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Showing posts with the label Dynamic Infinity Mapping Framework (DIMF)

Dynamic Infinity Mapping Framework (DIMF): An Adaptive Oncology Dosing Reinforcement Learning Approach

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Dynamic Infinity Mapping Framework (DIMF): An Adaptive Oncology Dosing Reinforcement Learning Approach Author- Shrishti Rastogi Abstract Dynamic Infinity Mapping Framework (DIMF) is a new computational paradigm to manage the stochastic evolution of subpopulations of cancer cells under therapeutic pressure. DIMF combines Markov Decision Processes (MDP), Dynamic Graph Neural Networks (GNNs), and Reinforcement Learning (RL) to offer a powerful framework for optimising the dosage of multiple drugs adaptively. This report outlines the mathematical modelling of state transitions, algorithmic implementation of the RL agent and an empirical calibration using quantitative interaction and toxicity data from the large clinical trials. Our framework shows better ability to cross the balance line between therapeutic effect and total toxicity than static modelling methods. Introduction New challenges for modern oncology are the emergence of acquired resistan...
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Dynamic Infinity Mapping Framework (DIMF): An Adaptive Oncology Dosing Reinforcement Learning Approach

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Dynamic Infinity Mapping Framework (DIMF): An Adaptive Oncology Dosing Reinforcement Learning Approach Author- Shrishti Rastogi Abstract Dynamic Infinity Mapping Framework (DIMF) is a new computational paradigm to manage the stochastic evolution of subpopulations of cancer cells under therapeutic pressure. DIMF combines Markov Decision Processes (MDP), Dynamic Graph Neural Networks (GNNs), and Reinforcement Learning (RL) to offer a powerful framework for optimising the dosage of multiple drugs adaptively. This report outlines the mathematical modelling of state transitions, algorithmic implementation of the RL agent and an empirical calibration using quantitative interaction and toxicity data from the large clinical trials. Our framework shows better ability to cross the balance line between therapeutic effect and total toxicity than static modelling methods. Introduction New challenges for modern oncology are the emergence of acquired resistan...
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Understanding the Laplacian of 1/r and the Dirac Delta Function Mathematical Foundations & SageMath Insights

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Heuristic Computation and the Discovery of Mersenne Primes

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Heuristic Computation and the Discovery of Mersenne Primes Heuristic Computation and the Discovery of Mersenne Primes “Where Strategy Meets Infinity: The Quest for Mersenne Primes” Introduction: The Dance of Numbers and Heuristics Mersenne primes are not just numbers—they are milestones in the vast landscape of mathematics. Defined by the formula: \[ M_p = 2^p - 1 \] where \( p \) is itself prime, these giants challenge our computational limits and inspire new methods of discovery. But why are these primes so elusive? As \( p \) grows, the numbers become astronomically large, making brute-force testing impossible. This is where heuristic computation steps in—guiding us with smart, experience-driven strategies. “In the infinite sea of numbers, heuristics are our compass.” Let’s explore how heuristics and algorithms intertwine to unveil these mathematical treasures. 1. Mersenne Primes — Giants of Number Theory Definition: Numbers of the form \( M_p = 2^p - 1 \...
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Neural Network Generalization in the Over-Parameterization Regime: Mechanisms, Benefits, and Limitations

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Neural Network Generalization in the Over-Parameterization Regime: Mechanisms, Benefits, and Limitations Neural Network Generalization in the Over-Parameterization Regime: Mechanisms, Benefits, and Limitations Introduction Over the past decade, deep neural networks (DNNs) have risen to prominence across a range of machine learning applications, achieving remarkable performance in domains such as computer vision, natural language processing, and reinforcement learning. A striking and counter-intuitive feature of modern DNNs is their propensity for over-parameterization: models often contain many more parameters than training samples, far exceeding the classical regime where statistical learning theory would predict rampant overfitting and poor generalization. Yet, these highly over-parameterized models not only fit the training data perfectly but also display outstanding generalization to unseen test data—often improving as the number of paramete...
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