Generalized Störmer-Cowell methods with efficient iterative solver for large-scale second-order stiff semilinear systems

2021 ◽  
Vol 400 ◽  
pp. 126062
Author(s):  
Hao Chen ◽  
Yeru Yang
Keyword(s):  
Large Scale ◽  
Second Order ◽  
Iterative Solver ◽  
Semilinear Systems

Behavior Models of Voltage Differencing Inverting Buffered Amplifier and Applications in Circuit Analysis

2019 ◽  
Vol 12 (4) ◽  
pp. 298-303
Author(s):  
YongAn LI
Keyword(s):  
Large Scale ◽  
Vlsi Design ◽  
Circuit Analysis ◽  
Second Order ◽  
Very Large Scale Integration ◽  
Behavioral Models ◽  
Order Filter ◽  
Large Scale Integration ◽  
Scale Integration ◽  
Behavior Models

Background: The symbolic nodal analysis acts as a pivotal part of the very large scale integration (VLSI) design. Methods: In this work, based on the terminal relations for the pathological elements and the voltage differencing inverting buffered amplifier (VDIBA), twelve alternative pathological models for the VDIBA are presented. Moreover, the proposed models are applied to the VDIBA-based second-order filter and oscillator so as to simplify the circuit analysis. Results: The result shows that the behavioral models for the VDIBA are systematic, effective and powerful in the symbolic nodal circuit analysis.</P>

scholarly journals Higher order Hamiltonian Monte Carlo sampling for cosmological large-scale structure analysis

2021 ◽  
Vol 502 (3) ◽  
pp. 3976-3992
Author(s):  
Mónica Hernández-Sánchez ◽  
Francisco-Shu Kitaura ◽  
Metin Ata ◽  
Claudio Dalla Vecchia
Keyword(s):  
Fourth Order ◽  
Large Scale ◽  
Equations Of Motion ◽  
Large Scale Structure ◽  
Real Space ◽  
Higher Order ◽  
Second Order ◽  
Scale Structure ◽  
Integration Schemes ◽  
Reconstruction Methods

ABSTRACT We investigate higher order symplectic integration strategies within Bayesian cosmic density field reconstruction methods. In particular, we study the fourth-order discretization of Hamiltonian equations of motion (EoM). This is achieved by recursively applying the basic second-order leap-frog scheme (considering the single evaluation of the EoM) in a combination of even numbers of forward time integration steps with a single intermediate backward step. This largely reduces the number of evaluations and random gradient computations, as required in the usual second-order case for high-dimensional cases. We restrict this study to the lognormal-Poisson model, applied to a full volume halo catalogue in real space on a cubical mesh of 1250 h−1 Mpc side and 2563 cells. Hence, we neglect selection effects, redshift space distortions, and displacements. We note that those observational and cosmic evolution effects can be accounted for in subsequent Gibbs-sampling steps within the COSMIC BIRTH algorithm. We find that going from the usual second to fourth order in the leap-frog scheme shortens the burn-in phase by a factor of at least ∼30. This implies that 75–90 independent samples are obtained while the fastest second-order method converges. After convergence, the correlation lengths indicate an improvement factor of about 3.0 fewer gradient computations for meshes of 2563 cells. In the considered cosmological scenario, the traditional leap-frog scheme turns out to outperform higher order integration schemes only when considering lower dimensional problems, e.g. meshes with 643 cells. This gain in computational efficiency can help to go towards a full Bayesian analysis of the cosmological large-scale structure for upcoming galaxy surveys.

scholarly journals An output stabilization of second order semilinear systems

2020 ◽  
Vol 53 (2) ◽  
pp. 5889-5894
Author(s):  
Lahcen Ezzaki ◽  
El Hassan Zerrik
Keyword(s):  
Second Order ◽  
Semilinear Systems ◽  
Output Stabilization

scholarly journals Meta-Descent for Online, Continual Prediction

2019 ◽  
Vol 33 ◽  
pp. 3943-3950
Author(s):  
Andrew Jacobsen ◽  
Matthew Schlegel ◽  
Cameron Linke ◽  
Thomas Degris ◽  
Adam White ◽  
...  
Keyword(s):  
Gradient Descent ◽  
Large Scale ◽  
Time Series Prediction ◽  
Real Data ◽  
Second Order ◽  
Stochastic Gradient Descent ◽  
Step Size ◽  
Vector Approximation ◽  
Prediction Problems ◽  
Stationary Problems

This paper investigates different vector step-size adaptation approaches for non-stationary online, continual prediction problems. Vanilla stochastic gradient descent can be considerably improved by scaling the update with a vector of appropriately chosen step-sizes. Many methods, including AdaGrad, RMSProp, and AMSGrad, keep statistics about the learning process to approximate a second order update—a vector approximation of the inverse Hessian. Another family of approaches use meta-gradient descent to adapt the stepsize parameters to minimize prediction error. These metadescent strategies are promising for non-stationary problems, but have not been as extensively explored as quasi-second order methods. We first derive a general, incremental metadescent algorithm, called AdaGain, designed to be applicable to a much broader range of algorithms, including those with semi-gradient updates or even those with accelerations, such as RMSProp. We provide an empirical comparison of methods from both families. We conclude that methods from both families can perform well, but in non-stationary prediction problems the meta-descent methods exhibit advantages. Our method is particularly robust across several prediction problems, and is competitive with the state-of-the-art method on a large-scale, time-series prediction problem on real data from a mobile robot.

