Understanding how the collective activity of neural populations relates to computation and ultimately behavior is a key goal in neuroscience. To this end, statistical methods which describe high-dimensional neural time series in terms of low-dimensional latent dynamics have played a fundamental role in characterizing neural systems. Yet, what constitutes a successful method involves two opposing criteria: (1) methods should be expressive enough to capture complex nonlinear dynamics, and (2) they should maintain a notion of interpretability often only warranted by simpler linear models. In this paper, we develop an approach that balances these two objectives: the Gaussian Process Switching Linear Dynamical System (gpSLDS). Our method builds on previous work modeling the latent state evolution via a stochastic differential equation whose nonlinear dynamics are described by a Gaussian process (GP-SDEs). We propose a novel kernel function which enforces smoothly interpolated locally linear dynamics, and therefore expresses flexible -- yet interpretable -- dynamics akin to those of recurrent switching linear dynamical systems (rSLDS). Our approach resolves key limitations of the rSLDS such as artifactual oscillations in dynamics near discrete state boundaries, while also providing posterior uncertainty estimates of the dynamics. To fit our models, we leverage a modified learning objective which improves the estimation accuracy of kernel hyperparameters compared to previous GP-SDE fitting approaches. We apply our method to synthetic data and data recorded in two neuroscience experiments and demonstrate favorable performance in comparison to the rSLDS.

Synthesis of music content generally leverages the underlying statistical structure of music to develop generative models, able to create new musical expressions within the same genre. In this work, we explore the statistical structure of a musical corpus and its effect on modulating the attention of listeners. The study specifically explores listeners' engagement to newly synthesized music and tests the hypothesis that maximizing statistical surprisal would result in increased auditory salience. The study employs a dynamical statistical model to estimate melodic line surprisal and develops an optimization procedure using parametrized codebooks to synthesize musical segments that maximize statistical surprisal. A behavioral experiment with a dichotic listening task is designed to probe salience of the synthesized melodies against original melodies by measuring listeners' engagement in a continuous-fashion. Results indicate that we can control the salience of sounds by manipulating the statistical surprisal, guided by the complexity of the temporal structure of the musical corpus. This work suggests that future work in automated music synthesis could leverage statistical models of music beyond musical aesthetics to also manipulate the degree of engagement.

We propose optic disc localization using a multiscale low-rank image decomposition technique, which separates the optic disc from other features on the retina. By decomposing the input image as the sum of$L$images, each at a specific scale and minimizing the rank of these blocks to emphasize the details at that scale. At one of the scales, the optic disc is isolated. Thereafter, we employ blob detection algorithms to localize the optic disc. The proposed method has been tested on seven fundus image databases amounting to a total of 2035 images, achieving an accuracy of 100%, 100%, 96.15%, 97.75%, 98.15%, 96.85% and 96.41% on DRIVE, DRIONS-DB, DIARETDBO, DIARETDB1, IDRiD-1, IDRiD-2, and MESSIDOR databases, respectively. Synthetically generated images with features at different scales were used to test the rate of convergence of the method as well.