Class Of Functions Research Articles

A new descriptive characterization of the HKr-integral and its inclusion in Burkill's integrals

We introduce a new class of functions, ACGr⁎, and compare it to the class of ACGr-functions which had been previously introduced by Musial and Sagher to characterize their Henstock–Kurzweil-type integral, the HKr-integral. We show that these two classes coincide and thereby we obtain a new descriptive characterization of the class of HKr-integrable functions. We then compare the HKr-integral with Burkill's CP-integral and obtain a de la Vallée Poussin-type theorem for the HKr-integral.

Multi-crowdsourced data fusion for modeling link-level traffic resilience to adverse weather events

Climate change leads to more frequent and intense weather events, posing escalating risks to road traffic. Crowdsourced data present new opportunities to monitor and investigate road traffic changes during adverse weather. This study utilizes two types of crowdsourced data: passively collected location data (PCLD) from mobile devices and actively collected user reports (ACUR) from the WAZE app, to examine the impact of floods, winter storms, and fog on road traffic. Three metrics derived from PCLD—speed change, event duration, and area under the curve (AUC)—along with an additional metric from ACUR, user-perceived severity, are utilized to assess link-level traffic resilience. All metrics are correlated with road characteristics such as functional class, number of lanes, divider types, road geometry, and historical traffic, to analyze underlying relationships and make forecasting. Using the Dallas–Fort Worth (DFW) metroplex in 2022 as a case, the study finds that overall, winter storms have the most substantial impact on road traffic, followed by floods and fog. Travel demand metrics, such as POI visits and traffic volume, experience a more significant decrease than traffic speed. The impact of weather also varies by road characteristics, with higher-class roads with greater volume and higher speed experiencing more substantial changes. Road geometry, such as minimal altitude and slopes, also significantly influences road traffic resilience under floods but not during winter storms. Moreover, the study reveals that ACUR may not accurately reflect the actual impact during extreme weather events, as few users are able to travel outside to actively act as “sensors”. In sum, this study evaluates a set of crowdsourced data for assessing link-level traffic resilience, designs various resilience metrics, and examines how they vary across road attributes and weather events, which are essential for guiding disaster preparedness, response, and recovery in road transportation systems.

Descent modulus and applications

The norm of the gradient ‖∇f(x)‖ measures the maximum descent of a real-valued smooth function f at x. For (nonsmooth) convex functions, this is expressed by the distance dist(0,∂f(x)) of the subdifferential to the origin, while for general real-valued functions defined on metric spaces by the notion of metric slope |∇f|(x). In this work we propose an axiomatic definition of descent modulus T[f](x) of a real-valued function f at every point x, defined on a general (not necessarily metric) space. The definition encompasses all above instances as well as average descents for functions defined on probability spaces. We show that a large class of functions are completely determined by their descent modulus and corresponding critical values. This result is already surprising in the smooth case: a one-dimensional information (norm of the gradient) turns out to be almost as powerful as the knowledge of the full gradient mapping. In the nonsmooth case, the key element for this determination result is the break of symmetry induced by a downhill orientation, in the spirit of the definition of the metric slope. The particular case of functions defined on finite spaces is studied in the last section. In this case, we obtain an explicit classification of descent operators that are, in some sense, typical.

The forgotten p-versine and p-coversine family of functions revisited.

This study delves into special class of generalized p-trigonometric functions, examining their connection to the established counterparts like p-cosine and p-sine functions. We here explore the new class of functions called the p-versine, p-coversine, p-haversine, and p-hacovercosine, by providing comprehensive definitions and properties. Grounded in the characteristics of p-cosine and p-sine functions, the newly proposed functions offer unique mathematical insights. Our work contributes towards a thorough understanding of these new special functions, showcasing their potential applications in diverse scientific domains, from mathematical analysis to physics and engineering. This paper contributes as a valuable resource for future applied mathematics researchers, engaging with these new mathematical functions, enhancing the ability to model complex patterns from diverse real-world applications.

