scholarly journals Estimation and inference with a (nearly) singular Jacobian

10.3982/qe989 ◽  
2019 ◽  
Vol 10 (3) ◽  
pp. 1019-1068 ◽  
Author(s):  
Sukjin Han ◽  
Adam McCloskey
Keyword(s):  
Nonlinear Models ◽  
Sample Selection ◽  
Model Parameters ◽  
Asymptotic Results ◽  
Household Expenditures ◽  
One Dimensional ◽  
Asymptotic Size ◽  
Threshold Crossing ◽  
Low Dimensional ◽  
Singular Jacobian

This paper develops extremum estimation and inference results for nonlinear models with very general forms of potential identification failure when the source of this identification failure is known. We examine models that may have a general deficient rank Jacobian in certain parts of the parameter space. When identification fails in one of these models, it becomes underidentified and the identification status of individual parameters is not generally straightforward to characterize. We provide a systematic reparameterization procedure that leads to a reparametrized model with straightforward identification status. Using this reparameterization, we determine the asymptotic behavior of standard extremum estimators and Wald statistics under a comprehensive class of parameter sequences characterizing the strength of identification of the model parameters, ranging from nonidentification to strong identification. Using the asymptotic results, we propose hypothesis testing methods that make use of a standard Wald statistic and data‐dependent critical values, leading to tests with correct asymptotic size regardless of identification strength and good power properties. Importantly, this allows one to directly conduct uniform inference on low‐dimensional functions of the model parameters, including one‐dimensional subvectors. The paper illustrates these results in three examples: a sample selection model, a triangular threshold crossing model, and a collective model for household expenditures.

A Theoretical Analysis of CO2 Absorption in Sun Versus Shade Leaves

1978 ◽  
Vol 100 (1) ◽  
pp. 20-24 ◽  
Author(s):  
R. H. Rand
Keyword(s):  
Experimental Data ◽  
Quantitative Estimate ◽  
Geometric Model ◽  
Model Parameters ◽  
Co2 Absorption ◽  
Temperature Model ◽  
Spongy Mesophyll ◽  
One Dimensional ◽  
Mesophyll Tissue ◽  
Shade Leaves

A one-dimensional, steady-state, constant temperature model of diffusion and absorption of CO2 in the intercellular air spaces of a leaf is presented. The model includes two geometrically distinct regions of the leaf interior, corresponding to palisade and spongy mesophyll tissue, respectively. Sun, shade, and intermediate light leaves are modeled by varying the thicknesses of these two regions. Values of the geometric model parameters are obtained by comparing geometric properties of the model with experimental data of other investigators found from dissection of real leaves. The model provides a quantitative estimate of the extent to which the concentration of gaseous CO2 varies locally within the leaf interior.

On shock-induced light-fluid-layer evolution

2021 ◽  
Vol 933 ◽  
Author(s):  
Yu Liang ◽  
Xisheng Luo
Keyword(s):  
Layer Thickness ◽  
Coupling Effect ◽  
Fluid Layer ◽  
Nonlinear Models ◽  
Interfacial Instability ◽  
Dimensional Theory ◽  
One Dimensional ◽  
Helium Gas ◽  
Wave Patterns ◽  
Thickness Variations

Shock-induced light-fluid-layer evolution is firstly investigated experimentally and theoretically. Specifically, three quasi-one-dimensional helium gas layers with different layer thicknesses are generated to study the wave patterns and interface motions. Six quasi-two-dimensional helium gas layers with diverse layer thicknesses and amplitude combinations are created to explore the Richtmyer–Meshkov instability of a light-fluid layer. Due to the multiple reflected shocks reverberating inside a light-fluid layer, the speeds of the two interfaces gradually converge, and the layer thickness saturates eventually. A general one-dimensional theory is adopted to describe the two interfaces’ motions and the layer thickness variations. It is found that, for the first interface, the end time of its phase reversal determines the influence of the reflected shocks on it. However, the reverberated shocks indeed lead to the second interface being more unstable. When the two interfaces are initially in phase, and the initial fluid layer is very thin, the two interfaces’ spike heads collide and stabilise the two interfaces. Linear and nonlinear models are successfully adopted by considering the interface-coupling effect and the reverberated shocks to predict the two interfaces’ perturbation growths in all regimes. The interfacial instability of a light-fluid layer is quantitatively compared with that of a heavy-fluid layer. It is concluded that the kind of waves reverberating inside a fluid layer significantly affects the fluid-layer evolution.

