Hypothesis testing near singularities and boundaries

The likelihood ratio statistic, with its asymptotic $\chi^2$ distribution at regular model points, is often used for hypothesis testing. At model singularities and boundaries, however, the asymptotic distribution may not be $\chi^2$, as highlighted by recent work of Drton. Indeed, poor behavior of a $\chi^2$ for testing near singularities and boundaries is apparent in simulations, and can lead to conservative or anti-conservative tests. Here we develop a new distribution designed for use in hypothesis testing near singularities and boundaries, which asymptotically agrees with that of the likelihood ratio statistic. For two example trinomial models, arising in the context of inference of evolutionary trees, we show the new distributions outperform a $\chi^2$.Comment: 32 pages, 12 figure

Infant Visual Habituation

The use of visual habituation in the study of infant cognition and learning is reviewed. This article traces the history of the technique, underlying theory, and procedural variation in its measurement. In addition, we review empirical findings with respect to the cognitive processes that presumably contribute to habituation, studies of developmental course and long-term prediction, as well as recent attempts to address or explain the phenomenon of visual habituation through the use of mathematical or quantitative models. The review ends with an appeal for a return to the study of habituation per se as a valid measure of infant learning, rather than relegating the phenomenon to its use as a technique for familiarizing infants in procedures testing for discrimination or recognition

Fluctuations and Pinch-Offs Observed in Viscous Fingering

Our experiments on viscous (Saffman-Taylor) fingering in Hele-Shaw channels reveal several phenomena that were not observed in previous experiments. At low flow rates, growing fingers undergo width fluctuations that intermittently narrow the finger as they evolve. The magnitude of these fluctuations is proportional to Ca^{-0.64}, where Ca is the capillary number, which is proportional to the finger velocity. This relation holds for all aspect ratios studied up to the onset of tip instabilities. At higher flow rates, finger pinch-off and reconnection events are observed. These events appear to be caused by an interaction between the actively growing finger and suppressed fingers at the back of the channel. Both the fluctuation and pinch-off phenomena are robust but not explained by current theory.Comment: 6 pages, 3 figures; to appear in Proceedings of the Seventh Experimental Chaos Conferenc

Fluctuations and Pinch-Offs Observed in Viscous Fingering

Our experiments on viscous (Saffman-Taylor) fingering in Hele-Shaw channels reveal several phenomena that were not observed in previous experiments. At low flow rates, growing fingers undergo width fluctuations that intermittently narrow the finger as they evolve. The magnitude of these fluctuations is proportional to Ca^{-0.64}, where Ca is the capillary number, which is proportional to the finger velocity. This relation holds for all aspect ratios studied up to the onset of tip instabilities. At higher flow rates, finger pinch-off and reconnection events are observed. These events appear to be caused by an interaction between the actively growing finger and suppressed fingers at the back of the channel. Both the fluctuation and pinch-off phenomena are robust but not explained by current theory.Comment: 6 pages, 3 figures; to appear in Proceedings of the Seventh Experimental Chaos Conferenc

VoroCrust: Voronoi Meshing Without Clipping

Polyhedral meshes are increasingly becoming an attractive option with particular advantages over traditional meshes for certain applications. What has been missing is a robust polyhedral meshing algorithm that can handle broad classes of domains exhibiting arbitrarily curved boundaries and sharp features. In addition, the power of primal-dual mesh pairs, exemplified by Voronoi-Delaunay meshes, has been recognized as an important ingredient in numerous formulations. The VoroCrust algorithm is the first provably-correct algorithm for conforming polyhedral Voronoi meshing for non-convex and non-manifold domains with guarantees on the quality of both surface and volume elements. A robust refinement process estimates a suitable sizing field that enables the careful placement of Voronoi seeds across the surface circumventing the need for clipping and avoiding its many drawbacks. The algorithm has the flexibility of filling the interior by either structured or random samples, while preserving all sharp features in the output mesh. We demonstrate the capabilities of the algorithm on a variety of models and compare against state-of-the-art polyhedral meshing methods based on clipped Voronoi cells establishing the clear advantage of VoroCrust output.Comment: 18 pages (including appendix), 18 figures. Version without compressed images available on https://www.dropbox.com/s/qc6sot1gaujundy/VoroCrust.pdf. Supplemental materials available on https://www.dropbox.com/s/6p72h1e2ivw6kj3/VoroCrust_supplemental_materials.pd

