Class Of Problems Research Articles

Existence, sign and asymptotic behaviour for a class of integro-differential elliptic type problems

Existence, sign and asymptotic behaviour for a class of integro-differential elliptic type problems

Existence results for boundary value problems of Hadamard fractional differential equations on unbounded domain

Abstract In this paper we investigate the existence and uniqueness of solutions for a class of boundary value problem for fractional differential equations involving the Hadamard’s fractional derivative, by applying a nonlinear alternative of Leray–Schauder due to Frigon and Granas for contraction maps in Fréchet spaces.

Various duality models associated with some constrained robust nonlinear optimal control problems

This paper deals with various duality results for a new class of constrained robust nonlinear control problems. Concretely, we introduce a minimisation problem associated with a vector of functionals of multiple integral type. In addition, the considered multi-objective controlled optimisation problem is governed by several mixed constraints generated by partial derivatives of second order and uncertain data. For this new class of control problems, we establish and characterise Wolfe, Mond-Weir and mixed type robust dual models. To this aim, by using the notion of convex multiple integral functional, generated by a controlled second-order Lagrangian with uncertain data, and the concept of robust weak efficient solution to the problem under study, we build a new mathematical context to state and prove the duality theorems.

The Global existence and blow-up of solutions for a class of Steklov parabolic problems

In this paper, we study weak solutions to the following Steklov parabolic problem: We prove theorems of existence of weak solutions, via Galerkin approximation. Moreover, we show the existence of solutions which blow up in a finite time.

A solution to the only one object problem with dissolution rules

AbstractIn the framework of membrane computing, (non-)uniform families of recognizer membrane systems are usually defined to solve abstract decision problems. In this sense, the use of finite resources for each member of the family makes the difference with respect to Turing machines solving these problems. While keeping the finite nature of these systems, it is interesting to know which type of problems can be solved by means of a single membrane system. For this purpose, the complexity class $$\textbf{PMC}^{1p}_{\mathcal {R}}$$ PMC R 1 p was defined as the class of problems that can be solved by means of a single membrane system in polynomial time. Due to the polynomial-time encoding of the input, at least all the problems from P can be solved with a trivial system. To go below P, the class $$\textbf{PMC}^{1f}_{\mathcal {R}}$$ PMC R 1 f restricts the definition of this encoding. In this work, we study the capability of different types of membrane systems to solve the problem, while having the encoding restriction.

Informed Adaptive Sensing.

For many inverse problems, the data on which the solution is based is acquired sequentially. We present an approach to the solution of such inverse problems where a sensor can be directed (or otherwise reconfigured on the fly) to acquire a particular measurement. An example problem is magnetic resonance image reconstruction. We use an estimate of mutual information derived from an empirical conditional distribution provided by a generative model to guide our measurement acquisition given measurements acquired so far. The conditionally generated data is a set of samples which are representative of the plausible solutions that satisfy the acquired measurements. We present experiments on toy and real world data sets. We focus on image data but we demonstrate that the method is applicable to a broader class of problems. We also show how a learned model such as a deep neural network can be leveraged to allow generalisation to unseen data. Our informed adaptive sensing method outperforms random sampling, variance based sampling, sparsity based methods, and compressed sensing.

Resources of curriculum materials that induce teachers' professional knowledge of the additive conceptual field

Assuming that curriculum materials reverberate the knowledge of teachers, we sought to identify and discuss features of the materials, related to the additive field, which induce professional knowledge in Mathematics. Through a documentary analysis of three 2nd, 3rd and 4th grade Mathematics Teacher's Manuals, the addition and subtraction problems were mapped and analyzed; the texts presenting the material and the units corresponding to the mapped problems were analyzed, as well as the specific guidelines for working with these problems. Considering the Conceptual Fields Theory and the Knowledge of Knowledge of Curriculum Embedded Mathematics as references, we identified a variety of problem classes, as well as guidelines on the different meanings of operations. We observed weaknesses in the approach taken in the 2nd grade Manual corresponding to the addition and subtraction approach, to the detriment of the other Manuals. We noted the absence of explicitly stated information in the three manuals, which may have an impact on the way teachers read and interpret the guidelines, and evaluate the problems, implying the teaching knowledge mobilized or constructed.

Characterization of the solution set of nonsmooth semi-infinite programming problems on Hadamard manifolds

This article is concerned with a class of nonsmooth semi-infinite programming problems on Hadamard manifolds (abbreviated as, (NSIP)). We introduce the Guignard constraint qualification (abbreviated as, (GCQ)) for (NSIP). Subsequently, by employing (GCQ), we establish the Karush-Kuhn-Tucker (abbreviated as, KKT) type necessary optimality conditions for (NSIP). Further, we derive that the Lagrangian function associated with a fixed Lagrange multiplier, corresponding to a known solution, remains constant on the solution set of (NSIP) under geodesic pseudoconvexity assumptions. Moreover, we derive certain characterizations of the solution set of the considered problem (NSIP) in the framework of Hadamard manifolds. We provide illustrative examples that highlight the importance of our established results. To the best of our knowledge, characterizations of the solution set of (NSIP) using Clarke subdifferentials on Hadamard manifolds have not been investigated before.

