The Fulton gap is a phenomenon in astrophysics caused by a dip in detected exoplanets between 1.5 and 2.0 Earth radii. This phenomenon was revealed after the California Kepler Survey obtained precise parameters for Kepler exoplanets. One leading explanation to the Fulton gap is photoevaporation. We aimed to determine whether current exoplanet data around the gap support the photoevaporation theory and to assess the role of RV modeling within this Fulton gap. We modeled specific planetary systems above and below the gap, including Kepler-10 and Kepler-36, alongside data from the California Kepler Survey. Then, we used the Exoplanet Population Observation Simulator to plot occurrence rates and detection efficiency. We used this simulation to also predict radii of exoplanets that currently only have mass parameters. Our models and simulations produced results that suggest the bimodal trend in Kepler planets appears due to photoevaporation. A negative slope of the radius valley on a logarithmic plot of radius and orbital period, also consistent with XUV-driven mass loss models, strongly suggests photoevaporation. Our prediction models also suggest that the radius valley will appear in other planetary systems detected by RV. Our results demonstrated the importance of detection limitations for RV and how RV detection remains important within the context of the Fulton gap.

It has been widely established that the Sun produces energy at its core; intense heat and pressure catalyzing nuclear fusion. However, due to the time it takes for this energy to propagate to its surface (100–200k years), it would be assumed that this energy is gradually released, rather than the reality of intense bursts via coronal mass ejections. Our presentation explores the hypothesis that nuclear fusion occurs on the Sun's surface–including its low-temperature “sun spots”–through electron-catalyzed proton-boron-11 fusion. Evidence for this idea is based on studies conducted by UCLA professor Alfred Y. Wong in electron-dense rotating plasma systems. In his experiments, CR-39 detectors observed MeV particles as a product of proton-boron-11 fusion. Optical spectroscopy of the fusion also identified helium production, a byproduct of the fusion reaction. Furthermore, this evidence of fusion was observed in a low-temperature, small-scale environment, indicating how the electron density enables fusion. High densities of electrons reduce the Coulomb barrier between nuclei, increasing the chance of quantum tunneling that allows fusion under less extreme conditions. This implies that fusion can be achieved and regulated on a smaller scale. Electron-catalyzed fusion would redefine how fusion occurs, offering a more practical method of generating renewable energy. By making fusion easier to produce, we could possess a near-limitless clean energy source that would significantly reduce resource-driven conflicts around the world.

The formation of Hot Jupiters, gas giants on a few-day orbits from their stars, presents a challenge to traditional theories of planet formation that posit gas giants should form at large orbital separations, like our Jupiter. One promising channel relies on having a faraway companion, either a star or a planet that can push the hot Jupiter progenitor inward, closer to its host star. The progenitors, also called cold Jupiters, are then placed on high elliptical orbits, where they spend a lot of time around their host stars, where tides can work to circularize them. This channel can readily migrate cold to hot Jupiters. However, recent observations show that more compact, warm, neither cold nor hot, planetary neighbors are also common. My research project investigates the dynamics in systems containing multiple Cold Jupiters in a mildly compact configuration. We perform population studies to understand what initial conditions lead to Hot and Warm Jupiter formation. Preliminary simulations suggest that both sets of planets may form through this process, and that inner planets may have much more massive outer companions, consistent with trends from observations.

CO2 is prevalent in secondary atmospheres in the solar system, for example at Mars and Venus, and potentially beyond at exoplanets too. Although CO2 outgassing is expected, the stability of CO2 at these planets was originally puzzling because photolysis by sunlight splits CO2 into CO and O. It has been previously shown that HOx chemistry (sourced by water photolysis) catalytically restores CO to CO2 at Mars. Venus is very dry, and instead relies on catalytic chlorine chemistry (initiated by HCl photolysis; eg, Yung & Demore 1999). At exoplanets, CO2 may not always be stable, and the distance to the host-star and the availability of water vapor may control CO buildup. Like Venus, volcanically released HCl could restore the CO to CO2, but would depend on outgassing rates. By questioning CO2’s stability, Hu et al. (2019) predicted a buildup of CO and O2 at exoplanets closely orbiting their host stars, but Ranjan et al. (2023) predicted the CO buildup was a numerical artifact of a short model height. Both works considered only earth-like planets (1% H2O) however. Here, we use a photochemical model to demonstrate the minimum amount of volcanically released HCl needed to maintain CO2 stability for a variety of exoplanets. We will present CO:CO2 mixing ratios for planets: (1) at different orbital distances; (2) around different star types; (3) for water contents ranging from 1 ppm to 10%; and (4) for different HCl outgassing rates.

Introductory statistics courses traditionally rely on printed distribution tables to obtain cumulative probabilities, quantiles, critical values, and obtain p-values for hypothesis tests. These methods introduce unnecessary procedural complexity, requiring students to navigate multi-step lookup and computation processes before interpreting results. This increases cognitive load and shifts focus away from statistical reasoning and conceptual understanding. We are developing the UCLA Stats Calculator, an interactive web application built using R Shiny to support both computation and conceptual learning in introductory statistics. The tool integrates key distributions - including binomial, normal, t, and chi-square - and supports one- and two-sample inference for proportions and means, enabling both cumulative probability calculations and inverse operations such as finding critical values. It provides real-time outputs, structured summaries of results, and options for confidence intervals and distribution visualizations, all within an intuitive, accessible interface. The tool is currently being piloted in STATS 10 - Introduction to Statistical Reasoning in Spring 2026 with 400 students. It offers a practical, learning-oriented platform that streamlines statistical computation and visualization, and can be expanded across all introductory statistics courses at UCLA (STATS 10, STATS 12, STATS 13, and STATS 15), reaching over 6,000 students annually, with potential for broader adoption beyond the university.

Missing data is ubiquitous in the behavioral, educational, and social sciences. The current standard has largely relied on multiple imputation (i.e., simulated predictions), which requires specifying a prediction model relating analysis variables to auxiliary variables. In practice, specifying these relationships is difficult and incorrect specification yields biased estimates and poor confidence interval coverage rates. In this research, we compare multiple imputation to an approach that models response (or missingness) probability instead, avoiding the predictive model altogether. By modeling response propensities directly, we can use machine learning approaches (e.g., classification trees and neural networks), then apply an inverse probability weighting method to correct bias from missing data. In a simulation study, we compared multiple imputation with parametric and nonparametric response models under settings where each of the approaches were misspecified. The response models outperformed multiple imputation when the predictive model was misspecified and performed comparably when it was correct. Conversely, when the response model was misspecified, multiple imputation outperformed the response models, although the machine learning methods remained competitive. This demonstrates a powerful alternative modeling approach and an application of machine learning methods for handling missing data in applied research.

We establish the following theorem. Let O_0, O_1, and R be random functions from {0,1}^n to {0,1}^m, where m and n are natural numbers satisfying m >= n >= 10. For any distinguisher D making at most q oracle queries, with q <= 2^n / (n + 1), there exists a polynomial-time oracle simulator Sim such that the distinguishing advantage is bounded as follows. The difference in the probability that D outputs 1 when interacting with the real system consisting of (O_0 + O_1) together with (O_0, O_1, O_0^{-1}, O_1^{-1}), and the probability that D outputs 1 when interacting with the ideal system consisting of R together with Sim^R, is at most 8 n q^2 / 2^m + 10 n^2 q^2 / 2^n. In contrast to prior work, we prove indifferentiability for all parameter settings where m >= n and n is sufficiently large.