Invariant measure selection by noise. An example

We consider a deterministic system with two conserved quantities and infinity many invariant measures. However the systems possess a unique invariant measure when enough stochastic forcing and balancing dissipation are added. We then show that as the forcing and dissipation are removed a unique limit of the deterministic system is selected. The exact structure of the limiting measure depends on the specifics of the stochastic forcing.

Test-pattern selection for screening small-delay defects in very-deep submicrometer integrated circuits

Timing-related defects are major contributors to test escapes and in-field reliability problems for very-deep submicrometer integrated circuits. Small delay variations induced by crosstalk, process variations, power-supply noise, as well as resistive opens and shorts can potentially cause timing failures in a design, thereby leading to quality and reliability concerns. We present a test-grading technique that uses the method of output deviations for screening small-delay defects (SDDs). A new gate-delay defect probability measure is defined to model delay variations for nanometer technologies. The proposed technique intelligently selects the best set of patterns for SDD detection from an n-detect pattern set generated using timing-unaware automatic test-pattern generation (ATPG). It offers significantly lower computational complexity and excites a larger number of long paths compared to a current generation commercial timing-aware ATPG tool. Our results also show that, for the same pattern count, the selected patterns provide more effective coverage ramp-up than timing-aware ATPG and a recent pattern-selection method for random SDDs potentially caused by resistive shorts, resistive opens, and process variations. © 2010 IEEE.

Analysis of an asymptotic preserving scheme for linear kinetic equations in the diffusion limit

We present a mathematical analysis of the asymptotic preserving scheme proposed in [M. Lemou and L. Mieussens, SIAM J. Sci. Comput., 31 (2008), pp. 334-368] for linear transport equations in kinetic and diffusive regimes. We prove that the scheme is uniformly stable and accurate with respect to the mean free path of the particles. This property is satisfied under an explicitly given CFL condition. This condition tends to a parabolic CFL condition for small mean free paths and is close to a convection CFL condition for large mean free paths. Our analysis is based on very simple energy estimates. © 2010 Society for Industrial and Applied Mathematics.

Hepcidin as a therapeutic tool to limit iron overload and improve anemia in β-thalassemic mice.

Excessive iron absorption is one of the main features of β-thalassemia and can lead to severe morbidity and mortality. Serial analyses of β-thalassemic mice indicate that while hemoglobin levels decrease over time, the concentration of iron in the liver, spleen, and kidneys markedly increases. Iron overload is associated with low levels of hepcidin, a peptide that regulates iron metabolism by triggering degradation of ferroportin, an iron-transport protein localized on absorptive enterocytes as well as hepatocytes and macrophages. Patients with β-thalassemia also have low hepcidin levels. These observations led us to hypothesize that more iron is absorbed in β-thalassemia than is required for erythropoiesis and that increasing the concentration of hepcidin in the body of such patients might be therapeutic, limiting iron overload. Here we demonstrate that a moderate increase in expression of hepcidin in β-thalassemic mice limits iron overload, decreases formation of insoluble membrane-bound globins and reactive oxygen species, and improves anemia. Mice with increased hepcidin expression also demonstrated an increase in the lifespan of their red cells, reversal of ineffective erythropoiesis and splenomegaly, and an increase in total hemoglobin levels. These data led us to suggest that therapeutics that could increase hepcidin levels or act as hepcidin agonists might help treat the abnormal iron absorption in individuals with β-thalassemia and related disorders.

Bayesian variable selection in structured high-dimensional covariate spaces with applications in genomics

We consider the problem of variable selection in regression modeling in high-dimensional spaces where there is known structure among the covariates. This is an unconventional variable selection problem for two reasons: (1) The dimension of the covariate space is comparable, and often much larger, than the number of subjects in the study, and (2) the covariate space is highly structured, and in some cases it is desirable to incorporate this structural information in to the model building process. We approach this problem through the Bayesian variable selection framework, where we assume that the covariates lie on an undirected graph and formulate an Ising prior on the model space for incorporating structural information. Certain computational and statistical problems arise that are unique to such high-dimensional, structured settings, the most interesting being the phenomenon of phase transitions. We propose theoretical and computational schemes to mitigate these problems. We illustrate our methods on two different graph structures: the linear chain and the regular graph of degree k. Finally, we use our methods to study a specific application in genomics: the modeling of transcription factor binding sites in DNA sequences. © 2010 American Statistical Association.

Bayes and empirical-Bayes multiplicity adjustment in the variable-selection problem

This paper studies the multiplicity-correction effect of standard Bayesian variable-selection priors in linear regression. Our first goal is to clarify when, and how, multiplicity correction happens automatically in Bayesian analysis, and to distinguish this correction from the Bayesian Ockham's-razor effect. Our second goal is to contrast empirical-Bayes and fully Bayesian approaches to variable selection through examples, theoretical results and simulations. Considerable differences between the two approaches are found. In particular, we prove a theorem that characterizes a surprising aymptotic discrepancy between fully Bayes and empirical Bayes. This discrepancy arises from a different source than the failure to account for hyperparameter uncertainty in the empirical-Bayes estimate. Indeed, even at the extreme, when the empirical-Bayes estimate converges asymptotically to the true variable-inclusion probability, the potential for a serious difference remains. © Institute of Mathematical Statistics, 2010.

