Secant cumulants and toric geometry

We study the secant line variety of the Segre product of projective spaces using special cumulant coordinates adapted for secant varieties. We show that the secant variety is covered by open normal toric varieties. We prove that in cumulant coordinates its ideal is generated by binomial quadrics. We present new results on the local structure of the secant variety. In particular, we show that it has rational singularities and we give a description of the singular locus. We also classify all secant varieties that are Gorenstein. Moreover, generalizing (Sturmfels and Zwiernik 2012), we obtain analogous results for the tangential variety.Comment: Some improvements to previous results, with other minor changes. Updated reference

Adolescent well-being and learning in times of COVID-19-A multi-country study of basic psychological need satisfaction, learning behavior, and the mediating roles of positive emotion and intrinsic motivation

The sudden switch to distance education to contain the outbreak of the COVID-19 pandemic has fundamentally altered adolescents' lives around the globe. The present research aims to identify psychological characteristics that relate to adolescents' well-being in terms of positive emotion and intrinsic learning motivation, and key characteristics of their learning behavior in a situation of unplanned, involuntary distance education. Following Self-Determination Theory, experienced competence, autonomy, and relatedness were assumed to relate to active learning behavior (i.e., engagement and persistence), and negatively relate to passive learning behavior (i.e., procrastination), mediated via positive emotion and intrinsic learning motivation. Data were collected via online questionnaires in altogether eight countries from Europe, Asia, and North America (N = 25,305) and comparable results across countries were expected. Experienced competence was consistently found to relate to positive emotion and intrinsic learning motivation, and, in turn, active learning behavior in terms of engagement and persistence. The study results further highlight the role of perceived relatedness for positive emotion. The high proportions of explained variance speak in favor of taking these central results into account when designing distance education in times of COVID-19.Peer reviewe

Secant varieties of toric varieties arising from simplicial complexes

Motivated by the study of the secant variety of the Segre-Veronese variety we propose a general framework to analyze properties of the secant varieties of toric embeddings of affine spaces defined by simplicial complexes. We prove that every such secant is toric, which gives a way to use combinatorial tools to study singularities. We focus on the Segre-Veronese variety for which we completely classify their secants that give Gorenstein or Q-Gorenstein varieties. We conclude providing the explicit description of the singular locus

Secant cumulants and toric geometry

We study the secant line variety of the Segre product of projective spaces using special cumulant coordinates adapted for secant varieties. We show that the secant variety is covered by open normal toric varieties. We prove that in cumulant coordinates its ideal is generated by binomial quadrics. We present new results on the local structure of the secant variety. In particular, we show that it has rational singularities and we give a description of the singular locus. Generalizing results of Sturmfels and Zwiernik, we also show analogous results for the tangential variety

