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.

Low demographic variability in wild primate populations: fitness impacts of variation, covariation, and serial correlation in vital rates.

In a stochastic environment, long-term fitness can be influenced by variation, covariation, and serial correlation in vital rates (survival and fertility). Yet no study of an animal population has parsed the contributions of these three aspects of variability to long-term fitness. We do so using a unique database that includes complete life-history information for wild-living individuals of seven primate species that have been the subjects of long-term (22-45 years) behavioral studies. Overall, the estimated levels of vital rate variation had only minor effects on long-term fitness, and the effects of vital rate covariation and serial correlation were even weaker. To explore why, we compared estimated variances of adult survival in primates with values for other vertebrates in the literature and found that adult survival is significantly less variable in primates than it is in the other vertebrates. Finally, we tested the prediction that adult survival, because it more strongly influences fitness in a constant environment, will be less variable than newborn survival, and we found only mixed support for the prediction. Our results suggest that wild primates may be buffered against detrimental fitness effects of environmental stochasticity by their highly developed cognitive abilities, social networks, and broad, flexible diets.

Assessing variability and long-term trends in burned area by merging multiple satellite fire products

Long term, high quality estimates of burned area are needed for improving both prognostic and diagnostic fire emissions models and for assessing feedbacks between fire and the climate system. We developed global, monthly burned area estimates aggregated to 0.5° spatial resolution for the time period July 1996 through mid-2009 using four satellite data sets. From 2001ĝ€ "2009, our primary data source was 500-m burned area maps produced using Moderate Resolution Imaging Spectroradiometer (MODIS) surface reflectance imagery; more than 90% of the global area burned during this time period was mapped in this fashion. During times when the 500-m MODIS data were not available, we used a combination of local regression and regional regression trees developed over periods when burned area and Terra MODIS active fire data were available to indirectly estimate burned area. Cross-calibration with fire observations from the Tropical Rainfall Measuring Mission (TRMM) Visible and Infrared Scanner (VIRS) and the Along-Track Scanning Radiometer (ATSR) allowed the data set to be extended prior to the MODIS era. With our data set we estimated that the global annual area burned for the years 1997ĝ€ "2008 varied between 330 and 431 Mha, with the maximum occurring in 1998. We compared our data set to the recent GFED2, L3JRC, GLOBCARBON, and MODIS MCD45A1 global burned area products and found substantial differences in many regions. Lastly, we assessed the interannual variability and long-term trends in global burned area over the past 13 years. This burned area time series serves as the basis for the third version of the Global Fire Emissions Database (GFED3) estimates of trace gas and aerosol emissions.

Intensification of summer rainfall variability in the southeastern United States during recent decades

The variability of summer precipitation in the southeastern United States is examined in this study using 60-yr (1948-2007) rainfall data. The Southeast summer rainfalls exhibited higher interannual variability with more intense summer droughts and anomalous wetness in the recent 30 years (1978-2007) than in the prior 30 years (1948-77). Such intensification of summer rainfall variability was consistent with a decrease of light (0.1-1 mm day-1) and medium (1-10 mm day-1) rainfall events during extremely dry summers and an increase of heavy (.10 mm day-1) rainfall events in extremely wet summers. Changes in rainfall variability were also accompanied by a southward shift of the region of maximum zonal wind variability at the jet stream level in the latter period. The covariability between the Southeast summer precipitation and sea surface temperatures (SSTs) is also analyzed using the singular value decomposition (SVD) method. It is shown that the increase of Southeast summer precipitation variability is primarily associated with a higher SST variability across the equatorial Atlantic and also SST warming in the Atlantic. © 2010 American Meteorological Society.

Telomere disruption results in non-random formation of de novo dicentric chromosomes involving acrocentric human chromosomes.

Genome rearrangement often produces chromosomes with two centromeres (dicentrics) that are inherently unstable because of bridge formation and breakage during cell division. However, mammalian dicentrics, and particularly those in humans, can be quite stable, usually because one centromere is functionally silenced. Molecular mechanisms of centromere inactivation are poorly understood since there are few systems to experimentally create dicentric human chromosomes. Here, we describe a human cell culture model that enriches for de novo dicentrics. We demonstrate that transient disruption of human telomere structure non-randomly produces dicentric fusions involving acrocentric chromosomes. The induced dicentrics vary in structure near fusion breakpoints and like naturally-occurring dicentrics, exhibit various inter-centromeric distances. Many functional dicentrics persist for months after formation. Even those with distantly spaced centromeres remain functionally dicentric for 20 cell generations. Other dicentrics within the population reflect centromere inactivation. In some cases, centromere inactivation occurs by an apparently epigenetic mechanism. In other dicentrics, the size of the alpha-satellite DNA array associated with CENP-A is reduced compared to the same array before dicentric formation. Extra-chromosomal fragments that contained CENP-A often appear in the same cells as dicentrics. Some of these fragments are derived from the same alpha-satellite DNA array as inactivated centromeres. Our results indicate that dicentric human chromosomes undergo alternative fates after formation. Many retain two active centromeres and are stable through multiple cell divisions. Others undergo centromere inactivation. This event occurs within a broad temporal window and can involve deletion of chromatin that marks the locus as a site for CENP-A maintenance/replenishment.

