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Current deep-learning techniques for processing sets are limited to a fixed cardinality, causing a steep increase in computational complexity when the set is large. To address this, we have taken techniques used to model long-term dependencies from natural language processing and combined them with the permutation equivariant architecture, Set Transformer (STr). The result is Set Transformer XL (STrXL), a novel deep learning model capable of extending to sets of arbitrary cardinality given fixed computing resources. STrXL’s extension capability lies in its recurrent architecture. Rather than processing the entire set at once, STrXL processes only a portion of the set at a time and uses a memory mechanism to provide additional input from the past. STrXL is particularly applicable to processing sets of highthroughput sequencing (HTS) samples of DNA sequences as their set sizes can range into hundreds of thousands. When tasked with classifying HTS prairie soil samples and MNIST digits, results show that STrXL exhibits an expected memory size-accuracy trade-off that scales proportionally with the complexity of downstream tasks, but, unlike STr, is capable of generalizing to sets of arbitrary cardinality. 

A compact acoustic waveguide demultiplexer configuration is studied via finite-element numerical modeling and audio frequency experiments. The demultiplexer consists of a Y-shaped waveguide with a single input and two outputs. The narrow transmission bands created by stubs side-loaded on each output arm lead to selective transmission of certain frequencies. The experimental work characterizes the broadband response along each output arm by using an impulse response method. Finite-element numerical simulations are conducted using COMSOL. The results of the experiment and the simulation are compared to an existing analytic theory. 

The application of acoustic ring resonator structures for the manipulation of audio frequency acoustic waves is demonstrated experimentally and via numerical simulation. Three ring resonator systems are demonstrated: a simple single ring structure that acts as a comb/notch filter, a single ring between two parallel waveguides that acts as an add-drop filter, and a sequential array of equally spaced rings that creates acoustic bandgaps. The experiments are conducted in linear waveguides using an impulse response method. The ring resonators were created via 3D printing. Finite element numerical simulations were conducted using COMSOL. 

We construct a West Nile virus epidemic model that includes the interaction between the bird hosts and mosquito vectors, mosquito life stages (eggs, larvae, adults), and the dynamics of both larvicide and adulticide. We derive the basic reproduction number for the epidemic as the spectral radius of the next generation matrix. We formulate two impulsive optimal control problems which seek to balance the cost of insecticide applications (both the timing and application level) with the benefit of (1) vector control: reducing the number of mosquitoes or (2) disease control: reducing the disease burden. We reformulate these impulsive optimal control problems as nonlinear optimization problems and derive associated necessary conditions for the optimal controls. Numerical simulations are used to address three questions: How does the control and its impact on the system vary with the objective type? Is it beneficial to optimize the treatment timing? How does the control and its impact on the population vary with the type of pesticide used?