Compact Extended Formulations for Low-Rank Functions with Indicator Variables

We study the mixed-integer epigraph of a special class of convex functions with nonconvex indicator constraints, which are often used to impose logical constraints on the support of the solutions. The class of functions we consider are defined as compositions of low-dimensional nonlinear functions with affine functions. Extended formulations describing the convex hull of such sets can easily be constructed via disjunctive programming although a direct application of this method often yields prohibitively large formulations, whose size is exponential in the number of variables. In this paper, we propose a new disjunctive representation of the sets under study, which leads to compact formulations with size exponential in the dimension of the nonlinear function but polynomial in the number of variables. Moreover, we show how to project out the additional variables for the case of dimension one, recovering or generalizing known results for the convex hulls of such sets (in the original space of variables). Our computational results indicate that the proposed approach can significantly improve the performance of solvers in structured problems. Funding: This work was supported by the National Science Foundation Division of Computing and Communication Foundations [Grant 2006762].

A prospective analysis of the correlation between ultrasonic B-lines, cardiac tissue doppler signals and left ventricular end-diastolic pressure in patients with severe aortic stenosis

BackgroundThe development of heart failure is a turning point in the natural course of aortic stenosis (AS). Pulmonary oedema and elevated left ventricular pressure (LVP) are cardinal features of heart failure. Evaluating pulmonary oedema by lung ultrasound involves taking the upper hand with a bedside noninvasive tool that may reflect LVP.AimWe sought to assess the correlation between sonographic pulmonary congestion, invasive LV pre-A pressure, and echocardiographic LV end-diastolic pressure (LVEDP) in symptomatic AS patients receiving transcatheter aortic valve replacement.MethodsForty-eight consecutive patients with severe AS and planned transcatheter aortic valve implantation (TAVI) were enrolled. LVEDP was estimated to be normal or elevated using the ASE/EACVI algorithm and transmitral Doppler indices, the E/A ratio, the E/e′, and the left atrial volume index. Invasive LV pre-A pressure was used as a reference, with > 12 mm Hg defined as elevated.ResultsForty-eight patients (25 women (52%), mean age 75 years, standard deviation (SD) ± 7.7 years) were enrolled in the study. We detected severe B-lines (≥ 30) in 13 (27%) patients and moderate B-lines (15–30) in 33 (68.6%) patients. The number of B-lines increased significantly with the severity of New York Heart Association (NYHA) functional classes (Fig. 1). The B-line count was 14 ± 13 in NYHA class I patients, 20 ± 20 in class II patients, and 44 ± 35 in class III patients (p < 0.05, rho = 0.384). The number of B-lines was correlated with the E/E’ ratio (R = 0.664, p < 0.0001) and the proBNP level (R = 0. 882, p < 0.008). We found no significant correlation with the LVEDP or LVEF. The LVEDP correlated well with the E/E’ ratio (R = 0.491, p < 0.001) but not at all with E/A, DT, or LAVI. All patients had an elevated LVEDP > 12, with a mean pressure of 26 mmHg, a minimum of 13 mmHg, and a maximum of 45 mmHg, with an SD of 7.85.ConclusionAssessing lung ultrasonic B-lines is a straightforward and practical approach to identifying pulmonary oedema in AS patients. The number of B-lines correlated with the E/E’ ratio and the functional status of patients but did not correlate with invasive LVEDP or LVEF. All patients had elevated LVEDP that correlated with E/E’.

On the matricial truncated moment problem. II

We continue the study of truncated matrix-valued moment problems begun in [12]. Let q∈N. Suppose that (X,X) is a measurable space and E is a finite-dimensional vector space of measurable mappings of X into Hq, the Hermitian q×q matrices. A linear functional Λ on E is called a moment functional if there exists a positive Hq-valued measure μ on (X,X) such that Λ(F)=∫X〈F,dμ〉 for F∈E.In this paper a number of special topics on the truncated matricial moment problem are treated. We restate a result from [11] to obtain a matricial version of the flat extension theorem. Assuming that X is a compact space and all elements of E are continuous on X we characterize moment functionals in terms of positivity and obtain an ordered maximal mass representing measure for each moment functional. The set of masses of representing measures at a fixed point and some related sets are studied. The class of commutative matrix moment functionals is investigated. We generalize the apolar scalar product for homogeneous polynomials to the matrix case and apply this to the matricial truncated moment problem.

