Equiconvergence of spectral decompositions of 1D Dirac operators with regular boundary conditions

One dimensional Dirac operators L_{bc}(v) y = i 1 & 0 0 & -1 \frac{dy}{dx} + v(x) y, \quad y = y_1 y_2, \quad x\in[0,\pi], considered with $L^2$-potentials v(x) = 0 & P(x) Q(x) & 0 and subject to regular boundary conditions ($bc$), have discrete spectrum. For strictly regular $bc,$ the spectrum of the free operator $L_{bc}(0)$ is simple while the spectrum of $L_{bc}(v)$ is eventually simple, and the corresponding normalized root function systems are Riesz bases. For expansions of functions of bounded variation about these Riesz bases, we prove the uniform equiconvergence property and point-wise convergence on the closed interval $[0,\pi].$ Analogous results are obtained for regular but not strictly regular $bc.

Criteria for existence of Riesz bases consisting of root functions of Hill and 1D Dirac operators

We study the system of root functions (SRF) of Hill operator $Ly = -y^{\prime \prime} +vy$ with a singular potential $v \in H^{-1}_{per}$ and SRF of 1D Dirac operator Ly = i {pmatrix} 1 & 0 0 & -1 {pmatrix} \frac{dy}{dx} + vy with matrix $L^2$-potential v={pmatrix} 0 & P Q & 0 {pmatrix}, subject to periodic or anti-periodic boundary conditions. Series of necessary and sufficient conditions (in terms of Fourier coefficients of the potentials and related spectral gaps and deviations) for SRF to contain a Riesz basis are proven. Equiconvergence theorems are used to explain basis property of SRF in $L^p$-spaces and other rearrangement invariant function spaces

Consensus statements and recommendations from the ESO-Karolinska Stroke Update Conference, Stockholm 11-13 November 2018

The purpose of the European Stroke Organisation-Karolinska Stroke Update Conference is to provide updates on recent stroke therapy research and to give an opportunity for the participants to discuss how these results may be implemented into clinical routine. The meeting started 22 years ago as Karolinska Stroke Update, but since 2014 it is a joint conference with European Stroke Organisation. Importantly, it provides a platform for discussion on the European Stroke Organisation guidelines process and on recommendations to the European Stroke Organisation guidelines committee on specific topics. By this, it adds a direct influence from stroke professionals otherwise not involved in committees and work groups on the guideline procedure. The discussions at the conference may also inspire new guidelines when motivated. The topics raised at the meeting are selected by the scientific programme committee mainly based on recent important scientific publications. This year's European Stroke Organisation-Karolinska Stroke Update Meeting was held in Stockholm on 11-13 November 2018. There were 11 scientific sessions discussed in the meeting including two short sessions. Each session except the short sessions produced a consensus statement (Full version with background, issues, conclusions and references are published as web-material and at and ) and recommendations which were prepared by a writing committee consisting of session chair(s), scientific secretary and speakers. These statements were presented to the 250 participants of the meeting. In the open meeting, general participants commented on the consensus statement and recommendations and the final document were adjusted based on the discussion from the general participants Recommendations (grade of evidence) were graded according to the 1998 Karolinska Stroke Update meeting with regard to the strength of evidence. Grade A Evidence: Strong support from randomised controlled trials and statistical reviews (at least one randomised controlled trial plus one statistical review). Grade B Evidence: Support from randomised controlled trials and statistical reviews (one randomised controlled trial or one statistical review). Grade C Evidence: No reasonable support from randomised controlled trials, recommendations based on small randomised and/or non-randomised controlled trials evidence.Peer reviewe

