Invariant submanifolds for affine control systems

Given an affine control system $\dot{\mathbf x} = f({\mathbf x}) + \sum_{j=1}^m g_j({\mathbf x}) u_j$ we present an algorithmic process of construction of submanifolds that are invariant under controls assuming that the linear span of $f, g_1, \ldots, g_m$ has constant rank. We use the method of reduction of Pfaffian systems to a largest integrable subsystem and finding the first integrals and the generalized first integrals for the vector fields.Comment: 11 page

Doctor of Philosophy

dissertationThis work studied the relationship between surfactant, oil, and water, by building ternary phase diagrams, the goal of which was to identify the oil-in-water phase composition. The resulting nano-sized emulsion was coated with dicalcium phosphate by utilizing the ionic affinity between calcium ions and the emulsion surface. Since the desired function of the particle is as an oxygen carrier, the particle stability, oxygen capacity, and oxygen release rate were investigated. The first step in the process was to construct ternary phase diagrams with 1,2-dioleoyl-sn-glycero-3-phosphate (DOPA) and soy derived lecithin. The results showed that the lecithin surfactant formed an oil-in-water phase region that was 36 times greater than that of DOPA. With the desired phase composition set, the lecithin emulsion was extruded, resulting in a well-dispersed nanosized particle. A pH titration study of the emulsion found an optimized calcium phosphate coating condition at pH 8.8, at which, the calcium ion had a greater affinity for the emulsion surface than phosphate. A Hill plot was used to show calcium cooperativeness on the emulsion surface which suggested one calcium ion binds to one lecithin molecule. The lecithin emulsion particles were then coated with calcium phosphate using a layering technique that allowed for careful control of the coating thickness. The overall particle hydrodynamic radius was consistent with the growth of the calcium phosphate coating, from 8 nm to 28 nm. This observation was further supported with cryo-TEM measurements. The stability of the coated emulsion was tested in conditions that simulate practical thermal, physical, and time-dependent conditions. Throughout the tests, the coated emulsion exhibited a constant mono-dispersed particle size, while the uncoated emulsion size fluctuated greatly and exhibited increased polydispersion. The fast mixing method with the stopped-flow apparatus was employed to test the product as an oxygen carrier, and it was shown that particles with thicker calcium phosphate coatings released smaller amounts of oxygen in a given timeframe. This study proved the hypothesis by showing a fundamental understanding of emulsion science, coating the flexible emulsion surface with a biocompatible material, and a strong particle performance with regard to stability and as an oxygen carrier

Influenza and the Respiratory Microbiome

Despite the availability of vaccines, influenza causes approximately 3-5 million cases of severe illness and 400,000 deaths each year. Prevention efforts might potentially be strengthened by harnessing the host microbiome, which plays an important role in maintaining human health by promoting host immunity and colonization resistance. Although vaccines are the best available means of prevention, vaccine effectiveness has been low to moderate in recent years and vaccine coverage remains low, especially in low- to middle-income countries. Exploring the relationship between influenza virus and the respiratory microbiome may contribute to alternative strategies of prevention. This dissertation explores the relationship between influenza virus and the respiratory microbiome. In chapter 2, we describe our current understanding of respiratory virus-bacteria interactions using systematic and targeted literature searches. We explore whether respiratory viruses can place selective pressures on bacteria in the upper respiratory tract. Further, as colonization in the upper respiratory tract is a necessary precursor for many respiratory pathogens, we explore whether virus-associated changes in the upper respiratory tract microbiome can influence the etiology of bacterial pneumonia. We found strong biological support for a link between respiratory viruses, the upper respiratory tract microbiome, and bacterial pneumonia. However, we found a lack of longitudinal studies among human populations that examined all three components. To address this knowledge gap, we used a household transmission study of influenza in Nicaragua to explore potential relationships between influenza and the respiratory microbiome. In chapter 3, we examine whether the respiratory microbiome mediates susceptibility to influenza virus infection and characterize structural changes to the respiratory microbiome during influenza virus infection. We used Dirichlet multinomial mixture models to assign nose/throat samples to bacterial community types and generalized linear mixed effects models which account for clustering by household. We found a single community type associated with decreased susceptibility to influenza. Further, we found high rates of change in the microbiome structure following influenza virus infection as well as among household contacts who were never infected with influenza during follow up. In chapter 4, we use secondary cases from the Nicaraguan household transmission study to investigate whether the respiratory microbiome impacts influenza symptomology and viral shedding. We used generalized linear mixed effects models to examine the presentation of symptoms and viral shedding. Further, we used accelerated failure time models with a generalized estimating equation approach to examine time-to-event outcomes including symptom duration, shedding duration, and time to infection. The duration of symptoms varied by bacterial community type both prior to and during influenza virus infection. Further, a community type with low diversity was associated with shorter duration of viral shedding and delayed time to infection among secondary cases. The results of these various analyses suggest the respiratory microbiome may be a potential target for reducing influenza risk, household transmission, and disease severity. In the final chapter, I review the skills I learned and the challenges I encountered during the dissertation process. Finally, I review future research directions that focus on deciphering the complex dynamics between the host, pathogen, and microbiome.PHDEpidemiological ScienceUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttps://deepblue.lib.umich.edu/bitstream/2027.42/143948/1/kyuhan_1.pd

