Class Of Functions Research Articles

New Class of Multivalent Functions Defined by Generalized (p,q)-Bernard Integral Operator

Making use of the generalized $(p, q)$-Bernardi integral operator, we introduce and study a new class $\mathcal{F J}_{p, q}^m(\alpha, \delta, \lambda, \gamma)$ of multivalent analytic functions with negative coefficients in the open unit disk $E$. Several geometric characteristics are obtained, like, coefficient estimate, radii of convexity, close-to-convexity and starlikeness, closure theorems, extreme points, integral means inequalities, neighborhood property and convolution properties for functions belonging to the class $\mathcal{F} \mathcal{J}_{p, q}^m(\alpha, \delta, \lambda, \gamma)$.

Optimal Estimators of Cross-Partial Derivatives and Surrogates of Functions

Computing cross-partial derivatives using fewer model runs is relevant in modeling, such as stochastic approximation, derivative-based ANOVA, exploring complex models, and active subspaces. This paper introduces surrogates of all the cross-partial derivatives of functions by evaluating such functions at N randomized points and using a set of L constraints. Randomized points rely on independent, central, and symmetric variables. The associated estimators, based on NL model runs, reach the optimal rates of convergence (i.e., O(N−1)), and the biases of our approximations do not suffer from the curse of dimensionality for a wide class of functions. Such results are used for (i) computing the main and upper bounds of sensitivity indices, and (ii) deriving emulators of simulators or surrogates of functions thanks to the derivative-based ANOVA. Simulations are presented to show the accuracy of our emulators and estimators of sensitivity indices. The plug-in estimates of indices using the U-statistics of one sample are numerically much stable.

Evaluation of heritability partitioning approaches in livestock populations

BackgroundHeritability partitioning approaches estimate the contribution of different functional classes, such as coding or regulatory variants, to the genetic variance. This information allows a better understanding of the genetic architecture of complex traits, including complex diseases, but can also help improve the accuracy of genomic selection in livestock species. However, methods have mainly been tested on human genomic data, whereas livestock populations have specific characteristics, such as high levels of relatedness, small effective population size or long-range levels of linkage disequilibrium.ResultsHere, we used data from 14,762 cows, imputed at the whole-genome sequence level for 11,537,240 variants, to simulate traits in a typical livestock population and evaluate the accuracy of two state-of-the-art heritability partitioning methods, GREML and a Bayesian mixture model. In simulations where a single functional class had increased contribution to heritability, we observed that the estimators were unbiased but had low precision. When causal variants were enriched in variants with low (< 0.05) or high (> 0.20) minor allele frequency or low (below 1st quartile) or high (above 3rd quartile) linkage disequilibrium scores, it was necessary to partition the genetic variance into multiple classes defined on the basis of allele frequencies or LD scores to obtain unbiased results. When multiple functional classes had variable contributions to heritability, estimators showed higher levels of variation and confounding between certain categories was observed. In addition, estimators from small categories were particularly imprecise. However, the estimates and their ranking were still informative about the contribution of the classes. We also demonstrated that using methods that estimate the contribution of a single category at a time, a commonly used approach, results in an overestimation. Finally, we applied the methods to phenotypes for muscular development and height and estimated that, on average, variants in open chromatin regions had a higher contribution to the genetic variance (> 45%), while variants in coding regions had the strongest individual effects (> 25-fold enrichment on average). Conversely, variants in intergenic or intronic regions showed lower levels of enrichment (0.2 and 0.6-fold on average, respectively).ConclusionsHeritability partitioning approaches should be used cautiously in livestock populations, in particular for small categories. Two-component approaches that fit only one functional category at a time lead to biased estimators and should not be used.

Early anticoagulation after aortic valve replacement with porcine bioprosthesis randomized control trial(ANTIPRO). 3 years follow-up

