Wireless communication systems with many antennas and users naturally give rise to large random channel matrices. In one-bit precoding, the transmitted signal is restricted to binary values and is designed using the channel matrix. It is then multiplied by the same channel matrix during transmission. This dependence, together with the entrywise sign nonlinearity, makes the performance difficult to characterize. Focusing on the standard i.i.d. Gaussian channel model, this talk studies the large-system behaviors of two classes of one-bit precoding schemes. For linear-quantized precoding, we use a recursive representation of Haar matrices, known as Householder Dice, to construct an asymptotic scalar signal-plus-independent-Gaussian-noise model.  We next consider nonlinear symbol-level precoding, focusing on a scheme based on convex relaxation followed by one-bit quantization. Using approximate message passing and state evolution, we characterize the limiting empirical laws of the relaxed solution and of the received signal–symbol pairs. These results provide explicit performance predictions and guidance for precoder design.

Cell proliferation has been widely studied across experimental systems and mathematical modelling frameworks, from early embryonic development to regenerating tissues. A characteristic feature of early embryonic development is that initially synchronous cell populations progressively lose synchrony after a species-specific number of divisions. Here, we use an age-dependent branching process to determine how variability in cell-cycle duration controls the persistence of synchrony. We derive analytical expressions for the mean and variance of cell number and show how they identify the underlying generation-time distribution. For gamma-distributed generation times, this establishes a direct relationship between cell-cycle variability and the number of synchronous divisions. We use these results to infer generation-time statistics from population-level cell counts and investigate how systematic changes in cell-cycle duration can bias inference under a stationary model. Our results provide a quantitative framework linking the precision of individual cell-cycle clocks to observable population-level dynamics.