMass), Department of Mathematics and Department of Neurology, MA, USA;  e-mail: yeliz.karaca@ieee.org

Prof. Dumitru Baleanu, Lebanese American University, Department of Computer Science and Mathematics, Beirut, Lebanon and Institute of Space Science, Magurele, Ilfov, Romania; e-mail: dumitru.baleanu@gmail.com


The functions and information processing of the brain, constituting the coordination of neuronal populations across different parts of the cortex, are among the most complex things concerning biology and human body. The detection and quantification of the interaction between the neuronal populations can give rise to insights into dynamic networks underlying brain functions, which also point to the control of the neuron dynamics by fractional operators lending some degrees of freedom. Dynamic behaviors generated by modified networks rely upon multiple parameter values of models and concurrent stimuli, yielding different patterns of periodic and excitable spiking, resting, chaos, bifurcation and bursting behaviors having minimum computational errors. In these regards, while neuron models govern the aforementioned neuron dynamics and neuronal modeling enables the capturing of the memory-genetic characteristics of biological neurons, the quantification of neuron dynamics includes limit cycle portrayal, measurement, bifurcation diagrams, eigenvalues, and so forth. In modern neuron modeling approaches, fractional-order differential equations are paramount to understanding intricate mathematical dynamical behaviors and patterns that underlie the experimental data. On the other hand, the spiking neural networks, as an assembly of small processing units aka neuron models, make up a special class of artificial neural networks (ANNS) as brain-inspired connectionist systems.

Processes of fractional dynamics, differentiation and systems in complex systems along the dynamical processes and dynamical systems of fractional order as regards natural and artificial phenomena are critical when their modeling by ordinary or partial differential equations with integer order, ordinary and partial differential equations is at stake. Accordingly, fractional calculus and fractional-order calculus approach with novel mathematical models and machine learning algorithms can enable one to obtain optimized solutions besides the entailment towards developing analytical and numerical methods. Fractional modeling as a sophisticated means extends the concept of ordinary differentiation and integration to fractional (non-integer) orders, and thus it can add depth to the understanding of complexity and its peculiarities. Therefore, the capability of fractional modeling can be considered to arise from its bridging the gap between simplicity and realism.

Within this framework, novel mathematical-informed schemes can provide a reliable and robust understanding of various complex processes constituting a variety of heterogeneous temporal and spatial scales, whereas Artificial Intelligence (AI), machine learning, deep learning and other applicable models can be utilized for attaining the maximization of model accuracy and minimization of functions. Given these considerations and complexities, holistic and comprehensive understanding into various processes is required based on integrative models having multiple stages for detecting significant attributes and irregularities on relevant scales so that complex systems, whose behavior and patterns are perplexing in terms of prediction, interpretability and control can be expounded toward the ultimate goal of accomplishing a global understanding while paying attention to the evolutionary path thereof. All these aspects serve for generating applicable solutions to problems encountered in different areas of medicine, neuroscience, genetics, biology, neurobiology, neurovirology, mathematical science, engineering, computer and data science, applied disciplines, and so forth.

Based on such sophisticated integrative and multi-stage approach across spatio-temporal scales with computer-assisted applications while building on our previous and ongoing special sessions, special issues and academic events, our special session intends to provide a bridge to merge interdisciplinary perspective to pave new junctions and crossroads both in real systems, other corresponding systems as well as realms.

The potential topics of our special session include but are not limited to:
  • Fractional calculus and neural-neuron dynamics
  • Application of fractional theory in quantum Support Vector Machines (SVMs) and/or neural networks
  • SpinDoctor and neuronal dynamics with applications in medicine, neurology and biology
  • Spike timing, chaos and machine learning
  • Synapses and sensibility of neural networks
  • Synchronization and phase oscillators 
  • Signal/image processing, information theory and optimization
  • Neuron dynamics and neuronal functions
  • Neurocomputation and neuronal circuits’ dynamics 
  • Recurrent neural networks
  • Biological systems modeling, spiking neural networks and AI algorithms
  • Fractional-order Fitzhugh-Nagumo model and/or fractional difference equations
  • Fractional-order Rulkov map of biological neurons
  • Fractional calculus, Bloch–Torrey equation with Nuclear Magnetic Resonance (NMR) and / or Magnetic Resonance Imaging (MRI)
  • Fractional-order neurons and fractional models of neurons
  • Multidimensional fractional wavelets
  • Applications of fractional entropy
  • Stochastic analysis, modeling and/or stochastic Markov processes
  • Fractional calculus and computational complexity
  • Bifurcation, control, oscillation and nonlinear dynamics
  • Theory and applications of differential equations (i.e. PDEs, ODEs, fractional differential equations)
  • Neuron difference equations
  • Hopfield-Enhanced Deep Neural Networks
  • Data mining with fractal / fractional calculus
  • Complexity measures for complex data analysis
  • Oscillations and stability of nonlinear dynamics
  • Computational medicine and/or fractional calculus in nonlinear systems
  • Fractional models in medicine/neurology/biology
  • Chaotic and fractional complex dynamics
  • Modern fractional calculus models
  • Spatiotemporal data analysis with temporal networks
  • Mathematical neuron models and neuronal dynamics
  • Mathematical modeling, applied mathematical methodologies and Artificial Intelligence (i.e. machine learning techniques, deep learning, LLM, NLP) in complex systems

Among the many other related points with mathematical, theoretical, numerical and computational modeling aspects.


Some Relevant References: 

[1] Karaca, Y., Baleanu, D., Moonis, M., Zhang, Y. D., & Gervasi, O. (2024). EDITORIAL SPECIAL ISSUE: PART IV-III-II-I SERIES: FRACTALS-FRACTIONAL AI-BASED ANALYSES AND APPLICATIONS TO COMPLEX SYSTEMS. Fractals, 31(10), 2302005.
[2] Baleanu, D., Karaca, Y., Vázquez, L., & Macías-Díaz, J. E. (2023). Advanced fractional calculus, differential equations and neural networks: Analysis, modeling and numerical computations. Physica Scripta, 98(11), 110201.