Saldžiųjų bulvių produktyvumo pokyčiai priklausomai nuo tręšimo azoto trąšomis

e-ISSN 2335-8947Šiuo metu vis labiau populiarėja saldžiųjų bulvių auginimas. Tyrimo tikslas – ištirti tręšimo įvairiomis normomis azoto (N) trąšų įtaką augalų fotosintezės efektyvumui, fotosintetiniam našumui, stiebagumbių derlingumui, baltymų ir sausųjų medžiagų kiekiui. Buvo tirti saldžiosios bulvės (Ipomoea batatas (L.) Lam.) augalų stiebagumbių derlingumo fiziologiniai ir fenotipiniai pokyčiai. Lauko eksperimentas atliktas 2013–2015 m. Uhnin vietovėje (51.5833° N, 23.0333° E), Vidurio Rytų Lenkijoje. Buvo tirta tręšimas įvairiomis normomis (0, 50, 100, 150 ir 200 kg ha-1 N) azoto trąšų. Eksperimento metu nustatyta, kad skirtingos metų sąlygos turėjo teigiamą įtaką sausųjų medžiagų kiekiui stiebagumbiuose bei jų derliui ir minimalią – chlorofilo fluorescencijos bei chlorofilo a kiekiui. Tręšimo ir metų sąveika mažiausią įtaką turėjo bendrajai dispersijai, didžiausią – chlorofilo b kiekiui. Azoto trąšos turėjo mažiausią įtaką chlorofilo fluorescencijos fiziologiniams pokyčiams, tačiau gana didelę – sausųjų medžiagų kiekiui stiebagumbiuose ir jų derlingumui. Tręšimas 150 kg ha-1 N palankiai paveikė elektronų judėjimo srautą, pradedant nuo augalų 6-ojo lapo augimo tarpsnio iki fiziologinės brandos. Taip pat nustatyta, kad tręšimas azotu stimuliuoja saldžiųjų bulvių fotosintezės efektyvumą augalų vegetacijos pabaigoje. Didinant azoto normas chlorofilo fluorescencija (Fm) mažėjo. Reikšmingas fotocheminio efektyvumo (PS) II (Y) padidėjimas ir fluorescencijos koeficiento (qP) mažėjimas vyko iki tręšimo 100 kg ha-1 N. Mažiausią chlorofilo fluorescencijos intensyvumą (F0 ), nefotochemį fluorescencijos silpnėjimo koeficientą (qN) ir elektronų judėjimo spartą (ETR) palankiausiai veikė tręšimas 150 kg ha-1 NCurrently, the cultivation of sweet potato (Ipomoea batatas (L.) Lam.) is gaining more and more popularity. The aim of the present study was to investigate the effect of different nitrogen (N) fertilization levels on the parameters related to the efficiency of the photosynthetic apparatus, plant photosynthetic productivity, tuber yield and tuber dry matter yield of I. batatas. The study also aimed to identify phenotypic variation in the physiological measures and tuber yield traits of I. batatas. To achieve these objectives, a field experiment was carried out during the period 2013–2015 in Uhnin (51.5833° N, 23.0333° E), central-eastern Poland. The experimental factor was different nitrogen fertilization rates (0, 50, 100, 150 and 200 kg ha-1 N). The conditions in the experimental years had the strongest effect on tuber dry matter content and yield and on minimum chlorophyll fluorescence yield and chlorophyll a content. The fertilization × year interaction had the lowest percentage contribution to the total variance, while its highest contribution was observed for chlorophyll b. Nitrogen fertilization had the lowest percentage contribution to the physiological measures of chlorophyll fluorescence, but a quite high contribution to tuber dry matter content and yield. Nitrogen fertilization up to a level of 150 kg ha-1 N beneficially affected electron flow at successive plant growth stages, beginning from the 6-leaf stage until physiological maturity. Nitrogen fertilization was also shown to have a stimulating effect on the photosynthetic efficiency of I. batatas at the end of the growing season. A decreasing trend was observed in the maximum chlorophyll fluorescence yield (Fm) as affected by increasing N rates. A significant increase in actual photochemical efficiency of photosystem (PS) II (Y) and in the photochemical fluorescence quenching coefficient (qP) was observed up to a level of 100 kg ha-1 NVytauto Didžiojo universitetasŽemės ūkio akademij

Existence of weak solutions for compressible Navier-Stokes equations with entropy transport

International audienc

Obstructive Sleep Apnea as a Risk Factor of Insulin Resistance in Nondiabetic Adults

Objective: The aim of this research was to assess the relationship between prevalence and severity of obstructive sleep apnea (OSA) and insulin resistance among patients with increased risk of OSA without diabetes mellitus. Method and materials: our study group involved 102 individuals with suspected OSA, mean age 53.02 ± 12.37 years. Data on medical history, medication usage, sleep habits, sleep quality and daytime sleepiness, were obtained using questionnaires. All patients underwent standardized full night polysomnography. Serum fasting insulin and glucose concentration were analyzed, the homeostatic model assessment-insulin resistance (HOMA-IR) index was calculated. Results: polysomnographic study indicated that in the group with OSA mean values of apnea–hypopnea index (AHI), oxygen desaturation index (ODI), duration of SpO2 < 90% and average desaturation drop were significantly higher compared to the group without OSA, while the minimum SpO2 was significantly lower. The carbohydrate metabolism parameters did not differ within those groups. Significantly higher fasting insulin concentration and HOMA-IR index were found in the group with AHI ≥ 15 compared to the group with AHI < 15 and in the group with AHI ≥ 30 compared to the group with AHI < 30. Higher AHI and ODI were independent risk factors for higher fasting insulin concentration and higher HOMA-IR index. Increased duration of SpO2 < 90% was an independent risk factor for higher fasting glucose concentration. Conclusions: Individuals with moderate to severe OSA without diabetes mellitus had a higher prevalence of insulin resistance

Obstructive Sleep Apnea as a Risk Factor of Insulin Resistance in Nondiabetic Adults

