Controlling target brain regions by optimal selection of input nodes.

The network control theory framework holds great potential to inform neurostimulation experiments aimed at inducing desired activity states in the brain. However, the current applicability of the framework is limited by inappropriate modeling of brain dynamics, and an overly ambitious focus on whole-brain activity control. In this work, we leverage recent progress in linear modeling of brain dynamics (effective connectivity) and we exploit the concept of target controllability to focus on the control of a single region or a small subnetwork of nodes. We discuss when control may be possible with a reasonably low energy cost and few stimulation loci, and give general predictions on where to stimulate depending on the subset of regions one wishes to control. Importantly, using the robustly asymmetric effective connectome instead of the symmetric structural connectome (as in previous research), we highlight the fundamentally different roles in- and out-hubs have in the control problem, and the relevance of inhibitory connections. The large degree of inter-individual variation in the effective connectome implies that the control problem is best formulated at the individual level, but we discuss to what extent group results may still prove useful.

A low dimensional embedding of brain dynamics enhances diagnostic accuracy and behavioral prediction in stroke.

Large-scale brain networks reveal structural connections as well as functional synchronization between distinct regions of the brain. The latter, referred to as functional connectivity (FC), can be derived from neuroimaging techniques such as functional magnetic resonance imaging (fMRI). FC studies have shown that brain networks are severely disrupted by stroke. However, since FC data are usually large and high-dimensional, extracting clinically useful information from this vast amount of data is still a great challenge, and our understanding of the functional consequences of stroke remains limited. Here, we propose a dimensionality reduction approach to simplify the analysis of this complex neural data. By using autoencoders, we find a low-dimensional representation encoding the fMRI data which preserves the typical FC anomalies known to be present in stroke patients. By employing the latent representations emerging from the autoencoders, we enhanced patients' diagnostics and severity classification. Furthermore, we showed how low-dimensional representation increased the accuracy of recovery prediction.

Subcortical-cortical dynamical states of the human brain and their breakdown in stroke.

The mechanisms controlling dynamical patterns in spontaneous brain activity are poorly understood. Here, we provide evidence that cortical dynamics in the ultra-slow frequency range (<0.01-0.1 Hz) requires intact cortical-subcortical communication. Using functional magnetic resonance imaging (fMRI) at rest, we identify Dynamic Functional States (DFSs), transient but recurrent clusters of cortical and subcortical regions synchronizing at ultra-slow frequencies. We observe that shifts in cortical clusters are temporally coincident with shifts in subcortical clusters, with cortical regions flexibly synchronizing with either limbic regions (hippocampus/amygdala), or subcortical nuclei (thalamus/basal ganglia). Focal lesions induced by stroke, especially those damaging white matter connections between basal ganglia/thalamus and cortex, provoke anomalies in the fraction times, dwell times, and transitions between DFSs, causing a bias toward abnormal network integration. Dynamical anomalies observed 2 weeks after stroke recover in time and contribute to explaining neurological impairment and long-term outcome.

Group-level inference of information-based measures for the analyses of cognitive brain networks from neurophysiological data.

The reproducibility crisis in neuroimaging and in particular in the case of underpowered studies has introduced doubts on our ability to reproduce, replicate and generalize findings. As a response, we have seen the emergence of suggested guidelines and principles for neuroscientists known as Good Scientific Practice for conducting more reliable research. Still, every study remains almost unique in its combination of analytical and statistical approaches. While it is understandable considering the diversity of designs and brain data recording, it also represents a striking point against reproducibility. Here, we propose a non-parametric permutation-based statistical framework, primarily designed for neurophysiological data, in order to perform group-level inferences on non-negative measures of information encompassing metrics from information-theory, machine-learning or measures of distances. The framework supports both fixed- and random-effect models to adapt to inter-individuals and inter-sessions variability. Using numerical simulations, we compared the accuracy in ground-truth retrieving of both group models, such as test- and cluster-wise corrections for multiple comparisons. We then reproduced and extended existing results using both spatially uniform MEG and non-uniform intracranial neurophysiological data. We showed how the framework can be used to extract stereotypical task- and behavior-related effects across the population covering scales from the local level of brain regions, inter-areal functional connectivity to measures summarizing network properties. We also present an open-source Python toolbox called Frites1 that includes the proposed statistical pipeline using information-theoretic metrics such as single-trial functional connectivity estimations for the extraction of cognitive brain networks. Taken together, we believe that this framework deserves careful attention as its robustness and flexibility could be the starting point toward the uniformization of statistical approaches.

Stroke-related alterations in inter-areal communication.

