Presenting a Mathematical Programming Model for Discovering Eulerian Paths (EP) in Certain Specific Graphs

In the modern era, graph theory is considered a useful tool for quantification and simplification of various dynamic components in complex systems. By representing elements as nodes and their connections as edges, graph theory can transform anything from urban planning to computer data into a meaningful mathematical language. Nowadays, numerous practical applications have been designed and developed based on graph theory. Graph theory is a branch of discrete mathematics that aims to describe and solve problems with discrete structures using points and edges. One of the problems concerning graphs is the Eulerian path problem. This research demonstrates that this problem can also be investigated from the perspective of Operations Research (OR). In a more general sense, the Eulerian path problem is a routing problem. This paper presents a pure mathematical model to describe the relationship between the variables of the Eulerian path problem. One of the features of the proposed mathematical model is its solvability by most optimization software. Finally, several numerical examples are provided to enhance the understanding of this model, and they are solved using the proposed approach. All the analyses in this research are conducted using one of the most advanced optimization software, MATLAB. The proposed mathematical model provides a systematic and efficient approach to discover Eulerian paths in specific graphs, contributing to the advancement of graph theory and its practical applications

Cutting-Edge Progress in Stimuli-Responsive Bioadhesives: From Synthesis to Clinical Applications

With the advent of “intelligent” materials, the design of smart bioadhesives responding to chemical, physical, or biological stimuli has been widely developed in biomedical applications to minimize the risk of wounds reopening, chronic pain, and inflammation. Intelligent bioadhesives are free-flowing liquid solutions passing through a phase shift in the physiological environment due to stimuli such as light, temperature, pH, and electric field. They possess great merits, such as ease to access and the ability to sustained release as well as the spatial transfer of a biomolecule with reduced side effects. Tissue engineering, wound healing, drug delivery, regenerative biomedicine, cancer therapy, and other fields have benefited from smart bioadhesives. Recently, many disciplinary attempts have been performed to promote the functionality of smart bioadhesives and discover innovative compositions. However, according to our knowledge, the development of multifunctional bioadhesives for various biomedical applications has not been adequately explored. This review aims to summarize the most recent cutting-edge strategies (years 2015–2021) developed for stimuli-sensitive bioadhesives responding to external stimuli. We first focus on five primary categories of stimuli-responsive bioadhesive systems (pH, thermal, light, electric field, and biomolecules), their properties, and limitations. Following the introduction of principal criteria for smart bioadhesives, their performances are discussed, and certain smart polymeric materials employed in their creation in 2015 are studied. Finally, advantages, disadvantages, and future directions regarding smart bioadhesives for biomedical applications are surveyed