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Purpose: To study the prevalence of cardiovascular diseases and the correlations of left ventricle global longitudinal strain (LV GLS) in patients 3 months after proven COVID-19 pneumonia.Material and methods. 369 patients with proven COVID-19 pneumonia underwent a comprehensive clinical examination and echocardiography (EchoCG) after 3 months ± 3 weeks after their discharge from the hospital. Mean age of the patients was 54 [46; 61]; 50.9% of them were women. LV GLS was studied in 284 (77%) of patients with optimal visualization quality during echocardiography. LV GLS was considered reduced in the limit of > –18%. Study Registration: ClinicalTrials.gov ID: NCT04501822.Results. 3 months after discharge, obesity was noted in 46.5% of patients, cardiovascular diseases were diagnosed in 73.4%, including de novo in 8.4%. Arterial hypertension occurred in 71.5% of patients, coronary artery disease — in 22.5%. The average left ventricle (LV) ejection fraction was 67.8 ± 5.0%, the average LV GLS was –19.5 ± 2.3%. LV GLS was reduced in 24.4% of the patients. LV GLS showed no correlation with the patient age, NYHA functional class and LV ejection fraction. Reduced LV GLS was independently associated with male sex (OR 1.399; 95% CI 1.239–1.580; p < 0.001), obesity (OR 1.268; 95% CI 1.132–1.421; p < 0.0001), diabetes mellitus (OR 1.204; 95 % CI 1.017–1.425; p = 0.031) and hypertension (OR 1.120; 95% CI 1.002–1.252; p = 0.046). LV GLS showed moderate positive correlations with echocardiographic parameters of right ventricle (RV): the length (r = 0.346), diastolic (r = 0.333) and systolic area (r = 0.326), width at the basal (r = 0.358) and midlevel (r = 0.321), as well as with the dimension of the proximal RV outfl ow tract (r = 0.302, all p < 0.001). LV GLS showed a weak correlation with the severity of lung lesions during hospitalization (r = 0.184; p = 0.002).Conclusions. 3 months after COVID-19 pneumonia, cardiovascular diseases were diagnosed in 73.4%. Reduced LV GLS was observed in 24.4% of survivors and was associated with male sex, obesity, diabetes mellitus, arterial hypertension and linear and planimetric RV dimensions.

Aim: To evaluate clinical and morpho-functional predictors of super-response to cardiac resynchronization therapy (CRT) in patients with heart failure and reduced ejection fraction (HFrEF) in the short-term period after implantation.Material and Methods. The study enrolled 86 patients (88.4% men, 54.0 ± 8.9 years mean age, New York Heart Association (NYHA) class II–IV). Patients were examined at baseline and in dynamics (mean follow-up was 10.6 ± 3.6 months). According to the change in left ventricular (LV) end-systolic volume (ESV) patients were divided into two groups: Group I (n = 19) with a decrease in LV ESV ≥ 30% (super-responders (SR) and Group II (n = 67) – decrease in LV ESV < 30% (non-super-responders (non-SR). Parameters of mechanical dyssynchrony (MD) were assessed in the two groups including LV pre-ejection period, interventricular mechanical delay (IVMD), intraventricular delay (IVD).Results. At baseline, traditional parameters of MD were higher in SR: LV pre-ejection period (156.8 ± 35.4 ms vs 135.0 ± 35.6 ms; p = 0.021) and IVMD (73.0 [43.0; 108.0] ms vs 47.0 [19.5; 70.0] ms; p = 0.017). Logistic regression results showed that female gender (HR 7.048; 95% CI 1.496–33.206; p = 0.014) and QRS width (HR 1.017; 95% CI 1.000–1.034; p = 0.048) had an independent association with super-response.Conclusion. In patients with HFrEF, more severe mechanical and electrical dyssynchrony is associated with super-response to CRT in a short-term follow-up period.

Background. Studying the impact of complicated course of new coronavirus infection on the cardiovascular system in the long term after patient discharge from hospital is of high significance.Purpose. To compare the clinical and echocardiographic parameters of persons with history of verified COVID-19 pneumonia one year after discharge from hospital depending on the value of left ventricular (LV) global longitudinal strain (GLS).Material and Methods. A total of 116 patients (50.4% men) aged 49.0 ± 14.4 years (from 19 to 84 years) with history of verified COVID-19 pneumonia were examined one year ± three weeks after discharge. The parameters of left ventricular global and segmental longitudinal strain were studied in 80 patients with optimal quality of echocardiographic visualization. Patients were divided into groups depending on the LV GLS value: group 1 included 35 patients with normal LV GLS (p = 0.145), severity of lung injury during hospitalization (p = 0.691), duration of hospitalization (p = 0.626), and frequency of stay in the intensive care unit (p = 0.420).Results. Abnormal values of LV GLS one year after discharge were found in 57.5% of patients with optimal visualization quality while the LV ejection fraction (EF) was normal in all patients. The majority of patients in group 2 were men (71.1% vs 28.6%, p < 0.001). A combination of coronary artery disease (CAD) and hypertension (AH) was more often diagnosed in this group (22% vs 6%, p = 0.040). The values of LV EF did not differ between the groups. The values of LV GLS were significantly worse in patients of group 2 (–17.6 ± 1.9% vs –21.8 ± 1.2%, p < 0.001). Moreover, the parameters of diastolic function including the left atrial emptying volume index (1.3 ± 0.3 mL/m2 vs 1.4 ± 0.3 mL/m2, р = 0.052) and velocity of the lateral part of the mitral valve fibrous ring e’ (10.8 ± 4 .4 cm/s vs 12.8 ± 4.0 cm/s, p = 0.045) were also lower in this group.Conclusions. The LV GLS was impaired in 57.5% patients with normal LV EF one year after COVID-19 pneumonia. In the group with impaired LV GLS, men predominated; coronary artery disease was more often detected in combination with AH; and parameters of LV diastolic function were worse compared with the corresponding parameters in the group of patients with normal LV GLS.

Aim. To assess association of different dynamics of sex hormones with 10-year survival in men with congestive heart failure (CHF) and implanted cardiac resynchronization therapy (CRT) devices.Methods. Based on tercile of testosterone at the end of the study (TESend), 157 men with CRT (mean age 58.7±9.7 years old; 95 men (60.5%) w/ ischemic CHF) were divided into 3 groups: gr. I (n=52) - TESend13.319.2 nmol/l. Parameters of echocardiography (Echo) were investigated in dynamics, N-terminal fragment of probrain natriuretic peptide (NT-proBNP), interleukin-6 (IL-6), total and free testosterone (TES), estradiol (E2), sex hormone-binding globulin (SHBG), progesterone (PGN), dehydroepiandrosterone sulfate (DHEAS), E2/TES ratio were tested in plasma. Survival in groups was assessed using Kaplan-Meier method.Results. Groups were comparable in age, presence of ischemic CHF, arterial hypertension and surgeries on myocardial revascularization. Higher incidence of atrial fibrillation, obesity, complete left bundle branch block, tendency to higher incidence of diabetes mellitus and higher body mass index was revealed in gr. I compared to gr. III. At baseline, groups didn’t differ in Echo parameters; the highest TES levels were found in gr. III. After CRT, there was less reverse cardiac remodeling, decrease of TES level (pConclusion. Obtained results indicated different dynamics of sex steroids after CRT. Sex hormones variation pattern, interrelated with increase in levels of testosterone, estradiol, dehydroepiandrosterone sulfate and decrease in testosterone to estradiol ratio, was associated with better 10-year survival in men with implantable CRT devices with greater reverse cardiac remodeling and reduction in activity of systemic immune inflammation.

