Replay: Roman (German Edition)

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In other words, in compressed replays, a wider variety of connections is activated at each t r : the real-time separation between activity patterns shrinks. To test this idea, we amplified this effect by shuffling the order of the replayed sequences and by randomizing the injection diagram, thus enforcing a nearly uniform pattern of injected activity across the simulated population of cell assemblies.

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The effect of random replays of the place cell sequences over the entire simulated navigation period shown in Figure 5 clearly illustrates the importance of replays for rapid encoding of topological maps: the fluctuations in the cognitive map are uniformly suppressed for the original values of the Betti numbers during all six instability periods without replays see Table 1 in Methods. Replays suppress topological fluctuations over the entire navigation period.

B Several examples of replayed trajectories over the navigated environment are shown in different colors see also Supporting Information Figure 1. C Spatial histograms of the centers of the links left panel and of the three-vertex simplexes right panel during the instability period I 5 in presence of the replays. The populations of simplexes over the south and the southwestern parts of the environment in presence of the replays have increased compared to the case shown on Figure 2C , which suppresses spurious topological loops in the coactivity complex.

D The Betti numbers b 1 computed for the eight sectors of the environment are also significantly reduced, indicating that the topological fluctuations are suppressed both locally and globally. The model discussed above suggests that replays of place cell activity help to learn and to sustain the topological structure of the cognitive map. The physiological accuracy of the replay simulation can be increased ad infinitum, by incorporating more and more parameters into the model.

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In this study we use only a few basic properties of the replays, which, however, capture several key functional aspects of the replay activity. On the other hand, low-speed periods define temporal windows during which the simulated replays are injected into the network, which work to suppress the topological instabilities. The results demonstrate that in order to strengthen the decaying connections in the hippocampal network effectively, the replays must 1 be produced at a sufficiently high rate that falls within the physiological range and 2 distribute without temporal clustering, in a semi-random order.

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An important aspect of the obtained results is a separation of the timescales at which different types of topological information is processed. On the one hand, rapid turnover of the information about local connectivity at the working memory timescale is represented by quick recycling of the cell assemblies and rapid spontaneous replays of the learned sequences. On the other hand, the large-scale topological structures of the cognitive map, described by the instantaneous homological characteristics of the coactivity complex, emerge at the intermediate memory timescale.

This observation provides a functional perspective on the role played by the place cell replays in learning: by reducing the fluctuations, replays help separating the fast and the slow information processing timescales and hence to extract stable topological information that can be used to build a long-term, qualitative representation of the environment.

This separation of timescales corroborates with the well-known observation that transient information is rapidly processed in the hippocampus and then the resulting memories are consolidated and stored in the cortical areas, but at slower timescales and for longer periods. Intuitively, they can be viewed, for example, as the simplicial paths described in The Model section.

Such combinations permit algebraic operations: they can be added, subtracted, and multiplied by a common factor, and so forth. Intuitively, cycles correspond to agglomerates of simplexes e. Note however, that although all boundaries are cycles, not all cycles are boundaries. The environment shown on Figure 1A is simulated after typical arenas used in typical electrophysiological experiments. The firing rate of a place cell c is defined by. The values during instability periods without replays is provided in Table 1.

Note that all values differ significantly from the Betti numbers exhibited by the coactivity complexes with replays see Results. This document was prepared as an account of work sponsored by the United States Government.

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While this document is believed to contain correct information, neither the United States Government nor any agency thereof, nor the Regents of the University of California, nor any of their employees, makes any warranty, express or implied, or assumes any legal responsibility for the accuracy, completeness, or usefulness of any information, apparatus, product, or process disclosed, or represents that its use would not infringe privately owned rights.

Reference herein to any specific commercial product, process, or service by its trade name, trademark, manufacturer, or otherwise, does not necessarily constitute or imply its endorsement, recommendation, or favoring by the United States Government or any agency thereof, or the Regents of the University of California. The views and opinions of authors expressed herein do not necessarily state or reflect those of the United States Government or any agency thereof or the Regents of the University of California.

