Regularity Conditions Research Articles

Teachers’ occupational strain and subjective well-being: digital teaching makes a difference

ABSTRACT This research examined predictors of Austrian secondary school teachers’ occupational strain (mental overload) and subjective well-being (positive emotions) under regular teaching conditions (Study 1, N = 513) and COVID-19 distance teaching (Study 2, N = 1251). Following self-efficacy theory, we assumed teaching self-efficacy and perceived student–teacher relationship to predict mental overload and positive emotions, with digital teaching ability indirectly affecting these outcomes via teaching self-efficacy and student–teacher relationship in Study 2. Structural equation modelling revealed all assumed effects in Study 1, except for the relation between student–teacher relationship and positive emotions. In Study 2, only digital teaching ability was significantly associated with the outcomes, indicating a change in factors relevant to teacher well-being and occupational strain in digital teaching settings.

Adaptive Phase Estimation with Squeezed Vacuum Approaching the Quantum Limit

Phase estimation plays a central role in communications, sensing, and information processing. Quantum correlated states, such as squeezed states, enable phase estimation beyond the shot-noise limit, and in principle approach the ultimate quantum limit in precision, when paired with optimal quantum measurements. However, physical realizations of optimal quantum measurements for optical phase estimation with quantum-correlated states are still unknown. Here we address this problem by introducing an adaptive Gaussian measurement strategy for optical phase estimation with squeezed vacuum states that, by construction, approaches the quantum limit in precision. This strategy builds from a comprehensive set of locally optimal POVMs through rotations and homodyne measurements and uses the Adaptive Quantum State Estimation framework for optimizing the adaptive measurement process, which, under certain regularity conditions, guarantees asymptotic optimality for this quantum parameter estimation problem. As a result, the adaptive phase estimation strategy based on locally-optimal homodyne measurements achieves the quantum limit within the phase interval of [0,π/2). Furthermore, we generalize this strategy by including heterodyne measurements, enabling phase estimation across the full range of phases from [0,π), where squeezed vacuum allows for unambiguous phase encoding. Remarkably, for this phase interval, which is the maximum range of phases that can be encoded in squeezed vacuum, this estimation strategy maintains an asymptotic quantum-optimal performance, representing a significant advancement in quantum metrology.

Molecular dynamics study of the thermal radiatively pressure-driven flow of two immiscible hybrid nanofluids through a curved pipe with viscous dissipation

Hybrid nanomaterials significantly enhance thermal systems through improved thermal conductivity, efficient energy storage, and customized thermomechanical properties. Due to their superior thermophysical characteristics, hybrid nanofluids are crucial in fields such as industry, biomedicine, transportation, and pharmaceuticals. Therefore, the current article scrutinizes the characteristics of heat transfer on the thermally radiative flow of two immiscible hybrid nanofluids through a curved pipe induced due to a pressure gradient in an axial direction. The pipe is divided into two distinct regions: namely, (i) Region 1 (core) is filled with base fluid kerosene oil containing copper (Cu) and carbon nanotube (CNT) nanoparticles, while (ii) Region 2 (peripheral) is filled with base fluid water containing zinc oxide (ZnO) and aluminum oxide (Al2O3) nanoparticles. The complex curvilinear coordinates called toroidal coordinates are used to form a mathematical model for the present problem. The fluid in the core region is assumed to be more viscous than that of the peripheral region as such types of flows are observed in real life (viz. blood flow through arteries). Equations governing the flow are considered without ignoring any curvature ratio terms and are solved analytically by considering the perturbation series. The continuity of velocities and shear stresses at the fluid-fluid interface is taken into account along with no-slip, symmetric, and regularity conditions while solving the two-fluid flow problem under consideration. The effect of various fluid parameters such as curvature ratio, Reynolds number, viscosity ratio, and density ratio on the axial velocity and temperature is studied through 2-dimensional graphs, contour plots, and streamlines. The results show that the axial velocity of immiscible fluids flow decreases with an increase in the concentration of nanomaterials. Heat transport characteristics of nanofluid are increased by the addition of nanomaterials.

