Genetically identical cells can show phenotypic variability. This is often caused by stochastic events that originate from randomness in biochemical processes involving in gene expression and other extrinsic cellular processes. From an engineering perspective, there have been efforts focused on theory and experiments to control noise levels by perturbing and replacing gene network components. H...

We investigate a conjecture of Paul Erdős, the last unsolved problem among those proposed in his landmark paper [2]. The conjecture states that there exists an absolute constant C > 0 such that, if v1, . . . , vn are unit vectors in a Hilbert space, then at least C 2 n of all ∈ {−1, 1} are such that | Pn i=1 ivi |≤ 1. We disprove the conjecture. For Hilbert spaces of dimension d > 2, the counte...

StyleGAN2 was demonstrated to be a powerful image generation engine that supports semantic editing. However, in order manipulate real-world image, one first needs able retrieve its corresponding latent representation StyleGAN’s space is decoded an as close possible the desired image. For many images, does not exist, which necessitates tuning of generator network. We present per-image optimizati...