A topological classifier to characterize brain states: When shape matters more than variance.

Despite the remarkable accuracies attained by machine learning classifiers to separate complex datasets in a supervised fashion, most of their operation falls short to provide an informed intuition about the structure of data, and, what is more important, about the phenomena being characterized by the given datasets. By contrast, topological data analysis (TDA) is devoted to study the shape of data clouds by means of persistence descriptors and provides a quantitative characterization of specific topological features of the dataset under scrutiny. Here we introduce a novel TDA-based classifier that works on the principle of assessing quantifiable changes on topological metrics caused by the addition of new input to a subset of data. We used this classifier with a high-dimensional electro-encephalographic (EEG) dataset recorded from eleven participants during a previous decision-making experiment in which three motivational states were induced through a manipulation of social pressure. We calculated silhouettes from persistence diagrams associated with each motivated state with a ready-made band-pass filtered version of these signals, and classified unlabeled signals according to their impact on each reference silhouette. Our results show that in addition to providing accuracies within the range of those of a nearest neighbour classifier, the TDA classifier provides formal intuition of the structure of the dataset as well as an estimate of its intrinsic dimension. Towards this end, we incorporated variance-based dimensionality reduction methods to our dataset and found that in most cases the accuracy of our TDA classifier remains essentially invariant beyond a certain dimension.

Latency correction in sparse neuronal spike trains.

BACKGROUND: In neurophysiological data, latency refers to a global shift of spikes from one spike train to the next, either caused by response onset fluctuations or by finite propagation speed. Such systematic shifts in spike timing lead to a spurious decrease in synchrony which needs to be corrected. NEW METHOD: We propose a new algorithm of multivariate latency correction suitable for sparse data for which the relevant information is not primarily in the rate but in the timing of each individual spike. The algorithm is designed to correct systematic delays while maintaining all other kinds of noisy disturbances. It consists of two steps, spike matching and distance minimization between the matched spikes using simulated annealing. RESULTS: We show its effectiveness on simulated and real data: cortical propagation patterns recorded via calcium imaging from mice before and after stroke. Using simulations of these data we also establish criteria that can be evaluated beforehand in order to anticipate whether our algorithm is likely to yield a considerable improvement for a given dataset. COMPARISON WITH EXISTING METHOD(S): Existing methods of latency correction rely on adjusting peaks in rate profiles, an approach that is not feasible for spike trains with low firing in which the timing of individual spikes contains essential information. CONCLUSIONS: For any given dataset the criterion for applicability of the algorithm can be evaluated quickly and in case of a positive outcome the latency correction can be applied easily since the source codes of the algorithm are publicly available.

Cortical propagation tracks functional recovery after stroke.

Stroke is a debilitating condition affecting millions of people worldwide. The development of improved rehabilitation therapies rests on finding biomarkers suitable for tracking functional damage and recovery. To achieve this goal, we perform a spatiotemporal analysis of cortical activity obtained by wide-field calcium images in mice before and after stroke. We compare spontaneous recovery with three different post-stroke rehabilitation paradigms, motor training alone, pharmacological contralesional inactivation and both combined. We identify three novel indicators that are able to track how movement-evoked global activation patterns are impaired by stroke and evolve during rehabilitation: the duration, the smoothness, and the angle of individual propagation events. Results show that, compared to pre-stroke conditions, propagation of cortical activity in the subacute phase right after stroke is slowed down and more irregular. When comparing rehabilitation paradigms, we find that mice treated with both motor training and pharmacological intervention, the only group associated with generalized recovery, manifest new propagation patterns, that are even faster and smoother than before the stroke. In conclusion, our new spatiotemporal propagation indicators could represent promising biomarkers that are able to uncover neural correlates not only of motor deficits caused by stroke but also of functional recovery during rehabilitation. In turn, these insights could pave the way towards more targeted post-stroke therapies.

Reconstruction scheme for excitatory and inhibitory dynamics with quenched disorder: application to zebrafish imaging.