Renewable estimation in expectile regression model with streaming data sets

Streaming data continually expands over time, making it challenging to apply traditional expectile regression methods due to memory limitations. Expectile regression is advantageous for studying the entire conditional distribution of the response to a predictor, but handling streaming data requires innovative approaches. This paper proposes an online renewable expectile regression strategy, which updates the estimator using both the current data and summary statistics from historical data. An ADMM algorithm is employed to efficiently compute the proposed estimator. We establish the consistency and asymptotic normality of this renewable estimator under regular conditions. Extensive simulations and real-data experiments demonstrate that our method performs comparably to the oracle estimator while maintaining computational efficiency and low storage requirements.

Efficient Nonparametric Estimation of 3D Point Cloud Signals through Distributed Learning

Advancements in technology have elevated the prominence of 3D point cloud data, making its analysis increasingly vital across various applications. This need drives the demand for advanced statistical analytic approaches to handle challenges such as size, sparsity, and irregularity in 3D point clouds while ensuring accurate and efficient information extraction. This paper introduces a novel nonparametric distributed (NPD) learning framework that utilizes trivariate spline smoothing over a triangulation of domain. The proposed NPD algorithm features a straightforward, scalable, and communication-efficient implementation scheme that can achieve near-linear speedup. In addition, we provide rigorous theoretical support for the NPD estimation framework and demonstrate that the NPD spline estimators attain the same convergence rate as the global spline estimators obtained using the entire dataset and achieve the optimal nonparametric convergence rate established by Stone (1982) under some regularity conditions. To evaluate the efficacy of the proposed NPD method, we conduct simulation studies comparing it with several global nonparametric estimation methods used to smooth the 3D data. The results demonstrate the superior performance of the NPD method in accurately and efficiently processing and learning from 3D point clouds, highlighting its potential to advance large and complex data analysis. Supplementary material, which contains related technical details, proofs of the theoretical results, and additional results in simulation studies, is available online.

Fixed points of regular set-valued mappings in quasi-metric spaces

Metric fixed point theory is becoming increasingly significant across various fields, including data science and iterative methods for solving optimization problems. This paper aims to introduce new fixed point theorems for set-valued mappings under novel regularity conditions, such as orbital regularity and orbital pseudo-Lipschitzness. Instead of traditional metric spaces, we adopt the framework of quasi-metric spaces, motivated by the need to address problems in spaces that are not necessarily metric, such as function spaces of homogeneous type. We also explore the stability of the set of fixed points under variations of the set-valued mapping. Additionally, we provide estimates for the distances from a given point to the set of fixed points and between two sets of fixed points. Building on these findings, we extend the discussion to similar problems involving fixed, coincidence, and cyclic/double fixed points within this framework. Our results generalize recent findings from the literature, including those in Ait Mansour M, Bahraoui MA, El Bekkali A. [Metric regularity and Lyusternik-Graves theorem via approximate fixed points of set-valued maps in noncomplete metric spaces. Set-Valued Var Anal. 2022;30(1):233–256. doi: 10.1007/s11228-020-00553-1], Dontchev AL, Rockafellar RT. [Implicit functions and solution mappings. a view from variational analysis. Dordrecht: Springer; 2009. Springer Monographs in Mathematics], Ioffe AD. [Variational analysis of regular mappings. Springer, Cham; 2017. Springer Monographs in Mathematics; theory and applications. doi: 10.1007/978-3-319-64277-2], Lim TC. [On fixed point stability for set-valued contractive mappings with applications to generalized differential equations. J Math Anal Appl. 1985;110(2):436–441. doi: 10.1016/0022-247X(85)90306-3] and Tron NH. [Coincidence and fixed points of set-valued mappings via regularity in metric spaces. Set-Valued Var Anal. 2023;31(2):22. Paper No. 17. doi: 10.1007/s11228-023-00680-5].