BackgroundMost evidence for anticoagulation in aortic bioprosthesis is centered on embolic events, bleeding and re-intervention risk. The effect of anticoagulation on hemodynamics has not been previously assessed. Our hypothesis was that patients with anticoagulation (AC) early after aortic valve replacement (AVR) with porcine bioprosthesis have better hemodynamics at 3 years of follow-up. MethodsThis is a follow-up evaluation of the ANTIPRO trial. All patients undergoing AVR with porcine bioprosthesis were consecutively recruited. The AC group received warfarin+aspirin and the non-AC(control) only aspirin. The primary outcome was mean gradient after 3 years of AVR and change in New York Heart Association (NYHA) class. Secondary outcomes were major and minor bleeding and embolic events. ResultsOf 140 participants in the study, 71 were assigned to the AC group and 69 to the control group. Mean age of the overall population was 72.4(SD: 7.1) years. Global euroSCORE was 7.65(SD: 5.73). At 3 years the mean gradient was similar between both groups (19.4(SD: 9.6 mmHg) and 18.6(SD: 8.2 mmHg) in the control and AC group respectively, p = 0.7). No differences in functional class at 3 years were found among groups. No differences were found among groups in the secondary outcomes. ConclusionsThe addition of 3 months of oral anticoagulation to anti-aggregation treatment did not affect bioprosthetic hemodynamics nor functional class at years after AVR.

Trigonometric Lagrange-Jacobi functions

This paper presents a class of trigonometric Lagrange-mesh functions constructed from the Lagrange-Jacobi functions. These functions extend the set of trigonometric Lagrange-mesh functions to beyond only those constructed directly from the sine and cosine functions. Trigonometric Lagrange-Chebyshev functions obtained from the presented trigonometric Lagrange-Jacobi functions are equivalent to known trigonometric Lagrange-Chebyshev functions constructed directly from the sine and cosine functions and generate identical matrix elements for the kinetic energy operator.

Fuzzy Differential Subordination for Classes of Admissible Functions Defined by a Class of Operators

Fuzzy Differential Subordination for Classes of Admissible Functions Defined by a Class of Operators

Eligibility of Asian and European registry patients for phase III trials in heart failure with reduced ejection fraction.

Traditional approaches to designing clinical trials for heart failure (HF) have historically relied on expertise and past practices. However, the evolving landscape of healthcare, marked by the advent of novel data science applications and increased data availability, offers a compelling opportunity to transition towards a data-driven paradigm in trial design. This research aims to evaluate the scope and determinants of disparities between clinical trials and registries by leveraging natural language processing for the analysis of trial eligibility criteria. The findings contribute to the establishment of a robust design framework for guiding future HF trials. Interventional phase III trials registered for HF on ClinicalTrials.gov as of the end of 2021 were identified. Natural language processing was used to extract and structure the eligibility criteria for quantitative analysis. The most common criteria for HF with reduced ejection fraction (HFrEF) were applied to estimate patient eligibility as a proportion of registry patients in the ASIAN-HF (N=4868) and BIOSTAT-CHF registries (N=2545). Of the 375 phase III trials for HF, 163 HFrEF trials were identified. In these trials, the most frequently encountered inclusion criteria were New York Heart Association (NYHA) functional class (69%), worsening HF (23%), and natriuretic peptides (18%), whereas the most frequent comorbidity-based exclusion criteria were acute coronary syndrome (64%), renal disease (55%), and valvular heart disease (47%). On average, 20% of registry patients were eligible for HFrEF trials. Eligibility distributions did not differ (P=0.18) between Asian [median eligibility 0.20, interquartile range (IQR) 0.08-0.43] and European registry populations (median 0.17, IQR 0.06-0.39). With time, HFrEF trials became more restrictive, where patient eligibility declined from 0.40 in 1985-2005 to 0.19 in 2016-2022 (P=0.03). When frequency among trials is taken into consideration, the eligibility criteria that were most restrictive were prior myocardial infarction, NYHA class, age, and prior HF hospitalization. Based on 14 trial criteria, only one-fifth of registry patients were eligible for phase III HFrEF trials. Overall eligibility rates did not differ between the Asian and European patient cohorts.

Eligibility of Asian and European registry patients for phase III trials in heart failure with reduced ejection fraction.

