Michael C. Haslam

Ikjyot Singh Kohli, Michael C. Haslam

The future asymptotic behaviour of a non-titled Bianchi Type IV viscous fluid model is analyzed. In particular, we consider the case of a viscous fluid without heat conduction, and constant expansion-normalized bulk and shear viscosity coefficients. We show using dynamical systems theory that the only future attracting equilibrium points are the flat Friedmann-LeMaitre (FL) solution, the open FL solution and the isotropic Milne universe solution. We also show the bifurcations exist with respect to an increasing expansion-normalized bulk viscosity coefficient. It is finally shown through an extensive numerical analysis, that the dynamical system isotropizes at late times.

Ikjyot Singh Kohli, Michael C. Haslam

In this paper, we explore the possibility of deriving a quantum wavefunction for continuous-time recurrent neural network (CTRNN). We did this by first starting with a two-dimensional dynamical system that describes the classical dynamics of a continuous-time recurrent neural network, and then deriving a Hamiltonian. After this, we quantized this Hamiltonian on a Hilbert space $\mathbb{H} = L^2(\mathbb{R})$ using Weyl quantization. We then solved the Schrodinger equation which gave us the wavefunction in terms of Kummer's confluent hypergeometric function corresponding to the neural network structure. Upon applying spatial boundary conditions at infinity, we were able to derive conditions/restrictions on the weights and hyperparameters of the neural network, which could potentially give insights on the the nature of finding optimal weights of said neural networks.