Comparative Performance of Autoencoders and Traditional Machine Learning Algorithms in Clinical Data Analysis for Predicting Post-Staged GKRS Tumor Dynamics.

Accurate prediction of tumor dynamics following Gamma Knife radiosurgery (GKRS) is critical for optimizing treatment strategies for patients with brain metastases (BMs). Traditional machine learning (ML) algorithms have been widely used for this purpose; however, recent advancements in deep learning, such as autoencoders, offer the potential to enhance predictive accuracy. This study aims to evaluate the efficacy of autoencoders compared to traditional ML models in predicting tumor progression or regression after GKRS.

A Holographic-Type Model in the Description of Polymer-Drug Delivery Processes.

A unitary model of drug release dynamics is proposed, assuming that the polymer-drug system can be assimilated into a multifractal mathematical object. Then, we made a description of drug release dynamics that implies, via Scale Relativity Theory, the functionality of continuous and undifferentiable curves (fractal or multifractal curves), possibly leading to holographic-like behaviors. At such a conjuncture, the Schrödinger and Madelung multifractal scenarios become compatible: in the Schrödinger multifractal scenario, various modes of drug release can be "mimicked" (via period doubling, damped oscillations, modulated and "chaotic" regimes), while the Madelung multifractal scenario involves multifractal diffusion laws (Fickian and non-Fickian diffusions).

Towards Multifractality through an Ernst-Type Potential in Complex Systems Dynamics.

Some possible correspondences between the Scale Relativity Theory and the Space-Time Theory can be established. Since both the multifractal Schrödinger equation from the Scale Relativity Theory and the General Relativity equations for a gravitational field with axial symmetry accept the same SL(2R)-type invariance, an Ernst-type potential (from General Relativity) and also a multi-fractal tensor (from Scale Relativity) are highlighted in the description of complex systems dynamics. In this way, a non-differentiable description of complex systems dynamics can become functional, even in the case of standard theories (General Relativity and Quantum Mechanics).

Coherences in the Dynamics of Physical Systems from a Multifractal Perspective of Motion.

Using an analogy between the multi-fractal Schrödinger equation and the dumped oscillator equation through a special ansatz, Stoler-type coherences in the dynamics of physical systems are highlighted. Such a result implies a Ricatti-type gauge, a process that can be considered a calibration of the difference between the kinetic and potential energy of a Lagrangian, specified as a perfect square in generic coordinates.