Curve Diagrams, Laminations, and the Geometric Complexity of Braids

Braids can be represented geometrically as curve diagrams. The geometric complexity of a braid is the minimal complexity of a curve diagram representing it. We introduce and study the corresponding notion of geometric generating function. We compute explicitly the geometric generating function for the group of braids on three strands and prove that it is neither rational nor algebraic, nor even holonomic. This result may appear as counterintuitive. Indeed, the standard complexity (due to the Artin presentation of braid groups) is algorithmically harder to compute than the geometric complexity, yet the associated generating function for the group of braids on three strands is rational.Comment: 33 pages, 19 figure

Reduction ratio of the IS-algorithm: worst and random cases

We study the IS-algorithm, a well-known linear-time algorithm for computing the suffix array of a word. This algorithm relies on transforming the input word $w$ into another word, called the reduced word of $w$, that will be at least twice shorter; then, the algorithm recursively computes the suffix array of the reduced word. In this article, we study the reduction ratio of the IS-algorithm, i.e., the ratio between the lengths of the input word and the word obtained after reducing $k$ times the input word. We investigate both worst cases, in which we find precise results, and random cases, where we prove some strong convergence phenomena. Finally, we prove that, if the input word is a randomly chosen word of length $n$, we should not expect much more than $\log(\log(n))$ recursive function calls.Comment: 21 pages. Article to be published in the proceedings of the 33rd Annual Symposium on Combinatorial Pattern Matching (CPM 2022

Diffusion Tensor Imaging in Sport-Related Concussion: A Systematic Review Using an a priori Quality Rating System

Diffusion tensor imaging (DTI) of brain white matter (WM) may be useful for characterizing the nature and degree of brain injury after sport-related concussion (SRC) and assist in establishing objective diagnostic and prognostic biomarkers. This study aimed to conduct a systematic review using an a priori quality rating strategy to determine the most consistent DTI-WM changes post-SRC. Articles published in English (until June 2020) were retrieved by standard research engine and gray literature searches (N = 4932), using PRISMA guidelines. Eligible studies were non-interventional naturalistic original studies that conducted DTI within 6 months of SRC in current athletes from all levels of play, types of sports, and sex. A total of 29 articles were included in the review, and after quality appraisal by two raters, data from 10 studies were extracted after being identified as high quality. High-quality studies showed widespread moderate-to-large WM differences when SRC samples were compared to controls during the acute to early chronic stage (days to weeks) post-SRC, including both increased and decreased fractional anisotropy and axial diffusivity and decreased mean diffusivity and radial diffusivity. WM differences remained stable in the chronic stage (2-6 months post-SRC). DTI metrics were commonly associated with SRC symptom severity, although standardized SRC diagnostics would improve future research. This indicates that microstructural recovery is often incomplete at return to play and may lag behind clinically assessed recovery measures. Future work should explore interindividual trajectories to improve understanding of the heterogeneous and dynamic WM patterns post-SRC

Effect of upper airway fat on tongue dilation during inspiration in awake people with obstructive sleep apnea

Study Objectives: To investigate the effect of upper airway fat composition on tongue inspiratory movement and obstructive sleep apnea (OSA). Methods: Participants without or with untreated OSA underwent a 3T magnetic resonance imaging (MRI) scan. Anatomical measurements were obtained from T2-weighted images. Mid-sagittal inspiratory tongue movements were imaged using tagged MRI during wakefulness. Tissue volumes and percentages of fat were quantified using an mDIXON scan. Results: Forty predominantly overweight participants with OSA were compared to 10 predominantly normal weight controls. After adjusting for age, BMI, and gender, the percentage of fat in the tongue was not different between groups (analysis of covariance [ANCOVA], p = 0.45), but apnoeic patients had a greater tongue volume (ANCOVA, p = 0.025). After adjusting for age, BMI, and gender, higher OSA severity was associated with larger whole tongue volume (r = 0.51, p < 0.001), and greater dilatory motion of the anterior horizontal tongue compartment (r = -0.33, p = 0.023), but not with upper airway fat percentage. Higher tongue fat percentage was associated with higher BMI and older age (Spearman r = 0.43, p = 0.002, and r =0.44, p = 0.001, respectively), but not with inspiratory tongue movements. Greater inspiratory tongue movement was associated with larger tongue volume (e.g. horizontal posterior compartment, r = -0.44, p = 0.002) and smaller nasopharyngeal airway (e.g. oblique compartment, r = 0.29, p = 0.040). Conclusions: Larger tongue volume and a smaller nasopharynx are associated with increased inspiratory tongue dilation during wakefulness in people with and without OSA. This compensatory response was not influenced by higher tongue fat content. Whether this is also true in more obese patient populations requires further investigation

