Dynamics and scaling of self-excited passive vortex generators for underwater propulsion

A series of experiments was conducted on the use of a device to passively generate vortex rings, henceforth a passive vortex generator (PVG). The device is intended as a means of propulsion for underwater vehicles, as the use of vortex rings has been shown to decrease the fuel consumption of a vehicle by up to 40% Ruiz (2010).

The PVG was constructed out of a collapsible tube encased in a rigid, airtight box. By adjusting the pressure within the airtight box while fluid was flowing through the tube, it was possible to create a pulsed jet with vortex rings via self-excited oscillations of the collapsible tube.

A study of PVG integration into an existing autonomous underwater vehicle (AUV) system was conducted. A small AUV was used to retrofit a PVG with limited alterations to the original vehicle. The PVG-integrated AUV was used for self-propelled testing to measure the hydrodynamic (Froude) efficiency of the system. The results show that the PVG-integrated AUV had a 22% increase in the Froude efficiency using a pulsed jet over a steady jet. The maximum increase in the Froude efficiency was realized when the formation time of the pulsed jet, a nondimensional time to characterize vortex ring formation, was coincident with vortex ring pinch-off. This is consistent with previous studies that indicate that the maximization of efficiency for a pulsed jet vehicle is realized when the formation of vortex rings maximizes the vortex ring energy and size.

The other study was a parameter study of the physical dimensions of a PVG. This study was conducted to determine the effect of the tube diameter and length on the oscillation characteristics such as the frequency. By changing the tube diameter and length by factors of 3, the frequency of self-excited oscillations was found to scale as f~D_0^{-1/2} L_0^0, where D_0 is the tube diameter and L_0 the tube length. The mechanism of operation is suggested to rely on traveling waves between the tube throat and the end of the tube. A model based on this mechanism yields oscillation frequencies that are within the range observed by the experiment.

A model of the olfactory bulb and beyond

The olfactory bulb of mammals aids in the discrimination of odors. A mathematical model based on the bulbar anatomy and electrophysiology is described. Simulations of the highly non-linear model produce a 35-60 Hz modulated activity, which is coherent across the bulb. The decision states (for the odor information) in this system can be thought of as stable cycles, rather than as point stable states typical of simpler neuro-computing models. Analysis shows that a group of coupled non-linear oscillators are responsible for the oscillatory activities. The output oscillation pattern of the bulb is determined by the odor input. The model provides a framework in which to understand the transformation between odor input and bulbar output to the olfactory cortex. This model can also be extended to other brain areas such as the hippocampus, thalamus, and neocortex, which show oscillatory neural activities. There is significant correspondence between the model behavior and observed electrophysiology.

It has also been suggested that the olfactory bulb, the first processing center after the sensory cells in the olfactory pathway, plays a role in olfactory adaptation, odor sensitivity enhancement by motivation, and other olfactory psychophysical phenomena. The input from the higher olfactory centers to the inhibitory cells in the bulb are shown to be able to modulate the response, and thus the sensitivity, of the bulb to odor input. It follows that the bulb can decrease its sensitivity to a pre-existing and detected odor (adaptation) while remaining sensitive to new odors, or can increase its sensitivity to discover interesting new odors. Other olfactory psychophysical phenomena such as cross-adaptation are also discussed.

Neural and computational representations of decision variables

These studies explore how, where, and when representations of variables critical to decision-making are represented in the brain. In order to produce a decision, humans must first determine the relevant stimuli, actions, and possible outcomes before applying an algorithm that will select an action from those available. When choosing amongst alternative stimuli, the framework of value-based decision-making proposes that values are assigned to the stimuli and that these values are then compared in an abstract “value space” in order to produce a decision. Despite much progress, in particular regarding the pinpointing of ventromedial prefrontal cortex (vmPFC) as a region that encodes the value, many basic questions remain. In Chapter 2, I show that distributed BOLD signaling in vmPFC represents the value of stimuli under consideration in a manner that is independent of the type of stimulus it is. Thus the open question of whether value is represented in abstraction, a key tenet of value-based decision-making, is confirmed. However, I also show that stimulus-dependent value representations are also present in the brain during decision-making and suggest a potential neural pathway for stimulus-to-value transformations that integrates these two results.

