Investigating complex networks with inverse models: analytical aspects of spatial leakage and connectivity estimation

Network theory and inverse modeling are two standard tools of applied physics, whose combination is needed when studying the dynamical organization of spatially distributed systems from indirect measurements. However, the associated connectivity estimation may be affected by spatial leakage, an artifact of inverse modeling that limits the interpretability of network analysis. This paper investigates general analytical aspects pertaining to this issue. First, the existence of spatial leakage is derived from the topological structure of inverse operators. Then, the geometry of spatial leakage is modeled and used to define a geometric correction scheme, which limits spatial leakage effects in connectivity estimation. Finally, this new approach for network analysis is compared analytically to existing methods based on linear regressions, which are shown to yield biased coupling estimates.Comment: 19 pages, 4 figures, including 5 appendices; v2: minor edits, 1 appendix added; v3: expanded version, v4: minor edit

Brownian forgery of statistical dependences

The balance held by Brownian motion between temporal regularity and randomness is embodied in a remarkable way by Levy's forgery of continuous functions. Here we describe how this property can be extended to forge arbitrary dependences between two statistical systems, and then establish a new Brownian independence test based on fluctuating random paths. We also argue that this result allows revisiting the theory of Brownian covariance from a physical perspective and opens the possibility of engineering nonlinear correlation measures from more general functional integrals.Comment: 13 pages, 2 figures, formatting based on revtex4; v2: revised proof of extended forgery and minor changes; v3: additional discussion on practical implementation and minor edits, published versio

Feeding Activity Book for Home Treatment Programs

Sensory processing challenges in children can have adverse effects on their ability to eat. These children may experience food temperatures, flavors and textures more intensely, causing them to have an aversion to many food types, which can potentially lead to the inability to get proper nutrition. In observing feeding therapy at Cascade Children’s Therapy (CCT), it was discovered that the therapists would benefit from a book to efficiently assign home treatment programs to these children with sensory processing challenges as an adjunct to in-clinic intervention. However, the home treatment programs needed to be playful in order to enhance adherence to the program. Eat, Play, Love is a book created for CCT containing 20 sensory-rich, playful food games and crafts from which therapists can efficiently reproduce, and assign to children and their caregivers as a home treatment program. This feeding activity book aims to improve food tolerance, and to increase food repertoire

The impact of the Geometric Correction Scheme on MEG functional topology at rest

Spontaneous activity is correlated across brain regions in large scale networks (RSN) closely resembling those recruited during several behavioral tasks and characterized by functional specialization and dynamic integration. Specifically, MEG studies revealed a set of central regions (dynamic core) possibly facilitating communication among differently specialized brain systems. However, source projected MEG signals, due to the fundamentally ill-posed inverse problem, are affected by spatial leakage, leading to the estimation of spurious, blurred connections that may affect the topological properties of brain networks and their integration. To reduce leakage effects, several correction schemes have been proposed including the Geometric Correction Scheme (GCS) whose theory, simulations and empirical results on topography of a few RSNs were already presented. However, its impact on the estimation of fundamental graph measures used to describe the architecture of interactions among brain regions has not been investigated yet. Here, we estimated dense, MEG band-limited power connectomes in theta, alpha, beta, and gamma bands from 13 healthy subjects (all young adults). We compared the connectivity and topology of MEG uncorrected and GCS-corrected connectomes. The use of GCS considerably reorganized the topology of connectivity, reducing the local, within-hemisphere interactions mainly in the beta and gamma bands and increasing across-hemisphere interactions mainly in the alpha and beta bands. Moreover, the number of hubs decreased in the alpha and beta bands, but the centrality of some fundamental regions such as the Posterior Cingulate Cortex (PCC), Supplementary Motor Area (SMA) and Middle Prefrontal Cortex (MPFC) remained strong in all bands, associated to an increase of the Global Efficiency and a decrease of Modularity. As a comparison, we applied orthogonalization on connectomes and ran the same topological analyses. The correlation values were considerably reduced, and orthogonalization mainly decreased local within-hemisphere interactions in all bands, similarly to GCS. Notably, the centrality of the PCC, SMA and MPFC was preserved in all bands, as for GCS, together with other hubs in the posterior parietal regions. Overall, leakage correction removes spurious local connections, but confirms the role of dynamic hub regions, specifically the anterior and posterior cingulate, in integrating information in the brain at rest