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Scale-Free Navigational Planning by Neuronal Traveling Waves.

Khajeh-Alijani A, Urbanczik R, Senn W - PLoS ONE (2015)

Bottom Line: The time needed to reach the steady state represents an estimate of an agent's waiting time before it heads off to the goal.Given typical waiting times we estimate the minimal number of neurons involved in the cognitive map.In the context of the planning model, forward and backward spread of neuronal activity, oscillatory waves, and phase precession get a functional interpretation, allowing for speculations about the biological counterpart.

View Article: PubMed Central - PubMed

Affiliation: Department of Physiology, University of Bern, Bern, Switzerland.

ABSTRACT
Spatial navigation and planning is assumed to involve a cognitive map for evaluating trajectories towards a goal. How such a map is realized in neuronal terms, however, remains elusive. Here we describe a simple and noise-robust neuronal implementation of a path finding algorithm in complex environments. We consider a neuronal map of the environment that supports a traveling wave spreading out from the goal location opposite to direction of the physical movement. At each position of the map, the smallest firing phase between adjacent neurons indicate the shortest direction towards the goal. In contrast to diffusion or single-wave-fronts, local phase differences build up in time at arbitrary distances from the goal, providing a minimal and robust directional information throughout the map. The time needed to reach the steady state represents an estimate of an agent's waiting time before it heads off to the goal. Given typical waiting times we estimate the minimal number of neurons involved in the cognitive map. In the context of the planning model, forward and backward spread of neuronal activity, oscillatory waves, and phase precession get a functional interpretation, allowing for speculations about the biological counterpart.

No MeSH data available.


Related in: MedlinePlus

Planning performance decreases with decreasing oscillation frequency and is worst for a solitary wave.(a) Planning performance as a function of the noise level for a 18 Hz (blue) and a 11 Hz (green) intrinsic oscillation frequency with 4 readout cycles to select a single action. For the solitary wave, planning performance was measured after averaging the path lengths across 4 sweeps. Error bars from 10 realizations. (b, c) Color coded spike times relative to the spike time of the goal position (1,1) for (b) the 18 Hz periodic traveling wave after reaching steady state and (c) the solitary wave, both with noise level σext = 0.2. For the solitary wave, the spike times do not faithfully represent distance from goal, and hence the action selection mechanism may yield a path to a non-goal position (the blue island in (c)).
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pone.0127269.g005: Planning performance decreases with decreasing oscillation frequency and is worst for a solitary wave.(a) Planning performance as a function of the noise level for a 18 Hz (blue) and a 11 Hz (green) intrinsic oscillation frequency with 4 readout cycles to select a single action. For the solitary wave, planning performance was measured after averaging the path lengths across 4 sweeps. Error bars from 10 realizations. (b, c) Color coded spike times relative to the spike time of the goal position (1,1) for (b) the 18 Hz periodic traveling wave after reaching steady state and (c) the solitary wave, both with noise level σext = 0.2. For the solitary wave, the spike times do not faithfully represent distance from goal, and hence the action selection mechanism may yield a path to a non-goal position (the blue island in (c)).

Mentions: A more subtle way to assure a high planning performance, beside increasing the readout time, is to increase the oscillation frequency of the planning neurons by injecting stronger external input currents. Fig 5a shows a comparison of the performance versus noise curve for a slow and a fast periodic traveling wave, and for a solitary wave. The performance is best for the fast traveling wave at a given noise level. Two reasons contribute to this effect. First, a high oscillation frequency requires stronger external input currents, and the neuron is shifted from the noise-driven regime into the drift-dominated regime where spike timing becomes more precise [20]. Second, the steady state with its phase-locking pattern represent an attractor of the phase dynamics and this attractor becomes more stable with higher frequency and hence cleans up the noise [21].


Scale-Free Navigational Planning by Neuronal Traveling Waves.

Khajeh-Alijani A, Urbanczik R, Senn W - PLoS ONE (2015)

Planning performance decreases with decreasing oscillation frequency and is worst for a solitary wave.(a) Planning performance as a function of the noise level for a 18 Hz (blue) and a 11 Hz (green) intrinsic oscillation frequency with 4 readout cycles to select a single action. For the solitary wave, planning performance was measured after averaging the path lengths across 4 sweeps. Error bars from 10 realizations. (b, c) Color coded spike times relative to the spike time of the goal position (1,1) for (b) the 18 Hz periodic traveling wave after reaching steady state and (c) the solitary wave, both with noise level σext = 0.2. For the solitary wave, the spike times do not faithfully represent distance from goal, and hence the action selection mechanism may yield a path to a non-goal position (the blue island in (c)).
© Copyright Policy
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4497724&req=5

pone.0127269.g005: Planning performance decreases with decreasing oscillation frequency and is worst for a solitary wave.(a) Planning performance as a function of the noise level for a 18 Hz (blue) and a 11 Hz (green) intrinsic oscillation frequency with 4 readout cycles to select a single action. For the solitary wave, planning performance was measured after averaging the path lengths across 4 sweeps. Error bars from 10 realizations. (b, c) Color coded spike times relative to the spike time of the goal position (1,1) for (b) the 18 Hz periodic traveling wave after reaching steady state and (c) the solitary wave, both with noise level σext = 0.2. For the solitary wave, the spike times do not faithfully represent distance from goal, and hence the action selection mechanism may yield a path to a non-goal position (the blue island in (c)).
Mentions: A more subtle way to assure a high planning performance, beside increasing the readout time, is to increase the oscillation frequency of the planning neurons by injecting stronger external input currents. Fig 5a shows a comparison of the performance versus noise curve for a slow and a fast periodic traveling wave, and for a solitary wave. The performance is best for the fast traveling wave at a given noise level. Two reasons contribute to this effect. First, a high oscillation frequency requires stronger external input currents, and the neuron is shifted from the noise-driven regime into the drift-dominated regime where spike timing becomes more precise [20]. Second, the steady state with its phase-locking pattern represent an attractor of the phase dynamics and this attractor becomes more stable with higher frequency and hence cleans up the noise [21].

Bottom Line: The time needed to reach the steady state represents an estimate of an agent's waiting time before it heads off to the goal.Given typical waiting times we estimate the minimal number of neurons involved in the cognitive map.In the context of the planning model, forward and backward spread of neuronal activity, oscillatory waves, and phase precession get a functional interpretation, allowing for speculations about the biological counterpart.

View Article: PubMed Central - PubMed

Affiliation: Department of Physiology, University of Bern, Bern, Switzerland.

ABSTRACT
Spatial navigation and planning is assumed to involve a cognitive map for evaluating trajectories towards a goal. How such a map is realized in neuronal terms, however, remains elusive. Here we describe a simple and noise-robust neuronal implementation of a path finding algorithm in complex environments. We consider a neuronal map of the environment that supports a traveling wave spreading out from the goal location opposite to direction of the physical movement. At each position of the map, the smallest firing phase between adjacent neurons indicate the shortest direction towards the goal. In contrast to diffusion or single-wave-fronts, local phase differences build up in time at arbitrary distances from the goal, providing a minimal and robust directional information throughout the map. The time needed to reach the steady state represents an estimate of an agent's waiting time before it heads off to the goal. Given typical waiting times we estimate the minimal number of neurons involved in the cognitive map. In the context of the planning model, forward and backward spread of neuronal activity, oscillatory waves, and phase precession get a functional interpretation, allowing for speculations about the biological counterpart.

No MeSH data available.


Related in: MedlinePlus