Traditional approaches to designing clinical trials for heart failure (HF) have historically relied on expertise and past practices. However, the evolving landscape of healthcare, marked by the advent of novel data science applications and increased data availability, offers a compelling opportunity to transition towards a data-driven paradigm in trial design. This research aims to evaluate the scope and determinants of disparities between clinical trials and registries by leveraging natural language processing for the analysis of trial eligibility criteria. The findings contribute to the establishment of a robust design framework for guiding future HF trials. Interventional phase III trials registered for HF on ClinicalTrials.gov as of the end of 2021 were identified. Natural language processing was used to extract and structure the eligibility criteria for quantitative analysis. The most common criteria for HF with reduced ejection fraction (HFrEF) were applied to estimate patient eligibility as a proportion of registry patients in the ASIAN-HF (N=4868) and BIOSTAT-CHF registries (N=2545). Of the 375 phase III trials for HF, 163 HFrEF trials were identified. In these trials, the most frequently encountered inclusion criteria were New York Heart Association (NYHA) functional class (69%), worsening HF (23%), and natriuretic peptides (18%), whereas the most frequent comorbidity-based exclusion criteria were acute coronary syndrome (64%), renal disease (55%), and valvular heart disease (47%). On average, 20% of registry patients were eligible for HFrEF trials. Eligibility distributions did not differ (P=0.18) between Asian [median eligibility 0.20, interquartile range (IQR) 0.08-0.43] and European registry populations (median 0.17, IQR 0.06-0.39). With time, HFrEF trials became more restrictive, where patient eligibility declined from 0.40 in 1985-2005 to 0.19 in 2016-2022 (P=0.03). When frequency among trials is taken into consideration, the eligibility criteria that were most restrictive were prior myocardial infarction, NYHA class, age, and prior HF hospitalization. Based on 14 trial criteria, only one-fifth of registry patients were eligible for phase III HFrEF trials. Overall eligibility rates did not differ between the Asian and European patient cohorts.

Decentralized asymptotic tracking control for time‐varying interconnected nonlinear systems with prescribed performance

AbstractThis article studies decentralized adaptive asymptotic tracking control of time‐varying interconnected nonlinear systems. To address the obstacles caused by interactions and these unknown time‐varying parameters, a smooth function and a bound estimation approach are introduced. Additionally, by means of a class of funnel functions and barrier Lyapunov function approach, a prescribed performance control strategy is constructed, allowing tracking accuracy and the settling time to be predetermined in accordance with control requirements, without relying on initial conditions or design parameters. Particularly, reasoned proofs have been given to confirm that the presented control method not only guarantees the prescribed transient performance, but also achieves the asymptotic tracking without requiring knowledge of high‐order derivatives of the reference signal. Ultimately, the efficiency of our approach is verified by simulation results.

Prognoses and risk stratification of thrombus-associated events in heart failure patients without atrial fibrillation.

We aim to assess the risk of thrombus-associated events (TAE) in patients with heart failure (HF) without atrial fibrillation (AF) and develop an effective scoring system for a risk stratification model. This retrospective study included 450 patients (median age 64.0years, interquartile range [55.0, 75.0]; 31.6% women) hospitalized for HF without AF and atrial flutter, but with a left ventricular ejection fraction (LVEF)≤55% and New York Heart Association (NYHA) functional class of III-IV. A median follow-up of 47months was conducted. In the present study, TAE during follow-up was independently associated with both all-cause death [hazard ratio (HR) 1.756, 95% confidence interval (CI) 1.324-2.328, P<0.001] and readmission for HF (HR 1.574, 95% CI 1.122-2.208, P=0.009) after adjustment for covariates. Hypertension (HR 1.573, 95% CI 1.018-2.429, P=0.041), atrial arrhythmia excluding AF (AAexAF) (HR 2.041, 95% CI 1.066-3.908, P=0.031), previous ischaemic stroke (HR 2.469, 95% CI 1.576-3.869, P<0.001), and vascular disease (HR 1.658, 95% CI 1.074-2.562, P=0.023) were independently associated with TAE. Age (HR 1.021, 95% CI 1.008-1.033, P=0.001), previous ischaemic stroke (HR 1.685, 95% CI 1.248-2.274, P=0.001), LVEF ([10, 25] vs. [40, 55]) HR 1.925, 95% CI 1.311-2.826, P=0.001; (25, 40] vs. (40, 55] HR 1.084, 95% CI 0.825-1.424, P=0.563), and creatinine clearance rate (Ccr) (HR 0.991, 95% CI 0.986-0.996, P=0.001) were independently associated with composite events of TAE and death (TAE-D). CHA2DS2VASc modestly predicted 5-year TAE [area under the receiver operating characteristic curves (AUC) 0.660, P<0.001 compared with 0.5] and TAE-D (AUC 0.639, P<0.001 compared with 0.5). (C)ACE, formed by incorporating AAexAF, LVEF, and Ccr into CHA2DS2VASc, had higher AUC for predicting 5-year TAE (0.694 vs. 0.660, P=0.018) and TAE-D (0.708 vs. 0.639, P<0.001) compared with CHA2DS2VASc. In patients with HF with reduced ejection fraction (HFrEF), (C)ACE and (C)ACEN [formed by incorporating NYHA into (C)ACE] had higher AUC compared with CHA2DS2VASc in predicting 5-year TAE (0.700 and 0.707 vs. 0.649, P=0.013 and 0.030, respectively) and TAE-D (0.712 and 0.713 vs. 0.622, P<0.001 and <0.001, respectively). The AUC did not improve statistically from (C)ACE to (C)ACEN (0.700 vs. 0.707, P=0.600 for TAE; 0.712 vs. 0.713, P=0.917 for TAE-D). In HF without AF, TAE during follow-up was associated with adverse prognoses. The independent risk factors of TAE or TAE-D improved CHA2DS2-VASc predictive ability, especially in patients with HFrEF. Our findings provide new evidence for TAE risk stratification in HF without AF, potentially guiding prophylactic anticoagulation.