Spectral properties of the gradient operator with nonconstant coefficients

In mathematical physics, the gradient operator with nonconstant coefficients encompasses various models, including Fourier’s law for heat propagation and Fick’s first law, that relates the diffusive flux to the gradient of the concentration. Specifically, consider n≥3\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$n\\ge 3$$\\end{document} orthogonal unit vectors e1,…,en∈Rn\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$e_1,\\ldots ,e_n\\in {\\mathbb {R}}^n$$\\end{document}, and let Ω⊆Rn\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Omega \\subseteq {\\mathbb {R}}^n$$\\end{document} be some (in general unbounded) Lipschitz domain. This paper investigates the spectral properties of the gradient operator T=∑i=1neiai(x)∂∂xi\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$T=\\sum _{i=1}^ne_ia_i(x)\\frac{\\partial }{\\partial x_i}$$\\end{document} with nonconstant positive coefficients ai:Ω¯→(0,∞)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$a_i:{\\overline{\\Omega }}\\rightarrow (0,\\infty )$$\\end{document}. Under certain regularity and growth conditions on the ai\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$a_i$$\\end{document}, we identify bisectorial or strip-type regions that belong to the S-resolvent set of T. Moreover, we obtain suitable estimates of the associated resolvent operator. Our focus lies in the spectral theory on the S-spectrum, designed to study the operators acting in Clifford modules V over the Clifford algebra Rn\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\mathbb {R}}_n$$\\end{document}, with vector operators being a specific crucial subclass. The spectral properties related to the S-spectrum of T are linked to the inversion of the operator Qs(T):=T2-2s0T+|s|2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$Q_s(T):=T^2-2s_0T+|s|^2$$\\end{document}, where s∈Rn+1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$s\\in {\\mathbb {R}}^{n+1}$$\\end{document} is a paravector, i.e., it is of the form s=s0+s1e1+⋯+snen\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$s=s_0+s_1e_1+\\cdots +s_ne_n$$\\end{document}. This spectral problem is substantially different from the complex one, since it allows to associate general boundary conditions to Qs(T)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$Q_s(T)$$\\end{document}, i.e., to the squared operator T2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$T^2$$\\end{document}.

Theoretical predictions to facilitate the method development in slalom chromatography for the separation of large DNA molecules

Slalom chromatography (SC) re-emerged in 2024 due to the availability of low adsorption ultra-high pressure liquid chromatography (UHPLC) packed columns/instruments and large modalities being investigated in the context of cell and gene therapies. The physico-chemical principles of SC retention combined with hydrodynamic chromatography (HDC) exclusion have been recently reported. In SC, DNA macromolecules are retarded because: (1) they can be stretched to lengths comparable to the particle diameter, and (2) their elastic relaxation time is long enough to maintain them in non-equilibrium extended conformations under regular UHPLC shear flow conditions. Here, a quantitative HDC-SC retention model is consolidated. A general plate height model accounting for the band broadening of long DNA biopolymers along packed beds is also derived for supporting method development and predicting speed-resolution performance in SC.For illustration, the chromatographic speed-resolution properties in SC are predicted for the separation of specific critical pairs (4.0/4.5, 10/11, and 25/27 kbp) of linear dsDNA polymers. The calculations are performed for two available custom-made particle sizes, dp= 1.7 and 2.5μm, at a constant pressure of 10,000 psi. The predictions are directly validated from experimental data acquired using low adsorption MaxPeakTM 4.6 mm i.d. Columns packed with 1.7μm BEHTM 45 Å (15 cm long column) and 2.5μm BEH 125 Å (30 cm long column) Particles, and by injecting six linear dsDNAs (λ DNA-Hind III Digest). The LC system is very low dispersion ACQUITYTM UPLCTM I-class PLUS System, and the mobile phase is a 100 mM phosphate buffer at pH 8. Maximum resolution is always achieved when the average extended lengths of linear dsDNAs are equal to a critical length, which is proportional to the particle diameter and to the square root of the applied shear rate. Most advantageously, the experimental results reveal that the relaxation times of linear dsDNAs observed under shear flow conditions are two orders of magnitude shorter than those expected in the absence of flow: this enables the detection of the longest linear dsDNAs up to 25 kbp without irremediable loss in column performance. Finally, the retention-efficiency model elaborated in this work can be used to rapidly anticipate and develop methods (selection of particle size, column length, and operating pressure) for any targeted DNA and time-resolution constraints.

