Bayesian Nonparametric Hidden Semi-Markov Models

There is much interest in the Hierarchical Dirichlet Process Hidden Markov Model (HDP-HMM) as a natural Bayesian nonparametric extension of the ubiquitous Hidden Markov Model for learning from sequential and time-series data. However, in many settings the HDP-HMM's strict Markovian constraints are undesirable, particularly if we wish to learn or encode non-geometric state durations. We can extend the HDP-HMM to capture such structure by drawing upon explicit-duration semi-Markovianity, which has been developed mainly in the parametric frequentist setting, to allow construction of highly interpretable models that admit natural prior information on state durations. In this paper we introduce the explicit-duration Hierarchical Dirichlet Process Hidden semi-Markov Model (HDP-HSMM) and develop sampling algorithms for efficient posterior inference. The methods we introduce also provide new methods for sampling inference in the finite Bayesian HSMM. Our modular Gibbs sampling methods can be embedded in samplers for larger hierarchical Bayesian models, adding semi-Markov chain modeling as another tool in the Bayesian inference toolbox. We demonstrate the utility of the HDP-HSMM and our inference methods on both synthetic and real experiments

Density regulation in strictly metric-free swarms

There is now experimental evidence that nearest-neighbour interactions in flocks of birds are metric free, i.e. they have no characteristic interaction length scale. However, models that involve interactions between neighbours that are assigned topologically are naturally invariant under spatial expansion, supporting a continuous reduction in density towards zero, unless additional cohesive interactions are introduced or the density is artificially controlled, e.g. via a finite system size. We propose a solution that involves a metric-free motional bias on those individuals that are topologically identified to be on an edge of the swarm. This model has only two primary control parameters, one controlling the relative strength of stochastic noise to the degree of co-alignment and another controlling the degree of the motional bias for those on the edge, relative to the tendency to co-align. We find a novel power-law scaling of the real-space density with the number of individuals N as well as a familiar order-to-disorder transition

Building the Infrastructure: The Effects of Role Identification Behaviors on Team Cognition Development and Performance

The primary purpose of this study was to extend theory and research regarding the emergence of mental models and transactive memory in teams. Utilizing Kozlowski et al.’s (1999) model of team compilation, we examine the effect of role identification behaviors and argue that such behaviors represent the initial building blocks of team cognition during the role compilation phase of team development. We then hypothesized that team mental models and transactive memory would convey the effects of these behaviors onto team performance in the team compilation phase of development. Results from 60 teams working on a command and control simulation supported our hypotheses

Selection of neutralizing antibody escape mutants with type A influenza virus HA-specific polyclonal antisera: possible significance for antigenic drift

Ten antisera were produced in rabbits by two or three intravenous injections of inactivated whole influenza type A virions. All contained haemagglutination-inhibition (HI) antibody directed predominantly to an epitope in antigenic site B and, in addition, various amounts of antibodies to an epitope in site A and in site D. The ability of untreated antisera to select neutralization escape mutants was investigated by incubating virus possessing the homologous haemagglutinin with antiserum adjusted to contain anti-B epitope HI titres of 100, 1000 and 10000 HIU/ml. Virus-antiserum mixtures were inoculated into embryonated hen's eggs, and progeny virus examined without further selection. Forty percent of the antisera at a titre of 1000 HIU/ml selected neutralizing antibody escape mutants as defined by their lack of reactivity to Mab HC10 (site B), and unchanged reactivity to other Mabs to site A and site D epitopes. All escape mutant-selecting antisera had a ratio of anti-site B (HC10)-epitope antibody[ratio]other antibodies of [gt-or-equal, slanted]2·0[ratio]1. The antiserum with the highest ratio (7·4[ratio]1) selected escape mutants in all eggs tested in four different experiments. No antiserum used at a titre of 10000 HIU/ml allowed multiplication of any virus. All antisera used at a titre of 100 HIU/ml permitted virus growth, but this was wild-type (wt) virus. We conclude that a predominant epitope-specific antibody response, a titre of [gt-or-equal, slanted]1000 HIU/ml, and a low absolute titre of other antibodies ([less-than-or-eq, slant]500 HIU/ml) are three requirements for the selection of escape mutants. None of the antisera in this study could have selected escape mutants without an appropriate dilution factor, so the occurrence of an escape mutant-selecting antiserum in nature is likely to be a rare event