A generalized AIC for models with singularities and boundaries

The Akaike information criterion (AIC) is a common tool for model selection. It is frequently used in violation of regularity conditions at parameter space singularities and boundaries. The expected AIC is generally not asymptotically equivalent to its target at singularities and boundaries, and convergence to the target at nearby parameter points may be slow. We develop a generalized AIC for candidate models with or without singularities and boundaries. We show that the expectation of this generalized form converges everywhere in the parameter space, and its convergence can be faster than that of the AIC. We illustrate the generalized AIC on example models from phylogenomics, showing that it can outperform the AIC and gives rise to an interpolated effective number of model parameters, which can differ substantially from the number of parameters near singularities and boundaries. We outline methods for estimating the often unknown generating parameter and bias correction term of the generalized AIC.Comment: 21 pages, 5 figure

Interspecific Competition for Pollination Lowers Seed Production and Outcrossing in Mimulus Ringens

Sympatric plant species with similar flowering phenologies and floral morphologies may compete for pollination, and as a consequence potentially influence each other\u27s reproductive success and mating system. Two likely competitors are Mimulus ringens and Lobelia siphilitica, which co-occur in wet meadows of central and eastern North America, produce blue zygomorphic flowers, and share several species of bumble bee pollinators. To test for effects of competition for pollination, we planted experimental arrays of Mimulus ringens, each consisting of genets with unique combinations of homozygous marker genotypes. In two arrays we planted mixtures of Mimulus and Lobelia. and in two additional arrays we planted Mimulus without a competitor for pollination. Bumble bee pollinators frequently moved between Mimulus and Lobelia flowers in the mixed-species arrays, with 42% of plant-to-plant movements being interspecific transitions. Pollinator movements between species were associated with a reduction in the amount of conspecific pollen arriving on Mimulus stigmas. The presence of Lobelia led to a significant 37% reduction in the mean number of Mimulus seeds per fruit. In addition, Mimulus had a significantly lower rate of outcrossing in the mixed-species arrays (0.43) than in the pure arrays (0.63). This is the first study to demonstrate that competition for pollination directly influences outcrossing rates. Our work suggests that in self-compatible populations with genetic load, competition for pollination may not only reduce seed quantity, but may also lower seed quality

Activin-A and Bmp4 Levels Modulate Cell Type Specification during CHIR-Induced Cardiomyogenesis

The use of human pluripotent cell progeny for cardiac disease modeling, drug testing and therapeutics requires the ability to efficiently induce pluripotent cells into the cardiomyogenic lineage. Although direct activation of the Activin-A and/or Bmp pathways with growth factors yields context-dependent success, recent studies have shown that induction of Wnt signaling using low molecular weight molecules such as CHIR, which in turn induces the Activin-A and Bmp pathways, is widely effective. To further enhance the reproducibility of CHIR-induced cardiomyogenesis, and to ultimately promote myocyte maturation, we are using exogenous growth factors to optimize cardiomyogenic signaling downstream of CHIR induction. As indicated by RNA-seq, induction with CHIR during Day 1 (Days 0–1) was followed by immediate expression of Nodal ligands and receptors, followed later by Bmp ligands and receptors. Co-induction with CHIR and high levels of the Nodal mimetic Activin-A (50–100 ng/ml) during Day 0–1 efficiently induced definitive endoderm, whereas CHIR supplemented with Activin-A at low levels (10 ng/ml) consistently improved cardiomyogenic efficiency, even when CHIR alone was ineffective. Moreover, co-induction using CHIR and low levels of Activin-A apparently increased the rate of cardiomyogenesis, as indicated by the initial appearance of rhythmically beating cells by Day 6 instead of Day 8. By contrast, co-induction with CHIR plus low levels (3–10 ng/ml) of Bmp4 during Day 0–1 consistently and strongly inhibited cardiomyogenesis. These findings, which demonstrate that cardiomyogenic efficacy is improved by optimizing levels of CHIR-induced growth factors when applied in accord with their sequence of endogenous expression, are consistent with the idea that Nodal (Activin-A) levels toggle the entry of cells into the endodermal or mesodermal lineages, while Bmp levels regulate subsequent allocation into mesodermal cell types