Georgia Institute of Technology College of Sciences

Treatment of bacterial infections with antibiotics is universally accepted as one of (if not THE) most significant contributions of medical intervention to reducing mortality and morbidity during last century. Surprisingly, basic knowledge about how antibiotics kill or prevent the growth of bacteria is only just beginning to emerge and the dose and term of antibiotic treatment has long been determined by clinicians empirically and intuitively. There is a recent drive to theoretically and experimentally rationalize antibiotic treatment protocols with the aim to them and to design protocols which maximize antibiotics’ efficacy while preventing resistance emergence. Central to these endeavors are the pharmacodynamics of the antibiotic(s) and bacteria, PD (the relationship between the concentration of the antibiotic and the rate of growth/death of bacteria), and the pharmacokinetics of the antibiotic, PK (the distribution and change in concentration of the antibiotics in a treated host) of each bacteria. The procedures for estimating of PD and PK parameters are well established and standardized worldwide. Although different PK parameters are commonly employed for the design of antibiotic treatment protocols most of these considerations, a single PD parameter is usually used, the minimum inhibitory concentration (MIC). The Clinical and Laboratory Standards Institute (CLSI) approved method for estimating MICs defines testing conditions that are optimal for the antibiotic, like low densities and exponential growth, rarely obtain outside of the laboratory and virtually never in the bacteria infecting mammalian hosts. Real infections with clinical symptoms commonly involve very high densities of bacteria, most of which are not replicating, and these bacteria are rarely planktonic, rather residing as colonies or within matrices called biofilms which sometimes include other species of bacteria. Refractoriness (non-inherited resistance) is the term used to describe an observed inefficacy of antibiotics on otherwise antibiotic-susceptible bacterial populations. This talk will focus on our efforts to describe the pharmacodynamic relationship between Staphylococcus aureus and antibiotics of six classes in the light of antibiotic refractoriness. I will begin by addressing the effects of cell density on the MIC index, after which I intend to present unpublished data descriptive of physiology-related effects on antibiotic efficacy. Additionally, we will explore the potential contribution of such in vitro results, to observed/predicted clinical outcomes using standard mathematical models of antibiotic treatment which also serve to generate testable hypotheses.

In recent literature, different mothods have been proposed on how to define and model stochastic mortality. In most of these approaches, the so-called spot force of mortality is modeled as a stochastic process. In contrast to such spot force models, forward force mortality models infer dynamics on the entire age/term-structure of mortality. This paper considers forward models defined based on best-estimate forecasts of survival probabilities as can be found in so-called best-estimate generation life tables. We provide a detailed analysis of forward mortality models deriven by finite-dimensional Brownian motion. In particular, we address the relationship to other modeling approaches, the consistency problem of parametric forward models, and the existence of finite dimensional realizations for Gaussian forward models. All results are illustrated based on a simple example with an affine specification.

We will introduce new constructions of infinite families of smooth structures on small 4-manifolds and infinite families of smooth knottings of surfaces.

Biologists tracking crab larvae, engineers designing pollution mitigation strategies, and climate scientists studying tracer transport in the oceans are among many who rely on trajectory predictions from ocean models. State-of-the-art models have been shown to produce reliable velocity forecasts for 48-72 hours, yet the predictability horizon for trajectories and related Lagrangian quantities remains significantly shorter. We investigate the potential for decreasing Lagrangian prediction errors by applying a constrained normal mode analysis (NMA) to blend drifter observations with model velocity fields. The properties of an unconstrained NMA and the effects of parameter choices are discussed. The constrained NMA technique is initially presented in a perfect model simulation, where the “true” velocity field is known and the resulting error can be directly assessed. Finally, we will show results from a recent experiment in the East Asia Sea, where real observations were assimilated into operational ocean model hindcasts.