Elevation of cell-associated HIV-1 transcripts in CSF CD4+ T cells, despite effective antiretroviral therapy, is linked to brain injury

Antiretroviral therapy (ART) can attain prolonged undetectable HIV-1 in plasma and cerebrospinal fluid (CSF), but brain injury remains prevalent in people living with HIV-1 infection (PLHIV). We investigated cell-associated (CA)-HIV-1 RNA transcripts in cells in CSF and blood, using the highly sensitive Double-R assay, together with proton Magnetic Resonance Spectroscopy (1H MRS) of major brain metabolites, in sixteen PLHIV. 14/16 CSF cell samples had quantifiable CA-HIV-1 RNA, at levels significantly higher than in their PBMCs (median 9,266 vs 185 copies /106 CD4+ T-cells; p<0.0001). In individual PLHIV, higher levels of HIV-1 transcripts in CSF cells were associated with greater brain injury in the frontal white matter (Std β=-0.73; p=0.007) and posterior cingulate (Std β=-0.61; p=0.03). 18-colour flow cytometry revealed that the CSF cells were 91% memory T-cells, equally CD4+ and CD8+ T-cells, but fewer B cells (0.4 %), and monocytes (3.1%). CXCR3+CD49d+integrin β7-, CCR5+CD4+ T-cells were highly enriched in CSF, compared with PBMC (p <0.001). However, CA-HIV-1 RNA could not be detected in 10/16 preparations of highly purified monocytes from PBMC, and was extremely low in the other six. Our data show that elevated HIV-1 transcripts in CSF cells were associated with brain injury, despite suppressive ART. The cellular source is most likely memory CD4+ T cells from blood, rather than trafficking monocytes. Future research should focus on inhibitors of this transcription to reduce local production of potentially neurotoxic and inflammatory viral products

The relationship between mandibular advancement, tongue movement, and treatment outcome in obstructive sleep apnea

Study Objectives: To characterize how mandibular advancement enlarges the upper airway via posterior tongue advancement in people with obstructive sleep apnea (OSA) and whether this is associated with mandibular advancement splint (MAS) treatment outcome. Methods: One-hundred and one untreated people with OSA underwent a 3T magnetic resonance (MRI) scan. Dynamic mid-sagittal posterior tongue and mandible movements during passive jaw advancement were measured with tagged MRI. Upper airway cross-sectional areas were measured with the mandible in a neutral position and advanced to 70% of maximum advancement. Treatment outcome was determined after a minimum of 9 weeks of therapy. Results: Seventy-one participants completed the study: 33 were responders (AHI50% AHI reduction), 11 were partial responders (>50% AHI reduction but AHI>10 events/hr), and 27 nonresponders (AHI reduction 4 mm). In comparison, a model using only baseline AHI correctly classified 50.0% of patients (5-fold cross-validated 52.5%, n = 40). Conclusions: Tongue advancement and upper airway enlargement with mandibular advancement in conjunction with baseline AHI improve treatment response categorization to a satisfactory level (69.2%, 5-fold cross-validated 62.5%)