A Large Scale Cross-Validation of Second-Order Personality Structure Defined by the 16PF

1986 ◽  
Vol 59 (2) ◽  
pp. 683-693 ◽  
Author(s):  
Samuel E. Krug ◽  
Edgar F. Johns
Keyword(s):  
Large Scale ◽  
Common Factor ◽  
Geographic Location ◽  
Second Order ◽  
Personality Factor ◽  
Personality Factor Questionnaire ◽  
Normal Males ◽  
Definition Of ◽  
High Degree ◽  
Factor Estimation

The second-order factors structure of the 16 Personality Factor Questionnaire (16PF) was cross-validated on a large sample ( N = 17,381) of normal males and females. Subjects were sampled across a broad range of ages, socioeconomic levels, education, geographic location, and ethnicity. The purposes of this investigation were (1) to provide a precise definition of 16PF second-order factor structure, (2) to shed additional light on the nature of two second-order factors that have been previously identified but described as “unstable” and “poorly reproduced,” and (3) to determine the extent to which common factor estimation formulas for men and women would prove satisfactory for applied work. The resulting solutions were congruent with previous studies and showed a high degree of simple structure. Support was provided for one, but not both, of the two additional second-order factors. Results also supported the use of simplified estimation formulas for applied use.

scholarly journals On the Sensitivity of Local Flexibility Markets to Forecast Error: A Bi-Level Optimization Approach

Energies ◽  
2020 ◽  
Vol 13 (8) ◽  
pp. 1959
Author(s):  
Delaram Azari ◽  
Shahab Shariat Torbaghan ◽  
Hans Cappon ◽  
Karel J. Keesman ◽  
Madeleine Gibescu ◽  
...  
Keyword(s):  
Distribution System ◽  
Large Scale ◽  
Optimization Problem ◽  
Distribution Networks ◽  
Second Order ◽  
Optimization Approach ◽  
Second Order Cone ◽  
Local Flexibility ◽  
Level Problem ◽  
Relaxation Error

The large-scale integration of intermittent distributed energy resources has led to increased uncertainty in the planning and operation of distribution networks. The optimal flexibility dispatch is a recently introduced, power flow-based method that a distribution system operator can use to effectively determine the amount of flexibility it needs to procure from the controllable resources available on the demand side. However, the drawback of this method is that the optimal flexibility dispatch is inexact due to the relaxation error inherent in the second-order cone formulation. In this paper we propose a novel bi-level optimization problem, where the upper level problem seeks to minimize the relaxation error and the lower level solves the earlier introduced convex second-order cone optimal flexibility dispatch (SOC-OFD) problem. To make the problem tractable, we introduce an innovative reformulation to recast the bi-level problem as a non-linear, single level optimization problem which results in no loss of accuracy. We subsequently investigate the sensitivity of the optimal flexibility schedules and the locational flexibility prices with respect to uncertainty in load forecast and flexibility ranges of the demand response providers which are input parameters to the problem. The sensitivity analysis is performed based on the perturbed Karush–Kuhn–Tucker (KKT) conditions. We investigate the feasibility and scalability of the proposed method in three case studies of standardized 9-bus, 30-bus, and 300-bus test systems. Simulation results in terms of local flexibility prices are interpreted in economic terms and show the effectiveness of the proposed approach.

Dynamics of collapse of an impact central uplift: Evidence from folds and faults in the collar of the Vredefort Dome, South Africa

2021 ◽  
Author(s):  
Shalene Manzi ◽  
Roger L. Gibson ◽  
Asinne Tshibubudze
Keyword(s):  
South Africa ◽  
Structural Analysis ◽  
Large Scale ◽  
Second Order ◽  
Upward Flow ◽  
Downward Flow ◽  
Kinematic Pattern ◽  
Central Uplift ◽  
Convergent Flow ◽  
Order Structures

ABSTRACT Structural analysis of overturned metasedimentary strata of the lower Witwatersrand Supergroup in the inner collar of the Vredefort Dome reveals the presence of tangential folds and faults associated with the 2.02 Ga impact. The folds are distinct from previously identified subradially oriented, vertical to plunging-inclined, gentle folds that are interpreted as the products of convergent flow (constriction) during the initial stages of central uplift formation. The tangential folds comprise disharmonic, open, asymmetric, horizontal to plunging-inclined anticline-syncline pairs with centripetally dipping axial planes and right-way-up intermediate limbs. They display centripetal-down vergence (anticline radially outward of the syncline) that is consistent with steep inward-directed shear of the overturned strata. We attribute this kinematic pattern to subvertical collapse of the Vredefort central uplift during the latter stages of crater modification. The folds are cut by pseudotachylite-bearing steep to vertical tangential faults that display center-down slip of &lt;10 m up to ~150 m. Both the tangential folds and the faults suggest that the large-scale overturning of strata related to outward collapse of the Vredefort central uplift was accompanied by a component of inward-directed collapse via layer-parallel shearing and folding, followed by faulting. Subradially oriented faults with conjugate strike separations of 1–2 km in the NNE collar of the dome suggest penecontemporaneous tangential extension of the inner collar rocks. This evidence indicates that second-order structures in the metasedimentary collar of the Vredefort Dome preserve a complex, multistage record of evolving strain associated with both initial convergent and upward flow (constriction) related to central uplift rise and later divergent and downward flow (flattening) linked to its collapse, and that centripetally directed collapse features may be important components of the structural inventory of very large central uplifts.

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