288 research outputs found
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
Large statistical learning models effectively forecast diverse chaotic systems
Chaos and unpredictability are traditionally synonymous, yet recent advances
in statistical forecasting suggest that large machine learning models can
derive unexpected insight from extended observation of complex systems. Here,
we study the forecasting of chaos at scale, by performing a large-scale
comparison of 24 representative state-of-the-art multivariate forecasting
methods on a crowdsourced database of 135 distinct low-dimensional chaotic
systems. We find that large, domain-agnostic time series forecasting methods
based on artificial neural networks consistently exhibit strong forecasting
performance, in some cases producing accurate predictions lasting for dozens of
Lyapunov times. Best-in-class results for forecasting chaos are achieved by
recently-introduced hierarchical neural basis function models, though even
generic transformers and recurrent neural networks perform strongly. However,
physics-inspired hybrid methods like neural ordinary equations and reservoir
computers contain inductive biases conferring greater data efficiency and lower
training times in data-limited settings. We observe consistent correlation
across all methods despite their widely-varying architectures, as well as
universal structure in how predictions decay over long time intervals. Our
results suggest that a key advantage of modern forecasting methods stems not
from their architectural details, but rather from their capacity to learn the
large-scale structure of chaotic attractors.Comment: 5 pages, 3 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
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