Funding Acknowledgements Type of funding sources: None. Background Coronavirus disease 2019 (COVID-19) is caused by the novel severe acute respiratory syndrome coronavirus 2. Pulmonary vascular resistance (PVR) is an important hemodynamic variable used in the management of patients with cardiovascular and pulmonary pathology. Doppler echocardiography has significantly impacted clinical medicine by its ability to assess intracardiac hemodynamics noninvasively. It seems actual to reveal the relationship between right heart function and lungs involvement in COVID-19. Purpose To assess the relationship right ventricular (RV) echocardiographic structural and functional parameters with indicators of increased pulmonary vascular resistance (PVR) in patients 3 months after COVID-19 pneumonia. Methods 96 patients (mean age 47.6 ± 15.2 years) were examined during hospitalization and at control visit (3 months follow-up). The equation tricuspid regurgitation velocity / time-velocity integral of the RV outflow tract X 10 + 0.16 has been used to determine PVR. Patients were divided into 2 groups: I group (n = 31) – patients with increase of PVR ≥1.5 Wood unit (WU) and II group (n = 65) – with decrease of PVR Results At baseline groups did not differ in main clinical characteristics, including severity of lung involvement in COVID-19 by computed tomography (32.7 ± 22.1% vs 36.5 ± 20.4%, р=0.418). Linear, planimetric and volumetric parameters did not differ significantly between groups. At the control visit RV free wall (FW) global endocardial longitudinal strain (LS) (-19.3 [-17.9; -25.8] % in group I vs -23.4 [-19.8; -27.8] % in group II, p = 0.048), tricuspid annular plane systolic excursion (21.7 ± 3.8 mm vs 23.3 ± 3.4 mm, p = 0.040) and RV maximum systolic velocity assessed by tissue Doppler imaging (12.3 ± 2.4 cm/s vs 13.4 ± 2.0 cm/s, p = 0.024) were significantly reduced in group I, systolic pulmonary artery pressure (sPAP) according to Otto C. (32.0 [26,0; 35.0] mm Hg vs 23.0 [20.0; 28.0] mm Hg, p Conclusion Hidden RV systolic dysfunction defined as decreased endocardial RV FW LS to -19.3% is associated with increased PVR ≥1.5 WU in patients 3 months after COVID-19 pneumonia. Abstract Figure. RV FW LS by STE

The relative entropy of entanglement $E_R$ is defined as the distance of a multi-partite quantum state from the set of separable states as measured by the quantum relative entropy. We show that this optimisation is always achieved, i.e. any state admits a closest separable state, even in infinite dimensions; also, $E_R$ is everywhere lower semi-continuous. We use this to derive a dual variational expression for $E_R$ in terms of an external supremum instead of infimum. These results, which seem to have gone unnoticed so far, hold not only for the relative entropy of entanglement and its multi-partite generalisations, but also for many other similar resource quantifiers, such as the relative entropy of non-Gaussianity, of non-classicality, of Wigner negativity $\unicode{8212}$ more generally, all relative entropy distances from the sets of states with non-negative $\lambda$-quasi-probability distribution. The crucial hypothesis underpinning all these applications is the weak*-closedness of the cone generated by free states, and for this reason the techniques we develop involve a bouquet of classical results from functional analysis. We complement our analysis by giving explicit and asymptotically tight continuity estimates for $E_R$ and closely related quantities in the presence of an energy constraint., Comment: 45 pages, no figures. In v2 we added a new main result, Thm 9, which gives a dual variational formula for the relative entropy of resource. We also corrected claim (c) in the previous Thm 4 (now Thm 5), which required a faithfulness hypothesis. Other minor typos have been fixed, and the presentation has been improved. v3 is very close to the published version

Introduction. Growth Differentiation Factor 15 (GDF-15) is known to be an independent predictor of cardiovascular and all-cause mortality, as well as major bleeding in patients (pts) with non-valvular atrial fibrillation (AF). Since GDF-15 is expressed by a wide array of cells in response to inflammation and myocardial stress, it is interesting to study which clinical and functional parameters are most associated with the level of GDF-15 in pts with non-valvular AF and preserved left ventricular ejection fraction. Aim. To study the relationship of GDF-15 level in blood serum with parameters of clinical and functional status and to determine independent predictors of GDF-15 level in pts with non-valvular AF. Material and methods. 87 pts with non-valvular AF were studied, with an average age of 56.9±9.2 years. A general clinical examination, echocardiography and laboratory tests were performed, including fasting serum glucose (mmol/l),highly sensitive C-reactive protein (h/s CRP) (mg/l), creatinine level (mkmol/l) and subsequent calculation of glomerular filtration rate (ml/min/1.73m2), and N-terminal pro-B-type natriuretic peptide (NT-proBNP) (pg/ml). The level of GDF15 (pg/ml) in blood serum was determined using an enzyme immunoassay with the help of the human GDF-15/MIC-1 ELISA analytical kit (BioVender, Czech Republic). Results. The increase in the GDF-15 level was associated with ageing, ischemic heart disease, severity of arterial hypertension and heart failure, raising the risk of stroke, according to the scale CHA2DS2-VASc, disturbances of carbohydrate metabolism and obesity, increasing the levels h/s CRP and NT-proBNP, enlargement of the right and left atria, signs of diastolic left ventricular dysfunction and structural remodeling in the form of eccentric hypertrophy. Multiple linear regression analysis revealed 2 independent predictors of GDF-15 levels: age and fasting glucose. Conclusion. GDF-15 appears as an integral biomarker of age-related metabolic disorders and structural and functional changes in the heart, which opens up prospects for further study of its prognostic significance in pts with non-valvular AF.

It is well known that the quantum mutual information and its conditional version do not increase under local channels. I this paper we show that the recently established lower semicontinuity of the quantum conditional mutual information implies (in fact, is equivalent to) the lower semicontinuity of the loss of the quantum (conditional) mutual information under local channels considered as a function on the Cartesian product of the set of all states of a composite system and the sets of all local channels (equipped with the strong convergence). Some applications of this property are considered. New continuity conditions for the quantum mutual information and for the squashed entanglement in both bipartite and multipartite infinite-dimensional systems are obtained. It is proved, in particular, that the multipartite squashed entanglement of any countably-non-decomposable separable state with finite marginal entropies is equal to zero. Special continuity properties of the information gain of a quantum measurement with and without quantum side information are established that can be treated as robustness (stability) of these quantities w.r.t. perturbation of the measurement and the measured state., Comment: 32 pages, preliminary version, any comments and references are welcome

We describe the class (semigroup) of quantum channels mapping states with finite entropy into states with finite entropy. We show, in particular, that this class is naturally decomposed into three convex subclasses, two of them are closed under concatenations and tensor products. We obtain asymptotically tight universal continuity bounds for the output entropy of two types of quantum channels: channels with finite output entropy and energy-constrained channels preserving finiteness of the entropy., 21 pages, preliminary version, any comments are welcome. arXiv admin note: substantial text overlap with arXiv:1704.01905, arXiv:1907.02458

