Computational topology with Regina: Algorithms, heuristics and implementations

Regina is a software package for studying 3-manifold triangulations and normal surfaces. It includes a graphical user interface and Python bindings, and also supports angle structures, census enumeration, combinatorial recognition of triangulations, and high-level functions such as 3-sphere recognition, unknot recognition and connected sum decomposition. This paper brings 3-manifold topologists up-to-date with Regina as it appears today, and documents for the first time in the literature some of the key algorithms, heuristics and implementations that are central to Regina's performance. These include the all-important simplification heuristics, key choices of data structures and algorithms to alleviate bottlenecks in normal surface enumeration, modern implementations of 3-sphere recognition and connected sum decomposition, and more. We also give some historical background for the project, including the key role played by Rubinstein in its genesis 15 years ago, and discuss current directions for future development.Comment: 29 pages, 10 figures; v2: minor revisions. To appear in "Geometry & Topology Down Under", Contemporary Mathematics, AM

Quadrilateral-octagon coordinates for almost normal surfaces

Normal and almost normal surfaces are essential tools for algorithmic 3-manifold topology, but to use them requires exponentially slow enumeration algorithms in a high-dimensional vector space. The quadrilateral coordinates of Tollefson alleviate this problem considerably for normal surfaces, by reducing the dimension of this vector space from 7n to 3n (where n is the complexity of the underlying triangulation). Here we develop an analogous theory for octagonal almost normal surfaces, using quadrilateral and octagon coordinates to reduce this dimension from 10n to 6n. As an application, we show that quadrilateral-octagon coordinates can be used exclusively in the streamlined 3-sphere recognition algorithm of Jaco, Rubinstein and Thompson, reducing experimental running times by factors of thousands. We also introduce joint coordinates, a system with only 3n dimensions for octagonal almost normal surfaces that has appealing geometric properties.Comment: 34 pages, 20 figures; v2: Simplified the proof of Theorem 4.5 using cohomology, plus other minor changes; v3: Minor housekeepin

Persistent symptoms following SARS-CoV-2 infection in a random community sample of 508,707 people

Introduction Long COVID, describing the long-term sequelae after SARS-CoV-2 infection, remains a poorly defined syndrome. There is uncertainty about its predisposing factors and the extent of the resultant public health burden, with estimates of prevalence and duration varying widely. Methods Within rounds 3–5 of the REACT-2 study, 508,707 people in the community in England were asked about a prior history of COVID-19 and the presence and duration of 29 different symptoms. We used uni- and multivariable models to identify predictors of persistence of symptoms (12 weeks or more). We estimated the prevalence of symptom persistence at 12 weeks, and used unsupervised learning to cluster individuals by symptoms experienced. Results Among the 508,707 participants, the weighted prevalence of self-reported COVID-19 was 19.2% (95% CI: 19.1,19.3). 37.7% of 76,155 symptomatic people post COVID-19 experienced at least one symptom, while 14.8% experienced three or more symptoms, lasting 12 weeks or more. This gives a weighted population prevalence of persistent symptoms of 5.75% (5.68, 5.81) for one and 2.22% (2.1, 2.26) for three or more symptoms. Almost a third of people 8,771/28,713 (30.5%) with at least one symptom lasting 12 weeks or more reported having had severe COVID-19 symptoms (“significant effect on my daily life”) at the time of their illness, giving a weighted prevalence overall for this group of 1.72% (1.69,1.76). The prevalence of persistent symptoms was higher in women than men (OR: 1.51 [1.46,1.55]) and, conditional on reporting symptoms, risk of persistent symptoms increased linearly with age by 3.5 percentage points per decade of life. Obesity, smoking or vaping, hospitalisation , and deprivation were also associated with a higher probability of persistent symptoms, while Asian ethnicity was associated with a lower probability. Two stable clusters were identified based on symptoms that persisted for 12 weeks or more: in the largest cluster, tiredness predominated, while in the second there was a high prevalence of respiratory and related symptoms. Interpretation A substantial proportion of people with symptomatic COVID-19 go on to have persistent symptoms for 12 weeks or more, which is age-dependent. Clinicians need to be aware of the differing manifestations of Long COVID which may require tailored therapeutic approaches. Managing the long-term sequelae of SARS-CoV-2 infection in the population will remain a major challenge for health services in the next stage of the pandemic

The sensitivity to change of the cluster headache quality of life scale assessed before and after deep brain stimulation of the ventral tegmental area.

