Talks

I introduce a unified framework for interpreting neural network classifiers tailored toward automated scientific discovery. In contrast to neural network-based regression, for classification, it is in general impossible to find a one-to-one mapping from the neural network to a symbolic equation even if the neural network itself bases its classification on a quantity that can be written as a closed-form equation. In this paper, I embed a trained neural network into an equivalence class of classifying functions that base their decisions on the same quantity. I interpret neural networks by finding an intersection between this equivalence class and human-readable equations defined by the search space of symbolic regression. The approach is not limited to classifiers or full neural networks and can be applied to arbitrary neurons in hidden layers or latent spaces or to simplify the process of interpreting neural network regressors.

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I’ll give a review of extended phase space in gauge theories and/or diffeomorphism-invariant theories, beginning with its original conception up to our most recent work. The primary focus in a classical theory is on the proper representation of symmetries and gauge symmetries on phase space. Correspondingly, this is understood in the quantum theory through the crossed product construction and conditional expectation. I’ll discuss several examples.

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The North American Nanohertz Observatory for Gravitational Waves (NANOGrav) collaboration has recently reported evidence for the background of low-frequency gravitational waves using an array of rapidly rotating, highly stable radio pulsars distributed across the galaxy. Each pulsar emits a radio beam that passes our line of sight and is observed as regular, pulsed emission. We measure the times of arrival of pulses and compare with a model that includes: the rotational motion of the pulsar, orbital motions, and interstellar propagation delays; random timing noise from pulsars themselves and from the interstellar medium; and finally a correlated gravitational-wave signal recently reported on in a suite of papers. I will highlight our recent results, including implications for the dynamics of supermassive black hole binary at the centers of merging galaxies, searches for individual supermassive black hole binary systems, and searches of gravitational wave signals from new physics. I will end by highlighting future prospects for radio facilities that will advance our look into this newly opened window to the Universe.

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The Sunyaev-Zel’dovich Effect—the Doppler boost of low-energy Cosmic Microwave Background photons scattering off free electrons—is an excellent probe of ionized gas residing in distant galaxies. Its two main constituents are the kinematic SZ effect (kSZ), where electrons have a non-zero line-of-sight (LOS) velocity and which probes the electron line-of-sight momentum, and the thermal SZ effect (tSZ), where electrons have high energies due to their temperature, and which probes the electron integrated pressure. These two effects provide complementary information to constrain the thermodynamic profile of gas residing in distant galaxies, which can be further used to understand feedback processes, a necessary ingredient to describe the evolution of the large-scale structure in our Universe. Both tSZ and kSZ can be measured in cross-correlation with large-scale structure. In this talk, I will discuss my past and ongoing measurements of the SZ-galaxy cross-correlation with unWISE galaxies, where to measure the kSZ effect I use the projected-fields estimator. unWISE is a galaxy catalog containing over 500 million galaxies on the full sky and consists of three subsamples of mean redshifts z=0.5, 1.1, 1.5, whose halo occupation distribution I have already constrained. If time permits, I will also present my work on mitigating foregrounds in the SZ cross-correlations, particularly the Cosmic Infrared Background (CIB).

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