Energy in Yang-Mills on a Riemann Surface

Sengupta's lower bound for the Yang-Mills action on smooth connections on a bundle over a Riemann surface generalizes to the space of connections whose action is finite. In this larger space the inequality can always be saturated. The Yang-Mills critical sets correspond to critical sets of the energy action on a space of paths. This may shed light on Atiyah and Bott's conjecture concerning Morse theory for the space of connections modulo gauge transformations.Comment: 7 pages, 2 figures, Latex2e with epsfig, submitted to Journal of Mathematical Physic

Water availability as a cross-scale driver of microbial functions and free viral abundance in soil

Viral infection is widespread in natural microbial communities, with extensive study in aquatic ecosystems demonstrating direct influence on host physiology, functional activity, and mortality. While similar dynamics are assumed to occur across ecosystems, soils are distinct microbial habitats where soil physiochemical structure and water availability constrain resource availability. These unique environmental conditions have been widely demonstrated to affect microbial distribution, diversity, and functional activity in bulk soil, while their influence on virus-microbe interactions and free viral abundance remains limited. To address this knowledge gap, this research had three broad aims: i) to investigate variability in microbial responses to drying-rewetting cycles at the scale of aggregate size fractions, ii) to explore potential for aggregate-scale variability in free viral abundance and net virus production rates over time, and iii) to study the influence of dynamic soil drying and rewetting processes on microbial stress responses relative to free viral abundance. Three multifactorial incubation experiments were conducted testing treatment effects of soil aggregate size (Large Macro, Small Macro, and Micro), induction of viral lysis using Mitomycin C (MMC), drying-rewetting processes (i.e., drought length, rewetting frequency), and time. Microbial activity was monitored by repeated sampling of respiration rates with destructive sampling was performed for analysis of dissolved organic carbon, inorganic nitrogen, aggregate stability, activities of hydrolytic extracellular microbial enzymes, and viral particles and bacterial cell abundances. Results from multivariate statistical analysis indicate overarching control of time and water availability on microbial activities, as well as viral abundance and net production rates, across aggregates and in response to induction of viral lysis. In bulk soil, free viral abundance was negatively affected by soil drying and sharply decreased with drying beyond 20% gravimetric water content. Rewetting of dry soil was associated with a burst of microbial activity along with a spike in lytic viral reproduction that increased viral abundance up to 40-fold within 24 h. Together, these findings illustrate the dynamic nature of the responses of soil microbial and viral processes to soil-specific environmental factors at lesser studied spatial and temporal scales

Negative Specific Heat of a Magnetically Self-Confined Plasma Torus

It is shown that the thermodynamic maximum entropy principle predicts negative specific heat for a stationary magnetically self-confined current-carrying plasma torus. Implications for the magnetic self-confinement of fusion plasma are considered.Comment: 10p., LaTeX, 2 eps figure file

Capturing the time-varying drivers of an epidemic using stochastic dynamical systems

Epidemics are often modelled using non-linear dynamical systems observed through partial and noisy data. In this paper, we consider stochastic extensions in order to capture unknown influences (changing behaviors, public interventions, seasonal effects etc). These models assign diffusion processes to the time-varying parameters, and our inferential procedure is based on a suitably adjusted adaptive particle MCMC algorithm. The performance of the proposed computational methods is validated on simulated data and the adopted model is applied to the 2009 H1N1 pandemic in England. In addition to estimating the effective contact rate trajectories, the methodology is applied in real time to provide evidence in related public health decisions. Diffusion driven SEIR-type models with age structure are also introduced.Comment: 21 pages, 5 figure

Model theory for modal logic—Part III existence and predication

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/43175/1/10992_2004_Article_BF00293421.pd