Simple proofs of certain inequalities with logarithmic coefficients of univalent functions

In this paper, we give simple proofs for the bounds (some of them sharp) of the difference of the moduli of the second and the first logarithmic coefficient for the general class of univalent functions and for the class of convex univalent functions.

Widths and entropy numbers of the classes of periodic functions of one and several variables in the space $B_{q,1}$

Exact-order estimates are obtained for the entropy numbers and several types of widths (Kolmogorov, linear, trigonometric and orthowidth) for the Sobolev and Nikol'skii-Besov classes of one and several variables in the space $B_{q,1}$, $1 &lt;q&lt; \infty$. It is shown, that in the multivariate case, in contrast to the univariate, the obtained estimates differ in order from the corresponding estimates in the space $L_q$.

Widths and entropy numbers of the classes of periodic functions of one and several variables in the space $B_{q,1}$

Exact-order estimates are obtained for the entropy numbers and several types of widths (Kolmogorov, linear, trigonometric and orthowidth) for the Sobolev and Nikol'skii-Besov classes of one and several variables in the space $B_{q,1}$, $1 &lt;q&lt; \infty$. It is shown, that in the multivariate case, in contrast to the univariate, the obtained estimates differ in order from the corresponding estimates in the space $L_q$.

Geometric Properties Connected with a Certain Multiplier Integral q−Analogue Operator

The topic concerning the introduction and investigation of new classes of analytic functions using subordination techniques for obtaining certain geometric properties alongside coefficient estimates and inclusion relations is enriched by the results of the present investigation. The prolific tools of quantum calculus applied in geometric function theory are employed for the investigation of a new class of analytic functions introduced by applying a previously defined generalized q−integral operator and the concept of subordination. Investigations are conducted on the new class, including coefficient estimates, integral representation for the functions of the class, linear combinations, forms of the weighted and arithmetic means involving functions from the class, and the estimation of the integral means results.

Broadcasters, receivers, functional groups of metabolites, and the link to heart failure by revealing metabolomic network connectivity.

Blood-based small molecule metabolites offer easy accessibility and hold significant potential for insights into health processes, the impact of lifestyle, and genetic variation on disease, enabling precise risk prevention. In a prospective study with records of heart failure (HF) incidence, we present metabolite profiling data from individuals without HF at baseline. We uncovered the interconnectivity of metabolites using data-driven and causal networks augmented with polygenic factors. Exploring the networks, we identified metabolite broadcasters, receivers, mediators, and subnetworks corresponding to functional classes of metabolites, and provided insights into the link between metabolomic architecture and regulation in health. We incorporated the network structure into the identification of metabolites associated with HF to control the effect of confounding metabolites. We identified metabolites associated with higher and lower risk of HF incidence, such as glycine, ureidopropionic and glycocholic acids, and LPC 18:2. These associations were not confounded by the other metabolites due to uncovering the connectivity among metabolites and adjusting each association for the confounding metabolites. Examples of our findings include the direct influence of asparagine on glycine, both of which were inversely associated with HF. These two metabolites were influenced by polygenic factors and only essential amino acids, which are not synthesized in the human body and are obtained directly from the diet. Metabolites may play a critical role in linking genetic background and lifestyle factors to HF incidence. Revealing the underlying connectivity of metabolites associated with HF strengthens the findings and facilitates studying complex conditions like HF.

Semi-c-periodicity, c-uniform recurrence and almost automorphy in the complex plane

This paper is devoted to develop the concepts of semi-c-periodicity, c-uniform recurrence and almost automorphy for functions defined on vertical strips in the complex plane, where c is a non-zero complex number. As an extension of the study performed for functions defined on the real axis, this work aims to investigate the main properties of these classes of functions and establish their connections with the more known class of c-almost periodic functions defined on vertical strips. In fact, we resolve an open problem which was raised in 2020 for the real case. Additionally, we also use this approach to introduce an asymptotic version of these new classes of functions.