Gradient Descent Provably Escapes Saddle Points in the Training of Shallow ReLU Networks

AbstractDynamical systems theory has recently been applied in optimization to prove that gradient descent algorithms bypass so-called strict saddle points of the loss function. However, in many modern machine learning applications, the required regularity conditions are not satisfied. In this paper, we prove a variant of the relevant dynamical systems result, a center-stable manifold theorem, in which we relax some of the regularity requirements. We explore its relevance for various machine learning tasks, with a particular focus on shallow rectified linear unit (ReLU) and leaky ReLU networks with scalar input. Building on a detailed examination of critical points of the square integral loss function for shallow ReLU and leaky ReLU networks relative to an affine target function, we show that gradient descent circumvents most saddle points. Furthermore, we prove convergence to global minima under favourable initialization conditions, quantified by an explicit threshold on the limiting loss.

Functional sufficient dimension reduction through distance covariance

Our research proposes a novel method for reducing the dimensionality of functional data, specifically for the case where the response is a scalar and the predictor is a random function. Our method utilizes distance covariance, and has several advantages over existing methods. Unlike current techniques which require restrictive assumptions such as linear conditional mean and constant covariance, our method has mild requirements on the predictor. Additionally, our method does not involve the use of the unbounded inverse of the covariance operator. The link function between the response and predictor can be arbitrary, and our proposed method maintains the advantage of being model-free, without the need to estimate the link function. Furthermore, our method is naturally suited for sparse longitudinal data. We utilize functional principal component analysis with truncation as a regularization mechanism in the development of our method. We provide justification for the validity of our proposed method, and establish statistical consistency of the estimator under certain regularization conditions. To demonstrate the effectiveness of our proposed method, we conduct simulation studies and real data analysis. The results show improved performance compared to existing methods.

Robust estimation for semiparametric spatial autoregressive models via weighted composite quantile regression

In this article, the robust estimation for a class of semiparametric spatial autoregressive models has been investigated. By combining the QR decomposition technique for matrix and the weighted composite quantile regression method, we propose a robust estimation procedure for the parametric and non parametric components. Under certain regularity conditions, asymptotic properties of the resulting estimators are proved. Several simulation analyses have been conducted for further illustrating the performance of the proposed method, and the simulation results demonstrate that the proposed method improve the robustness of the models.

Rheological impact of viscous fluid in the core region of heated curved pipe surrounded by Casson rheological fluid

The immiscible fluids can help design more efficient systems for drug delivery and understanding the blood flow through diseased arteries. It can also have implications for the design of flow control devices or medical implants that involve curved geometries. Therefore, the current article scrutinizes the characteristics of heat transfer on the flow of two immiscible Casson and Newtonian fluids through a curved pipe induced due to a pressure gradient in an axial direction. The pipe is divided into two distinct regions: namely, (i) Region 1 (core) is filled with Newtonian fluid while (ii) Region 2 (peripheral) is filled with non-Newtonian Casson fluid. The complex curvilinear coordinates called toroidal coordinates are used to form a mathematical model for the present problem. Equations governing the flow are considered without ignoring any curvature ratio terms and are solved analytically by considering the perturbation series. The continuity of velocities and shear stresses at the fluid-fluid interface is taken into account along with no-slip, symmetric, and regularity conditions while solving the two-fluid flow problem under consideration. The effect of various fluid parameters such as curvature ratio, Casson fluid parameter, Reynolds number, viscosity ratio, density ratio, Eckert number, and conductivity ratio on the axial velocity and temperature is studied through 2-dimensional graphs and contour plots. In addition, the volumetric flow rate and shear stress are also presented to evaluate the effects of various key parameters. The results show that the axial velocity of immiscible fluids flow increases with an increase in the values of the viscosity ratio parameter and the fluid temperature is decreased by increasing the conductivity ratio parameter.

