The smallest matrix of given period and primitive roots of unity

AbstractA nonsingular matrix A has period n if An = I but Ak ≠ I for 0 < k < n. We investigate the number rK(n), which is the smallest r such that there is an r × r matrix, with entries in the field K, that has period n. We compute this number as a function of the common degree θK(j) of the irreducible factors of the cyclotomic polynomial cj(x). Thus, we are led to an investigation of roots of unity in order to better understand the function θ

Lymphocyte Cc Chemokine Receptor 9 and Epithelial Thymus-Expressed Chemokine (Teck) Expression Distinguish the Small Intestinal Immune Compartment: Epithelial Expression of Tissue-Specific Chemokines as an Organizing Principle in Regional Immunity

The immune system has evolved specialized cellular and molecular mechanisms for targeting and regulating immune responses at epithelial surfaces. Here we show that small intestinal intraepithelial lymphocytes and lamina propria lymphocytes migrate to thymus-expressed chemokine (TECK). This attraction is mediated by CC chemokine receptor (CCR)9, a chemoattractant receptor expressed at high levels by essentially all CD4+ and CD8+ T lymphocytes in the small intestine. Only a small subset of lymphocytes in the colon are CCR9+, and lymphocytes from other tissues including tonsils, lung, inflamed liver, normal or inflamed skin, inflamed synovium and synovial fluid, breast milk, and seminal fluid are universally CCR9−. TECK expression is also restricted to the small intestine: immunohistochemistry reveals that intense anti-TECK reactivity characterizes crypt epithelium in the jejunum and ileum, but not in other epithelia of the digestive tract (including stomach and colon), skin, lung, or salivary gland. These results imply a restricted role for lymphocyte CCR9 and its ligand TECK in the small intestine, and provide the first evidence for distinctive mechanisms of lymphocyte recruitment that may permit functional specialization of immune responses in different segments of the gastrointestinal tract. Selective expression of chemokines by differentiated epithelium may represent an important mechanism for targeting and specialization of immune responses

Effectiveness of a clinical pathway for acute stroke care in a district general hospital: an audit

BACKGROUND: Organised stroke care saves lives and reduces disability. A clinical pathway might be a form of organised stroke care, but the evidence for the effectiveness of this model of care is limited. METHODS: This study was a retrospective audit study of consecutive stroke admissions in the setting of an acute general medical unit in a district general hospital. The case-notes of patients admitted with stroke for a 6-month period before and after introduction of the pathway, were reviewed to determine data on length of stay, outcome, functional status, (Barthel Index, BI and Modified Rankin Scale, MRS), Oxfordshire Community Stroke Project (OCSP) sub-type, use of investigations, specific management issues and secondary prevention strategies. Logistic regression was used to adjust for differences in case-mix. RESULTS: N = 77 (prior to the pathway) and 76 (following the pathway). The median (interquartile range, IQR) age was 78 years (67.75–84.25), 88% were European NZ and 37% were male. The median (IQR) BI at admission for the pre-pathway group was less than the post-pathway group: 6 (0–13.5) vs. 10 (4–15.5), p = 0.018 but other baseline variables were statistically similar. There were no significant differences between any of the outcome or process of care variables, except that echocardiograms were done less frequently after the pathway was introduced. A good outcome (MRS<4) was obtained in 66.2% prior to the pathway and 67.1% after the pathway. In-hospital mortality was 20.8% and 23.1%. However, using logistic regression to adjust for the differences in admission BI, it appeared that admission after the pathway was introduced had a significant negative effect on the probability of good outcome (OR 0.29, 95%CI 0.09-0.99). CONCLUSION: A clinical pathway for acute stroke management appeared to have no benefit for the outcome or processes of care and may even have been associated with worse outcomes. These data support the conclusions of a recent Cochrane review

Inflammatory Markers and Poor Outcome after Stroke: A Prospective Cohort Study and Systematic Review of Interleukin-6

