A mathematical theory of stochastic microlensing. II. Random images, shear, and the Kac-Rice formula

Continuing our development of a mathematical theory of stochastic microlensing, we study the random shear and expected number of random lensed images of different types. In particular, we characterize the first three leading terms in the asymptotic expression of the joint probability density function (pdf) of the random shear tensor due to point masses in the limit of an infinite number of stars. Up to this order, the pdf depends on the magnitude of the shear tensor, the optical depth, and the mean number of stars through a combination of radial position and the star's mass. As a consequence, the pdf's of the shear components are seen to converge, in the limit of an infinite number of stars, to shifted Cauchy distributions, which shows that the shear components have heavy tails in that limit. The asymptotic pdf of the shear magnitude in the limit of an infinite number of stars is also presented. All the results on the random microlensing shear are given for a general point in the lens plane. Extending to the general random distributions (not necessarily uniform) of the lenses, we employ the Kac-Rice formula and Morse theory to deduce general formulas for the expected total number of images and the expected number of saddle images. We further generalize these results by considering random sources defined on a countable compact covering of the light source plane. This is done to introduce the notion of global expected number of positive parity images due to a general lensing map. Applying the result to microlensing, we calculate the asymptotic global expected number of minimum images in the limit of an infinite number of stars, where the stars are uniformly distributed. This global expectation is bounded, while the global expected number of images and the global expected number of saddle images diverge as the order of the number of stars. © 2009 American Institute of Physics.

Early-life soy exposure and age at menarche.

This study examines the timing of menarche in relation to infant-feeding methods, specifically addressing the potential effects of soy isoflavone exposure through soy-based infant feeding. Subjects were participants in the Avon Longitudinal Study of Parents and Children (ALSPAC). Mothers were enrolled during pregnancy and their children have been followed prospectively. Early-life feeding regimes, categorised as primarily breast, early formula, early soy and late soy, were defined using infant-feeding questionnaires administered during infancy. For this analysis, age at menarche was assessed using questionnaires administered approximately annually between ages 8 and 14.5. Eligible subjects were limited to term, singleton, White females. We used Kaplan-Meier survival curves and Cox proportional hazards models to assess age at menarche and risk of menarche over the study period. The present analysis included 2920 girls. Approximately 2% of mothers reported that soy products were introduced into the infant diet at or before 4 months of age (early soy). The median age at menarche [interquartile range (IQR)] in the study sample was 153 months [144-163], approximately 12.8 years. The median age at menarche among early soy-fed girls was 149 months (12.4 years) [IQR, 140-159]. Compared with girls fed non-soy-based infant formula or milk (early formula), early soy-fed girls were at 25% higher risk of menarche throughout the course of follow-up (hazard ratio 1.25 [95% confidence interval 0.92, 1.71]). Our results also suggest that girls fed soy products in early infancy may have an increased risk of menarche specifically in early adolescence. These findings may be the observable manifestation of mild endocrine-disrupting effects of soy isoflavone exposure. However, our study is limited by few soy-exposed subjects and is not designed to assess biological mechanisms. Because soy formula use is common in some populations, this subtle association with menarche warrants more in-depth evaluation in future studies.

Olfactory conditioning facilitates diet transition in human infants.

We evaluated whether Pavlovian conditioning methods could be used to increase the ingestion of non-preferred solutions by formula-fed human infants. In baseline measures, 5-7 month old infants sucked less frequently and consumed less water than regular formula. During a 3-day olfactory conditioning period, parents placed a small scented disk, the conditioned stimulus, on the rim of their infants' formula bottle at every feeding. Following this training, infants' responses to water were tested when their water bottles had a disk scented with the training odor, a novel odor, or no odor. Infants tested with the training odor sucked more frequently and consumed significantly more water than they had at baseline. Infants tested with no odor or a novel odor consumed water at or below baseline levels. These data demonstrate that olfactory conditioning can be used to enhance ingestion in infants and suggest that such methods may be useful for infants experiencing difficulty when making transitions from one diet to another.

Overview of FEED, the feeding experiments end-user database.

The Feeding Experiments End-user Database (FEED) is a research tool developed by the Mammalian Feeding Working Group at the National Evolutionary Synthesis Center that permits synthetic, evolutionary analyses of the physiology of mammalian feeding. The tasks of the Working Group are to compile physiologic data sets into a uniform digital format stored at a central source, develop a standardized terminology for describing and organizing the data, and carry out a set of novel analyses using FEED. FEED contains raw physiologic data linked to extensive metadata. It serves as an archive for a large number of existing data sets and a repository for future data sets. The metadata are stored as text and images that describe experimental protocols, research subjects, and anatomical information. The metadata incorporate controlled vocabularies to allow consistent use of the terms used to describe and organize the physiologic data. The planned analyses address long-standing questions concerning the phylogenetic distribution of phenotypes involving muscle anatomy and feeding physiology among mammals, the presence and nature of motor pattern conservation in the mammalian feeding muscles, and the extent to which suckling constrains the evolution of feeding behavior in adult mammals. We expect FEED to be a growing digital archive that will facilitate new research into understanding the evolution of feeding anatomy.

Muscle Logic: New Knowledge Resource for Anatomy Enables Comprehensive Searches of the Literature on the Feeding Muscles of Mammals.

BACKGROUND: In recent years large bibliographic databases have made much of the published literature of biology available for searches. However, the capabilities of the search engines integrated into these databases for text-based bibliographic searches are limited. To enable searches that deliver the results expected by comparative anatomists, an underlying logical structure known as an ontology is required. DEVELOPMENT AND TESTING OF THE ONTOLOGY: Here we present the Mammalian Feeding Muscle Ontology (MFMO), a multi-species ontology focused on anatomical structures that participate in feeding and other oral/pharyngeal behaviors. A unique feature of the MFMO is that a simple, computable, definition of each muscle, which includes its attachments and innervation, is true across mammals. This construction mirrors the logical foundation of comparative anatomy and permits searches using language familiar to biologists. Further, it provides a template for muscles that will be useful in extending any anatomy ontology. The MFMO is developed to support the Feeding Experiments End-User Database Project (FEED, https://feedexp.org/), a publicly-available, online repository for physiological data collected from in vivo studies of feeding (e.g., mastication, biting, swallowing) in mammals. Currently the MFMO is integrated into FEED and also into two literature-specific implementations of Textpresso, a text-mining system that facilitates powerful searches of a corpus of scientific publications. We evaluate the MFMO by asking questions that test the ability of the ontology to return appropriate answers (competency questions). We compare the results of queries of the MFMO to results from similar searches in PubMed and Google Scholar. RESULTS AND SIGNIFICANCE: Our tests demonstrate that the MFMO is competent to answer queries formed in the common language of comparative anatomy, but PubMed and Google Scholar are not. Overall, our results show that by incorporating anatomical ontologies into searches, an expanded and anatomically comprehensive set of results can be obtained. The broader scientific and publishing communities should consider taking up the challenge of semantically enabled search capabilities.