Applications of Algebraic Geometric Codes to Polar Coding

In recent groundbreaking work, Arikan developed polar codes as an explicit construction of symmetric capacity achieving codes for binary discrete memoryless channels with low encoding and decoding complexities. In this construction, a specific kernel matrix G is considered and is used to encode a block of channels. As the number of channels grows, each channel becomes either a noiseless channel or a pure-noise channel, and the rate of this polarization is related to the kernel matrix used. Since Arikan\u27s original construction, polar codes have been generalized to q-ary discrete memoryless channels, where q is a power of a prime, and other matrices have been considered as kernels. In our work, we expand on the ideas of Mori and Tanaka and Korada, Sasoglu, and Urbanke by employing algebraic geometric codes to produce kernels of polar codes, specifically codes from maximal and optimal function fields

Democrats make more large spending cuts than Republicans because they must counteract their prior partisan increases in spending

The Democratic Party is characterized by its willingness to increase government spending to pursue their policy goals. However, when they do make cuts, Democrats tend to make more large cuts than Republicans. Sarah E. Anderson and Laurel Harbridge use data from U.S. budgetary spending reports from 1955-2002 to explain this paradox, arguing that Democrats make cuts as corrections to balance prior partisan decisions

Representations of the Multicast Network Problem

We approach the problem of linear network coding for multicast networks from different perspectives. We introduce the notion of the coding points of a network, which are edges of the network where messages combine and coding occurs. We give an integer linear program that leads to choices of paths through the network that minimize the number of coding points. We introduce the code graph of a network, a simplified directed graph that maintains the information essential to understanding the coding properties of the network. One of the main problems in network coding is to understand when the capacity of a multicast network is achieved with linear network coding over a finite field of size q. We explain how this problem can be interpreted in terms of rational points on certain algebraic varieties.Comment: 24 pages, 19 figure

Clinical studies of the high-intensity narrow-spectrum light environmental decontamination system (HINS-light EDS), for continuous disinfection in the burn unit inpatient and outpatient settings

Infections are the leading cause of morbidity and mortality in burn patients and prevention of contamination from exogenous sources including the hospital environment is becoming increasingly emphasised. The High-Intensity Narrow-Spectrum light Environmental Decontamination System (HINS-light EDS) is bactericidal yet safe for humans, allowing continuous disinfection of the environment surrounding burn patients. Environmental samples were collected from inpatient isolation rooms and the outpatient clinic in the burn unit, and comparisons were then made between the bacterial contamination levels observed with and without use of the HINS-light EDS. Over 1000 samples were taken. Inpatient studies, with sampling carried out at 0800 h, demonstrated a significant reduction in the average number of bacterial colonies following HINS-light EDS use of between 27% and 75%, (p<0.05). There was more variation when samples were taken at times of increased activity in the room. Outpatient studies during clinics demonstrated a 61% efficacy in the reduction of bacterial contamination on surfaces throughout the room during the course of a clinic (p=0.02). The results demonstrate that use of the HINS-light EDS allows efficacious bacterial reductions over and above that achieved by standard cleaning and infection control measures in both inpatient and outpatient settings in the burn unit

Orientable total domination in graphs

Given a directed graph $D$, a set $S \subseteq V(D)$ is a total dominating set of $D$ if each vertex in $D$ has an in-neighbor in $S$. The total domination number of $D$, denoted $\gamma_t(D)$, is the minimum cardinality among all total dominating sets of $D$. Given an undirected graph $G$, we study the maximum and minimum total domination numbers among all orientations of $G$. That is, we study the upper (or lower) orientable domination number of $G$, $\rm{DOM}_t(G)$ (or $\rm{dom}_t(G)$), which is the largest (or smallest) total domination number over all orientations of $G$. We characterize those graphs with $\rm{DOM}_t(G) =\rm{dom}_t(G)$ when the girth is at least $7$ as well as those graphs with $\rm{dom}_t(G) = |V(G)|-1$. We also consider how these parameters are effected by removing a vertex from $G$, give exact values of $\rm{DOM}_t(K_{m,n})$ and $\rm{dom}_t(K_{m,n})$ and bound these parameters when $G$ is a grid graph

