Examples for Souslin forcing

We give a model where there is a ccc Souslin forcing which does not satisfy the Knaster condition. Next, we present a model where there is a sigma-linked not sigma-centered Souslin forcing such that all its small subsets are sigma-centered but Martin Axiom fails for this order. Furthermore, we construct a totally nonhomogeneous Souslin forcing and we build a Souslin forcing which is proper but not ccc that does not contain a perfect set of mutually incompatible conditions. Finally we show that ccc Sigma^1_2-notions of forcing may not be indestructible ccc

Understanding the Impact of Fluid Viscosity on the Growth and Conjugation of Antimicrobial Resistant Donors and Recipients Pairs

To combat the spread of antimicrobial resistance (AMR), it is vital to link the behavior of donor and recipient bacteria in dynamic environments to horizontal gene transfer (HGT) potential- specifically, conjugation the primary means of spread of AMR genes. However, HGT is poorly understood under dynamic conditions, such as those in the gut of humans and animals. Most experiments are done under static conditions at viscosities similar to water, but these methods do not accurately represent the higher gut viscosities or movement. Hence, a next step to increase understanding of conjugation is with experiments using generic donor and recipient pairs at different viscosities. Accordingly, it is necessary to establish the relationship between viscosity and bacterial growth in these experiments, for which our hypothesis is that the rate of bacterial growth in fluids with higher viscosities will be lower due to water displacement. To test this hypothesis, experiments were designed to measure the number of donors, recipients and transconjugant bacteria using optical density. Varying concentrations of the thickeners agar and xanthan gum will be used to achieve different viscosity levels in the media. Media of thicknesses closer to that of bodily fluids, which are more alike to pancake syrup or batter, will be evaluated. Concentrations will be tracked at half hour intervals as a means to obtain data and to formulate a growth curve model. Some preliminary results indicate that our hypothesis has a good probability of being correct. Linear growth curve models were applied to the data for comparison purposes

Topological fermion condensates from anomalies

We show that a class of fermion theory formulated on a compact, curved manifold will generate a condensate whose magnitude is determined only by the volume and Euler characteristic of the space. The construction requires that the fermions be treated as K\"{a}hler-Dirac fields and the condensate arises from an anomaly associated with a $U(1)$ global symmetry which is subsequently broken to a discrete subgroup. Remarkably the anomaly survives under discretization of the space which allows us to compute the condensate on an arbitrary triangulation. The results, being topological in character, should hold in a wide range of gravitationally coupled fermion theories both classical and quantumComment: 10 pages, 2 figures, 2 tables. minor corrections. Version published in JHE