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Complex systems, as interwoven miscellaneous interacting entities that emerge and evolve through self-organization in a myriad of spiraling contexts, exhibit subtleties on global scale besides steering the way to understand complexity which has been under evolutionary processes with unfolding cumulative nature wherein order is viewed as the unifying framework. Indicating the striking feature of non-separability in components, a complex system cannot be understood in terms of the individual isolated constituents’ properties per se, it can rather be comprehended as a way to multilevel approach systems behavior with systems whose emergent behavior and pattern transcend the characteristics of ubiquitous units composing the system itself. This observation specifies a change of scientific paradigm, presenting that a reductionist perspective does not by any means imply a constructionist view; and in that vein, complex systems science, associated with multiscale problems, is regarded as ascendancy of emergence over reductionism and level of mechanistic insight evolving into complex system. While evolvability being related to the species and humans owing their existence to their ancestors’ capability with regards to adapting, emerging and evolving besides the relation between complexity of models, designs, visualization and optimality, a horizon that can take into account the subtleties making their own means of solutions applicable is to be entailed by complexity. Such views attach their germane importance to the future science of complexity which may probably be best regarded as a minimal history congruent with observable variations, namely the most parallelizable or symmetric process which can turn random inputs into regular outputs. Interestingly enough, chaos and nonlinear systems come into this picture as cousins of complexity which with tons of its components are involved in a hectic interaction with one another in a nonlinear fashion amongst the other related systems and fields. Relation, in mathematics, is a way of connecting two or more things, which is to say numbers, sets or other mathematical objects, and it is a relation that describes the way the things are interrelated to facilitate making sense of complex mathematical systems. Accordingly, mathematical modeling and scientific computing are proven principal tools toward the solution of problems arising in complex systems’ exploration with sound, stimulating and innovative aspects attributed to data science as a tailored-made discipline to enable making sense out of voluminous (-big) data. Regarding the computation of the complexity of any mathematical model, conducting the analyses over the run time is related to the sort of data determined and employed along with the methods. This enables the possibility of examining the data applied in the study, which is dependent on the capacity of the computer at work. Besides these, varying capacities of the computers have impact on the results; nevertheless, the application of the method on the code step by step must be taken into consideration. In this sense, the definition of complexity evaluated over different data lends a broader applicability range with more realism and convenience since the process is dependent on concrete mathematical foundations. All of these indicate that the methods need to be investigated based on their mathematical foundation together with the methods. In that way, it can become foreseeable what level of complexity will emerge for any data desired to be employed. With relation to fractals, fractal theory and analysis are geared toward assessing the fractal characteristics of data, several methods being at stake to assign fractal dimensions to the datasets, and within that perspective, fractal analysis provides expansion of knowledge regarding the functions and structures of complex systems while acting as a potential means to evaluate the novel areas of research and to capture the roughness of objects, their nonlinearity, randomness, and so on. The idea of fractional-order integration and differentiation as well as the inverse relationship between them lends fractional calculus applications in various fields spanning across science, medicine and engineering, amongst the others. The approach of fractional calculus, within mathematics-informed frameworks employed to enable reliable comprehension into complex processes which encompass an array of temporal and spatial scales notably provides the novel applicable models through fractional-order calculus to optimization methods. Computational science and modeling, notwithstanding, are oriented toward the simulation and investigation of complex systems through the use of computers by making use of domains ranging from mathematics to physics as well as computer science. A computational model consisting of numerous variables that characterize the system under consideration allows the performing of many simulated experiments via computerized means. Furthermore, Artificial Intelligence (AI) techniques whether combined or not with fractal, fractional analysis as well as mathematical models have enabled various applications including the prediction of mechanisms ranging extensively from living organisms to other interactions across incredible spectra besides providing solutions to real-world complex problems both on local and global scale. While enabling model accuracy maximization, AI can also ensure the minimization of functions such as computational burden. Relatedly, level of complexity, often employed in computer science for decision-making and problem-solving processes, aims to evaluate the difficulty of algorithms, and by so doing, it helps to determine the number of required resources and time for task completion. Computational (-algorithmic) complexity, referring to the measure of the amount of computing resources (memory and storage) which a specific algorithm consumes when it is run, essentially signifies the complexity of an algorithm, yielding an approximate sense of the volume of computing resources and seeking to prove the input data with different values and sizes. Computational complexity, with search algorithms and solution landscapes, eventually points toward reductions vis à vis universality to explore varying degrees of problems with different ranges of predictability. Taken together, this line of sophisticated and computer-assisted proof approach can fulfill the requirements of accuracy, interpretability, predictability and reliance on mathematical sciences with the assistance of AI and machine learning being at the plinth of and at the intersection with different domains among many other related points in line with the concurrent technical analyses, computing processes, computational foundations and mathematical modeling. Consequently, as distinctive from the other ones, our special issue series provides a novel direction for stimulating, refreshing and innovative interdisciplinary, multidisciplinary and transdisciplinary understanding and research in model-based, data-driven modes to be able to obtain feasible accurate solutions, designed simulations, optimization processes, among many more. Hence, we address the theoretical reflections on how all these processes are modeled, merging all together the advanced methods, mathematical analyses, computational technologies, quantum means elaborating and exhibiting the implications of applicable approaches in real-world systems and other related domains.