scholarly journals Atomic-scale one-dimensional materials identified from graph theory

2021 ◽  
Author(s):  
Shunning Li ◽  
Zhefeng Chen ◽  
Zhi Wang ◽  
Mouyi Weng ◽  
Jianyuan Li ◽  
...  
Keyword(s):  
Graph Theory ◽  
Structural Information ◽  
Functional Materials ◽  
Atomic Scale ◽  
Computational Techniques ◽  
Electronic Band ◽  
One Dimensional ◽  
Atomic Chains ◽  
Future Data ◽  
Low Dimensional

Abstract The past decades have witnessed an exponential growth in the discovery of functional materials, benefited from our unprecedented capabilities in characterizing their structure, chemistry, and morphology with the aid of advanced imaging, spectroscopic and computational techniques. Among these materials, atomic-scale low-dimensional compounds, as represented by the two-dimensional (2D) atomic layers, one-dimensional (1D) atomic chains and zero-dimensional (0D) atomic clusters, have long captivated scientific interest due to their unique topological motifs and exceptional properties. Their tremendous potentials in various applications make it a pressing urgency to establish a complete database of their structural information, especially for the underexplored 1D species. Here we apply graph theory in combination with first-principles high-throughput calculations to identify atomic-scale 1D materials that can be conceptually isolated from their parent bulk crystals. In total, two hundred and fifty 1D atomic chains are shown to be potentially exfoliable. We demonstrate how the lone electron pairs on cations interact with the p-orbitals of anions and hence stabilize their edge sites. Data analysis of the 2D and 1D materials also reveals the dependence of electronic band gap on the cationic percolation network determined by graph theory. The library of 1D compounds systematically identified in this work will pave the way for the predictive discovery of material systems for quantum engineering, and can serve as a source of stimuli for future data-driven design and understanding of functional materials with reduced dimensionality.

Reduced-order modelling of the flow around a high-lift configuration with unsteady Coanda blowing

2016 ◽  
Vol 800 ◽  
pp. 72-110 ◽  
Author(s):  
Richard Semaan ◽  
Pradeep Kumar ◽  
Marco Burnazzi ◽  
Gilles Tissot ◽  
Laurent Cordier ◽  
...  
Keyword(s):  
Transient Flow ◽  
Stokes Equations ◽  
Lift Coefficient ◽  
Mean Field ◽  
Galerkin Projection ◽  
Validation Dataset ◽  
Model Parameters ◽  
High Lift ◽  
Modal Expansion ◽  
Low Dimensional

We propose a hierarchy of low-dimensional proper orthogonal decomposition (POD) models for the transient and post-transient flow around a high-lift airfoil with unsteady Coanda blowing over the trailing edge. The modal expansion comprises actuation modes as a lifting method for wall actuation following Graham et al. (Intl J. Numer. Meth. Engng, vol. 44 (7), 1999, pp. 945–972) and Kasnakoğlu et al. (Intl J. Control, vol. 81 (9), 2008, pp. 1475–1492). A novel element is separate actuation modes for different frequencies. The structure of the dynamic model rests on a Galerkin projection using the Navier–Stokes equations, simplifying mean-field considerations, and a stochastic term representing the background turbulence. The model parameters are identified with a data assimilation (4D-Var) method. We propose a model hierarchy from a linear oscillator explaining the suppression of vortex shedding by blowing to a fully nonlinear model resolving unactuated and actuated transients with steady and high-frequency modulation of blowing. The models’ accuracy is assessed through the mode amplitudes and an estimator for the lift coefficient. The robustness of the model is physically justified, and then observed for the training and the validation dataset.

scholarly journals A Simple Alternating Direction Method for the Conic Trust Region Subproblem

2018 ◽  
Vol 2018 ◽  
pp. 1-9
Author(s):  
Honglan Zhu ◽  
Qin Ni
Keyword(s):  
Trust Region ◽  
Alternating Direction Method ◽  
New Method ◽  
Quadratic Model ◽  
Descent Direction ◽  
Orthogonal Direction ◽  
Trust Region Subproblem ◽  
One Dimensional ◽  
Alternating Direction ◽  
Low Dimensional

A simple alternating direction method is used to solve the conic trust region subproblem of unconstrained optimization. By use of the new method, the subproblem is solved by two steps in a descent direction and its orthogonal direction, the original conic trust domain subproblem into a one-dimensional subproblem and a low-dimensional quadratic model subproblem, both of which are very easy to solve. Then the global convergence of the method under some reasonable conditions is established. Numerical experiment shows that the new method seems simple and effective.

