scholarly journals Variance Bounding of Delayed-Acceptance Kernels

2021 ◽  
Author(s):  
Chris Sherlock ◽  
Anthony Lee
Keyword(s):  
Asymptotic Variance ◽  
Sufficient Conditions ◽  
Ergodic Average ◽  
Computational Time ◽  
Local Algorithms ◽  
Non Local ◽  
Computationally Expensive ◽  
Computational Budget ◽  
Independence Sampler ◽  
Average Computational Time

AbstractA delayed-acceptance version of a Metropolis–Hastings algorithm can be useful for Bayesian inference when it is computationally expensive to calculate the true posterior, but a computationally cheap approximation is available; the delayed-acceptance kernel targets the same posterior as its associated “parent” Metropolis-Hastings kernel. Although the asymptotic variance of the ergodic average of any functional of the delayed-acceptance chain cannot be less than that obtained using its parent, the average computational time per iteration can be much smaller and so for a given computational budget the delayed-acceptance kernel can be more efficient. When the asymptotic variance of the ergodic averages of all $$L^2$$ L 2 functionals of the chain are finite, the kernel is said to be variance bounding. It has recently been noted that a delayed-acceptance kernel need not be variance bounding even when its parent is. We provide sufficient conditions for inheritance: for non-local algorithms, such as the independence sampler, the discrepancy between the log density of the approximation and that of the truth should be bounded; for local algorithms, two alternative sets of conditions are provided. As a by-product of our initial, general result we also supply sufficient conditions on any pair of proposals such that, for any shared target distribution, if a Metropolis-Hastings kernel using one of the proposals is variance bounding then so is the Metropolis-Hastings kernel using the other proposal.

scholarly journals De Sitter and power-law solutions in non-local Gauss–Bonnet gravity

2018 ◽  
Vol 15 (11) ◽  
pp. 1850188 ◽  
Author(s):  
E. Elizalde ◽  
S. D. Odintsov ◽  
E. O. Pozdeeva ◽  
S. Yu. Vernov
Keyword(s):  
Power Law ◽  
Sufficient Conditions ◽  
Model Parameters ◽  
Local Form ◽  
De Sitter ◽  
Dynamical Equations ◽  
Non Local ◽  
Necessary And Sufficient ◽  
The Universe ◽  
Universe Evolution

The cosmological dynamics of a non-locally corrected gravity theory, involving a power of the inverse d’Alembertian, is investigated. Casting the dynamical equations into local form, the fixed points of the models are derived, as well as corresponding de Sitter and power-law solutions. Necessary and sufficient conditions on the model parameters for the existence of de Sitter solutions are obtained. The possible existence of power-law solutions is investigated, and it is proven that models with de Sitter solutions have no power-law solutions. A model is found, which allows to describe the matter-dominated phase of the Universe evolution.

scholarly journals Performances of different DFT functionals to calculate the anodic limit of fluorinated sulphonyl-imide anions for lithium cells

2021 ◽  
Vol 2090 (1) ◽  
pp. 012078
Author(s):  
A Paolone ◽  
S Brutti
Keyword(s):  
Ionic Liquids ◽  
Lithium Batteries ◽  
Basis Set ◽  
Basis Sets ◽  
Computational Time ◽  
Generalized Gradient ◽  
Neutral Species ◽  
Generalized Gradient Approximation ◽  
Model Based ◽  
Computationally Expensive

Abstract In this paper we investigated the calculation of the anodic limit of two anions of ionic liquids, largely used as electrolyte of lithium batteries. Starting from a model based on calculations performed on single ions at the MP2 level of theory, we showed that the matching between calculation and experiments decreases while using more expanded basis set with respect to 6-31G**, possibly because of the destabilization of the neutral species when larger basis sets are considered. Additionally, in order to decrease the computational time, the performances for the calculation of the anodic limit obtained by means of a series of DFT functionals with increasing level of complexity (from the Generalized Gradient Approximation to the Range Separated Hybrid meta-Generalized Gradient Approximation) were compared. Overall, the best performing functionals are BMK, ωB97M-V and MN12-SX, while acceptable results can be obtained by M06-2X, M11, M08-HX and M11-L. Some less computationally expensive functionals, like CAM-B3LYP and ωB97X-D, also provide reasonable values of the anodic limit.

scholarly journals Uniqueness and Stability Results on Non-local Stochastic Random Impulsive Integro-Differential Equations

