Rényi entanglement entropy of a spin chain with generative neural networks.

We describe a method to estimate Rényi entanglement entropy of a spin system which is based on the replica trick and generative neural networks with explicit probability estimation. It can be extended to any spin system or lattice field theory. We demonstrate our method on a one-dimensional quantum Ising spin chain.

pSTAT3 Expression is Increased in Advanced Prostate Cancer in Post-Initiation of Androgen Deprivation Therapy.

Background: The transcription factor Signal Transducer and Activator of Transcription 3 (STAT3) plays a role in carcinogenesis and is involved in processes, such as proliferation, differentiation, drug resistance and immunosuppression. STAT3 can be activated by phosphorylation of tyrosine at position 705 (pSTAT3) or serine at 727 (pSTAT3). High expression levels of pSTAT3 are implicated in advanced stages of prostate cancer (PCa) and are known to interact with the androgen receptor signaling pathway.

A Recipe for Successful Metastasis: Transition and Migratory Modes of Ovarian Cancer Cells.

One of the characteristic features of ovarian cancer is its early dissemination. Metastasis and the invasiveness of ovarian cancer are strongly dependent on the phenotypical and molecular determinants of cancer cells. Invasive cancer cells, circulating tumor cells, and cancer stem cells, which are responsible for the metastatic process, may all undergo different modes of transition, giving rise to mesenchymal, amoeboid, and redifferentiated epithelial cells.

Random allocation models in the thermodynamic limit.

We discuss the phase transition and critical exponents in the random allocation model (urn model) for different statistical ensembles. We provide a unified presentation of the statistical properties of the model in the thermodynamic limit, uncover relationships between the thermodynamic potentials, and fill some lacunae in previous results on the singularities of these potentials at the critical point and behavior in the thermodynamic limit. The presentation is intended to be self-contained, so we carefully derive all formulas step by step throughout.

Rényi entropy of zeta urns.

We calculate analytically the Rényi entropy for the zeta-urn model with a Gibbs measure definition of the microstate probabilities. This allows us to obtain the singularities in the Rényi entropy from those of the thermodynamic potential, which is directly related to the free-energy density of the model. We enumerate the various possible behaviors of the Rényi entropy and its singularities, which depend on both the value of the power law in the zeta urn and the order of the Rényi entropy under consideration.