Identifying Gene–Environment Interactions With Robust Marginal Bayesian Variable Selection

In high-throughput genetics studies, an important aim is to identify gene–environment interactions associated with the clinical outcomes. Recently, multiple marginal penalization methods have been developed and shown to be effective in G×E studies. However, within the Bayesian framework, marginal variable selection has not received much attention. In this study, we propose a novel marginal Bayesian variable selection method for G×E studies. In particular, our marginal Bayesian method is robust to data contamination and outliers in the outcome variables. With the incorporation of spike-and-slab priors, we have implemented the Gibbs sampler based on Markov Chain Monte Carlo (MCMC). The proposed method outperforms a number of alternatives in extensive simulation studies. The utility of the marginal robust Bayesian variable selection method has been further demonstrated in the case studies using data from the Nurse Health Study (NHS). Some of the identified main and interaction effects from the real data analysis have important biological implications.

The Coupled Volume of Fluid and Brinkman Penalization Methods for Simulation of Incompressible Multiphase Flows

In this work, we contribute to the development of numerical algorithms for the direct simulation of three-dimensional incompressible multiphase flows in the presence of multiple fluids and solids. The volume of fluid method is used for interface tracking, and the Brinkman penalization method is used to treat solids; the latter is assumed to be perfectly superhydrophobic or perfectly superhydrophilic, to have an arbitrary shape, and to move with a prescribed velocity. The proposed algorithm is implemented in the open-source software Basilisk and is validated on a number of test cases, such as the Stokes flow between a periodic array of cylinders, vortex decay problem, and multiphase flow around moving solids.

Concentration of bound states for fractional Schrödinger-Poisson system via penalization methods

<p style='text-indent:20px;'>In this paper, we study the following fractional Schrödinger-Poiss-on system</p><p style='text-indent:20px;'><disp-formula> <label/> <tex-math id="FE1"> \begin{document}$ \begin{equation*} \begin{cases} \varepsilon^{2s}(-\Delta)^su+V(x)u+\phi u = g(u) &amp; \hbox{in $\mathbb{R}^3$,} \\ \varepsilon^{2t}(-\Delta)^t\phi = u^2,\,\, u&gt;0&amp; \hbox{in $\mathbb{R}^3$,} \end{cases} \end{equation*} $\end{document} </tex-math></disp-formula></p><p style='text-indent:20px;'>where <inline-formula><tex-math id="M1">\begin{document}$ s,t\in(0,1) $\end{document}</tex-math></inline-formula>, <inline-formula><tex-math id="M2">\begin{document}$ \varepsilon&gt;0 $\end{document}</tex-math></inline-formula> is a small parameter. Under some local assumptions on <inline-formula><tex-math id="M3">\begin{document}$ V(x) $\end{document}</tex-math></inline-formula> and suitable assumptions on the nonlinearity <inline-formula><tex-math id="M4">\begin{document}$ g $\end{document}</tex-math></inline-formula>, we construct a family of positive solutions <inline-formula><tex-math id="M5">\begin{document}$ u_{\varepsilon}\in H_{\varepsilon} $\end{document}</tex-math></inline-formula> which concentrate around the global minima of <inline-formula><tex-math id="M6">\begin{document}$ V(x) $\end{document}</tex-math></inline-formula> as <inline-formula><tex-math id="M7">\begin{document}$ \varepsilon\rightarrow0 $\end{document}</tex-math></inline-formula>.</p>

Strong Convergence of Extragradient-Type Method to Solve Pseudomonotone Variational Inequalities Problems

A number of applications from mathematical programmings, such as minimax problems, penalization methods and fixed-point problems can be formulated as a variational inequality model. Most of the techniques used to solve such problems involve iterative algorithms, and that is why, in this paper, we introduce a new extragradient-like method to solve the problems of variational inequalities in real Hilbert space involving pseudomonotone operators. The method has a clear advantage because of a variable stepsize formula that is revised on each iteration based on the previous iterations. The key advantage of the method is that it works without the prior knowledge of the Lipschitz constant. Strong convergence of the method is proved under mild conditions. Several numerical experiments are reported to show the numerical behaviour of the method.

Histopathological imaging features- versus molecular measurements-based cancer prognosis modeling

For lung and many other cancers, prognosis is essentially important, and extensive modeling has been carried out. Cancer is a genetic disease. In the past 2 decades, diverse molecular data (such as gene expressions and DNA mutations) have been analyzed in prognosis modeling. More recently, histopathological imaging data, which is a “byproduct” of biopsy, has been suggested as informative for prognosis. In this article, with the TCGA LUAD and LUSC data, we examine and directly compare modeling lung cancer overall survival using gene expressions versus histopathological imaging features. High-dimensional penalization methods are adopted for estimation and variable selection. Our findings include that gene expressions have slightly better prognostic performance, and that most of the gene expressions are weakly correlated imaging features. This study may provide additional insight into utilizing the two types of important data in cancer prognosis modeling and into lung cancer overall survival.

The asymptotic coarse-graining formulation of slender-rods, bio-filaments and flagella

The inertialess fluid–structure interactions of active and passive inextensible filaments and slender-rods are ubiquitous in nature, from the dynamics of semi-flexible polymers and cytoskeletal filaments to cellular mechanics and flagella. The coupling between the geometry of deformation and the physical interaction governing the dynamics of bio-filaments is complex. Governing equations negotiate elastohydrodynamical interactions with non-holonomic constraints arising from the filament inextensibility. Such elastohydrodynamic systems are structurally convoluted, prone to numerical errors, thus requiring penalization methods and high-order spatio-temporal propagators. The asymptotic coarse-graining formulation presented here exploits the momentum balance in the asymptotic limit of small rod-like elements which are integrated semi-analytically. This greatly simplifies the elastohydrodynamic interactions and overcomes previous numerical instability. The resulting matricial system is straightforward and intuitive to implement, and allows for a fast and efficient computation, more than a hundred times faster than previous schemes. Only basic knowledge of systems of linear equations is required, and implementation achieved with any solver of choice. Generalizations for complex interaction of multiple rods, Brownian polymer dynamics, active filaments and non-local hydrodynamics are also straightforward. We demonstrate these in four examples commonly found in biological systems, including the dynamics of filaments and flagella. Three of these systems are novel in the literature. We additionally provide a Matlab code that can be used as a basis for further generalizations.