17 research outputs found
Scalability of asynchronous networks is limited by one-to-one mapping between effective connectivity and correlations
Network models are routinely downscaled because of a lack of computational resources, often without explicit mention of the limitations this entails. While reliable methods have long existed to adjust parameters such that the first-order statistics of network dynamics is conserved, here we show that this is generally impossible already for second-order statistics. We argue that studies in computational biology need to make the scaling applied explicit, and that results should be verified where possible by full-scale simulations. We consider neuronal networks, where the importance of correlations in network dynamics is obvious because they directly interact with synaptic plasticity, the neuronal basis of learning, but the conclusions are generic. We derive conditions for the preservation of both mean activities and correlations under a change in numbers of neurons or synapses in the asynchronous regime typical of cortical networks. Analytical and simulation results are obtained for networks of binary and networks of leaky integrate-and-fire model neurons, randomly connected with or without delays. The structure of average pairwise correlations in such networks is determined by the effective population-level connectivity. We show that in the absence of symmetries or zeros in the population-level connectivity or correlations, the converse is also true. This is in line with earlier work on inferring connectivity from correlations, but implies that such network reconstruction should be possible for a larger class of networks than hitherto considered. When changing in-degrees, effective connectivity and hence correlation structure can be maintained by an appropriate scaling of the synaptic weights, but only over a limited range of in-degrees determined by the extrinsic variance. Our results show that the reducibility of asynchronous networks is fundamentally limited
Transition to Reconstructibility in Weakly Coupled Networks
Across scientific disciplines, thresholded pairwise measures of statistical
dependence between time series are taken as proxies for the interactions
between the dynamical units of a network. Yet such correlation measures often
fail to reflect the underlying physical interactions accurately. Here we
systematically study the problem of reconstructing direct physical interaction
networks from thresholding correlations. We explicate how local common cause
and relay structures, heterogeneous in-degrees and non-local structural
properties of the network generally hinder reconstructibility. However, in the
limit of weak coupling strengths we prove that stationary systems with dynamics
close to a given operating point transition to universal reconstructiblity
across all network topologies.Comment: 15 pages, 4 figures, supplementary material include
Topological exploration of artificial neuronal network dynamics
One of the paramount challenges in neuroscience is to understand the dynamics
of individual neurons and how they give rise to network dynamics when
interconnected. Historically, researchers have resorted to graph theory,
statistics, and statistical mechanics to describe the spatiotemporal structure
of such network dynamics. Our novel approach employs tools from algebraic
topology to characterize the global properties of network structure and
dynamics.
We propose a method based on persistent homology to automatically classify
network dynamics using topological features of spaces built from various
spike-train distances. We investigate the efficacy of our method by simulating
activity in three small artificial neural networks with different sets of
parameters, giving rise to dynamics that can be classified into four regimes.
We then compute three measures of spike train similarity and use persistent
homology to extract topological features that are fundamentally different from
those used in traditional methods. Our results show that a machine learning
classifier trained on these features can accurately predict the regime of the
network it was trained on and also generalize to other networks that were not
presented during training. Moreover, we demonstrate that using features
extracted from multiple spike-train distances systematically improves the
performance of our method
Usage and Scaling of an Open-Source Spiking Multi-Area Model of Monkey Cortex
We are entering an age of `big' computational neuroscience, in which neural
network models are increasing in size and in numbers of underlying data sets.
Consolidating the zoo of models into large-scale models simultaneously
consistent with a wide range of data is only possible through the effort of
large teams, which can be spread across multiple research institutions. To
ensure that computational neuroscientists can build on each other's work, it is
important to make models publicly available as well-documented code. This
chapter describes such an open-source model, which relates the connectivity
structure of all vision-related cortical areas of the macaque monkey with their
resting-state dynamics. We give a brief overview of how to use the executable
model specification, which employs NEST as simulation engine, and show its
runtime scaling. The solutions found serve as an example for organizing the
workflow of future models from the raw experimental data to the visualization
of the results, expose the challenges, and give guidance for the construction
of ICT infrastructure for neuroscience
Fundamental activity constraints lead to specific interpretations of the connectome
The continuous integration of experimental data into coherent models of the
brain is an increasing challenge of modern neuroscience. Such models provide a
bridge between structure and activity, and identify the mechanisms giving rise
to experimental observations. Nevertheless, structurally realistic network
models of spiking neurons are necessarily underconstrained even if experimental
data on brain connectivity are incorporated to the best of our knowledge.
