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.

Utility of telomerase-pot1 fusion protein in vascular tissue engineering.

While advances in regenerative medicine and vascular tissue engineering have been substantial in recent years, important stumbling blocks remain. In particular, the limited life span of differentiated cells that are harvested from elderly human donors is an important limitation in many areas of regenerative medicine. Recently, a mutant of the human telomerase reverse transcriptase enzyme (TERT) was described, which is highly processive and elongates telomeres more rapidly than conventional telomerase. This mutant, called pot1-TERT, is a chimeric fusion between the DNA binding protein pot1 and TERT. Because pot1-TERT is highly processive, it is possible that transient delivery of this transgene to cells that are utilized in regenerative medicine applications may elongate telomeres and extend cellular life span while avoiding risks that are associated with retroviral or lentiviral vectors. In the present study, adenoviral delivery of pot1-TERT resulted in transient reconstitution of telomerase activity in human smooth muscle cells, as demonstrated by telomeric repeat amplification protocol (TRAP). In addition, human engineered vessels that were cultured using pot1-TERT-expressing cells had greater collagen content and somewhat better performance in vivo than control grafts. Hence, transient delivery of pot1-TERT to elderly human cells may be useful for increasing cellular life span and improving the functional characteristics of resultant tissue-engineered constructs.

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.

Protocol for the "Implementation, adoption, and utility of family history in diverse care settings" study.

BACKGROUND: Risk assessment with a thorough family health history is recommended by numerous organizations and is now a required component of the annual physical for Medicare beneficiaries under the Affordable Care Act. However, there are several barriers to incorporating robust risk assessments into routine care. MeTree, a web-based patient-facing health risk assessment tool, was developed with the aim of overcoming these barriers. In order to better understand what factors will be instrumental for broader adoption of risk assessment programs like MeTree in clinical settings, we obtained funding to perform a type III hybrid implementation-effectiveness study in primary care clinics at five diverse healthcare systems. Here, we describe the study's protocol. METHODS/DESIGN: MeTree collects personal medical information and a three-generation family health history from patients on 98 conditions. Using algorithms built entirely from current clinical guidelines, it provides clinical decision support to providers and patients on 30 conditions. All adult patients with an upcoming well-visit appointment at one of the 20 intervention clinics are eligible to participate. Patient-oriented risk reports are provided in real time. Provider-oriented risk reports are uploaded to the electronic medical record for review at the time of the appointment. Implementation outcomes are enrollment rate of clinics, providers, and patients (enrolled vs approached) and their representativeness compared to the underlying population. Primary effectiveness outcomes are the percent of participants newly identified as being at increased risk for one of the clinical decision support conditions and the percent with appropriate risk-based screening. Secondary outcomes include percent change in those meeting goals for a healthy lifestyle (diet, exercise, and smoking). Outcomes are measured through electronic medical record data abstraction, patient surveys, and surveys/qualitative interviews of clinical staff. DISCUSSION: This study evaluates factors that are critical to successful implementation of a web-based risk assessment tool into routine clinical care in a variety of healthcare settings. The result will identify resource needs and potential barriers and solutions to implementation in each setting as well as an understanding potential effectiveness. TRIAL REGISTRATION: NCT01956773.

Clinical utility of a Web-enabled risk-assessment and clinical decision support program.

PURPOSE: Risk-stratified guidelines can improve quality of care and cost-effectiveness, but their uptake in primary care has been limited. MeTree, a Web-based, patient-facing risk-assessment and clinical decision support tool, is designed to facilitate uptake of risk-stratified guidelines. METHODS: A hybrid implementation-effectiveness trial of three clinics (two intervention, one control). PARTICIPANTS: consentable nonadopted adults with upcoming appointments. PRIMARY OUTCOME: agreement between patient risk level and risk management for those meeting evidence-based criteria for increased-risk risk-management strategies (increased risk) and those who do not (average risk) before MeTree and after. MEASURES: chart abstraction was used to identify risk management related to colon, breast, and ovarian cancer, hereditary cancer, and thrombosis. RESULTS: Participants = 488, female = 284 (58.2%), white = 411 (85.7%), mean age = 58.7 (SD = 12.3). Agreement between risk management and risk level for all conditions for each participant, except for colon cancer, which was limited to those <50 years of age, was (i) 1.1% (N = 2/174) for the increased-risk group before MeTree and 16.1% (N = 28/174) after and (ii) 99.2% (N = 2,125/2,142) for the average-risk group before MeTree and 99.5% (N = 2,131/2,142) after. Of those receiving increased-risk risk-management strategies at baseline, 10.5% (N = 2/19) met criteria for increased risk. After MeTree, 80.7% (N = 46/57) met criteria. CONCLUSION: MeTree integration into primary care can improve uptake of risk-stratified guidelines and potentially reduce "overuse" and "underuse" of increased-risk services.Genet Med 18 10, 1020-1028.

Utility of a molecular prescreening program in advanced colorectal cancer for enrollment on biomarker-selected clinical trials.

BACKGROUND: Incorporation of multiple enrichment biomarkers into prospective clinical trials is an active area of investigation, but the factors that determine clinical trial enrollment following a molecular prescreening program have not been assessed. PATIENTS AND METHODS: Patients with 5-fluorouracil-refractory metastatic colorectal cancer at the MD Anderson Cancer Center were offered screening in the Assessment of Targeted Therapies Against Colorectal Cancer (ATTACC) program to identify eligibility for companion phase I or II clinical trials with a therapy targeted to an aberration detected in the patient, based on testing by immunohistochemistry, targeted gene sequencing panels, and CpG island methylation phenotype assays. RESULTS: Between August 2010 and December 2013, 484 patients were enrolled, 458 (95%) had a biomarker result, and 157 (32%) were enrolled on a clinical trial (92 on biomarker-selected and 65 on nonbiomarker selected). Of the 458 patients with a biomarker result, enrollment on biomarker-selected clinical trials was ninefold higher for predefined ATTACC-companion clinical trials as opposed to nonpredefined biomarker-selected clinical trials, 17.9% versus 2%, P < 0.001. Factors that correlated positively with trial enrollment in multivariate analysis were higher performance status, older age, lack of standard of care therapy, established patient at MD Anderson, and the presence of an eligible biomarker for an ATTACC-companion study. Early molecular screening did result in a higher rate of patients with remaining standard of care therapy enrolling on ATTACC-companion clinical trials, 45.1%, in contrast to nonpredefined clinical trials, 22.7%; odds ratio 3.1, P = 0.002. CONCLUSIONS: Though early molecular prescreening for predefined clinical trials resulted in an increase rate of trial enrollment of nonrefractory patients, the majority of patients enrolled on clinical trials were refractory to standard of care therapy. Within molecular prescreening programs, tailoring screening for preidentified and open clinical trials, temporally linking screening to treatment and optimizing both patient and physician engagement are efforts likely to improve enrollment on biomarker-selected clinical trials. CLINICAL TRIALS NUMBER: The study NCT number is NCT01196130.