Subset currents on free groups

We introduce and study the space of \emph{subset currents} on the free group $F_N$. A subset current on $F_N$ is a positive $F_N$-invariant locally finite Borel measure on the space $\mathfrak C_N$ of all closed subsets of $\partial F_N$ consisting of at least two points. While ordinary geodesic currents generalize conjugacy classes of nontrivial group elements, a subset current is a measure-theoretic generalization of the conjugacy class of a nontrivial finitely generated subgroup in $F_N$, and, more generally, in a word-hyperbolic group. The concept of a subset current is related to the notion of an "invariant random subgroup" with respect to some conjugacy-invariant probability measure on the space of closed subgroups of a topological group. If we fix a free basis $A$ of $F_N$, a subset current may also be viewed as an $F_N$-invariant measure on a "branching" analog of the geodesic flow space for $F_N$, whose elements are infinite subtrees (rather than just geodesic lines) of the Cayley graph of $F_N$ with respect to $A$.Comment: updated version; to appear in Geometriae Dedicat

Intersection form, laminations and currents on free groups

Let $F_N$ be a free group of rank $N\ge 2$, let $\mu$ be a geodesic current on $F_N$ and let $T$ be an $\mathbb R$-tree with a very small isometric action of $F_N$. We prove that the geometric intersection number $$ is equal to zero if and only if the support of $\mu$ is contained in the dual algebraic lamination $L^2(T)$ of $T$. Applying this result, we obtain a generalization of a theorem of Francaviglia regarding length spectrum compactness for currents with full support. As another application, we define the notion of a \emph{filling} element in $F_N$ and prove that filling elements are "nearly generic" in $F_N$. We also apply our results to the notion of \emph{bounded translation equivalence} in free groups.Comment: revised version, to appear in GAF

The effects of high frequency subthalamic stimulation on balance performance and fear of falling in patients with Parkinson's disease

<p>Abstract</p> <p>Background</p> <p>Balance impairment is one of the most distressing symptoms in Parkinson's disease (PD) even with pharmacological treatment (levodopa). A complementary treatment is high frequency stimulation in the subthalamic nucleus (STN). Whether STN stimulation improves postural control is under debate. The aim of this study was to explore the effects of STN stimulation alone on balance performance as assessed with clinical performance tests, subjective ratings of fear of falling and posturography.</p> <p>Methods</p> <p>Ten patients (median age 66, range 59–69 years) with bilateral STN stimulation for a minimum of one year, had their anti-PD medications withdrawn overnight. Assessments were done both with the STN stimulation turned OFF and ON (start randomized). In both test conditions, the following were assessed: motor symptoms (descriptive purposes), clinical performance tests, fear of falling ratings, and posturography with and without vibratory proprioceptive disturbance.</p> <p>Results</p> <p>STN stimulation alone significantly (p = 0.002) increased the scores of the Berg balance scale, and the median increase was 6 points. The results of all timed performance tests, except for sharpened Romberg, were significantly (p ≤ 0.016) improved. The patients rated their fear of falling as less severe, and the total score of the Falls-Efficacy Scale(S) increased (p = 0.002) in median with 54 points. All patients completed posturography when the STN stimulation was turned ON, but three patients were unable to do so when it was turned OFF. The seven patients with complete data showed no statistical significant difference (p values ≥ 0.109) in torque variance values when comparing the two test situations. This applied both during quiet stance and during the periods with vibratory stimulation, and it was irrespective of visual input and sway direction.</p> <p>Conclusion</p> <p>In this sample, STN stimulation alone significantly improved the results of the clinical performance tests that mimic activities in daily living. This improvement was further supported by the patients' ratings of fear of falling, which were less severe with the STN stimulation turned ON. Posturography could not be performed by three out of the ten patients when the stimulation was turned OFF. The posturography results of the seven patients with complete data showed no significant differences due to STN stimulation.</p

Spatially dissociated intracerebral maps for face- and house-selective activity in the human ventral occipito-temporal cortex