Oxidative stress and culture atmosphere effects on bioactive compounds and laccase activity in the white rot fungus Phlebia radiata on birch wood substrate

Wood-decaying white rot fungi live in changing environmental conditions and may switch from aerobic to fermentative metabolism under oxygen depletion. Decomposition of wood and lignocellulose by fungi is dependent on enzymatic and oxidative biochemistry including generation of reactive oxygen species. In this study, we subjected semi-solid wood-substrate cultures of the white rot fungus Phlebia radiata to oxidative stress by addition of hydrogen peroxide under aerobic and anaerobic cultivation conditions. Wood decomposition and fungal metabolism were followed by analysis of extracellular organic compounds, mycelial growth, and laccase activity. Under both atmospheric conditions, accumulation of bioactive aromatic compounds from birch wood occurred into the culture supernatants after hydrogen peroxide treatment. The supernatants inhibited both fungal growth and laccase activity. However, the fungus recovered from the oxidative stress quickly in a few days, especially when cultivated under regular aerobic conditions. With repeated hydrogen peroxide treatments, laccase suppressive-recovery effect was observed. Culture supernatants demonstrated antioxidant and antimicrobial effects, in concert with emergence of chlorinated birch-derived organic compounds. Bioactivities in the cultures disappeared in the same pace as the chlorinated compounds were transformed and de-chlorinated by the fungus. Our results indicate tolerance of white rot fungi against excessive oxidative stress and wood-derived, growth-inhibiting and harmful agents.

Modulation instability and rogue waves for two and three dimensional nonlinear Klein-Gordon equation.

We perform the modulation instability analysis of the 2D and 3D nonlinear Klein-Gordon equation. The instability region depends on dispersion and wavenumbers of the plane wave. The N-breathers of the nonlinear Klein-Gordon equation are constructed directly from its 2N-solitons obtained in history. The regularity conditions of breathers are established. The dynamic behaviors of breathers of the 2D nonlinear Klein-Gordon equation are consistent with modulation instability analysis. Furthermore, by means of the bilinear method together with improved long-wave limit technique, we obtain general high order rogue waves of the 2D and 3D nonlinear Klein-Gordon equation. In particular, the first- and second-order rogue waves and lumps of the 2D nonlinear Klein-Gordon equation are investigated by using their explicit expressions. We find that their dynamic behaviors are similar to the nonlinear Schrödinger equation. Finally, the first-order rational solutions are illustrated for the 3D nonlinear Klein-Gordon equation. It is demonstrated that the rogue waves of the 2D and 3D nonlinear Klein-Gordon equation always exist by choosing dispersion and wavenumber of plane waves.

Curving and running resistance of freight trains: current experience with on-track measurements

Curving resistance affects the railway vehicle running through curves. For its estimation in train dynamics calculations, different empirical formulas are used in various countries. It is practically impossible to determine its exact value because of its dependency on various – to some extent random – parameters. In the framework of the experimental research of running resistance of freight trains at the Faculty of Transport Engineering of the University of Pardubice, measurements in regular operation conditions on the Czech railway network were realised in recent years. Because some of these results can be used to quantify the curving resistance, the applied evaluation methods and the relevant results are presented in this paper. Besides that, a new general formula of running resistance for freight trains, based on the measurement results, is proposed. Attention is also paid to the effect of track quality on the vehicle running resistance.