Variability in frontotemporal brain structure: the importance of recruitment of African Americans in neuroscience research.

BACKGROUND: Variation in brain structure is both genetically and environmentally influenced. The question about potential differences in brain anatomy across populations of differing race and ethnicity remains a controversial issue. There are few studies specifically examining racial or ethnic differences and also few studies that test for race-related differences in context of other neuropsychiatric research, possibly due to the underrepresentation of ethnic minorities in clinical research. It is within this context that we conducted a secondary data analysis examining volumetric MRI data from healthy participants and compared the volumes of the amygdala, hippocampus, lateral ventricles, caudate nucleus, orbitofrontal cortex (OFC) and total cerebral volume between Caucasian and African-American participants. We discuss the importance of this finding in context of neuroimaging methodology, but also the need for improved recruitment of African Americans in clinical research and its broader implications for a better understanding of the neural basis of neuropsychiatric disorders. METHODOLOGY/PRINCIPAL FINDINGS: This was a case control study in the setting of an academic medical center outpatient service. Participants consisted of 44 Caucasians and 33 ethnic minorities. The following volumetric data were obtained: amygdala, hippocampus, lateral ventricles, caudate nucleus, orbitofrontal cortex (OFC) and total cerebrum. Each participant completed a 1.5 T magnetic resonance imaging (MRI). Our primary finding in analyses of brain subregions was that when compared to Caucasians, African Americans exhibited larger left OFC volumes (F (1,68) = 7.50, p = 0.008). CONCLUSIONS: The biological implications of our findings are unclear as we do not know what factors may be contributing to these observed differences. However, this study raises several questions that have important implications for the future of neuropsychiatric research.

Variability of particulate matter concentrations along roads and motorways determined by a moving measurement unit

The spatial variability of aerosol number and mass along roads was determined in different regions (urban, rural and coastal-marine) of the Netherlands. A condensation particle counter (CPC) and an optical aerosol spectrometer (LAS-X) were installed in a van along with a global positioning system (GPS). Concentrations were measured with high-time resolutions while driving allowing investigations not possible with stationary equipment. In particular, this approach proves to be useful to identify those locations where numbers and mass attain high levels ('hot spots'). In general, concentrations of number and mass of particulate matter increase along with the degree of urbanisation, with number concentration being the more sensitive indicator. The lowest particle numbers and PM1-concentrations are encountered in a coastal and rural area: <5000cm-3 and 6μgm-3, respectively. The presence of sea-salt material along the North-Sea coast enhances PM>1-concentrations compared to inland levels. High-particle numbers are encountered on motorways correlating with traffic intensity; the largest average number concentration is measured on the ring motorway around Amsterdam: about 160000cm-3 (traffic intensity 100000vehday-1). Peak values occur in tunnels where numbers exceed 106cm-3. Enhanced PM1 levels (i.e. larger than 9μgm-3) exist on motorways, major traffic roads and in tunnels. The concentrations of PM>1 appear rather uniformly distributed (below 6μgm-3 for most observations). On the urban scale, (large) spatial variations in concentration can be explained by varying intensities of traffic and driving patterns. The highest particle numbers are measured while being in traffic congestions or when behind a heavy diesel-driven vehicle (up to 600×103cm-3). Relatively high numbers are observed during the passages of crossings and, at a decreasing rate, on main roads with much traffic, quiet streets and residential areas with limited traffic. The number concentration exhibits a larger variability than mass: the mass concentration on city roads with much traffic is 12% higher than in a residential area at the edge of the same city while the number of particles changes by a factor of two (due to the presence of the ultrafine particles (aerodynamic diameter <100nm). It is further indicated that people residing at some 100m downwind a major traffic source are exposed to (still) 40% more particles than those living in the urban background areas. © 2004 Elsevier Ltd. All rights reserved.

The impact of geologic variability on capacity and cost estimates for storing CO 2 in deep-saline aquifers

While numerous studies find that deep-saline sandstone aquifers in the United States could store many decades worth of the nation's current annual CO 2 emissions, the likely cost of this storage (i.e. the cost of storage only and not capture and transport costs) has been harder to constrain. We use publicly available data of key reservoir properties to produce geo-referenced rasters of estimated storage capacity and cost for regions within 15 deep-saline sandstone aquifers in the United States. The rasters reveal the reservoir quality of these aquifers to be so variable that the cost estimates for storage span three orders of magnitude and average>$100/tonne CO 2. However, when the cost and corresponding capacity estimates in the rasters are assembled into a marginal abatement cost curve (MACC), we find that ~75% of the estimated storage capacity could be available for<$2/tonne. Furthermore, ~80% of the total estimated storage capacity in the rasters is concentrated within just two of the aquifers-the Frio Formation along the Texas Gulf Coast, and the Mt. Simon Formation in the Michigan Basin, which together make up only ~20% of the areas analyzed. While our assessment is not comprehensive, the results suggest there should be an abundance of low-cost storage for CO 2 in deep-saline aquifers, but a majority of this storage is likely to be concentrated within specific regions of a smaller number of these aquifers. © 2011 Elsevier B.V.

