The CRA: 30 years of wealth building and what we must do to finish the job

Community Reinvestment Act of 1977

Second-order cone optimization of the gradostat

We maximize the production of biogas in a gradostat at steady state. The physical decision variables are the water, substrate, and biomass entering each tank and the flows through the interconnecting pipes. Our main technical focus is the nonconvex constraint describing microbial growth. We formulate a relaxation and prove that it is exact when the gradostat is outflow connected, its system matrix is irreducible, and the growth rate satisfies a simple condition. The relaxation has second-order cone representations for the Monod and Contois growth rates. We extend the steady state models to the case of multiple time periods by replacing the derivatives with numerical approximations instead of setting them to zero. The resulting optimizations are second-order cone programs, which can be solved at large scales using standard industrial software

A Comparison of Correlation-Agnostic Techniques for Magnetic Navigation

Navigation using a Global Navigation Satellite System (GNSS) is common for autonomous vehicles (ground or air). Unfortunately, GNSS-based navigation solutions are often susceptible to jamming, interference, and a limited number of satellites. A proposed technique to aid in navigation when a GNSS-based system fails is magnetic navigation - navigation using the Earth\u27s magnetic anomaly field. This solution comes with its own set of problems including the need for quality magnetic maps in every area in which magnetic navigation will be used. Many of the currently available magnetic maps are generated from a combination of dated magnetic surveys, resulting in maps riddled with spatially correlated errors, the correlation structure of which is largely unknown. The correlations are further confounded while navigating because they depend on how fast a vehicle moves through the map in addition to the original correlated error structure. Traditionally, this spatial correlation has been handled by introducing a First Order Gauss-Markov (FOGM) noise model into the estimation routine, with the FOGM parameters set somewhat arbitrarily. In this paper, we investigate the possibility of using correlation agnostic fusion techniques (i.e., Covariance Intersection and Probabilistically Conservative Fusion) for magnetic navigation. These techniques have the advantage of not requiring any parameter tuning; the same method and tuning parameters are used regardless of the spatial correlation. We demonstrate that utilizing probabilistically conservative fusion leads to navigation results that are better than many tuned approaches and reasonably close to the best possible tuning parameters of a FOGM

Convex optimization of bioprocesses

We optimize a general model of bioprocesses, which is nonconvex due to the microbial growth in the biochemical reactors. We formulate a convex relaxation and give conditions guaranteeing its exactness in both the transient and steady state cases. When the growth kinetics are modeled by the Monod function under constant biomass or the Contois function, the relaxation is a second-order cone program, which can be solved efficiently at large scales. We implement the model on a numerical example based on a wastewater treatment system

K-12 Security System Final Project Report

Current emergency technology for school shootings is very basic, relying largely on faculty training and basic alarm technology. Alarms are usually activated via emergency buttons arranged throughout the school or online programs requiring a log-in. These methods are cheap and easy to install, however running to an emergency button or logging into a computer program takes time and current school alarms provide very little information about the location of the threat. The K- 12 Security System Team proposes the design and implementation of a system to aid school authorities to minimize the risk posed to students and staff in case of gun threats in K-12 schools. The system must be quick and unobtrusive to activate and should be able to locate and communicate the source of the activation. The system must also have two levels of alarm- a subtle alarm for pre-shooter situations where de-escalation may be possible and a blaring alarm for active shooter situations. The preliminary system design should also be cheap enough for a school to purchase, which our advisor recommended to be a total budget of around $3,200. Since this is a proof of concept, our prototype stayed well under that constraint as well as Trinity’s own$1200 budget cap. The system also needs to be active for the entirety of the school day, so any mobile components should have a battery that lasts at least a semester or a rechargeable battery. To satisfy the requirements the security team broke the project up into 3 subsystems. These subsystems include the central computing unit (CCU), portal beacon, and handheld fob device. Splitting up the project in this manner allowed for us to better track our progress and ensure that each subsystem can run on its own. The team experienced time production slowdowns due to the pandemic keeping one of our three members off campus, winter storm delivery delays, and several faulty Arduino systems. Despite these limitations, the K-12 security team was able to build the fob, portal beacon, and CCU subsystems and successfully update a database using signals sent from a phone-sized, handheld fob. The prototype has multiple alarm levels and stores both the alarm level and ID number of the fob

Non-Renormalization Theorems for Operators with Arbitrary Numbers of Derivatives in N=4{\cal N}=4 Yang Mills Theory

We generalize the proof of the non-renormalization of the four derivative operators in ${\cal N}=4$ Yang Mills theory with gauge group SU(2) to show that certain terms with 2N derivatives are not renormalized in the theory with gauge group SU(N). These terms may be determined exactly by a simple perturbative computation. Similar results hold for finite ${\cal N}=2$ theories. We comment on the implications of these results.Comment: 14 pages, late