Aim To study the relationship between the serum level of growth differentiation factor 15 (GDF-15) and clinical and functional characteristics and severity of left atrial (LA) fibrosis in patients with nonvalvular atrial fibrillation (AF).Material and methods The study included 87 patients with nonvalvular AF (62 patients with paroxysmal AF and 25 patients with persistent AF) aged 27 to 72 years (mean age, 56.9±9.2 years, 32 women). 85 % of these patients had arterial hypertension (AH), 33 % had AH and ischemic heart disease, and 12.6 % had isolated AF and were hospitalized for primary catheter ablation. General clinical evaluation, echocardiography, laboratory tests including measurement of GDF-15 and NT-proBNP concentrations in blood were performed. As a surrogate substrate of LA fibrosis during the electroanatomical voltage mapping, the area of low-voltage (Results Median concentration of GDF-15 was 767.5 [590.0; 951.0] pg /ml. The GDF-15 level positively correlated with age, presence and severity of AH and chronic heart failure, body mass index, and degree of obesity, CHA2DS2 VASc score, level of NT-proBNP, and LA fibrosis area (Sf and Sf%) and negatively correlated with the indexes of left ventricular diastolic function, e′ septal and e′ lateral. The area of fibrosis increased with increasing GDF-15 concentrations divided into quartiles; Sf% exceeded 20 % at GDF-15 levels higher than median. After a comparative analysis of patients with Sf% ≤20 % and >20 %, statistically significantly different variables were included into a stepwise logistic regression analysis. Two independent predictors of LA fibrosis >20% were identified: a concentration of GDF-15 higher than median (odd ratio (OR), 3.318, 95 % confidence interval (CI): 1.184–9.298) and LA volume index (OR, 1.079, 95 % CI: 1.014–1.147). According to results of the ROC analysis, the area under the curve (AUC) was 0.762 (p=0.000), the model specificity was 72.3 %, sensitivity was 72.4 %, and the prediction accuracy was 72.4 %.Conclusion Blood levels of GDF-15 were associated with the presence and severity of major risk factors for AF and the area of LA fibrosis. In this study, a level of GDF-15 above the median and the LA volume index were independent predictors of LA fibrosis > 20% of the LA area.

We consider a family of equivalent norms (called operator -norms) on the algebra of all bounded operators on a separable Hilbert space induced by a positive densely defined operator on . By choosing different generating operators we can obtain the operator -norms producing different topologies, in particular, the strong operator topology on bounded subsets of . We obtain a generalised version of the Kretschmann-Schlingemann- Werner theorem, which shows that the Stinespring representation of completely positive linear maps is continuous with respect to the energy-constrained norm of complete boundedness on the set of completely positive linear maps and the operator -norm on the set of Stinespring operators. The operator -norms induced by a positive operator are well defined for linear operators relatively bounded with respect to the operator , and the linear space of such operators equipped with any of these norms is a Banach space. We obtain explicit relations between operator -norms and the standard characteristics of -bounded operators. Operator -norms allow us to obtain simple upper bounds and continuity bounds for some functions depending on -bounded operators used in applications. Bibliography: 29 titles.

Objectives – to identify a relationship of septal flash (SF) with a super-response to cardiac resynchronization therapy (CRT), apical rocking (AR) and signs of left bundle brunch block (LBBB) in patients with congestive heart failure (CHF). Material and methods. The study included 38 patients (92.1% men; mean age 54.3±9.4 years) with II-IV NYHA functional class CHF. Left bundle brunch block (LBBB) was diagnosed according to 3 criteria: American Heart Association (AHA) 2009, European Society of Cardiology (ESC) 2013, Strauss. Septal flash (SF, mechanical anomaly of interventricular septum (IVS) movement) is determined according to speckle tracking echocardiography (STE) and tissue Doppler imaging (TDI). The patients were divided into two groups: with SF (I group, n=8) and without SF (II group, n=30). Mean follow-up was 34.5 [13.8;55.3]. Results. At baseline the groups did not differ in main clinical characteristics including QRS. The left ventricular (LV) ejection fraction (EF) was higher in group I (33.1%±1.7 and 30.0%±4.0; p=0.044). Basal segment of IVS longitudinal strain (LS) delay by STE (258.0 [144.0;294.0] ms vs 323.5 [273.3;385.0] ms; р=0.024) and LS delay by TDI (176.0 [146.8;287.3] ms vs 415.5 [315.8;493.5] ms; р

Aim: to assess morpho-functional properties of left ventricle (LV) in patients with superresponse (SR) to CRT using the helical ventriсular band concept (HVB).Materials and methods: 56 patients were examined (mean age 54.0±9.9 years) at baseline and during follow-up visit: 48.8±25.6 months. Patients were divided into groups: I group (n=34) with decrease of LV end-systolic volume (ESV) ≥30% (superresponders) and II group (n=22) - decrease of LV ESV ˂30% (nonsuperresponders).Results: apical loop descendens segment (DS) and ascendens segment (AS) of HVB were evaluated according to the concept of F. Torrent-Guasp et al. According to the logistic regression mechanical interventricular delay (MID) (OR 1.072, 95% CI 1.017-1.131; p=0.01) and systolic thickening fraction (STF) of interventricular septum (IVS) DS (OR 0.944, 95% CI 0.895 - 0.995; p = 0.033) had an independent relationship with CRT SR. According to the ROC analysis the sensitivity and specificity of this model were 72.7% and 66.7% (AUC=0.769; р=0.001). AS STF of IVS was higher in SR (22.5 [0.0;40.0]% и 0.0 [0.0;25.0]%; р=0.005). The survival rate in group I was 85.1%, in group II was 63.6% (Log-Rank test p=0.019).Conclusion: SR is associated with a higher AS STF of IVS, higher MID, also with a higher survival rate.

We analyse possibility to extend a quantum operation (sub-unital normal completely positive linear map on the algebra $$\mathfrak{B}(\mathcal{H})$$ of bounded operators on a separable Hilbert space $$\mathcal{H}$$ ) to the space of all operators on $$\mathcal{H}$$ relatively bounded w.r.t. a given positive unbounded operator. We show that a quantum operation $$\Phi$$ can be uniquely extended to a bounded linear operator on the Banach space of all $$\sqrt{G}$$ -bounded operators on $$\mathcal{H}$$ provided that the operation $$\Phi$$ is $$G$$ -limited: the predual operation $$\Phi_{*}$$ maps the set of positive trace class operators $$\rho$$ with finite value of $$\textrm{Tr}\rho G$$ into itself. Assuming that $$G$$ has discrete spectrum of finite multiplicity we prove that for a wide class of quantum operations the existence of the above extension implies the $$G$$ -limited property. Applications to the theory of Bosonic Gaussian channels are considered.

Aim. To investigate the relationship between echocardiographic parameters and laboratory immune inflammation signs in patients after coronavirus disease 2019 (COVID-19) pneumonia depending on the left ventricular (LV) involvement according to speckle tracking echocardiography (STE).Material and methods. The study included 216 patients (men, 51,1%, mean age, 50,1±11,1 years). The examination was carried out in patients 3 months after COVID-19 pneumonia. Patients were divided in 3 groups: group I (n=41) — diffuse decrease (≥4 segments the same LV level) of longitudinal strain (LS) according to STE; group II (n=67) — patients with regional decrease (LS reduction ≥3 segments corresponding to systems of the anterior, circumflex or right coronary arteries); group III — patients without visual left ventricle involvement (n=108).Results. There were no significant differences in LV ejection fraction — 68,9±4,1% in group I, 68,5±4,4% in group II and 68,6±4,3 in group III (p=0,934). A decrease in the global longitudinal left ventricle strain was detected significantly more often in groups I and II compared with group III (-17,8±2,0, -18,5±2,0 and -20,8±1,8%, respectively; pConclusion. A relationship was found between diffuse and regional left ventricular involvement according to STE and signs of immune inflammation in patients 3 months after COVID-19 pneumonia.

