On neural encoding: Its estimation, application, and developmen

The spiking activity of neurons encodes information about sensory stimuli and about planned or executed motor outputs. An important problem in computational neuroscience is the development of predictive models that describe the relationship between neural spiking and sensory inputs and motor outputs. This dissertation explores different aspects and applications of neural encoding.;First, a common family of models used to capture this relationship -- known as linear non-linear Poisson (LNP) models -- is described. Natural stimuli and motor outputs often exhibit strong auto-correlations, which presents challenges to model fitting. Ways of dealing with these issues are discussed, and an application is presented in primary motor cortical data from a non-human primate while performing a grip-and-reach task.;Determining the nature of encoding in primary motor cortex is a long-standing problem in studies of the motor system. For instance, it is unclear if primary motor neurons are best thought of as encoding information about movement kinetics or kinematics. These issues carry weight in the design of brain-computer interfaces (BCIs). A study into how primary motor cortical activity adapts to a coordination task which involves concurrent control of a BCI and motor output is presented. The task, known as a dual-control BCI, requires a monkey implanted with an intracortical electrode array in primary motor cortex control one axis of a cursor through brain control and the other axes through wrist control. During the dual control task, an effective connectivity analysis shows that the units directly controlling the cursor specifically dissociate their from other units. Further, factors such as control unit tuning to wrist motion do not predict task performance. Only the control units variability is shown to be predictive of performance, which is useful when considering unit selection in such BCIs.;Second, this dissertation examines a phenomenon that occurs during the developing nervous system. Correlated spontaneous activity in the developing retina, known as retinal waves, is known to have a role in the receptive field development in higher visual areas. However the exact role of this activity in development is unknown -- whether the form of the spontaneous activity actively drives the development specific features, or whether it merely plays a permissive role. This dissertation presents a reaction-diffusion model of retinal waves mediated through cholinergic signaling. This allows for a semi-analytic analysis to identify when the retinal medium is excitable and can support wave activity, which can be useful in determine appropriate pharmacological manipulations in order to better study retinal waves' role in development.;Finally, advances in optical imaging mean that it is possible now to record from comprehensive populations of neurons from an entire brain or organism. Such studies promise to reveal much about how neural activity encodes and processes information. Hydra, a cnidarian, is a promising, novel model organism for such studies. Their nervous system is structured as a diffuse nerve net, which permits whole-animal calcium imaging of their neural activity. In order to extract this activity and relate it to behavior the neurons must be registered and tracked throughout imaging. Deformable object tracking is a challenging computer vision problem. This dissertation presents two methods that may aid in this neuron tracking problem -- one based on an extended Kalman filter accelerated through a GPU implementation, and the other based on a combination of multi-frame optic flow and image registration methods.