Class Of Functions Research Articles

Using $$P_\tau $$ property for designing bent functions provably outside the completed Maiorana–McFarland class

AbstractIn this article, we identify certain instances of bent functions, constructed using the so-called $$P_\tau $$ P τ property, that are provably outside the completed Maiorana–McFarland ($${\mathcal{M}\mathcal{M}}^\#$$ M M # ) class. This also partially answers an open problem in posed by Kan et al. (IEEE Trans Inf Theory, https://doi.org/10.1109/TIT.2022.3140180, 2022). We show that this design framework (using the $$P_\tau $$ P τ property), can provide instances of bent functions that are outside the known classes of bent functions, including the classes $${\mathcal{M}\mathcal{M}}^\#$$ M M # , $${{\mathcal {C}}},{{\mathcal {D}}}$$ C , D and $${{\mathcal {D}}}_0$$ D 0 , where the latter three were introduced by Carlet in the early nineties. We provide two generic methods for identifying such instances, where most notably one of these methods uses permutations that may admit linear structures. For the first time, a set of sufficient conditions for the functions of the form $$h(y,z)=Tr(y\pi (z)) + G_1(Tr_1^m(\alpha _1y),\ldots ,Tr_1^m(\alpha _ky))G_2(Tr_1^m(\beta _{k+1}z),\ldots ,Tr_1^m(\beta _{\tau }z))+ G_3(Tr_1^m(\alpha _1y),\ldots ,Tr_1^m(\alpha _ky))$$ h ( y , z ) = T r ( y π ( z ) ) + G 1 ( T r 1 m ( α 1 y ) , … , T r 1 m ( α k y ) ) G 2 ( T r 1 m ( β k + 1 z ) , … , T r 1 m ( β τ z ) ) + G 3 ( T r 1 m ( α 1 y ) , … , T r 1 m ( α k y ) ) to be bent and outside $${\mathcal{M}\mathcal{M}}^\#$$ M M # is specified without a strong assumption that the components of the permutation $$\pi $$ π do not admit linear structures.

Simultaneous transapical transcatheter aortic and mitral valve replacement in patients with severe valve dysfunction: initial experience.

Simultaneous transcatheter mitral valve in valve (VIV) replacement and aortic valve replacement experience is limited. We report our initial experience with simultaneous transapical transcatheter aortic and mitral valve replacement in patients with severe valve dysfunction. A total of 8 patients had simultaneous transcatheter heart valve implants for severe mitral bioprosthesis failure (VIV), with a second valve procedure that included native aortic regurgitation (n = 3) or degenerated bioprostheses in the aortic position (n = 5). All patients were treated with a self-expandable J-valve transcatheter valve, using the transapical approach. The mean age of the patients was 73.1 ± 6.2years. The mean Society of Thoracic Surgeons score was 13.8 ± 6.3%. Device success was 100% according to Valve Academic Research Consortium-2 criteria. No other procedure-associated complications occurred, including left ventricular outflow tract obstruction and valve migration. The mean hospital lengths of stay after the procedure were 11.5 ± 8.0days. No deaths occurred at 30days. At a median follow-up period of 28.7 ± 22.3months, no patients died. All patients were in New York Heart Association functional classes I-II. Echocardiographic parameters at follow-up showed a normofunctioning J valve in the mitral position and a mean max mitral flow velocity of 2.0 ± 0.5m/s; the J valve in the aortic position was also normofunctioning, and the mean max aortic flow velocity was 2.3 ± 0.5m/s. Simultaneous transapical transcatheter aortic and mitral valve replacement using the self-expandable J valve appears to be a feasible and effective alternative to redo surgery.

Evaluation of the European Society of Cardiology Risk Assessment Score in Incident Systemic Sclerosis-Associated Pulmonary Arterial Hypertension.

Patients with pulmonary arterial hypertension (PAH) may be stratified as low, intermediate, or high risk of 1-year mortality. In 2022, the European Society of Cardiology (ESC) updated and simplified its risk stratification tool, based on three variables: World Health Organization functional class, serum N-terminal pro-brain type natriuretic peptide and six-minute walk distance, applied at follow-up visits, intended to guide therapy over time. We applied the 2022 ESC risk assessment tool at baseline and follow-up (within 2 years) to a multinational incident cohort of systemic sclerosis-associated PAH (SSc-PAH). Kaplan-Meier curves, Cox hazards regression, and accelerated failure time models were used to evaluate survival by risk score. At baseline (n = 260), the majority of SSc-PAH (72.2%) were graded as intermediate risk of death according to the 2022 tool. At follow-up, according to 2022 tool, half (55.5%) of the cohort were classified as low or intermediate-low risk. The 2022 risk model at follow-up was able to differentiate survival between risk strata. All three individual parameters (World Health Organization functional class, N-terminal pro-brain type natriuretic peptide, six-minute walk distance) were significantly associated with mortality at baseline and/or follow-up. The 2022 ESC risk assessment strategy applied at baseline and follow-up predicts survival in SSc-PAH. Treatment decisions for SSc-PAH should include risk assessments, aiming to achieve low-risk status according to the 2022 ESC guidelines.

