Transition to anomalous dynamics in a simple random map.

The famous doubling map (or dyadic transformation) is perhaps the simplest deterministic dynamical system exhibiting chaotic dynamics. It is a piecewise linear time-discrete map on the unit interval with a uniform slope larger than one, hence expanding, with a positive Lyapunov exponent and a uniform invariant density. If the slope is less than one, the map becomes contracting, the Lyapunov exponent is negative, and the density trivially collapses onto a fixed point.

PUF60-activated exons uncover altered 3' splice-site selection by germline missense mutations in a single RRM.

PUF60 is a splicing factor that binds uridine (U)-rich tracts and facilitates association of the U2 small nuclear ribonucleoprotein with primary transcripts. PUF60 deficiency (PD) causes a developmental delay coupled with intellectual disability and spinal, cardiac, ocular and renal defects, but PD pathogenesis is not understood. Using RNA-Seq, we identify human PUF60-regulated exons and show that PUF60 preferentially acts as their activator.

Gene expression dynamics with stochastic bursts: Construction and exact results for a coarse-grained model.

We present a theoretical framework to analyze the dynamics of gene expression with stochastic bursts. Beginning with an individual-based model which fully accounts for the messenger RNA (mRNA) and protein populations, we propose an expansion of the master equation for the joint process. The resulting coarse-grained model reduces the dimensionality of the system, describing only the protein population while fully accounting for the effects of discrete and fluctuating mRNA population.

Origin of the exponential decay of the Loschmidt echo in integrable systems.

We address the time decay of the Loschmidt echo, measuring the sensitivity of quantum dynamics to small Hamiltonian perturbations, in one-dimensional integrable systems. Using a semiclassical analysis, we show that the Loschmidt echo may exhibit a well-pronounced regime of exponential decay, similar to the one typically observed in quantum systems whose dynamics is chaotic in the classical limit. We derive an explicit formula for the exponential decay rate in terms of the spectral properties of the unperturbed and perturbed Hamilton operators and the initial state.

Large-scale chaos and fluctuations in active nematics.

We show that dry active nematics, e.g., collections of shaken elongated granular particles, exhibit large-scale spatiotemporal chaos made of interacting dense, ordered, bandlike structures in a parameter region including the linear onset of nematic order.

Endemic infections are always possible on regular networks.

We study the dependence of the largest component in regular networks on the clustering coefficient, showing that its size changes smoothly without undergoing a phase transition. We explain this behavior via an analytical approach based on the network structure, and provide an exact equation describing the numerical results. Our work indicates that intrinsic structural properties always allow the spread of epidemics on regular networks.