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.

Detecting separate time scales in genetic expression data.

BACKGROUND: Biological processes occur on a vast range of time scales, and many of them occur concurrently. As a result, system-wide measurements of gene expression have the potential to capture many of these processes simultaneously. The challenge however, is to separate these processes and time scales in the data. In many cases the number of processes and their time scales is unknown. This issue is particularly relevant to developmental biologists, who are interested in processes such as growth, segmentation and differentiation, which can all take place simultaneously, but on different time scales. RESULTS: We introduce a flexible and statistically rigorous method for detecting different time scales in time-series gene expression data, by identifying expression patterns that are temporally shifted between replicate datasets. We apply our approach to a Saccharomyces cerevisiae cell-cycle dataset and an Arabidopsis thaliana root developmental dataset. In both datasets our method successfully detects processes operating on several different time scales. Furthermore we show that many of these time scales can be associated with particular biological functions. CONCLUSIONS: The spatiotemporal modules identified by our method suggest the presence of multiple biological processes, acting at distinct time scales in both the Arabidopsis root and yeast. Using similar large-scale expression datasets, the identification of biological processes acting at multiple time scales in many organisms is now possible.

Eco-evolutionary trophic dynamics: loss of top predators drives trophic evolution and ecology of prey.

Ecosystems are being altered on a global scale by the extirpation of top predators. The ecological effects of predator removal have been investigated widely; however, predator removal can also change natural selection acting on prey, resulting in contemporary evolution. Here we tested the role of predator removal on the contemporary evolution of trophic traits in prey. We utilized a historical introduction experiment where Trinidadian guppies (Poecilia reticulata) were relocated from a site with predatory fishes to a site lacking predators. To assess the trophic consequences of predator release, we linked individual morphology (cranial, jaw, and body) to foraging performance. Our results show that predator release caused an increase in guppy density and a "sharpening" of guppy trophic traits, which enhanced food consumption rates. Predator release appears to have shifted natural selection away from predator escape ability and towards resource acquisition ability. Related diet and mesocosm studies suggest that this shift enhances the impact of guppies on lower trophic levels in a fashion nuanced by the omnivorous feeding ecology of the species. We conclude that extirpation of top predators may commonly select for enhanced feeding performance in prey, with important cascading consequences for communities and ecosystems.

When strangers pass: processing of mutual and averted social gaze in the superior temporal sulcus.

Using functional magnetic resonance imaging (fMRI), we investigated brain activity evoked by mutual and averted gaze in a compelling and commonly experienced social encounter. Through virtual-reality goggles, subjects viewed a man who walked toward them and shifted his neutral gaze either toward (mutual gaze) or away (averted gaze) from them. Robust activity was evoked in the superior temporal sulcus (STS) and fusiform gyrus (FFG). For both conditions, STS activity was strongly right lateralized. Mutual gaze evoked greater activity in the STS than did averted gaze, whereas the FFG responded equivalently to mutual and averted gaze. Thus, we show that the STS is involved in processing social information conveyed by shifts in gaze within an overtly social context. This study extends understanding of the role of the STS in social cognition and social perception by demonstrating that it is highly sensitive to the context in which a human action occurs.

Impaired formation of beta-adrenergic receptor-nucleotide regulatory protein complexes in pseudohypoparathyroidism.

Decreased activity of the guanine nucleotide regulatory protein (N) of the adenylate cyclase system is present in cell membranes of some patients with pseudohypoparathyrodism (PHP-Ia) whereas others have normal activity of N (PHP-Ib). Low N activity in PHP-Ia results in a decrease in hormone (H)-stimulatable adenylate cyclase in various tissues, which might be due to decreased ability to form an agonist-specific high affinity complex composed of H, receptor (R), and N. To test this hypothesis, we compared beta-adrenergic agonist-specific binding properties in erythrocyte membranes from five patients with PHP-Ia (N = 45% of control), five patients with PHP-Ib (N = 97%), and five control subjects. Competition curves that were generated by increasing concentrations of the beta-agonist isoproterenol competing with [125I]pindolol were shallow (slope factors less than 1) and were computer fit to a two-state model with corresponding high and low affinity for the agonist. The agonist competition curves from the PHP-Ia patients were shifted significantly (P less than 0.02) to the right as a result of a significant (P less than 0.01) decrease in the percent of beta-adrenergic receptors in the high affinity state from 64 +/- 22% in PHP-Ib and 56 +/- 5% in controls to 10 +/- 8% in PHP-Ia. The agonist competition curves were computer fit to a "ternary complex" model for the two-step reaction: H + R + N in equilibrium HR + N in equilibrium HRN. The modeling was consistent with a 60% decrease in the functional concentration of N, and was in good agreement with the biochemically determined decrease in erythrocyte N protein activity. These in vitro findings in erythrocytes taken together with the recent observations that in vivo isoproterenol-stimulated adenylate cyclase activity is decreased in patients with PHP (Carlson, H. E., and A. S. Brickman, 1983, J. Clin. Endocrinol. Metab. 56:1323-1326) are consistent with the notion that N is a bifunctional protein interacting with both R and the adenylate cyclase. It may be that in patients with PHP-Ia a single molecular and genetic defect accounts for both decreased HRN formation and decreased adenylate cyclase activity, whereas in PHP-Ib the biochemical lesion(s) appear not to affect HRN complex formation.

