The entropy models have been recently adopted in many studies to evaluate the distribution of the shear stress in circular channels. However, the uncertainty in their predictions and their reliability remains an open question. We present a novel method to evaluate the uncertainty of four popular entropy models, including Shannon, Shannon-Power Low (PL), Tsallis, and Renyi, in shear stress estimation in circular channels. The Bayesian Monte-Carlo (BMC) uncertainty method is simplified considering a 95% Confidence Bound (CB). We developed a new statistic index called as FREE_opt-based OCB (FOCB) using the statistical indices Forecasting Range of Error Estimation (FREE) and the percentage of observed data in the CB (N_in), which integrates their combined effect. The Shannon and Shannon PL entropies had close values of the FOCB equal to 8.781 and 9.808, respectively, had the highest certainty in the calculation of shear stress values in circular channels followed by traditional uniform flow shear stress and Tsallis models with close values of 14.491 and 14.895, respectively. However, Renyi entropy with much higher values of FOCB equal to 57.726 has less certainty in the estimation of shear stress than other models. Using the presented results in this study, the amount of confidence in entropy methods in the calculation of shear stress to design and implement different types of open channels and their stability is determined.

The aim of this paper is to investigate whether multifractal analysis can be applied to study choroidal blood vessels and help ophthalmologists for the early diagnosis of retinitis pigmentosa (RP). In a case study, we use Spectral Domain Optical Coherence Tomography (SDOCT), which is a non-invasive and highly sensitive imaging technique of the retina and choroid. The image of a choroidal branching pattern can be regarded as a multifractal. Therefore, we calculate generalized Renyi point-centered dimensions, which is considered a measure of inhomogeneity of data, to prove that it increases in the patients with RP with respect to the control group.

This proposal advocates using energy states as fundamental units for quantum computer programming. Each programming unit is conceptualized as an energy state, manifested as an essence-unit. The essence-unit, defined as the minimal form encapsulating complete uniqueness or specificity, serves as the cornerstone of this paradigm. This approach allows recording various forms of matter on quantum computers in essence-units representing their energy states. Recording energy states is achieved through the creation of four distinct coherent potentials facilitated by quantum dots or crystals. It is crucial to note that these energy states, embodied in essence-units, cannot be subdivided. The study examines the intricate relationship between similarity, fractals, and uniqueness in quantum dot operations, elucidating their profound implications for information transfer efficiency. Normalized entropy quantifies the charge localization in quantum dot impurities in systems exhibiting distortions. Utilizing N-level recording and entropy-fractal dimension equivalence enables this paper to elucidate the potential of quantum dots in reducing transmission time and modeling complex systems. The proposed methodology represents a significant departure from the current state of quantum computing, offering unprecedented potential for overcoming previously intractable challenges.