Characterization and optimization of bilosomes for oral vaccine delivery

Oral vaccines offer significant benefits due to the ease of administration, better patient compliance and non-invasive, needle-free administration. However, this route is marred by the harsh gastro intestinal environment which is detrimental to many vaccine formats. To address this, a range of delivery systems have been considered including bilosomes; these are bilayer vesicles constructed from non-ionic surfactants combined with the inclusion of bile salts which can stabilize the vesicles in the gastro intestinal tract by preventing membrane destabilization. The aim of this study was to investigate the effect of formulation parameters on bilosome carriers using Design of Experiments to select an appropriate formulation to assess in vivo. Bilosomes were constructed from monopalmitoylglycerol, cholesterol, dicetyl phosphate and sodium deoxycholate at different blends ratios. The optimized bilosome formulation was identified and the potential of this formulation as an oral vaccine delivery system were assessed in biodistribution and vaccine efficacy studies. Results showed that the larger bilosomes vesicles (~6 µm versus 2 µm in diameter) increased uptake within the Peyer's patches and were able to reduce median temperature differential change and promote a reduction in viral cell load in an influenza challenge study

Consideration of the efficacy of non-ionic vesicles in the targeted delivery of oral vaccines

The fundamentals of this research were to exploit non-ionic surfactant technology for delivery and administration of vaccine antigens across the oral route and to gain a better understanding of vaccine trafficking. Using a newly developed method for manufacture of non-ionic surfactant vesicles (niosomes and bilosomes) lower process temperatures were adopted thus reducing antigen exposure to potentially damaging conditions. Vesicles prepared by this method offered high protection to enzymatic degradation, with only ~10 % antigen loss measured when vesicles incorporating antigen were exposed to enzyme digestion. Interestingly, when formulated using this new production method, the addition of bile salt to the vesicles offered no advantage in terms of stability within simulated gastro-intestinal conditions. Considering their ability to deliver antigen to their target site, results demonstrated that incorporation of antigen within vesicles enhanced delivery and targeting of the antigen to the Peyer's Patch, again with niosomes and bilosomes offering similar efficiency. Delivery to both the Peyer's patches and mesentery lymphatics was shown to be dose dependent at lower concentrations, with saturation kinetics applying at higher concentrations. This demonstrates that in the formulation of vaccine delivery systems, the lipid/antigen dose ratio is not only a key factor in production cost, but is equally a key factor in the kinetics of delivery and targeting of a vaccine system

Scanning Electron Microscopy Analysis of Murine Renal, Aortic, and Cardiac Tissue

Scanning electron microscopy (SEM) is a tool that provides detailed insight into objects invisible to the human eye. As the name suggests, an electron beam is used to create an image down to the nanometer scale. The beam focuses on the surface of a sample using lenses in the electron column. In this project, we use SEM to study three types of murine tissue. First, we examine the glomerulus, found in the kidney, that is primarily responsible for filtering blood. Following a left renal vein (LRV) stenosis, SEM is used to observe changes to the glomeruli. Differences in the left and right kidney glomeruli are noted, with glomeruli appearing intact from the right kidney, while glomeruli from the left kidney are broken down. These findings are vital for preeclampsia studies, where these glomerular changes are likely a result of renal ischemia induced by the LRV stenosis. Second, cross sections of the murine descending aorta with a type B aortic dissection are examined under SEM. High magnification images reveal the morphology of red blood cell types in the false lumen. These findings will be used for studies in evaluating medical interventions for aortic dissection. Third, we examine tissue from the left ventricle and atrium of the murine heart. SEM can be used to detect if hypertrophy caused by transverse aortic constriction causes changes to cells lining the endocardium. This project demonstrates that SEM provides high resolution and magnification images, revealing new information that is pivotal to current and future biomedical studies