Forks, Noodles and the Burau representation for n=4n=4

\begin{abstract} The reduced Burau representation is a natural action of the braid group $B_n$ on the first homology group $H_1({\tilde{D}}_n;\mathbb{Z})$ of a suitable infinite cyclic covering space ${\tilde{D}}_n$ of the $n$--punctured disc $D_n$. It is known that the Burau representation is faithful for $n\le 3$ and that it is not faithful for $n\ge 5$. We use forks and noodles homological techniques and Bokut--Vesnin generators to analyze the problem for $n=4$. We present a Conjecture implying faithfulness and a Lemma explaining the implication. We give some arguments suggesting why we expect the Conjecture to be true. Also, we give some geometrically calculated examples and information about data gathered using a C\texttt{++} program.Comment: 24 pages, 21 figure

Safety and efficacy of intensive vs. guideline antiplatelet therapy in high-risk patients with recent ischemic stroke or transient ischemic attack: rationale and design of the Triple Antiplatelets for Reducing Dependency after Ischaemic Stroke (TARDIS) trial (ISRCTN47823388)

RATIONALE: The risk of recurrence following a stroke or transient ischemic attack is high, especially immediately after the event. HYPOTHESIS: Because two antiplatelet agents are superior to one in patients with non-cardioembolic events, more intensive treatment might be even more effective. SAMPLE SIZE ESTIMATES: The sample size of 4100 patients will allow a shift to less recurrence, and less severe recurrence, to be detected (odds ratio 0·68) with 90% power at 5% significance. METHODS AND DESIGN: Triple Antiplatelets for Reducing Dependency after Ischaemic Stroke (ISRCTN47823388) is comparing the safety and efficacy of intensive (combined aspirin, clopidogrel, and dipyridamole) vs. guideline antiplatelet therapy, both given for one-month. This international collaborative parallel-group prospective randomized open-label blinded-end-point phase III trial plans to recruit 4100 patients with acute ischemic stroke or transient ischemic attack. Randomization and data collection are performed over a secure Internet site with real-time data validation and concealment of allocation. Outcomes, serious adverse events, and neuroimaging are adjudicated centrally with blinding to treatment allocation. STUDY OUTCOME: The primary outcome is stroke recurrence and its severity ('ordinal recurrence' based on modified Rankin Scale) at 90 days, with masked assessment centrally by telephone. Secondary outcomes include vascular events, functional measures (disability, mood, cognition, quality of life), and safety (bleeding, death, serious adverse events). DISCUSSION: The trial has recruited more than 50% of its target sample size (latest number: 2399) and is running in 104 sites in 4 countries. One-third of patients presented with a transient ischemic attack

Peculiarities of the relationship to disease and level of anxiety in children under treatment in the stationary conditions

The article describes the types of attitudes of children under treatment in the cardiological, gastroenterological and nephrology departments to the disease, assessed their levels of anxiety, revealed and justified the relationship between the attitude to the disease and anxietyВ статье рассмотрены типы отношения детей, находящихся на лечении в кардиологическом, гастроэнтерологическом и нефрологическом отделениях, к болезни, оценены уровни их тревожности, выявлена и обоснована взаимосвязь между отношением к болезни и тревожностью

Baseline characteristics of the 3096 patients recruited into the 'Triple Antiplatelets for Reducing Dependency after Ischemic Stroke' trial.

Background The risk of recurrence following ischemic stroke or transient ischemic attack is highest immediately after the event. Antiplatelet agents are effective in reducing the risk of recurrence and two agents are superior to one in the early phase after ictus. Design The triple antiplatelets for reducing dependency after ischemic stroke trial was an international multicenter prospective randomized open-label blinded-endpoint trial that assessed the safety and efficacy of short-term intensive antiplatelet therapy with three agents (combined aspirin, clopidogrel and dipyridamole) as compared with guideline treatment in acute ischemic stroke or transient ischemic attack. The primary outcome was stroke recurrence and its severity, measured using the modified Rankin Scale at 90 days. Secondary outcomes included recurrent vascular events, functional measures (cognition, disability, mood, quality of life), and safety (bleeding, death, serious adverse events). Data are number (%) or mean (standard deviation, SD). Results Recruitment ran from April 2009 to March 2016; 3096 patients were recruited from 106 sites in four countries (Denmark 1.6%, Georgia 2.7%, New Zealand 0.2%, UK 95.4%). Randomization characteristics included: age 69.0 (10.1) years; male 1945 (62.8%); time onset to randomization 29.4 (11.9) h; stroke severity (National Institutes for Health Stroke Scale) 2.8 (3.6); blood pressure 143.5 (18.2)/79.5 (11.4) mmHg; IS 2143 (69.2%), transient ischemic attack 953 (30.8%). Conclusion Triple antiplatelets for reducing dependency after ischemic stroke was a large trial of intensive/triple antiplatelet therapy in acute ischemic stroke and transient ischemic attack, and included participants from four predominantly Caucasian countries who were representative of patients in many western stroke services

