Detection and Classification of Whale Acoustic Signals

This dissertation focuses on two vital challenges in relation to whale acoustic signals: detection and classification.

In detection, we evaluated the influence of the uncertain ocean environment on the spectrogram-based detector, and derived the likelihood ratio of the proposed Short Time Fourier Transform detector. Experimental results showed that the proposed detector outperforms detectors based on the spectrogram. The proposed detector is more sensitive to environmental changes because it includes phase information.

In classification, our focus is on finding a robust and sparse representation of whale vocalizations. Because whale vocalizations can be modeled as polynomial phase signals, we can represent the whale calls by their polynomial phase coefficients. In this dissertation, we used the Weyl transform to capture chirp rate information, and used a two dimensional feature set to represent whale vocalizations globally. Experimental results showed that our Weyl feature set outperforms chirplet coefficients and MFCC (Mel Frequency Cepstral Coefficients) when applied to our collected data.

Since whale vocalizations can be represented by polynomial phase coefficients, it is plausible that the signals lie on a manifold parameterized by these coefficients. We also studied the intrinsic structure of high dimensional whale data by exploiting its geometry. Experimental results showed that nonlinear mappings such as Laplacian Eigenmap and ISOMAP outperform linear mappings such as PCA and MDS, suggesting that the whale acoustic data is nonlinear.

We also explored deep learning algorithms on whale acoustic data. We built each layer as convolutions with either a PCA filter bank (PCANet) or a DCT filter bank (DCTNet). With the DCT filter bank, each layer has different a time-frequency scale representation, and from this, one can extract different physical information. Experimental results showed that our PCANet and DCTNet achieve high classification rate on the whale vocalization data set. The word error rate of the DCTNet feature is similar to the MFSC in speech recognition tasks, suggesting that the convolutional network is able to reveal acoustic content of speech signals.

Calcium/Calmodulin-Dependent Protein Kinase II Serves as a Biochemical Integrator of Calcium Signals for the Induction of Synaptic Plasticity

Repetitive Ca2+ transients in dendritic spines induce various forms of synaptic plasticity by transmitting information encoded in their frequency and amplitude. CaMKII plays a critical role in decoding these Ca2+ signals to initiate long-lasting synaptic plasticity. However, the properties of CaMKII that mediate Ca2+ decoding in spines remain elusive. Here, I measured CaMKII activity in spines using fast-framing two-photon fluorescence lifetime imaging. Following each repetitive Ca2+ elevations, CaMKII activity increased in a stepwise manner. This signal integration, at the time scale of seconds, critically depended on Thr286 phosphorylation. In the absence of Thr286 phosphorylation, only by increasing the frequency of repetitive Ca2+ elevations could high peak CaMKII activity or plasticity be induced. In addition, I measured the association between CaMKII and Ca2+/CaM during spine plasticity induction. Unlike CaMKII activity, association of Ca2+/CaM to CaMKII plateaued at the first Ca2+ elevation event. This result indicated that integration of Ca2+ signals was initiated by the binding of Ca2+/CaM and amplified by the subsequent increases in Thr286-phosphorylated form of CaMKII. Together, these findings demonstrate that CaMKII functions as a leaky integrator of repetitive Ca2+ signals during the induction of synaptic plasticity, and that Thr286 phosphorylation is critical for defining the frequencies of such integration.

Analytic Torsion, the Eta Invariant, and Closed Differential Forms on Spaces of Metrics

The central idea of this dissertation is to interpret certain invariants constructed from Laplace spectral data on a compact Riemannian manifold as regularized integrals of closed differential forms on the space of Riemannian metrics, or more generally on a space of metrics on a vector bundle. We apply this idea to both the Ray-Singer analytic torsion

and the eta invariant, explaining their dependence on the metric used to define them with a Stokes' theorem argument. We also introduce analytic multi-torsion, a generalization of analytic torsion, in the context of certain manifolds with local product structure; we prove that it is metric independent in a suitable sense.