Beyond causing local ischemia and cell damage at the site of injury, stroke strongly affects long-range anatomical connections, perturbing the functional organization of brain networks. Several studies reported functional connectivity abnormalities parallelling both behavioral deficits and functional recovery across different cognitive domains. FC alterations suggest that long-range communication in the brain is altered after stroke. However, standard FC analyses cannot reveal the directionality and time scale of inter-areal information transfer. We used resting-state fMRI and covariance-based Granger causality analysis to quantify network-level information transfer and its alteration in stroke. Two main large-scale anomalies were observed in stroke patients. First, inter-hemispheric information transfer was significantly decreased with respect to healthy controls. Second, stroke caused inter-hemispheric asymmetries, as information transfer within the affected hemisphere and from the affected to the intact hemisphere was significantly reduced. Both anomalies were more prominent in resting-state networks related to attention and language, and they correlated with impaired performance in several behavioral domains. Overall, our findings support the hypothesis that stroke provokes asymmetries between the affected and spared hemisphere, with different functional consequences depending on which hemisphere is lesioned.

The dimensionality and structure of species trait spaces.

Trait-based ecology aims to understand the processes that generate the overarching diversity of organismal traits and their influence on ecosystem functioning. Achieving this goal requires simplifying this complexity in synthetic axes defining a trait space and to cluster species based on their traits while identifying those with unique combinations of traits. However, so far, we know little about the dimensionality, the robustness to trait omission and the structure of these trait spaces. Here, we propose a unified framework and a synthesis across 30 trait datasets representing a broad variety of taxa, ecosystems and spatial scales to show that a common trade-off between trait space quality and operationality appears between three and six dimensions. The robustness to trait omission is generally low but highly variable among datasets. We also highlight invariant scaling relationships, whatever organismal complexity, between the number of clusters, the number of species in the dominant cluster and the number of unique species with total species richness. When species richness increases, the number of unique species saturates, whereas species tend to disproportionately pack in the richest cluster. Based on these results, we propose some rules of thumb to build species trait spaces and estimate subsequent functional diversity indices.

Data segmentation based on the local intrinsic dimension.

One of the founding paradigms of machine learning is that a small number of variables is often sufficient to describe high-dimensional data. The minimum number of variables required is called the intrinsic dimension (ID) of the data. Contrary to common intuition, there are cases where the ID varies within the same data set. This fact has been highlighted in technical discussions, but seldom exploited to analyze large data sets and obtain insight into their structure. Here we develop a robust approach to discriminate regions with different local IDs and segment the points accordingly. Our approach is computationally efficient and can be proficiently used even on large data sets. We find that many real-world data sets contain regions with widely heterogeneous dimensions. These regions host points differing in core properties: folded versus unfolded configurations in a protein molecular dynamics trajectory, active versus non-active regions in brain imaging data, and firms with different financial risk in company balance sheets. A simple topological feature, the local ID, is thus sufficient to achieve an unsupervised segmentation of high-dimensional data, complementary to the one given by clustering algorithms.

Automatic classification of single-molecule force spectroscopy traces from heterogeneous samples.

MOTIVATION: Single-molecule force spectroscopy (SMFS) experiments pose the challenge of analysing protein unfolding data (traces) coming from preparations with heterogeneous composition (e.g. where different proteins are present in the sample). An automatic procedure able to distinguish the unfolding patterns of the proteins is needed. Here, we introduce a data analysis pipeline able to recognize in such datasets traces with recurrent patterns (clusters). RESULTS: We illustrate the performance of our method on two prototypical datasets: ∼50 000 traces from a sample containing tandem GB1 and ∼400 000 traces from a native rod membrane. Despite a daunting signal-to-noise ratio in the data, we are able to identify several unfolding clusters. This work demonstrates how an automatic pattern classification can extract relevant information from SMFS traces from heterogeneous samples without prior knowledge of the sample composition. AVAILABILITY AND IMPLEMENTATION: https://github.com/ninailieva/SMFS_clustering. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

Brain network dynamics during spontaneous strategy shifts and incremental task optimization.

With practice, humans improve their performance in a task by either optimizing a known strategy or discovering a novel, potentially more fruitful strategy. We investigated the neural processes underlying these two fundamental abilities by applying fMRI in a task with two possible alternative strategies. For analysis we combined time-resolved network analysis with Coherence Density Peak Clustering (Allegra et al., 2017), univariate GLM, and multivariate pattern classification. Converging evidence showed that the posterior portion of the default network, i.e. the precuneus and the angular gyrus bilaterally, has a central role in the optimization of the current strategy. These regions encoded the relevant spatial information, increased the strength of local connectivity as well as the long-distance connectivity with other relevant regions in the brain (e.g., visual cortex, dorsal attention network). The connectivity increase was proportional to performance optimization. By contrast, the anterior portion of the default network (i.e. medial prefrontal cortex) and the rostral portion of the fronto-parietal network were associated with new strategy discovery: an early increase of local and long-range connectivity centered on these regions was only observed in the subjects who would later shift to a new strategy. Overall, our findings shed light on the dynamic interactions between regions related to attention and with cognitive control, underlying the balance between strategy exploration and exploitation. Results suggest that the default network, far from being "shut-down" during task performance, has a pivotal role in the background exploration and monitoring of potential alternative courses of action.

fMRI single trial discovery of spatio-temporal brain activity patterns.

