The auxiliary region method: A hybrid method for coupling PDE- and Brownian-based dynamics for reaction-diffusion systems

Reaction-diffusion systems are used to represent many biological and physical phenomena. They model the random motion of particles (diffusion) and interactions between them (reactions). Such systems can be modelled at multiple scales with varying degrees of accuracy and computational efficiency. When representing genuinely multiscale phenomena, fine-scale models can be prohibitively expensive, whereas coarser models, although cheaper, often lack sufficient detail to accurately represent the phenomenon at hand. Spatial hybrid methods couple two or more of these representations in order to improve efficiency without compromising accuracy. In this paper, we present a novel spatial hybrid method, which we call the auxiliary region method (ARM), which couples PDE and Brownian-based representations of reaction-diffusion systems. Numerical PDE solutions on one side of an interface are coupled to Brownian-based dynamics on the other side using compartment-based "auxiliary regions". We demonstrate that the hybrid method is able to simulate reaction-diffusion dynamics for a number of different test problems with high accuracy. Further, we undertake error analysis on the ARM which demonstrates that it is robust to changes in the free parameters in the model, where previous coupling algorithms are not. In particular, we envisage that the method will be applicable for a wide range of spatial multi-scales problems including, filopodial dynamics, intracellular signalling, embryogenesis and travelling wave phenomena.Comment: 29 pages, 14 figures, 2 table

Dependence relationships between Gene Ontology terms based on TIGR gene product annotations

The Gene Ontology is an important tool for the representation and processing of information about gene products and functions. It provides controlled vocabularies for the designations of cellular components, molecular functions, and biological processes used in the annotation of genes and gene products. These constitute three separate ontologies, of cellular components), molecular functions and biological processes, respectively. The question we address here is: how are the terms in these three separate ontologies related to each other? We use statistical methods and formal ontological principles as a first step towards finding answers to this question

Private Graphon Estimation for Sparse Graphs

We design algorithms for fitting a high-dimensional statistical model to a large, sparse network without revealing sensitive information of individual members. Given a sparse input graph $G$, our algorithms output a node-differentially-private nonparametric block model approximation. By node-differentially-private, we mean that our output hides the insertion or removal of a vertex and all its adjacent edges. If $G$ is an instance of the network obtained from a generative nonparametric model defined in terms of a graphon $W$, our model guarantees consistency, in the sense that as the number of vertices tends to infinity, the output of our algorithm converges to $W$ in an appropriate version of the $L_2$ norm. In particular, this means we can estimate the sizes of all multi-way cuts in $G$. Our results hold as long as $W$ is bounded, the average degree of $G$ grows at least like the log of the number of vertices, and the number of blocks goes to infinity at an appropriate rate. We give explicit error bounds in terms of the parameters of the model; in several settings, our bounds improve on or match known nonprivate results.Comment: 36 page

Concentration dependent aerosol substrates: UV-vis attenuation measurement

Ultraviolet and visible (UV/vis) light were used to determine the composition of aerosol samples taken from several military bases located in the Middle East. The aerosols were collected using a cascade impactor placing time resolved aerosols on strips of Mylar. These strips were then fed into a fiber optic UV/vis spectrometer which passes light through the Mylar strip and detects the amount of transmitted light relative to a blank standard. By measuring the light transmitted, the amount of aerosol on the Mylar strip was determined proportional to a calibration curve of standard mass depositions. The UV/vis tests were then compared to results from β-gauge analysis performed on the same samples to determine the validity of optical transparency as a substitute for electron attenuation studies. It was determined that the UV/vis data is largely comparable to the β -gauge data showing that UV/vis is a viable alternative to the β -gauge method as well as being more convenient, expedient, and easier to perform