We report a comprehensive mapping of the human ventral occipito-temporal cortex (VOTC) for selective responses to frequency-tagged faces or landmarks (houses) presented in rapid periodic trains of objects, with intracerebral recordings in a large sample (Nn=n75). Face-selective contacts are three times more numerous than house-selective contacts and show a larger amplitude, with a right hemisphere advantage for faces. Most importantly, these category-selective contacts are spatially dissociated along the lateral-to-medial VOTC axis, respectively, consistent with neuroimaging evidence. At the minority of "overlap" contacts responding selectively to both faces and houses, response amplitude to the two categories is not correlated, suggesting a contribution of distinct populations of neurons responding selectively to each category. The medio-lateral dissociation also extends into the underexplored anterior temporal lobe (ATL). In this region, a relatively high number of intracerebral recording contacts show category-exclusive responses (i.e., without any response to baseline visual objects) to faces but rarely to houses, in line with the proposed role of this region in processing people-related semantic information. Altogether, these observations shed novel insight on the neural basis of human visual recognition and strengthen the validity of the frequency-tagging approach coupled with intracerebral recordings in epileptic patients to understand human brain function

Dissociated face- and word-selective intracerebral responses in the human ventral occipito-temporal cortex

Item does not contain fulltextThe extent to which faces and written words share neural circuitry in the human brain is actively debated. We provide an original contribution to this debate by comparing face-selective and word-selective responses in a large group of patients (N=37) implanted with intracerebral electrodes in the ventral occipito-temporal cortex (VOTC). Both face-selective (i.e., significantly different responses to faces vs. nonface objects) and word-selective (i.e., significantly different responses to words vs. pseudofonts) neural activity is isolated through frequency-tagging (Jonas et al., 2016; Lochy et al., 2018, respectively). Critically, this approach allows disentangling category-selective neural responses from general visual responses. Overall, we find that 69.26% of significant contacts show either face- or word-selectivity, with the expected right and left hemispheric dominance, respectively (Fig.1A,B). Moreover, the center of mass for word-contacts is more lateral than for face-contacts, with no differences in postero-anterior axis (Fig.2A). Spatial dissociations are also found within core regions of face and word processing, with a medio-lateral dissociation in the fusiform gyrus (FG) and surrounding sulci (FG+sulci;Fig.2B), while a postero-anterior dissociation is found in the inferior occipital gyrus (IOG;Fig.2C). Despite their spatial dissociations in the FG+sulci and IOG, most overlap in category-selective responses is found in these regions (Fig.1C). Critically, in the overlap-contacts, across the whole brain or specifically in the FG+sulci, between-category (word-face) selective-amplitudes showed no-to-weak correlations, despite strong correlations for within-category (face-face, word-word) selective-amplitudes (Fig.3A), and a strong correlation in non-selective general-amplitudes to words-faces. Moreover, substantial overlap and no-to-weak correlations were observed between faces and a control category (houses) known to be functionally dissociated from faces. Overall, we conclude that category-selectivity for faces and words is largely dissociated in the human VOTC, with a limited spatial overlap likely due to the distant recording of dissociated populations of neurons rather than to shared category-selective representations.1 p

Modalités de décision de limitation thérapeutique chez les traumatisés crâniens sévères : enquête auprès des neurochirurgiens en France

International audienc

Bilateral subthalamic nucleus stimulation improves balance control in Parkinson's disease

Background: Parkinson's disease (PD), the most common basal ganglia degenerative disease, affects balance control, especially when patients change balance strategy during postural tasks. Bilateral chronic stimulation of the subthalamic nucleus (STN) is therapeutically useful in advanced PD, and reduces the motor signs of patients. Nevertheless, the effects of STN stimulation on postural control are still debatable. Aims: To assess the impact of bilateral STN stimulation on balance control in PD and to determine how basal ganglia related sensorimotor modifications act on neurosensorial organisation of balance and motor postural programming. Methods: Twelve subjects aged 45–70 years underwent unified Parkinson's disease rating scale motor (part III) clinical tests, static and dynamic posturography, including sensory organisation and adaptation tests, shortly before and six months after bilateral implantation of electrodes into the STN. Results: The postoperative static test showed an improvement in postural control precision both in eyes open and eyes closed conditions. The dynamic test highlighted the decreased number of falls and the ability of the patients to develop more appropriate sensorimotor strategies when stimulated. The sensory organisation test showed an improvement of equilibrium score and, thus, a better resolution of sensorial conflicts. Conclusions: STN stimulation allowed a reduction in rigidity and therefore an improvement in the ability to use muscular proprioception as reliable information, resulting in vestibulo-proprioceptive conflict suppression. STN stimulation has a synergistic effect with levodopa for postural control. Accordingly, non-dopaminergic pathways could be involved in postural regulation and STN stimulation may influence the functioning of these pathways