Class Of Problems Research Articles

Role of shift constant in Energy Shifted SAV for Hamiltonian Systems

In recent years, considerable work has been devoted to the design of energy-stable numerical methods, a class of geometrical integration technique in which the discrete energy or pseudo-energy remains conserved. This property finds practical applications in systems for which the energy is bounded from below since the growth of the solutions is then itself bounded, yielding a form of stability. Such a property may be further exploited to transform the energy overall into a quadratic form, representing the core of recent numerical techniques such as the invariant energy quadratization (IEQ) and the scalar auxiliary variable (SAV) approaches. These methods have been applied to a large class of problems due to their remarkable efficiency. Yet, several aspects of such techniques have seen little investigation. In this work, the role of the “shift” constant in the expression of the potential energy in Hamiltonian systems is investigated. This is a positive gauge constant that may be used to augment the expression of the energy. Since Hamilton’s equations are given in terms of gradients of the Hamiltonian, such a constant has no influence on the resulting dynamics in the continuous system. However, empirical evidence has suggested that the convergence properties of the associated SAV approaches are affected by the magnitude of the shift factor. In this work, the behaviour of the relative global error of SAV schemes in the cases of the harmonic and Duffing oscillators is numerically investigated. The results reveal an optimal shift factor that increases the convergence rate. Using the optimal shift factor, the proposed method displays variable order accuracy ranging from second to twelfth order.

Flux Flattening Large Heavy Water Power Reactors with Accelerator-Driven Photoneutron Source

Flux flattening and power uprating of large heavy water power reactors (HWRs) are demonstrated as an application of an accelerator-driven photoneutron source (ADS) in the ADS-CANDU concept where an array of electron linear accelerators is configured around the periphery of a subcritical CANDU-6 core. The localized ADS generated through (e−,γ,n) reactions in the HWR lattice perturbs the reactor power distribution by increasing the power of low-power bundles and depressing the power at the core center relative to the fundamental mode power distribution. Gross power uprating is feasible when the system is near critical, but the ADS array consumes tens of megawatts electric exceeding the power gained by a factor of more than 2 for the conservative ADS performance specifications assumed in the analysis. Several important challenges of fixed-source Monte Carlo simulations of near-critical multiplying media are investigated including severe load imbalance issues with distributed-memory parallel computing architecture and correlated local tallies in nonanalog (implicit absorption) Monte Carlo radiation transport. All subcritical fixed-source simulations in the study readily exceed the default random number stride used in most production Monte Carlo codes, and the stride exceedance causes both bias in local tally results (bundle powers) and spatial autocorrelation of these errors/biases in the large core. A legacy stride exceedance is critically reviewed, and the conclusions and subsequent interpretations of those conclusions are rejected. Several classes of radiation transport Monte Carlo problems are likely to be susceptible to stride exceedance, and this issue needs to be promptly addressed by the Monte Carlo analyst and code developer communities.

Pride and Probability

Abstract Bayesian agents, argues Belot (2013), are orgulous: they believe in inductive success even when guaranteed to fail on a topologically typical collection of data streams. Here we shed light on how pervasive this phenomenon is. We identify several classes of inductive problems for which Bayesian convergence to the truth is topologically typical. However, we also show that, for all sufficiently complex classes, there are inductive problems for which convergence is topologically atypical. Lastly, we identify specific topologically typical collections of data streams, observing which guarantees convergence to the truth across all problems from certain natural classes of effective inductive problems.