Objective: The aim of this research was to assess the relationship between prevalence and severity of obstructive sleep apnea (OSA) and insulin resistance among patients with increased risk of OSA without diabetes mellitus. Method and materials: our study group involved 102 individuals with suspected OSA, mean age 53.02 ± 12.37 years. Data on medical history, medication usage, sleep habits, sleep quality and daytime sleepiness, were obtained using questionnaires. All patients underwent standardized full night polysomnography. Serum fasting insulin and glucose concentration were analyzed, the homeostatic model assessment-insulin resistance (HOMA-IR) index was calculated. Results: polysomnographic study indicated that in the group with OSA mean values of apnea–hypopnea index (AHI), oxygen desaturation index (ODI), duration of SpO2 < 90% and average desaturation drop were significantly higher compared to the group without OSA, while the minimum SpO2 was significantly lower. The carbohydrate metabolism parameters did not differ within those groups. Significantly higher fasting insulin concentration and HOMA-IR index were found in the group with AHI ≥ 15 compared to the group with AHI < 15 and in the group with AHI ≥ 30 compared to the group with AHI < 30. Higher AHI and ODI were independent risk factors for higher fasting insulin concentration and higher HOMA-IR index. Increased duration of SpO2 < 90% was an independent risk factor for higher fasting glucose concentration. Conclusions: Individuals with moderate to severe OSA without diabetes mellitus had a higher prevalence of insulin resistance

Genetic Variants of the TERT Gene and Telomere Length in Obstructive Sleep Apnea

Introduction: Obstructive sleep apnea (OSA) is a worldwide breathing disorder that has been diagnosed globally in almost 1 billion individuals aged 30–69 years. It is characterized by repeated upper airway collapses during sleep. Telomerase reverse transcriptase (TERT) is involved in the prevention of telomere shortening. This prospective, observational study aimed to investigate the relationship between single nucleotide polymorphisms (SNPs) of TERT and the severity of OSA, taking into account hypertension and diabetes prevalence. Methods: A total of 149 patients with OSA were diagnosed using one-night video-polysomnography based on the American Academy of Sleep Medicine guidelines. The TERT SNPs and telomere length (TL) were detected using real-time quantitative polymerase chain reaction. Results: Statistical analysis showed that there is no relationship between the rs2853669 and rs2736100 polymorphisms of TERT, and the severity of OSA (p > 0.05). Moreover, no relationship between TL and the severity of OSA was observed. The G allele in the locus of rs2736100 TERT was associated with hypertension prevalence and was more prevalent in hypertensives patients (46.00% vs. 24.49%, p = 0.011). The prevalence of hypertension was higher in patients with the C allele in the locus of rs2853669 than in patients without this allele (50.79% vs. 30.23%, p = 0.010). Moreover, a lower prevalence of diabetes was observed in homozygotes of rs2736100 TERT than in heterozygotes (5.63% vs. 15.38%, p = 0.039). Conclusion: This study showed no relationship between OSA and TERT SNPs. However, SNPs of the TERT gene (rs2736100 and rs2853669) were found to affect arterial hypertension and diabetes prevalence

Telemetric Assessment of Continuous Positive Airways Pressure (CPAP) Effectiveness and Adherence in Obstructive Sleep Apnea during COVID-19 Pandemic

Obstructive sleep apnea is the most common sleep-related breathing disorder. In the pandemic times of the new coronavirus SARS-CoV-2, CPAP (Continuous Positive Airway Pressure) therapy of obstructive sleep apnea became even more challenging. After the pandemic outbreak in March 2020, most CPAP treatment recommendations changed because of rising concerns about CPAP usage safety for patients and their families. Therefore, we examined the effectiveness of CPAP and adherence to the therapy of 149 adults with obstructive sleep apnea in the period of two years from 4 March 2019 to 3 March 2021 (before pandemic breakout and during the first year of pandemic). Data on CPAP parameters and adherence to therapy were obtained via a telemetric system. Together, our results demonstrated that the COVID-19 pandemic had no significant impact on CPAP therapy parameters and adherence in whole study group. However, detailed analysis acknowledged that some demographic and clinical features influenced CPAP therapy. The results showed that across subgroups of patients differentiated on the basis of age, gender, co-existing diabetes mellitus, or hypertension, the COVID-19 pandemic seemed to affect CPAP effectiveness. Our results provide a good starting point for discussion on CPAP therapy recommendations during pandemic times