2021 ◽  
Vol 2 (3) ◽  
pp. 9-20
Author(s):  
VARSHINI S ◽  
BANUPRIYA K ◽  
RAMKUMAR K ◽  
RAVIKUMAR K
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Point Theorem ◽  
Sufficient Conditions ◽  
Banach Fixed Point Theorem ◽  
Local Conditions ◽  
Non Local ◽  
Inequality Techniques ◽  
Stability Results

The paper is concerned with stochastic random impulsive integro-differential equations with non-local conditions. The sufficient conditions guarantees uniqueness of mild solution derived using Banach fixed point theorem. Stability of the solution is derived by incorporating Banach fixed point theorem with certain inequality techniques.

Positive solutions to Sturm–Liouville problems with non-local boundary conditions

2014 ◽  
Vol 144 (1) ◽  
pp. 119-138 ◽  
Author(s):  
T. Jankowski
Keyword(s):  
Positive Solutions ◽  
Sufficient Conditions ◽  
Deviating Arguments ◽  
Local Boundary ◽  
Second Order Differential Equations ◽  
Existence Of Positive Solutions ◽  
Delayed Arguments ◽  
Non Local ◽  
Sturm Liouville ◽  
Advanced And Delayed Arguments

In this paper, the existence of at least three non-negative solutions to non-local boundary-value problems for second-order differential equations with deviating arguments α and ϛ is investigated. Sufficient conditions, which guarantee the existence of positive solutions, are obtained using the Avery–Peterson theorem. We discuss our problem for both advanced and delayed arguments. An example is added to illustrate the results.

The Application of Fuzzification for Solving Quadratic Functions

2021 ◽  
Author(s):  
Lunshan Gao
Keyword(s):  
Approximate Solution ◽  
Approximation Algorithm ◽  
Critical Point ◽  
Numerical Experiments ◽  
Optimization Problems ◽  
Local Minimizer ◽  
Quadratic Functions ◽  
Computational Time ◽  
Computational Results ◽  
Average Computational Time

Abstract This paper describes an approximation algorithm for solving standard quadratic optimization problems(StQPs) over the standard simplex by using fuzzification technique. We show that the approximate solution of the algorithm is an epsilon -critical point and satisfies epsilon-delta condition. The algorithm is compared with IBM ILOG CPLEX (short for CPLEX). The computational results indicate that the new algorithm is faster than CPLEX. Especially for infeasible problems. Furthermore, we calculate 100 instances for different size StQP problems. The numerical experiments show that the average computational time of the new algorithm for calculating the first local minimizer is in BigO(n) when the size of the problems is less or equal to 450.

Approximate controllability of semilinear impulsive functional differential systems with non-local conditions

2020 ◽  
Vol 37 (4) ◽  
pp. 1070-1088 ◽  
Author(s):  
Sumit Arora ◽  
Soniya Singh ◽  
Jaydev Dabas ◽  
Manil T Mohan
Keyword(s):  
Fixed Point ◽  
Hilbert Spaces ◽  
Resolvent Operator ◽  
Approximate Controllability ◽  
Sufficient Conditions ◽  
Differential Systems ◽  
Local Conditions ◽  
Functional Differential Systems ◽  
Non Local ◽  
Functional Differential

Abstract This paper is concerned with the approximate controllability of semilinear impulsive functional differential systems in Hilbert spaces with non-local conditions. We establish sufficient conditions for approximate controllability of such systems via resolvent operator and Schauder’s fixed point theorem. An application involving the impulse effect associated with delay and non-local conditions is presented to verify our claimed results.

scholarly journals Comparison of Genetic Algorithm and Harmony Search Method for 2D Geometry Optimization.

2018 ◽  
Vol 159 ◽  
pp. 01009 ◽  
Author(s):  
Mohammad Ghozi ◽  
Anik Budiati
Keyword(s):  
Genetic Algorithm ◽  
Harmony Search ◽  
Geometry Optimization ◽  
Steel Structure ◽  
Search Method ◽  
Geometric Optimization ◽  
Computational Time ◽  
Time Required ◽  
Average Computational Time ◽  
Better Than

There are many applications of Genetic Algorithm (GA) and Harmony Search (HS) Method for solving problems in civil engineering design. The question is, still, which method is better for geometry optimization of a steel structure. The purpose of this paper is to compare GA and HS performance for geometric optimization of a steel structure. This problem is solved by optimizing a steel structure using GA and HS and then comparing the structure’s weight as well as the time required for the calculation. In this study, GA produced a structural weight of 2308.00 kg to 2387.00 kg and HS scored 2193.12 kg to 2239.48 kg. The average computational time required by GA is 607 seconds and HS needed 278 seconds. It concludes that HS is faster and better than GA for geometry optimization of a steel structure.

