Mathematical modeling is geared toward establishing models based on actual problems reflecting different aspects of the real world along with its reciprocal dynamics and interactions through mathematics whilst addressing universal notions, which foregrounds their uniqueness enabling the conceptualization, mechanization and automation of intellectual activity. This very essence sets out the solutions for real-life challenges in line with the results commensurately devised and calculated, which suggests that the core of a mathematical model lies in the factuality that it represents a dynamic simulation, rather than a reductionist and fixed way of reasoning. Hence, mathematical modeling entails flexibility in employing the pertinent knowledge of mathematics and keen observation as well as analysis of different phenomena and problems in life so that the optimally applicable mathematical model can be extracted. Complexity can be measured since there notably exist a number of complexity measures with complex systems possessing many degrees of freedom. Nonetheless, the mere description or measurement of complexity would not be sufficient to understand complex systems. Besides this, the property of self-organization draws profoundly from the source of qualitative innovation in complex systems. Derived from nonlinear system theory, the treatment of chaotic along with the advent and advancements of nonlinear dynamics in physics has made it interlaced with progresses made in computer technologies and the computing power for handling nonlinearity numerically. These have highlighted further evidence regarding the existence and prevalence of complex and unstable phenomena with nonlinear systems having a few degrees of freedom exhibiting structural, static, mechanic and dynamical instabilities which are concerned with implicit metaphysical and methodological convictions, rendering them highly valued owing to constituting the nomological nucleus of pattern formation, processes of growth processes, phase transitions and self-organization. Fractals as objects that infinitely replicate their shape within their structure appear the same independently regardless of their form or their magnification level. Thus, fractals can continually be magnified, containing other fractals of the same form, shape and characteristic. Across these strands, fractal analysis is resorted to for explaining complex systems manifesting self-similarity across different scales whose multiplicity structure and behavior of fractals ensure the decomposition of time series data into different levels of granularity. This merit is particularly significant in certain fields that involve quantitative trends in which the pertinent data are inclined to exhibit similar patterns regardless of the time scale. Moreover, multiple nonlinear systems demonstrate phenomena in which fluctuations are inclined to enhance synchronization and periodic behaviors of the system. In this respect, fractal-fractional and wavelet methods are among those employed as techniques for characterizing complex and dynamic patterns in various domains to be able to detect specificity, regularity, self-similarity, singularity and significant attributes, which could all designate facilitating functions. Neural networks as the simplified models of the biological nervous system are comprised of highly interconnected network of a large number of processing elements or neurons in a human brain-inspired architecture. Furthermore, machines’ ability of replicating the capacities of living systems, in particular of human intelligence is one of the most notable achievements in the context of emerging technologies. Being able to recognize objects and make decisions through many of the perceptual and cognitive abilities of live systems inspires Artificial Intelligence (AI)-based technologies whose potential could be utilized optimally in the biological world, including medical and clinical research and applications, bioengineering, biomedicine, genetics, and so forth, having facilitating functions in the early identification of the disease and its precise treatment based on personalized medicine targeted at individual patients. All these developments and opportunities signify the possibility of applying different AI-based mathematical modeling techniques and computing systems to various applications of numerous domains, considering the future of AI in the sphere of complex systems, nonlinear dynamics, singularity and chaos. Computational complexity characterizes the class of computational problems relying on their inherent difficulty and relating those classes to one another. A problem is inherently difficult if its solution requires significant resources irrespective of what algorithm is utilized. This initiation is formalized by computational complexity through mathematical models of computation for probing the problems and quantifying the number of resources, such as time and storage toward their solution. Levels of complexity are assigned to different collections of problems, so an understanding of the theoretical framework entails a substantial background and expertise in theoretical computer science considering the intriguing conjectures about such levels of complexity. Complexity science and systems science point toward bridging the gap between micro-level analysis and holistic perspectives, providing the means required for investigating interconnected, nonlinear and adaptive phenomena. Within such systems, fractals and wavelet methods are employed for identifying self-similar patterns, singularities and regularities that stem from otherwise irregular data. Consequently, the theoretical reflections on how all these processes are modeled, merging all together the advanced mathematical modeling, methods, optimization, analyses, computational and emerging technologies are addressed in our special issue which elaborates on and showcases the implications of solution-oriented applicable approaches in real-world systems and other related domains. Thus, our special issue aims at extrapolating new mathematical theoretical directions in view of the sound groundwork of pure (theoretical) mathematics in conjunction with mathematical modeling, analyses and applications that could be justified from a decision-theoretic viewpoint of constructively based solution and proof procedures enhanced by exponential growth of data volume, algorithmizing, computer affordances, hardware and storage capacities in science, medicine, biology, engineering through applied sciences, and many more realms pondering on the computability of the universe.
KARACA et al. (Thu,) studied this question.