Parabolic Regularity of Spectral Functions

This paper is devoted to the study of the second-order variational analysis of spectral functions. It is well-known that spectral functions can be expressed as a composite function of symmetric functions and eigenvalue functions. We establish several second-order properties of spectral functions when their associated symmetric functions enjoy these properties. Our main attention is given to characterize parabolic regularity for this class of functions. It was observed recently that parabolic regularity can play a central rule in ensuring the validity of important second-order variational properties, such as twice epi-differentiability. We demonstrates that for convex spectral functions, their parabolic regularity amounts to that of their symmetric functions. As an important consequence, we calculate the second subderivative of convex spectral functions, which allows us to establish second-order optimality conditions for a class of matrix optimization problems. Funding: The research of A. Mohammadi is funded by a postdoctoral fellowship from Georgetown University. E. Sarabi is partially supported by the U.S. National Science Foundation [Grant DMS 2108546].

Survival benefit of ICD implantation for primary prevention in dilated cardiomyopathy

Objectives: Dilated cardiomyopathy (DCM) represents a significant cause of heart failure unrelated to ischemic heart disease, posing a high risk of sudden cardiac death (SCD) due to low left ventricular ejection fraction (LVEF). This study evaluates the survival benefits of implantable cardiac defibrillators (ICDs) for primary prevention in DCM patients. Methods: We enrolled 52 symptomatic non-ischemic cardiomyopathy patients (LVEF ≤ 35%, NYHA class II-III) eligible for ICD implantation in Afshar Hospital, Yazd, Iran, from 2014 to 2015. Exclusion criteria included those with ischemic indications or requiring cardiac resynchronization therapy. We divided patients into ICD recipients and those on a waiting list, collected the baseline data (age, functional class, LVEF), then followed up with patients to assess mortality rates. Results: Among 45 patients, 64.5% received ICDs while 35.5% were on the waiting list. The mean age was 57±13 years, predominantly male (67.3%). The ICD group had a significantly lower mortality rate (17.3%) than the waiting list group (42.7%, p = 0.54). Although age and functional class did not significantly predict outcomes, lower LVEF was a crucial factor for long-term survival. Despite some studies suggesting no survival benefit in non-ischemic heart failure, our findings highlight the efficacy of ICDs in reducing mortality among DCM patients. Conclusions: ICD implantation in DCM patients substantially reduces all-cause mortality compared to those awaiting the procedure, underscoring the importance of timely ICD deployment for primary prevention in this population.

Mid-term results of percutaneous transmitral commissurotomy (PTMC) in central iran

Objectives: Percutaneous Trans-Mitral Commissurotomy (PTMC) is an effective non-surgical treatment in patients with severe rheumatic mitral valve stenosis. This study aimed to evaluate the mid-term results of this procedure in central Iran. Methods: This retrospective study was performed on 101 patients with severe mitral valve stenosis who underwent successful PTMC from March 2011 to September 2018 in Afshar Hospital in Yazd. At follow-up, all patients underwent clinical examination, two-dimensional and color Doppler echocardiography, and events were recorded. Data were analyzed using SPSS software version 19. Results: The mean age of the patients was 44.79± 11.72 years, and 83.3% were female. The mean follow-up time was 38.98 23.33 months (6-94 months).25.8% had AF rhythm, and 12% had previous PTMC or OMVC or CMVC. After percutaneous Trans-Mitral Commissurotomy, 97% of patients were in NYHA functional class I, II and the mitral valve area (MVA) increased from 0.92 ± 0.18 to 1.66± 0.29 cm2 (p&lt;0.0001). Pulmonary artery systolic pressure decreased from 46.96± 18.56 mmHg to 38.43±14.02 mmHg (p&lt;0.0001). The Mean mitral valve gradient decreased from 12.37± 3.99 mmHg to 4.79± 2.38 mmHg (p&lt;0.0001). Restenosis rate and severe mitral regurgitation resulting in mitral valve replacement (MVR) were 10.9% and 2%, respectively. Two patients died because of intracranial hemorrhage (ICH). During the follow-up event, free survival was 82.2%. Multivariable analysis revealed that the predictors of shorter event-free survival were AF rhythm (HR; 4.5, 95%CI;1.59-12.9, P=0.005) and post PTMC higher NYHA functional class (HR;2.2, CI;1-4.8,p=0.049). Conclusions: Mid-term results of percutaneous transmitral commissurotomy (PTMC) in central Iran are the same as in other parts of the world. This procedure is an effective and low-risk treatment for severe mitral valve stenosis.

Sex-related differences among patients undergoing surgical aortic valve replacement-a propensity score matched study.

