Mapping Out Phase Diagrams with Generative Classifiers.

One of the central tasks in many-body physics is the determination of phase diagrams. However, mapping out a phase diagram generally requires a great deal of human intuition and understanding. To automate this process, one can frame it as a classification task. Typically, classification problems are tackled using discriminative classifiers that explicitly model the probability of the labels for a given sample. Here we show that phase-classification problems are naturally suitable to be solved using generative classifiers based on probabilistic models of the measurement statistics underlying the physical system. Such a generative approach benefits from modeling concepts native to the realm of statistical and quantum physics, as well as recent advances in machine learning. This leads to a powerful framework for the autonomous determination of phase diagrams with little to no human supervision that we showcase in applications to classical equilibrium systems and quantum ground states.

Leveraging Julia's automated differentiation and symbolic computation to increase spectral DCM flexibility and speed.

Using neuroimaging and electrophysiological data to infer neural parameter estimations from theoretical circuits requires solving the inverse problem. Here, we provide a new Julia language package designed to i) compose complex dynamical models in a simple and modular way with ModelingToolkit.jl, ii) implement parameter fitting based on spectral dynamic causal modeling (sDCM) using the Laplace approximation, analogous to MATLAB implementation in SPM12, and iii) leverage Julia's unique strengths to increase accuracy and speed by employing Automatic Differentiation during the fitting procedure. To illustrate the utility of our flexible modular approach, we provide a method to improve correction for fMRI scanner field strengths (1.5T, 3T, 7T) when fitting models to real data.

Error analysis of free probability approximations to the density of states of disordered systems.

Theoretical studies of localization, anomalous diffusion and ergodicity breaking require solving the electronic structure of disordered systems. We use free probability to approximate the ensemble-averaged density of states without exact diagonalization. We present an error analysis that quantifies the accuracy using a generalized moment expansion, allowing us to distinguish between different approximations. We identify an approximation that is accurate to the eighth moment across all noise strengths, and contrast this with perturbation theory and isotropic entanglement theory.

Density of states of quantum spin systems from isotropic entanglement.

We propose a method that we call isotropic entanglement (IE), which predicts the eigenvalue distribution of quantum many body (spin) systems with generic interactions. We interpolate between two known approximations by matching fourth moments. Though such problems can be QMA-complete, our examples show that isotropic entanglement provides an accurate picture of the spectra well beyond what one expects from the first four moments alone. We further show that the interpolation is universal, i.e., independent of the choice of local terms.

Enhancing the acquisition efficiency of fast magnetic resonance imaging via broadband encoding of signal content.

Current efficient magnetic resonance imaging (MRI) methods such as parallel-imaging and k-t methods encode MR signals using a set of effective encoding functions other than the Fourier basis. This work revisits the proposition of directly manipulating the set of effective encoding functions at the radiofrequency excitation step in order to increase MRI efficiency. This approach, often termed "broadband encoding," enables the application of algebraic matrix factorization technologies to extract efficiency by representing and encoding MR signal content in a compacted form. Broadband imaging equivalents of fast multiecho, parallel and k-t MRI are developed and analyzed. The potential of these techniques to increase the time efficiency of data acquisition is experimentally verified on a commercial MRI scanner using simple spin-echo imaging. A three-dimensional gradient-echo dynamic imaging application that demonstrates the potential benefits of this approach compared to the present state of the art for certain applications is also presented.

Non-Fourier-encoded parallel MRI using multiple receiver coils.

This paper describes a general theoretical framework that combines non-Fourier (NF) spatially-encoded MRI with multichannel acquisition parallel MRI. The two spatial-encoding mechanisms are physically and analytically separable, which allows NF encoding to be expressed as complementary to the inherent encoding imposed by RF receiver coil sensitivities. Consequently, the number of NF spatial-encoding steps necessary to fully encode an FOV is reduced. Furthermore, by casting the FOV reduction of parallel imaging techniques as a dimensionality reduction of the k-space that is NF-encoded, one can obtain a speed-up of each digital NF spatial excitation in addition to accelerated imaging. Images acquired at speed-up factors of 2x to 8x with a four-element RF receiver coil array demonstrate the utility of this framework and the efficiency afforded by it.