Department of Energy. The U. Government retains, and the publisher, by accepting the article for publication, acknowledges, that the U. Government retains a non-exclusive, paid-up, irrevocable, world-wide license to publish or reproduce the published form of this manuscript, or allow others to do so, for U. Government purposes. Dmitriy Morozov: Methodology; Software. National Center for Biotechnology Information , U. Journal List Netw Neurosci v. Netw Neurosci. Published online Author information Article notes Copyright and License information Disclaimer. Competing Interests: The authors have declared that no competing interests exist.

Received Jul 19; Accepted Dec This is an open-access article distributed under the terms of the Creative Commons Attribution License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Associated Data Supplementary Materials netns Abstract The spiking activity of the hippocampal place cells plays a key role in producing and sustaining an internalized representation of the ambient space—a cognitive map.

Keywords: Learning and memory, Hippocampal replays, Transient networks, Zigzag homology theory. Open in a separate window.

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Figure 1. Topological Structure of the Coactivity Complex The topological structure of the coactivity complex provides a convenient framework for representing spatial information encoded by the place cells. Dynamics of the Coactivity Complexes In practice, the coactivity complexes can be designed to reflect particular physiological properties of the cell assemblies. Figure 2. Dynamics of the Coactivity Graph Physiologically, place cell spiking is synchronized with the components of the extracellular local field potential—the so-called brain waves that also define the timescale of place cell coactivity Buzsaki, Replays of Place Cell Sequences Replays of place cell sequences may in general represent both spatial and nonspatial memories.

RESULTS Initial Testing The effect produced by the replays on the cognitive map depends on the parameters of the model: the selection of replayed trajectories, the injection times, the frequency of the replays, and so forth. Figure 3. Implementation of the Replays Electrophysiological data shows that the frequency of the replays ranges between 0.

Figure 4. Figure 5. Table 1. The corresponding geometric simplicial complexes are multidimensional polyhedra that have a shape and a structure that does not change with simplex deformations, for example, disconnected components, holes, cavities of different dimensionality, and so on. This structure, commonly referred to as topological Aleksandrov, , is identical in a geometric simplicial complex to and in the abstract complex built over the vertexes of the geometric simplexes.

Thus, abstract simplicial complexes may be viewed as structural representations of the conventional geometric shapes. The set of equivalent cycles forms a homology class. Spike Simulations The environment shown on Figure 1A is simulated after typical arenas used in typical electrophysiological experiments. The Statistics of the Betti Numbers The values during instability periods without replays is provided in Table 1. Supplementary Material Click here for additional data file.

Click here for additional data file. It is believed that a cognitive map of a given environment emerges from the combined activity of place cells. Cognitive map: An internal neural representation of the environment, used by the animals e. It is generally accepted that the hippocampus plays a key role in producing and sustaining cognitive maps.

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Hippocampal cell assemblies: Transient, functionally interconnected groups of place cells that exhibit frequent coactivity. The organized activity of cells in the hippocampal and cortical assemblies is believed to underlie learning and memory mechanisms. Replays of place cell sequences: The endogenous activities in the hippocampal network that recapitulate sequential place cell firing during physical exploration of an environment. Spontaneous replays are observed during sleep, quiescent wakeful states, and active navigation.

Elementary concepts of topology. New York: Ungar. Rats build and update topological representations through exploration. Animal Cognition , 15 3 , — The effects of theta precession on spatial learning and simplicial complex dynamics in a topological model of the hippocampal spatial map. PLoS Computational Biology , 10 6 , e Instantaneous modulation of gamma oscillation frequency by balancing excitation with inhibition.

Neuron , 62 4 , — Topological schemas of cognitive maps and spatial learning. Frontiers in Computational Neuroscience , 10 , Persistent memories in transient networks. Cham, Switzerland: Springer.

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Transient cell assembly networks encode stable spatial memories. Scientific Reports , 7 1 , Topological schemas of memory spaces.

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Frontiers in Computational Neuroscience , 12 , A topological model of the hippocampal cell assembly network. Robust spatial memory maps encoded by networks with transient connections. PLoS Computational Biology , 14 9 , e Dynamic analyses of information encoding in neural ensembles.