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 This paper has not been peer reviewed.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

DNA methylation associated with postpartum depressive symptoms overlaps findings from a genome-wide association meta-analysis of depression

Background Perinatal depressive symptoms have been linked to adverse maternal and infant health outcomes. The etiology associated with perinatal depressive psychopathology is poorly understood, but accumulating evidence suggests that understanding inter-individual differences in DNA methylation (DNAm) patterning may provide insight regarding the genomic regions salient to the risk liability of perinatal depressive psychopathology. Results Genome-wide DNAm was measured in maternal peripheral blood using the Infinium MethylationEPIC microarray. Ninety-two participants (46% African-American) had DNAm samples that passed all quality control metrics, and all participants were within 7 months of delivery. Linear models were constructed to identify differentially methylated sites and regions, and permutation testing was utilized to assess significance. Differentially methylated regions (DMRs) were defined as genomic regions of consistent DNAm change with at least two probes within 1 kb of each other. Maternal age, current smoking status, estimated cell-type proportions, ancestry-relevant principal components, days since delivery, and chip position served as covariates to adjust for technical and biological factors. Current postpartum depressive symptoms were measured using the Edinburgh Postnatal Depression Scale. Ninety-eight DMRs were significant (false discovery rate \u3c 5%) and overlapped 92 genes. Three of the regions overlap loci from the latest Psychiatric Genomics Consortium meta-analysis of depression. Conclusions Many of the genes identified in this analysis corroborate previous allelic, transcriptomic, and DNAm association results related to depressive phenotypes. Future work should integrate data from multi-omic platforms to understand the functional relevance of these DMRs and refine DNAm association results by limiting phenotypic heterogeneity and clarifying if DNAm differences relate to the timing of onset, severity, duration of perinatal mental health outcomes of the current pregnancy or to previous history of depressive psychopathology

Discovery of the brightest T dwarf in the northern hemisphere

We report the discovery of a bright (H=12.77) brown dwarf designated SIMP J013656.5+093347. The discovery was made as part of a near-infrared proper motion survey, SIMP (Sondage Infrarouge de Mouvement Propre), which uses proper motion and near-infrared/optical photometry to identify brown dwarf candidates. A low resolution (lambda/dlambda~40) spectrum of this brown dwarf covering the 0.88-2.35 microns wavelength interval is presented. Analysis of the spectrum indicates a spectral type of T2.5+/-0.5. A photometric distance of 6.4+/-0.3 pc is estimated assuming it is a single object. Current observations rule out a binary of mass ratio ~1 and separation >5 AU. SIMP 0136 is the brightest T dwarf in the northern hemisphere and is surpassed only by Eps Indi Bab over the whole sky. It is thus an excellent candidate for detailed studies and should become a benchmark object for the early-T spectral class.Comment: 4 pages, 3 figures, To be published in November 1, 2006 issue of ApJL. Following IAU recommendation, the survey acronym (IBIS) was changed to SIM

Obtaining interpretable parameters from reparameterizing longitudinal models: transformation matrices between growth factors in two parameter-spaces

The linear spline growth model (LSGM), which approximates complex patterns using at least two linear segments, is a popular tool for examining nonlinear change patterns. Among such models, the linear-linear piecewise change pattern is the most straightforward one. An earlier study has proved that other than the intercept and slopes, the knot (or change-point), at which two linear segments join together, can be estimated as a growth factor in a reparameterized longitudinal model in the latent growth curve modeling framework. However, the reparameterized coefficients were no longer directly related to the underlying developmental process and therefore lacked meaningful, substantive interpretation, although they were simple functions of the original parameters. This study proposes transformation matrices between parameters in the original and reparameterized models so that the interpretable coefficients directly related to the underlying change pattern can be derived from reparameterized ones. Additionally, the study extends the existing linear-linear piecewise model to allow for individual measurement occasions, and investigates predictors for the individual-differences in change patterns. We present the proposed methods with simulation studies and a real-world data analysis. Our simulation studies demonstrate that the proposed method can generally provide an unbiased and consistent estimation of model parameters of interest and confidence intervals with satisfactory coverage probabilities. An empirical example using longitudinal mathematics achievement scores shows that the model can estimate the growth factor coefficients and path coefficients directly related to the underlying developmental process, thereby providing meaningful interpretation. For easier implementation, we also provide the corresponding code for the proposed models.Comment: Draft version 1.6, 07/28/2020. This paper has not been peer reviewed. Please do not copy or cite without author's permissio

Notes on Captive Sea Otters

Notes on the behaviour of three yearlings kept two and a half months in 1954 in a dry environment at Amchitka in the Aleutians. Their sleeping, preening, reaction to man and feeding habits, drinking, locomotion, handling, food and sociability voice, etc., are discussed in detail. Their anatomy and environment in captivity are also discussed: water for swimming was found desirable, if not necessary. Results of physiological investigations are reported by D.E. Stullken and C.M. Kirkpatrick, q.v

