Cuts and flows of cell complexes

We study the vector spaces and integer lattices of cuts and flows associated with an arbitrary finite CW complex, and their relationships to group invariants including the critical group of a complex. Our results extend to higher dimension the theory of cuts and flows in graphs, most notably the work of Bacher, de la Harpe and Nagnibeda. We construct explicit bases for the cut and flow spaces, interpret their coefficients topologically, and give sufficient conditions for them to be integral bases of the cut and flow lattices. Second, we determine the precise relationships between the discriminant groups of the cut and flow lattices and the higher critical and cocritical groups with error terms corresponding to torsion (co)homology. As an application, we generalize a result of Kotani and Sunada to give bounds for the complexity, girth, and connectivity of a complex in terms of Hermite's constant.Comment: 30 pages. Final version, to appear in Journal of Algebraic Combinatoric

Prediction of Ideas Number During a Brainstorming Session

International audienceIn this paper, we present an approach allowing the prediction of ideas number during a brainstorming session. This prediction is based on two dynamic models of brainstorming, the non-cognitive and the cognitive models proposed by Brown and Paulus (Small Group Res 27(1):91–114, 1996). These models describe for each participant, the evolution of ideas number over time, and are formalized by differential equations. Through solution functions of these models, we propose to calculate the number of ideas of each participant on any time intervals and thus in the future (called prediction). To be able to compute solution functions, it is necessary to determine the parameters of these models. In our approach, we use optimization model for model parameters calculation in which solution functions are approximated by numerical methods. We developed two generic optimization models, one based on Euler’s and the other on the fourth order Runge–Kutta’s numerical methods for the solving of differential equations, and we apply them to the non-cognitive and respectively to the cognitive models. Through some feasibility tests, we show the adequacy of the proposed approach to our prediction context

Endovascular Neuromodulation: Safety Profile and Future Directions

Endovascular neuromodulation is an emerging technology that represents a synthesis between interventional neurology and neural engineering. The prototypical endovascular neural interface is the StentrodeTM, a stent-electrode array which can be implanted into the superior sagittal sinus via percutaneous catheter venography, and transmits signals through a transvenous lead to a receiver located subcutaneously in the chest. Whilst the StentrodeTM has been conceptually validated in ovine models, questions remain about the long term viability and safety of this device in human recipients. Although technical precedence for venous sinus stenting already exists in the setting of idiopathic intracranial hypertension, long term implantation of a lead within the intracranial veins has never been previously achieved. Contrastingly, transvenous leads have been successfully employed for decades in the setting of implantable cardiac pacemakers and defibrillators. In the current absence of human data on the StentrodeTM, the literature on these structurally comparable devices provides valuable lessons that can be translated to the setting of endovascular neuromodulation. This review will explore this literature in order to understand the potential risks of the StentrodeTM and define avenues where further research and development are necessary in order to optimize this device for human application

Feasibility of identifying the ideal locations for motor intention decoding using unimodal and multimodal classification at 7T-fMRI

Invasive Brain-Computer Interfaces (BCIs) require surgeries with high health-risks. The risk-to-benefit ratio of the procedure could potentially be improved by pre-surgically identifying the ideal locations for mental strategy classification. We recorded high-spatiotemporal resolution blood-oxygenation-level-dependent (BOLD) signals using functional MRI at 7 Tesla in eleven healthy participants during two motor imagery tasks. BCI diagnostic task isolated the intent to imagine movements, while BCI simulation task simulated the neural states that may be yielded in a real-life BCI-operation scenario. Imagination of movements were classified from the BOLD signals in sub-regions of activation within a single or multiple dorsal motor network regions. Then, the participant's decoding performance during the BCI simulation task was predicted from the BCI diagnostic task. The results revealed that drawing information from multiple regions compared to a single region increased the classification accuracy of imagined movements. Importantly, systematic unimodal and multimodal classification revealed the ideal combination of regions that yielded the best classification accuracy at the individual-level. Lastly, a given participant's decoding performance achieved during the BCI simulation task could be predicted from the BCI diagnostic task. These results show the feasibility of 7T-fMRI with unimodal and multimodal classification being utilized for identifying ideal sites for mental strategy classification

