Contingent derivatives and regularization for noncoercive inverse problems

Abstract

We study the inverse problem of parameter identification in noncoercive variational problems that commonly appear in applied models. We examine the differentiability of the set-valued parameter-to-solution map using the first-order and the second-order contingent derivatives. We explore the inverse problem using the output least-squares and the modified output least-squares objectives. By regularizing the noncoercive variational problem, we obtain a single-valued regularized parameter-to-solution map and investigate its smoothness and boundedness. We also consider optimization problems using the output least-squares and the modified output least-squares objectives for the regularized variational problem. We give a complete convergence analysis showing that for the output least-squares and the modified output least-squares, the regularized minimization problems approximate the original optimization problems suitably. We also provide the first-order and the second-order adjoint method for the computation of the first-order and the second-order derivatives of the output least-squares objective. We provide discrete formulas for the gradient and the Hessian calculation and present numerical results.     

求解矩阵方程AXB+CXD=F参数迭代法的最优参数分析

本文针对求矩阵方程AXB+CXD=F唯一解的参数迭代法，分析当矩阵A，B，C，D均是Hermite正（负）定矩阵时，迭代矩阵的特征值表达式，给出了最优参数的确定方法，并提出了相应的加速算法.     

On modifying properties of polymeric melts by nanoscopic particles

We study geometric and energetic factors that partake in modifying properties of polymeric melts via inserting well‐dispersed nanoscopic particles (NP). Model systems are cis‐1,4‐polybutadiene melts including a single atomic clusters of size varied in the range 10–150 atoms (3–7 Å in radius; 0.1–1.5% v/v). We modify the interactions between the chains and the particle by tuning attractive van der Waals interactions. Using molecular dynamics, we study equilibrium fluctuations and dynamical properties at the interface. The NPs move in the polymer matrix in two different regimes corresponding to trapped and free diffusion, depending on the NP size. Furthermore, degree of crowding around the NP by the polymer chains is quantified. Effect of NP size and interaction strength both on volume and volumetric fluctuations is manifested in mechanical properties, quantified here by bulk modulus, K. Tuning NP size and nonbonded interactions results in ～15% enhancement in K by addition of a maximum of 1.5% v/v NP. © 2012 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys, 2012     

Bilevel convex programming models

Bilevel convex models are studied after being cast into a parametric programming form. This form has a lexicographic inner-outer structure where the optimal value of the outer model is optimized on the set of optimal solutions of the inner model. Optimal solutions are characterized using a Lagrangian saddle-point approach and a marginal value formula is given for the outer model. These are used to formulate a general method for finding an optimal solution by input optimization.     

Dynamics of plasma channel in a parallel-plate plasma gun

Lumped parameter models for describing dynamics of the plasma channel in a parallel-plate plasma gun are compared with the experimental results obtained from two plasma guns with different rail geometries. Comparison between the experiments and the numerical calculations reveals that the lumped parameter models can be utilized to describe the dynamic motion of the plasma channel quite well. Parametric study shows that minimizing the line inductance and increasing the charging voltage on a capacitor as well as minimizing the gas injection time for reducing the mass of the plasma channel are the key factors to increase the flow velocity of the plasma jet ejected from the plasma gun.     

改进的pair-copula参数估计方法在经济研究中的应用

对于pair-copula中的参数估计,大多假设copula函数的参数和条件变量独立,将参数简化成一个不依赖于条件变量的常数.本文假设copula函数的参数和条件变量不独立,该参数是以条件变量为自变量的一元函数.应用该方法实证分析了“克强指数”三个指标铁路货运量、工业用电量和贷款发放量的对数增长率之间的关系,研究发现该方法优于简化的pair-copula参数估计,并且得出在固定铁路货运量不变时,工业用电量和银行贷款发放量成负相关关系,且这种负相关性随铁路货运量增加而减弱.     

A cosmological study in massive gravity theory

A detailed study of the various cosmological aspects in massive gravity theory has been presented in the present work. For the homogeneous and isotropic FLRW model, the deceleration parameter has been evaluated, and, it has been examined whether there is any transition from deceleration to acceleration in recent past, or not. With the proper choice of the free parameters, it has been shown that the massive gravity theory is equivalent to Einstein gravity with a modified Newtonian gravitational constant together with a negative cosmological constant. Also, in this context, it has been examined whether the emergent scenario is possible, or not, in massive gravity theory. Finally, we have done a cosmographic analysis in massive gravity theory.     

Orientational order parameter studies on 3.Om and 3O.Om liquid crystals

Orientational order parameter S is evaluated in the nematic phase of six liquid crystal compounds, N-(p-n-propyl benzylidene)-p-n-alkoxy anilines, 3.Om and N-(p-n-propyloxy benzylidene)-p-n-alkoxy anilines, 3O.Om compounds with m = 6, 7 and 8, using different methods. The techniques employed are S from birefringence δn, Haller's approximation from (1?T/T_c) ^β, effective geometry parameter α_g and Vuks’ scaling factor S_C. The values of S obtained using the above methods are compared with one another and with the results on a number of liquid crystals; the liquid crystals favor isotropic Vuks’ method.     

DOT2: Macromolecular docking with improved biophysical models

Computational docking is a useful tool for predicting macromolecular complexes, which are often difficult to determine experimentally. Here, we present the DOT2 software suite, an updated version of the DOT intermolecular docking program. DOT2 provides straightforward, automated construction of improved biophysical models based on molecular coordinates, offering checkpoints that guide the user to include critical features. DOT has been updated to run more quickly, allow flexibility in grid size and spacing, and generate an infinitive complete list of favorable candidate configurations. Output can be filtered by experimental data and rescored by the sum of electrostatic and atomic desolvation energies. We show that this rescoring method improves the ranking of correct complexes for a wide range of macromolecular interactions and demonstrate that biologically relevant models are essential for biologically relevant results. The flexibility and versatility of DOT2 accommodate realistic models of complex biological systems, improving the likelihood of a successful docking outcome. © 2013 Wiley Periodicals, Inc.