BACKGROUND: Cluster headache (CH) is a trigeminal autonomic cephalalgia (TAC) characterized by a highly disabling headache that negatively impacts quality of life and causes limitations in daily functioning as well as social functioning and family life. Since specific measures to assess the quality of life (QoL) in TACs are lacking, we recently developed and validated the cluster headache quality of life scale (CH-QoL). The sensitivity of CH-QoL to change after a medical intervention has not been evaluated yet. METHODS: This study aimed to test the sensitivity to change of the CH-QoL in CH. Specifically we aimed to (i) assess the sensitivity of CH-QoL to change before and following deep brain stimulation of the ventral tegmental area (VTA-DBS), (ii) evaluate the relationship of changes on CH-QoL with changes in other generic measures of quality of life, as well as indices of mood and pain. Ten consecutive CH patients completed the CH-QoL and underwent neuropsychological assessment before and after VTA-DBS. The patients were evaluated on headache frequency, severity, and load (HAL) as well as on tests of generic quality of life (Short Form-36 (SF-36)), mood (Beck Depression Inventory, Hospital Anxiety and Depression Rating Scale), and pain (McGill Pain Questionnaire, Headache Impact Test, Pain Behaviour Checklist). RESULTS: The CH-QoL total score was significantly reduced after compared to before VTA-DBS. Changes in the CH-QoL total score correlated significantly and negatively with changes in HAL, the SF-36, and positively and significantly with depression and the evaluative domain on the McGill Pain Questionnaire. CONCLUSIONS: Our findings demonstrate that changes after VTA-DBS in CH-QoL total scores are associated with the reduction of frequency, duration, and severity of headache attacks after surgery. Moreover, post VTA-DBS improvement in CH-QoL scores is associated with an amelioration in quality of life assessed with generic measures, a reduction of depressive symptoms, and evaluative pain experience after VTA-DBS. These results support the sensitivity to change of the CH-QoL and further demonstrate the validity and applicability of CH-QoL as a disease specific measure of quality of life for CH

A block to pre-prepared movement in gait freezing, relieved by pedunculopontine nucleus stimulation

Gait freezing and postural instability are disabling features of Parkinsonian disorders, treatable with pedunculopontine nucleus stimulation. Both features are considered deficits of proximal and axial musculature, innervated predominantly by reticulospinal pathways and tend to manifest when gait and posture require adjustment. Adjustments to gait and posture are amenable to pre-preparation and rapid triggered release. Experimentally, such accelerated release can be elicited by loud auditory stimuli—a phenomenon known as ‘StartReact’. We observed StartReact in healthy and Parkinsonian controls. However, StartReact was absent in Parkinsonian patients with severe gait freezing and postural instability. Pedunculopontine nucleus stimulation restored StartReact proximally and proximal reaction times to loud stimuli correlated with gait and postural disturbance. These findings suggest a relative block to triggered, pre-prepared movement in gait freezing and postural instability, relieved by pedunculopontine nucleus stimulation

Pedunculopontine Nucleus Deep Brain Stimulation for Parkinsonian Disorders: A Case Series

