Persistent Memories in Transient Networks

Babichev, Andrey; Dabaghian, Yu.

doi:10.1007/978-3-319-47810-4_14

Cited by 13 publications

(16 citation statements)

References 30 publications

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“…It is natural to view the coactivity complexes F ( i ) as instances of a single flickering coactivity complex F , F (t i ) = F ( i ), having appearing and disappearing maximal simplexes (see Fig. 2B and [52]). In the following, we will use F as a model of transient cell assembly network and study whether such a network can encode a stable topological map of the environment on the moment-by-moment basis.…”

Section: The Modelmentioning

confidence: 99%

Transient cell assembly networks encode stable spatial memories

Babichev

Dabaghian

2017

Sci Rep

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One of the mysteries of memory is that it can last despite changes in the underlying synaptic architecture. How can we, for example, maintain an internal spatial map of an environment over months or years when the underlying network is full of transient connections? In the following, we propose a computational model for describing the emergence of the hippocampal cognitive map in a network of transient place cell assemblies and demonstrate, using methods of algebraic topology, how such a network can maintain spatial memory over time.

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Section: The Modelmentioning

confidence: 99%

Transient cell assembly networks encode stable spatial memories

Babichev

Dabaghian

2017

Sci Rep

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“…Among other applications, it has been used to determine differences in brain networks of children with hyperactivity disorders and autism spectrum in comparison to normal situations 25 , study the effect of the psychoactive component of "magic mushrooms" (psilocybin mushrooms) on functional brain networks of humans 26 , analyze covariates that influence neural spike-train data 27 , and study structural and functional organization of neural microcircuits 28 . Other neuronal applications have included consideration of place cells in the hippocampus of rats during spatial navigation [29][30][31] , analysis of mathematical models of transient hippocampal networks 32 , and a demonstration that topological features of networks of brain arteries in humans are correlated with their age 33 . We also note that PH is not the only topological method that has been used to study the human brain or time series.…”

Section: Introductionmentioning

confidence: 99%

Persistent homology of time-dependent functional networks constructed from coupled time series

Stolz

Harrington

Porter

2017

Chaos: An Interdisciplinary Journal of Nonlinear Science

103

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We use topological data analysis to study "functional networks" that we construct from time-series data from both experimental and synthetic sources. We use persistent homology with a weight rank clique filtration to gain insights into these functional networks, and we use persistence landscapes to interpret our results. Our first example uses time-series output from networks of coupled Kuramoto oscillators. Our second example consists of biological data in the form of functional magnetic resonance imaging data that were acquired from human subjects during a simple motor-learning task in which subjects were monitored for three days during a five-day period. With these examples, we demonstrate that (1) using persistent homology to study functional networks provides fascinating insights into their properties and (2) the position of the features in a filtration can sometimes play a more vital role than persistence in the interpretation of topological features, even though conventionally the latter is used to distinguish between signal and noise. We find that persistent homology can detect differences in synchronization patterns in our data sets over time, giving insight both on changes in community structure in the networks and on increased synchronization between brain regions that form loops in a functional network during motor learning. For the motor-learning data, persistence landscapes also reveal that on average the majority of changes in the network loops take place on the second of the three days of the learning process.

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“…The algebraic-topological properties of the coactivity complexes were studied in Dabaghian et al ( 2012 ), Babichev et al ( 2016b ), and Babichev and Dabaghian ( 2017a , b ). There it was demonstrated that if place cell populations operate within biological parameters, then the number of topological loops in different dimensions of the coactivity complex—the Betti numbers

(Munkres, 2000 )—match the Betti numbers of the environment

.…”

Section: Resultsmentioning

confidence: 99%

“…Importantly, the learning times and other global characteristics of

produced via algebraic topology techniques are insensitive to many details of the place cell spiking activity (Dabaghian et al, 2012 ; Babichev et al, 2016b ; Babichev and Dabaghian, 2017a , b ). For example, the learning time T min depends mostly on the mean place field sizes and the mean peak firing rates, but it does not depend strongly on the spatial layout of the place fields or on the limited spiking variations.…”

Section: Resultsmentioning

confidence: 99%

Topological Schemas of Memory Spaces

Babichev

Dabaghian

2018

Front. Comput. Neurosci.

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Hippocampal cognitive map—a neuronal representation of the spatial environment—is widely discussed in the computational neuroscience literature for decades. However, more recent studies point out that hippocampus plays a major role in producing yet another cognitive framework—the memory space—that incorporates not only spatial, but also non-spatial memories. Unlike the cognitive maps, the memory spaces, broadly understood as “networks of interconnections among the representations of events,” have not yet been studied from a theoretical perspective. Here we propose a mathematical approach that allows modeling memory spaces constructively, as epiphenomena of neuronal spiking activity and thus to interlink several important notions of cognitive neurophysiology. First, we suggest that memory spaces have a topological nature—a hypothesis that allows treating both spatial and non-spatial aspects of hippocampal function on equal footing. We then model the hippocampal memory spaces in different environments and demonstrate that the resulting constructions naturally incorporate the corresponding cognitive maps and provide a wider context for interpreting spatial information. Lastly, we propose a formal description of the memory consolidation process that connects memory spaces to the Morris' cognitive schemas-heuristic representations of the acquired memories, used to explain the dynamics of learning and memory consolidation in a given environment. The proposed approach allows evaluating these constructs as the most compact representations of the memory space's structure.

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Persistent Memories in Transient Networks

Cited by 13 publications

References 30 publications

Transient cell assembly networks encode stable spatial memories

Transient cell assembly networks encode stable spatial memories

Persistent homology of time-dependent functional networks constructed from coupled time series

Topological Schemas of Memory Spaces

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