On semigroups of matrices with eigenvalue 1 in small dimensions

AbstractLet S⊂M4(C) be a semigroup such that 1 is an eigenvalue of every s∈S. It is shown that S is reducible. A complete list of irreducible semigroups S⊂M3(C) with this spectral property is given

On selfadjoint extensions of semigroups of partial isometries

First published in Transactions of the American Mathematical Society in volume 368, 2016, published by the American Mathematical Society. https://doi.org/10.1090/tran/6619Let S be a semigroup of partial isometries acting on a complex, infinite- dimensional, separable Hilbert space. In this paper we seek criteria which will guarantee that the selfadjoint semigroup T generated by S consists of partial isometries as well. Amongst other things, we show that this is the case when the set Q(S) of final projections of elements of S generates an abelian von Neumann algebra of uniform finite multiplicity.Research supported in part by ARRS (Slovenia). Research supported in part by NSERC (Canada)

ALGEBRAIC DEGREE IN SPATIAL MATRICIAL NUMERICAL RANGES OF LINEAR OPERATORS

First published in Proceedings of the American Mathematical Society in volume 149, issue 10 in 2021, published by the American Mathematical SocietyWe study the maximal algebraic degree of principal ortho-compressions of linear operators that constitute spatial matricial numerical ranges of higher order. We demonstrate (amongst other things) that for a (possibly unbounded) operator L on a Hilbert space, every principal m-dimensional ortho-compression of L has algebraic degree less than m if and only if rank(L − λI) ≤ m − 2 for some λ ∈ CThe first author’s research was supported in part by Research and Development Agency of Slovenia grant P1-0222. The second author’s research was supported by Colby College Natural Sciences Division Grant. The third, fourth, and fifth authors’ research was supported in part by NSERC (Canada)

La Main-Out

arm with text, halftone, stencil

Neinvazivno predrojstveno testiranje prostih plodov DNA za downov sindrom in ostale kromosomske nepravilnosti

Background: Chorionic villus sampling and amniocentesis as definitive diagnostic procedures represent a gold standard for prenatal diagnosis of chromosomal abnormalities. The methods are invasive and lead to a miscarriage and fetal loss in approximately 0.5–1 %. Non-invasive prenatal DNA testing (NIPT) is based on the analysis of cell-free fetal DNA from maternal blood. It rep- resents a highly accurate screening test for detecting the most common fetal chromosomal abnormalities. In our study we present the results of NIPT testing in the Diagnostic Center Strah, Slovenia, over the last 3 years. Methods: In our study, 123 pregnant women from 11th to 18th week of pregnancy were included. All of them had First trimester assessment of risk for trisomy 21, done before NIPT testing. Results: 5 of total 6 high-risk NIPT cases (including 3 cases of Down syndrome and 2 cases of Klinefelter’s syndrome) were confirmed by fetal karyotyping. One case–Edwards syndrome was false positive. Patau syndrome, triple X syndrome or Turner syndrome were not observed in any of the cases. Furthermore, there were no false negative cases reported. In general, NIPT testing had 100 % sensitivity (95 % confidence interval: 46.29 %–100.00 %) and 98.95 % specificity (95 % confidence interval: 93.44 %–99.95 %). In determining Down syndrome alone, specificity (95 % confidence interval: 95.25 %- 100.00 %) and sensitivity (95 % confidence interval: 31.00 %–100.00 %) turned out to be 100 %. In 2015, the average turnaround time for analysis was 8.3 days from the day when the sample was taken. Repeated blood sampling was required in 2 cases (redraw rate = 1.6 %). Conclusions: Our results confirm that NIPT rep- resents a fast, safe and highly accurate advanced screening test for most common chromosomal abnormalities. In current clinical practice, NIPT would significantly decrease the number of unnecessary invasive procedures and the rate of fetal loss caused by invasive diagnostics.Izhodišča: Amniocenteza in biopsija horionskih resic kot dokončni diagnostični metodi sta zlati standard predrojstvene diagnostike za ugotavljanje kromosomskih nepravilnosti ploda. Metodi sta invazivni in v približno 0,5–1 % povzročita prekinitev nosečnosti zaradi spontanega splava po posegu. Neinvazivno predrojstveno DNA testiranje (NIPT) temelji na analizi proste plodove DNA iz krvi nosečnice. Je visoko zanesljiv presejalni test za odkrivanje najpogostejših kromosomskih nepravilnosti ploda. V naši raziskavi predstavljamo rezultate testiranja NIPT v Diagnostičnem centru Strah v zadnjih 3 letih. Metode: V raziskavo je bilo vključenih 123 no- sečnic med 11. in 18. tednom nosečnosti. Vsaka nosečnica je opravila priporočeni ultrazvočni pregled zgodnje morfologije ploda z merjenjem nuhalne svetline. Določeno je bilo bodisi nizko bodisi visoko tveganje za kromosomske nepravilnosti. Rezultati: 5 od skupno 6 primerov, pri katerih je NIPT določil visoko tveganje (3 primeri Downovega sindroma in 2 primera Klinefelterjevega sindroma) je bilo potrjenih s kariotipizacijo. 1 primer – Edwardsov sindrom – je bil lažno pozitiven. Kromosomske nepravilnosti sindrom Patau, trojni X-sindrom ali Turnerjev sindrom niso bile zaznane pri nobeni nosečnici. O lažno negativnih primerih ni bilo poročano. Glede na podatke, pridobljene v raziskavi, je testiranje NIPT za vse omenjene kromosomske nepravilnosti pokazalo 100-odstotno občutljivost (95-odstotni interval zaupanja: 46,29 % – 100,00 %) in 98,95-odstotno specifičnost (95-odstotni interval zaupanja: 93,44 % – 99,95 %). Pri določanju le Downovega sindroma sta tako občutljivost (95 % interval zaupanja: 31,00 % – 100,00 %) kot specifičnost (95-odstotni interval zaupanja: 95,25 % – 100,00 %) enaki 100 %. V letu 2015 je bilo povprečno trajanje analize vzorca 8,3 dni od dneva odvzema krvi. V 2 primerih (1,6 %) je bil zaradi neuspešne analize potreben ponoven odvzem vzorca. Zaključki: Naši rezultati potrjujejo, da je NIPT hiter, varen in visoko zanesljiv napreden presejalni test za določanje najpogostejših kromosomskih nepravilnosti pri plodu. NIPT bi v do sedaj uveljavljeni klinični praksi lahko značilno znižal število nepotrebnih invazivnih preiskav in s tem tudi število spontanih splavov, ki jih invazivna diagnostika lahko povzroči