Hydraulic Model Tests for a Pontoon-Type Floating Structure with a Horizontal Damping Plate

In this study, hydraulic model tests were conducted to investigate the effect of a horizontal damping plate on the motion of the pontoon-type floating structure. The floating structures with and without the horizontal damping plates were fabricated with the scale of 1/20 and their motion responses to the regular and irregular wave conditions were investigated. From the comparison for the responses of each model with 16 wave conditions, it could be known that the damping plate made the response of the the pontoon to be smaller by about 5 to 10 % compared with the normal rectangular pontoon.

Robust direction estimation in single-index models via cumulative divergence

In this paper, we address direction estimation in single-index models, with a focus on heavy-tailed data applications. Our method utilizes cumulative divergence to directly capture the conditional mean dependence between the response variable and the index predictor, resulting in a model-free property that obviates the need for initial link function estimation. Furthermore, our approach allows heavy-tailed predictors and is robust against the presence of outliers, leveraging the rank-based nature of cumulative divergence. We establish theoretical properties for our proposal under mild regularity conditions and illustrate its solid performance through comprehensive simulations and real data analysis.

Divergent downstream biosynthetic pathways are supported by L-cysteine synthases of Mycobacterium tuberculosis.

Mycobacterium tuberculosis's (Mtb) autarkic lifestyle within the host involves rewiring its transcriptional networks to combat host-induced stresses. With the help of RNA sequencing performed under various stress conditions, we identified that genes belonging to Mtb sulfur metabolism pathways are significantly upregulated during oxidative stress. Using an integrated approach of microbial genetics, transcriptomics, metabolomics, animal experiments, chemical inhibition, and rescue studies, we investigated the biological role of non-canonical L-cysteine synthases, CysM and CysK2. While transcriptome signatures of RvΔcysM and RvΔcysK2 appear similar under regular growth conditions, we observed unique transcriptional signatures when subjected to oxidative stress. We followed pool size and labelling (34S) of key downstream metabolites, viz. mycothiol and ergothioneine, to monitor L-cysteine biosynthesis and utilization. This revealed the significant role of distinct L-cysteine biosynthetic routes on redox stress and homeostasis. CysM and CysK2 independently facilitate Mtb survival by alleviating host-induced redox stress, suggesting they are not fully redundant during infection. With the help of genetic mutants and chemical inhibitors, we show that CysM and CysK2 serve as unique, attractive targets for adjunct therapy to combat mycobacterial infection.

Second-order Karush/Kuhn–Tucker conditions and duality for constrained multiobjective optimization problems

In this paper, we investigate the second-order strong Karush/Kuhn–Tucker conditions and duality of a constrained multiobjective optimization problem (CMOP). Exploiting a second-order regularization condition, we obtain second-order strong KKT necessary conditions of Borwein-properly efficient solution of CMOP without convexity assumptions. Further, second-order sufficient conditions for the second-order KKT point to be an efficient solution of CMOP are derived under the generalized second-order convexity assumptions. Finally, we establish duality results between CMOP and its second-order Wolfe-type dual problem.

Copula-based analysis of dependent current status data with semiparametric linear transformation model.

This paper discusses regression analysis of current status data with dependent censoring, a problem that often occurs in many areas such as cross-sectional studies, epidemiological investigations and tumorigenicity experiments. Copula model-based methods are commonly employed to tackle this issue. However, these methods often face challenges in terms of model and parameter identification. The primary aim of this paper is to propose a copula-based analysis for dependent current status data, where the association parameter is left unspecified. Our method is based on a general class of semiparametric linear transformation models and parametric copulas. We demonstrate that the proposed semiparametric model is identifiable under certain regularity conditions from the distribution of the observed data. For inference, we develop a sieve maximum likelihood estimation method, using Bernstein polynomials to approximate the nonparametric functions involved. The asymptotic consistency and normality of the proposed estimators are established. Finally, to demonstrate the effectiveness and practical applicability of our method, we conduct an extensive simulation study and apply the proposed method to a real data example.