Projective Cross-Ratio on Hypercomplex Numbers

The paper presents a new cross-ratio of hypercomplex numbers based on projective geometry. We discuss the essential properties of the projective cross-ratio, notably its invariance under Mobius transformations. Applications to the geometry of conic sections and Mobius-invariant metrics on the upper half-plane are also given

Results in Metric and Analytic Number Theory

The following Thesis consists of five chapters. The first three chapters come from Metric Number theory. Chapter 1 discusses algorithms for calculating the continued fraction of algebraic numbers, as well as presenting experimental results on how well algebraic numbers fit well known conjectures on the distribution of their partial quotients. Chapter 2 discusses the Singular and Extremality theories of so called ``well separated Dirichlet type systems''. Chapter 3 presents an effective version of the Khintchine-Groshev theorem for simultaneously small linear forms. The last two chapters are mostly in the area of uniform distribution. Chapter 4 proves a central limit theorem for the count of the fractional parts of imaginary parts of the zeros of the Riemann zeta function within an interval. Chapter 5 discusses the upper and lower distribution functions mod $1$ of sequences of the form $(0.a_na_{n+1}a_{n+2} \dots)_{n \in\mathbb N}$, where the sequence $(a_n)_{n \in \mathbb N}$ has polynomial growth

A Rapid Caspase-11 Response Induced by IFNg Priming Is Independent of Guanylate Binding Proteins

In mammalian cells, inflammatory caspases detect Gram-negative bacterial invasion by binding lipopolysaccharides (LPS). Murine caspase-11 binds cytosolic LPS, stimulates pyroptotic cell death, and drives sepsis pathogenesis. Extracellular priming factors enhance caspase-11-dependent pyroptosis. Herein we compare priming agents and demonstrate that IFNγ priming elicits the most rapid and amplified macrophage response to cytosolic LPS. Previous studies indicate that IFN-induced expression of caspase-11 and guanylate binding proteins (GBPs) are causal events explaining the effects of priming on cytosolic LPS sensing. We demonstrate that these events cannot fully account for the increased response triggered by IFNγ treatment. Indeed, IFNγ priming elicits higher pyroptosis levels in response to cytosolic LPS when macrophages stably express caspase-11. In macrophages lacking GBPs encoded on chromosome 3, IFNγ priming enhanced pyroptosis in response to cytosolic LPS as compared with other priming agents. These results suggest an unknown regulator of caspase-11-dependent pyroptosis exists, whose activity is upregulated by IFNγ

A Salmonella Typhi RNA thermosensor regulates virulence factors and innate immune evasion in response to host temperature.

Sensing and responding to environmental signals is critical for bacterial pathogens to successfully infect and persist within hosts. Many bacterial pathogens sense temperature as an indication they have entered a new host and must alter their virulence factor expression to evade immune detection. Using secondary structure prediction, we identified an RNA thermosensor (RNAT) in the 5' untranslated region (UTR) of tviA encoded by the typhoid fever-causing bacterium Salmonella enterica serovar Typhi (S. Typhi). Importantly, tviA is a transcriptional regulator of the critical virulence factors Vi capsule, flagellin, and type III secretion system-1 expression. By introducing point mutations to alter the mRNA secondary structure, we demonstrate that the 5' UTR of tviA contains a functional RNAT using in vitro expression, structure probing, and ribosome binding methods. Mutational inhibition of the RNAT in S. Typhi causes aberrant virulence factor expression, leading to enhanced innate immune responses during infection. In conclusion, we show that S. Typhi regulates virulence factor expression through an RNAT in the 5' UTR of tviA. Our findings demonstrate that limiting inflammation through RNAT-dependent regulation in response to host body temperature is important for S. Typhi's "stealthy" pathogenesis

Genetic variation in the MacAB-TolC efflux pump influences pathogenesis of invasive Salmonella isolates from Africa

The various sub-species of Salmonella enterica cause a range of disease in human hosts. The human-adapted Salmonella enterica serovar Typhi enters the gastrointestinal tract and invades systemic sites to cause enteric (typhoid) fever. In contrast, most non-typhoidal serovars of Salmonella are primarily restricted to gut tissues. Across Africa, invasive non-typhoidal Salmonella (iNTS) have emerged with an ability to spread beyond the gastrointestinal tract and cause systemic bloodstream infections with increased morbidity and mortality. To investigate this evolution in pathogenesis, we compared the genomes of African iNTS isolates with other Salmonella enterica serovar Typhimurium and identified several macA and macB gene variants unique to African iNTS. MacAB forms a tripartite efflux pump with TolC and is implicated in Salmonella pathogenesis. We show that macAB transcription is upregulated during macrophage infection and after antimicrobial peptide exposure, with macAB transcription being supported by the PhoP/Q two-component system. Constitutive expression of macAB improves survival of Salmonella in the presence of the antimicrobial peptide C18G. Furthermore, these macAB variants affect replication in macrophages and influence fitness during colonization of the murine gastrointestinal tract. Importantly, the infection outcome resulting from these macAB variants depends upon both the Salmonella Typhimurium genetic background and the host gene Nramp1, an important determinant of innate resistance to intracellular bacterial infection. The variations we have identified in the MacAB-TolC efflux pump in African iNTS may reflect evolution within human host populations that are compromised in their ability to clear intracellular Salmonella infections