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- All Subjects: Jazz
- All Subjects: Songs (High voice) with piano
overall dynamics of the system and how they depend on the incidence
function. I consider both an epidemic and endemic perspective of the
model, but in both cases, three classes of incidence
functions are identified.
In the epidemic form,
power incidences, where the infective portion $I^p$ has $p\in(0,1)$,
cause unconditional host extinction,
homogeneous incidences have host extinction for certain parameter constellations and
host survival for others, and upper density-dependent incidences
never cause host extinction. The case of non-extinction in upper
density-dependent
incidences extends to the case where a latent period is included.
Using data from experiments with rhanavirus and salamanders,
maximum likelihood estimates are applied to the data.
With these estimates,
I generate the corrected Akaike information criteria, which
reward a low likelihood and punish the use of more parameters.
This generates the Akaike weight, which is used to fit
parameters to the data, and determine which incidence functions
fit the data the best.
From an endemic perspective, I observe
that power incidences cause initial condition dependent host extinction for
some parameter constellations and global stability for others,
homogeneous incidences have host extinction for certain parameter constellations and
host survival for others, and upper density-dependent incidences
never cause host extinction.
The dynamics when the incidence function is homogeneous are deeply explored.
I expand the endemic considerations in the homogeneous case
by adding a predator into the model.
Using persistence theory, I show the conditions for the persistence of each of the
predator, prey, and parasite species. Potential dynamics of the system include parasite mediated
persistence of the predator, survival of the ecosystem at high initial predator levels and
ecosystem collapse at low initial predator levels, persistence of all three species, and much more.
The purpose of this project is to create a useful tool for musicians that utilizes the harmonic content of their playing to recommend new, relevant chords to play. This is done by training various Long Short-Term Memory (LSTM) Recurrent Neural Networks (RNNs) on the lead sheets of 100 different jazz standards. A total of 200 unique datasets were produced and tested, resulting in the prediction of nearly 51 million chords. A note-prediction accuracy of 82.1% and a chord-prediction accuracy of 34.5% were achieved across all datasets. Methods of data representation that were rooted in valid music theory frameworks were found to increase the efficacy of harmonic prediction by up to 6%. Optimal LSTM input sizes were also determined for each method of data representation.
My proposed project is an educational application that will seek to simplify the<br/>process of internalizing the chord symbols most commonly seen by those learning<br/>musical improvisation. The application will operate like a game, encouraging the<br/>user to identify chord tones within time limits and award points for successfully<br/>doing so.