Last year at VSS, Bullot, Droulez & Pylyshyn reported studies using a Modified Traveling Salesman Paradigm in which a virtual vehicle had to visit up to 10 targets once and only once, and in which the invisible targets were identified only by line segments pointing from the vehicle toward each target. We hypothesized that subjects used two distinct strategies: A “location-based strategy”, which kept track of where targets were located in screen coordinates, and a “segment-based strategy” that kept track of (...) which segments corresponded to visited targets. We report new studies that further explore these two strategies. Subjects passively observed a computer-controlled virtual vehicle that visited a number of targets. Two forms of display were used: an “Allocentric” display, in which the vehicle moved and the targets remained fixed in screen coordinates, and an “Egocentric” display, in which the vehicle's position on the screen remained fixed while the targets moved -- as if the environment were being viewed by an observer on the vehicle. At the end of each trial, the directional segments were extended to the edge of the screen and subjects were asked to perform two tasks by referring to these segments. In the “status task” observers had to indicate for each segment whether the corresponding target had been visited or not. In the “locating task” they had to locate each target along its directional segment. Performance on these two tasks measures the use of the two hypothesized strategies. Results showed that observers do well on the status task with 4 or 6 targets in both display conditions, but do poorly on the locating task, especially in the egocentric condition when there are more targets. These results are consistent with the hypothesis that in the egocentric condition the MTSP task is carried out primarily by segment-tracking, which can be viewed as a deictic strategy. (shrink)

This study investigates a new experimental paradigm called the Modified Traveling Salesman Problem. This task requires subjects to visit once and only once n invisible targets in a 2D display, using a virtual vehicle controlled by the subject. Subjects can only see the directions of the targets from the current location of the vehicle, displayed by a set of oriented segments that can be viewed inside a circular window surrounding the vehicle. Two conditions were compared. In the “allocentric” condition, subjects (...) see the vehicle move across the screen and change orientation under their command. The “egocentric” condition is similar except for how the information is provided: the position and orientation of the vehicle icon remains fixed at the center of the screen and only target directions, as indicated by the oriented segments, change as the subject “moves” the vehicle. The unexpected finding was that this task can be performed, in either condition, for up to 10 targets. We consider two possible strategies that might be used, a location-based strategy and a segment strategy. The location-based strategy relies on spatial memory and attempts to infer the locations of all the targets. The segment strategy is more local and focuses on the directional segments themselves, keeping track of the ones that represent already-visited targets. A number of observations suggest that the segment strategy was used, at least for larger numbers of targets. According to our hypothesis, keeping track of the segments requires one to use indexical reference for associating the segments with their status in the task - given by current status predicates Visited or Not-visited -, perhaps using visual indexes, deictic pointers, or object files. (shrink)

When we perceive the external world, our brain has to deal with the incompleteness and uncertainty associated with sensory inputs, memory and prior knowledge. In theoretical neuroscience probabilistic approaches have received a growing interest recently, as they account for the ability to reason with incomplete knowledge and to efficiently describe perceptive and behavioral tasks. How can the probability distributions that need to be estimated in these models be represented and processed in the brain, in particular at the single cell level? (...) We consider the basic function carried out by photoreceptor cells which consists in detecting the presence or absence of light. We give a system-level understanding of the process of phototransduction based on a bayesian formalism: we show that the process of phototransduction is equivalent to a temporal probabilistic inference in a Hidden Markov Model (HMM), for estimating the presence or absence of light. Thus, the biochemical mechanisms of phototransduction underlie the estimation of the current state probability distribution of the presence of light. A classical descriptive model describes the interactions between the different molecular messengers, ions, enzymes and channel proteins occurring within the photoreceptor by a set of nonlinear coupled differential equations. In contrast, the probabilistic HMM model is described by a discrete recurrence equation. It appears that the binary HMM has a general solution in the case of constant input. This allows a detailed analysis of the dynamics of the system. The biochemical system and the HMM behave similarly under steady-state conditions. Consequently a formal equivalence can be found between the biochemical system and the HMM. Numerical simulations further extend the results to the dynamic case and to noisy input. All in all, we have derived a probabilistic model equivalent to a classical descriptive model of phototransduction, which has the additional advantage of assigning a function to phototransduction. The example of phototransduction shows how simple biochemical interactions underlie simple probabilistic inferences. (shrink)