Antiplatelet therapy with aspirin, clopidogrel, and dipyridamole versus clopidogrel alone or aspirin and dipyridamole in patients with acute cerebral ischaemia (TARDIS): a randomised, open-label, phase 3 superiority trial

Background: Intensive antiplatelet therapy with three agents might be more effective than guideline treatment for preventing recurrent events in patients with acute cerebral ischaemia. We aimed to compare the safety and efficacy of intensive antiplatelet therapy (combined aspirin, clopidogrel, and dipyridamole) with that of guideline-based antiplatelet therapy. Methods: We did an international, prospective, randomised, open-label, blinded-endpoint trial in adult participants with ischaemic stroke or transient ischaemic attack (TIA) within 48 h of onset. Participants were assigned in a 1:1 ratio using computer randomisation to receive loading doses and then 30 days of intensive antiplatelet therapy (combined aspirin 75 mg, clopidogrel 75 mg, and dipyridamole 200 mg twice daily) or guideline-based therapy (comprising either clopidogrel alone or combined aspirin and dipyridamole). Randomisation was stratified by country and index event, and minimised with prognostic baseline factors, medication use, time to randomisation, stroke-related factors, and thrombolysis. The ordinal primary outcome was the combined incidence and severity of any recurrent stroke (ischaemic or haemorrhagic; assessed using the modified Rankin Scale) or TIA within 90 days, as assessed by central telephone follow-up with masking to treatment assignment, and analysed by intention to treat. This trial is registered with the ISRCTN registry, number ISRCTN47823388. Findings: 3096 participants (1556 in the intensive antiplatelet therapy group, 1540 in the guideline antiplatelet therapy group) were recruited from 106 hospitals in four countries between April 7, 2009, and March 18, 2016. The trial was stopped early on the recommendation of the data monitoring committee. The incidence and severity of recurrent stroke or TIA did not differ between intensive and guideline therapy (93 [6%] participants vs 105 [7%]; adjusted common odds ratio [cOR] 0·90, 95% CI 0·67–1·20, p=0·47). By contrast, intensive antiplatelet therapy was associated with more, and more severe, bleeding (adjusted cOR 2·54, 95% CI 2·05–3·16, p<0·0001). Interpretation: Among patients with recent cerebral ischaemia, intensive antiplatelet therapy did not reduce the incidence and severity of recurrent stroke or TIA, but did significantly increase the risk of major bleeding. Triple antiplatelet therapy should not be used in routine clinical practice

Brief Consent Methods Enable Rapid Enrollment in Acute Stroke Trial: Results From the TICH-2 Randomized Controlled Trial

BACKGROUND AND PURPOSE: Seeking consent rapidly in acute stroke trials is crucial as interventions are time sensitive. We explored the association between consent pathways and time to enrollment in the TICH-2 (Tranexamic Acid in Intracerebral Haemorrhage-2) randomized controlled trial. METHODS: Consent was provided by patients or by a relative or an independent doctor in incapacitated patients, using a 1-stage (full written consent) or 2-stage (initial brief consent followed by full written consent post-randomization) approach. The computed tomography-to-randomization time according to consent pathways was compared using the Kruskal-Wallis test. Multivariable logistic regression was performed to identify variables associated with onset-to-randomization time of ≤3 hours. RESULTS: Of 2325 patients, 817 (35%) gave self-consent using 1-stage (557; 68%) or 2-stage consent (260; 32%). For 1507 (65%), consent was provided by a relative (1 stage, 996 [66%]; 2 stage, 323 [21%]) or a doctor (all 2-stage, 188 [12%]). One patient did not record prerandomization consent, with written consent obtained subsequently. The median (interquartile range) computed tomography-to-randomization time was 55 (38-93) minutes for doctor consent, 55 (37-95) minutes for 2-stage patient, 69 (43-110) minutes for 2-stage relative, 75 (48-124) minutes for 1-stage patient, and 90 (56-155) minutes for 1-stage relative consents (P<0.001). Two-stage consent was associated with onset-to-randomization time of ≤3 hours compared with 1-stage consent (adjusted odds ratio, 1.9 [95% CI, 1.5-2.4]). Doctor consent increased the odds (adjusted odds ratio, 2.3 [1.5-3.5]) while relative consent reduced the odds of randomization ≤3 hours (adjusted odds ratio, 0.10 [0.03-0.34]) compared with patient consent. Only 2 of 771 patients (0.3%) in the 2-stage pathways withdrew consent when full consent was sought later. Two-stage consent process did not result in higher withdrawal rates or loss to follow-up. CONCLUSIONS: The use of initial brief consent was associated with shorter times to enrollment, while maintaining good participant retention. Seeking written consent from relatives was associated with significant delays. Registration: URL: https://www.isrctn.com; Unique identifier: ISRCTN93732214