The missense of smell: functional variability in the human odorant receptor repertoire.

Humans have ~400 intact odorant receptors, but each individual has a unique set of genetic variations that lead to variation in olfactory perception. We used a heterologous assay to determine how often genetic polymorphisms in odorant receptors alter receptor function. We identified agonists for 18 odorant receptors and found that 63% of the odorant receptors we examined had polymorphisms that altered in vitro function. On average, two individuals have functional differences at over 30% of their odorant receptor alleles. To show that these in vitro results are relevant to olfactory perception, we verified that variations in OR10G4 genotype explain over 15% of the observed variation in perceived intensity and over 10% of the observed variation in perceived valence for the high-affinity in vitro agonist guaiacol but do not explain phenotype variation for the lower-affinity agonists vanillin and ethyl vanillin.

Changes to the North Atlantic subtropical high and its role in the intensification of summer rainfall variability in the southeastern United States

This study investigates the changes of the North Atlantic subtropical high (NASH) and its impact on summer precipitation over the southeastern (SE) United States using the 850-hPa geopotential height field in the National Centers forEnvironmental Prediction (NCEP) reanalysis, the 40-yr European Centre for Medium-Range Weather Forecasts (ECMWF) Re-Analysis (ERA-40), long-term rainfall data, and Intergovernmental Panel on Climate Change (IPCC) Fourth Assessment Report (AR4) model simulations during the past six decades (1948-2007). The results show that the NASH in the last 30 yr has become more intense, and its western ridge has displaced westward with an enhanced meridional movement compared to the previous 30 yr. When the NASH moved closer to the continental United States in the three most recent decades, the effect of the NASH on the interannual variation of SE U.S. precipitation is enhanced through the ridge's north-south movement. The study's attribution analysis suggested that the changes of the NASH are mainly due to anthropogenic warming. In the twenty-first century with an increase of the atmospheric CO2 concentration, the center of the NASH would be intensified and the western ridge of the NASH would shift farther westward. These changes would increase the likelihood of both strong anomalously wet and dry summers over the SEUnited States in the future, as suggested by the IPCC AR4 models. © 2011 American Meteorological Society.

Gene selection using iterative feature elimination random forests for survival outcomes.

Although many feature selection methods for classification have been developed, there is a need to identify genes in high-dimensional data with censored survival outcomes. Traditional methods for gene selection in classification problems have several drawbacks. First, the majority of the gene selection approaches for classification are single-gene based. Second, many of the gene selection procedures are not embedded within the algorithm itself. The technique of random forests has been found to perform well in high-dimensional data settings with survival outcomes. It also has an embedded feature to identify variables of importance. Therefore, it is an ideal candidate for gene selection in high-dimensional data with survival outcomes. In this paper, we develop a novel method based on the random forests to identify a set of prognostic genes. We compare our method with several machine learning methods and various node split criteria using several real data sets. Our method performed well in both simulations and real data analysis.Additionally, we have shown the advantages of our approach over single-gene-based approaches. Our method incorporates multivariate correlations in microarray data for survival outcomes. The described method allows us to better utilize the information available from microarray data with survival outcomes.

Regularity of invariant densities for 1D systems with random switching

© 2015 IOP Publishing Ltd & London Mathematical Society.This is a detailed analysis of invariant measures for one-dimensional dynamical systems with random switching. In particular, we prove the smoothness of the invariant densities away from critical points and describe the asymptotics of the invariant densities at critical points.

Stochastic switching in infinite dimensions with applications to random parabolic PDE

© 2015 Society for Industrial and Applied Mathematics.We consider parabolic PDEs with randomly switching boundary conditions. In order to analyze these random PDEs, we consider more general stochastic hybrid systems and prove convergence to, and properties of, a stationary distribution. Applying these general results to the heat equation with randomly switching boundary conditions, we find explicit formulae for various statistics of the solution and obtain almost sure results about its regularity and structure. These results are of particular interest for biological applications as well as for their significant departure from behavior seen in PDEs forced by disparate Gaussian noise. Our general results also have applications to other types of stochastic hybrid systems, such as ODEs with randomly switching right-hand sides.

Cross-cultural variability of component processes in autobiographical remembering: Japan, Turkey, and the USA.

Although the underlying mechanics of autobiographical memory may be identical across cultures, the processing of information differs. Undergraduates from Japan, Turkey, and the USA rated 30 autobiographical memories on 15 phenomenological and cognitive properties. Mean values were similar across cultures, with means from the Japanese sample being lower on most measures but higher on belief in the accuracy of their memories. Correlations within individuals were also similar across cultures, with correlations from the Turkish sample being higher between measures of language and measures of recollection and belief. For all three cultures, in multiple regression analyses, measures of recollection were predicted by visual imagery, auditory imagery, and emotions, whereas measures of belief were predicted by knowledge of the setting. These results show subtle cultural differences in the experience of remembering.