56 research outputs found
Topological Schemas of Memory Spaces
Hippocampal cognitive map---a neuronal representation of the spatial
environment---is broadly discussed in the computational neuroscience literature
for decades. More recent studies point out that hippocampus plays a major role
in producing yet another cognitive framework that incorporates not only
spatial, but also nonspatial memories---the memory space. However, unlike
cognitive maps, memory spaces have been barely studied from a theoretical
perspective. Here we propose an approach for modeling hippocampal memory spaces
as an epiphenomenon of neuronal spiking activity. First, we suggest that the
memory space may be viewed as a finite topological space---a hypothesis that
allows treating both spatial and nonspatial aspects of hippocampal function on
equal footing. We then model the topological properties of the memory space to
demonstrate that this concept naturally incorporates the notion of a cognitive
map. Lastly, we suggest a formal description of the memory consolidation
process and point out a connection between the proposed model of the memory
spaces to the so-called Morris' schemas, which emerge as the most compact
representation of the memory structure.Comment: 24 pages, 8 Figures, 1 Suppl. Figur
Robust spatial memory maps encoded in networks with transient connections
The spiking activity of principal cells in mammalian hippocampus encodes an
internalized neuronal representation of the ambient space---a cognitive map.
Once learned, such a map enables the animal to navigate a given environment for
a long period. However, the neuronal substrate that produces this map remains
transient: the synaptic connections in the hippocampus and in the downstream
neuronal networks never cease to form and to deteriorate at a rapid rate. How
can the brain maintain a robust, reliable representation of space using a
network that constantly changes its architecture? Here, we demonstrate, using
novel Algebraic Topology techniques, that cognitive map's stability is a
generic, emergent phenomenon. The model allows evaluating the effect produced
by specific physiological parameters, e.g., the distribution of connections'
decay times, on the properties of the cognitive map as a whole. It also points
out that spatial memory deterioration caused by weakening or excessive loss of
the synaptic connections may be compensated by simulating the neuronal
activity. Lastly, the model explicates functional importance of the
complementary learning systems for processing spatial information at different
levels of spatiotemporal granularity, by establishing three complementary
timescales at which spatial information unfolds. Thus, the model provides a
principal insight into how can the brain develop a reliable representation of
the world, learn and retain memories despite complex plasticity of the
underlying networks and allows studying how instabilities and memory
deterioration mechanisms may affect learning process.Comment: 24 pages, 10 figures, 4 supplementary figure
Dynamical ansatz for path integrals and nonperturbative trace formulas
It is shown that a recently discovered representation of the Green’s function is equivalent to a certain “dynamical ansatz” for the corresponding path integral, which brings about a convenient method of nonperturbative approximations. Based on this observation, a set of nonperturbative approximations to the trace of the Green’s function is established
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