Maternal religiosity and adolescent mental health: A UK prospective cohort study

BackgroundPrevious research has examined associations between parental religiosity and offspring mental health, but findings are inconsistent, and few studies have focused on late adolescence when mental health problems are more common. This study examines the prospective relationship between maternal religiosity and offspring mental health in late adolescence. MethodsWe used data from the Avon Longitudinal Study of Parents and Children to examine the prospective association between latent classes of maternal religiosity (Highly Religious, Moderately Religious, Agnostic, Atheist) and self-reported mental health problems including common mental disorders, ICD 10 depression, depressive symptoms, generalised anxiety symptoms, self-harm acts, self-harm thoughts, and disordered eating outcomes at age 17–18 years (n = 7714). We used multivariable logistic regression analysis adjusted for maternal mental health, maternal adverse childhood experiences, and socioeconomic variables. ResultsCompared with adolescent offspring of parents in the Agnostic class, offspring of the Atheist class had increased odds of depressive symptoms ((1.31[1.03,1.67]) and offspring of the Highly Religious class had increased odds of self-harm thoughts (1.43[1.04,1.97]). There was also weak evidence (95 % confidence intervals crossed the null) of increased odds of depression in the offspring of Moderately religious and Highly religious classes (1.26 [0.97,1.65], and 1.30 [0.99,1.70], respectively)) and self-harm acts in the offspring of the Highly religious class (1.31[0.98,1.74]). There was no evidence of associations with the disordered eating outcomes or generalised anxiety disorder symptoms. ConclusionsWe found evidence that adolescents whose mothers are Atheist, Moderately Religious, and Highly Religious are more likely to have depressive symptoms than those whose mothers are Agnostic. There was also evidence for an increased likelihood of self-harm (thoughts and acts) amongst adolescents of Highly Religious parents. Further research is needed to examine possible mechanisms that could explain these observed associations as well as a repetition of our analyses in a non-UK sample.

On a Class of Nonlinear Elliptic Equations with General Growth in the Gradient

In this paper, we prove an existence and uniqueness result for a class of Dirichlet boundary value problems whose model is −Δpu=β|∇u|q+c|u|p−2u+finΩ,u=0on∂Ω, where Ω is an open bounded subset of RN, N≥2, 1<p<N, Δpu is the so-called p-Laplace operator, and p−1<q<p. We assume that β is a positive constant, c and f are measurable functions belonging to suitable Lorentz spaces. Our approach is based on Schauder fixed point theorem.

Necessary and sufficient condition for existence for a case of eigenvalues of multiplicity two

We establish necessary and sufficient condition for existence of solutions for a class of semilinear Dirichlet problems with the linear part at resonance at eigenvalues of multiplicity two. The result is applied to give a condition for unboundness of all solutions of the corresponding semilinear heat equation.
 For more information see https://ejde.math.txstate.edu/Volumes/2024/09/abstr.html

A novel stepsize for gradient descent method

We propose a novel adaptive stepsize for the gradient descent scheme to solve unconstrained nonlinear optimization problems. With the convex and smooth objective satisfying locally Lipschitz gradient we obtain the complexity O(1k) of f(xk)−f⁎ at most. By using the idea of the new stepsize, we propose another new algorithm based on the projected gradient for solving a class of nonconvex optimization problems over a closed convex set. The computational experiments show the efficiency of the new method.

Deep neural-network prior for orbit recovery from method of moments

Orbit recovery problems are a class of problems that often arise in practice and various forms. In these problems, we aim to estimate an unknown function after being distorted by a group action and observed via a known operator. Typically, the observations are contaminated with a non-trivial level of noise. Two particular orbit recovery problems of interest in this paper are multireference alignment and single-particle cryo-EM modeling. In order to suppress the noise, we suggest using the method of moments approach for both problems while introducing deep neural network priors. In particular, our neural networks should output the signals and the distribution of group elements, with moments being the input. In the multireference alignment case, we demonstrate the advantage of using the NN to accelerate the convergence for the reconstruction of signals from the moments. Finally, we use our method to reconstruct simulated and biological volumes in the cryo-EM setting.

On Tempered (κ, ψ)-Hilfer Fractional Boundary Value Problems

Our research is primarily focused on applying the tempered (κ, ψ)-fractional operators to investigate the existence, uniqueness, and κ-Mittag-Leffler-Ulam-Hyers stability of a specific class of boundary value problems involving implicit nonlinear fractional differential equations and tempered (κ, ψ)-Hilfer fractional derivatives. To accomplish this, we make use of the fixed point theorem of Banach and a generalization of the well-known Gronwall inequality. Additionally, we provide illustrative examples to demonstrate the practical effectiveness of our main findings.

