Alex Williams

Projects

Unsupervised learning methods for large-scale, multi-trial neural data
A common paradigm in systems neuroscience is to simultaneously record the activity of many neurons over repeated experimental trials (e.g., multiple presentations of a sensory stimulus, or a repeated motor action). The resulting datasets can be very large, potentially containing recordings from thousands of neurons over thousands of experimental trials. I'm interested in finding general-purpose statistical approaches for understanding datasets of this form. See Williams et al. (2018) and Williams et al. (2019). Also check out this tutorial (from 2017) for a broader overview of this subject.

Automated segmentation and detection of motifs in high-dimensional time series
Trial-structured data (described above) are convienent for data analysis---in particular, if neural dynamics on different trials follow a similar (though not identical) trajectory, we can build a model that isolates this structure while discarding the remaining "noise" (for lack of a better term). A more challenging problem is how to extract scientifically interpretable features from unstructured neural and behavioral data streams (e.g. during unconstrained natural behaviors). I am working on models that extract temporal motifs or pseudo-trials from these unannotated time series. See Mackevicius et al. (2019) and Degleris et al. (2019).

tensortools — My Python toolbox for fitting tensor decompositions.
affinewarp — Time warping models for neural data.
PyNeuronToolbox — A package I wrote to enable better NEURON simulations in Jupyter notebooks.

Universality and individuality in neural dynamics across large populations of recurrent networks
Maheswaranathan N, Williams AH, Golub MD, Ganguli S, Sussillo D (2019). arXiv. 1907.08549

Reverse engineering recurrent networks for sentiment classification reveals line attractor dynamics
Maheswaranathan N, Williams AH, Golub MD, Ganguli S, Sussillo D (2019). arXiv. 1906.1072

Fast Convolutive Nonnegative Matrix Factorization Through Coordinate and Block Coordinate Updates
Degleris A, Antin B, Ganguli S, Williams AH (2019). arXiv. 1907.00139

Discovering precise temporal patterns in large-scale neural recordings through robust and interpretable time warping
Williams AH, Poole B, Maheswaranathan N, Dhawale AK, Fisher T, Wilson CD, Brann DH, Trautmann E, Ryu S, Shusterman R, Rinberg D, Ölveczky BP, Shenoy KV, Ganguli S (2019). bioRXiv. 661165

Unsupervised discovery of temporal sequences in high-dimensional datasets, with applications to neuroscience
Mackevicius EL, Bahle AH, Williams AH, Gu S, Denissenko NI, Goldman MS, Fee MS (2019). eLife. 8:e38471

Unsupervised discovery of demixed, low-dimensional neural dynamics across multiple timescales through tensor components analysis
Williams AH, Kim TH, Wang F, Vyas S, Ryu SI, Shenoy KV, Schnitzer M, Kolda TG, Ganguli S (2018). Neuron. 98(6):1099–1115.e8

Distinct or shared actions of peptide family isoforms: II. Multiple pyrokinins exert similar effects in the lobster stomatogastric nervous system.
Dickinson PS, Kurland SC, Qu X, Parker BO, Sreekrishnan A, Kwiatkowski MA, Williams AH, Ysasi AB, Christie AE (2015). J Exp Biol. 218:2905-17

Summary of the DREAM8 parameter estimation challenge: Toward parameter identification for whole-cell models.
Karr JR, Williams AH, Zucker JD, Raue A, Steiert B, Timmer J, Kreutz C, DREAM8 Parameter Estimation Challenge Consortium, Wilkinson S, Allgood BA, Bot BM, Hoff BR, Kellen MR, Covert MW, Stolovitzky GA, Meyer P (2015). PLoS Comput Biol. 11(5):e1004096

Cell types, network homeostasis and pathological compensation from a biologically plausible ion channel expression model.
O’Leary T, Williams AH, Franci A, Marder E (2014). Neuron. 82(4):809-21

Many parameter sets in a multicompartment model oscillator are robust to temperature perturbations.
Caplan JS, Williams AH, Marder E (2014). J Neurosci. 34(14):4963-75

The neuromuscular transform of the lobster cardiac system explains the opposing effects of a neuromodulator on muscle output.
Williams AH, Calkins A, O’Leary T, Symonds R, Marder E, Dickinson PS (2013). J Neurosci. 33(42):16565-75

Correlations in ion channel expression emerge from homeostatic regulation mechanisms.
O’Leary T, Williams AH, Caplan JS, Marder E (2013). Proc Natl Acad Sci USA. 110(28):E2645-54

Animal-to-animal variability in the phasing of the crustacean cardiac motor pattern: an experimental and computational analysis.
Williams AH, Kwiatkoswki MA, Mortimer AL, Marder E, Zeeman ML, Dickinson PS (2013). (2013). J Neurophysiol. 109:2451-65.

Neuromodulation in Small Networks.
Williams AH, Hamood AW, Marder E (2015). Springer Encyclopedia of Computational Neuroscience.