An inverse procedure is developed and tested to recover functional and structural information from global signals of brains activity. The method assumes a leaky-integrate and fire model with excitatory and inhibitory neurons, coupled via a directed network. Neurons are endowed with a heterogenous current value, which sets their associated dynamical regime. By making use of a heterogenous mean-field approximation, the method seeks to reconstructing from global activity patterns the distribution of in-coming degrees, for both excitatory and inhibitory neurons, as well as the distribution of the assigned currents. The proposed inverse scheme is first validated against synthetic data. Then, time-lapse acquisitions of a zebrafish larva recorded with a two-photon light sheet microscope are used as an input to the reconstruction algorithm. A power law distribution of the in-coming connectivity of the excitatory neurons is found. Local degree distributions are also computed by segmenting the whole brain in sub-regions traced from annotated atlas.

Impact of local network characteristics on network reconstruction.

When a network is inferred from data, two types of errors can occur: false positive and false negative conclusions about the presence of links. We focus on the influence of local network characteristics on the probability α of false positive conclusions, and on the probability ß of false negative conclusions, in the case of networks of coupled oscillators. We demonstrate that false conclusion probabilities are influenced by local connectivity measures such as the shortest path length and the detour degree, which can also be estimated from the inferred network when the true underlying network is not known a priori. These measures can then be used for quantification of the confidence level of link conclusions, and for improving the network reconstruction via advanced concepts of link weights thresholding.

Analytical approach to network inference: Investigating degree distribution.

When the network is reconstructed, two types of errors can occur: false positive and false negative errors about the presence or absence of links. In this paper, the influence of these two errors on the vertex degree distribution is analytically analyzed. Moreover, an analytic formula of the density of the biased vertex degree distribution is found. In the inverse problem, we find a reliable procedure to reconstruct analytically the density of the vertex degree distribution of any network based on the inferred network and estimates for the false positive and false negative errors based on, e.g., simulation studies.

Improving network inference: The impact of false positive and false negative conclusions about the presence or absence of links.

BACKGROUND: A reliable inference of networks from data is of key interest in the Neurosciences. Several methods have been suggested in the literature to reliably determine links in a network. To decide about the presence of links, these techniques rely on statistical inference, typically controlling the number of false positives, paying little attention to false negatives. NEW METHOD: In this paper, by means of a comprehensive simulation study, we analyse the influence of false positive and false negative conclusions about the presence or absence of links in a network on the network topology. We show that different values to balance false positive and false negative conclusions about links should be used in order to reliably estimate network characteristics. We propose to run careful simulation studies prior to making potentially erroneous conclusion about the network topology. RESULTS: Our analysis shows that optimal values to balance false positive and false negative conclusions about links depend on the network topology and characteristic of interest. COMPARISON WITH EXISTING METHODS: Existing methods rely on a choice of the rate for false positive conclusions. They aim to be sure about individual links rather than the entire network. The rate of false negative conclusions is typically not investigated. CONCLUSIONS: Our investigation shows that the balance of false positive and false negative conclusions about links in a network has to be tuned for any network topology that is to be estimated. Moreover, within the same network topology, the results are qualitatively the same for each network characteristic, but the actual values leading to reliable estimates of the characteristics are different.

3-hydroxykynurenine as a substrate/activator for mushroom tyrosinase.

3-Hydroxykynurenine is a tryptophan metabolite with an o-aminophenol structure. It is both a tyrosinase activator and a substrate, reducing the lag phase, stimulating the monophenolase activity, and being oxidized to xanthommatin. In the early stage of monophenol hydroxylation, catechol accumulation takes place, whereas 3-hydroxykynurenine is substantially unchanged and no significant amounts of the o-quinone are produced. These results suggest an activating action of 3-hydroxykynurenine toward o-hydroxylation of monophenols. 3-Hydroxykynurenine could therefore well act as a physiological device to control phenolics metabolism to catechols and quinonoids.