Sailing league problems

AbstractWe describe a class of combinatorial design problems which typically occur in professional sailing league competitions. We discuss connections to resolvable block designs and equitable coverings and to scheduling problems in operations research. We in particular give suitable boolean quadratic and integer linear optimization problem formulations, as well as further heuristics and restrictions, that can be used to solve sailing league problems in practice. We apply those techniques to three case studies obtained from real sailing leagues and compare the results with previously used tournament plans.

Fast Sampling via Spectral Independence Beyond Bounded-degree Graphs

Spectral independence is a recently developed framework for obtaining sharp bounds on the convergence time of the classical Glauber dynamics. This new framework has yielded optimal O(n log n) sampling algorithms on bounded-degree graphs for a large class of problems throughout the so-called uniqueness regime, including, for example, the problems of sampling independent sets, matchings, and Ising-model configurations. Our main contribution is to relax the bounded-degree assumption that has so far been important in establishing and applying spectral independence. Previous methods for avoiding degree bounds rely on using L p -norms to analyse contraction on graphs with bounded connective constant (Sinclair, Srivastava, and Yin, FOCS’13). The non-linearity of L p -norms is an obstacle to applying these results to bound spectral independence. Our solution is to capture the L p -analysis recursively by amortising over the subtrees of the recurrence used to analyse contraction. Our method generalises previous analyses that applied only to bounded-degree graphs. As a main application of our techniques, we consider the random graph G (n, d/n) , where the previously known algorithms run in time n O (log d ) or applied only to large d . We refine these algorithmic bounds significantly, and develop fast nearly linear algorithms based on Glauber dynamics that apply to all constant d , throughout the uniqueness regime.

Minimizing Total Completion Time, Total Earliness Time, and Maximum Tardiness for a Single Machine scheduling problem

Machine scheduling problems (MSP) are considered as one of the most important classes of combinatorial optimization problems. In this paper, the problem of job scheduling on a single machine is studied to minimize the multiobjective and multiobjective objective function. This objective function is: total completion time, total lead time and maximum tardiness time, respectively, which are formulated as are formulated. In this study, a mathematical model is created to solve the research problem. This problem can be divided into several sub-problems and simple algorithms have been found to find the solutions to these sub-problems and compare them with efficient solutions. For this problem, some rules that provide efficient solutions have been proved and some special cases have been introduced and proved since the problem is an NP-hard problem to find some efficient solutions that are efficient for the discussed problem 1// and good or optimal solutions for the multi-objective functions 1// ,, and emphasize the importance of the dominance rule (DR), which can be applied to this problem to improve efficient solutions.

Existence of solution sets for Φ-Laplacian for random impulsive differential equations

In this article, we provide results on the existence and compactness of the set of solutions for a class of initial-value problem representing a first-order random impulsive differential equation. The key tool to achieve our goal is based on an alternative nonlinear Leary-Schauder type theorem in the settings of generalized Banach spaces.

On existence of solutions for some classes of elliptic problems with supercritical exponential growth

On existence of solutions for some classes of elliptic problems with supercritical exponential growth

Uniform estimates for conforming Galerkin method for anisotropic singularly perturbed elliptic problems

In this article, we study some anisotropic singular perturbations for a class of linear elliptic problems. A uniform estimates for conforming Q 1 finite element method are derived, and some other results of convergence and regularity for the continuous problem are proved. The arguments are based on the tensorization trick and standard elliptic regularity theory tools.

Equivariant volume extremization and holography

In a previous paper two of us (D.M. and A.Z.) proposed that a vast class of gravitational extremization problems in holography can be formulated in terms of the equivariant volume of the internal geometry, or of the cone over it. We substantiate this claim by analysing supergravity solutions corresponding to branes partially or totally wrapped on a four-dimensional orbifold, both in M-theory as well as in type II supergravities. We show that our approach recovers the relevant gravitational central charges/free energies of several known supergravity solutions and can be used to compute these also for solutions that are not known explicitly. Moreover, we demonstrate the validity of previously conjectured gravitational block formulas for M5 and D4 branes. In the case of M5 branes we make contact with a recent approach based on localization of equivariant forms, constructed with Killing spinor bilinears.