In a prospective cohort study of patient outcomes following stroke, William Whiteley and colleagues find that markers of inflammatory response are associated with poor outcomes. However, addition of these markers to existing prognostic models does not improve outcome prediction

Effects of antiplatelet therapy on stroke risk by brain imaging features of intracerebral haemorrhage and cerebral small vessel diseases: subgroup analyses of the RESTART randomised, open-label trial

Background Findings from the RESTART trial suggest that starting antiplatelet therapy might reduce the risk of recurrent symptomatic intracerebral haemorrhage compared with avoiding antiplatelet therapy. Brain imaging features of intracerebral haemorrhage and cerebral small vessel diseases (such as cerebral microbleeds) are associated with greater risks of recurrent intracerebral haemorrhage. We did subgroup analyses of the RESTART trial to explore whether these brain imaging features modify the effects of antiplatelet therapy

Bridge to the future: Important lessons from 20 years of ecosystem observations made by the OzFlux network

In 2020, the Australian and New Zealand flux research and monitoring network, OzFlux, celebrated its 20th anniversary by reflecting on the lessons learned through two decades of ecosystem studies on global change biology. OzFlux is a network not only for ecosystem researchers, but also for those ‘next users’ of the knowledge, information and data that such networks provide. Here, we focus on eight lessons across topics of climate change and variability, disturbance and resilience, drought and heat stress and synergies with remote sensing and modelling. In distilling the key lessons learned, we also identify where further research is needed to fill knowledge gaps and improve the utility and relevance of the outputs from OzFlux. Extreme climate variability across Australia and New Zealand (droughts and flooding rains) provides a natural laboratory for a global understanding of ecosystems in this time of accelerating climate change. As evidence of worsening global fire risk emerges, the natural ability of these ecosystems to recover from disturbances, such as fire and cyclones, provides lessons on adaptation and resilience to disturbance. Drought and heatwaves are common occurrences across large parts of the region and can tip an ecosystem\u27s carbon budget from a net CO2 sink to a net CO2 source. Despite such responses to stress, ecosystems at OzFlux sites show their resilience to climate variability by rapidly pivoting back to a strong carbon sink upon the return of favourable conditions. Located in under-represented areas, OzFlux data have the potential for reducing uncertainties in global remote sensing products, and these data provide several opportunities to develop new theories and improve our ecosystem models. The accumulated impacts of these lessons over the last 20 years highlights the value of long-term flux observations for natural and managed systems. A future vision for OzFlux includes ongoing and newly developed synergies with ecophysiologists, ecologists, geologists, remote sensors and modellers

Bridge to the future: Important lessons from 20 years of ecosystem observations made by the OzFlux network

In 2020, the Australian and New Zealand flux research and monitoring network, OzFlux, celebrated its 20th anniversary by reflecting on the lessons learned through two decades of ecosystem studies on global change biology. OzFlux is a network not only for ecosystem researchers, but also for those ‘next users’ of the knowledge, information and data that such networks provide. Here, we focus on eight lessons across topics of climate change and variability, disturbance and resilience, drought and heat stress and synergies with remote sensing and modelling. In distilling the key lessons learned, we also identify where further research is needed to fill knowledge gaps and improve the utility and relevance of the outputs from OzFlux. Extreme climate variability across Australia and New Zealand (droughts and flooding rains) provides a natural laboratory for a global understanding of ecosystems in this time of accelerating climate change. As evidence of worsening global fire risk emerges, the natural ability of these ecosystems to recover from disturbances, such as fire and cyclones, provides lessons on adaptation and resilience to disturbance. Drought and heatwaves are common occurrences across large parts of the region and can tip an ecosystem's carbon budget from a net CO2 sink to a net CO2 source. Despite such responses to stress, ecosystems at OzFlux sites show their resilience to climate variability by rapidly pivoting back to a strong carbon sink upon the return of favourable conditions. Located in under-represented areas, OzFlux data have the potential for reducing uncertainties in global remote sensing products, and these data provide several opportunities to develop new theories and improve our ecosystem models. The accumulated impacts of these lessons over the last 20 years highlights the value of long-term flux observations for natural and managed systems. A future vision for OzFlux includes ongoing and newly developed synergies with ecophysiologists, ecologists, geologists, remote sensors and modellers.</p