This paper explains the Moire chromatography technique and the optical characteristics when the light crosses the 3D air flow field. Based on this, taking grating, CCD camera, optical filter and diaphragm as the main device, a multi-direction Moire chromatography optical system was designed. The system consists of five detective light paths, in each detective light path there is parallel and same periodic grating and filtering minipore placed on the lens' focal length plane; the grating is used to adjust the space length and angle between the two gratings, and the filtering minipore is used to remove the unorderly high frequency intermix in the Moire fringe. Utilizing the computer escalator method to convert the tested value, the vivid interference fringe of tested parameter can be obtained. The application of this system in precision measurement and medicine is also analyzed and discussed.

Based on the comprehensive observation of medicine, we made a diachronic summarization and synchronic comparison on medicine, including traditional medicine and modern medicine as well as Chinese traditional medicine (CTM) and Western traditional medicine. We focused on the connotation of several predominant medicines, the evolution of medical civilization, the problems and challenges of medicine at present, the prospect and framework of medicine in the future, and finally put forward the new system of CTM together with the integration of traditional medicine and modern medicine so as to contribute to the thinking, research and construction of medicine for mankind, which will add to its positive development and scientific practice.

On 25 October 2018, National Essential Medicine List (NEML) of China was formally published by National Health Commission and it has been executed since 1 November. The new NEML, which includes 685 drugs with more than 1110 kinds of dosage forms and more than 1810 kinds of specifications, further standardizes dosage forms and specifications of drugs. The new catalog not only increases the number of categories, but also optimizes the structure of the drug list. It highlights the need for basic drugs in aspects of common diseases, chronic diseases, serious diseases and public health. Besides, the normalization of dosage forms and specifications, and the persistence of emphasizing the combination of Western and Chinese medicine are both the characteristics of it. This news report is composed of several parts including brief introduction of NEML, the difference between NEML and National Directory of Health Insurance (NDHI) which is likely to be confused with NEML, the dissection of the change of medicine varieties, relevant policies and potential issues of NEML. We intend to give a comprehensive interpretation of NEML from different perspectives.

The rapid advancement of artificial intelligence and machine learning (AI/ML) technologies in healthcare presents significant opportunities for enhancing patient care through innovative diagnostic tools, monitoring systems, and personalized treatment plans. However, these innovative advancements might result in regulatory challenges given recent Supreme Court decisions that impact the authority of regulatory agencies like the Food and Drug Administration (FDA). This paper explores the implications of regulatory uncertainty for the healthcare industry related to balancing innovation in biotechnology and biocomputing with ensuring regulatory uniformity and patient safety. We examine key Supreme Court cases, including Loper Bright Enterprises v. Raimondo, Relentless, Inc. v. Department of Commerce, and Corner Post, Inc. v. Board of Governors of the Federal Reserve System, and their impact on the Chevron doctrine. We also discuss other relevant cases to highlight shifts in judicial approaches to agency deference and regulatory authority that might affect how science is handled in regulatory spaces, including how biocomputing and other health sciences are governed, how scientific facts are applied in policymaking, and how scientific expertise guides decision making. Through a detailed analysis, we assess the potential impact of regulatory uncertainty in healthcare. Additionally, we provide recommendations for the medical community on navigating these challenges.