Mathematical models for erosion and the optimal transportation of sediment

We investigate a mathematical theory for the erosion of sediment which begins with the study of a non-linear, parabolic, weighted 4-Laplace equation on a rectangular domain corresponding to a base segment of an extended landscape. Imposing natural boundary conditions, we show that the equation admits entropy solutions and prove regularity and uniqueness of weak solutions when they exist. We then investigate a particular class of weak solutions studied in previous work of the first author and produce numerical simulations of these solutions. After introducing an optimal transportation problem for the sediment flow, we show that this class of weak solutions implements the optimal transportation of the sediment

Diversity strengthens competing teams

How does the composition of a collection of individuals affect its outcome in competition with other collections of individuals? Assuming that individuals can be different, we develop a model to interpolate between individual-level interactions and collective-level consequences. Rooted in theoretical mathematics, the model is not constrained to any specific context. Potential applications include research, education, sports, politics, ecology, agriculture, algorithms and finance. Our first main contribution is a game theoretic model that interpolates between the internal composition of an ensemble of individuals and the repercussions for the ensemble as a whole in competition with others. The second main contribution is the rigorous identification of all equilibrium points and strategies. These equilibria suggest a mechanistic underpinning for biological and physical systems to tend towards increasing diversity due to the strength it imparts to the system in competition with others.Peer reviewe

Diversity strengthens competing teams

How does the composition of a collection of individuals affect its outcome in competition with other collections of individuals? Assuming that individuals can be different, we develop a model to interpolate between individual-level interactions and collective-level consequences. Rooted in theoretical mathematics, the model is not constrained to any specific context. Potential applications include research, education, sports, politics, ecology, agriculture, algorithms and finance. Our first main contribution is a game theoretic model that interpolates between the internal composition of an ensemble of individuals and the repercussions for the ensemble as a whole in competition with others. The second main contribution is the rigorous identification of all equilibrium points and strategies. These equilibria suggest a mechanistic underpinning for biological and physical systems to tend towards increasing diversity due to the strength it imparts to the system in competition with others.Peer reviewe

Site-Directed Mutagenesis of Malate Dehydrogenase: A Class Project

Malate dehydrogenase (MDH) is an important enzyme in an organism’s metabolic pathways. MDH is found in almost all living cells and catalyzes the conversion of malate to oxaloacetate which also involves nicotinamide dehydrogenase (NAD) as a coenzyme. A method to study how an enzyme operates is to alter one of its amino acids and compare the activity of the enzyme before and after the mutation. As a class project in Advanced Biochemistry during the spring semester of 2018, we are working as a team to propose and carry out a point-based mutation on MDH

Biogeography of the Intestinal Mucosal and Lumenal Microbiome in the Rhesus Macaque

SummaryThe gut microbiome is widely studied by fecal sampling, but the extent to which stool reflects the commensal composition at intestinal sites is poorly understood. We investigated this relationship in rhesus macaques by 16S sequencing feces and paired lumenal and mucosal samples from ten sites distal to the jejunum. Stool composition correlated highly with the colonic lumen and mucosa and moderately with the distal small intestine. The mucosal microbiota varied most based on location and was enriched in oxygen-tolerant taxa (e.g., Helicobacter and Treponema), while the lumenal microbiota showed inter-individual variation and obligate anaerobe enrichment (e.g., Firmicutes). This mucosal and lumenal community variability corresponded to functional differences, such as nutrient availability. Additionally, Helicobacter, Faecalibacterium, and Lactobacillus levels in stool were highly predictive of their abundance at most other gut sites. These results quantify the composition and biogeographic relationships between gut microbial communities in macaques and support fecal sampling for translational studies

Review of battery electric vehicle propulsion systems incorporating flywheel energy storage

The development of battery electric vehicles (BEV) must continue since this can lead us towards a zero emission transport system. There has been an advent of the production BEVs in recent years; however their low range and high cost still remain the two important drawbacks. The battery is the element which strongly affects the cost and range of the BEV. The batteries offer either high specific power or high specific energy but not both. To provide the BEVs with the characteristic to compete with conventional vehicles it is beneficial to hybridize the energy storage combining a high energy battery with a high power source. This shields the battery from peak currents and improves its capacity and life. There are various devices which could qualify as a secondary storage system for the BEV such as high power battery, supercapacitor and high speed flywheel (FW). This paper aims to review a specific type of hybridisation of energy storage which combines batteries and high speed flywheels. The flywheel has been used as a secondary energy system in BEVs from the early 1970s when the oil crises triggered an interest in BEVs. Since the last decade the interest in flywheels has strengthened and their application in the kinetic energy recovery system (KERS) in Formula 1 has further bolstered the case for flywheels. With a number of automotive manufacturers getting involved in developing flywheels for road applications, the authors believe commercial flywheel based powertrains are likely to be seen in the near future. It is hence timely to produce a review of research and development in the area of flywheel assisted BEVs

The Role of Oligomerization and Cooperative Regulation in Protein Function: The Case of Tryptophan Synthase

The oligomerization/co-localization of protein complexes and their cooperative regulation in protein function is a key feature in many biological systems. The synergistic regulation in different subunits often enhances the functional properties of the multi-enzyme complex. The present study used molecular dynamics and Brownian dynamics simulations to study the effects of allostery, oligomerization and intermediate channeling on enhancing the protein function of tryptophan synthase (TRPS). TRPS uses a set of α/β–dimeric units to catalyze the last two steps of L-tryptophan biosynthesis, and the rate is remarkably slower in the isolated monomers. Our work shows that without their binding partner, the isolated monomers are stable and more rigid. The substrates can form fairly stable interactions with the protein in both forms when the protein reaches the final ligand–bound conformations. Our simulations also revealed that the α/β–dimeric unit stabilizes the substrate–protein conformation in the ligand binding process, which lowers the conformation transition barrier and helps the protein conformations shift from an open/inactive form to a closed/active form. Brownian dynamics simulations with a coarse-grained model illustrate how protein conformations affect substrate channeling. The results highlight the complex roles of protein oligomerization and the fine balance between rigidity and dynamics in protein function