scholarly journals Inference of a Mesoscopic Population Model from Population Spike Trains

2020 ◽  
Vol 32 (8) ◽  
pp. 1448-1498 ◽  
Author(s):  
Alexandre René ◽  
André Longtin ◽  
Jakob H. Macke
Keyword(s):  
Population Model ◽  
Single Neuron ◽  
Simulated Data ◽  
Population Data ◽  
Model Parameters ◽  
Population Activity ◽  
Mcmc Sampling ◽  
Wide Range ◽  
Low Dimensional ◽  
Aggregate Population

Understanding how rich dynamics emerge in neural populations requires models exhibiting a wide range of behaviors while remaining interpretable in terms of connectivity and single-neuron dynamics. However, it has been challenging to fit such mechanistic spiking networks at the single-neuron scale to empirical population data. To close this gap, we propose to fit such data at a mesoscale, using a mechanistic but low-dimensional and, hence, statistically tractable model. The mesoscopic representation is obtained by approximating a population of neurons as multiple homogeneous pools of neurons and modeling the dynamics of the aggregate population activity within each pool. We derive the likelihood of both single-neuron and connectivity parameters given this activity, which can then be used to optimize parameters by gradient ascent on the log likelihood or perform Bayesian inference using Markov chain Monte Carlo (MCMC) sampling. We illustrate this approach using a model of generalized integrate-and-fire neurons for which mesoscopic dynamics have been previously derived and show that both single-neuron and connectivity parameters can be recovered from simulated data. In particular, our inference method extracts posterior correlations between model parameters, which define parameter subsets able to reproduce the data. We compute the Bayesian posterior for combinations of parameters using MCMC sampling and investigate how the approximations inherent in a mesoscopic population model affect the accuracy of the inferred single-neuron parameters.

Upper and Lower Bounds for the Parameters of One-Dimensional Theories for Sandwich Fracture Specimens

2020 ◽  
Vol 88 (3) ◽  
Author(s):  
Roberta Massabò
Keyword(s):  
Crack Length ◽  
Lower Bounds ◽  
Beam Theory ◽  
Approximate Solutions ◽  
Upper And Lower Bounds ◽  
Model Parameters ◽  
One Dimensional ◽  
Limit Value ◽  
Elastic Mismatch ◽  
Fracture Specimens

Abstract Upper and lower bounds for the parameters of one-dimensional theories used in the analysis of sandwich fracture specimens are derived by matching the energy release rate with two-dimensional elasticity solutions. The theory of a beam on an elastic foundation and modified beam theory are considered. Bounds are derived analytically for foundation modulus and crack length correction in single cantilever beam (SCB) sandwich specimens and verified using accurate finite element results and experimental data from the literature. Foundation modulus and crack length correction depend on the elastic mismatch between face sheets and core and are independent of the core thickness if this is above a limit value, which also depends on the elastic mismatch. The results in this paper clarify conflicting results in the literature, explain the approximate solutions, and highlight their limitations. The bounds of the model parameters can be applied directly to specimens satisfying specific geometrical/material ratios, which are given in the paper, or used to support and validate numerical calculations and define asymptotic limits.

Nonlinear Transient Localization and Beat Phenomena due to Backlash in a Coupled Flexible System

2001 ◽  
Author(s):  
Xianghong Ma ◽  
Alexander F. Vakakis
Keyword(s):  
Nonlinear Models ◽  
Order Reduction ◽  
Nonlinear Effects ◽  
Computationally Efficient ◽  
Nonlinear Localization ◽  
Flexible System ◽  
Energy Transfers ◽  
System Reconstruction ◽  
Nonlinear Transient ◽  
Low Dimensional

Abstract Transient nonlinear localization and beat phenomena are studied in a system of two rods coupled with a nonlinear backlash spring. The method of Karhunen-Loeve (K-L) decomposition is used to reduce the order of the dynamics, and to study nonlinear effects by considering energy transfers between leading K-L modes. The computed K-L modes are used to discretize the governing partial differential equations, thus creating accurate and computationally efficient low-dimensional nonlinear models of the system. Reconstruction of transient nonlinear responses using these low dimensional models reveals the accuracy of the order reduction. Poincare’ maps are utilized to study the nonlinear localization and beat phenomena caused by the clearance connecting the coupled rods.

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