At Neuromitosis.com, we explore the intricate mathematical relationships between neural networks and cellular division. Our research utilizes advanced mathematical modeling to bridge the gap between artificial intelligence and biological processes.
The sigmoid function, commonly used in neural networks, is defined as:
This function's derivative, crucial for backpropagation, is given by:
The progression of the cell cycle can be modeled using ordinary differential equations. A simplified model of cyclin concentration over time might look like:
Where C is cyclin concentration, t is time, k1 is the synthesis rate, k2 is the degradation rate, k3 is the APC-mediated degradation rate, and [APC] is the concentration of the anaphase-promoting complex.
Inspired by cellular division rates, we propose a novel adaptive learning rate for neural networks:
Where η(t) is the learning rate at time t, η0 is the initial learning rate, λ is the decay rate, and α and ω control the amplitude and frequency of oscillations, mimicking the cyclical nature of cell division.
We explore the fractal nature of neural networks using the box-counting dimension:
Where D is the fractal dimension, ε is the size of the box, and N(ε) is the number of boxes needed to cover the network structure.
Dive deeper into our mathematical models and simulations:
Join our interdisciplinary team of mathematicians, computer scientists, and biologists in advancing the field of neuromitosis: