scholarly journals Hypergeometric Functions by Direct Path Integration

1990 ◽  
Vol 4 (3) ◽  
pp. 320 ◽  
Author(s):  
William H. Press ◽  
Saul A. Teukolsky
2020 ◽  
Author(s):  
Joseph L. Woodgate ◽  
Craig Perl ◽  
Thomas S. Collett

SummaryThe prevailing account of visually controlled routes is that an ant learns views as it follows a route, while guided by other path-setting mechanisms. Once a set of route views is memorised, the insect follows the route by turning and moving forwards when the view on the retina matches a stored view. We have engineered a situation in which this account cannot suffice in order to discover whether there may be additional components to the performance of routes. One-eyed wood ants were trained to navigate a short route in the laboratory guided by a single black, vertical bar placed in the blinded visual field. Ants thus had to turn away from the route to see the bar. They often turned to look at or beyond the bar and then turned to face in the direction of the goal. Tests in which the bar was shifted to be more peripheral or more frontal than in training produced a corresponding change in the ants’ paths, demonstrating that they were guided by the bar, presumably obtaining information during scanning turns towards the bar. Examination of the endpoints of turns away from the bar suggest that ants use the bar for guidance by learning how large a turn-back is needed to face the goal. We suggest that the ants’ zigzag paths are an integral part of visually guided route following. In addition, on some runs in which ants did not take a direct path to the goal, they still turned to face and sometimes approach the goal for a short stretch. This off-route goal facing indicates that they store a vector from start to goal and use path integration to track their position relative to the endpoint of the vector.


2011 ◽  
Vol 7 (6) ◽  
pp. 856-858 ◽  
Author(s):  
Sebastian Schwarz ◽  
Antoine Wystrach ◽  
Ken Cheng

Many animals rely on path integration for navigation and desert ants are the champions. On leaving the nest, ants continuously integrate their distance and direction of travel so that they always know their current distance and direction from the nest and can take a direct path to home. Distance information originates from a step-counter and directional information is based on a celestial compass. So far, it has been assumed that the directional information obtained from ocelli contribute to a single global path integrator, together with directional information from the dorsal rim area (DRA) of the compound eyes and distance information from the step-counter. Here, we show that ocelli mediate a distinct compass from that mediated by the compound eyes. After travelling a two-leg outbound route, untreated foragers headed towards the nest direction, showing that both legs of the route had been integrated. In contrast, foragers with covered compound eyes but uncovered ocelli steered in the direction opposite to the last leg of the outbound route. Our findings suggest that, unlike the DRA, ocelli cannot by themselves mediate path integration. Instead, ocelli mediate a distinct directional system, which buffers the most recent leg of a journey.


2012 ◽  
Author(s):  
Xiaoli Chen ◽  
Timothy P. McNamara ◽  
Jonathan W. Kelly
Keyword(s):  

2006 ◽  
Author(s):  
Xiaoang Irene Wan ◽  
Ranxiao Frances Wang ◽  
James A. Crowell

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