Facts and Fictions: Feminist Literary Criticism and Cultural Critique, 1968-2012

"Facts and Fictions: Feminist Literary Criticism and Cultural Critique, 1968-2012" is a critical history of the unfolding of feminist literary study in the US academy. It contributes to current scholarly efforts to revisit the 1970s by reconsidering often-repeated narratives about the critical naivety of feminist literary criticism in its initial articulation. As the story now goes, many of the most prominent feminist thinkers of the period engaged in unsophisticated literary analysis by conflating lived social reality with textual representation when they read works of literature as documentary evidence of real life. As a result, the work of these "bad critics," particularly Kate Millett and Andrea Dworkin, has not been fully accounted for in literary critical terms.

This dissertation returns to Dworkin and Millett's work to argue for a different history of feminist literary criticism. Rather than dismiss their work for its conflation of fact and fiction, I pay attention to the complexity at the heart of it, yielding a new perspective on the history and persistence of the struggle to use literary texts for feminist political ends. Dworkin and Millett established the centrality of reality and representation to the feminist canon debates of "the long 1970s," the sex wars of the 1980s, and the more recent feminist turn to memoir. I read these productive periods in feminist literary criticism from 1968 to 2012 through their varied commitment to literary works.

Chapter One begins with Millett, who de-aestheticized male-authored texts to treat patriarchal literature in relation to culture and ideology. Her mode of literary interpretation was so far afield from the established methods of New Criticism that she was not understood as a literary critic. She was repudiated in the feminist literary criticism that followed her and sought sympathetic methods for reading women's writing. In that decade, the subject of Chapter Two, feminist literary critics began to judge texts on the basis of their ability to accurately depict the reality of women's experiences.

Their vision of the relationship between life and fiction shaped arguments about pornography during the sex wars of the 1980s, the subject of Chapter Three. In this context, Dworkin was feminism's "bad critic." I focus on the literary critical elements of Dworkin's theories of pornographic representation and align her with Millett as a miscategorized literary critic. In the decades following the sex wars, many of the key feminist literary critics of the founding generation (including Dworkin, Jane Gallop, Carolyn Heilbrun, and Millett) wrote memoirs that recounted, largely in experiential terms, the history this dissertation examines. Chapter Four considers the story these memoirists told about the rise and fall of feminist literary criticism. I close with an epilogue on the place of literature in a feminist critical enterprise that has shifted toward privileging theory.

Monitoring maternal Beta carotene and retinol consumption may decrease the incidence of neurodevelopmental disorders in offspring.

Retinoic acids (13-cis and 13-trans) are known teratogens, and their precursor is retinol, a form of vitamin A. In 1995, Rothman et al demonstrated an association between excessive vitamin A, >10,000 IU/day, during the first trimester of pregnancy and teratogenic effects, particularly in the central nervous system. However, vitamin A deficiency has long been known to be deleterious to the mother and fetus. Therefore, there may be a narrow therapeutic ratio for vitamin A during pregnancy that has not previously been fully appreciated. Neurodevelopmental disorders may not be apparent by macroscopic brain examination or imaging, and proving the existence of a behavioral teratogen is not straightforward. However, an excess of retinoic acid and some neurodevelopmental disorders are both associated with abnormalities in cerebellar morphology. Physical and chemical evidence strongly supports the notion that beta carotene crosses the placenta and is metabolized to retinol. Only very limited amounts of beta carotene are stored in fetal fat cells as evidenced by the fact that maternal fat is yellow from beta carotene, whereas non-brown neonatal fat is white. Furthermore, newborns of carotenemic mothers do not share the yellow complexion of their mothers. The excess 13-trans retinoic acid derived from metabolized beta carotene in the fetus increases the concentration of the more teratogenic 13-cis retinoic acid since the isomerization equilibrium is shifted to the left. Therefore, this paper proposes that consideration be given to monitoring all potential sources of fetal 13-cis and 13-trans retinoic acid, including nutritional supplements, dietary retinol, and beta carotene, particularly in the first trimester of pregnancy.