We investigated the sex-related difference in characteristics and 2-year outcomes after surgical aortic valve replacement (SAVR) by propensity-score matching (PSM). Data from 2 prospective registries, the INSPIRIS RESILIA Durability Registry (INDURE) and IMPACT, were merged, resulting in a total of 933 patients: 735 males and 253 females undergoing first-time SAVR. The PSM was performed to assess the impact of sex on the SAVR outcomes, yielding 433 males and 243 females with comparable baseline characteristics. Females had a lower body mass index (median 27.1 vs 28.0 kg/m2; P = 0.008), fewer bicuspid valves (52% vs 59%; P = 0.036), higher EuroSCORE II (mean 2.3 vs 1.8%; P < 0.001) and Society of Thoracic Surgeons score (mean 1.6 vs 0.9%; P < 0.001), were more often in New York Heart Association functional class III/IV (47% vs 30%; P < 0.001) and angina Canadian Cardiovascular Society III/IV (8.2% vs 4.4%; P < 0.001), but had a lower rate of myocardial infarction (1.9% vs 5.2%; P = 0.028) compared to males. These differences vanished after PSM, except for the EuroSCORE II and Society of Thoracic Surgeons scores, which were still significantly higher in females. Furthermore, females required smaller valves (median diameter 23.0 vs 25.0 mm, P < 0.001). There were no differences in the length of hospital stay (median 8 days) or intensive care unit stay (median 24 vs 25 hours) between the 2 sexes. At 2 years, post-SAVR outcomes were comparable between males and females, even after PSM. Despite females presenting with a significantly higher surgical risk profile, 2-year outcomes following SAVR were comparable between males and females.

А COMPREHENSIVE STUDY OF PATIENTS WITH ISCHEMIC HEART DISEASE: AGE, GENDER, AND COMORBIDITY ASPECTS

The purpose of the study was to analyze the clinical characteristics, comorbid status, individual biochemical indicators, and systemic inflammation activity in patients with ischemic heart disease (IHD) depending on age, gender distribution, and diagnosis influence.Materials and methods. The study included 144 patients with IHD, who were divided into two groups – the main and the control. The main group comprised 120 patients with stable angina pectoris (SAP) II-III functional class (FC). The control group consisted of 24 patients with STEMI. All patients underwent a comprehensive examination: general clinical, anthropometric, laboratory (complete blood count, biochemical analysis), and instrumental (office blood pressure measurement, heart rate, and echocardiography). The comorbid profile of patients with IHD was assessed using the Charlson comorbidity index. The severity of systemic inflammation syndrome in the selected patient groups was assessed by the cellular composition of peripheral blood upon admission to the hospital, and based on the obtained data, the values of leukocyte inflammatory markers were calculated.Results. Patients in the main group were younger than those in the control group (54.78 ± 1.11 vs. 63.50 ± 1.82) (p&lt;0.001). A statistically significant predominance of men over women was found among the cohort of IHD patients (63.33% and 36.67%, respectively) (p&lt;0.001), with a tendency towards male predominance among patients with SAP II-III FC compared to those with STEMI (p = 0.074). Patients in the main group compared to those in the control group had significantly higher left ventricular ejection fraction (p&lt;0.001), systolic blood pressure (p&lt;0.001), and diastolic blood pressure (p=0.001). In the control group compared to the main group, more cases of patients with high levels of comorbidity were found (p&lt;0.001). Lower levels of creatinine, fibrinogen, prothrombin time, and glucose were observed in patients in the main group. Patients with SAP II-III FC compared to those with STEMI had lower levels of leukocyte inflammatory markers, such as neutrophil-to-lymphocyte ratio (NLR) (p&lt;0.001), systemic immune inflammation index (SII) (p=0.002), systemic inflammation response index (SIRI) (p=0.007), and aggregate index of systemic inflammation (AISI) (p=0.011).Conclusions. The study underscores the need for an individualized approach to each patient with ischemic heart disease, considering their age, gender, and comorbid characteristics, as well as laboratory peculiarities, to improve therapy outcomes and prevent complications.