Input Regularization for Integer Optimal Control in BV with Applications to Control of Poroelastic and Poroviscoelastic Systems

We revisit a class of integer optimal control problems for which a trust-region method has been proposed and analyzed in arXiv:2106.13453v3 [math.OC]. While the algorithm proposed in arXiv:2106.13453v3 [math.OC] successfully solves the class of optimization problems under consideration, its convergence analysis requires restrictive regularity assumptions. There are many examples of integer optimal control problems involving partial differential equations where these regularity assumptions are not satisfied. In this article we provide a way to bypass the restrictive regularity assumptions by introducing an additional partial regularization of the control inputs by means of mollification and proving a $\Gamma$-convergence-type result when the support parameter of the mollification is driven to zero. We highlight the applicability of this theory in the case of fluid flows through deformable porous media equations that arise in biomechanics. We show that the regularity assumptions are violated in the case of poro-visco-elastic systems, and thus one needs to use the regularization of the control input introduced in this article. Associated numerical results show that while the homotopy can help to find better objective values and points of lower instationarity, the practical performance of the algorithm without the input regularization may be on par with the homotopy.

Existence and regularity results for a class of singular parabolic problems with L1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$L^1$$\\end{document} data

In this paper we prove existence and regularity results for a class of parabolic problems with irregular initial data and lower order terms singular with respect to the solution. We prove that, even if the initial datum is not bounded but only in L1(Ω)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$L^1(\\Omega )$$\\end{document}, there exists a solution that “instantly” becomes bounded. Moreover we study the behavior in time of these solutions showing that this class of problems admits global solutions which all have the same behavior in time independently of the size of the initial data.

Existence and multiplicity of nontrivial solutions to a class of elliptic Kirchhoff-Boussinesq type problems

Existence and multiplicity of nontrivial solutions to a class of elliptic Kirchhoff-Boussinesq type problems

Differential evolutionary using opposition-based learning for multimodal multi-objective optimization

The correspondence between the decision space and the objective space is often many-to-one in multi-objective optimization problems. Therefore, a class of problems with such mapping relationships is defined as a MMOPs. For these problems, how to ensure the final solution converges to each Pareto solution set and guarantees the diversity of the algorithm is an urgent problem. The method of the paper with opposition-based strategy, a multimodal multi-objective optimization algorithm, is proposed. The algorithm proposed is called MMODE_OP, which is framed by a differential evolutionary algorithm, and opposition-based learning is applied to the initialization phase and generation-hopping phase to filter out the more promising individuals in the population for iteration to enhance the global search capability and the diversity of population. In addition, different Gaussian perturbation strategies are adopted with iteration to achieve the search of the neighborhood, which can further not only improve the quality of the Pareto solution set but also enable the convergence of the Pareto solution set quickly. This method improves the algorithm’s local and global search ability, and enables multiple the Pareto solution set and improving the convergence. In the meantime, adaptive scaling factors and crossover factors are designed in this paper to enhance the improved search capability. Finally, the experiment results of MMODE_OP and other excellent algorithms on 13 test problems corroborate the proposed methods have superior performance.

Guiding Fuzzy Cognitive Mapping With Structured Decision Making to Inform Complex Natural Resource Management Problems in Waiʻanae Hawaiʻi

AbstractFire is one example of a larger class of wicked environmental management problems that require community‐based management for long‐term success. This study aimed to support participatory decision making in a data poor and complex system by using Fuzzy Cognitive Mapping (FCM) within the decision‐making framework Structured Decision Making (SDM) to develop a community‐based wildfire management plan in partnership with a local group in Wai‘anae Hawaiʻi. SDM is an organized process to create and evaluate decisions that can clarify trade‐offs and increase transparency. FCM is a semi‐quantitative method to describe system relationships that can handle low data and high uncertainty. We used SDM to define the problem, articulate community concerns related to wildfire, and identify management actions. We then used FCM to model how these actions affected valued ecosystem services and other stakeholder‐identified objectives. Modeling results highlighted the trade‐offs across three valued ecosystem services from three community‐led wildfire management actions. We found that native species outplanting was the most beneficial action to each of the three valued ecosystem services. Through this participatory research, we conclude that the SDM and FCM pairing provided an inclusive and cost‐effective way to engage with a specific wildfire management context, and that the process effectively engaged stakeholders while tackling uncertainty. This process also aided consensus‐building and group member communication. This pairing can be used to aid community decision‐making across diverse management problems as it provides a way to elicit objectives and model trade‐offs, even under uncertainty and data limitations, while including stakeholders impacted by such decisions.