We describe a generalized version of the result called quantum Dini lemma that was used previously for analysis of local continuity of basic correlation and entanglement measures. The generalization consists in considering sequences of functions instead of a single function. It allows us to expand the scope of possible applications of the method. We prove two general dominated convergence theorems and the theorem about preserving local continuity under convex mixtures. By using these theorems we obtain several convergence conditions for the quantum relative entropy and for the mutual information of a quantum channel considered as a function of a pair (channel, input state). A simple convergence criterion for the von Neumann entropy is also obtained., Comment: 32 pages, any comments are welcome. arXiv admin note: text overlap with arXiv:2201.11477

Aim To study changes in clinical and echocardiographic parameters in patients after documented COVID-19 pneumonia at 3 months and one year following discharge from the hospital. Material and methods The study included 116 patients who have had documented COVID-19 pneumonia. Patients underwent a comprehensive clinical evaluation at 3 months ± 2 weeks (visit 1) and at one year ± 3 weeks after discharge from the hospital (visit 2). Mean age of the patients was 49.0±14.4 years (from 19 to 84 years); 49.6 % were women. Parameters of global and segmentary longitudinal left ventricular (LV) myocardial strain were studied with the optimal quality of visualization during visit 1 in 99 patients and during visit 2 in 80 patients.Results During the follow-up period, the incidence rate of cardiovascular diseases (CVD) increased primarily due to development of arterial hypertension (AH) (58.6 vs. 64.7 %, р=0.039) and chronic heart failure (CHF) (35.3% vs. 40.5 %, р=0.031). Echocardiography (EchoCG) showed decreases in values of end-diastolic dimension and volume, LV end-systolic and stroke volumes (25.1±2.6 vs. 24.5±2.2 mm /m2, pConclusion Patients after COVID-19 pneumonia one year after discharge from the hospital, compared to the follow-up data 3 months after the discharge, had an increased incidence of CVD, primarily due to the development of AH and CHF. EchoCG revealed changes in ventricular geometry associated with impairment of LV diastolic and systolic function evident as decreases in LV global longitudinal strain and LV myocardial apical and partially mid-cavity strain.

Background COVID-19 affects firstly the respiratory system of patients however cardiovascular system is also damaged. To study the impact of a novel coronavirus infection on the cardiovascular system, in particular on echocardiographic parameters after SARS-CoV-2 is very important. Purpose To compare echocardiographic parameters in patients with COVID-19 pneumonia in hospital and 3 months after hospital discharge. Methods A total of 106 patients with confirmed COVID-19 pneumonia were included in the period from April to July 2020 within “One-year Cardiac Follow-up of COVID-19 Pneumonia”. All patients underwent clinical examination including transthoracic echocardiography in hospital and 3 months ± 2 weeks after discharge. Mean age of patients was 47±16 years (19–84 years), mean body mass index was 28.2±5.7 kg/m2, females were 49%. During hospitalization, chest computed tomography detected mild lesions in 29.2%, moderate lesions in 31.1%, severe lesions in 27.4% and critical lesions in 5.7%. Cardiovascular pathology detected in 52% of patients. Results Three months after discharge significant dynamics of mean echocardiographic parameters was observed. Left ventricular end-diastolic, end-systolic and stroke volume decreased (113.8±26.8 vs 93.5±29.4 ml; 37.7±13.0 vs 31.3±14.2 ml; 77.2±17.8 vs 62.2±18.7 ml, respectively; all p Conclusions In patients after COVID-19 pneumonia echocardiography showed decrease of the load predominantly on the right heart 3 months after discharge. A subgroup analysis is planned depending on the severity of lung damage and presence of cardiovascular pathology. Funding Acknowledgement Type of funding sources: None.

Introduction It is currently unknown what effect SARS-CoV-2 infection has on the parameters of aseptic inflammation in patients with cardiovascular diseases (CVD) in the long-term follow-up period and whether there is a relationship between the prolonged inflammatory response and the indicators of the global longitudinal strain, as the earliest marker of systolic dysfunction of left and right ventricles. Purpose To study the dynamics of markers of the inflammatory response and to assess the potential relationship of biomarkers of inflammation with parameters of left and right ventricular systolic function in patients with CVD who underwent COVID-19-associated pneumonia at the reference point 3 months after hospitalization. Methods The study included 63 patients (mean age 49.0±16.0 years) within “One-year Cardiac Follow-up of COVID-19 Pneumonia”. Group 1 (n=26) included patients without a history of CVD, group 2 (n=37) - patients with CVD. Three months after discharge from the hospital, patients came for a visit, where blood sampling and echocardiography with speckle tracking analysis were performed. Results At the stage of hospitalization, according to the computed tomography data, there were no differences in the volume of lung lesions in the groups. Patients with CVD had a higher level of highly sensitive C-reactive protein (CRP) upon admission to the hospital (group 1 – 33.12 [4.70–45.00] mg/l; group 2 – 47.16 [7.75–76.40] mg/L, p=0.039). Naturally, in the general group after 3 months, the indicators reflecting the inflammatory response significantly decreased: CRP from 26.10 [5.02–57.5] mg/L to 1.86 [0.76–3.43] mg/L, p In group 1, there were no laboratory biomarkers associated with the parameters of myocardial systolic function. In group 2 negative relationship was recorded between the global longitudinal strain of the left ventricle and the CRP level c (r=−0.388; p=0.037) and with the platelet-lymphocyte ratio (PLR) (r=−0.383; p=0.040); endocardial global longitudinal strain of the right ventricle with CRP level (r=−0.386; p=0.039). Conclusions In patients who underwent COVID-19-associated pneumonia, after 3 months, the dynamics of laboratory markers of the inflammatory response did not depend on the presence of concomitant cardiac pathology, but only in patients with CVD there was a negative relationship between indicators of systolic function of the left and right ventricles and biomarkers of the inflammatory response. Funding Acknowledgement Type of funding sources: None.