MICROPHERRET: MICRObial PHEnotypic tRait ClassifieR using Machine lEarning Techniques

BackgroundIn recent years, there has been a rapid increase in the number of microbial genomes reconstructed through shotgun sequencing, and obtained by newly developed approaches including metagenomic binning and single-cell sequencing. However, our ability to functionally characterize these genomes by experimental assays is orders of magnitude less efficient. Consequently, there is a pressing need for the development of swift and automated strategies for the functional classification of microbial genomes.ResultsThe present work leverages a suite of supervised machine learning algorithms to establish a range of 86 metabolic and other ecological functions, such as methanotrophy and plastic degradation, starting from widely obtainable microbial genome annotations. Tests performed on independent datasets demonstrated robust performance across complete, fragmented, and incomplete genomes above a 70% completeness level for most of the considered functions. Application of the algorithms to the Biogas Microbiome database yielded predictions broadly consistent with current biological knowledge and correctly detecting functionally-related nuances of archaeal genomes. Finally, a case study focused on acetoclastic methanogenesis demonstrated how the developed machine learning models can be refined or expanded with models describing novel functions of interest.ConclusionsThe resulting tool, MICROPHERRET, incorporates a total of 86 models, one for each tested functional class, and can be applied to high-quality microbial genomes as well as to low-quality genomes derived from metagenomics and single-cell sequencing. MICROPHERRET can thus aid in understanding the functional role of newly generated genomes within their micro-ecological context.

Synaptic cell adhesion molecule Cdh6 identifies a class of sensory neurons with novel functions in colonic motility.

Intrinsic sensory neurons are an essential part of the enteric nervous system (ENS) and play a crucial role in gastrointestinal tract motility and digestion. Neuronal subtypes in the ENS have been distinguished by their electrophysiological properties, morphology, and expression of characteristic markers, notably neurotransmitters and neuropeptides. Here we investigated synaptic cell adhesion molecules as novel cell type markers in the ENS. Our work identifies two Type II classic cadherins, Cdh6 and Cdh8, specific to sensory neurons in the mouse colon. We show that Cdh6+ neurons demonstrate all other distinguishing classifications of enteric sensory neurons including marker expression of Calcb and Nmu, Dogiel type II morphology and AH-type electrophysiology and I H current. Optogenetic activation of Cdh6+ sensory neurons in distal colon evokes retrograde colonic motor complexes (CMCs), while pharmacologic blockade of rhythmicity-associated current I H disrupts the spontaneous generation of CMCs. These findings provide the first demonstration of selective activation of a single neurochemical and functional class of enteric neurons, and demonstrate a functional and critical role for sensory neurons in the generation of CMCs.

Nikishin’s theorem and factorization through Marcinkiewicz spaces

Consider L 0 L^0 , the F F -space of all equivalence classes of measurable functions on a finite measure space equipped with the topology of convergence in measure. Inspired by Nikishin’s classical result on the factorization of sublinear continuous operators from a Banach space to L 0 L^0 , we prove a theorem that characterizes those maps from any quasi-metric space into L 0 L^0 that factor strongly through Marcinkiewicz weighted spaces. We show applications to sublinear operators on a certain class of quasi-Banach spaces with generalized Rademacher type generated by Orlicz sequence spaces.

Searching for Sonin kernels

AbstractThe causal shift-invariant convolution is studied from the point of view of inversion. Abel’s algorithm, used in the tautochrone problem, is considered and Sonin’s existence condition is deduced. To generate pairs of functions verifying Sonin’s condition, the class of Mittag-Leffler type functions is used. In particular, functions that are impulse responses of ARMA(N,N) systems serve as a basis. The possible use of Abel’s procedure as a support for introducing generalized fractional derivatives is evaluated.

Generalization of quantum calculus and corresponding Hermite–Hadamard inequalities

The aim of this paper is first to introduce generalizations of quantum integrals and derivatives which are called (ϕ-h)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$(\\phi \\,-\\,h)$$\\end{document} integrals and (ϕ-h)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$(\\phi \\,-\\,h)$$\\end{document} derivatives, respectively. Then we investigate some implicit integral inequalities for (ϕ-h)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$(\\phi \\,-\\,h)$$\\end{document} integrals. Different classes of convex functions are used to prove these inequalities for symmetric functions. Under certain assumptions, Hermite–Hadamard-type inequalities for q-integrals are deduced. The results presented herein are applicable to convex, m-convex, and ħ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\hbar $$\\end{document}-convex functions defined on the non-negative part of the real line.

Midterm Outcomes of Percutaneous Intramyocardial Septal Radiofrequency Ablation for Hypertrophic Cardiomyopathy: A Single-Center, Observational Study.

