Mathematical sciences with inherent sui generis vitality serve as the foundation across interdisciplinary studies with a complex connection that represents a mode of thought which relies on abstraction, maintaining accuracy as well as precision by means of explicit calculation aside from external effectiveness as well as internal abstractness. In this regard, what is signified by mathematical modeling is a process by which real world situations and relations are expressed through equations enabling the understanding of the problem.
Complexity theory besides complexity forms a connection that crosses over the quantitative and qualitative facets of real life, ensuring a comprehensive contemplation process regarding diverse systems from as cells to human beings, ecosystems to organizations. Traditional scientific methods can help with partial comprehension per se, and with these considerations, it can be noted that complexity reflects the disentangling of nonlinear, adaptive, evolutionary, emergent, complex, dynamic, complicated, systems, and many more. Furthermore, complexity facilitates the observation of problems from the lenses of multiple viewpoints by examining both the micro and macro issues and understanding how they are interdependent. Complexity science with these aspects combines the two solitudes of both the analysis of the parts and holistic analysis ranging across varying from human genome to evolutionary biology across the spectra of natural and human systems. As for the patterns in complex systems, systems that have multiple components manifest a spontaneous form of organization into macroscopic structures with simple rules bringing about unpredictable behaviors. Thus, complexity science pursues the discovery of underlying rules and laws, theoretical components of emergence with an orientation to employ them with applications. In that way, different sorts of worlds, namely physical, biological and social, can be comprehended across the pedestal of emergence of chaos and order as the characteristic properties of natural systems besides the systems that are designed. The theories of complex systems besides these points provide the ideas indicative of how intractable the world is when it is considered that even the very simple phenomenon constitutes enormous and even incalculable complexity.
As a consequence, many applications of science have transformed into cases and experiments with multi methods resting upon evolving knowledge in time and over time.
The mathematics of data, by encompassing a multifaceted blend of mathematical techniques and models, is pivotal for tackling voluminous datasets and extracting significant insights from them. Complexity viewpoints span across process complexity, tooling complexity, social complexity and system complexity so in order to meet customization demands, there can be multiple instances and variants of a base system. With these in mind, complexity viewpoints compile and generalize the essential objects of the design context where the objects essentially answer the framework’s question of “who causes complexity?”. Furthermore, by designating a viewpoint to each of the identified objects, they can be used as dimensions to structure the complexity characterization. While proposing solutions to complexity, methodology and lessons derived from case studies could be of benefit. As for measure, the provision of qualitative or quantitative means to measure the system’s complexity could be resorted to, while characterization entails the types of complexity along with its subtle details regarding the causes, effects, elements and other relevant aspects [Morales, G., et al. (2023)]. Considering these points, solution-oriented vision minding the peculiar needs of the systems becomes of critical importance in attaining applicable and optimal outcomes in different branches of science. Computation of the complexity of a particular mathematical model requires the carrying out of the analyses over the run time, which is concerned with and based on the type of data (big data) identified, determined and employed along with the methods. While providing the tools required to navigate through the complexities of data, Artificial Intelligence (AI) as well as data analysis rely on foundational mathematical concepts, which can pave the way for novice perspectives, solutions to challenges and directions for the future elements to arise. Such an interplay emerging on dynamic scales can highlight mutually enriching association between mathematics and data in the ever-evolving digitizing landscape and ecology science, computer science, informatics, medicine, biology, applied sciences, engineering, bioengineering, and so forth, towards the integration, analysis, processing of models and data-centric prediction-based domains to name some.
To these ends, the aim could be towards the unification and implementation of the diverse and evolving approaches to complexity theory, mathematical sciences and applied complexity science for providing a key into understanding the current and conceivable complex problems so that mathematical frameworks can serve as the plinth to understand the role of AI, machine learning, differential equations, mathematical modelling, and so forth considering the future science of complexity.
In accordance with these scopes, the following themes along with the relevant ones can be addressed with a focus on mathematical, numerical, computational modeling aspects, among other corresponding realms. You may visit...
Seminars
Articles
Contact