Sexual selection and canine dimorphism in New World monkeys.

Social and ecological factors are important in shaping sexual dimorphism in Anthropoidea, but there is also a tendency for body-size dimorphism and canine dimorphism to increase with increased body size (Rensch's rule) (Rensch: Evolution Above the Species Level. London: Methuen, 1959.) Most ecologist interpret Rensch's rule to be a consequence of social and ecological selective factors that covary with body size, but recent claims have been advanced that dimorphism is principally a consequence of selection for increased body size alone. Here we assess the effects of body size, body-size dimorphism, and social structure on canine dimorphism among platyrrhine monkeys. Platyrrhine species examined are classified into four behavioral groups reflecting the intensity of intermale competition for access to females or to limiting resources. As canine dimorphism increases, so does the level of intermale competition. Those species with monogamous and polyandrous social structures have the lowest canine dimorphism, while those with dominance rank hierarchies of males have the most canine dimorphism. Species with fission-fusion social structures and transitory intermale breeding-season competition fall between these extremes. Among platyrrhines there is a significant positive correlation between body size and canine dimorphism However, within levels of competition, no significant correlation was found between the two. Also, with increased body size, body-size dimorphism tends to increase, and this correlation holds in some cases within competition levels. In an analysis of covariance, once the level of intermale competition is controlled for, neither molar size nor molar-size dimorphism accounts for a significant part of the variance in canine dimorphism. A similar analysis using body weight as a measure of size and dimorphism yields a less clear-cut picture: body weight contributes significantly to the model when the effects of the other factors are controlled. Finally, in a model using head and body length as a measure of size and dimorphism, all factors and the interactions between them are significant. We conclude that intermale competition among platyrrhine species is the most important factor explaining variations in canine dimorphism. The significant effects of size and size dimorphism in some models may be evidence that natural (as opposed to sexual) selection also plays a role in the evolution of increased canine dimorphism.

Targeting Gbeta gamma signaling in arterial vascular smooth muscle proliferation: a novel strategy to limit restenosis.

Restenosis continues to be a major problem limiting the effectiveness of revascularization procedures. To date, the roles of heterotrimeric G proteins in the triggering of pathological vascular smooth muscle (VSM) cell proliferation have not been elucidated. betagamma subunits of heterotrimeric G proteins (Gbetagamma) are known to activate mitogen-activated protein (MAP) kinases after stimulation of certain G protein-coupled receptors; however, their relevance in VSM mitogenesis in vitro or in vivo is not known. Using adenoviral-mediated transfer of a transgene encoding a peptide inhibitor of Gbetagamma signaling (betaARKct), we evaluated the role of Gbetagamma in MAP kinase activation and proliferation in response to several mitogens, including serum, in cultured rat VSM cells. Our results include the striking finding that serum-induced proliferation of VSM cells in vitro is mediated largely via Gbetagamma. Furthermore, we studied the effects of in vivo adenoviral-mediated betaARKct gene transfer on VSM intimal hyperplasia in a rat carotid artery restenosis model. Our in vivo results demonstrated that the presence of the betaARKct in injured rat carotid arteries significantly reduced VSM intimal hyperplasia by 70%. Thus, Gbetagamma plays a critical role in physiological VSM proliferation, and targeted Gbetagamma inhibition represents a novel approach for the treatment of pathological conditions such as restenosis.

Development of a decision aid to inform patients' and families' renal replacement therapy selection decisions.

BACKGROUND: Few educational resources have been developed to inform patients' renal replacement therapy (RRT) selection decisions. Patients progressing toward end stage renal disease (ESRD) must decide among multiple treatment options with varying characteristics. Complex information about treatments must be adequately conveyed to patients with different educational backgrounds and informational needs. Decisions about treatment options also require family input, as families often participate in patients' treatment and support patients' decisions. We describe the development, design, and preliminary evaluation of an informational, evidence-based, and patient-and family-centered decision aid for patients with ESRD and varying levels of health literacy, health numeracy, and cognitive function. METHODS: We designed a decision aid comprising a complementary video and informational handbook. We based our development process on data previously obtained from qualitative focus groups and systematic literature reviews. We simultaneously developed the video and handbook in "stages." For the video, stages included (1) directed interviews with culturally appropriate patients and families and preliminary script development, (2) video production, and (3) screening the video with patients and their families. For the handbook, stages comprised (1) preliminary content design, (2) a mixed-methods pilot study among diverse patients to assess comprehension of handbook material, and (3) screening the handbook with patients and their families. RESULTS: The video and handbook both addressed potential benefits and trade-offs of treatment selections. The 50-minute video consisted of demographically diverse patients and their families describing their positive and negative experiences with selecting a treatment option. The video also incorporated health professionals' testimonials regarding various considerations that might influence patients' and families' treatment selections. The handbook was comprised of written words, pictures of patients and health care providers, and diagrams describing the findings and quality of scientific studies comparing treatments. The handbook text was written at a 4th to 6th grade reading level. Pilot study results demonstrated that a majority of patients could understand information presented in the handbook. Patient and families screening the nearly completed video and handbook reviewed the materials favorably. CONCLUSIONS: This rigorously designed decision aid may help patients and families make informed decisions about their treatment options for RRT that are well aligned with their values.