Percutaneous intramyocardial septal radiofrequency ablation (PIMSRA) has been reported to be safe and effective at midterm follow-up to treat drug-refractory hypertrophic obstructive cardiomyopathy in a single center. However, data from other centers are lacking. This retrospective cohort study aimed to investigate the efficacy and safety of PIMSRA from another independent center. PIMSRA was performed in 76 patients with hypertrophic obstructive cardiomyopathy in our center from April 2020 to June 2023. The primary outcome was the reduction of left ventricular outflow tract gradient after 6 months or more post-PIMSRA. Secondary outcomes were periprocedural major adverse clinical events. Sixty-one patients returned to the hospital for follow-up 6 to 30 (median, 14) months after the procedure. At the last follow-up of the 61 patients, the maximum septal thickness decreased from a median of 23.6 (interquartile range, 20.5-26.4) to 19.1 (interquartile range, 16.0-22.1) mm (P<0.001) and the left ventricular outflow tract peak gradient at rest decreased from a median of 70.0 (interquartile range, 29.1-107.5) to 20.0 (interquartile range, 10.8-48.8) mm Hg (P<0.001). The percentage of patients with symptoms of New York Heart Association functional class III/IV decreased from 51% to 0%. Of all 76 patients, there was no in-hospital or 30-day death, no right or left branch block, and no permanent pacemaker implantation. Six (8%) patients had pericardial effusion, with 1 experiencing cardiac tamponade and ventricular fibrillation, and 1 (1%) patient developed septal branch aneurysm that was treated with coil occlusion. PIMSRA allows for the reduction in the left ventricular outflow tract gradient and enhances symptomatic improvement, with a limited incidence of adverse events and complications among patients with hypertrophic obstructive cardiomyopathy.

Contemporary Outcomes and Trends for the Transseptal Mitral Valve-in-Valve Procedure Using Balloon Expandable Transcatheter Valves in the United States.

Previous transcatheter valve therapy registry analyses of transcatheter mitral valve in valve (MViV) replacement of degenerated bioprosthesis reported early experience in the United States. Given recent increases in transseptal MViV volumes and introduction of the SAPIEN 3 Ultra valve, it is important to determine contemporary outcomes for patients undergoing transseptal SAPIEN 3/SAPIEN 3 Ultra MViV replacement. The Society of Thoracic Surgeons (STS)/American College of Cardiology Transcatheter Valve Therapy Registry was used to extract data for all patients undergoing transseptal SAPIEN 3/SAPIEN 3 Ultra MViV from 2015 to September 2022. Primary efficacy outcome was 1-year all-cause mortality. Secondary end points included 30-day mortality, functional class, quality of life, and mitral valve performance. Primary safety outcomes were device success and in-hospital complications. A total of 4243 patients with a mean STS score of 9.2±7.7 underwent transseptal MViV at 455 sites. The rate of Mitral Valve Academic Research Consortium technical (96.6%) success was high, and procedural complications were low. All-cause in-hospital, 30-day, and 1-year mortality rates were 3.2%, 4.3%, and 13.4%, respectively. Significant improvements in New York Heart Association class (New York Heart Association I/II, 18% to 87%) and quality of life (Kansas City Cardiomyopathy Questionnaire score, 38 to 78) were noted at 1 year (P<0.0001 for both) after MViV. Upon stratifying by STS scores, it was observed that the low-risk group (STS<4) had a significantly lower in-hospital mortality rate of 0.4%, whereas the intermediate-risk group (STS, 4-8) had an in-hospital mortality rate of 1.9%. From 2015 to 2022, the number of transseptal MViV cases/year increased significantly, whereas procedure times, length of stay, and intensive care unit hours shortened significantly. At the same time, there was a significant trend toward reduced in-hospital (P=0.0005), 30-day (P=0.004), and 1-year mortality rates (P=0.01). This multicenter, prospective study reports excellent procedural outcomes, 1-year mortality rates, and a significant improvement in quality of life for patients undergoing transseptal MViV in the contemporary era. Patients in the low-risk and intermediate-risk STS score categories had significantly better outcomes compared with those in the high-risk category. MViV is a reasonable therapy for the majority of patients with degenerated bioprosthetic mitral valves, who are anatomical candidates.

Cauchy Problem for the Korteweg–De Vries Equation in the Class of Periodic Infinite-Gap Functions

Cauchy Problem for the Korteweg–De Vries Equation in the Class of Periodic Infinite-Gap Functions