Zero-dimensional symplectic isolated complete intersection singularities

We study the local symplectic algebra of the 0-dimensional isolated complete intersection singularities. We use the method of algebraic restrictions to classify these symplectic singularities. We show that there are non-trivial symplectic invariants in this classification.Comment: 9 pages. arXiv admin note: text overlap with arXiv:1101.517

Symplectic T7T_7, T8T_8 singularities and Lagrangian tangency orders

We study the local symplectic algebra of curves. We use the method of algebraic restrictions to classify symplectic $T_7$ singularities. We define discrete symplectic invariants - the Lagrangian tangency orders. We use these invariants to distinguish symplectic singularities of classical $A-D-E$ singularities of planar curves, $S_5$ singularity and $T_7$ singularity. We also give the geometric description of these symplectic singularities

Cerebral venous and sinus thrombosis diagnosis: preliminary study of clinical picture and D-dimer concentration correlation

Aim of the study. We investigated whether D-dimer (DD) concentration is elevated in cerebral venous and sinus thrombosis (CVST), as has been reported in the literature. Clinical rationale for the study. CVST is a disease with variable clinical presentations and a challenging diagnosis. We looked into whether D-dimer concentration might be an indicator of CVST, and the need for neuroimaging tests correlated with clinical factors. Materials and methods. We included all consecutive patients (mean age 41.6 years) with CVST treated in our neurology department from 2014 to 2018 whose DD levels had been measured. DD concentrations were categorised as normal (≤ 0.5 μg/ml) or elevated ( > 0.5 μg/ml). Appropriate imaging confirmed the diagnosis of CVST. The results were compared to those of a control group consisting of 22 age- and sex-matched patients (mean age 40 years) with a diagnosis of primary headache (tension type or migraine) hospitalised to exclude secondary causes. Results. In 20 patients in the CVST study group, median level of DD was 1.0 + 0.57 μg/ml (range 0.19–2.45 μg/ml), compared to the control group’s mean DD level of 0.50 + 0.45 μg/ml (range 0.15–1.73 μg/ml), with p < 0.005. Higher DD levels were associated with complications of the disease and fatal course (p < 0.005). One female and one male patient died because of CVST with DD levels of (respectively) 2.45 and 1.80 μg/ml — the two highest concentrations in our study group. Conclusions and clinical implications. DD concentration, especially in headache patients, may be a factor to predict CVST and an indicator for further diagnostic procedures with venography. But in clinical practice, low levels of DD cannot be taken to exclude CVST

Migraine headache facilitators in a population of Polish women and their association with migraine occurrence — preliminary results

Aim of the study. The occurrence of migraine is linked with some common lifestyle activities and conditions preceding the attack. Our study presents known and presumptive lifestyle factors and activities related to migraine, and compares them to the frequency of headache attacks. Material and methods. 40 female patients of the Headache Outpatient Clinic in Warsaw, Poland, diagnosed with migraine, mean age 44.6 years, and 40 female participants from the control group, mean age 39.5 years, were included in the study. The study employed questionnaires reporting the presence of lifestyle factors and socioeconomic predispositions as well as the Migraine Disability Assessment Test (MIDAS) as data collection methods. Results. Correlations between some of the lifestyle factors and the frequency of migraines occurred statistically significantly. Conclusions. Some factors and lifestyle activities such as stress, relaxation, specific dietary products, fasting, fatigue, bright light, noise, weather changes or menstruation may have an influence on migraine frequency and severity in female patients, which can have an impact on migraine prevention

Even Dimensional Improper Affine Spheres

There are exactly two different types of bi-dimensional improper affine spheres: the non-convex ones can be modeled by the center-chord transform of a pair of planar curves while the convex ones can be modeled by a holomorphic map. In this paper, we show that both constructions can be generalized to arbitrary even dimensions: the former class corresponds to the center-chord transform of a pair of Lagrangian submanifolds while the latter is related to special K\"ahler manifolds. Furthermore, we show that the improper affine spheres obtained in this way are solutions of certain exterior differential systems. Finally, we also discuss the problem of realization of simple stable Legendrian singularities as singularities of these improper affine spheres.Comment: 26 page

Elektromiografia pojedynczego włókna u chorych na klasterowy ból głowy

Background and purpose Mutations of CACNA1A, which encodes a neuronal P/Q Ca2+ channel, are present in patients with familial hemiplegic migraine, and possibly in other types of migraine as well. This calcium channel is also involved in neuromuscular transmission. In our previous study we confirmed that the single-fibre electromyography (SFEMG) method can demonstrate a neuromuscular transmission deficit in migraine with aura. The aim of our present study was to estimate the neurotransmitter dysfunction in cluster headache and to compare the results between patients with cluster headache and those with migraine with aura. Material and methods We selected 6 patients with cluster headache and 6 patients with migraine with typical aura. SFEMG of the voluntarily activated extensor digitorum communis muscle was performed. Results The SFEMG results were in the normal range in the cluster headache group and in the healthy controls. Slight neuromuscular transmission disturbances were present in patients with migraine with aura. Conclusions The abnormal neuromuscular transmission detectable by SFEMG may reflect a genetically determined dysfunction of the P/Q Ca2+ channels in a group of migraineurs with aura. Conversely, absence of neuromuscular abnormalities in cluster headache patients could be explained by different aetiology not resulting in channelopathy. Single-fibre electromyography could be a helpful tool in clinically questionable cases in differentiating between cluster headache and migraine with aura.Wstęp i cel pracy U chorych na migrenę rodzinną połowiczoporaźną, a także z innymi postaciami migreny z aurą stwierdzono mutację w genie CACNA1A dla kanału wapniowego P/Q. Z uszkodzeniem tego kanału wapniowego związane są zaburzenia przewodzenia nerwowo-mięśniowego. We wcześniejszej pracy autorzy opisali badanie za pomocą elektromiografii pojedynczego włókna (SFEMG) zaburzeń przewodzenia nerwowo-mięśniowego u osób z migreną, stwierdzając ich obecność u części pacjentów z migreną z aurą. Celem niniejszego badania jest odpowiedź na pytanie, czy u pacjentów z klasterowym bólem głowy występują podobne zaburzenia, i porównanie wyników otrzymanych u osób z klasterowym bólem głowy z wynikami pacjentów z migreną z aurą. Materiał i metody Elektromiografię pojedynczego włókna wykonaną z mięśnia zginacza długiego palców przeprowadzono u 6 pacjentów z klasterowym bólem głowy i zestawiono ją z wynikami 6 chorych na migrenę z aurą. Wyniki Wyniki SFEMG w grupie chorych na klasterowy ból głowy mieściły się w prawidłowych granicach, podobnie jak w grupie kontrolnej zdrowych osób. W grupie pacjentów z migreną z aurą stwierdzono łagodne zaburzenia transmisji nerwowo-mięśniowej. Wnioski Nieprawidłowe wyniki SFEMG mogą wskazywać na genetycznie uwarunkowaną dysfunkcję kanału wapniowego w grupie chorych na migrenę z aurą w przeciwieństwie do chorych na klasterowy ból głowy, u których najprawdopodobniej etiologia choroby ma inne podłoże. Badanie SFEMG może być badaniem pomocniczym w różnicowaniu niepewnych przypadków klasterowego bólu głowy imitujących migrenowy ból głowy