Constrained hyperbolic divergence cleaning in smoothed particle magnetohydrodynamics with variable cleaning speeds

We present an updated constrained hyperbolic/parabolic divergence cleaning algorithm for smoothed particle magnetohydrodynamics (SPMHD) that remains conservative with wave cleaning speeds which vary in space and time. This is accomplished by evolving the quantity $\psi / c_h$ instead of $\psi$. Doing so allows each particle to carry an individual wave cleaning speed, $c_h$, that can evolve in time without needing an explicit prescription for how it should evolve, preventing circumstances which we demonstrate could lead to runaway energy growth related to variable wave cleaning speeds. This modification requires only a minor adjustment to the cleaning equations and is trivial to adopt in existing codes. Finally, we demonstrate that our constrained hyperbolic/parabolic divergence cleaning algorithm, run for a large number of iterations, can reduce the divergence of the field to an arbitrarily small value, achieving $\nabla \cdot B=0$ to machine precision.Comment: 23 pages, 16 figures, accepted for publication in Journal of Computational Physic

Distance and intersection number in the curve graph of a surface

In this work, we study the cellular decomposition of $S$ induced by a filling pair of curves $v$ and $w$, $Dec_{v,w}(S) = S - (v \cup w)$, and its connection to the distance function $d(v,w)$ in the curve graph of a closed orientable surface $S$ of genus $g$. Efficient geodesics were introduced by the first author in joint work with Margalit and Menasco in 2016, giving an algorithm that begins with a pair of non-separating filling curves that determine vertices $(v,w)$ in the curve graph of a closed orientable surface $S$ and computing from them a finite set of {\it efficient} geodesics. We extend the tools of efficient geodesics to study the relationship between distance $d(v,w)$, intersection number $i(v,w)$, and $Dec_{v,w}(S)$. The main result is the development and analysis of particular configurations of rectangles in $Dec_{v,w}(S)$ called \textit{spirals}. We are able to show that, in some special cases, the efficient geodesic algorithm can be used to build an algorithm that reduces $i(v,w)$ while preserving $d(v,w)$. At the end of the paper, we note a connection of our work to the notion of extending geodesics.Comment: 20 pages, 17 figures. Changes: A key lemma (Lemma 5.6) was revised to be more precise, an irrelevant proposition (Proposition 2.1) and example were removed, unnecessary background material was taken out, some of the definitions and cited results were clarified (including added figures,) and Proposition 5.7 and Theorem 5.8 have been merged into a single theorem, Theorem 4.

Efficacy of Morphological Characters for Distinguishing Nymphs of \u3ci\u3eEpitheca Cynosura\u3c/i\u3e and \u3ci\u3eEpitheca Spinigera\u3c/i\u3e (Odonata: Corduliidae) in Wisconsin

Attempts to distinguish exuviae and last-instar nymphs of Epitheca cynosura (Say) and Epitheca spinigera (Selys) (Odonata: Corduliidae) using lateral spine characters have proven to be unreliable, and recent use of setae counts on only one side of the prementum or one labial palp have led to confusion because these structures often hold unequal numbers of setae on the two sides of the same specimen. Based on exuviae of 67 reared E. cynosura and 55 reared E. spinigera from lakes throughout Wisconsin, we tested the efficacy of previously used character states for distinguishing these species and searched for new characters to improve the reliability of regional keys. The most reliable diagnostic character was the combined number of setae on both sides of the prementum and on both labial palps (≤ 35 – E. cynosura; ≥ 36 – E. spinigera), which correctly determined 96% of our specimens. For the small percentage of specimens that lie in the region of overlap in total setae number, we found that total exuviae length, cerci ÷ epiproct ratios of females, tubercle distance ÷ epiproct ratios of males, and the shape of the dorsal hook on segment 8 could be used to strengthen determinations