Background The presence of left atrial/left atrial appendage (LA/LAA) thrombus is used as a surrogate marker of potential stroke in patients (pts) with atrial fibrillation (AF). Purpose To assess the role of growth differentiation factor 15 (GDF-15) level, clinical and echocardiographic (EchoCG) data as predictors of LA/LAA thrombus in pts with nonvalvular AF. Methods Out of 158 pts with nonvalvular AF admitted to Cardiology Center for radiofrequency ablation or elective cardioversion in 2019–2020 2 groups were formed according to transesophageal EchoCG results: group 1 included pts without LA/LAA thrombus (n=102, mean age 59.5±6.0 years) and group 2 (n=42, mean age 60.9±8.8 years) – pts with LA/LAA thrombus. Arterial hypertension was found in 93 pts of group 1 (91%) and in 40 pts of group 2 (95%, p=0.42), coronary artery disease - in 53 pts (52%) and 29 pts (69%), respectively (p=0.06). Both groups did not differ in frequency and spectrum of oral anticoagulants administration. General clinical assessment, EchoCG, and laboratory tests were performed, including GDF-15 (pg/ml) levels using Human GDF-15/MIC-1 ELISA kit and NT-proBNP (pg/ml) in blood. Results Pts with LA/LAA thrombus more often had persistent AF, while paroxysmal AF was more common in pts without thrombus. There was a tendency to more significant congestive heart failure in group 2. Mean CHA2DS2-VASc score was higher in pts with LA/LAA thrombus, also there was a tendency to a larger proportion of pts with scores ≥3. According to EchoCG data, sizes and volumes of both atria, right ventricle, end-systolic volume, left ventricular (LV) size, pulmonary artery systolic pressure and LV mass index were higher in group 2; LV ejection fraction (LVEF) was normal in both groups, but it was significantly lower in pts with LA/LAA thrombus: 59.1±5.1 and 64.0±7.3, respectively (p935.0 pg/ml for GDF-15 (AUC=0.705, 95% CI 0.609–0.800, p143 pg/ml for NT-proBNP (AUC=0.759, 95% CI 0.670–0.849, p935.0 pg/ml (OR=4.132, 95% CI 1.305–13.084) and LVEF (OR=0.859, 95% CI 0.776–0.951). According to ROC analysis, the model had a good quality: AUC=0.776 (p Conclusion High level of GDF-15 (>935.0 pg/ml) along with lower LVEF are independent predictors of LA/LAA thrombus in pts with nonvalvular AF. Funding Acknowledgement Type of funding sources: None.

We show that for any energy observable every extreme point of the set of quantum states with bounded energy is a pure state. This allows us to write every state with bounded energy in terms of a continuous convex combination of pure states of bounded energy. Furthermore, we prove that any quantum state with finite energy can be represented as a continuous convex combination of pure states with the same energy. We discuss examples from quantum information theory., Comment: Preliminary version. Any comments and references are welcome

The article presents the experience of organizing research activities of schoolchildren at the Institute of Nuclear Physics and the Faculty of Physics of Moscow State University. The subject matter of the works is connected with different sections of nuclear physics, the study of which is especially important in secondary school. In the process of preparing for their implementation schoolchildren listen to a short course devoted to computer methods in physics. They then develop programmes to simulate various nuclear phenomena. A laboratory experiment is then conducted to check and correct the results of the simulation. The article presents two examples of works, the authors of which have successfully performed at various scientific and practical conferences for schoolchildren. The first one is related to the absorption of gamma radiation and the second to the study of cosmic radiation background. It is especially important to note that these works were conducted with pupils of Lyceum № 87 of Nizhny Novgorod in a partly remote format. This suggests that such work can be successfully performed by schoolchildren living in other cities and not having the opportunity to visit the laboratory frequently.

In the developing theory of infinite-dimensional quantum channels the relevance of the energy-constrained diamond norms was recently corroborated both from physical and information-theoretic points of view. In this paper we study necessary and sufficient conditions for differentiability with respect to these norms of the strongly continuous semigroups of quantum channels (quantum dynamical semigroups). We show that these conditions can be expressed in terms of the generator of the semigroup. We also analyze conditions for representation of a strongly continuous semigroup of quantum channels as an exponential series converging w.r.t. the energy-constrained diamond norm. Examples of semigroups having such a representation are presented.

For a given positive operator G we consider the cones of linear maps between Banach spaces of trace class operators characterized by the Stinespring-like representation with $$\sqrt G $$ -bounded and $$\sqrt G $$ -infinitesimal operators correspondingly. We prove the completeness of both cones w.r.t. the energy-constrained diamond norm induced by G (as an energy observable) and the coincidence of the second cone with the completion of the cone of completely positive linear maps w.r.t. this norm. We show that the sets of quantum channels and quantum operations are complete w.r.t. the energy-constrained diamond norm for any energy observable. Some properties of the maps belonging to the introduced cones are described. In particular, the corresponding generalization of the Kretschmann-Schlingemann-Werner theorem is obtained. We also give a nonconstructive description of the completion of the set of all Hermitian-preserving completely bounded linear maps w.r.t. the energy-constrained diamond norm.

Aim. To assess clinical and morpho-functional features of the heart in patients with congestive heart failure (CHF) after cardiac resynchronization therapy (CRT) depending on septal flash (SF).Materials and methods. The study enrolled 60 patients (92.0% men, 8.0% women; mean age 54.5 ± 10.4 years; 70.0% had left bundle branch block (LBBB) with II-IV NYHA functional class CHF. SF (mechanical anomaly of interventricular septum (IVS) movement) is determined according to speckle tracking echocardiography (STE) and tissue Doppler imaging (TDI). Patients were divided into two groups: with SF (I group, n = 10) and without SF (II group, n = 50).Results. At baseline the groups did not differ in main clinical characteristics including QRS width and LBBB. Mechanical interventricular delay was higher in group I (65.5 ms [53.5; 95.5] vs 31.0 ms [15.0; 64.5]; р = 0.026). Basal segment of IVS longitudinal strain (LS) delay by STE (257.5 ms [156.3; 293.8] vs 323.5 ms [262.5; 377.8]; р = 0.024) and LS delay by TDI (204.0 ms [170.8; 260.3] vs 434.0 ms [370.0; 489.0]; р < 0.001) were significantly lower in group with SF. According to logistic regression a combination of LS apical segment of IVS by STE (HR 0.607; 95% Cl 0.369–0.989; р = 0.048) and LS delay basal segment of IVS by TDI (HR 0.969; 95% Cl 0.0945–0.993; р = 0.011) had a relationship with SF. According to ROC analysis sensitivity and specificity of this model in SF definition in patients with CRT were 87.5% and 86.5% (AUC = 0.939; p < 0.01). Mean changes in LV ESV (52.0 ml [32.5; 72.8] vs 19,0 ml [1.3; 40.0]; р = 0.002) and LV ejection fraction (EF) (13.0% [5.5; 18.8] vs 4.0% [2.0; 9.0]; р = 0.002) were significantly higher in patients with SF. All patients in group I had a superresponse to CRT (ESV LV decrease ≥30%); 42.0% patients in group II were superresponders (р < 0.001).Conclusion. SF could be determined by STE and TDI. SF is associated with severe mechanical interventricular dyssynchrony and superresponse to CRT. Patients with SF have significantly better LV EF dynamics after CRT.

By using estimates for the variation of quantum mutual information and the relative entropy of entanglement, we obtain e-exact lower estimates for distances from a given quantum channels to sets of degradable, antidegradable, and entanglement-breaking channels. As an auxiliary result, we obtain e-exact lower estimates for the distance from a given two-particle state to the set of all separable states.

We present a family of easily computable upper bounds for the Holevo (information) quantity of an ensemble of quantum states depending on a reference state (as a free parameter). These upper bounds are obtained by combining probabilistic and metric characteristics of the ensemble. We show that an appropriate choice of the reference state gives tight upper bounds for the Holevo quantity which in many cases improve the estimates existing in the literature. We also present an upper bound for the Holevo quantity of a generalized ensemble of quantum states with finite average energy depending on the metric divergence of an ensemble. In the case of a multi-mode quantum oscillator, this upper bound is tight for large energy. Upper bounds for the Holevo capacity of finite-dimensional quantum channels depending on metric characteristics of the channel output are obtained.