More broadly speaking, there is both neural and behavioral evidence that two distinct control systems are at work during action selection. These two systems compose the “goal-directed system”, which selects actions based on an internal model of the environment, and the “habitual” system, which generates responses based on antecedent stimuli only. Computational characterizations of these two systems imply that they have different informational requirements in terms of input stimuli, actions, and possible outcomes. Associative learning theory predicts that the habitual system should utilize stimulus and action information only, while goal-directed behavior requires that outcomes as well as stimuli and actions be processed. In Chapter 3, I test whether areas of the brain hypothesized to be involved in habitual versus goal-directed control represent the corresponding theorized variables.

The question of whether one or both of these neural systems drives Pavlovian conditioning is less well-studied. Chapter 4 describes an experiment in which subjects were scanned while engaged in a Pavlovian task with a simple non-trivial structure. After comparing a variety of model-based and model-free learning algorithms (thought to underpin goal-directed and habitual decision-making, respectively), it was found that subjects’ reaction times were better explained by a model-based system. In addition, neural signaling of precision, a variable based on a representation of a world model, was found in the amygdala. These data indicate that the influence of model-based representations of the environment can extend even to the most basic learning processes.

Knowledge of the state of hidden variables in an environment is required for optimal inference regarding the abstract decision structure of a given environment and therefore can be crucial to decision-making in a wide range of situations. Inferring the state of an abstract variable requires the generation and manipulation of an internal representation of beliefs over the values of the hidden variable. In Chapter 5, I describe behavioral and neural results regarding the learning strategies employed by human subjects in a hierarchical state-estimation task. In particular, a comprehensive model fit and comparison process pointed to the use of "belief thresholding". This implies that subjects tended to eliminate low-probability hypotheses regarding the state of the environment from their internal model and ceased to update the corresponding variables. Thus, in concert with incremental Bayesian learning, humans explicitly manipulate their internal model of the generative process during hierarchical inference consistent with a serial hypothesis testing strategy.

Search for Higgs Boson Production Beyond the Standard Model Using the Razor Kinematic Variables in pp Collisions at √s=8 TeV and Optimization of Higgs Boson Identification Using a Quantum Annealer

In the first part of this thesis we search for beyond the Standard Model physics through the search for anomalous production of the Higgs boson using the razor kinematic variables. We search for anomalous Higgs boson production using proton-proton collisions at center of mass energy √s=8 TeV collected by the Compact Muon Solenoid experiment at the Large Hadron Collider corresponding to an integrated luminosity of 19.8 fb^-1.

In the second part we present a novel method for using a quantum annealer to train a classifier to recognize events containing a Higgs boson decaying to two photons. We train that classifier using simulated proton-proton collisions at √s=8 TeV producing either a Standard Model Higgs boson decaying to two photons or a non-resonant Standard Model process that produces a two photon final state.

The production mechanisms of the Higgs boson are precisely predicted by the Standard Model based on its association with the mechanism of electroweak symmetry breaking. We measure the yield of Higgs bosons decaying to two photons in kinematic regions predicted to have very little contribution from a Standard Model Higgs boson and search for an excess of events, which would be evidence of either non-standard production or non-standard properties of the Higgs boson. We divide the events into disjoint categories based on kinematic properties and the presence of additional b-quarks produced in the collisions. In each of these disjoint categories, we use the razor kinematic variables to characterize events with topological configurations incompatible with typical configurations found from standard model production of the Higgs boson.

We observe an excess of events with di-photon invariant mass compatible with the Higgs boson mass and localized in a small region of the razor plane. We observe 5 events with a predicted background of 0.54 ± 0.28, which observation has a p-value of 10^-3 and a local significance of 3.35σ. This background prediction comes from 0.48 predicted non-resonant background events and 0.07 predicted SM higgs boson events. We proceed to investigate the properties of this excess, finding that it provides a very compelling peak in the di-photon invariant mass distribution and is physically separated in the razor plane from predicted background. Using another method of measuring the background and significance of the excess, we find a 2.5σ deviation from the Standard Model hypothesis over a broader range of the razor plane.

In the second part of the thesis we transform the problem of training a classifier to distinguish events with a Higgs boson decaying to two photons from events with other sources of photon pairs into the Hamiltonian of a spin system, the ground state of which is the best classifier. We then use a quantum annealer to find the ground state of this Hamiltonian and train the classifier. We find that we are able to do this successfully in less than 400 annealing runs for a problem of median difficulty at the largest problem size considered. The networks trained in this manner exhibit good classification performance, competitive with the more complicated machine learning techniques, and are highly resistant to overtraining. We also find that the nature of the training gives access to additional solutions that can be used to improve the classification performance by up to 1.2% in some regions.