0718 Latent Classes of Sleep Problems and Subjective Cognitive Decline Among U.S. Middle-Aged and Older Adults

0718 Latent Classes of Sleep Problems and Subjective Cognitive Decline Among U.S. Middle-Aged and Older Adults

Formulating and heuristic solving of contact problems in hybrid data-driven computational mechanics

In this work we consider the hybrid Data-Driven Computational Mechanics (DDCM) approach, in which a smooth constitutive manifold is reconstructed to obtain a well-behaved nonlinear optimization problem (NLP) rather than the much harder discrete-continuous NLP (DCNLP) of the direct DDCM approach. The key focus is on the addition of geometric inequality constraints to the hybrid DDCM formulation. Therein, the required constraint force leads to a contact problem in the form of a mathematical program with complementarity constraints (MPCC), a problem class that is still less complex than the DCNLP. For this MPCC we propose a heuristic quick-shot solution approach, which can produce verifiable solutions by solving up to four NLPs. We perform various numerical experiments on three different contact problems of increasing difficulty to demonstrate the potential and limitations of this approach.

Evolutionary simultaneous under and oversampling of instances for dealing with class-imbalance datasets in multilabel problems

Multilabel classification has recently attracted great attention from the data mining research community. Multilabel classification is concerned with learning where each instance can be associated with multiple classes (or labels). Class-imbalance problems appear in any classification task when the class distribution of the instances is very different. In multilabel classification, this problem is ubiquitous, as a large percentage of labels suffer from a class-imbalanced distribution. The adaptation of single-label methods to deal with the class-imbalance problem in multilabel learning is problematic as many of their basic concepts are not easily transferred. In this paper, we propose the use of evolutionary computation to simultaneously oversample the minority class and undersample the majority class for multilabel problems. Letting the algorithm autonomously select the instances to undersample and oversample allows us to extend these two successful paradigms to the multilabel task. An extensive comparison setup of 35 datasets shows the advantages of using this approach to deal with class-imbalance datasets for multilabel problems compared with previously published methods as well as the basic classification algorithms with the original datasets.

Antithetic multilevel particle filters

Abstract In this paper we consider the filtering of partially observed multidimensional diffusion processes that are observed regularly at discrete times. This is a challenging problem which requires the use of advanced numerical schemes based upon time-discretization of the diffusion process and then the application of particle filters. Perhaps the state-of-the-art method for moderate-dimensional problems is the multilevel particle filter of Jasra et al. (SIAM J. Numer. Anal.55 (2017), 3068–3096). This is a method that combines multilevel Monte Carlo and particle filters. The approach in that article is based intrinsically upon an Euler discretization method. We develop a new particle filter based upon the antithetic truncated Milstein scheme of Giles and Szpruch (Ann. Appl. Prob.24 (2014), 1585–1620). We show empirically for a class of diffusion problems that, for $\epsilon>0$ given, the cost to produce a mean squared error (MSE) of $\mathcal{O}(\epsilon^2)$ in the estimation of the filter is $\mathcal{O}(\epsilon^{-2}\log(\epsilon)^2)$ . In the case of multidimensional diffusions with non-constant diffusion coefficient, the method of Jasra et al. (2017) requires a cost of $\mathcal{O}(\epsilon^{-2.5})$ to achieve the same MSE.

Automatic deforestation detectors based on frequentist statistics and their extensions for other spatial objects

AbstractThis article is devoted to the problem of detection of forest and nonforest areas on Earth images. We propose two statistical methods to tackle this problem: one based on multiple hypothesis testing with parametric distribution families, another one—on nonparametric tests. The parametric approach is novel in the literature and relevant to a larger class of problems—detection of natural objects, as well as anomaly detection. We develop mathematical background for each of the two methods, build self‐sufficient detection algorithms using them and discuss practical aspects of their implementation. We also compare our algorithms with each other and with those from standard machine learning using satellite data.

The modified fractional‐order quasi‐reversibility method for a class of direct and inverse problems governed by time‐fractional heat equations with involution perturbation

This study aims to explore two classes of ill‐posed problems governed by a nonclassical fractional heat equation with an involution perturbation. To achieve a stable solution, we introduce a modified pseudo‐parabolic regularization method that involves a correction term through a mixed fractional derivation operator, resulting in a sequence of well‐posed problems that depend on a regularization parameter . We rigorously demonstrate that the resulting approximate problems are well‐posed and present convergence results for this regularization approach.

Uniqueness and stability of nonnegative solutions for a class of nonpositone problems in a ball

Uniqueness and stability of nonnegative solutions for a class of nonpositone problems in a ball