Scheduling of Multicast and Unicast Services under Limited Feedback by using Rateless Codes

Many opportunistic scheduling techniques are impractical because they require accurate channel state information (CSI) at the transmitter. In this paper, we investigate the scheduling of unicast and multicast services in a downlink network with a very limited amount of feedback information. Specifically, unicast users send imperfect (or no) CSI and infrequent acknowledgements (ACKs) to a base station, and multicast users only report infrequent ACKs to avoid feedback implosion. We consider the use of physical-layer rateless codes, which not only combats channel uncertainty, but also reduces the overhead of ACK feedback. A joint scheduling and power allocation scheme is developed to realize multiuser diversity gain for unicast service and multicast gain for multicast service. We prove that our scheme achieves a near-optimal throughput region. Our simulation results show that our scheme significantly improves the network throughput over schemes employing fixed-rate codes or using only unicast communications

Improved Receding Horizon Fourier Analysis for Quasi-periodic Signals

In this paper, an efficient short-time Fourier analysis method for the quasi-periodic signals is proposed via an optimal fixed-lag finite impulse response (FIR) smoother approach using a receding horizon scheme. In order to deal with time-varying Fourier coefficients (FCs) of quasi-periodic signals, a state space model including FCs as state variables is augmented with the variants of FCs. Through an optimal fixed-lag FIR smoother, FCs and their increments are estimated simultaneously and combined to produce final estimates. A lag size of the optimal fixed-lag FIR smoother is chosen to minimize the estimation error. Since the proposed estimation scheme carries out the correction process with the estimated variants of FCs, it is highly probable that the smaller estimation error is achieved compared with existing approaches not making use of such a process. It is shown through numerical simulation that the proposed scheme has better tracking ability for estimating time-varying FCs compared with existing ones.111Ysciescopuskc

Rampant exchange of the structure and function of extramembrane domains between membrane and water soluble proteins.

Of the membrane proteins of known structure, we found that a remarkable 67% of the water soluble domains are structurally similar to water soluble proteins of known structure. Moreover, 41% of known water soluble protein structures share a domain with an already known membrane protein structure. We also found that functional residues are frequently conserved between extramembrane domains of membrane and soluble proteins that share structural similarity. These results suggest membrane and soluble proteins readily exchange domains and their attendant functionalities. The exchanges between membrane and soluble proteins are particularly frequent in eukaryotes, indicating that this is an important mechanism for increasing functional complexity. The high level of structural overlap between the two classes of proteins provides an opportunity to employ the extensive information on soluble proteins to illuminate membrane protein structure and function, for which much less is known. To this end, we employed structure guided sequence alignment to elucidate the functions of membrane proteins in the human genome. Our results bridge the gap of fold space between membrane and water soluble proteins and provide a resource for the prediction of membrane protein function. A database of predicted structural and functional relationships for proteins in the human genome is provided at sbi.postech.ac.kr/emdmp

Network rewiring is an important mechanism of gene essentiality change.

Gene essentiality changes are crucial for organismal evolution. However, it is unclear how essentiality of orthologs varies across species. We investigated the underlying mechanism of gene essentiality changes between yeast and mouse based on the framework of network evolution and comparative genomic analysis. We found that yeast nonessential genes become essential in mouse when their network connections rapidly increase through engagement in protein complexes. The increased interactions allowed the previously nonessential genes to become members of vital pathways. By accounting for changes in gene essentiality, we firmly reestablished the centrality-lethality rule, which proposed the relationship of essential genes and network hubs. Furthermore, we discovered that the number of connections associated with essential and non-essential genes depends on whether they were essential in ancestral species. Our study describes for the first time how network evolution occurs to change gene essentiality