Formality and Star Products

These notes, based on the mini-course given at the PQR2003 Euroschool held in Brussels in 2003, aim to review Kontsevich's formality theorem together with his formula for the star product on a given Poisson manifold. A brief introduction to the employed mathematical tools and physical motivations is also given.Comment: 49 pages, 9 figures; proceedings of the PQR2003 Euroschool. Version 2 has minor correction

An Algebraic Approach to Shadowed Sets

Abstract After the introduction of shadowed sets and the investigation of their relation with fuzzy sets, we present BZMV dM algebras as an abstract environment for both shadowed and fuzzy sets. Then, we introduce the weaker notion of pre-BZMV dM algebra. This structure enables us to algebraically define a mapping from fuzzy sets to shadowed sets

Novel asleep techniques for intraoperative assessment of brain connectivity

[no abstract available

Fallers after stroke: a retrospective study to investigate the combination of postural sway measures and clinical information in faller’s identification

BackgroundFalls can have devastating effects on quality of life. No clear relationships have been identified between clinical and stabilometric postural measures and falling in persons after stroke.ObjectiveThis cross-sectional study investigates the value of including stabilometric measures of sway with clinical measures of balance in models for identification of faller chronic stroke survivors, and the relations between variables.MethodsClinical and stabilometric data were collected from a convenience sample of 49 persons with stroke in hospital care. They were categorized as fallers (N = 21) or non-fallers (N = 28) based on the occurrence of falls in the previous 6 months. Logistic regression (model 1) was performed with clinical measures, including the Berg Balance scale (BBS), Barthel Index (BI), and Dynamic Gait Index (DGI). A second model (model 2) was run with stabilometric measures, including mediolateral (SwayML) and anterior–posterior sway (SwayAP), velocity of antero-posterior (VelAP) and medio-lateral sway (VelML), and absolute position of center of pressure (CopX abs). A third stepwise regression model was run including all variables, resulting in a model with SwayML, BBS, and BI (model 3). Finally, correlations between independent variables were analyzed.ResultsThe area under the curve (AUC) for model 1 was 0.68 (95%CI: 0.53–0.83, sensitivity = 95%, specificity = 39%) with prediction accuracy of 63.3%. Model 2 resulted in an AUC of 0.68 (95%CI: 0.53–0.84, sensitivity = 76%, specificity = 57%) with prediction accuracy of 65.3%. The AUC of stepwise model 3 was 0.74 (95%CI: 0.60–0.88, sensitivity = 57%, specificity = 81%) with prediction accuracy of 67.4%. Finally, statistically significant correlations were found between clinical variables (p < 0.05), only velocity parameters were correlated with balance performance (p < 0.05).ConclusionA model combining BBS, BI, and SwayML was best at identifying faller status in persons in the chronic phase post stroke. When balance performance is poor, a high SwayML may be part of a strategy protecting from falls

Feasibility of cerebello-cortical stimulation for intraoperative neurophysiological monitoring of cerebellar mutism

BACKGROUND: Cerebellar mutism can occur in a third of children undergoing cerebellar resections. Recent evidence proposes it may arise from uni- or bilateral damage of cerebellar efferents to the cortex along the cerebello-dento-thalamo-cortical pathway. At present, no neurophysiological procedure is available to monitor this pathway intraoperatively. Here, we specifically aimed at filling this gap.METHODS: We assessed 10 patients undergoing posterior fossa surgery using a conditioning-test stimulus paradigm. Electrical conditioning stimuli (cStim) were delivered to the exposed cerebellar cortex at interstimulus intervals (ISIs) of 8-24 ms prior to transcranial electric stimulation of the motor cortex, which served as test stimulus (tStim). The variation of motor-evoked potentials (MEP) to cStim + tStim compared with tStim alone was taken as a measure of cerebello-cortical connectivity.RESULTS: cStim alone did not produce any MEP. cStim preceding tStim produced a significant inhibition at 8 ms (p < 0.0001) compared with other ISIs when applied to the lobules IV-V-VI in the anterior cerebellum and the lobule VIIB in the posterior cerebellum. Mixed effects of decrease and increase in MEP amplitude were observed in these areas for longer ISIs.CONCLUSIONS: The inhibition exerted by cStim at 8 ms on the motor cortex excitability is likely to be the product of activity along the cerebello-dento-thalamo-cortical pathway. We show that monitoring efferent cerebellar pathways to the motor cortex is feasible in intraoperative settings. This study has promising implications for pediatric posterior fossa surgery with the aim to preserve the cerebello-cortical pathways and thus prevent cerebellar mutism

Effect of immersive virtual reality training on hand-to-mouth task performance in people with Multiple Sclerosis: A quantitative kinematic study

