The mathematical structure of some natural phenomena of nonlinear physical and engineering systems can be described by a combination of fuzzy differential equations that often behave in a way that cannot be fully understood. In this work, an accurate numeric-analytic algorithm is proposed, based upon the use of the residual power series, to investigate the fuzzy approximate solution for a nonlinear fuzzy Duffing oscillator, along with suitable uncertain guesses under strongly generalized differentiability. The proposed approach optimizes the approximate solution by minimizing a residual function to generate r-level representation with a rapidly convergent series solution. The influence, capacity, and feasibility of the method are verified by testing some applications. Level effects of the parameter r are given graphically and quantitatively, showing good agreement between the fuzzy approximate solutions of upper and lower bounds, that together form an almost symmetric triangular structure, that can be determined by central symmetry at r = 1 in a convex region. At this point, the fuzzy number is a convex fuzzy subset of the real line, with a normalized membership function. If this membership function is symmetric, the triangular fuzzy number is called the symmetric triangular fuzzy number. Symmetrical fuzzy estimates of solutions curves indicate a sense of harmony and compatibility around the parameter r = 1. The results are compared numerically with the crisp solutions and those obtained by other existing methods, which illustrate that the suggested method is a convenient and remarkably powerful tool in solving numerous issues arising in physics and engineering.

Medical imaging is gaining significant attention in healthcare, including breast cancer. Breast cancer is the most common cancer-related death among women worldwide. Currently, histopathology image analysis is the clinical gold standard in cancer diagnosis. However, the manual process of microscopic examination involves laborious work and can be misleading due to human error. Therefore, this study explored the research status and development trends of deep learning on breast cancer image classification using bibliometric analysis. Relevant works of literature were obtained from the Scopus database between 2014 and 2021. The VOSviewer and Bibliometrix tools were used for analysis through various visualization forms. This study is concerned with the annual publication trends, co-authorship networks among countries, authors, and scientific journals. The co-occurrence network of the authors’ keywords was analyzed for potential future directions of the field. Authors started to contribute to publications in 2016, and the research domain has maintained its growth rate since. The United States and China have strong research collaboration strengths. Only a few studies use bibliometric analysis in this research area. This study provides a recent review on this fast-growing field to highlight status and trends using scientific visualization. It is hoped that the findings will assist researchers in identifying and exploring the potential emerging areas in the related field.

Numerical simulation of physical issues is often performed by nonlinear modeling, which typically involves solving a set of concurrent fractional differential equations through effective approximate methods. In this paper, an analytic-numeric simulation technique, called residual power series (RPS), is proposed in obtaining the numerical solution a class of fractional Bagley–Torvik problems (FBTP) arising in a Newtonian fluid. This approach optimizes the solutions by minimizing the residual error functions that can be directly applied to generate fractional PS with a rapidly convergent rate. The RPS description is presented in detail to approximate the solution of FBTPs by highlighting all the steps necessary to implement the algorithm in addressing some test problems. The results indicate that the RPS algorithm is reliable and suitable in solving a wide range of fractional differential equations applying in physics and engineering.

Most biological tissues grow by the synthesis of new material close to the tissue's interface, where spatial interactions can exert strong geometric influences on the local rate of growth. These geometric influences may be mechanistic or cell behavioural in nature. The control of geometry on tissue growth has been evidenced in many in vivo and in vitro experiments, including bone remodelling, wound healing, and tissue engineering scaffolds. In this paper, we propose a generalisation of a mathematical model that captures the mechanistic influence of curvature on the joint evolution of cell density and tissue shape during tissue growth. This generalisation allows us to simulate abrupt topological changes such as tissue fragmentation and tissue fusion, as well as three dimensional cases, through a level‐set‐based method. The level‐set method developed introduces another Eulerian field than the level‐set function. This additional field represents the surface density of tissue‐synthesising cells, anticipated at future locations of the interface. Numerical tests performed with this level‐set‐based method show that numerical conservation of cells is a good indicator of simulation accuracy, particularly when cusps develop in the tissue's interface. We apply this new model to several situations of curvature‐controlled tissue evolutions that include fragmentation and fusion.