Synthesis of Optimal Correction Functions in the Class of Disjunctive Normal Forms

The paper proposes to consider individual heuristics as unreliably operating parts of the information processing system. In a separate case, several different heuristics are adopted to solve the same problem, and the results obtained are adjusted in a certain way. In this case, problems arise that are close in methodology to the problems of synthesizing reliable circuits from unreliable elements or making a collective expert decision. The work solves the problem of constructing an optimal correction function based on control material; classes of functions of k-valued logic under monotonicity restrictions are studied. A theorem on the completeness of the class of monotonic functions of k-valued logic for arbitrary k is proved, and a basis in the given class is proved and constructed. The problem of constructing an optimal corrector in the class of disjunctive normal forms of k-valued functions is solved.

Synthesis of Optimal Correction Functions in the Class of Disjunctive Normal Forms

The paper proposes to consider individual heuristics as unreliably operating parts of the information processing system. In a separate case, several different heuristics are adopted to solve the same problem, and the results obtained are adjusted in a certain way. In this case, problems arise that are close in methodology to the problems of synthesizing reliable circuits from unreliable elements or making a collective expert decision. The work solves the problem of constructing an optimal correction function based on control material; classes of functions of k-valued logic under monotonicity restrictions are studied. A theorem on the completeness of the class of monotonic functions of k-valued logic for arbitrary k is proved, and a basis in the given class is proved and constructed. The problem of constructing an optimal corrector in the class of disjunctive normal forms of k-valued functions is solved.

Some characterizations on isoquants of homogeneous and quasi-sum production functions in microeconomics

Production function is an important concept in neoclassical economics and of great significance in economics and management. In the theory of geometric variations, the minimality of surfaces describes the optimal solutions of energy equations. Due to the nature of minimum energy, beautiful shape and stable structure, the theory of minimal surfaces is widely utilized in the fields of engineering, architecture, physics and molecular chemistry. In this article, we investigate homogeneous production functions and quasi-sum production functions with minimal isoquants, which solves two problems proposed by Neacşu et al. After meticulous calculations, the complete classifications of homogeneous production functions and quasi-sum production functions are reached. The research results interestingly indicate that homogeneous production functions with minimal isoquants are closely related to harmonic functions, which is a classical concept in mathematics and have widely applications.

Deep learning prediction of survival in patients with heart failure using chest radiographs.

Heart failure (HF) is associated with high rates of morbidity and mortality. The value of deep learning survival prediction models using chest radiographs in patients with heart failure is currently unclear. The aim of our studyisto develop and validate a deep learning survival prediction model using chest X-ray (DLSPCXR) in patients with HF. The study retrospectively enrolled a cohort of 353 patients with HF who underwent chest X-ray (CXR) at our institution between March 2012 and March 2017. The dataset was randomly divided into training (n = 247) and validation (n = 106) datasets. Univariate and multivariate Cox analysis were conducted on the training dataset to develop clinical and imaging survival prediction models. The DLSPCXR was trained and the selected clinical parameters were incorporated into DLSPCXR to establish a new model called DLSPinteg. Discrimination performance was evaluated using the time-dependent area under the receiver operating characteristic curves (TD AUC) at 1, 3, and 5-years survival. Delong's test was employed for the comparison of differences between two AUCs of different models. The risk-discrimination capability of the optimal model was evaluated by the Kaplan-Meier curve. In multivariable Cox analysis, older age, higher N-terminal pro-B-type natriuretic peptide (NT-ProBNP), systolic pulmonary artery pressure (sPAP) > 50mmHg, New York Heart Association (NYHA) functional class III-IV and cardiothoracic ratio (CTR) ≥ 0.62 in CXR were independent predictors of poor prognosis in patients with HF. Based on the receiver operating characteristic (ROC) curve analysis, DLSPCXR had better performance at predicting 5-year survival than the imaging Cox model in the validation cohort (AUC: 0.757 vs. 0.561, P = 0.01). DLSPinteg as the optimal model outperforms the clinical Cox model (AUC: 0.826 vs. 0.633, P = 0.03), imaging Cox model (AUC: 0.826 vs. 0.555, P < 0.001), and DLSPCXR (AUC: 0.826 vs. 0.767, P = 0.06). Deep learning models using chest radiographs can predict survival in patients with heart failure with acceptable accuracy.