Article
Management
Jie Jiang, Shen Peng
Summary: This paper discusses mathematical programs with distributionally robust chance constraints (MPDRCC), where the ambiguity set is determined by general moment information. The qualitative statistical robustness of MPDRCC is studied from the contaminated data-driven viewpoint. Discrete approximation of MPDRCC is also investigated to achieve computational tractability, with established convergence results. A reformulation of the approximated problem under standard assumptions is presented, which is then applied to approximately solve MPDRCC based on the convergence results. Two applications are reported, showing the practicality and effectiveness of the statistical robustness assertion and the discrete approximation scheme.
EUROPEAN JOURNAL OF OPERATIONAL RESEARCH
(2024)
Article
Operations Research & Management Science
Pablo Koch-Medina, Cosimo Munari
Summary: We contribute to the literature on statistical robustness of risk measures by computing the index of qualitative robustness for risk measures based on utility functions. This problem is intimately related to finding the natural domain of finiteness and continuity of such risk measures.
ANNALS OF OPERATIONS RESEARCH
(2022)
Article
Optics
Kohdai Kuroiwa, Hayata Yamasaki
Summary: Quantum resource theories offer a unified framework for quantitatively analyzing inherent quantum properties as resources for quantum information processing. This paper introduces an alternative resource measurement axiom, asymptotic consistency, which allows for quantifying resources without contradicting transformation rates. Relative entropic measures are shown to be consistent with transformation rates for various types of resources, demonstrating widely applicable quantitative analysis of quantum properties.
Article
Physics, Multidisciplinary
Jonathan Schluck, Glaucia Murta, Hermann Kampermann, Dagmar Bruss, Nikolai Wyderka
Summary: Robustness measures are quantifiers of quantum resources such as entanglement and coherence. However, their usefulness is hindered by unclear mathematical properties, especially when the set of resource-free states is non-convex. This paper investigates the continuity properties of different robustness functions and shows that their continuity depends on the shape of the set of free states. Specific examples of non-continuous measures are provided. The applicability of the results is illustrated by defining a robustness of teleportability and quantum discord.
JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL
(2023)
Article
Computer Science, Theory & Methods
Lucian Coroianu
Summary: This paper demonstrates that the nearest trapezoidal approximation of fuzzy numbers can be obtained via quadratic programs, and improves the Lipschitz constant of the approximation operator while preserving ambiguity. Analytical expressions or quadratic programs can be used to achieve the same results, providing Lipschitz constants for the approximation operator even when an analytical expression is not available for similar problems.
FUZZY SETS AND SYSTEMS
(2021)
Article
Computer Science, Artificial Intelligence
Yanping He, TaiBen Nan, Haidong Zhang
Summary: This paper discusses the reverse triple I method based on the Pythagorean fuzzy set, introducing the concepts of Pythagorean t-norm, Pythagorean t-conorm, residual Pythagorean fuzzy implication operator, and Pythagorean fuzzy biresiduum. The reverse triple I method for Pythagorean fuzzy modus ponens and Pythagorean fuzzy modus tollens is established, and the properties of robustness, continuity, and reversibility are analyzed. The effectiveness of the reverse triple I method in decision-making problems is illustrated through a practical example, highlighting its advantages over existing methods.
JOURNAL OF INTELLIGENT & FUZZY SYSTEMS
(2022)
Article
Automation & Control Systems
TaiBen Nan, Haidong Zhang, Yanping He
Summary: This paper focuses on the research of full implication triple I method in the Pythagorean fuzzy environment. Concepts and models are proposed and analyzed, and an application in medical diagnosis is discussed. Compared to existing methods, this approach bases on logical reasoning and provides more accurate expression of decision information.
INTERNATIONAL JOURNAL OF FUZZY SYSTEMS
(2022)
Article
Computer Science, Software Engineering
Lei Guo, Xiaojun Chen
Summary: In this paper, we propose necessary optimality conditions and tailored qualifications for a class of mathematical programs with complementarity constraints involving a non-Lipschitz sparsity-inducing term. These qualifications ensure that local minimizers satisfy the necessary optimality conditions, which existing constraint qualifications cannot guarantee due to the presence of the non-Lipschitz term. Additionally, an approximation method for solving the non-Lipschitz MPCC is presented along with its convergence analysis, and numerical examples demonstrate the effectiveness of the proposed method.