Dial-a-Ride Problem with Users’ Accept/Reject Decisions Based on Service Utilities

2020 ◽  
Vol 2674 (10) ◽  
pp. 55-67
Author(s):  
Xiaotong Dong ◽  
David Rey ◽  
S. Travis Waller
Keyword(s):  
Minimum Cost ◽  
Collective Choice ◽  
Profit Margin ◽  
User Preference ◽  
Computational Time ◽  
Optimal Solutions ◽  
Mobility Service ◽  
Shared Mobility ◽  
Computationally Expensive ◽  
The Impact

The classic dial-a-ride problem (DARP) aims at designing the minimum-cost routing that accommodates all requests under a set of constraints. However, several modeling and computational challenges have hindered the successful deployment of dial-a-ride solutions. This work proposes incorporating user preference decisions within a rich DARP formulation. Specifically, it is considered that two travel modes are available: a shared mobility (DARP) service and a private travel option. Utility functions for each travel mode are integrated and it is assumed that the utility of the shared mobility service depends on the collective choice of travelers whereas the utility of private travel is fixed. Assuming that travelers are rational and seek to maximize their trip utility, extra variables and constraints are added to ensure that all requests are served by the mode with the higher utility. The behavior of the proposed integrated DARP with formulation of user preference constraints is examined by comparing the optimal solutions and computational time of this model with its classic DARP counterpart. Furthermore, the impact of various formulations of fare and the tolerance of the integrated DARP model is explored. Results show that user-personalized fare formulation improves model tolerance and profit margin, albeit it is rather computationally expensive.

scholarly journals Systematic reduction of complex tropospheric chemical mechanisms using sensitivity and time-scale analyses

2004 ◽  
Vol 4 (4) ◽  
pp. 3721-3783 ◽  
Author(s):  
L. E. Whitehouse ◽  
A. S. Tomlin ◽  
M. J. Pilling
Keyword(s):  
Sensitivity Analysis ◽  
Time Scales ◽  
Rate Sensitivity ◽  
Chemical Mechanism ◽  
Computational Time ◽  
Local Perturbation ◽  
Important Species ◽  
Reduced Mechanism ◽  
Wide Range ◽  
Computationally Expensive

Abstract. Explicit mechanisms describing the complex degradation pathways of atmospheric volatile organic compounds (VOCs) are important, since they allow the study of the contribution of individual VOCS to secondary pollutant formation. They are computationally expensive to solve however, since they contain large numbers of species and a wide range of time-scales causing stiffness in the resulting equation systems. This paper and the following companion paper describe the application of systematic and automated methods for reducing such complex mechanisms, whilst maintaining the accuracy of the model with respect to important species and features. The methods are demonstrated via application to version 2 of the Leeds Master Chemical Mechanism. The methods of local concentration sensitivity analysis and overall rate sensitivity analysis proved to be efficient and capable of removing the majority of redundant reactions and species in the scheme across a wide range of conditions relevant to the polluted troposphere. The application of principal component analysis of the rate sensitivity matrix was computationally expensive due to its use of the decomposition of very large matrices, and did not produce significant reduction over and above the other sensitivity methods. The use of the quasi-steady state approximation (QSSA) proved to be an extremely successful method of removing the fast time-scales within the system, as demonstrated by a local perturbation analysis at each stage of reduction. QSSA species were automatically selected via the calculation of instantaneous QSSA errors based on user-selected tolerances. The application of the QSSA led to the removal of a large number of alkoxy radicals and excited Criegee bi-radicals via reaction lumping. The resulting reduced mechanism was shown to reproduce the concentration profiles of the important species selected from the full mechanism over a wide range of conditions, including those outside of which the reduced mechanism was generated. As a result of a reduction in the number of species in the scheme of a factor of 2, and a reduction in stiffness, the computational time required for simulations was reduced by a factor of 4 when compared to the full scheme.

Sign in / Sign up

Export Citation Format

Share Document