Long-duration animal tracking in difficult lighting conditions.

High-throughput analysis of animal behavior requires software to analyze videos. Such software typically depends on the experiments' being performed in good lighting conditions, but this ideal is difficult or impossible to achieve for certain classes of experiments. Here, we describe techniques that allow long-duration positional tracking in difficult lighting conditions with strong shadows or recurring "on"/"off" changes in lighting. The latter condition will likely become increasingly common, e.g., for Drosophila due to the advent of red-shifted channel rhodopsins. The techniques enabled tracking with good accuracy in three types of experiments with difficult lighting conditions in our lab. Our technique handling shadows relies on single-animal tracking and on shadows' and flies' being accurately distinguishable by distance to the center of the arena (or a similar geometric rule); the other techniques should be broadly applicable. We implemented the techniques as extensions of the widely-used tracking software Ctrax; however, they are relatively simple, not specific to Drosophila, and could be added to other trackers as well.

A whole-cell and single-channel study of the voltage-dependent outward potassium current in avian hepatocytes.

Voltage-dependent membrane currents were studied in dissociated hepatocytes from chick, using the patch-clamp technique. All cells had voltage-dependent outward K+ currents; in 10% of the cells, a fast, transient, tetrodotoxin-sensitive Na+ current was identified. None of the cells had voltage-dependent inward Ca2+ currents. The K+ current activated at a membrane potential of about -10 mV, had a sigmoidal time course, and did not inactivate in 500 ms. The maximum outward conductance was 6.6 +/- 2.4 nS in 18 cells. The reversal potential, estimated from tail current measurements, shifted by 50 mV per 10-fold increase in the external K+ concentration. The current traces were fitted by n2 kinetics with voltage-dependent time constants. Omitting Ca2+ from the external bath or buffering the internal Ca2+ with EGTA did not alter the outward current, which shows that Ca2+-activated K+ currents were not present. 1-5 mM 4-aminopyridine, 0.5-2 mM BaCl2, and 0.1-1 mM CdCl2 reversibly inhibited the current. The block caused by Ba was voltage dependent. Single-channel currents were recorded in cell-attached and outside-out patches. The mean unitary conductance was 7 pS, and the channels displayed bursting kinetics. Thus, avian hepatocytes have a single type of K+ channel belonging to the delayed rectifier class of K+ channels.

The frontal eye field sends predictively remapped visual signals to the superior colliculus

We perceive a stable visual world even though saccades often move our retinas. One way the brain may achieve a stable visual percept is through predictive remapping of visual receptive fields: just before a saccade, the receptive field of many neurons moves from its current location ("current receptive field") to the location it is expected to occupy after the saccade ("future receptive field"). Goldberg and colleagues found such remapping in cortical areas, e.g. in the frontal eye field (FEF), as well as in the intermediate layers of the superior colliculus (SC). In the present study we investigated the source of the SC's remapped visual signals. Do some of them come from the FEF? We identified FEF neurons that project to the SC using antidromic stimulation. For neurons with a visual response, we tested whether the receptive field shifted just prior to making a saccade. Saccadic amplitudes were chosen to be as small as possible while clearly separating the current and future receptive fields; they ranged from 5-30 deg. in amplitude and were directed contraversively. The saccadic target was a small red spot. We probed visual responsiveness at the current and future receptive field locations using a white spot flashed at various times before or after the saccade. Predictive remapping was indicated by a visual response to a probe flashed in the future receptive field just before the saccade began. We found that many FEF neurons projecting to the SC exhibited predictive remapping. Moreover, the remapping was as fast and strong as any previously reported for FEF or SC. It is clear, therefore, that remapped visual signals are sent from FEF to SC, providing direct evidence that the FEF is one source of the SC's remapped visual signals. Because remapping requires information about an imminent saccade, we hypothesize that remapping in FEF depends on corollary discharge signals such as those ascending from the SC through MD thalamus (Sommer and Wurtz 2002).