Hidden Spin-Isospin Exchange Symmetry.

The strong interactions among nucleons have an approximate spin-isospin exchange symmetry that arises from the properties of quantum chromodynamics in the limit of many colors, N_{c}. However this large-N_{c} symmetry is well hidden and reveals itself only when averaging over intrinsic spin orientations. Furthermore, the symmetry is obscured unless the momentum resolution scale is close to an optimal scale that we call Λ_{large-N_{c}}. We show that the large-N_{c} derivation requires a momentum resolution scale of Λ_{large-N_{c}}∼500 MeV. We derive a set of spin-isospin exchange sum rules and discuss implications for the spectrum of ^{30}P and applications to nuclear forces, nuclear structure calculations, and three-nucleon interactions.

Addition and removal energies of circular quantum dots.

We present and compare several many-body methods as applied to two-dimensional quantum dots with circular symmetry. We calculate the approximate ground state energy using a harmonic oscillator basis optimized by Hartree-Fock (HF) theory and further improve the ground state energy using two post-HF methods: in-medium similarity renormalization group and coupled cluster with singles and doubles. With the application of quasidegenerate perturbation theory or the equations-of-motion method to the results of the previous two methods, we obtain addition and removal energies as well. Our results are benchmarked against full configuration interaction and diffusion Monte Carlo where available. We examine the rate of convergence and perform extrapolations to the infinite basis limit using a power-law model.

Solving the nuclear pairing model with neural network quantum states.

We present a variational Monte Carlo method that solves the nuclear many-body problem in the occupation number formalism exploiting an artificial neural network representation of the ground-state wave function. A memory-efficient version of the stochastic reconfiguration algorithm is developed to train the network by minimizing the expectation value of the Hamiltonian. We benchmark this approach against widely used nuclear many-body methods by solving a model used to describe pairing in nuclei for different types of interaction and different values of the interaction strength. Despite its polynomial computational cost, our method outperforms coupled-cluster and provides energies that are in excellent agreement with the numerically exact full configuration-interaction values.

Novel features of nuclear forces and shell evolution in exotic nuclei.

Novel simple properties of the monopole component of effective nucleon-nucleon interactions are presented, leading to the so-called monopole-based universal interaction. Shell structures are shown to change as functions of N and Z, consistent with experiments. Some key cases of this shell evolution are discussed, clarifying the effects of central and tensor forces. The validity of the present tensor force is examined in terms of the low-momentum interaction V(lowk) and the Q(box) formalism.

Predicting time to graduation at a large enrollment American university.

The time it takes a student to graduate with a university degree is mitigated by a variety of factors such as their background, the academic performance at university, and their integration into the social communities of the university they attend. Different universities have different populations, student services, instruction styles, and degree programs, however, they all collect institutional data. This study presents data for 160,933 students attending a large American research university. The data includes performance, enrollment, demographics, and preparation features. Discrete time hazard models for the time-to-graduation are presented in the context of Tinto's Theory of Drop Out. Additionally, a novel machine learning method: gradient boosted trees, is applied and compared to the typical maximum likelihood method. We demonstrate that enrollment factors (such as changing a major) lead to greater increases in model predictive performance of when a student graduates than performance factors (such as grades) or preparation (such as high school GPA).