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The use of Digital Twins (DTs) or the digital replicas of physical entities has provided benefits to several industry sectors, most notably manufacturing. To date, the application of DTs in the healthcare sector has been minimal, however. But, as pressure increases for more precise and personalized treatments, it behooves us to investigate the potential for DTs in the healthcare context. As a proof-of-concept demonstration prior to working with real patients, we attempt in this paper, to explore the potential for creating and using DTs. We do this in a synthetic environment at this stage, making use of data that is all computer-generated. DTs of synthetic present patients are created making use of data of synthetic past patients. In the real world, the clinical objective for creating such DTs of real patients would be to enable enhanced real-time clinical decision support to enable more precise and personalized care. The objective of the numerical experiment reported in this paper, is to envisage the possibilities and challenges of such an approach. We attempt to better understand the strengths and weaknesses of applying DTs in the healthcare context to support more precise and personalized treatments. [ABSTRACT FROM AUTHOR]

In the current scenario Programming in Python plays a vital role in research arena as it preserves much of the man power. Converting the research work into the format of coding helps any researcher across the globe as it serves as a ready reckoner. Topology is one of the main branches of Mathematics. A Polish Mathematician named Kazimierz Kuratowski defined essential axioms in Topology with the aid of a closure operator named after him. In this paper, we have developed a Python program to find the closure and interior for the subsets of the given set. We will be using dictionary in Python with each subset as the key and the respective closure as its value. Subsequently we will be finding int(cl(A)), cl(int(A)), int(cl(int(A))), cl(int(cl(A))), for any subset A of the given set. [ABSTRACT FROM AUTHOR]

The development of mathematics stands as one of the most important achievements of humanity, and the development of the calculus, both the differential calculus and integral calculus is one of the most important achievements in mathematics. Differential calculus is about finding the slope of a tangent to the graph of a function, or equivalently, differential calculus is about finding the rate of change of one quantity with respect to another quantity. On the other hand, integration is an important concept in mathematics and, together with its inverse, differentiation, is one of the two main operations in calculus. Integrals and derivatives became the basic tools of calculus, with numerous applications in science and engineering. Category theory is a mathematical approach to the study of alge-braic structure that has become an important tool in theoretical computing science, particularly for semantics-based research. The notion of a limit in category theory generalizes various types of universal constructions that occur in diverse areas of mathematics. In our paper we show how to represent some parts of infinitesimal calculus in categorical structures. [ABSTRACT FROM AUTHOR]