A report of fifty cases with incidental diagnosis of anomalous origin of the right coronary artery from the left sinus of Valsalva

IntroductionAnomalous origin of the right coronary artery from the left sinus of Valsalva (R-ACAOS) is a relatively rare condition that can potentially lead to devastating outcomes. The current study aims to investigate the cardiac-related disorders among patients with incidental R-ACAOS diagnosis through computed tomography angiography (CTA). MethodsThe current cross-sectional study has been conducted on 50 patients diagnosed with R-ACAOS who underwent CTA. Based on CTA, the patients' were categorized as R-ACAOS with interarterial course and non-interarterial course. The demographic and medical characteristics, any history of cardiac intervention and New York Heart Association (NYHA) Functional Classification at the time of diagnosis were recruited. Patients were revisited to assess cardiac-associated variables, including symptoms, the presence of heart failure and current NYHA function class. ResultsThe variables including the history of cardiac intervention (P-value<0.001), the presence of heart failure (P-value = 0.010) and NYHA function class at the time of diagnosis (P-value = 0.006) were remarkably higher among those with interarterial course of R-ACAOS; while, the other variables including chest pain at rest (P-value = 0.55) or on exertion (P-value = 0.12), current NYHA function class, current cardiac-associated symptoms except for dyspnea at rest (P-value = 0.012), mortality and coronary calium score did not differ (P-value>0.05). coronary interventions led to significantly improved NYHA function class (P-value<0.05). ConclusionBased on the findings of the current study, R-ACAOS with interarterial course leads to significantly higher rates of atherosclerotic-related symptoms and events compared with the other types of RCA anomalies. Moreover, coronary interventions led to significantly improved NYHA functional class regardless of R-ACAOS category.

On a Class of Certain Non-univalent Functions

On a Class of Certain Non-univalent Functions

Nitroprusside Combined with Leg Raise at the Time of Right Heart Catheterization to Differentiate Precapillary from Other Hemodynamic Forms of Pulmonary Hypertension: A Single-Center Pilot Study.

Pulmonary hypertension (PH) can arise from several distinct disease processes, with a percentage presenting with combined pre- and postcapillary pulmonary hypertension (cpcPH). Patients with cpcPH are unsuitable candidates for PH-directed therapies due to elevated pulmonary capillary wedge pressures (PCWPs); however, the PCWP is dynamic and is affected by both preload and afterload. Many patients that are diagnosed with cpcPH are hypertensive at the time of right heart catheterization which has the potential to increase the PCWP and, therefore, mimic a more postcapillary-predominant phenotype. In this small pilot study, we examine the effect of nitroprusside combined with dynamic preload augmentation with a passive leg raise maneuver in hypertensive cpcPH patients at the time of right heart catheterization to identify a more precapillary-dominant PH phenotype. Patients that met the criteria of PCWP ≤ 15 mmHg with nitroprusside infusion and PCWP ≤ 18 mmHg with nitroprusside infusion and simultaneous leg raise were started on pulmonary vascular-targeted therapy. Long-term PH therapy was well tolerated, with increased six-minute walk distance, improved WHO functional class, decreased NT-proBNP, and improved REVEAL 2.0 Lite Risk Score in this precapillary-dominant PH phenotype. This small study highlights the importance of characterizing patient physiology beyond resting conditions at the time of right heart catheterization.

Bridging the p-Special Functions between the Generalized Hyperbolic and Trigonometric Families

Here, we study the extension of p-trigonometric functions sinp and cosp family in complex domains and p-hyperbolic functions sinhp and the coshp family in hyperbolic complex domains. These functions satisfy analogous relations as their classical counterparts with some unknown properties. We show the relationship of these two classes of special functions viz. p-trigonometric and p-hyperbolic functions with imaginary arguments. We also show many properties and identities related to the analogy between these two groups of functions. Further, we extend the research bridging the concepts of hyperbolic and elliptical complex numbers to show the properties of logarithmic functions with complex arguments.

Inclusion Results on Hypergeometric Functions in a Class of Analytic Functions Associated with Linear Operators

Inclusion Results on Hypergeometric Functions in a Class of Analytic Functions Associated with Linear Operators

Self-Reported Cancer-Related Cognitive Impairment in Patients With Breast Cancer Is Associated With Potassium Channel Gene Polymorphisms.

