Recurrences reveal shared causal drivers of complex time series

Many experimental time series measurements share unobserved causal drivers. Examples include genes targeted by transcription factors, ocean flows influenced by large-scale atmospheric currents, and motor circuits steered by descending neurons. Reliably inferring this unseen driving force is necessary to understand the intermittent nature of top-down control schemes in diverse biological and engineered systems. Here, we introduce a new unsupervised learning algorithm that uses recurrences in time series measurements to gradually reconstruct an unobserved driving signal. Drawing on the mathematical theory of skew-product dynamical systems, we identify recurrence events shared across response time series, which implicitly define a recurrence graph with glass-like structure. As the amount or quality of observed data improves, this recurrence graph undergoes a percolation transition manifesting as weak ergodicity breaking for random walks on the induced landscape -- revealing the shared driver's dynamics, even in the presence of strongly corrupted or noisy measurements. Across several thousand random dynamical systems, we empirically quantify the dependence of reconstruction accuracy on the rate of information transfer from a chaotic driver to the response systems, and we find that effective reconstruction proceeds through gradual approximation of the driver's dominant orbit topology. Through extensive benchmarks against classical and neural-network-based signal processing techniques, we demonstrate our method's strong ability to extract causal driving signals from diverse real-world datasets spanning ecology, genomics, fluid dynamics, and physiology.Comment: 8 pages, 5 figure

Rapid behavioral transitions produce chaotic mixing by a planktonic microswimmer

Despite their vast morphological diversity, many invertebrates have similar larval forms characterized by ciliary bands, innervated arrays of beating cilia that facilitate swimming and feeding. Hydrodynamics suggests that these bands should tightly constrain the behavioral strategies available to the larvae; however, their apparent ubiquity suggests that these bands also confer substantial adaptive advantages. Here, we use hydrodynamic techniques to investigate "blinking," an unusual behavioral phenomenon observed in many invertebrate larvae in which ciliary bands across the body rapidly change beating direction and produce transient rearrangement of the local flow field. Using a general theoretical model combined with quantitative experiments on starfish larvae, we find that the natural rhythm of larval blinking is hydrodynamically optimal for inducing strong mixing of the local fluid environment due to transient streamline crossing, thereby maximizing the larvae's overall feeding rate. Our results are consistent with previous hypotheses that filter feeding organisms may use chaotic mixing dynamics to overcome circulation constraints in viscous environments, and it suggests physical underpinnings for complex neurally-driven behaviors in early-divergent animals.Comment: 20 pages, 4 figure

Curiosity search for non-equilibrium behaviors in a dynamically learned order parameter space

Exploring the spectrum of novel behaviors a physical system can produce can be a labor-intensive task. Active learning is a collection of iterative sampling techniques developed in response to this challenge. However, these techniques often require a pre-defined metric, such as distance in a space of known order parameters, in order to guide the search for new behaviors. Order parameters are rarely known for non-equilibrium systems \textit{a priori}, especially when possible behaviors are also unknown, creating a chicken-and-egg problem. Here, we combine active and unsupervised learning for automated exploration of novel behaviors in non-equilibrium systems with unknown order parameters. We iteratively use active learning based on current order parameters to expand the library of known behaviors and then relearn order parameters based on this expanded library. We demonstrate the utility of this approach in Kuramoto models of coupled oscillators of increasing complexity. In addition to reproducing known phases, we also reveal previously unknown behavior and related order parameters

The millenium ark: How long a voyage, how many staterooms, how many passengers?

Barring holocausts, demographic forecasts suggest a “demographic winter” lasting 500–1,000 years and eliminating most habitat for wildlife in the tropics. About 2,000 species of large, terrestrial animals may have to be captively bred if they are to be saved from extinction by the mushrooming human population. Improvements in biotechnology may facilitate the task of protecting these species, but it probably will be decades at least before cryotechnology per se is a viable alternative to captive breeding for most species of endangered wildlife. We suggest that a principle goal of captive breeding be the maintenance of 90% of the genetic variation in the source (wild) population over a period of 200 years. Tables are provided that permit the estimation of the ultimate minimum size of the captive group, given knowledge of the exponential growth rate of the group, and the number of founders. In most cases, founder groups will have to be above 20 (effective) individuals.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/38475/1/1430050205_ftp.pd