Hybridizing two-step growth mixture model and exploratory factor analysis to examine heterogeneity in nonlinear trajectories

Empirical researchers are usually interested in investigating the impacts of baseline covariates have when uncovering sample heterogeneity and separating samples into more homogeneous groups. However, a considerable number of studies in the structural equation modeling (SEM) framework usually start with vague hypotheses in terms of heterogeneity and possible reasons. It suggests that (1) the determination and specification of a proper model with covariates is not straightforward, and (2) the exploration process may be computational intensive given that a model in the SEM framework is usually complicated and the pool of candidate covariates is usually huge in the psychological and educational domain where the SEM framework is widely employed. Following \citet{Bakk2017two}, this article presents a two-step growth mixture model (GMM) that examines the relationship between latent classes of nonlinear trajectories and baseline characteristics. Our simulation studies demonstrate that the proposed model is capable of clustering the nonlinear change patterns, and estimating the parameters of interest unbiasedly, precisely, as well as exhibiting appropriate confidence interval coverage. Considering the pool of candidate covariates is usually huge and highly correlated, this study also proposes implementing exploratory factor analysis (EFA) to reduce the dimension of covariate space. We illustrate how to use the hybrid method, the two-step GMM and EFA, to efficiently explore the heterogeneity of nonlinear trajectories of longitudinal mathematics achievement data.Comment: Draft version 1.6, 08/08/2020. This paper has not been peer reviewed. Please do not copy or cite without author's permissio

Mixing of Ground States in Vertex Models

We consider the analogue of the 6-vertex model constructed from alternating spin n/2 and spin m/2 lines, where $1\leq n<m$. We identify the transfer matrix and the space on which it acts in terms of the representation theory of $U_q(sl_2)$. We diagonalise the transfer matrix and compute the S-matrix. We give a trace formula for local correlation functions. When n=1, the 1-point function of a spin m/2 local variable for the alternating lattice with a particular ground state is given as a linear combination of the 1-point functions of the pure spin m/2 model with different ground states. The mixing ratios are calculated exactly and are expressed in terms of irreducible characters of $U_q(sl_2)$ and the deformed Virasoro algebra.Comment: 12 pages, LaTeX, typos correcte

Effect of Charge Fluctuations on the Persistent Current through a Quantum Dot

We study coherent charge transfer between an Aharonov-Bohm ring and a side-attached quantum dot. The charge fluctuation between the two sub-structures is shown to give rise to algebraic suppression of the persistent current circulating the ring as the size of the ring becomes relatively large. The charge fluctuation at resonance provides transition between the diamagnetic and the paramagnetic states. Universal scaling, crossover behavior of the persistent current from a continuous to a discrete energy limit in the ring is also discussed.Comment: 5 pages, 4 figure

Categorification of Highest Weight Modules via Khovanov-Lauda-Rouquier Algebras

In this paper, we prove Khovanov-Lauda's cyclotomic categorification conjecture for all symmetrizable Kac-Moody algebras. Let $U_q(g)$ be the quantum group associated with a symmetrizable Cartan datum and let $V(\Lambda)$ be the irreducible highest weight $U_q(g)$-module with a dominant integral highest weight $\Lambda$. We prove that the cyclotomic Khovanov-Lauda-Rouquier algebra $R^{\Lambda}$ gives a categorification of $V(\Lambda)$.Comment: Typoes correcte

Collagen matrix stiffness influences on fibroblast contraction force

Cell-embedded hydrogel has been widely used as engineered tissue equivalents in biomedical applications. In this study, contraction force in human aortic adventitial fibroblasts seeded within a 3D collagen matrix was quantified by a novel force sensing technique. We demonstrate that contraction forces in cells treated with histamine are regulated by the gel stiffness in a linear manner. These findings provide novel insights for the design of collagen-based biomaterials for tissue engineering and clinical applications

Characterization of Semi-Autonomous On-Orbit Assembly CubeSat Constellation

Demand for more complex space systems is ever increasing as the scale of the future missions expands. Accordingly, much focus has been given recently to innovations in on-orbit assembly and servicing to ensure those missions are executed in a time-efficient manner. The past on-orbit servicing demonstrations have involved large satellites that were designed to dock/berth and service specific client satellites, and did not leverage the current advancements in small satellite technology. The U.S. Naval Academy (USNA) is contributing to advancing the onorbit servicing and assembly technology with a next-generation robotic arm Intelligent Space Assembly Robot (ISAR) system, which is envisioned to operate independently or as a constellation of 3U CubeSats and seeks to demonstrate semi-autonomous robotic assembly capabilities on-orbit on a nano-satellite scale. This paper will present an overview of the ISAR system, outline design, operation, and demonstration modifications for the on-orbit demonstrator, analyze the results from the ground test platform, and discuss the interfacing between existing robotic operations structures and advanced sensors. It will also focus on the analysis of cost effectiveness of the proposed mission architecture by characterizing the operation envelope of CubeSat-based assembly satellite constellations and volumetric efficiency analysis of on-orbit assembly using “Bin of Parts”

Advances in Low-Cost Manufacturing and Folding of Solar Sail Membranes

Solar sail membranes must have a high area-to-mass ratio and high solid volume fraction when stowed. In order to meet mission requirements, current solar sail projects, such as NASAs Near Earth Asteroid Scout, require metallized sail membranes with thicknesses on the order of 2-3 m. These very thin membranes do not retain creases like thicker membranes, solar panels, or paper models. For Cubesat-class spacecraft, volume, rather than mass, is often the driving requirement for deployable structural elements. These two factors make it both difficult and highly desirable to characterize the practical differences between solar sail membrane packaging methods with laboratory demonstrations. This paper presents lessons gathered from lab work with solar sail membranes at a 10-meter scale