@article {47124,
	title = {Clique topology reveals intrinsic geometric structure in neural correlations.},
	journal = {Proceedings of the National Academy of Sciences of the United States of America},
	volume = {112},
	year = {2015},
	month = {2015 Nov 3},
	pages = {13455-60},
	abstract = {<p>Detecting meaningful structure in neural activity and connectivity data is challenging in the presence of hidden nonlinearities, where traditional eigenvalue-based methods may be misleading. We introduce a novel approach to matrix analysis, called clique topology, that extracts features of the data invariant under nonlinear monotone transformations. These features can be used to detect both random and geometric structure, and depend only on the relative ordering of matrix entries. We then analyzed the activity of pyramidal neurons in rat hippocampus, recorded while the animal was exploring a 2D environment, and confirmed that our method is able to detect geometric organization using only the intrinsic pattern of neural correlations. Remarkably, we found similar results during nonspatial behaviors such as wheel running and rapid eye movement (REM) sleep. This suggests that the geometric structure of correlations is shaped by the underlying hippocampal circuits and is not merely a consequence of position coding. We propose that clique topology is a powerful new tool for matrix analysis in biological settings, where the relationship of observed quantities to more meaningful variables is often nonlinear and unknown.</p>
},
	issn = {1091-6490},
	doi = {10.1073/pnas.1506407112},
	author = {Giusti, Chad and Pastalkova, Eva and Curto, Carina and Itskov, Vladimir}
}
@article {2341,
	title = {Cell assembly sequences arising from spike threshold adaptation keep track of time in the hippocampus.},
	journal = {The Journal of Neuroscience: The Official Journal of the Society for Neuroscience},
	volume = {31},
	year = {2011},
	month = {2011 Feb 23},
	pages = {2828-34},
	abstract = {<p>Hippocampal neurons can display reliable and long-lasting sequences of transient firing patterns, even in the absence of changing external stimuli. We suggest that time-keeping is an important function of these sequences, and propose a network mechanism for their generation. We show that sequences of neuronal assemblies recorded from rat hippocampal CA1 pyramidal cells can reliably predict elapsed time (15-20 s) during wheel running with a precision of 0.5 s. In addition, we demonstrate the generation of multiple reliable, long-lasting sequences in a recurrent network model. These sequences are generated in the presence of noisy, unstructured inputs to the network, mimicking stationary sensory input. Identical initial conditions generate similar sequences, whereas different initial conditions give rise to distinct sequences. The key ingredients responsible for sequence generation in the model are threshold-adaptation and a Mexican-hat-like pattern of connectivity among pyramidal cells. This pattern may arise from recurrent systems such as the hippocampal CA3 region or the entorhinal cortex. We hypothesize that mechanisms that evolved for spatial navigation also support tracking of elapsed time in behaviorally relevant contexts.</p>
},
	issn = {1529-2401},
	doi = {10.1523/JNEUROSCI.3773-10.2011},
	author = {Itskov, Vladimir and Curto, Carina and Pastalkova, Eva and Buzs{\'a}ki, Gy{\"o}rgy}
}