Current commands for high-efficiency torque control of DC shunt motor

The current commands for a high-efficiency torque control of a DC shunt motor are described. In the proposed control method, the effect of a magnetic saturation and an armature reaction are taken into account by representing the coefficients of an electromotive force and a torque as a function of the field current, the armature current and the revolving speed. The current commands at which the loss of the motor drive system becomes a minimum are calculated as an optimal problem. The proposed control technique of a motor is implemented on the microprocessor-based control system. The effect of the consideration of the magnetic saturation and the armature reaction on the produced torque and the minimisation of the loss are discussed analytically and experimentally </p

Effects of antiplatelet therapy on stroke risk by brain imaging features of intracerebral haemorrhage and cerebral small vessel diseases:Subgroup analyses of the RESTART randomised, open-label trial

BACKGROUND: Findings from the RESTART trial suggest that starting antiplatelet therapy might reduce the risk of recurrent symptomatic intracerebral haemorrhage compared with avoiding antiplatelet therapy. Brain imaging features of intracerebral haemorrhage and cerebral small vessel diseases (such as cerebral microbleeds) are associated with greater risks of recurrent intracerebral haemorrhage. We did subgroup analyses of the RESTART trial to explore whether these brain imaging features modify the effects of antiplatelet therapy. METHODS: RESTART was a prospective, randomised, open-label, blinded-endpoint, parallel-group trial at 122 hospitals in the UK that assessed whether starting antiplatelet therapy might reduce the risk of recurrent symptomatic intracerebral haemorrhage compared with avoiding antiplatelet therapy. For this prespecified subgroup analysis, consultant neuroradiologists masked to treatment allocation reviewed brain CT or MRI scans performed before randomisation to confirm participant eligibility and rate features of the intracerebral haemorrhage and surrounding brain. We followed participants for primary (recurrent symptomatic intracerebral haemorrhage) and secondary (ischaemic stroke) outcomes for up to 5 years (reported elsewhere). For this report, we analysed eligible participants with intracerebral haemorrhage according to their treatment allocation in primary subgroup analyses of cerebral microbleeds on MRI and in exploratory subgroup analyses of other features on CT or MRI. The trial is registered with the ISRCTN registry, number ISRCTN71907627. FINDINGS: Between May 22, 2013, and May 31, 2018, 537 participants were enrolled, of whom 525 (98%) had intracerebral haemorrhage: 507 (97%) were diagnosed on CT (252 assigned to start antiplatelet therapy and 255 assigned to avoid antiplatelet therapy, of whom one withdrew and was not analysed) and 254 (48%) underwent the required brain MRI protocol (122 in the start antiplatelet therapy group and 132 in the avoid antiplatelet therapy group). There were no clinically or statistically significant hazards of antiplatelet therapy on recurrent intracerebral haemorrhage in primary subgroup analyses of cerebral microbleed presence (2 or more) versus absence (0 or 1) (adjusted hazard ratio [HR] 0·30 [95% CI 0·08-1·13] vs 0·77 [0·13-4·61]; pinteraction=0·41), cerebral microbleed number 0-1 versus 2-4 versus 5 or more (HR 0·77 [0·13-4·62] vs 0·32 [0·03-3·66] vs 0·33 [0·07-1·60]; pinteraction=0·75), or cerebral microbleed strictly lobar versus other location (HR 0·52 [0·004-6·79] vs 0·37 [0·09-1·28]; pinteraction=0·85). There was no evidence of heterogeneity in the effects of antiplatelet therapy in any exploratory subgroup analyses (all pinteraction>0·05). INTERPRETATION: Our findings exclude all but a very modest harmful effect of antiplatelet therapy on recurrent intracerebral haemorrhage in the presence of cerebral microbleeds. Further randomised trials are needed to replicate these findings and investigate them with greater precision. FUNDING: British Heart Foundation