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Allometric relations between two observables are a widespread phenomenon in biology. The volume of nuclei, for example, has frequently been reported to scale linearly with cell volume, V_{N}∼V_{C}, but conflicting, sublinear power-law correlations have also been found. Given that nuclei are vital organelles that harbor and maintain the DNA of cells, an understanding of allometric nuclear volumes that ultimately define the concentration and accessibility of chromatin is of great interest. Using the model organism Caenorhabditis elegans, we show here that the allometry of nuclei is a dynamically adapting phenomenon; i.e., we find V_{N}∼V_{C}^{α} with a time-dependent scaling exponent α (“dynamic allometry”). This finding is due to relaxation growth of nuclear volumes at a rate that scales with cell size. If cell division stops the relaxation of nuclei in a premature stage, α

Anomalous diffusion or, more generally, anomalous transport, with nonlinear dependence of the mean-squared displacement on the measurement time, is ubiquitous in nature. It has been observed in processes ranging from microscopic movement of molecules to macroscopic, large-scale paths of migrating birds. Using data from multiple empirical systems, spanning 12 orders of magnitude in length and 8 orders of magnitude in time, we employ a method to detect the individual underlying origins of anomalous diffusion and transport in the data. This method decomposes anomalous transport into three primary effects: long-range correlations (“Joseph effect”), fat-tailed probability density of increments (“Noah effect”), and nonstationarity (“Moses effect”). We show that such a decomposition of real-life data allows us to infer nontrivial behavioral predictions and to resolve open questions in the fields of single-particle tracking in living cells and movement ecology.

Quantum technologies that rely on photonic qubits require a precise controllability of their properties. For this purpose hybrid approaches are particularly attractive because they offer a large flexibility to address different aspects of the photonic degrees of freedom. When combining photonics with other quantum platforms like phonons, quantum transducers have to be realized that convert between the mechanical and optical domain. Here, we realize this interface between phonons in the form of surface acoustic waves (SAWs) and single photons, mediated by a single semiconductor quantum dot exciton. In this combined theoretical and experimental study, we show that the different sidebands exhibit characteristic blinking dynamics that can be controlled by detuning the laser from the exciton transition. By developing analytical approximations we gain a better understanding of the involved internal dynamics. Our specific SAW approach allows us to reach the ideal frequency range of around 1 GHz that enables simultaneous temporal and spectral phonon sideband resolution close to the combined fundamental time-bandwidth limit.

Time-dependent processes are often analyzed using the power spectral density (PSD) calculated by taking an appropriate Fourier transform of individual trajectories and finding the associated ensemble average. Frequently, the available experimental datasets are too small for such ensemble averages, and hence, it is of a great conceptual and practical importance to understand to which extent relevant information can be gained from S(f,T), the PSD of a single trajectory. Here we focus on the behavior of this random, realization-dependent variable parametrized by frequency f and observation time T, for a broad family of anomalous diffusions—fractional Brownian motion with Hurst index H—and derive exactly its probability density function. We show that S(f,T) is proportional—up to a random numerical factor whose universal distribution we determine—to the ensemble-averaged PSD. For subdiffusion (H1/2) S(f,T)∼BT^{2H-1}/f^{2} with random amplitude B. Remarkably, for H>1/2 the PSD exhibits the same frequency dependence as Brownian motion, a deceptive property that may lead to false conclusions when interpreting experimental data. Notably, for H>1/2 the PSD is ageing and is dependent on T. Our predictions for both sub- and superdiffusion are confirmed by experiments in live cells and in agarose hydrogels and by extensive simulations.