An Optimally Generalized Steepest-Descent Algorithm for Solving Ill-Posed Linear Systems

Liu, Chein‐Shan

doi:10.1155/2013/154358

Cited by 5 publications

(3 citation statements)

References 37 publications

(50 reference statements)

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“…We used the ff99SB force field for the protein, and the corresponding parameters were generated using the LEaP program in AMBER. − The above systems were then solvated using the TIP3P water . The resulting systems were subsequently energy minimized by the steepest descent algorithm and the conjugate gradient methods. , After that, the systems were heated and equilibrated in the NPT ensemble at a pressure of 1 bar and a temperature of 300 K for 1 ns, and then the molecular dynamics (MD) simulations were carried out in the canonical ( NVT ) ensemble at 300 K for 20 ns using the AMBER18 program . During the MD simulation, the distance constraints were applied on all bonds involving H atoms using SHAKE .…”

Section: Computational Detailsmentioning

confidence: 99%

Free Energy Landscapes of the Tautomeric Interconversion of Pyridoxal 5′-Phosphate Aldimines at the Active Site of Ornithine Decarboxylase in Aqueous Media

Rastogi,

Chandra

2023

J. Phys. Chem. B

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The pyridoxal 5′-phosphate (PLP) acts as a coenzyme for a large number of biochemical reactions. It exists in mainly two bound forms at the active site of the concerned enzyme: the internal aldimine, in which the PLP is bound with the ϵ-amino group of lysine at the active site, and the external aldimine, where the PLP is bound to the substrate amino acid. Both the internal and external aldimines have Schiff base linkage (N−H−O) and can exist in two tautomeric structures of ketoenamine and enolimine forms. In this work, we have investigated the free energy landscape for the tautomeric proton transfer in the internal and external aldimines at the active site of the ornithine decarboxylase enzyme in an aqueous medium. We performed hybrid quantum-classical metadynamics and force field-based molecular dynamics simulations, which revealed that the ketoenamine tautomer is more stable than the enolimine form. The QM/MM metadynamics calculations show that the free energy difference between the ketoenamine and enolimine forms for the internal aldimine is 3.9 kcal/mol, and it is found to be 5.8 kcal/mol for the external aldimine, with the ketoenamine form being more stable in both cases. The results are further supported by calculations of the binding free energies from classical simulations and static quantum chemical calculations in different environments. We have also analyzed the configurational structure of the microenvironment at the active site in order to have better insights into the interactions of the active site residues with the PLP in its two tautomeric forms.

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Section: Computational Detailsmentioning

confidence: 99%

Free Energy Landscapes of the Tautomeric Interconversion of Pyridoxal 5′-Phosphate Aldimines at the Active Site of Ornithine Decarboxylase in Aqueous Media

Rastogi,

Chandra

2023

J. Phys. Chem. B

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“…Image reconstruction is an ill-posed problem, and it is generally known that Tikhonov regularization is an efficient way to solve ill-posed problems. Its basic idea is to transform equation (1) into an optimization problem [20][21][22][23][24]:…”

Section: Image Reconstructionmentioning

confidence: 99%

Research on Coal-Rock Fracture Image Edge Detection Based on Tikhonov Regularization and Fractional Order Differential Operator

Liu

Ren

2019

Journal of Electrical and Computer Engineering

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Aiming at the conventional image edge detection algorithm, the first-order differential edge detection method is easy to lose the image details and the second-order differential edge detection method is more sensitive to noise. To deal with the problem, the Tikhonov regularization method is adopted to reconstruct the input coal-rock infrared images, so as to reduce the noise interference, and then, the reconstructed image is transformed by gray level. Finally, we consider the frequency characteristics and long memory properties of fractional differential, the classical first-order Sobel and second-order Laplacian edge detection algorithms are extended to fractional order pattern, and a new pattern of fractional order differential image edge detection is constructed to realize the coal-rock fracture edge features identification. The results show that, compared with integer order differential, the error rate and omission rate of fractional order differential algorithm are smaller, the quality factor is larger, and the execution time and memory footprint are smaller. From the point of view of location criteria and location accuracy, the fractional order differential algorithm is better than the integer order. In addition, the proposed method is compared with Canny algorithm, B-spline wavelet transform, and multidirection fuzzy morphological edge detection method, can detect more coal-rock fracture infrared image edge details, and is more robust to noise.

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“…In this paper, an improved super-memory gradient (ISMG) method was introduced to solve objective function of (15). Most of the well-known iterative algorithms for solving (15) take the following form [46][47][48][49]:…”

Section: The Algorithm For Solving Unconstrained Optimization Problemmentioning

confidence: 99%

A Novel Fractional Tikhonov Regularization Coupled with an Improved Super-Memory Gradient Method and Application to Dynamic Force Identification Problems

Wang

Ren

Liu

2018

Mathematical Problems in Engineering

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This paper presents a novel inverse technique to provide a stable optimal solution for the ill-posed dynamic force identification problems. Due to ill-posedness of the inverse problems, conventional numerical approach for solutions results in arbitrarily large errors in solution. However, in the field of engineering mathematics, there are famous mathematical algorithms to tackle the illposed problem, which are known as regularization techniques. In the current study, a novel fractional Tikhonov regularization (NFTR) method is proposed to perform an effective inverse identification, then the smoothing functional of the ill-posed problem processed by the proposed method is regarded as an optimization problem, and finally a stable optimal solution is obtained by using an improved super-memory gradient (ISMG) method. The result of the present method is compared with that of the standard TR method and FTR method; new findings can be obtained; that is, the present method can improve accuracy and stability of the inverse identification problem, robustness is stronger, and the rate of convergence is faster. The applicability and efficiency of the present method in this paper are demonstrated through a mathematical example and an engineering example.

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An Optimally Generalized Steepest-Descent Algorithm for Solving Ill-Posed Linear Systems

Cited by 5 publications

References 37 publications

Free Energy Landscapes of the Tautomeric Interconversion of Pyridoxal 5′-Phosphate Aldimines at the Active Site of Ornithine Decarboxylase in Aqueous Media

Free Energy Landscapes of the Tautomeric Interconversion of Pyridoxal 5′-Phosphate Aldimines at the Active Site of Ornithine Decarboxylase in Aqueous Media

Research on Coal-Rock Fracture Image Edge Detection Based on Tikhonov Regularization and Fractional Order Differential Operator

A Novel Fractional Tikhonov Regularization Coupled with an Improved Super-Memory Gradient Method and Application to Dynamic Force Identification Problems

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