Background Although the use of Virtual Reality (VR) has received increasing interest as an add-on treatment in neurorehabilitation programs in the last fifteen years, there is scarce information about the effectiveness of fully immersive VR-based treatments on upper limb (UL) motor function in people with Multiple Sclerosis (PwMS). Methods In this bicentric 2-period interventional crossover study, 19 PwMS with moderate to severe disability (mean EDSS score 5.5) and relevant UL impairment underwent 12 immersive-VR sessions over a period of 4 weeks, using commercially available VR platform (Oculus Quest) and games (Fruit Ninja, Beat Saber and Creed - Rise to Glory). Possible changes associated with the treatment were objectively assessed through instrumental kinematic analysis of the “hand-to-mouth” (HTM) movement by means of optical motion capture system. Clinical tests to assess gross and fine manual dexterity (i.e., the Box and Blocks and Nine Hole Peg Test) were also administered. Results The results of the kinematic analysis suggest that the VR training positively impacted the ability of the tested PwMS to perform the HTM task. In particular, a significant reduction of the overall time required to complete the task of approximately 20% for both most and least affected limb, and an improved degree of precision and stability of the movement, as indicated by the reduced value of adjusting sway, especially for the most affected limb (-60%). Conclusion Based on the results of the quantitative analysis, a 4-week treatment with immersive VR is able to improve speed and stability of the HTM movement in PwMS. This suggests that such an approach might be considered suitable to facilitate an immediate transfer of the possible positive effects associated with the training to common activities of daily living

VOCs Measurements in Residential Buildings: Quantification via Thermal Desorption and Assessment of Indoor Concentrations in a Case-Study

Volatile organic compounds (VOCs) represent one of the most important categories of pollutants, influencing the air quality and human health and well-being in indoor environments. In the present study, 12 selected VOCs were sampled using Tenax TA tubes and analyzed by thermal desorption combined with gas chromatography and a flame ionization detector (TD-GC-FID). The TD-GC-FID method was optimized to obtain the separation of all the analytical peaks (including m- and p-xylene) and a satisfactory sensitivity, with low detection (between 0.14 and 0.31 ng) and quantification (between 0.47 and 1.02 ng) limits. The whole procedure was firstly assessed with the analysis of four co-located tubes exposed at an outdoor monitoring site, with results that revealed a very low inter-tubes variability (relative standard deviations of parallel measurements <5%). Then, the measurement protocol was used to quantify the indoor concentrations of the target VOCs in nine different homes during the dishwasher washing cycle. The most abundant detected VOC in all dwellings was d-limonene (mean: 231 µg/m3; maximum: 611 µg/m3). All the other compounds were monitored at concentration levels one or two orders of magnitude lower than d-limonene, and were generally comparable with those found in the scientific literature. In terms of health concerns, the measured concentrations were always well below the safe levels established for the protection of the general population in living environments

High-order Harmonic Generation in Thermotropic Liquid Crystals

Thermotropic liquid crystals are versatile optical materials that exhibit a state of matter intermediate between liquids and solids. Their properties can change significantly with temperature, pressure, or other external factors, leading to different phases. The transport properties within these materials in different phases are still largely unexplored and their understanding would enable exciting prospects for innovative technological advancements. High-order harmonic spectroscopy proved to be a powerful spectroscopic tool for investigating the electronic and nuclear dynamics in matter. Here we report the first experimental observation of high-order harmonic generation in thermotropic liquid crystals in two different phase states, nematic and isotropic. We found the harmonic emission in the nematic phase to be strongly dependent on the relative orientation of the driving field polarization with respect to the liquid crystal alignment. Specifically, the harmonic yield has a maximum when the molecules are aligned perpendicularly to the polarization of the incoming radiation. Our results establish the first step for applying high-order harmonic spectroscopy as a tool for resolving ultrafast electron dynamics in liquid crystals with unprecedented temporal and spatial resolution.Comment: The paper is composed by 12 pages including references. Five images are presen

Long-term motor deficit in brain tumour surgery with preserved intra-operative motor-evoked potentials

Muscle motor-evoked potentials are commonly monitored during brain tumour surgery in motor areas, as these are assumed to reflect the integrity of descending motor pathways, including the corticospinal tract. However, while the loss of muscle motor-evoked potentials at the end of surgery is associated with long-term motor deficits (muscle motor-evoked potential-related deficits), there is increasing evidence that motor deficit can occur despite no change in muscle motor-evoked potentials (muscle motor-evoked potential-unrelated deficits), particularly after surgery of non-primary regions involved in motor control. In this study, we aimed to investigate the incidence of muscle motor-evoked potential-unrelated deficits and to identify the associated brain regions. We retrospectively reviewed 125 consecutive patients who underwent surgery for peri-Rolandic lesions using intra-operative neurophysiological monitoring. Intraoperative changes in muscle motor-evoked potentials were correlated with motor outcome, assessed by the Medical Research Council scale. We performed voxel-lesion-symptom mapping to identify which resected regions were associated with short- and long-term muscle motor-evoked potential-associated motor deficits. Muscle motor-evoked potentials reductions significantly predicted long-term motor deficits. However, in more than half of the patients who experienced long-term deficits (12/22 patients), no muscle motor-evoked potential reduction was reported during surgery. Lesion analysis showed that muscle motor-evoked potential-related long-term motor deficits were associated with direct or ischaemic damage to the corticospinal tract, whereas muscle motor-evoked potential-unrelated deficits occurred when supplementary motor areas were resected in conjunction with dorsal premotor regions and the anterior cingulate. Our results indicate that long-term motor deficits unrelated to the corticospinal tract can occur more often than currently reported. As these deficits cannot be predicted by muscle motor-evoked potentials, a combination of awake and/or novel asleep techniques other than muscle motor-evoked potentials monitoring should be implemented