Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Applications of Discrete Mathematics for Understanding Dynamics of
  Synapses and Networks in Neuroscience   Mathematical modeling has broad applications in neuroscience whether modeling
the dynamics of a single synapse or an entire network of neurons. In Part I, we
model vesicle replenishment and release at the photoreceptor synapse to better
understand how visual information is processed. In Part II, we explore a simple
model of neural networks with the goal of discovering how network structure
shapes the behavior of the network.
  To fully understand how visual information is processed requires an
understanding of the way signals are transformed at the ribbon synapse of
photoreceptor neurons. These synapses possess a ribbon-like structure capable
of storing around 100 synaptic vesicles, allowing graded responses through the
release of different numbers of vesicles in response to visual input. These
responses depend critically on the ability of the ribbon to replenish itself as
ribbon sites empty upon release. The rate of vesicle replenishment is thus an
important factor in shaping neural coding in the retina. In collaboration with
experimental neuroscientists we developed a mathematical model to describe the
dynamics of vesicle release and replenishment at the ribbon synapse.
  To learn more about how network architecture shapes the dynamics of the
network, we study a specific type of threshold-linear network that is
constructed from a simple directed graph. The network construction guarantees
that differences in dynamics arise solely from differences in the connectivity
of the underlying graph. By design, the activity of these networks is bounded
and there are no stable fixed points. Computational experiments show that most
of these networks yield limit cycles where the neurons fire in sequence. We
devised an algorithm to predict the sequence of firing using the structure of
the underlying graph. Using the algorithm we classify all the networks of this
type on five or fewer nodes.

16
The categories of this paper are: stat
0
The categories of this paper are: hep-ph
37
The categories of this paper are: supr-con
18
The categories of this paper are: econ
32
The categories of this paper are: atom-ph
33
The categories of this paper are: plasm-ph
3
The categories of this paper are: physics
26
The categories of this paper are: bayes-an
31
The categories of this paper are: ao-sci
1
The categories of this paper are: cs
4
The categories of this paper are: cond-mat
20
The categories of this paper are: acc-phys
21
The categories of this paper are: adap-org
29
The categories of this paper are: funct-an
22
The categories of this paper are: chao-dyn
15
The categories of this paper are: nucl-ex