Zero biasing and growth processes

The tools of zero biasing are adapted to yield a general result suitable for analyzing the behavior of certain growth processes. The main theorem is applied to prove central limit theorems, with explicit error terms in the L^1 metric, for certain statistics of the Jack measure on partitions and for the number of balls drawn in a Polya-Eggenberger urn process.Comment: 21 pages. Error in one term of the bound of the main theorem has been corrected, resulting in some changes to the bound for urn proces

Stein's method and the rank distribution of random matrices over finite fields

With ${\mathcal{Q}}_{q,n}$ the distribution of $n$ minus the rank of a matrix chosen uniformly from the collection of all $n\times(n+m)$ matrices over the finite field $\mathbb{F}_q$ of size $q\ge2$, and ${\mathcal{Q}}_q$ the distributional limit of ${\mathcal{Q}}_{q,n}$ as $n\rightarrow\infty$, we apply Stein's method to prove the total variation bound $\frac{1}{8q^{n+m+1}}\leq\|{\mathcal{Q}}_{q,n}-{\mathcal{Q}}_q\|_{\mathrm{TV}}\leq\frac{3}{q^{n+m+1}}$. In addition, we obtain similar sharp results for the rank distributions of symmetric, symmetric with zero diagonal, skew symmetric, skew centrosymmetric and Hermitian matrices.Comment: Published at http://dx.doi.org/10.1214/13-AOP889 in the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org

Influence of Natural Inshore and Offshore Thermal Regimes on Egg Development and Time of Hatch in American lobsters, Homarus americanus

Some egg-bearing (ovigerous) American lobsters (Homarus americanus) make seasonal inshore-to-offshore movements, subjecting their eggs to different thermal regimes than those of eggs carried by lobsters that do not make these movements. Our goal was to determine if differences in thermal regimes influence the rate of egg development and the subsequent time of hatch. We subjected ovigerous lobsters to typical inshore or offshore water temperatures from September to August in the laboratory (n = 8 inshore and 8 offshore, each year) and in the field (n = 8 each, inshore and offshore), over 2 successive years. Although the rate of egg development did not differ significantly between treatments in the fall (P ∼ 0.570), eggs exposed to inshore thermal regimes developed faster in the spring (P \u3c 0.001). “Inshore” eggs hatched about 30 days earlier (mean = 26 June) than “offshore” eggs (mean = 27 July), and their time of development from the onset of eyespot to hatch was significantly shorter (inshore = 287 ± 11 days vs. offshore: 311.5 ± 7.5 days, P = 0.034). Associated growing degree-days (GDD) did not differ significantly between inshore and offshore thermal treatments (P = 0.061). However, eggs retained by lobsters exposed to offshore thermal regimes accumulated more GDD in the winter than did eggs carried by inshore lobsters, while eggs exposed to inshore temperatures acquired them more rapidly in the spring. Results suggest that seasonal movements of ovigerous lobsters influence the time and location of hatching, and thus the transport and recruitment of larvae to coastal and offshore locations

Descriptions of the setae on the pereiopods of scyllarid lobsters, Scyllarides aequinoctialis, S. latus, and S. nodifer, with observations on the feeding sequence during consumption of bivalves and gastropods

The morphological and behavioral aspects of slipper lobster feeding have remained largely unexplored. Using Scanning Electron Microscopy (SEM), the gross morphological structure of all segments of the pereiopods were described for three species of scyllarid lobsters: Scyllarides aequinoctialis, S. latus, and S. nodifer. Five types of setae within three broad categories were found: simple (long and miniature), cuspidate (robust and conate), and teasel (a type of serrulate setae). Setae were arranged in a highly organized, row-like pattern on the ventral and dorsal surfaces. Cuspidate setae were found on all surfaces of all segments. Simple setae were found only on the dactyl, whereas teazel setae were concentrated on the lateral-most edge of the alate carina on the merus in S. aequinoctialis only. Comparisons among species demonstrate that S. nodifer bears the same setae and setal pattern as S. latus, but S. aequinoctialis differs. The setal patterns of slipper lobsters contrast with those of nephropid and palinurid lobsters, likely due to the more rigorous use of the pereiopods in accessing their food. Feeding sequences of S. aequinoctialis on bivalves were videotaped, analyzed as Markovian chains, and showed a complex suite of behaviors involving contact chemoreception by the antennules as part of an initial assessment of food items, followed by mouthpart and leg probing, and eventual wedging behavior as previously described for S. squammosus. Feeding sequences of S. latus on gastropods and bivalves also demonstrate extensive use of the pereiopods (instead of the mouthparts) first to pry these prey items from the substrate and then to remove the foot. Use of antennules for food assessment and recruitment of many of the perieopods for food handling with minimal use of mouthparts also contrasts with the feeding sequences typical of nephropid and palinurid lobsters and may be an important adaptation

The role of self-discrepancies in American Jewish identities on mental and spiritual well-being.