Feasibility of a Chronic, Minimally Invasive Endovascular Neural Interface

Development of a neural interface that can be implanted without risky, open brain surgery will increase the safety and viability of chronic neural recording arrays. We have developed a minimally invasive surgical procedure and an endovascular electrode-array that can be delivered to overlie the cortex through blood vessels. Here, we describe feasibility of the endovascular interface through electrode viability, recording potential and safety. Electrochemical impedance spectroscopy demonstrated that electrode impedance was stable over 91 days and low frequency phase could be used to infer electrode incorporation into the vessel wall. Baseline neural recording were used to identify the maximum bandwidth of the neural interface, which remained stable around 193 Hz for six months. Cross-sectional areas of the implanted vessels were non-destructively measured using the Australian Synchrotron. There was no case of occlusion observed in any of the implanted animals. This work demonstrates the feasibility of an endovascular neural interface to safely and efficaciously record neural information over a chronic time course

Distinct Neural Correlates Underlie Inhibitory Mechanisms of Motor Inhibition and Motor Imagery Restraint

There is evidence to suggest that motor execution and motor imagery both involve planning and execution of the same motor plan, however, in the latter the output is inhibited. Currently, little is known about the underlying neural mechanisms of motor output inhibition during motor imagery. Uncovering the distinctive characteristics of motor imagery may help us better understand how we abstract complex thoughts and acquire new motor skills. The current study aimed to dissociate the cognitive processes involved in two distinct inhibitory mechanisms of motor inhibition and motor imagery restraint. Eleven healthy participants engaged in an imagined GO/NO-GO task during a 7 Tesla fMRI experiment. Participants planned a specific type of motor imagery, then, imagined the movements during the GO condition and restrained from making a response during the NO-GO condition. The results revealed that specific sub-regions of the supplementary motor cortex (SMC) and the primary motor cortex (M1) were recruited during the imagination of specific movements and information flowed from the SMC to the M1. Such condition-specific recruitment was not observed when motor imagery was restrained. Instead, general recruitment of the posterior parietal cortex (PPC) was observed, while the BOLD activity in the SMC and the M1 decreased below the baseline at the same time. Information flowed from the PPC to the SMC, and recurrently between the M1 and the SMC, and the M1 and the PPC. These results suggest that motor imagery involves task-specific motor output inhibition partly imposed by the SMC to the M1, while the PPC globally inhibits motor plans before they are passed on for execution during the restraint of responses

7T-fMRI: Faster temporal resolution yields optimal BOLD sensitivity for functional network imaging specifically at high spatial resolution

Recent developments in accelerated imaging methods allow faster acquisition of high spatial resolution images. This could improve the applications of functional magnetic resonance imaging at 7 Tesla (7T-fMRI), such as neurosurgical planning and Brain Computer Interfaces (BCIs). However, increasing the spatial and temporal resolution will both lead to signal-to-noise ratio (SNR) losses due to decreased net magnetization per voxel and T1-relaxation effect, respectively. This could potentially offset the SNR efficiency gains made with increasing temporal resolution. We investigated the effects of varying spatial and temporal resolution on fMRI sensitivity measures and their implications on fMRI-based BCI simulations. We compared temporal signal-to-noise ratio (tSNR), observed percent signal change (%∆S), volumes of significant activation, Z-scores and decoding performance of linear classifiers commonly used in BCIs across a range of spatial and temporal resolution images acquired during an ankle-tapping task. Our results revealed an average increase of 22% in %∆S (p=0.006) and 9% in decoding performance (p=0.015) with temporal resolution only at the highest spatial resolution of 1.5×1.5×1.5mm3, despite a 29% decrease in tSNR (p0.05) across spatial resolution specifically at the highest temporal resolution of 500ms. These results demonstrate that the overall BOLD sensitivity can be increased significantly with temporal resolution, granted an adequately high spatial resolution with minimal physiological noise level. This shows the feasibility of diffuse motor-network imaging at high spatial and temporal resolution with robust BOLD sensitivity with 7T-fMRI. Importantly, we show that this sensitivity improvement could be extended to an fMRI application such as BCIs