Network Marketing on a Small-World Network

We investigate a dynamic model of network marketing in a small-world network structure artificially constructed similarly to the Watts-Strogatz network model. Different from the traditional marketing, consumers can also play the role of the manufacturer's selling agents in network marketing, which is stimulated by the referral fee the manufacturer offers. As the wiring probability $\alpha$ is increased from zero to unity, the network changes from the one-dimensional regular directed network to the star network where all but one player are connected to one consumer. The price $p$ of the product and the referral fee $r$ are used as free parameters to maximize the profit of the manufacturer. It is observed that at $\alpha=0$ the maximized profit is constant independent of the network size $N$ while at $\alpha \neq 0$, it increases linearly with $N$. This is in parallel to the small-world transition. It is also revealed that while the optimal value of $p$ stays at an almost constant level in a broad range of $\alpha$, that of $r$ is sensitive to a change in the network structure. The consumer surplus is also studied and discussed.Comment: 12 pages, to appear in Physica

Rapid Sampling for Visualizations with Ordering Guarantees

Visualizations are frequently used as a means to understand trends and gather insights from datasets, but often take a long time to generate. In this paper, we focus on the problem of rapidly generating approximate visualizations while preserving crucial visual proper- ties of interest to analysts. Our primary focus will be on sampling algorithms that preserve the visual property of ordering; our techniques will also apply to some other visual properties. For instance, our algorithms can be used to generate an approximate visualization of a bar chart very rapidly, where the comparisons between any two bars are correct. We formally show that our sampling algorithms are generally applicable and provably optimal in theory, in that they do not take more samples than necessary to generate the visualizations with ordering guarantees. They also work well in practice, correctly ordering output groups while taking orders of magnitude fewer samples and much less time than conventional sampling schemes.Comment: Tech Report. 17 pages. Condensed version to appear in VLDB Vol. 8 No.

Characterizing Immune Responses to Marburg Virus Infection in Animal Hosts Using Statistical Transcriptomic Analysis

Marburg virus (MARV)–along with Ebola Virus–comprises Filoviridae, a family of virus which causes the life-threatening hemorrhagic fever in human and non-human primates for which there is no clinically approved vaccine. For this reason, this virus can potentially lend itself to pandemic and weapons of bioterrorism. Strikingly, this virus yields asymptomatic responses in its recently discovered host Rousettus aegyptiacus. Understanding of the interaction between MARV and different animal hosts will enable the improved understanding of filovirus immunology and the development of effective therapeutic agents. Although cell lines and primary cells have been used to investigate gene expression analysis of this virus, the transcriptomic view of MARV infection on the tissue samples of animal hosts has been an uncharted territory. The comprehensive analysis of transcriptome in hosts and spillover hosts will shed light on the immune responses on a molecular level and potentially allow the comparative analysis to understand the phenotypical differences. However, there have been gaps in resources necessary to carry the transcriptome research for MARV. For example, MARV host Rousettus aegyptiacus genome and transcriptome had not been available. Furthermore, the statistical machinery necessary to analyze multi-tissue/multi-time data was not available. In this dissertation, I introduce the two items that fill these gaps and show the application of the tools I built for novel biological discovery. In particular, I have built 1) the comprehensive de novo transcriptome reference of Rousettus aegyptiacus and 2) the Multilevel Analysis of Gene Expression (MAGE) pipeline to analyze the RNA-seq data with the complex experimental design. I show the application of MAGE in multi-time, multi-tissue transcriptome data of Macaca mulata infected with MARV. In this study, 15 rhesus macaques were sequentially sacrificed via aerosol exposure to MARV Angola over the course of 9 days, and 3 types of lymph node tissues (tracheobronchial, mesenteric, and inguinal) were extracted from each sample and sequenced for gene expression analysis. With MAGE pipeline, I discovered that the posterior median log2FC of genes separates the samples based on day post infection and viral load. I discovered the set of genes such as CD40LG and TMEM197 with interesting trends over time and how similar and different pathways have been influenced in three lymph nodes. I also identified the biologically meaningful clusters of genes based on the topology-based clustering algorithm known as Mapper. Using the MAGE posterior samples, I also determined the genes that are preferentially expressed in tracheobronchial lymph nodes. In addition to new analysis tools and biological findings, I built the gene expression exploration tool for biologists to examine differential gene expression over time in various immune-related pathways and contributing members of the pathways. In conclusion, I have contributed to the two important components in the transcriptome analysis in MARV research and discovered novel biological insights. The MAGE pipeline is modular and extensible and will be useful for the transcriptome research with the complex experimental designs which are becoming increasingly prevalent with the decrease in the cost of sequencing

Fundamentals of Irreversible Thermodynamics for Coupled Transport

Engineering phenomena occur in open systems undergoing irreversible, non-equilibrium processes for coupled mass, energy, and momentum transport. The momentum transport often becomes a primary or background process, on which driving forces of physical gradients govern mass and heat transfer rates. Although in the steady state no physical variables have explicit variation with time, entropy increases with time as long as the systems are open. The degree of irreversibility can be measured by the entropy-increasing rate, first proposed by L. Onsager. This book conceptually reorganizes the entropy and its rate in broader aspects. Diffusion is fully described as an irreversible, i.e., entropy increasing, phenomenon using four different physical pictures. Finally, an irreversible thermodynamic formalism using effective driving forces is established as an extension to the Onsager’s reciprocal theorem, which was applied to core engineering phenomena of fundamental importance: solute diffusion and thermal flux. In addition, the osmotic and thermal fluxes are explained in the unified theoretical framework