How does the brain convert sensory information into abstract representations that can support complex behaviours? The rodent head-direction (HD) system, whose cell ensembles represent head direction in the horizontal plane, is a striking example of a “cognitive” representation without a direct sensory correlate. It can be updated by sensory inputs fromdifferentmodalities, yet persists in the absence of external input. Together with cells tuned for place, the HD system is thought to be fundamental for navigation and spatial information processing. However, relatively few studies have sought to characterise the connection between the HD system and spatial behaviour directly, and their overall outcome has been inconclusive. In the experiments that make up the first part of this thesis, we approach this issue by isolating the self-motion component of the HDsystem. We developed an (angular) path integration task in which we show that rats rely on their internal sense of direction to return to a trial-unique starting location, allowing us to investigate the contribution of the HD system to this behaviour without influences from uncontrolled external cues. Using this path integration task, we show that rats with bilateral lesions of the lateral mammillary nuclei (LMN) are significantly impaired compared to sham-operated controls. Lesions of the LMN, which contains HDcells, are known to abolish directional firing in downstream HD areas, suggesting that impairment on the task is due to loss of HD activity. We also recorded HD cell activity as rats are performing the path integration task, and found the HD representation to correlate with the rats’ choice of return journey. Thus, we provide both causal and correlational experimental evidence for a critical role of the HD system in path integration. For the second part of this thesis, we implemented a computational model of how the HD system is updated by head movements during path integration, providing a novel explanation for HD cells’ ability to anticipate the animal’s head direction. The model predicts that such anticipatory time intervals (ATIs) should depend on the frequency spectrum of the rats’ head movements. In direct comparison with experimental recording data, we show that the model can explain up to 80% of the experimentally observed variance, where none was explained by previous models. We also consider the effects of propagating the HD signal through multiple layers, identifying several potential sources of anticipation and lag. In summary, this thesis provides behavioural, lesion, and unit-recording evidence that during path integration, rats use a directional signal provided by the head direction system. The neural mechanisms responsible for the generation and maintenance of this signal are explored computationally. The finding that ATIs depend on the statistics of head movements has methodological implications and constrains models of the HD system.

In this research the stochastic nonlinear dynamic behaviors and probability density function of ship rolling are studied by nonlinear dynamic method and probability theory. The probability density function of rolling response is evaluated through solving the stochastic differential equations by using path integral method based on Gauss-Legendre interpolation scheme. The time-dependent probability of ship rolling restricted within the safe domain is provided and capsizing is investigated in the probability‟s view. The random differential equation of ships‟ rolling motion is established considering the nonlinear damping, nonlinear restoring moment, the white noise wave excitation, and the colored noise wave excitation. As an example, an ocean survey vessel T-AGOS is considered to sail in the seas of Pierson-Moskowitz wave spectrum. It is found that the probability decreases as time progresses and it decreases much more quickly for the high intensity of the noise. The ship will finally leave the safe domain and capsize in the probability‟s view. It is also shown the similarity of probability density contours between the case of white noise wave excitation and the case of colored noise wave excitation.

Interaction with the world is necessary for both animals and robots to complete tasks. This interaction requires a sense of self, or the orientation of the robot or animal with respect to the world. Creating and maintaining this model is a task which is easily maintained by animals, however can be difficult for robots due to the uncertainties in the world, sensing, and movement of the robot. This estimation difficulty is increased in sensory deprived environments, where no external, inputs are available to correct the estimate. Therefore, self generated cues of movement are needed, such as vestibular input in an animal, or accelerometer input in a robot. In spite of the difficulties, animals can easily maintain this model. This leads to the question of whether we can learn from nature by examining the biological mechanisms for pose estimation in animals. Previous work has shown that neural fields coupled with a mechanism for updating the estimate can be used to maintain a pose estimate through a sustained area of activity called a packet. Analysis of this mechanism however has shown conditions where the field can provide unexpected results or break down due to high accelerations input into the field. This analysis illustrates the challenges of controlling the activity packet size under strong inputs, and a limited speed capability using the existing mechanism. As a result of this, a novel weight combination method is proposed to provide a higher speed and increased robustness. The results of this is an increase of over two times the existing speed capability, and a resistance of the field to break down under strong rotational inputs. This updated neural field model provides a method for maintaining a stable pose estimate. To show this, a novel comparison between the proposed neural field model and the Kalman filter is considered, resulting in comparable performance in pose prediction. This work shows that an updated neural field model provides a biologically plausible pose prediction model using Bayesian inference, providing a biological analogue to a Kalman filter.

No description available.