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.

Sticky central limit theorems on open books

Given a probability distribution on an open book (a metric space obtained by gluing a disjoint union of copies of a half-space along their boundary hyperplanes), we define a precise concept of when the Fréchet mean (barycenter) is sticky. This nonclassical phenomenon is quantified by a law of large numbers (LLN) stating that the empirical mean eventually almost surely lies on the (codimension 1 and hence measure 0) spine that is the glued hyperplane, and a central limit theorem (CLT) stating that the limiting distribution is Gaussian and supported on the spine.We also state versions of the LLN and CLT for the cases where the mean is nonsticky (i.e., not lying on the spine) and partly sticky (i.e., is, on the spine but not sticky). © Institute of Mathematical Statistics, 2013.

Scaling limits of a model for selection at two scales

The dynamics of a population undergoing selection is a central topic in evolutionary biology. This question is particularly intriguing in the case where selective forces act in opposing directions at two population scales. For example, a fast-replicating virus strain outcompetes slower-replicating strains at the within-host scale. However, if the fast-replicating strain causes host morbidity and is less frequently transmitted, it can be outcompeted by slower-replicating strains at the between-host scale. Here we consider a stochastic ball-and-urn process which models this type of phenomenon. We prove the weak convergence of this process under two natural scalings. The first scaling leads to a deterministic nonlinear integro-partial differential equation on the interval $[0,1]$ with dependence on a single parameter, $\lambda$. We show that the fixed points of this differential equation are Beta distributions and that their stability depends on $\lambda$ and the behavior of the initial data around $1$. The second scaling leads to a measure-valued Fleming-Viot process, an infinite dimensional stochastic process that is frequently associated with a population genetics.

Human Non-neutralizing HIV-1 Envelope Monoclonal Antibodies Limit the Number of Founder Viruses during SHIV Mucosal Infection in Rhesus Macaques.

HIV-1 mucosal transmission begins with virus or virus-infected cells moving through mucus across mucosal epithelium to infect CD4+ T cells. Although broadly neutralizing antibodies (bnAbs) are the type of HIV-1 antibodies that are most likely protective, they are not induced with current vaccine candidates. In contrast, antibodies that do not neutralize primary HIV-1 strains in the TZM-bl infection assay are readily induced by current vaccine candidates and have also been implicated as secondary correlates of decreased HIV-1 risk in the RV144 vaccine efficacy trial. Here, we have studied the capacity of anti-Env monoclonal antibodies (mAbs) against either the immunodominant region of gp41 (7B2 IgG1), the first constant region of gp120 (A32 IgG1), or the third variable loop (V3) of gp120 (CH22 IgG1) to modulate in vivo rectal mucosal transmission of a high-dose simian-human immunodeficiency virus (SHIV-BaL) in rhesus macaques. 7B2 IgG1 or A32 IgG1, each containing mutations to enhance Fc function, was administered passively to rhesus macaques but afforded no protection against productive clinical infection while the positive control antibody CH22 IgG1 prevented infection in 4 of 6 animals. Enumeration of transmitted/founder (T/F) viruses revealed that passive infusion of each of the three antibodies significantly reduced the number of T/F genomes. Thus, some antibodies that bind HIV-1 Env but fail to neutralize virus in traditional neutralization assays may limit the number of T/F viruses involved in transmission without leading to enhancement of viral infection. For one of these mAbs, gp41 mAb 7B2, we provide the first co-crystal structure in complex with a common cyclical loop motif demonstrated to be critical for infection by other retroviruses.

Evaluating marker-guided treatment selection strategies

© 2014, The International Biometric Society.A potential venue to improve healthcare efficiency is to effectively tailor individualized treatment strategies by incorporating patient level predictor information such as environmental exposure, biological, and genetic marker measurements. Many useful statistical methods for deriving individualized treatment rules (ITR) have become available in recent years. Prior to adopting any ITR in clinical practice, it is crucial to evaluate its value in improving patient outcomes. Existing methods for quantifying such values mainly consider either a single marker or semi-parametric methods that are subject to bias under model misspecification. In this article, we consider a general setting with multiple markers and propose a two-step robust method to derive ITRs and evaluate their values. We also propose procedures for comparing different ITRs, which can be used to quantify the incremental value of new markers in improving treatment selection. While working models are used in step I to approximate optimal ITRs, we add a layer of calibration to guard against model misspecification and further assess the value of the ITR non-parametrically, which ensures the validity of the inference. To account for the sampling variability of the estimated rules and their corresponding values, we propose a resampling procedure to provide valid confidence intervals for the value functions as well as for the incremental value of new markers for treatment selection. Our proposals are examined through extensive simulation studies and illustrated with the data from a clinical trial that studies the effects of two drug combinations on HIV-1 infected patients.