To evaluate for associations of polymorphisms for potassium channel genes in patients with breast cancer who were classified as having high or low-moderate levels of cancer-related cognitive impairment (CRCI). 397 women who were scheduled to undergo surgery for breast cancer on one breast were recruited from breast care centers located in a comprehensive cancer center, two public hospitals, and four community practices. CRCI was assessed using the Attentional Function Index prior to and for six months after surgery. The attentional function classes were identified using growth mixture modeling. Differences between patients in the high versus low-moderate attentional function classes were evaluated. Six single nucleotide polymorphisms for potassium channel genes were associated with low-moderate class membership. The results contribute to knowledge of the mechanisms for CRCI. These findings may lead to the identification of high-risk patients and the development of novel therapeutics.

Circulating miRNA in functional tricuspid regurgitation. Unveiling novel links to heart failure: A pilot study.

Severe functional tricuspid regurgitation (FTR) is associated with high risk of cardiovascular events, particularly heart failure (HF) and mortality. MicroRNAs (miRNAs) have been recently identified as novel biomarkers in different cardiovascular conditions, but no studies have focused on FTR. We sought to (1) to identify and validate circulating miRNAs as regulators of FTR and (2) to test association of miRNA with heart failure and mortality in FTR. Consecutive patients with isolated severe FTR (n=100) evaluated in the outpatient Heart Valve Clinic and age- and gender-matched subjects with no TR (controls, n=50) were prospectively recruited. The experimental design included (1) a screening phase to identify candidate miRNA differentially expressed in FTR (n=8) compared with controls (n=8) through miRNA array profiling of 192 miRNAs using quantitative reverse transcription PCR arrays [qRT-PCR]) and (2) a validation phase in which candidate miRNAs identified in the initial screening were selected for further validation by qRT-PCR in a prospectively recruited cohort of FTR (n=92) and controls (n=42). Bioinformatics analysis was used to predict their potential target genes and functional pathways elicited. A combined endpoint of hospital admission due to heart failure (HF) and all-cause mortality was defined. Initial screening identified 16 differentially expressed miRNAs in FTR compared with controls, subsequently confirmed in the validation phase (n=16 were excluded due to significant haemolysis). miR-186-5p, miR-30e-5p, and miR-152-3p identified FTR with high predictive value [AUC of 0.93 (0.88-0.97), 0.83 (0.75-0.91) and 0.84 (0.76-0.92), respectively]. During a median follow-up of 20.4months (IQR 8-35months), 32% of FTR patients reached the combined endpoint. Patients with low relative expression of miR-15a-5p, miR-92a-3p, miR101-3p, and miR-363-3p, miR-324-3p, and miR-22-3p showed significantly higher rates of events (log-rank test for all P<0.01). Both miR-15a-5p [hazard ratio: 0.21 (0.06-0.649, P=0.007) and miR-92a-3p (0.27 (0.09-0.76), P=0.01] were associated with outcomes after adjusting for age, gender, and New York Heart Association functional class. Circulating miRNAs are novel diagnostic and prognostic biomarkers in severe FTR. The quantification of miR-186-5p, miR-30e-5p, and miR-152-3p held strong diagnostic value, and the quantification of miR-15a-5p and miR-92a-3p are independently associated with outcomes. The recognition of specific miRNAs offers a novel perspective for TR evaluation.

[Initial experience with cardiac contractility modulation devices in Latin America for the treatment of heart failure].

To describe the initial experience of cardiac contractility modulation (CCM) implantation in Latin America. We present the first two cases in Latin America of patients with heart failure with reduced left ventricular ejection fraction (LVEF) not candidates for cardiac resynchronization therapy in whom a CCM device was implanted. Results. In both patients we described improvement of the 6-minute walk test, functional class according to the NYHA and LVEF. The modulation of cardiac contractility is currently a treatment option for patients with heart failure in functional class III-IV, with LVEF 25-45%, and a QRS < 130 ms who are not candidates for cardiac resynchronization therapy.

Concurrent Resistance and Cardiorespiratory Training in Patients with Hypertrophic Cardiomyopathy: A Pilot Study.

Background: Exercise training in patients with HCM has evidenced benefits on functional capacity, cardiac function, and a reversion of adverse cardiac remodeling. The objective of this study was to assess the effect of a concurrent resistance and cardiorespiratory training program on functional capacity, biochemical parameters, and echocardiographic variables in a pilot group. Methods: Two HCM patients were evaluated before and after 12 weeks of individualized concurrent training with two sessions/week. Pre- and post-training data were compared for each patient. Evaluations included a cardiopulmonary exercise test (CPET), body composition, echocardiography, electrocardiography, and blood analysis. Results: Training promoted an increase in functional capacity (+4 mL·kg-1·min-1), ventilatory thresholds, and other CPET-derived variables associated with a better prognosis and long-term survival. Muscular mass was augmented (0.8 and 1.2 kg), along with a mean increase of 62% in upper and lower body strength. Echocardiographic features demonstrated the maintenance of cardiac function with signs of positive left ventricular remodeling and an improvement in diastolic function. Blood analyses, including cardiac troponins and NT-proBNP, displayed uneven changes in each patient, but the values fell into normal ranges in both cases. Conclusions: The available data suggest a positive effect of concurrent resistance and cardiorespiratory training on patients' functional capacity and cardiac function that may improve their functional class, quality of life, and long-term prognosis. The replication of this protocol in a larger cohort of patients is warranted to confirm these preliminary results.

