Enumeration of three term arithmetic progressions in fixed density sets

Additive combinatorics is built around the famous theorem by Szemer\'edi which asserts existence of arithmetic progressions of any length among the integers. There exist several different proofs of the theorem based on very different techniques. Szemer\'edi's theorem is an existence statement, whereas the ultimate goal in combinatorics is always to make enumeration statements. In this article we develop new methods based on real algebraic geometry to obtain several quantitative statements on the number of arithmetic progressions in fixed density sets. We further discuss the possibility of a generalization of Szemer\'edi's theorem using methods from real algebraic geometry.Comment: 62 pages. Update v2: Corrected some references. Update v3: Incorporated feedbac

Tissue repair in lung disorders

The remodeling phase of tissue repair in lung disorders such as idiopathic pulmonary disease, asthma, obliterative bronchiolitis, and after lung transplantation is not well understood. One of the key players in fibrosis is the fibroblast and its progenitor, the fibrocyte. The fibroblast is the main producer of extracellular matrix molecules such as collagen, versican, perlecan, biglycan, and decorin. Fibrocytes are recruited from the bone marrow to the site of injury. It is possible that the stromal cell-derived factor-1/CXCL12 builds up in a gradient to recruit CXCR4 expressing fibrocytes, at least in the case of idiopathic pulmonary fibrosis. Patients with obliterative bronchilitis have an enlarged vessel lumen and a larger endothelial layer area, which has been shown to be correlated to more fibrocytes in the tissue. A correlation was found between the numbers of fibrocytes identified in tissue and structural changes in the lung. In idiopathic pulmonary fibrosis, a correlation was found between numbers of fibrocytes and numbers of fibroblastic foci, and in patients with obliterative bronchiolitis there was a correlation between fibrocyte numbers and thickening of the alveolar parenchyma. Eventually the fibrocyte enters the tissue and can differentiate into a fibroblast. Matrix production by fibroblasts in patients who have undergone lung transplantation and in asthmatic subjects involves both the central and the distal parts of the lung. In lung-transplanted patients, the production of proteoglycans in the distal part was found to be double that in the central part. Versican production was particularly elevated compared to controls. The production of proteoglycans was further correlated with proliferation rate. A common feature of fibroblasts in patients after lung transplantation and asthmatic subjects was that these cells proliferated more slowly than in control subjects. Distally-derived fibroblasts from asthmatic subjects produced more veriscan, were immobile, and had many protrusions. The distal parts of the lungs were also rich in collagen. A better understanding of fibrocyte and fibroblast function will help us to characterise the mechanisms behind idiopathic pulmonary disease, asthma, obliterative bronchiolitis. This knowledge can then be applied to other types of fibrotic disorders

The Impact of Tiny Organisms: Microbial Communities and Disease States

In the last decade, primarily through the use of sequencing, much has been learned about the trillions of microorganisms that reside in human hosts. These microorganisms play a wide range of roles including helping our immune systems develop, digesting our food, and protecting us from the invasion of pathogenic organisms. My thesis focuses on the characterization of fungal, viral, and bacterial communities in humans, investigating the use of defined microbial communities to cure diseases in animal models, and examining the effects of human microbiome modifications through fecal microbiota transfers. In the first part of this thesis, I use deep sequencing of ribosomal RNA gene tags to characterize the composition of the bacterial, fungal, and archaeal microbiota in pediatric patients with Inflammatory Bowel Disease and healthy controls. Archaeal reads were rare in the pediatric samples, whereas an abundant amount of fungal reads was recovered. Pediatric IBD was found to be associated with reduced diversity in both fungal and bacterial gut microbiota, and specific Candida taxa were increased in abundance in the IBD samples. I, then, describe my use of a variety of experimental and computational methods to study the viral communities of immune-compromised lung transplant recipients. Anelloviruses, circular, single-stranded DNA viruses, were found in all lung samples but were 56 times more abundant in samples from lung transplant recipients as compared to healthy controls or HIV+ subjects. In the third part of this thesis, I describe the use of defined microbial communities in mice, and its ability to reduce the production of ammonia long term and mitigate hepatic encephalopathy. This was shown to be true in both mice on a normal protein diet or a low protein diet. Last, I investigate the transfer of viral communities between humans through FMT and characterize features associated with efficient transmission. A case series where feces from a single donor were used to treat three children with ulcerative colitis was used for the analysis. Ultimately this work showed that multiple viral lineages do transfer between human individuals through fecal microbiota transplants, but in this case series none of the viruses were known to infect human cells. In this thesis, I elucidate numerous roles for the microbiome in pediatric patients with IBD and lung-transplant recipients, show exciting new finding about engineering the microbiota to help with hyperammonia, and finally investigate a possible limitation about using microbial communities as therapeutics. Together this body of work provides insights into the assemblage of tiny organisms that live within us, constantly contributing

Second Harmonic 60-GHz Power Amplifiers in 130-nm CMOS

Two different frequency doubling power amplifier topologies have been compared, one with differential input and one with single-ended, both with single-ended output at 60 GHz. The frequency doubling capability is valuable from at least two perspectives, 1) the high frequency signal is on the chip as little as possible 2) the voltage controlled oscillator and power amplifier are at different frequencies easing the isolation of the two in a transceiver. The topologies have been simulated in a 1p8M 130-nm CMOS process. The resonant nodes are tuned with on-chip transmission lines. These have been simulated in ADS and compared to a standard Cadence component, tline3. The Cadence component gives a somewhat pessimistic estimation of the losses in the transmission line. The single ended input amplifier outputs a maximum of 3.7 dBm and draws 27 mA from a 1.2 V supply, while the one with differential input outputs 5.0 dBm and draws 28 mA. The 3-dB bandwidth of the amplifiers are 5.9 GHz and 6.8 GHz, respectively

A 1.8 GHz CMOS VCO with reduced phase noise

A 2 V, 6 mA, 15% tuning range, 1.8 GHz VCO implemented in a standard 0.35 μm CMOS process is presented. The phase noise of the VCO has been greatly reduced by means of on-chip filters and one off-chip low frequency inductor. The phase noise measured at 3 MHz offset from the carrier is between -141.5 dBc/Hz and -138.5 dBc/Hz over the whole tuning rang