Contemporary American Jews individually define their own Jewish identity developed through both religious and cultural foundations (Cohen & Eisen, 2000), yet there is limited empirical research on the experience of Jewish identity and its impact on mental and spiritual well-being. Beyond denominational affiliation, each Jewish individual builds a Jewish identity based on personally desired levels of participation in one’s Jewish community (Ideal Jewish Identity) as well as perceived expectations and obligations of a Jewish life (Ought Jewish Identity), although the internalized desires and expectations may not be fulfilled. Building upon the foundation established by Rogers (1954) and Higgins (1986), the perception of not being a “good enough Jew” can be conceptualized as self-discrepancies in one’s Jewish identity and may result in negative psychological and spiritual consequences. A large sample (N = 829) of Americans self-identifying as Jewish participated in an online survey which included completion of the American Jewish Identity Scale (Friedlander et al., 2010) from two different perspectives to calculate discrepancies. Results showed that Jews identified both Ideal and Ought Jewish self-discrepancies, religious Ideal and cultural Ought discrepancies demonstrated small positive effects on the presence of anxiety and depressive symptoms, and religious discrepancies positively impacted religious well-being. The perception of failing to meet the idiosyncratically defined desires and expectations of one’s Jewish identity, particularly concerning level of involvement in one’s cultural community, appears to reduce mental well-being while also stimulating motivation to increase religious participation. Exploration of Jewish identity, whether within empirical studies or affirmative therapy for Jewish individuals, would benefit from expanding the scope of understanding beyond denominational affiliation to include self-discrepancies in one’s religious and cultural identities

The impact of seasonal movements by ovigerous American lobsters (Homarus americanus) on egg development and larval release

The American lobster (Homarus americanus) supports one of the most economically successful fisheries in the Gulf of Maine. The continued success of this fishery is attributed in part to vigilant broodstock conservation through the preservation of ovigerous (egg-bearing) females. Previous studies of ovigerous lobster movements indicate that some, if not most, display seasonal inshore-to-offshore movement patterns. While it has been assumed that these movements serve to expose eggs to thermal regimes that are optimal for development, this theory has never been rigorously tested. In Chapter 1, I present results from ultrasonic tracking studies designed to determine if lobsters in coastal New Hampshire waters exhibit this inshore-offshore pattern and also to identify where ovigerous females overwinter. In Chapter 2, I assess how the movements of ovigerous lobsters would influence the temperature regimes they experienced and thus the development of their eggs. I evaluate this question using a combination of laboratory and field experiments that expose animals to seasonally fluctuating water temperatures they would experience if they remained inshore or moved offshore; data from these experiments were then used to determine the influence of these thermal regimes on egg development, time to hatch, and larval survival. Finally, in Chapter 3, I present results from a study using experimental ocean drifters deployed in areas where ovigerous females were located when their eggs hatched, to determine where these larvae might drift. Ultrasonic tracking revealed that most lobsters move offshore in the fall and ovigerous lobsters tend to remain there until after their eggs hatch the following summer (Chapter 1). Eggs exposed to disparate thermal regimes (inshore and offshore) demonstrated that eggs carried by lobsters that moved offshore actually hatched later than those exposed to inshore temperatures (Chapter 2). Finally, most drifters released in offshore hatching locations were carried south or to offshore locations at the time when larvae would settle (Chapter 3). Taken together, these results suggest that seasonal movements of ovigerous lobsters have a strong influence on when and where eggs hatch and, subsequently, where larvae may settle. These findings have significant implications for population connectivity and management of the lobster fishery

A Noninvasive Method For In situ Determination of Mating Success in Female American Lobsters (Homarus americanus)

Despite being one of the most productive fisheries in the Northwest Atlantic, much remains unknown about the natural reproductive dynamics of American lobsters. Recent work in exploited crustacean populations (crabs and lobsters) suggests that there are circumstances where mature females are unable to achieve their full reproductive potential due to sperm limitation. To examine this possibility in different regions of the American lobster fishery, a reliable and noninvasive method was developed for sampling large numbers of female lobsters at sea. This method involves inserting a blunt-tipped needle into the female\u27s seminal receptacle to determine the presence or absence of a sperm plug and to withdraw a sample that can be examined for the presence of sperm. A series of control studies were conducted at the dock and in the laboratory to test the reliability of this technique. These efforts entailed sampling 294 female lobsters to confirm that the presence of a sperm plug was a reliable indicator of sperm within the receptacle and thus, mating. This paper details the methodology and the results obtained from a subset of the total females sampled. Of the 230 female lobsters sampled from George\u27s Bank and Cape Ann, MA (size range = 71-145 mm in carapace length), 90.3% were positive for sperm. Potential explanations for the absence of sperm in some females include: immaturity (lack of physiological maturity), breakdown of the sperm plug after being used to fertilize a clutch of eggs, and lack of mating activity. The surveys indicate that this technique for examining the mating success of female lobsters is a reliable proxy that can be used in the field to document reproductive activity in natural populations