Long‐term efficacy and safety of tailored immunosuppressive therapy in immune‐mediated biopsy‐proven myocarditis: A propensity‐weighted study

AbstractAimsStandardized immunosuppressive therapy (IS) had been previously investigated in biopsy‐proven (BP) lymphocytic myocarditis with heart failure (HF). This study evaluated efficacy and safety of tailored IS in BP immune‐mediated myocarditis, irrespective of histology and clinical presentation.Methods and resultsConsecutive BP myocarditis patients treated with long‐term tailored IS on top of optimal medical therapy (OMT), were compared with OMT non‐IS controls using propensity‐score weighting. The primary outcome was a composite of death or heart transplant, the secondary outcome was a composite of biventricular function, New York Heart Association (NYHA) class variation, and relapse. IS was managed by a multidisciplinary Cardioimmunology Team, involved a safety checklist and active patients' education. Ninety‐one IS patients were compared with 267 non‐IS patients. IS patients more frequently had systemic immune‐mediated diseases (35% vs. 9.7%), lower baseline echocardiographic left ventricular ejection fraction (35% vs. 43%), lower right ventricular fractional area change (34% vs. 41%) and higher frequency of active lymphocytic, eosinophilic and giant cell myocarditis (71% vs. 58%, 12% vs. 1.1%, and 6.6% vs. 1.5%, respectively). At 5‐year follow up, no difference was observed in the primary outcome (survival rate 93% in IS vs. 87% in non‐IS), but IS patients had a higher relapse rate. Thus, IS patients, with a lower biventricular function and a higher risk profile at baseline, presented similar biventricular function and NYHA class to non‐IS patients at follow‐up. Minor adverse drug reactions occurred in 13% of patients, all resolved with therapy switch.ConclusionsProlonged tailored IS is effective and safe in BP immune‐mediated myocarditis irrespective of histology and clinical presentation.

Variable selection using data splitting and projection for principal fitted component models in high dimension

Sufficient dimension reduction (SDR) is such an effective way to detect nonlinear relationship between response variable and covariates by reducing the dimensionality of covariates without information loss. The principal fitted component (PFC) model is a way to implement SDR using some class of basis functions, however the PFC model is not efficient when there are many irrelevant or noisy covariates. There have been a few studies on the selection of variables in the PFC model via penalized regression or sequential likelihood ratio test. A novel variable selection technique in the PFC model has been proposed by incorporating a recent development in multiple testing such as mirror statistics and random data splitting. It is highlighted how we construct a mirror statistic in the PFC model using the idea of projection of coefficients to the other space generated from data splitting. The proposed method is superior to some existing methods in terms of false discovery rate (FDR) control and applicability to high-dimensional cases. In particular, the proposed method outperforms other methods as the number of covariates tends to be getting larger, which would be appealing in high dimensional data analysis. Simulation studies and analyses of real data sets have been conducted to show the finite sample performance and the gain that it yields compared to existing methods.

A global method for relaxation for multi-levelled structured deformations

We prove an integral representation result for a class of variational functionals appearing in the framework of hierarchical systems of structured deformations via a global method for relaxation. Some applications to specific relaxation problems are also provided.

Non occurrence of the Lavrentiev gap for a class of nonautonomous functionals

Non occurrence of the Lavrentiev gap for a class of nonautonomous functionals

Some properties of a class of holomorphic functions associated with tangent function

Abstract In this study, we define new class of holomorphic functions associated with tangent function. Furthermore, we examine the differential subordination implementation results related to Janowski and tangent functions. Also, we investigate some extreme point theorem and partial sums results, necessary and sufficient conditions, convex combination, closure theorem, growth and distortion bounds, and radii of close-to-starlikeness and starlikeness for this newly defined functions class of holomorphic functions.

Distortion, Radius of Concavity and Several Other Radii Results for Certain Classes of Functions

Distortion, Radius of Concavity and Several Other Radii Results for Certain Classes of Functions

Majorization property for specific classes of analytic functions

Majorization property for specific classes of analytic functions

Summation formulae of multiplicative functions over arithmetic progressions and applications

Abstract In this paper, we investigate the asymptotic distribution of a class of multiplicative functions over arithmetic progressions without the Ramanujan conjecture. We also apply these results to some interesting arithmetic functions in automorphic context, such as coefficients of automorphic L-functions, coefficients of their Rankin–Selberg.