Time-series forecasting is a challenging problem that traditionally requires specialized models custom-trained for the specific task at hand. Recently, inspired by the success of large language models, foundation models pre-trained on vast amounts of time-series data from diverse domains have emerged as a promising candidate for general-purpose time-series forecasting. The defining characteristic of these foundation models is their ability to perform zero-shot learning, that is, forecasting a new system from limited context data without explicit re-training or fine-tuning. Here, we evaluate whether the zero-shot learning paradigm extends to the challenging task of forecasting chaotic systems. Across 135 distinct chaotic dynamical systems and $10^8$ timepoints, we find that foundation models produce competitive forecasts compared to custom-trained models (including NBEATS, TiDE, etc.), particularly when training data is limited. Interestingly, even after point forecasts fail, large foundation models are able to preserve the geometric and statistical properties of the chaotic attractors. We attribute this success to foundation models' ability to perform in-context learning and identify context parroting as a simple mechanism used by these models to capture the long-term behavior of chaotic dynamical systems. Our results highlight the potential of foundation models as a tool for probing nonlinear and complex systems.

MOTIVATION: Single-cell sequencing technology maps cells to a high-dimensional space encoding their internal activity. Recently-proposed virtual cell models extend this concept, enriching cells' representations based on patterns learned from pretraining on vast cell atlases. RESULTS: This review explores how advances in understanding the structure of natural language embeddings informs ongoing efforts to analyze single-cell datasets. Both fields process unstructured data by partitioning datasets into tokens embedded within a high-dimensional vector space. We discuss how the context of tokens influences the geometry of embedding space, and how low-dimensional manifolds shape this space's robustness and interpretation. We highlight how new developments in foundation models for language, such as interpretability probes and in-context reasoning, can inform efforts to construct cell atlases and train virtual cell models. AVAILABILITY AND IMPLEMENTATION: Code is available at https://github.com/williamgilpin/celltoken.

Living systems operate far from equilibrium, yet few general frameworks provide global bounds on biological transients. In high-dimensional biological networks like ecosystems, long transients arise from the separate timescales of interactions within versus among subcommunities. Here, we use tools from computational complexity theory to frame equilibration in complex ecosystems as the process of solving an analogue optimization problem. We show that functional redundancies among species in an ecosystem produce difficult, ill-conditioned problems, which physically manifest as transient chaos. We find that the recent success of dimensionality reduction methods in describing ecological dynamics arises due to preconditioning, in which fast relaxation decouples from slow solving timescales. In evolutionary simulations, we show that selection for steady-state species diversity produces ill-conditioning, an effect quantifiable using scaling relations originally derived for numerical analysis of complex optimization problems. Our results demonstrate the physical toll of computational constraints on biological dynamics.

Experimental measurements of physical systems often have a limited number of independent channels, causing essential dynamical variables to remain unobserved. However, many popular methods for unsupervised inference of latent dynamics from experimental data implicitly assume that the measurements have higher intrinsic dimensionality than the underlying system---making coordinate identification a dimensionality reduction problem. Here, we study the opposite limit, in which hidden governing coordinates must be inferred from only a low-dimensional time series of measurements. Inspired by classical analysis techniques for partial observations of chaotic attractors, we introduce a general embedding technique for univariate and multivariate time series, consisting of an autoencoder trained with a novel latent-space loss function. We show that our technique reconstructs the strange attractors of synthetic and real-world systems better than existing techniques, and that it creates consistent, predictive representations of even stochastic systems. We conclude by using our technique to discover dynamical attractors in diverse systems such as patient electrocardiograms, household electricity usage, neural spiking, and eruptions of the Old Faithful geyser---demonstrating diverse applications of our technique for exploratory data analysis.

In many ecosystems, natural selection can occur quickly enough to influence the population dynamics and thus future selection. This suggests the importance of extending classical population dynamics models to include such eco-evolutionary processes. Here, we describe a predator-prey model in which the prey population growth depends on a prey density-dependent fitness landscape. We show that this two-species ecosystem is capable of exhibiting chaos even in the absence of external environmental variation or noise, and that the onset of chaotic dynamics is the result of the fitness landscape reversibly alternating between epochs of stabilizing and disruptive selection. We draw an analogy between the fitness function and the free energy in statistical mechanics, allowing us to use the physical theory of first-order phase transitions to understand the onset of rapid cycling in the chaotic predator-prey dynamics. We use quantitative techniques to study the relevance of our model to observational studies of complex ecosystems, finding that the evolution-driven chaotic dynamics confer community stability at the "edge of chaos" while creating a wide distribution of opportunities for speciation during epochs of disruptive selection-a potential observable signature of chaotic eco-evolutionary dynamics in experimental studies.

SUMMARY: We have created a Python programming interface for the RCSB Protein Data Bank (PDB) that allows search and data retrieval for a wide range of result types, including BLAST and sequence motif queries. The API relies on the existing XML-based API and operates by creating custom XML requests from native Python types, allowing extensibility and straightforward modification. The package has the ability to perform many types of advanced search of the PDB that are otherwise only available through the PDB website. AVAILABILITY AND IMPLEMENTATION: PyPDB is implemented exclusively in Python 3 using standard libraries for maximal compatibility. The most up-to-date version, including iPython notebooks containing usage tutorials, is available free-of-charge under an open-source MIT license via GitHub at https://github.com/williamgilpin/pypdb, and the full API reference is at http://williamgilpin.github.io/pypdb_docs/html/. The latest stable release is also available on PyPI. CONTACT: [email protected].