Besov regularity for a class of elliptic obstacle problems with double-phase Orlicz growth

In this paper, we consider local Besov regularity of to the elliptic variational inequality with double-phase Orlicz growth:∫Ω〈A(x,Du),D(u−φ)〉dx≤∫Ω〈B(x,F),D(u−φ)〉dx∀φ∈Kψ(Ω), where Kψ(Ω) is an admissible set constrained by an obstacle function ψ(x). Here, each of nonlinearities A and B is supposed to be (Φ1,Φ2) double-phase with Orlicz type growth, respectively, under the assumption supt∈R+⁡Φ2(t)Φ1(t)+Φ11+α/n(t)<+∞ for a Hölder exponent α∈(0,1] of the coefficient a(x). We prove that a fractional differentiability of Du is reflected by extra differentiability assumption on the obstacle function and the external force, under a suitable regularity on the coefficient 0≤a(x)∈C0,α(Ω). This is an extension of recent work [44] from the elliptic problems of (p,q) growth to the setting of double phase Orlicz growth.

A numerical method for solutions of tempered fractional differential equations

The main objective of this paper is to develop a technique for approximating the numerical solution of certain class of tempered fractional differential equations. The proposed technique is based on the Newton–Cotes quadrature formula, and it is established by using generalized Lagrange interpolation polynomials. The product integration technique is used to develop a formula for the left and right-sided tempered fractional integrals. Next, by using these formulas, a method is developed for solving a general class of tempered fractional differential equations. Furthermore, three distinct classes of initial value problems and one of the terminal value problems for tempered fractional differential equations are taken into consideration and each class is illustrated by a numerical experiment to demonstrate the validity and effectiveness of the proposed methodology. Moreover, upper bound of error in the numerical approximations have been provided.

Using common redundancy components for suppliers in a supply chain network design problem considering energy costs and environmental effects

Improving the reliability of factories and suppliers through appropriate allocation of redundancy components is crucial in responding to customer demand. However, if individual factories independently buy and allocate redundancy components, huge investments will be required. To optimize the reliability level and costs of the supply chain network, the present study allocates these components to suppliers based on customer demand. While allocating redundancy components to factories improves the chain's reliability, it increases energy consumption and greenhouse gas emissions. Therefore, a balance between cost, reliability, and pollution needs to be established. The study considers a three-level supply chain, including the supplier (factories), distributor, and retailer, with stochastic and normally distributed demand assumed for each retailer. To address demand fluctuations, the risk pooling effect is implemented. As the problem belongs to the class of NP-hard problems, the study develops three multi-objective meta-heuristic algorithms, namely Non-dominated Sorting Genetic Algorithm II (NSGAII), Archived Multi-Objective Simulated Annealing (AMOSA), and Multi-Objective Artificial Bee Colony (MOABC) to solve it. The performance of these algorithms is evaluated using the results of the complete enumeration method. The comparison results based on six multi-objective performance metrics show that the MOABC algorithm has better performance in finding high-quality solutions in less time, while the NSGAII algorithm provides more diverse Pareto optimal solutions.

Locally unitarily invariantizable NEPv and convergence analysis of SCF

We consider a class of eigenvector-dependent nonlinear eigenvalue problems (NEPv) without the unitary invariance property. Those NEPv commonly arise as the first-order optimality conditions of a particular type of optimization problems over the Stiefel manifold, and previously, special cases have been studied in the literature. Two necessary conditions, a definiteness condition and a rank-preserving condition, on an eigenbasis matrix of the NEPv that is a global optimizer of the associated optimization problem are revealed, where the definiteness condition has been known for the special cases previously investigated. We show that, locally close to the eigenbasis matrix satisfying both necessary conditions, the NEPv can be reformulated as a unitarily invariant NEPv, the so-called aligned NEPv, through a basis alignment operation — in other words, the NEPv is locally unitarily invariantizable. Numerically, the NEPv is naturally solved by a self-consistent field (SCF)-type iteration. By exploiting the differentiability of the coefficient matrix of the aligned NEPv, we establish a closed-form local convergence rate for the SCF-type iteration and analyze its level-shifted variant. Numerical experiments confirm our theoretical results.