I am a dynamicist who is perplexed by the behavior of space, time, and brains. I am an assistant professor in the Department of Physics at New York Institute of Technology in Manhattan, and research associate in the Department of Astrophysics at the American Museum of Natural History. Here’s my CV and publications.
- neutrino astrophysics, biological neuronal networks, and epidemiology
- the information content of communication signals
- analysis of information flow in nonlinear systems
- statistical data assimilation (SDA) – an inference methodology – for state and parameter estimation in nonlinear models
- dynamical systems modeling
When the pandemic hit in 2020, I applied SDA to estimate unknown parameters in an epidemiological model for COVID-19. The aim was to demonstrate to the field of epidemiology how SDA can be used to inform policy on social behavior. Here is our publication.
Statistical data assimilation for solving nonlinear problems in neutrino flavor evolution and nuclear astrophysics — funded by National Science Foundation EAGER grant 2139004
Neutrinos are created in energetic events such as core-collapse supernovae (SNe), and possess a property called “flavor”, which defines their interactions with matter. Neutrino flavor in part sets the local neutron-to-proton ratio, and core-collapse SNe are candidate sites for the creation of some elements heavier than iron. To recover the observed cosmic elemental abundances, 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 computationally intractable. Consequently, undesirable simplifications are made: 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 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 nearer radii.
Inference may be a viable alternative for investigating these problems. Specifically, statistical data assimilation (DA) is a method to optimize a dynamical model together with observation. Using simulated data, one may ascertain which observations must – in principle – be made (and what new instrumentation must, perhaps, be built) in order to complete the associated model. DA is efficient in that one may choose which regions of state space to search, and which are – by comparison – unlikely to be relevant to the specific problem at hand. Further, an optimization formulation of DA may permit the identification of an optimal set of parameter estimates among degeneracies.
Our first publication applied DA to 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. We found that an optimization formulation of DA can infer complete flavor evolution history, given a measurement of neutrino flavor only at the detector location and an assumed initial emitted flavor distribution. In our second publication, we identified a means of discriminating among degenerate solutions. In our most recent submission, we demonstrated the ability of SDA to infer flavor evolution at early radii near the supernova core, based solely on measurements made at Earth and requiring no assumptions on initial conditions at the core. In addition, I have recently shown that inference can solve a problem involving direction-changing collisions — a problem that cannot be solved via the traditional method of integration; here is the manuscript.
Inference for mining large-scale surveys for binary stars, to examine their relationship to galactic evolution
I collaborate with Michael Shara and David Zurek at AMNH, to mine surveys for binary stars, in order to probe the relationship between binary star formation and the chemical and luminosity evolution of galaxies. Check back for an update.
Inference for modeling exoplanet atmospheres
I have begun a conversation with the exoplanet research group of Jackie Faherty at AMNH. We are working on an optimal inference procedure – or atmospheric retrieval method – to infer atmospheric chemical composition, given an observed flux across wavelengths. It is an exciting new problem. Check back for an update.
NEUROSCIENCE and COMMUNICATION: on hold, to be revisited in the near future
The following two projects focus on the songbird. The songbird provides an excellent lab in which to study neuronal dynamics underlying acoustic communication. First, it offers an example of learning to communicate via audition, and a significantly simpler example than that of a human being. 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.
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.