There is growing interest in the description of short-lived patterns in the spatiotemporal cortical activity monitored via neuroimaging. Most traditional analysis methods, designed to estimate relatively long-term brain dynamics, are not always appropriate to capture these patterns. Here we introduce a novel data-driven approach for detecting short-lived fMRI brain activity patterns. Exploiting Density Peak Clustering (Rodriguez and Laio [2014]), our approach reveals well localized clusters by identifying and grouping together voxels whose time-series are similar, irrespective of their brain location, even when very short time windows (∼10 volumes) are used. The method, which we call Coherence Density Peak Clustering (CDPC), is first tested on simulated data and compared with a standard unsupervised approach for fMRI analysis, independent component analysis (ICA). CDPC identifies activated voxels with essentially no false-positives and proves more reliable than ICA, which is troubled by a number of false positives comparable to that of true positives. The reliability of the method is demonstrated on real fMRI data from a simple motor task, containing brief iterations of the same movement. The clusters identified are found in regions expected to be involved in the task, and repeat synchronously with the paradigm. The methodology proposed is especially suitable for the study of short-time brain dynamics and single trial experiments, where the event or task of interest cannot be repeated for the same subject, as happens, for instance, in problem-solving, learning and decision-making. A GUI implementation of our method is available for download at https://github.com/micheleallegra/CDPC. Hum Brain Mapp 38:1421-1437, 2017. © 2016 Wiley Periodicals, Inc.

Quantum brachistochrone curves as geodesics: obtaining accurate minimum-time protocols for the control of quantum systems.

Most methods of optimal control cannot obtain accurate time-optimal protocols. The quantum brachistochrone equation is an exception, and has the potential to provide accurate time-optimal protocols for a wide range of quantum control problems. So far, this potential has not been realized, however, due to the inadequacy of conventional numerical methods to solve it. Here we show that the quantum brachistochrone problem can be recast as that of finding geodesic paths in the space of unitary operators. We expect this brachistochrone-geodesic connection to have broad applications, as it opens up minimal-time control to the tools of geometry. As one such application, we use it to obtain a fast numerical method to solve the brachistochrone problem, and apply this method to two examples demonstrating its power.

Topology and energy transport in networks of interacting photosynthetic complexes.

We address the role of topology in the energy transport process that occurs in networks of photosynthetic complexes. We take inspiration from light-harvesting networks present in purple bacteria and simulate an incoherent dissipative energy transport process on more general and abstract networks, considering both regular structures (Cayley trees and hyperbranched fractals) and randomly generated ones. We focus on the the two primary light-harvesting complexes of purple bacteria, i.e., the LH1 and LH2, and we use network-theoretical centrality measures in order to select different LH1 arrangements. We show that different choices cause significant differences in the transport efficiencies, and that for regular networks, centrality measures allow us to identify arrangements that ensure transport efficiencies which are better than those obtained with a random disposition of the complexes. The optimal arrangements strongly depend on the dissipative nature of the dynamics and on the topological properties of the networks considered, and depending on the latter, they are achieved by using global versus local centrality measures. For randomly generated networks, a random arrangement of the complexes already provides efficient transport, and this suggests the process is strong with respect to limited amount of control in the structure design and to the disorder inherent in the construction of randomly assembled structures. Finally, we compare the networks considered with the real biological networks and find that the latter have in general better performances, due to their higher connectivity, but the former with optimal arrangements can mimic the real networks' behavior for a specific range of transport parameters. These results show that the use of network-theoretical concepts can be crucial for the characterization and design of efficient artificial energy transport networks.

Role of initial entanglement and non-Gaussianity in the decoherence of photon-number entangled states evolving in a noisy channel.

We address the degradation of continuous variable (CV) entanglement in a noisy channel focusing on the set of photon-number entangled states. We exploit several separability criteria and compare the resulting separation times with the value of non-Gaussianity at any time, thus showing that in the low-temperature regime: (i) non-Gaussianity is a bound for the relative entropy of entanglement and (ii) Simon's criterion provides a reliable estimate of the separation time also for non-Gaussian states. We provide several evidences supporting the conjecture that Gaussian entanglement is the most robust against noise, i.e., it survives longer than a non-Gaussian one, and that this may be a general feature for CV systems in Markovian channels.