Selected acute phase CSF factors in ischemic stroke: findings and prognostic value

<p>Abstract</p> <p>Background</p> <p>Study aimed at investigation of pathogenic role and prognostic value of several selected cerebrospinal fluid acute phase factors that can reflect the severity of ischemic brain damage.</p> <p>Methods</p> <p>Ninety five acute ischemic stroke patients were investigated. Ischemic region visualized at the twenty fourth hour by conventional Magnetic Resonance Imaging. Stroke severity evaluated by National Institute Health Stroke Scale. One month outcome of disease was assessed by Barthel Index. Cerebrospinal fluid was taken at the sixth hour of stroke onset. CSF pro- and anti-inflammatory cytokines were studied by Enzyme Linked Immunosorbent Assay. Nitric Oxide and Lipoperoxide radical were measured by Electron Paramagnetic Resonance. CSF Nitrate levels were detected using the Griess reagent. Statistics performed by SPSS-11.0.</p> <p><b>Results</b></p> <p>At the sixth hour of stroke onset, cerebrospinal fluid cytokine levels were elevated in patients against controls. Severe stroke patients had increased interleukin-6 content compared to less severe strokes (P < 0.05). Cerebrospinal fluid Electron Paramagnetic Resonance signal of nitric oxide was increased in patients against controls. Severe stroke group had an elevated Electron Paramagnetic Resonance signal of lipoperoxiradical compared to less severe stroke. Cerebrospinal fluid nitrate levels in less severe stroke patients were higher than those for severe stroke and control. Positive correlation was established between the initial interleukin-6 content and ischemic lesion size as well as with National Institute Health Stroke Scale score on the seventh day. Initial interleukin-6 and nitrate levels in cerebrospinal fluid found to be significant for functional outcome of stroke at one month.</p> <p><b>Conclusion</b></p> <p>According to present study the cerebrospinal fluid contents of interleukin-6 and nitrates seem to be the most reliable prognostic factors in acute phase of ischemic stroke.</p

Effects of blood pressure and tranexamic acid in spontaneous intracerebral haemorrhage: a secondary analysis of a large randomised controlled trial

BACKGROUND: Tranexamic acid reduced haematoma expansion and early death, but did not improve functional outcome in the tranexamic acid for hyperacute spontaneous intracerebral haemorrhage-2 (TICH-2) trial. In a predefined subgroup, there was a statistically significant interaction between prerandomisation baseline systolic blood pressure (SBP) and the effect of tranexamic acid on functional outcome (p=0.019). METHODS: TICH-2 was an international prospective double-blind placebo-controlled randomised trial evaluating intravenous tranexamic acid in patients with acute spontaneous intracerebral haemorrhage (ICH). Prerandomisation baseline SBP was split into predefined ≤170 and >170 mm Hg groups. The primary outcome at day 90 was the modified Rankin Scale (mRS), a measure of dependency, analysed using ordinal logistic regression. Haematoma expansion was defined as an increase in haematoma volume of >33% or >6 mL from baseline to 24 hours. Data are OR or common OR (cOR) with 95% CIs, with significance at p170 mm Hg. Tranexamic acid was associated with a favourable shift in mRS at day 90 in those with baseline SBP≤170 mm Hg (cOR 0.73, 95% CI 0.59 to 0.91, p=0.005), but not in those with baseline SBP>170 mm Hg (cOR 1.05, 95% CI 0.85 to 1.30, p=0.63). In those with baseline SBP≤170 mm Hg, tranexamic acid reduced haematoma expansion (OR 0.62, 95% CI 0.47 to 0.82, p=0.001), but not in those with baseline SBP>170 mm Hg (OR 1.02, 95% CI 0.77 to 1.35, p=0.90). CONCLUSIONS: Tranexamic acid was associated with improved clinical and radiological outcomes in ICH patients with baseline SBP≤170 mm Hg. Further research is needed to establish whether certain subgroups may benefit from tranexamic acid in acute ICH. TRIAL REGISTRATION NUMBER: ISRCTN93732214