BACKGROUND: Deep brain stimulation (DBS) of the pedunculopontine nucleus (PPN) has been investigated for the treatment of levodopa-refractory gait dysfunction in parkinsonian disorders, with equivocal results so far. OBJECTIVES: To summarize the clinical outcomes of PPN-DBS-treated patients at our centre and elicit any patterns that may guide future research. MATERIALS AND METHODS: Pre- and post-operative objective overall motor and gait subsection scores as well as patient-reported outcomes were recorded for 6 PPN-DBS-treated patients, 3 with Parkinson’s disease (PD), and 3 with progressive supranuclear palsy (PSP). Electrodes were implanted unilaterally in the first 3 patients and bilaterally in the latter 3, using an MRI-guided MRI-verified technique. Stimulation was initiated at 20–30 Hz and optimized in an iterative manner. RESULTS: Unilaterally treated patients did not demonstrate significant improvements in gait questionnaires, UPDRS-III or PSPRS scores or their respective gait subsections. This contrasted with at least an initial response in bilaterally treated patients. Diurnal cycling of stimulation in a PD patient with habituation to the initial benefit reproduced substantial improvements in freezing of gait (FOG) 3 years post-operatively. Among the PSP patients, 1 with a parkinsonian subtype had a sustained improvement in FOG while another with Richardson syndrome (PSP-RS) did not benefit. CONCLUSIONS: PPN-DBS remains an investigational treatment for levodopa-refractory FOG. This series corroborates some previously reported findings: bilateral stimulation may be more effective than unilateral stimulation; the response in PSP patients may depend on the disease subtype; and diurnal cycling of stimulation to overcome habituation merits further investigation

Long-term success of low-frequency subthalamic nucleus stimulation for Parkinson's disease depends on tremor severity and symptom duration

Patients with Parkinson's disease can develop axial symptoms, including speech, gait and balance difficulties. Chronic high-frequency (>100 Hz) deep brain stimulation can contribute to these impairments while low-frequency stimulation (<100 Hz) may improve symptoms but only in some individuals. Factors predicting which patients benefit from low-frequency stimulation in the long term remain unclear. This study aims to confirm that low-frequency stimulation improves axial symptoms, and to go further to also explore which factors predict the durability of its effects. We recruited patients who developed axial motor symptoms while using high-frequency stimulation and objectively assessed the short-term impact of low-frequency stimulation on axial symptoms, other aspects of motor function and quality of life. A retrospective chart review was then conducted on a larger cohort to identify which patient characteristics were associated with not only the need to trial low-frequency stimulation, but also those which predicted its sustained use. Among 20 prospective patients, low-frequency stimulation objectively improved mean motor and axial symptom severity and quality of life in the short term. Among a retrospective cohort of 168 patients, those with less severe tremor and those in whom axial symptoms had emerged sooner after subthalamic nucleus deep brain stimulation were more likely to be switched to and remain on long-term low-frequency stimulation. These data suggest that low-frequency stimulation results in objective mean improvements in overall motor function and axial symptoms among a group of patients, while individual patient characteristics can predict sustained long-term benefits. Longer follow-up in the context of a larger, controlled, double-blinded study would be required to provide definitive evidence of the role of low-frequency deep brain stimulation

The use of human papillomavirus DNA methylation in cervical intraepithelial neoplasia : A systematic review and meta-analysis

Background: Methylation of viral DNA has been proposed as a novel biomarker for triage of human papillomavirus (HPV) positive women at screening. This systematic review and meta-analysis aims to assess how methylation levels change with disease severity and to determine diagnostic test accuracy (DTA) in detecting high-grade cervical intra-epithelial neoplasia (CIN). Methods: We performed searches in MEDLINE, EMBASE and CENTRAL from inception to October 2019. Studies were eligible if they explored HPV methylation levels in HPV positive women. Data were extracted in duplicate and requested from authors where necessary. Random-effects models and a bivariate mixed-effects binary regression model were applied to determine pooled effect estimates. Findings: 44 studies with 8819 high-risk HPV positive women were eligible. The pooled estimates for positive methylation rate in HPV16 L1 gene were higher for high-grade CIN (>= CIN2/high-grade squamous intra-epithelial lesion (HSIL) (95% confidence interval (95%CI:72.7% (47 8-92.2))) vs. low-grade CIN (= CIN2/HSIL vs. = CIN2/HSIL vs. Interpretation: Higher HPV methylation is associated with increased disease severity, whilst HPV16 L1/L2 genes demonstrated high diagnostic accuracy to detect high-grade CIN in HPV16 positive women. Direct clinical use is limited by the need for a multi-genotype and standardised assays. Next-generation multiplex HPV sequencing assays are under development and allow potential for rapid, automated and low-cost methylation testing. (C) 2019 The Authors. Published by Elsevier B.V.Peer reviewe