Aim. To study the changes of morphological and functional right ventricular (RV) parameters depending on the severity of coronavirus infection 2019 (COVID-19) pneumonia over long-term follow-up.Material and methods. A total of 200 patients (men, 51,5%, mean age, 51,4±10,9 years) were examined at 2 control visits (3, 12 months after receiving two negative polymerase chain reaction tests). Patients were divided into following groups: group I (n=94) — lung tissue involvement ≥50% according to inhospital chest computed tomography (chest CT), group II (n=106) — lung tissue involvement˂50% according to chest CT.Results. The groups were comparable in key clinical and functional parameters 3 months after COVID-19 pneumonia. Speckle tracking echocardiography (STE) revealed a significant increase in following global longitudinal strain (LS) parameters: RV free wall endocardial LS (-22,7±3,2% and -24,3±3,8% in group I, p˂0,001; -23,2±3,5% and -24,5±3,4% in group II, p˂0,001), and RV endocardial LS (-21,0±3,1% and -22,5±3,7% in group I, p˂0,001, -21,5±3,2% and -22,6±3,3% in group II, p=0,001 ). Significant increase of segmental endocardial LS was revealed in group I in the basal segments of RV free wall (-26,2±5,1% and -28,1±5,1%, p=0,004) and interventricular septum (IVS) (-16,2 [13,9; 19,5]% and -17,5 [14,6; 21,4]%, p=0,024), IVS middle segment (-20,3±4,1% and -21,5±4,8%, p=0,030), as well as in group II in the apical segments of RV free wall (-21,9±6,7% and -24,4±5,2%, p=0,001) and IVS (-23,7±4,7% and -24,9±4,8%, p=0,014).Conclusion. Recovery of RV function during a 12-month follow-up period in patients with both severe and moderate/mild lung involvement in COVID-19 was detected using the STE method.

For a general renormalizable $\mathcal{N}=1$ supersymmetric gauge theory with a simple gauge group we verify the ultraviolet (UV) finiteness of the two-loop matter contribution to the triple gauge-ghost vertices. These vertices have one leg of the quantum gauge superfield and two legs corresponding to the Faddeev--Popov ghost and antighost. By an explicit calculation made with the help of the higher covariant derivative regularization we demonstrate that the sum of the corresponding two-loop supergraphs containing a matter loop is not UV divergent in the case of using a general $\ensuremath{\xi}$-gauge. In the considered approximation this result confirms the recently proved theorem that the triple gauge-ghost vertices are UV finite in all orders, which is an important ingredient of the all-loop perturbative derivation of the Novikov-Shifman-Vainshtein-Zakharov relation.

In [arXiv:1712.03219] the existence of a strongly (pointwise) converging sequence of quantum channels that can not be represented as a reduction of a sequence of unitary channels strongly converging to a unitary channel is shown. In this work we give a simple characterization of sequences of quantum channels that have the above representation. The corresponding convergence is called the strong* convergence, since it is related to the convergence of selective Stinespring isometries of quantum channels in the strong* operator topology. Some properties of the strong* convergence of quantum channels are considered. It is shown that for Bosonic Gaussian channels the strong* convergence coincides with the strong convergence., Comment: 18 pages, this is a strengthened extension of sections 6 and 7 from the previous version of arXiv:1712.03219, in v2 minor corrections are made and the case of Gaussian channels is added, any comments are welcome

Aim To study the role of blood concentration of growth differentiation factor 15 (GDF-15) as a predictor of left atrial/left atrial appendage (LA/LAA) thrombosis in patients with nonvalvular atrial fibrillation (AF).Material and methods 538 patients with nonvalvular AF were admitted to the Tyumen Cardiology Research Center in 2019–2020 for radiofrequency ablation and elective cardioversion. According to findings of transesophageal echocardiography (EcoCG), 42 (7.8%) of these patients had LA/LAA thrombosis and 79 (14.7%) of them had the effect of spontaneous echo contrast (SEC). This comparative, cross-sectional, cohort study included at the initial stage 158 successively hospitalized patients with nonvalvular AF: group 1 (with LA/LAA thrombosis, n=42) and group 2 (without LA/LAA thrombosis and without SEC, n=116). To eliminate significant differences in age between the groups, an additional inclusion criterium was introduced, age from 45 to 75 years. Finally, 144 patients were included into the study: group 1 (with LA/LAA thrombosis, n=42, mean age 60.9±7.2 years) and group 2 (without LA/LAA thrombosis and without SEC, n=116, mean age 59.5±6.0 years). 93 (91%) patients in group 1 and 40 (95%) patients in group 2 had arterial hypertension (p=0.4168); 53 (52%) and 29 (^(%), respectively, had ischemic heart disease (p=0.0611). The groups did not differ in sex, profile of major cardiovascular diseases, or frequency and range of oral anticoagulant treatment. General clinical evaluation, EchoCG, and laboratory tests, including measurements of blood concentrations of GDF-15 and NT-proBNP, were performed.Results In the group with LA/LAA thrombosis, 1) persistent AF prevailed whereas paroxysmal AF was more frequently observed in patients without thrombosis; 2) a tendency toward more pronounced chronic heart failure was observed; 3) tendencies toward a high median CHA2DS2‑VASc score and toward a greater proportion of patients with scores ≥3 were observed. According to EchoCG findings, group 1 had higher values of sizes and volumes of both atria and the right ventricle, left ventricular (LV) end-systolic volume and size, pulmonary artery systolic blood pressure, and LV myocardial mass index. LV ejection fraction (EF) was in the normal range in both groups but it was significantly lower for patients with LA/LAA thrombosis, 59.1±5.1 and 64.0±7.3, respectively (p=0.00006). Concentrations of GDF-15 (p=0.00025) and NT-proBNP were significantly higher in group 1 than in group 2 (p=0.000001). After determining the threshold values for both biomarkers using the ROC analysis, two independent predictors of LA/LAA thrombosis were obtained by the stepwise multiple regression analysis: GDF-15 >935.0 pg/ml (OR=4.132, 95 % CI 1.305–13.084) and LV EF (OR=0.859, 95 % CI 0.776–0.951). The ROC analysis assessed the model quality as good: AUC=0.776 (pConclusion For patients with nonvalvular AF, both increased GDF-15 (>935.0 pg/ml) and LV EF are independent predictors for LA/LAA thrombosis.

We consider a class (convex set) of quantum states containing all finite rank states and infinite rank states with the sufficient rate of decreasing of eigenvalues (in particular, all Gaussian states). Quantum states from this class are characterized by the property (called the FA-property) that allows to obtain several results concerning finite-dimensional approximation of basic entropic and information characteristics of quantum systems and channels. We obtain a simple sufficient condition of the FA-property. We show that this property implies finiteness of the von Neumann entropy, but leave unsolved the question concerning the converse implication. We obtain uniform approximation results for characteristics depending on a pair (channel, input state) and for characteristics depending on a pair (channel, input ensemble). We establish the uniform continuity of the above characteristics as functions of a channel w.r.t. the strong convergence provided that the FA-property holds either for the input state or for the average state of input ensemble., Comment: 26 pages, any comments are welcome

Objective The search for predictors of severe (>35 %) left atrial (LA) fibrosis in patients (pts) with nonvalvular atrial fibrillation (AF) directed for catheter ablation (CA).Materials and Methods 69 pts with nonvalvular AF (57 paroxismal and 12 persistent) aged from 32 to 69 years (mean age 57.1±8.4, 28 females) were included in the study, among them 59 pts (86 %) with arterial hypertension (AH), 24 (34.8 %) – with AH and CAD. Complete physical study, laboratory tests (including NT-proBNP level), comprehensive echocardiography were performed. As a surrogate substrate of LA fibrosis, the area of low-voltage (35 % were calculated. Degree IV of fibrosis was considered as severe fibrosis.Results Extent of fibrosis didn’t depend on sex, age, body weight, presence of diabetes, CHA2DS2VASc scores, duration of AF history. There was a tendency to smaller Sf in pts with spontaneous termination of AF compared to those who required cardioversion: 7.2 cm2 (4.4; 17.1) and 12.6 cm2 (4.2; 30.5), respectively (p=0.069). Although NT-proBNP level was normal in 62 % of pts (128 pg / ml – OR=6.184 (1.01; 37.99), LA volume index >34 ml / m2 – OR=5.92 (1.05; 33.38). According to ROC analysis, the area of the curve AUC = 0.839 (p35 %) LA fibrosis were LV geometry type in the form of eccentric LV hypertrophy, LA volume index >34 ml / m2 and NT-proBNP >128 pg / ml.