Guided by physiological observations, any model must therefore explore the
parameter ranges within the uncertainty of the data. Based on simulation
results alone, however, the mechanisms underlying stable and physiologically
realistic activity often remain obscure. We here employ a mean-field reduction
of the dynamics, which allows us to include activity constraints into the
process of model construction. We shape the phase space of a multi-scale
network model of the vision-related areas of macaque cortex by systematically
refining its connectivity. Fundamental constraints on the activity, i.e.,
prohibiting quiescence and requiring global stability, prove sufficient to
obtain realistic layer- and area-specific activity. Only small adaptations of
the structure are required, showing that the network operates close to an
instability. The procedure identifies components of the network critical to its
collective dynamics and creates hypotheses for structural data and future
experiments. The method can be applied to networks involving any neuron model
with a known gain function.Comment: J. Schuecker and M. Schmidt contributed equally to this wor
Construction of a multi-scale spiking model of macaque visual cortex
Understanding the relationship between structure and dynamics of the mammalian cortex is a key challenge of neuroscience. So far, it has been tackled in two ways: by modeling neurons or small circuits in great detail, and through large-scale models representing each area with a small number of differential equations. To bridge the gap between these two approaches, we construct a spiking network model extending earlier work on the cortical microcircuit by Potjans & Diesmann (2014) to all 32 areas of the macaque visual cortex in the parcellation of Felleman & Van Essen (1991). The model takes into account spe- cific neuronal densities and laminar thicknesses of the individual areas. The connectivity of the model combines recently updated binary tracing data from the CoCoMac database (Stephan et al., 2001) with quantitative tracing data providing connection densities (Markov et al., 2014a) and laminar connection patterns (Stephan et al., 2001; Markov et al., 2014b). We estimate missing data using structural regular- ities such as the exponential decay of connection densities with distance between areas (Ercsey-Ravasz et al., 2013) and a fit of laminar patterns versus logarithmic ratios of neuron densities. The model integrates a large body of knowledge on the structure of macaque visual cortex into a consistent framework that allows for progressive refinement
Integration of continuous-time dynamics in a spiking neural network simulator
Contemporary modeling approaches to the dynamics of neural networks consider
two main classes of models: biologically grounded spiking neurons and
functionally inspired rate-based units. The unified simulation framework
presented here supports the combination of the two for multi-scale modeling
approaches, the quantitative validation of mean-field approaches by spiking
network simulations, and an increase in reliability by usage of the same
simulation code and the same network model specifications for both model
classes. While most efficient spiking simulations rely on the communication of
discrete events, rate models require time-continuous interactions between
neurons. Exploiting the conceptual similarity to the inclusion of gap junctions
in spiking network simulations, we arrive at a reference implementation of
instantaneous and delayed interactions between rate-based models in a spiking
network simulator. The separation of rate dynamics from the general connection
and communication infrastructure ensures flexibility of the framework. We
further demonstrate the broad applicability of the framework by considering
various examples from the literature ranging from random networks to neural
field models. The study provides the prerequisite for interactions between
rate-based and spiking models in a joint simulation
VIOLA - A multi-purpose and web-based visualization tool for neuronal-network simulation output
Neuronal network models and corresponding computer simulations are invaluable
tools to aid the interpretation of the relationship between neuron properties,
connectivity and measured activity in cortical tissue. Spatiotemporal patterns
of activity propagating across the cortical surface as observed experimentally
can for example be described by neuronal network models with layered geometry
and distance-dependent connectivity. The interpretation of the resulting stream
of multi-modal and multi-dimensional simulation data calls for integrating
interactive visualization steps into existing simulation-analysis workflows.
Here, we present a set of interactive visualization concepts called views for
the visual analysis of activity data in topological network models, and a
corresponding reference implementation VIOLA (VIsualization Of Layer Activity).
The software is a lightweight, open-source, web-based and platform-independent
application combining and adapting modern interactive visualization paradigms,
such as coordinated multiple views, for massively parallel neurophysiological
data. For a use-case demonstration we consider spiking activity data of a
two-population, layered point-neuron network model subject to a spatially
confined excitation originating from an external population. With the multiple
coordinated views, an explorative and qualitative assessment of the
spatiotemporal features of neuronal activity can be performed upfront of a
detailed quantitative data analysis of specific aspects of the data.
Furthermore, ongoing efforts including the European Human Brain Project aim at
providing online user portals for integrated model development, simulation,
analysis and provenance tracking, wherein interactive visual analysis tools are
one component. Browser-compatible, web-technology based solutions are therefore
required. Within this scope, with VIOLA we provide a first prototype.Comment: 38 pages, 10 figures, 3 table