Constructing exact representations of quantum many-body systems with deep neural networks

We develop a constructive approach to generate artificial neural networks representing the exact ground states of a large class of many-body lattice Hamiltonians. It is based on the deep Boltzmann machine architecture, in which two layers of hidden neurons mediate quantum correlations among physical degrees of freedom in the visible layer. The approach reproduces the exact imaginary-time Hamiltonian evolution, and is completely deterministic. In turn, compact and exact network representations for the ground states are obtained without stochastic optimization of the network parameters. The number of neurons grows linearly with the system size and total imaginary time, respectively. Physical quantities can be measured by sampling configurations of both physical and neuron degrees of freedom. We provide specific examples for the transverse-field Ising and Heisenberg models by implementing efficient sampling. As a compact, classical representation for many-body quantum systems, our approach is an alternative to the standard path integral, and it is potentially useful also to systematically improve on numerical approaches based on the restricted Boltzmann machine architecture

Asynchronous Rhythm of Steroidogenic Factor 1 and Period Homolog 2 mRNA Expression in Mouse Y1 Adrenocorticol Tumor Cells

The relationship between the expression of Steroidogenic factor 1 (Sf1) and the circadian-related gene, period homolog 2 (Per2), in the adrenal cortex is still unknown. We show here that in Y1 adrenocortical tumor cells, expression of steroidogenic-related genes such as P450scc mRNA and Sf1 mRNA were asynchronous with Per2 mRNA. SF1 promoter analyses showed that the E-box element functions in a rhythmic pattern. Rhythmic expression of Upstream factor 1 mRNA, correlated well with Sf1 mRNA expression. We propose that tumorigenesis of adrenocortical lesions cause disruption of synchronous expression of steroidogenic-related and circadian-related genes