Clustering of solutions in the random satisfiability problem

Using elementary rigorous methods we prove the existence of a clustered phase in the random $K$-SAT problem, for $K\geq 8$. In this phase the solutions are grouped into clusters which are far away from each other. The results are in agreement with previous predictions of the cavity method and give a rigorous confirmation to one of its main building blocks. It can be generalized to other systems of both physical and computational interest.Comment: 4 pages, 1 figur

FIRE Spectroscopy of Five Late-type T Dwarfs Discovered with the Wide-field Infrared Survey Explorer

We present the discovery of five late-type T dwarfs identified with the Wide-field Infrared Survey Explorer (WISE). Low-resolution near-infrared spectroscopy obtained with the Magellan Folded-port InfraRed Echellette (FIRE) reveal strong water and methane absorption in all five sources, and spectral indices and comparison to spectral templates indicate classifications ranging from T5.5 to T8.5:. The spectrum of the latest-type source, WISE J1812+2721, is an excellent match to that of the T8.5 companion brown dwarf Wolf 940B. WISE-based spectrophotometric distance estimates place these T dwarfs at 12-13 pc from the Sun, assuming they are single. Preliminary fits of the spectral data to the atmosphere models of Saumon & Marley indicate effective temperatures ranging from 600 K to 930 K, both cloudy and cloud-free atmospheres, and a broad range of ages and masses. In particular, two sources show evidence of both low surface gravity and cloudy atmospheres, tentatively supporting a trend noted in other young brown dwarfs and exoplanets. In contrast, the high proper motion T dwarf WISE J2018-7423 exhibits a suppressed K-band peak and blue spectrophotometric J-K colors indicative of an old, massive brown dwarf; however, it lacks the broadened Y-band peak seen in metal-poor counterparts. These results illustrate the broad diversity of low-temperature brown dwarfs that will be uncovered with WISE.Comment: 19 pages, 13 figures; accepted for publication to Ap

The statistical mechanics of complex signaling networks : nerve growth factor signaling

It is becoming increasingly appreciated that the signal transduction systems used by eukaryotic cells to achieve a variety of essential responses represent highly complex networks rather than simple linear pathways. While significant effort is being made to experimentally measure the rate constants for individual steps in these signaling networks, many of the parameters required to describe the behavior of these systems remain unknown, or at best, estimates. With these goals and caveats in mind, we use methods of statistical mechanics to extract useful predictions for complex cellular signaling networks. To establish the usefulness of our approach, we have applied our methods towards modeling the nerve growth factor (NGF)-induced differentiation of neuronal cells. Using our approach, we are able to extract predictions that are highly specific and accurate, thereby enabling us to predict the influence of specific signaling modules in determining the integrated cellular response to the two growth factors. We show that extracting biologically relevant predictions from complex signaling models appears to be possible even in the absence of measurements of all the individual rate constants. Our methods also raise some interesting insights into the design and possible evolution of cellular systems, highlighting an inherent property of these systems wherein particular ''soft'' combinations of parameters can be varied over wide ranges without impacting the final output and demonstrating that a few ''stiff'' parameter combinations center around the paramount regulatory steps of the network. We refer to this property -- which is distinct from robustness -- as ''sloppiness.''Comment: 24 pages, 10 EPS figures, 1 GIF (makes 5 multi-panel figs + caption for GIF), IOP style; supp. info/figs. included as brown_supp.pd

Synthesizing and tuning chemical reaction networks with specified behaviours

We consider how to generate chemical reaction networks (CRNs) from functional specifications. We propose a two-stage approach that combines synthesis by satisfiability modulo theories and Markov chain Monte Carlo based optimisation. First, we identify candidate CRNs that have the possibility to produce correct computations for a given finite set of inputs. We then optimise the reaction rates of each CRN using a combination of stochastic search techniques applied to the chemical master equation, simultaneously improving the of correct behaviour and ruling out spurious solutions. In addition, we use techniques from continuous time Markov chain theory to study the expected termination time for each CRN. We illustrate our approach by identifying CRNs for majority decision-making and division computation, which includes the identification of both known and unknown networks.Comment: 17 pages, 6 figures, appeared the proceedings of the 21st conference on DNA Computing and Molecular Programming, 201

Space-time Phase Transitions in Driven Kinetically Constrained Lattice Models

Kinetically constrained models (KCMs) have been used to study and understand the origin of glassy dynamics. Despite having trivial thermodynamic properties, their dynamics slows down dramatically at low temperatures while displaying dynamical heterogeneity as seen in glass forming supercooled liquids. This dynamics has its origin in an ergodic-nonergodic first-order phase transition between phases of distinct dynamical "activity". This is a "space-time" transition as it corresponds to a singular change in ensembles of trajectories of the dynamics rather than ensembles of configurations. Here we extend these ideas to driven glassy systems by considering KCMs driven into non-equilibrium steady states through non-conservative forces. By classifying trajectories through their entropy production we prove that driven KCMs also display an analogous first-order space-time transition between dynamical phases of finite and vanishing entropy production. We also discuss how trajectories with rare values of entropy production can be realized as typical trajectories of a mapped system with modified forces