I am a dynamicist who is perplexed by the behavior of space, time, sound, and brains. As of September 2019, I am an assistant professor in the Department of Physics at New York Institute of Technology in Manhattan. Here’s my CV.
- nonlinear processes in astrophysical settings;
- geometric dynamical systems approaches to analyzing natural acoustic signals;
- biological neurons and pattern-generating networks that are associated with auditory signaling;
- inference methods for model state-and-parameter estimation.
- dynamical systems, optimization and control, statistical physics, information theory.
My parents tell me that when they strolled me as a baby at nighttime, I would point up at the sky and stare at them with a question mark.
These days I work on nonlinear dynamics in astrophysical settings, and on how data assimilation – an inference procedure designed to optimize a model with observation – may yield insight into such problems.
Specifically, I study neutrino flavor evolution in astrophysical events. Neutrinos are created in energetic events such as core-collapse supernovae, and they possess a property called “flavor”, a term that defines the manner in which they interact with matter. Neutrino interaction with matter in large part sets the abundances of the heavy elements in the Universe. In order, then, to account for the current constituency of the Universe (including the existence of gold, uranium, and your brother-in-law), we must understand how flavor evolves following these events. And it’s a deliciously complicated beast of a problem.
The method of attacking these problems is typically numerical integration. This technique is limited in two main ways. First, the high dimensionality of realistic models renders parameter estimation via numerical integration computationally intractable. Consequently, undesirable model simplifications are made, and many parameters that are poorly constrained (by either theory or observation) are taken to be known. Secondly, numerical integration is inadequate for probing some nonlinear aspects of neutrino flavor evolution, such as the “halo effect”, where flavor states at large radii from the surface of the proto-neutron star may affect states at shorter radii.
Inference for solving nonlinear problems in neutrino flavor evolution
An inference procedure may be a viable alternative tool for investigating these problems. Specifically, data assimilation (DA) is a method to optimize a dynamical model together with observation. Here, the observation may be real or simulated. In the latter case, the DA aim is to ascertain which observations must – in principle – be made (e.g. what new instrumentation must, perhaps, be built) in order to complete the associated dynamical model.
DA parameter estimation is efficient in that one may choose which regions of state space to search, and which are – by comparison – highly unlikely to be relevant and thus ignorable. Further, DA works optimally when the model associated with the observations is nonlinear in nature.
We’ve taken a published first stab at unleashing DA on a post-core-collapse flavor evolution scenario. In this case, we sought to ascertain what information an Earth-based detector must receive in order to pinpoint the Mikheyev-Smirnov-Wolfenstein (MSW) resonance location in a highly simplified steady-state two-flavor model. For that model, we found that an optimization formulation of data assimilation can infer complete flavor evolution history, given a measurement of neutrino flavor only at the detector location and an assumed initial emitted flavor distribution (Armstrong et al. 2017). Currently we are adding more realistic complications to the model and modifying the optimization procedure accordingly.
Moreover, we are investigating the power and efficiency of DA – relative to traditional numerical methods – to calculate the values of parameters that are commonly either assumed to be known or omitted entirely from models of neutrino evolution in supernovae.
NEUROSCIENCE AND BIRDSONG
The following three projects focus on the songbird. I choose the songbird for three reasons. First, it offers an example of learning to communicate via audition. Second, audition in the songbird is an illustration that central pattern generators (CPGs) can underlie a reliable observable behavior in a large neuronal network. Understanding the neural underpinnings of vocalization and audition in this species offers hints for how to probe more complicated problems such as human language, and in principle can inform clinical approaches to human disorders of speech, hearing, and communication. Third, I am interested in developing geometric dynamical systems approaches to analyzing the information content of natural sounds.
Pattern generation for acoustic signaling: I’m interested in ferreting out fundamental organizing principles of the central nervous system, particularly those that give rise to reliable patterned neural activity associated with the generation or processing of acoustic information. Nearly all research on neuronal circuits that behave as central pattern generators (CPGs) has been done on small (~ 30-cell) circuits in crustaceans, because these circuits can be isolated from the animal and the large cell size facilitates whole-cell recording. By contrast, little effort has been made to examine how CPG activity is effected in a much larger circuit. Nucleus HVC of the songbird brain appears to be such a circuit: with ~ 10^5 cells, it has a well-demonstrated ability to generate reliable patterned activity. I created a toy model of HVC’s pattern-generating mechanism (Armstrong & Abarbanel, J. Neurophysiol. 2016). Currently I am working with colleagues who study zebra finch learning to expand this model in terms of its learning capacity and connections to other areas of the song system associated with timing. Collaborators: Ofer Tchernichovski, Julia Hyland Bruno, Tiberiu Teliseanu.
The information content of natural acoustic signals: Female songbirds display observable preferences for songs of particular males, given song as the sole information about each male. Further, isolated females will independently rank a set of songs in a similar order. Traditional acoustic analysis tools have failed to uncover a metric for these innate preferences. That is unsurprising: vocal production is a nonlinear process, while acoustic studies are based mostly on linear spectral analysis. We approach this problem by assuming that some unknown dynamical system produced the song. We employ time-delay embedding to visualize the orbit of the acoustic pressure time series in reconstructed phase space.
We are employing these orbits as training data to reconstruct – and manipulate – songs. This procedure involves writing a polynomial model whose variables are the phase space coordinates, and using statistical data assimilation to recover the parameters of the model. Mating season is upon us, and we are amid playback experiments to assess female responses to these songs. The aim is to develop a reliable tool that can systematically probe what acoustic information these females are listening for. Further, it has been shown that lesions to the female song circuit result in the dissolution of their song preferences. A long-term goal is to involve both both lesioned and non-lesioned birds in playback experiments, to probe not only what information the females recognize as significant, but also where and how that information is stored within the neural circuitry.
Finally, we are examining the connection of the phase space representation to an existing dynamical model of the syrinx, to gain an understanding of the physical significance of these orbits. Collaborators: Alicia Zeng, David White, Andrew Gersick, Marc Schmidt, Vijay Balasubramanian, Ammon Perkes, Luke Anderson., Youngmin Park.
The role of vocalization in songbird social dynamics, and the neural underpinnings of those dynamics: During mating season, songbirds engage in a societal evolution wherein monogamous pairs form and a hierarchy of social dominance is established. The means by which this structure forms is unknown, although the role of song is significant. Further, lesions of the song circuit disrupt the formation of this social structure. We aim to characterize a basic relationship between vocalizations and pair bonding within an aviary of non-lesioned birds. We tackle this problem with inference approaches based in statistical physics. We find that an Ising model is able to capture the statistics of the data in terms of pairwise interactions between individuals, but that it is likely that higher-order interactions, particularly triads, need to be considered. This would be the first quantification of a general consensus within the experimental community that triadic interactions guide societal evolution. A long-term goal is to examine what this framework can tell us about the societal changes resulting from electrophysiological manipulations of the song-related neural circuitry. Collaborators: Clelia de Mulatier, Marc Schmidt, David White, Vijay Balasubramanian, Ammon Perkes, Luke Anderson.
Most recently I was a postdoctoral fellow at the Computational Neuroscience Initiative at the University of Pennsylvania. There I developed the current projects on geometrical analysis of birdsong, described above. Previously I was a postdoctoral scholar at the BioCircuits Institute at the University of California, San Diego. There I worked with Henry Abarbanel on a dynamical model of the avian song nucleus HVC. We tested models via statistical data assimilation, using experimental data from collaborators in the laboratory of Daniel Margoliash at the University of Chicago.