gradient model
Recently Published Documents


TOTAL DOCUMENTS

254
(FIVE YEARS 67)

H-INDEX

27
(FIVE YEARS 4)

2021 ◽  
Author(s):  
Tian Lu ◽  
Qinxue Chen

The independent gradient model (IGM) originally proposed in Phys. Chem. Chem. Phys., 19, 17928 (2017) has been increasingly popular in visual analysis of intramolecular and intermolecular interactions in recent years, and it has many clear advantages over the widely employed noncovalent interaction (NCI) method, such as intrafragment and interfragment interactions can be elegantly isolated and thus separately studied, the isosurfaces are smoother and less jaggy. However, we frequently observed that there is an evident shortcoming of IGM map in graphically studying weak interactions, that is its isosurfaces are usually too bulgy; in these cases, not only the graphical effect is poor, but also the color on some areas on the isosurfaces is inappropriate and may lead to erroneous analysis conclusions. In addition, the IGM method was originally proposed based on promolecular density, which is quite crude and does not take actual electronic structure into account. In this article, we first present a detailed overview of the IGM analysis, and then propose our new variant of IGM, namely IGM based on Hirshfeld partition of molecular density (IGMH), which replaces the free-state atomic densities involved in the IGM method with the atomic densities derived by Hirshfeld partition of actual molecular electron density. This change makes IGM have more rigorous physical background. In addition, we describe some indices defined on the top of IGM or IGMH framework to quantify contributions from various atoms or atom pairs to interaction between specific fragments. A large number of application examples in this article, including molecular and periodic systems, weak and chemical bond interactions, fully demonstrate the important value of IGMH in intuitively understanding interactions in chemical systems. Comparisons also showed that the IGMH usually has markedly better graphical effect than IGM and overcomes known problems in IGM. Currently IGMH analysis has been efficiently supported in our freely available and user-friendly wavefunction analysis code Multiwfn (http://sobereva.com/multiwfn), and a detailed tutorial is presented. We hope that IGMH will become a new popular method among chemists for exploring interactions in wide variety of chemical systems.


2021 ◽  
Author(s):  
Karin Labek ◽  
Elisa Sittenberger ◽  
Valerie Kienhoefer ◽  
Luna Rabl ◽  
Irene Messina ◽  
...  

Recent meta-analytic studies of social cognition and the functional imaging of empathy have exposed the overlap between their neural substrates and heteromodal association areas. The 'gradient model' of cortical organization proposes a close relationship between these areas and highly connected hubs in the default mode network, a set of cortical areas deactivated by demanding tasks. Here, we used a decision-making task and representational similarity analysis with classic 'empathy for pain' visual stimuli to probe the relationship between high-level representations of imminent pain in others and the high end of the gradient of this model. High-level representations were found to co-localize with task deactivations or the transitions from activations to deactivations. These loci belonged to two groups: those that loaded on the high end of the principal cortical gradient and were associated by meta-analytic decoding with the default mode network, and those that appeared to accompany functional repurposing of somatosensory cortex in the presence of visual stimuli. In contrast to the nonspecific meta-analytic decoding of these loci, low-level representations, such as those of body parts involved in pain or of pain itself, were decoded with matching topics terms. These findings suggest that that task deactivations may set out cortical areas that host high-level representations, but whose functional characterization in terms of simple mappings is unlikely. We anticipate that an increased understanding of the cortical correlates of high-level representations may improve neurobiological models of social interactions and psychopathology.


2021 ◽  
Author(s):  
Tian Lu ◽  
Qinxue Chen

The independent gradient model (IGM) originally proposed in Phys. Chem. Chem. Phys., 19, 17928 (2017) has been increasingly popular in visual analysis of intramolecular and intermolecular interactions in recent years, and it has many clear advantages over the widely employed noncovalent interaction (NCI) method, such as intrafragment and interfragment interactions can be elegantly isolated and thus separately studied, the isosurfaces are smoother and less jaggy. However, we frequently observed that there is an evident shortcoming of IGM map in graphically studying weak interactions, that is its isosurfaces are usually too bulgy; in these cases, not only the graphical effect is poor, but also the color on some areas on the isosurfaces is inappropriate and may lead to erroneous analysis conclusions. In addition, the IGM method was originally proposed based on promolecular density, which is quite crude and does not take actual electronic structure into account. In this article, we first present a detailed overview of the IGM analysis, and then propose our new variant of IGM, namely IGM based on Hirshfeld partition of molecular density (IGMH), which replaces the free-state atomic densities involved in the IGM method with the atomic densities derived by Hirshfeld partition of actual molecular electron density. This change makes IGM have more rigorous physical background. In addition, we describe some indices defined on the top of IGM or IGMH framework to quantify contributions from various atoms or atom pairs to interaction between specific fragments. A large number of application examples in this article, including molecular and periodic systems, weak and chemical bond interactions, fully demonstrate the important value of IGMH in intuitively understanding interactions in chemical systems. Comparisons also showed that the IGMH usually has markedly better graphical effect than IGM and overcomes known problems in IGM. Currently IGMH analysis has been efficiently supported in our freely available and user-friendly wavefunction analysis code Multiwfn (http://sobereva.com/multiwfn), and a detailed tutorial is presented. We hope that IGMH will become a new popular method among chemists for exploring interactions in wide variety of chemical systems.


2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Ibrahim Ajani ◽  
Cong Lu

Purpose This paper aims to develop a mathematical method to analyze the assembly variation of the non-rigid assembly, considering the manufacturing variations and the deformation variations of the non-rigid parts during the assembly process. Design/methodology/approach First, this paper proposes a deformation gradient model, which represents the deformation variations during the assembly process by considering the forces and the self-weight of the non-rigid parts. Second, the developed deformation gradient models from the assembly process are integrated into the homogenous transformation matrix to model the deformation variations and manufacturing variations of the deformed non-rigid part. Finally, a mathematical model to analyze the assembly variation propagation is developed to predict the dimensional and geometrical variations due to the manufacturing variations and the deformation variations during the assembly process. Findings Through the case study with a crosshead non-rigid assembly, the results indicate that during the assembly process, the individual deformation values of the non-rigid parts are small. However, the cumulative deformation variations of all the non-rigid parts and the manufacturing variations present a target value (w) of −0.2837 mm as compared to a target value of −0.3995 mm when the assembly is assumed to be rigid. The difference in the target values indicates that the influence of the non-rigid part deformation variations during the assembly process on the mechanical assembly accuracy cannot be ignored. Originality/value In this paper, a deformation gradient model is proposed to obtain the deformation variations of non-rigid parts during the assembly process. The small deformation variation, which is often modeled using a finite-element method in the existing works, is modeled using the proposed deformation gradient model and integrated into the nominal dimensions. Using the deformation gradient models, the non-rigid part deformation variations can be computed and the accumulated deformation variation can be easily obtained. The assembly variation propagation model is developed to predict the accuracy of the non-rigid assembly by integrating the deformation gradient models into the homogeneous transformation matrix.


NeuroImage ◽  
2021 ◽  
pp. 118674
Author(s):  
Nadine N. Graedel ◽  
Lars Kasper ◽  
Maria Engel ◽  
Jennifer Nussbaum ◽  
Bertram J. Wilm ◽  
...  
Keyword(s):  

Sign in / Sign up

Export Citation Format

Share Document