Aim. The aim is to assess clinical features of organism and morpho-functional properties of heart and to study the dynamics of mechanical dyssynchrony in patients with congestive heart failure and superresponse to cardiac resynchronization therapy.Material and Methods. 72 patients were examined (mean age 54.3±8.9 years) at baseline and during follow-up visits: 10.5±3.7 months, 52.0±21.4 months. Patients were divided into groups: I group (n=31) with decrease of left ventricle endsystolic volume ≥30% (superresponders) and II group (n=41) — decrease of left ventricle endsystolic volume Results. At baseline there were differences in the presence of myocardial infarction (22.5% in I group vs 46.3% in II group; p=0.038), the groups were comparable in severity of electrical and mechanical dyssynchrony. Left ventricle pre-ejection period in I group was statistically significantly decreased at both control visits, in group II there was no significant change. Right ventricular pre-ejection period significantly increased only in I group at the second control visit compared to baseline values. The mechanical interventricular delay significantly decreased in I group at both control visits compared to baseline values, in II group only at first control visit. The Intraventricular dyssynchrony assessed by tissue doppler imaging significantly decreased in both groups compared to baseline values. The survival rate in I group was 87.1%, in group II was 65.9% (Log-Rank test p=0.038).Discussion. Based on the results of the subanalysis of the Echo-CRT study, it was shown that a decrease in mechanical dyssynchrony in patients with cardiac resynchronization therapy is associated with a lower incidence of hospitalization due to heart failure or death. Persistent or worsening dyssynchrony according to echocardiography may be a marker of a severity of the disease in patients with congestive heart failure and has a prognostic value. It is important to note that in our study the described facts confirm the preservation of cardiac resynchronization therapy effect with long follow-up in superresponders and limited cardiac resynchronization therapy effect with short follow-up in nonsuperresponders.Conclusion. Superresponse is associated with a decrease of mechanical dyssynchrony with a long-term follow-up also with a higher survival rate.

The aim.To evaluate clinical, morphological, functional features and mortality in patients with congestive heart failure (CHF) and super-response to cardiac resynchronization therapy (CRT), to assess presence and severity of mechanical dyssynchrony in patients with super-response and to find potential predictors of super-response to CRT.Methods.106 CRT patients (mean age 54.7 ± 9.9 years; 83% men) with CHF II–IV NYHA functional class were enrolled for the study. At baseline and each 6 months after implantation clinical, electrocardiographic and echocardiographic parameters, NT-proBNP level were evaluated. According to the best decrease of left ventricular endsystolic volume (LVESV) (mean follow-up period 34.9 ± 16.1 months) patients were classified as super-responders (SR) (n = 45; reduction in LVESV ≥30%) and non-SR (n = 61; reduction in LVESV Results.At baseline groups were matched for main clinical characteristics. The proportion of patients with atrial fibrillation, width of the QRS complex, and the presence of left bundle-branch block were comparable between groups. Parameters of mechanical dyssynchrony were higher in SR: left ventricular pre-ejection period (LVPEP) (153.0 ± 35.9 ms vs 126.6 ± 35.1 ms; р = 0.005), interventricular mechanical delay (55.9 ± 30.8 ms vs 40.4 ± 29.9 ms; р = 0.049), systolic dyssynchrony index (9.6 ± 2.6% vs 7.2 ± 0.7%; р = 0.048). NT-proBNP level was lower in SR. SR demonstrated better dynamics of LVESV, LVEF. At baseline and in dynamics level of NT-proBNP was lower in SR. In both groups NT-proBNP decreased significantly, but reduction of NT-proBNP was more evident in SR. The survival rates were 100%in SR and 83.6% in non-SR (log rank test p = 0.002).According to multiple logistic regression analysis LVPEP (HR 1.025; 95% CI 1.006–1.044; p = 0.010) and baseline NT-proBNP level (HR 0.624; 95% CI 0.426–0.913; p = 0.015) were independent predictors for CRT super-response with sensitivity 71.9% and specificity 78.6%.Conclusion.In patients with CHF greater mechanical dyssynchrony and lower level of NT-proBNP are associated with CRT super-response. SR demonstrate better survival and better dynamics of functional parameters in long-term period. LVPEP and NT-proBNP level can be used as independent predictors of CRT super-response.

We consider a family of energy-constrained diamond norms on the set of Hermitian- preserving linear maps (superoperators) between Banach spaces of trace class operators. We prove that any norm from this family generates strong (pointwise) convergence on the set of all quantum channels (which is more adequate for describing variations of infinite-dimensional channels than the diamond norm topology). We obtain continuity bounds for information characteristics (in particular, classical capacities) of energy-constrained infinite-dimensional quantum channels (as functions of a channel) with respect to the energy-constrained diamond norms, which imply uniform continuity of these characteristics with respect to the strong convergence topology.

Coronavirus disease 2019 (COVID-19) affects the function of all organs and systems. Today, studying the effect of COVID-19 on cardiovascular system, including on echocardiographic characteristics, is relevant.Aim. To study the prevalence of symptoms, cardiovascular disease and changes in echocardiographic data in persons after documented COVID-19 pneumonia 3 months after discharge from the hospital.Material and methods. The study included 106 patients after documented COVID-19 pneumonia. The patients underwent a comprehensive examination during hospitalization and 3 months±2 weeks after discharge from the hospital. The mean age of participants was 47±16 years (19-84 years); 49% of subjects were women.Results. Three months after hospital discharge, the symptoms persisted in 86% of examined patients. There were significant echocardiographic changes as follows: a decrease in LV end-diastolic, end-systolic and stroke volume (113,8±26,8 ml vs 93,5±29,4 ml; 37,7±13,0 ml vs 31,3±14,2 ml; 77,2±17,8 ml vs 62,2±18,7 ml, respectively, pConclusion. In survivors of COVID-19 pneumonia three months after hospital discharge, complaints persisted in 86% of cases. Cardiovascular diseases were detected in 52% of participants, including hypertension in 48,1% and coronary artery disease in 15,1%. Compared with in-hospital data, the echocardiographic characteristics improved, which was expressed mainly in a decrease in right heart load.

