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The current study focuses on investigating the solutions of the mathematical model in the form of special functions. The phenomenon is described by a set of partial differential equations, which are then transformed into non-dimensional form. In order to improve the rheology of the Casson fluid, a fractional model is developed by using a new fractional operator Constant Proportional Caputo (CPC) approach to investigate and formulate the dynamics of Casson fluid flow and heat transfer phenomena subjected to ramped wall temperature. The fluid flow is elaborated near an infinitely vertical plate with characteristics velocity u 0 . We began by introducing appropriate variables to transform the mathematical model into non-dimensional form. Laplace transformation operator applied to gain the solution from fractional model, then obtained results expressed in the form of well-known special functions. The influence of various pertinent parameters involving in the solution was carefully examined to unveil intriguing findings. Upon comparison, we observed that the CPC approach yielded better results, after comparison with classical models documented in the literature, with graphical representations provided to illustrate these outcomes. To comprehensively analyze the dynamics of the proposed problem, physical influence of various parameters is studied and repercussions are graphically highlighted and discussed. Additionally, we derived results in a limiting sense, including Casson and viscous fluid models transitioning from the classical form to the fractionalized fluid model. [ABSTRACT FROM AUTHOR]

The primary objective of this research is to develop a mathematical model, analyze the dynamic occurrence of thermal shock and exploration of how thermal memory with moving line impact of heat transfer within biological tissues. An extended version of the Pennes equation as its foundational framework, a new fractional modelling approach called the Prabhakar fractional operator to investigate and a novel time-fractional interpretation of Fourier's law that incorporates its historical behaviour. This fractional operator has multi parameter generalized Mittag-Leffler kernel. The fractional formulation of heat flow, achieved through a generalized fractional operator with a non-singular type kernel, enables the representation of the finite propagation speed of heat waves. Furthermore, the dynamics of thermal source continually generates a linear thermal shock at predefined locations within the tissue. Introduced the appropriate set of variables to transform the governing equations into dimensionless form. Laplace transform (LT) is operated on the fractional system of equations and results are presented in series form and also expressed the solution in the form of special functions. The article derives analytical solutions for the heat transfer phenomena of both the generalized model, in the Laplace domain, and the ordinary model in the real domain, employing Laplace inverse transformation. The pertinent parameter's influence, such as α, β, γ, a0, b0, to gain insights into the impact of the thermal memory parameter on heat transfer, is brought under consideration to reveal the interesting results with graphical representations of the findings. [ABSTRACT FROM AUTHOR]

This study explores the modified Oskolkov equation, which depicts the behavior of the incompressible viscoelastic Kelvin–Voigt fluid. The primary focus of this research lies in several key areas. Firstly, the Lie symmetries of the considered equation are identified. These symmetries are utilized to transform the discussed model into an ordinary differential equation. Analytical solutions are subsequently derived using the new auxiliary equation technique. Next, a comprehensive analysis of the equation's dynamic nature is undertaken from multiple aspects. Bifurcation is carried out at fixed points within the system, and chaotic behavior is unveiled by introducing an external force to the dynamic system. Various tools, including 3D and 2D phase plots, time series, Poincaré maps, and multistability analysis, are employed to identify the chaotic nature of the system. Furthermore, the sensitivity of the model is explored across diverse initial conditions. In general, comprehending the dynamic characteristics of systems holds immense significance in forecasting outcomes and innovating new technologies. [ABSTRACT FROM AUTHOR]

The examination of new (3 + 1)-dimensional wave equations is undertaken in this study. Initially, the identification of the Lie symmetries of the model is carried out through the utilization of the Lie symmetry approach. The commutator and adjoint table of the symmetries are presented. Subsequently, the model under discussion is transformed into an ordinary differential equation using these symmetries. The construction of several bright, kink, and dark solitons for the suggested equation is then achieved through the utilization of the new auxiliary equation method. Subsequently, an analysis of the dynamical nature of the model is conducted, encompassing various angles such as bifurcation, chaos, and sensitivity. Bifurcation occurs at critical points within a dynamical system, accompanied by the application of an outward force, which unveils the emergence of chaotic phenomena. Two-dimensional plots, time plots, multistability, and Lyapunov exponents are presented to illustrate these chaotic behaviors. Furthermore, the sensitivity of the investigated model is executed utilizing the Runge–Kutta method. This analysis confirms that the stability of the solution is minimally affected by small changes in initial conditions. The attained outcomes show the effectiveness of the presented methods in evaluating solitons of multiple nonlinear models. [ABSTRACT FROM AUTHOR]

Summary Access pathways in enzymes are crucial for the passage of substrates and products of catalysed reactions. The process can be studied by computational means with variable degrees of precision. Our in-house approximative method CaverDock provides a fast and easy way to set up and run ligand binding and unbinding calculations through protein tunnels and channels. Here we introduce pyCaverDock, a Python3 API designed to improve user experience with the tool and further facilitate the ligand transport analyses. The API enables users to simplify the steps needed to use CaverDock, from automatizing setup processes to designing screening pipelines. Availability and implementation pyCaverDock API is implemented in Python 3 and is freely available with detailed documentation and practical examples at https://loschmidt.chemi.muni.cz/caverdock/. [ABSTRACT FROM AUTHOR]

Artificial intelligence (AI) is undergoing a revolution thanks to the breakthroughs of machine learning algorithms in computer vision, speech recognition, natural language processing and generative modelling. Recent works on publicly available pharmaceutical data showed that AI methods are highly promising for Drug Target prediction. However, the quality of public data might be different than that of industry data due to different labs reporting measurements, different measurement techniques, fewer samples and less diverse and specialized assays. As part of a European funded project (ExCAPE), that brought together expertise from pharmaceutical industry, machine learning, and high-performance computing, we investigated how well machine learning models obtained from public data can be transferred to internal pharmaceutical industry data. Our results show that machine learning models trained on public data can indeed maintain their predictive power to a large degree when applied to industry data. Moreover, we observed that deep learning derived machine learning models outperformed comparable models, which were trained by other machine learning algorithms, when applied to internal pharmaceutical company datasets. To our knowledge, this is the first large-scale study evaluating the potential of machine learning and especially deep learning directly at the level of industry-scale settings and moreover investigating the transferability of publicly learned target prediction models towards industrial bioactivity prediction pipelines. [ABSTRACT FROM AUTHOR]