An Unstructured Mesh Convergent Reaction-Diffusion Master Equation for Reversible Reactions

The convergent reaction-diffusion master equation (CRDME) was recently developed to provide a lattice particle-based stochastic reaction-diffusion model that is a convergent approximation in the lattice spacing to an underlying spatially-continuous particle dynamics model. The CRDME was designed to be identical to the popular lattice reaction-diffusion master equation (RDME) model for systems with only linear reactions, while overcoming the RDME's loss of bimolecular reaction effects as the lattice spacing is taken to zero. In our original work we developed the CRDME to handle bimolecular association reactions on Cartesian grids. In this work we develop several extensions to the CRDME to facilitate the modeling of cellular processes within realistic biological domains. Foremost, we extend the CRDME to handle reversible bimolecular reactions on unstructured grids. Here we develop a generalized CRDME through discretization of the spatially continuous volume reactivity model, extending the CRDME to encompass a larger variety of particle-particle interactions. Finally, we conclude by examining several numerical examples to demonstrate the convergence and accuracy of the CRDME in approximating the volume reactivity model.Comment: 35 pages, 9 figures. Accepted, J. Comp. Phys. (2018

Two likelihood-based semiparametric estimation methods for panel count data with covariates

We consider estimation in a particular semiparametric regression model for the mean of a counting process with ``panel count'' data. The basic model assumption is that the conditional mean function of the counting process is of the form $E\{\mathbb{N}(t)|Z\}=\exp(\beta_0^TZ)\Lambda_0(t)$ where $Z$ is a vector of covariates and $\Lambda_0$ is the baseline mean function. The ``panel count'' observation scheme involves observation of the counting process $\mathbb{N}$ for an individual at a random number $K$ of random time points; both the number and the locations of these time points may differ across individuals. We study semiparametric maximum pseudo-likelihood and maximum likelihood estimators of the unknown parameters $(\beta_0,\Lambda_0)$ derived on the basis of a nonhomogeneous Poisson process assumption. The pseudo-likelihood estimator is fairly easy to compute, while the maximum likelihood estimator poses more challenges from the computational perspective. We study asymptotic properties of both estimators assuming that the proportional mean model holds, but dropping the Poisson process assumption used to derive the estimators. In particular we establish asymptotic normality for the estimators of the regression parameter $\beta_0$ under appropriate hypotheses. The results show that our estimation procedures are robust in the sense that the estimators converge to the truth regardless of the underlying counting process.Comment: Published in at http://dx.doi.org/10.1214/009053607000000181 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Surface-wave group-delay and attenuation kernels

We derive both 3-D and 2-D Fréchet sensitivity kernels for surface-wave group-delay and anelastic attenuation measurements. A finite-frequency group-delay exhibits 2-D off-ray sensitivity either to the local phase-velocity perturbation δc/c or to its dispersion ω(∂/∂ω)(δc/c) as well as to the local group-velocity perturbation δC/C. This dual dependence makes the ray-theoretical inversion of measured group delays for 2-D maps of δC/C a dubious procedure, unless the lateral variations in group velocity are extremely smooth

The SNARE protein FolVam7 mediates intracellular trafficking to regulate conidiogenesis and pathogenicity in Fusarium oxysporum f. sp. lycopersici.

Soluble N-ethylmaleimide-sensitive factor attachment protein receptors (SNAREs) are conserved in fungi, plants and animals. The Vam7 gene encodes a v-SNARE protein that involved in vesicle trafficking in fungi. Here, we identified and characterized the function of FolVam7, a homologue of the yeast SNARE protein Vam7p in Fusarium oxysporum f. sp. lycopersici (Fol), a fungal pathogen of tomato. FolVam7 contains SNARE and PX (Phox homology) domains that are indispensable for normal localization and function of FolVam7. Targeted gene deletion showed that FolVam7-mediated vesicle trafficking is important for vegetative growth, asexual development, conidial morphology and plant infection. Further cytological examinations revealed that FolVam7 is localized to vesicles and vacuole membranes in the hyphae stage. Moreover, the ΔFolvam7 mutant is insensitive to salt and osmotic stresses and hypersensitive to cell wall stressors. Taken together, our results suggested that FolVam7-mediated vesicle trafficking promotes vegetative growth, conidiogenesis and pathogenicity of Fol

Reciprocity in Social Networks with Capacity Constraints

Directed links -- representing asymmetric social ties or interactions (e.g., "follower-followee") -- arise naturally in many social networks and other complex networks, giving rise to directed graphs (or digraphs) as basic topological models for these networks. Reciprocity, defined for a digraph as the percentage of edges with a reciprocal edge, is a key metric that has been used in the literature to compare different directed networks and provide "hints" about their structural properties: for example, are reciprocal edges generated randomly by chance or are there other processes driving their generation? In this paper we study the problem of maximizing achievable reciprocity for an ensemble of digraphs with the same prescribed in- and out-degree sequences. We show that the maximum reciprocity hinges crucially on the in- and out-degree sequences, which may be intuitively interpreted as constraints on some "social capacities" of nodes and impose fundamental limits on achievable reciprocity. We show that it is NP-complete to decide the achievability of a simple upper bound on maximum reciprocity, and provide conditions for achieving it. We demonstrate that many real networks exhibit reciprocities surprisingly close to the upper bound, which implies that users in these social networks are in a sense more "social" than suggested by the empirical reciprocity alone in that they are more willing to reciprocate, subject to their "social capacity" constraints. We find some surprising linear relationships between empirical reciprocity and the bound. We also show that a particular type of small network motifs that we call 3-paths are the major source of loss in reciprocity for real networks