We prove that for any infinite-dimensional quantum channel the entropic disturbance (defined as difference between the $\chi$-quantity of a generalized ensemble and that of the image of the ensemble under the channel) is lower semicontinuous on the natural set of its definition. We establish a number of useful corollaries of this property, in particular, we prove the continuity of the output $\chi\textrm{-}$quantity and the existence of $\chi$-optimal ensemble for any quantum channel under the energy-type input constraint., Comment: 22 pages, improved version

Background Superresponders to cardiac resynchronization therapy (CRT) demonstrate significant reverse remodeling, improvement in cardiac function, decrease in inflammatory mediators and markers of cardiac fibrosis. It is not clear if superresponse (SR) can be early or late and if the time of SR to CRT is associated with different degree of biochemical improvement. Aim To assess structural and functional heart parameters, sympathetic activity, levels of biomarkers of myocardial fibrosis, inflammatory and neurohormonal mediators in patients with various time of SR to CRT. Methods The study enrolled 82 superresponders to CRT (decrease in left ventricular end-systolic volume (LVESV) >30%) (mean age 60.4±9.3 years; 80.5% men, 19.5% women; 54.9% with ischemic etiology of heart failure). Patients were divided into two groups: group 1 (n=19) – SR was achieved within 24 months (14.0 [8.0; 21.0] months); group 2 (n=63) - SR was achieved after 24 months (59 [43.0; 84.0] months). Echocardiographic parameters, plasma levels of epinephrine, norepinephrine, NT-proBNP, interleukin (IL) 1β, IL-6, IL-10, tumor necrosis factor alpha (TNF-α), metalloproteinase (MMP) 9, tissue inhibitors of metalloproteinase (TIMP) 1 and 4 were evaluated. Results At baseline there were no differences in demographic, clinical and echocardiographic characteristics between the groups. Levels of epinephrine (1.1 [0.1; 2.2] ng/ml vs 2.1 [0.7; 3.4] ng/ml; p=0.049) and IL-10 (1.8 [1.5; 3.5] pg/ml vs 3.9 [2.7; 5.1] pg/ml; p=0.019) were significantly higher in group 2. Both groups demonstrated significant improvement in echocardiographic parameters. On follow-up left ventricular (LV) end-systolic dimension (p=0.041), LV end-diastolic dimension (p=0.049), LVESV (p=0.014), LV end-diastolic volume (p=0.045) were lower in group 2. In group 1 IL-6 (p=0.047), TNF-α (p=0.047) decreased significantly and there was a tendency for IL-1β (p=0.064) and norepinephrine (p=0.069) levels to increase. In group 2 levels of IL-1β (p Conclusion CRT modulates sympathetic, neurohumoral, immune and fibrotic activity. Late SR to CRT is associated with decrease of sympathetic and inflammatory activity and more pronounced LV reverse remodeling.

We find the three-loop contribution to the $\beta$-function of ${\cal N}=1$ supersymmetric gauge theories regularized by higher covariant derivatives produced by the supergraphs containing loops of the Faddeev--Popov ghosts. This is done using a recently proposed algorithm, which essentially simplifies such multiloop calculations. The result is presented in the form of an integral of double total derivatives in the momentum space. The considered contribution to the $\beta$-function is compared with the two-loop anomalous dimension of the Faddeev--Popov ghosts. This allows verifying the validity of the NSVZ equation written as a relation between the $\beta$-function and the anomalous dimensions of the quantum superfields. It is demonstrated that in the considered approximation the NSVZ equation is satisfied for the renormalization group functions defined in terms of the bare couplings. The necessity of the nonlinear renormalization for the quantum gauge superfield is also confirmed., Comment: 20 pages, 4 figures, minor corrections, the final version to appear in Eur.Phys.J. C

Hypothesis, internal, and output paths of the airborne, seaborne, and ground-based objects in a complex informational environment (low probability of detection, uncertainty and incompleteness of coordinates, maneuvering and group objects) onboard an aircraft are discussed. All measurements of internal and external sources operating in survey, passive detection, and tracking modes are used for calculation. For external sources the composition of transmitted data is determined. In the partial measurement of the coordinates, a complex aircraft control system is formed, which increases the accuracy of the paths of such objects and puts the aircraft in the conditions of a rocket launch with the maximum range.

Quantitative analysis of discontinuity of information characteristics of quantum states and channels is presented. Estimates for discontinuity jump (loss) of the von Neumann entropy for a given converging sequence of states are obtained. It is shown, in particular, that for any sequence the loss of entropy is upper bounded by the loss of mean energy (with the coefficient characterizing the Hamiltonian of a system). Then we prove that discontinuity jumps of basic measures of classical and quantum correlations in composite quantum systems are upper bounded by the loss of one of the marginal entropies (with a corresponding coefficient). Quantitative discontinuity analysis of the output entropy of a quantum operation and of basic information characteristics of a quantum channel considered as functions of a pair (channel, input state) is presented.

We show that a sequence $\{\Phi_n\}$ of quantum channels strongly converges to a quantum channel $\Phi_0$ if and only if there exist a common environment for all the channels and a corresponding sequence $\{V_n\}$ of Stinespring isometries strongly converging to a Stinespring isometry $V_0$ of the channel $\Phi_0$. We also give a quantitative description of the above characterization of the strong convergence in terms of the appropriate metrics on the sets of quantum channels and Stinespring isometries. As a result, the uniform selective continuity of the complementary operation with respect to the strong convergence is established. We show discontinuity of the unitary dilation by constructing a strongly converging sequence of channels which can not be represented as a reduction of a strongly converging sequence of unitary channels. The Stinespring representation of strongly converging sequences of quantum channels allows to prove the lower semicontinuity of the entropic disturbance as a function of a pair (channel, input ensemble). Some corollaries of this property are considered., Comment: 23 pages, in v6 the main results are strengthened essentially, in v5 section 6 devoted to application of the main results in quantum information theory is added, while sections 6-7 of v4 are replaced to a separate paper (arXiv:1802.05632)

We verify a recently proposed method for obtaining a β-function of N = 1 supersymmetric gauge theories regularized by higher derivatives by an explicit calculation. According to this method, a β-function can be found by calculating specially modified vacuum supergraphs instead of a much larger number of the two-point superdiagrams. The result is produced in the form of a certain integral of double total derivatives with respect to the loop momenta. Here we compare the results obtained for the three-loop β-function of N = 1 SQED in the general ξ-gauge with the help of this method and with the help of the standard calculation. Their coincidence confirms the correctness of the new method and the general argumentation used for its derivation. Also we verify that in the considered approximation the NSVZ relation is valid for the renormalization group functions defined in terms of the bare coupling constant and for the ones defined in terms of the renormalized coupling constant in the HD+MSL scheme, both its sides being gauge-independent.

We consider energy-constrained infinite-dimensional quantum channels from a given system (satisfying a certain condition) to any other systems. We show that dealing with basic capacities of these channels we may assume (accepting arbitrarily small error $\varepsilon$) that all channels have the same finite-dimensional input space -- the subspace corresponding to the $m(\varepsilon)$ minimal eigenvalues of the input Hamiltonian. We also show that for the class of energy-limited channels (mapping energy-bounded states to energy-bounded states) the above result is valid with substantially smaller dimension $m(\varepsilon)$. The uniform finite-dimensional approximation allows to prove the uniform continuity of the basic capacities on the set of all quantum channels with respect to the strong (pointwise) convergence topology. For all the capacities we obtain continuity bounds depending only on the input energy bound and the energy-constrained-diamond-norm distance between quantum channels (generating the strong convergence on the set of quantum channels)., Comment: 35 pages. In v.2 specification for energy-limited channels is added. Any comments are welcome. arXiv admin note: text overlap with arXiv:1610.08870