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.

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.

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.

Anatomical identification of extracellularly recorded cells in large-scale multielectrode recordings.

This study combines for the first time two major approaches to understanding the function and structure of neural circuits: large-scale multielectrode recordings, and confocal imaging of labeled neurons. To achieve this end, we develop a novel approach to the central problem of anatomically identifying recorded cells, based on the electrical image: the spatiotemporal pattern of voltage deflections induced by spikes on a large-scale, high-density multielectrode array. Recordings were performed from identified ganglion cell types in the macaque retina. Anatomical images of cells in the same preparation were obtained using virally transfected fluorescent labeling or by immunolabeling after fixation. The electrical image was then used to locate recorded cell somas, axon initial segments, and axon trajectories, and these signatures were used to identify recorded cells. Comparison of anatomical and physiological measurements permitted visualization and physiological characterization of numerically dominant ganglion cell types with high efficiency in a single preparation.

Lack of evidence for ectopic sprouting of genetically labeled Aβ touch afferents in inflammatory and neuropathic trigeminal pain.

BACKGROUND: Mechanical and in particular tactile allodynia is a hallmark of chronic pain in which innocuous touch becomes painful. Previous cholera toxin B (CTB)-based neural tracing experiments and electrophysiology studies had suggested that aberrant axon sprouting from touch sensory afferents into pain-processing laminae after injury is a possible anatomical substrate underlying mechanical allodynia. This hypothesis was later challenged by experiments using intra-axonal labeling of A-fiber neurons, as well as single-neuron labeling of electrophysiologically identified sensory neurons. However, no studies have used genetically labeled neurons to examine this issue, and most studies were performed on spinal but not trigeminal sensory neurons which are the relevant neurons for orofacial pain, where allodynia oftentimes plays a dominant clinical role. FINDINGS: We recently discovered that parvalbumin::Cre (Pv::Cre) labels two types of Aβ touch neurons in trigeminal ganglion. Using a Pv::CreER driver and a Cre-dependent reporter mouse, we specifically labeled these Aβ trigeminal touch afferents by timed taxomifen injection prior to inflammation or infraorbital nerve injury (ION transection). We then examined the peripheral and central projections of labeled axons into the brainstem caudalis nucleus after injuries vs controls. We found no evidence for ectopic sprouting of Pv::CreER labeled trigeminal Aβ axons into the superficial trigeminal noci-receptive laminae. Furthermore, there was also no evidence for peripheral sprouting. CONCLUSIONS: CreER-based labeling prior to injury precluded the issue of phenotypic changes of neurons after injury. Our results suggest that touch allodynia in chronic orofacial pain is unlikely caused by ectopic sprouting of Aβ trigeminal afferents.

Hydraulic redistribution of soil water by roots affects whole-stand evapotranspiration and net ecosystem carbon exchange.

*Hydraulic redistribution (HR) of water via roots from moist to drier portions of the soil occurs in many ecosystems, potentially influencing both water use and carbon assimilation. *By measuring soil water content, sap flow and eddy covariance, we investigated the temporal variability of HR in a loblolly pine (Pinus taeda) plantation during months of normal and below-normal precipitation, and examined its effects on tree transpiration, ecosystem water use and carbon exchange. *The occurrence of HR was explained by courses of reverse flow through roots. As the drought progressed, HR maintained soil moisture above 0.15 cm(3) cm(-3) and increased transpiration by 30-50%. HR accounted for 15-25% of measured total site water depletion seasonally, peaking at 1.05 mm d(-1). The understory species depended on water redistributed by the deep-rooted overstory pine trees for their early summer water supply. Modeling carbon flux showed that in the absence of HR, gross ecosystem productivity and net ecosystem exchange could be reduced by 750 and 400 g C m(-2) yr(-1), respectively. *Hydraulic redistribution mitigated the effects of soil drying on understory and stand evapotranspiration and had important implications for net primary productivity by maintaining this whole ecosystem as a carbon sink.

Persistent Homology Analysis of Brain Artery Trees.

New representations of tree-structured data objects, using ideas from topological data analysis, enable improved statistical analyses of a population of brain artery trees. A number of representations of each data tree arise from persistence diagrams that quantify branching and looping of vessels at multiple scales. Novel approaches to the statistical analysis, through various summaries of the persistence diagrams, lead to heightened correlations with covariates such as age and sex, relative to earlier analyses of this data set. The correlation with age continues to be significant even after controlling for correlations from earlier significant summaries.

Radiolabeled inhibitors as probes for imaging mutant IDH1 expression in gliomas: Synthesis and preliminary evaluation of labeled butyl-phenyl sulfonamide analogs.

INTRODUCTION: Malignant gliomas frequently harbor mutations in the isocitrate dehydrogenase 1 (IDH1) gene. Studies suggest that IDH mutation contributes to tumor pathogenesis through mechanisms that are mediated by the neomorphic metabolite of the mutant IDH1 enzyme, 2-hydroxyglutarate (2-HG). The aim of this work was to synthesize and evaluate radiolabeled compounds that bind to the mutant IDH1 enzyme with the goal of enabling noninvasive imaging of mutant IDH1 expression in gliomas by positron emission tomography (PET). METHODS: A small library of nonradioactive analogs were designed and synthesized based on the chemical structure of reported butyl-phenyl sulfonamide inhibitors of mutant IDH1. Enzyme inhibition assays were conducted using purified mutant IDH1 enzyme, IDH1-R132H, to determine the IC50 and the maximal inhibitory efficiency of the synthesized compounds. Selected compounds, 1 and 4, were labeled with radioiodine ((125)I) and/or (18)F using bromo- and phenol precursors, respectively. In vivo behavior of the labeled inhibitors was studied by conducting tissue distribution studies with [(125)I]1 in normal mice. Cell uptake studies were conducted using an isogenic astrocytoma cell line that carried a native IDH1-R132H mutation to evaluate the potential uptake of the labeled inhibitors in IDH1-mutated tumor cells. RESULTS: Enzyme inhibition assays showed good inhibitory potency for compounds that have iodine or a fluoroethoxy substituent at the ortho position of the phenyl ring in compounds 1 and 4 with IC50 values of 1.7 μM and 2.3 μM, respectively. Compounds 1 and 4 inhibited mutant IDH1 activity and decreased the production of 2-HG in an IDH1-mutated astrocytoma cell line. Radiolabeling of 1 and 4 was achieved with an average radiochemical yield of 56.6 ± 20.1% for [(125)I]1 (n = 4) and 67.5 ± 6.6% for [(18)F]4 (n = 3). [(125)I]1 exhibited favorable biodistribution characteristics in normal mice, with rapid clearance from the blood and elimination via the hepatobiliary system by 4 h after injection. The uptake of [(125)I]1 in tumor cells positive for IDH1-R132H was significantly higher compared to isogenic WT-IDH1 controls, with a maximal uptake ratio of 1.67 at 3 h post injection. Co-incubation of the labeled inhibitors with the corresponding nonradioactive analogs, and decreasing the normal concentrations of FBS (10%) in the incubation media substantially increased the uptake of the labeled inhibitors in both the IDH1-mutant and WT-IDH1 tumor cell lines, suggesting significant non-specific binding of the synthesized labeled butyl-phenyl sulfonamide inhibitors. CONCLUSIONS: These data demonstrate the feasibility of developing radiolabeled probes for the mutant IDH1 enzyme based on enzyme inhibitors. Further optimization of the labeled inhibitors by modifying the chemical structure to decrease the lipophilicity and to increase potency may yield compounds with improved characteristics as probes for imaging mutant IDH1 expression in tumors.