This thesis explores the role of path integration on the firing of hippocampal place cells and medial entorhinal grid cells. Grid cells fire at equidistant locations in an environment, indicating that they keep track of the distance and direction an animal has moved in an environment. One class of model of path integration uses a continuous attractor network to update position information. The first part of this thesis showed that such a network can generate a "look-ahead" of neural activity that sweeps through the positions just visited and about to be visited, on the short time scale that is observed<italic>in vivo</italic>. Adding intrinsic currents to the neurons in the network model allowed this look-ahead to recur every theta cycle, and generate grid fields of a size comparable to data. Grid cells are a major input the hippocampus, and are hypothesized to be the source of the place specificity of place cells. When an animal explores an open environment, place cells are active in a particular location regardless of the direction in which the animal travels through it. While performing a specific task, such as visiting specific locations in the environment in sequence, however, most place cells are active only in one direction. The second part of this thesis studied the development of this directionality. It was determined that upon the initial appearance of place fields in a novel environment, place cells fired in all directions, supporting the hypothesis that the path integration is the primary determinant of place specificity. The directionality of place fields developed gradually, possibly as a result of learning. Ideas about how this directionality could develop are explored.

No description available.

No description available.

No description available.

Spatial memory and navigation relies on estimation of location. This can be achieved through several strategies, including the use of landmarks and by path integration. The latter involves inferring location from direction and distance moved relative to a known start point. The neural mechanisms of path integration are not well understood and implementation of experiments that dissociate path integration from alternative strategies is challenging. The roles of specific cell types are also unknown. Although grid cells in layer 2 of the medial entorhinal cortex (MEC) are theorised to be involved given their periodic and repeating firing fields that form a grid-like map that tiles the environment. Two excitatory cell populations have been identified in layer 2 of the MEC. Clusters of pyramidal cells that project to the CA1 are surrounded by dentate gyrus (DG) projecting stellate cells. Both populations have been shown to exhibit grid-like activity. The extent to which these cell types contribute to path integration or other strategies for solving spatial tasks is unknown. To investigate these issues, I developed a spatial memory task for mice, which uses virtual reality to generate sensitive measures of an animal’s ability to path integrate. In this task mice are trained to locate a reward zone marked with a visual cue within a virtual linear track. Use of path integration strategies can be tested in trials in which the reward zone is unmarked. In this task mice can locate the reward zone using either a local beaconing cue or path integration strategies. To assess whether self-motion derived motor information or visual feedback is used for path integration, I manipulated the translation between physical and virtual movement, putting optic and motor feedback in conflict. These manipulations suggest that mice use motor information to locate the reward zone on path integration trials. To test roles of stellate cells in the task I injected adeno-associated virus expressing the light chain of tetanus toxin, conditionally on the presence of Cre, into the MEC of mice expressing Cre specifically in stellate cells. This abolishes synaptic output from stellate cells therefore preventing them from influencing downstream neurons. I find mice with dorsal expression of the tetanus toxin virus in layer 2 stellate cells are unable to locate the reward zone using a local beaconing cue or path integration strategies. In contrast, mice with expression of green fluorescent protein (GFP) were able to locate the reward zone using both strategies. Locating the reward zone using path integration strategies first requires animal’s to learn the reward zone location, as denoted in trials with a beacon cue. To distinguish the role of stellate cells in learning versus execution of the tasks, I temporally modified the activity of stellate cells after mice had learnt to locate the reward zone using both strategies. Temporal control was achieved by use of cre-dependent adeno-associated viruses expressing mutant human muscarinic 4 receptor (hM4). When activated by clozapine - N - oxide (CNO), this receptor opens G-protein inwardly rectifying potassium (GIRK) channels and attenuates neuronal firing. Using this method, the activity of stellate cells can be temporally controlled during task execution and potentially distinguish their involvement in learning and execution of spatial memory tasks. No effect on behavioural performance was seen under these conditions. This may indicate stellate cells are required for learning but not execution of spatial memory tasks that require the use of local beaconing cues or path integration.

Distance sampling and spatial capture-recapture are statistical methods to estimate the number of animals in a wild population based on encounters between these animals and scientific detectors. Both methods estimate the probability an animal is detected during a survey, but do not explicitly model animal movement. The primary challenge is that animal movement in these surveys is unobserved; one must average over all possible paths each animal could have travelled during the survey. In this thesis, a general statistical model, with distance sampling and spatial capture-recapture as special cases, is presented that explicitly incorporates animal movement. An efficient algorithm to integrate over all possible movement paths, based on quadrature and hidden Markov modelling, is given to overcome the computational obstacles. For distance sampling, simulation studies and case studies show that incorporating animal movement can reduce the bias in estimated abundance found in conventional models and expand application of distance sampling to surveys that violate the assumption of no animal movement. For spatial capture-recapture, continuous-time encounter records are used to make detailed inference on where animals spend their time during the survey. In surveys conducted in discrete occasions, maximum likelihood models that allow for mobile activity centres are presented to account for transience, dispersal, and heterogeneous space use. These methods provide an alternative when animal movement causes bias in standard methods and the opportunity to gain richer inference on how animals move, where they spend their time, and how they interact.