MATHEMATICAL PROGRAMMING
(2021)
Article
Management
Pengfei Yu, Ruotian Gao, Wenxun Xing
Summary: This study examines the maximization of perturbation radius of an ellipsoidal set under perturbed uncertain coefficients for each constraint, in the context of robust convex quadratically constrained quadratic programming problems. By formulating a fractional programming problem and reformulating it into linear conic programs solvable in polynomial time, the proposed sensitivity analysis concept is demonstrated through numerical experiments related to robust Markowitz's portfolio selection. Comparative numerical results show the efficiency of direct solutions of linear conic programs versus a bisection method for the corresponding fractional programming problem.
EUROPEAN JOURNAL OF OPERATIONAL RESEARCH
(2021)
Article
Multidisciplinary Sciences
Andres R. Munoz-Rojas, Ilana Kelsey, Jenna L. Pappalardo, Meibin Chen, Kathryn Miller-Jensen
Summary: The study using single-cell RNA sequencing to explore co-stimulated macrophages reveals cell-to-cell heterogeneity in transcription and mutually exclusive expression of specific genes, supporting the maintenance of specialized functions for at least 48 hours. This suggests that increasing functional diversity in the macrophage population is an effective strategy to respond to conflicting environmental cues.
NATURE COMMUNICATIONS
(2021)
Article
Mathematics, Applied
Sebastian Neumayer, Alexis Goujon, Pakshal Bohra, Michael Unser
Summary: Although Lipschitz-constrained neural networks are widely used in machine learning, designing and training expressive Lipschitz-constrained networks is challenging. To overcome the disadvantages of rectified linear-unit networks, we propose using learnable spline activation functions with three linear regions or more. We prove that our choice is universal among all 1-Lipschitz activation functions and can approximate a larger class of functions compared to other weight-constrained architectures. Our choice is also at least as expressive as the non-componentwise Groupsort activation function for spectral-norm-constrained weights. The theoretical findings align with prior numerical results.
SIAM JOURNAL ON MATHEMATICS OF DATA SCIENCE
(2023)
Article
Computer Science, Software Engineering
Bin Hu, Peter Seiler, Laurent Lessard
Summary: A convergence rate analysis for biased stochastic gradient descent is presented, with stochastic quadratic constraints and a small linear matrix inequality formulated to provide convergence bounds. A sequential minimization approach is developed to analyze trade-offs involving stepsize selection, convergence rate, optimization accuracy, and robustness to gradient inaccuracy. Theoretical formulas are obtained to quantify the convergence properties of biased SGD under various assumptions on the loss functions.
MATHEMATICAL PROGRAMMING
(2021)
Article
Computer Science, Interdisciplinary Applications
Qiang Zou, Hsi-Yung Feng
Summary: This paper introduces a novel reverse detection method to address the challenge of geometry-topology inconsistencies during push-pull operations, and presents a robust method for push-pull direct modeling while preserving smooth connections. Case studies and comparisons have demonstrated the effectiveness of the method.
ENGINEERING WITH COMPUTERS
(2022)
Review
Nursing
Nicole Hainsworth, Eileen Dowse, Lyn Ebert, Maralyn Foureur
Summary: This study provided a comprehensive analysis of governance and empirical evidence of knowledge, practice, and enablers to support continuity of care experiences within pre-registration midwifery education. Various factors were identified to support the implementation of continuity of care experiences, but there was little consensus regarding the pedagogical intent and further research is needed in countries where the predominant model of maternity care is fragmented and not woman-centred.
Article
Mathematics
Samer Al Ghour, Hanan Al-Saadi
Summary: Soft omega-theta-continuity and soft weak-theta(omega)-continuity are introduced and investigated as two new concepts of continuity. The links between these forms of soft mappings and their general topological relatives are explored. Examples are used to show that soft omega-theta-continuity lies between soft theta-continuity and soft weak-continuity, while soft weak-theta omega-continuity lies between soft continuity (i.e., soft theta(omega)-continuity) and soft weak-continuity.