Complexity, as a scientific theory, puts forth that some systems display behavioral and pattern-wise phenomena completely inexplicable by conventional analyses of the constituent parts of systems. Complexity characterizes a system or model’s behavior of a system or model whose components may interact in multiple manners while following local rules, which brings about collective dynamics, non-linearity, randomness, hierarchy and emergence, to name some.  Complex systems’ ubiquity is evident in engineering-related and scientific fields, from nonlinear dynamics to physical and biological systems through continuous and discrete dynamical systems along with the underlying mechanisms concerning the transitions in complex systems. While mathematical and computational modeling provide the basic means required to comprehend the behaviors and patterns of complex systems, sound theoretical foundations facilitate with the development and analysis of mathematical models.

Chaos, as a random-like and long-term behavior manifested by many nonlinear complex dynamic systems, induces that the system itself is disordered inherently, which requires the disclosure of representative and accessible paths towards affluence of complexity, simulations, clinical and experimental processes in order that robustness, novelty and diversity can be generated. Given these aspects, complexity theory focuses on non-deterministic systems, whereas chaos theory relies on deterministic systems. In the terrain of such dynamics, complexity usually arises in the case when numerous interacting subprocesses or components in the system lead to nontrivial, emergent and hard-to-describe behavior, which is greater than the sum of its parts. A system which exhibits high complexity encompasses a sequence of bifurcations resulting in an onset of chaos.

These points demonstrate that chaos and complexity theory entail a synthesis of emerging wholes of individual components rather than the orientation of analyzing systems in isolation, which points toward the fact that mathematical modeling and scientific computing are among the principal tools to address the challenges concerned with complex and chaotic systems through innovative ways attributed to data science with a precisely customized approach that can examine the data applied in an accurate and timely manner. Moreover, resorting to chaos theory can be regarded as a way to better understand the internal machinations of neural networks, and the amalgamation of chaos theory as well as Artificial Intelligence (AI) can pave the way for stimulating possibilities and providing enhancements in predictive capabilities through the introduction of adaptability, which enables chaos theory to respond to even slight changes in the input data to ensure higher levels of accuracy in prediction.

The confluence between mathematical formalisms and neurons constitutes the scaffolding of modern computational sciences, laying out quantitative frameworks regarding the complexities of neural coding, cognitive functions, patterns, systems, network dynamics, information processing as well as synaptic plasticity. Within these constructs, mathematical modeling is for capturing processes of functioning of both natural and artificial types of neural networks. The spatial and temporal aggregation of a plethora of synaptic inputs in chaotic neurons can be employed for unsupervised learning. Spontaneous activity in neural networks brings about a reduction in computational performance, suggesting that the Artificial Neural Networks (ANNs) operated at the edge of chaos at which the network is stable yet highly susceptible to input information. All these peculiarities reveal the crucial aspect of modeling and complexity of a single neuron for understanding the whole brain dynamics, patterns, biological systems and neuromodulation.

Mathematical and computational approaches in neuroscience, bioengineering, biology, biomedicine, and so forth comprise various techniques, from to machine learning techniques to advanced statistical methods each of which are established and designed to be able to identify significant patterns in voluminous and high-dimensional data. Integrating and using these are essential in elucidating connectivity of neural dynamics and information processing across different levels at which brain function develops simultaneously on different dimensions or axes within which several scales exist.

Furthermore, AI arising from the complex interactions of simpler components that result in capabilities and behaviors not explicitly programmed have led researchers and practitioners to systematically explore the current challenges alongside its facilitating opportunities. At this conjecture, convergence of AI and complexity science marks the significance of examining how different domains mutually inform and enhance one another while addressing real-world complex systems in an increasingly more interconnected and data-intensive setting. Hence, medicine, biology, engineering and computational sciences are poised for implementing transformation through its pervasive use, leading the way to the current paradigm of mathematics as a whole, computing affordances and computational methods.

In view of these aspects, opportunities, subtleties and challenges, the panel chair and panel speakers are going to be involved in delivering presentations by exchanging ideas and maintaining discussions. Besides these, our interactive panel is going to include the seeking of solutions and answers to problems in a solution-oriented way concerning domains ranging from medicine, biology, engineering, computational sciences to complexity, chaos and their applications, nonlinearity and connectivity, either idiosyncratically and / or converged, with the aim of capturing and exploring complex, real-world applications and dynamics.