Treatment and logistics of acute ischemic stroke : safety and outcomes

BACKGROUND: Stroke, both ischemic and hemorrhagic, accounts for over 20000 hospital admissions in Sweden yearly. The vast majority of patients (85%), suffer from ischemic stroke, an occlusion of a cerebral artery that can be treated pharmacologically with systemic intravenous thrombolysis (IVT) or mechanically with endovascular thrombectomy (EVT). Treatment with IVT carries the risk of symptomatic intracerebral hemorrhage (SICH) in 2-5% of cases, potentially leading to severe disability or death. There remain unanswered questions regarding the safety of IVT in specific subgroups: (1) patients without ischemic stroke, but who present with stroke-like symptoms, known as stroke mimics, and (2) patients suffering from stroke in the posterior cerebral circulation (PCS). EVT is an effective treatment, but only possible for patients suffering from stroke caused by a large artery occlusion (LAO stroke) and is restricted to thrombectomy capable centers with trained neurointerventionists. The Stockholm Stroke Triage System (SSTS) was implemented in 2017 to detect and route patients with suspected LAO stroke and eligible for EVT directly to the thrombectomy center. The first half of this thesis concerns safety and outcomes after IVT in patients with stroke mimics (study I) and PCS (study II). The second half of the thesis concerns acute stroke logistics through use of the SSTS. Study III investigated if outcomes after EVT have improved after implementation of the SSTS. Study IV described patients incorrectly routed using the system and investigated if the system could be improved using statistical modeling. Studies I-II were performed using data from the Safe Implementation of Treatments in Stroke International Stroke Thrombolysis Registry (SITS-ISTR), an international database. Studies III-IV included prospectively recruited patients with suspected acute stroke transported by ambulance in the Stockholm region. Study I included patients treated with IVT between 2003-2017 with MRI follow-up. Outcomes were parenchymal hematoma, SICH, and modified Rankin scale score and death at 3 months after treatment, with comparison between stroke mimics and ischemic stroke. Five parenchymal hemorrhages, and two SICH were identified in 429 stroke mimic patients treated with IVT. Functional symptoms, headache and seizure were the three most common mimicking conditions (>60% total). There was a higher proportion with excellent functional outcome and lower proportion of dead patients in the stroke mimic group. IVT treatment was concluded to be reasonable safe in patients with a stroke mimic diagnosis. Study II included patients treated with IVT between 2013-2017 with available angiographic occlusion data. Outcomes were the same as in study I, with comparison between anterior and posterior circulation stroke. Adjustment of baseline differences using inverse probability treatment weighting, and a systematic review and meta-analysis were performed. Of ~5000 included patients, ~15% had PCS. Both the primary data and the metaanalysis showed fewer hemorrhagic complications in PCS. After adjustment, PCS patients had a slightly higher risk of death after treatment, with no differences in functional outcomes. Study III included patients treated with EVT between October 2017 and October 2019 (during use of the SSTS) in the Stockholm region. Comparison was performed with historical controls treated during the two years prior. The main outcome was modified Rankin Scale scores with adjustment for baseline differences. Secondary outcomes were death, change in NIHSS 24 h post treatment, recanalization, and SICH. Time from onset to EVT was faster during SSTS by 69 minutes. Functional outcomes were better in the SSTS group with no differences in safety outcomes (hemorrhage and death). Study IV included suspected stroke patients transported by ambulance between October 2017 and October 2018 in the Stockholm region. Three alternative triage algorithms were modelled using prehospital data and compared to the SSTS using decision curve analysis. All models included a test for hemiparesis and had similar sensitivity, specificity, and AUC. Comparison of net benefit, (correct routing of patients for EVT without increasing mistriage) showed that the SSTS was superior to the alternative models

A randomized cross-over study of the acute effects of running 5 km on glucose, insulin, metabolic rate, cortisol and Troponin T

Background We aimed to study the impact by running 5 km, at maximal speed, on the normal variations of metabolic variables related to glucose, insulin, insulin sensitivity, cortisol, glucagon, Troponin T and metabolic rate. Material and methods Five women and 12 men 25.7 +/- 5.2 years of age with a body-mass-index of 22.5 +/- 2.3 kg/m(2) where recruited to run 5 km at individual maximal speed in the morning, and to a corresponding day of rest, followed by standardized breakfast and lunch meals. Blood sampling and measurement of indirect calorimetry were done before and after meals. The participants were randomized regarding the order of the two trial-days in this cross-over study. Results Insulin and cortisol levels were higher, and insulin sensitivity was lower, on the race-day compared with the day of rest (linear mixed model: pamp;lt;0.0001 for all three analyses). However, glucose levels and metabolic rate did not differ between the two trial days (p = 0.29 and p = 0.53, respectively). When analyzing specific time-points we found that glucose increased from 5.01 +/- 0.37 mmol/l to 6.36 +/- 1.3 mmol/l, pamp;lt;0.0001, by running, while serum insulin concomitantly increased from 42 21 to 90 54 pmo1/1, pamp;lt;0.0001. In accordance, the QUICKI index of serum sensitivity, 1/(log(10)insulin+log(10)glucose), was lowered post-race, pamp;lt;0.0001. Serum cortisol levels increased from 408 137 nmol/l to 644 171 nmol/l, pamp;lt;0.0001, post-race while serum glucagon levels were unaffected. Troponin T was detectable in serum post-race in 12 out of the 17 participants and reached or surpassed the clinical reference level of 15 ng/l in three subjects. Post-race electrocardiograms displayed no pathologies. Conclusions Relatively short running-races can apparently induce a reduction in insulin sensitivity that is not fully compensated by concomitantly increased insulin secretion intended to ensure euglycemia. Since also Troponin T was detected in plasma in a majority of the participants, our data suggest that it is possible to induce considerable metabolic stress by running merely 5 km, when striving for maximal speed.Funding Agencies|University Hospital of Linkoping Research Funds, Linkoping University; County Council of Ostergotland, Sweden</p

Consort flow diagram of the study.

<p>Consort flow diagram of the study.</p

Effects of running 5 km on Troponin T in 17 healthy subjects.

<p>Individual consecutive changes in Troponin T are displayed by the aligned filled circles. Undetectable levels were set as zero in the graph.</p

Histogram of the times it took for the participants to run 5 km at individual maximal speed.

<p>Data was missing in one subject for technical reasons.</p

Effects of running 5 km (continuous line) on insulin sensitivity by QUICKI index 1/(log₁₀insulin+log₁₀glucose) compared with a non-exercise day (dashed line) in 17 healthy subjects studied on two separate occasions.

<p>Running took place after the baseline test on the day of the run. Data are means and standard errors. Linear mixed model for analyzing the effect of the race compared with the day of rest: p < 0.0001. *corresponds to p < 0.0001 when comparing QUICKI index before and after the race on the day of the race.</p

Effects of running 5 km (continuous line) on serum insulin levels compared with a non-exercise day (dashed line) in 17 healthy subjects studied on two separate occasions.

<p>Running took place after the baseline test on the day of the run. Data are means and bars reflect SEM. Linear mixed model for estimating the effects of the race: p < 0.0001. Serum insulin levels increased after the race on the race-day, * p < 0.0001.</p