local geometry
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Author(s):  
Gil Bor ◽  
Omid Makhmali ◽  
Paweł Nurowski

AbstractWe study the local geometry of 4-manifolds equipped with a para-Kähler-Einstein (pKE) metric, a special type of split-signature pseudo-Riemannian metric, and their associated twistor distribution, a rank 2 distribution on the 5-dimensional total space of the circle bundle of self-dual null 2-planes. For pKE metrics with non-zero scalar curvature this twistor distribution has exactly two integral leaves and is ‘maximally non-integrable’ on their complement, a so-called (2,3,5)-distribution. Our main result establishes a simple correspondence between the anti-self-dual Weyl tensor of a pKE metric with non-zero scalar curvature and the Cartan quartic of the associated twistor distribution. This will be followed by a discussion of this correspondence for general split-signature metrics which is shown to be much more involved. We use Cartan’s method of equivalence to produce a large number of explicit examples of pKE metrics with non-zero scalar curvature whose anti-self-dual Weyl tensor have special real Petrov type. In the case of real Petrov type D,  we obtain a complete local classification. Combined with the main result, this produces twistor distributions whose Cartan quartic has the same algebraic type as the Petrov type of the constructed pKE metrics. In a similar manner, one can obtain twistor distributions with Cartan quartic of arbitrary algebraic type. As a byproduct of our pKE examples we naturally obtain para-Sasaki-Einstein metrics in five dimensions. Furthermore, we study various Cartan geometries naturally associated to certain classes of pKE 4-dimensional metrics. We observe that in some geometrically distinguished cases the corresponding Cartan connections satisfy the Yang-Mills equations. We then provide explicit examples of such Yang-Mills Cartan connections.


2021 ◽  
Author(s):  
Yinan Xu ◽  
Nicole LiBretto ◽  
Guanghui Zhang ◽  
Jeffrey Miller ◽  
Jeffrey Greeley

Amorphous, single site, silica-supported main group metal catalysts have recently been found to promote olefin oligomerization with high activity at moderate temperatures and pressures (~250°C and 1 atm). Herein, we explore the molecular-level relationship between active site structures and the associated oligomerization mechanisms by developing amorphous, silica-supported Ga3+ models from periodic, first-principles calculations. Representative Ga3+ sites, including three- and four-coordinated geometries, are tested for multiple ethylene oligomerization pathways. We show that the three-coordinated Ga3+ site promotes oligomerization through a facile initiation process that generates a Ga-alkyl intermediate, followed by a Ga-alkyl-centered Cossee-Arlman mechanism. The strained geometry of a three-coordinated site enables a favorable free energy landscape with a kinetically accessible ethylene insertion transition state (1.7 eV) and a previously unreported β-hydride transfer step (1.0 eV) to terminate further C-C bond formation. This result, in turn, suggests that Ga3+ does not favor polymerization chemistry, while microkinetic modeling confirms that ethylene insertion is the rate-determining step. The study demonstrates promising flexibility of main group ions for hydrocarbon transformations and, more generally, highlights the importance of the local geometry of metal ions on amorphous oxides in determining catalytic properties.


2021 ◽  
Vol 15 ◽  
Author(s):  
Shreyas Fadnavis ◽  
Stefan Endres ◽  
Qiuting Wen ◽  
Yu-Chien Wu ◽  
Hu Cheng ◽  
...  

In this work, we shed light on the issue of estimating Intravoxel Incoherent Motion (IVIM) for diffusion and perfusion estimation by characterizing the objective function using simplicial homology tools. We provide a robust solution via topological optimization of this model so that the estimates are more reliable and accurate. Estimating the tissue microstructure from diffusion MRI is in itself an ill-posed and a non-linear inverse problem. Using variable projection functional (VarPro) to fit the standard bi-exponential IVIM model we perform the optimization using simplicial homology based global optimization to better understand the topology of objective function surface. We theoretically show how the proposed methodology can recover the model parameters more accurately and consistently by casting it in a reduced subspace given by VarPro. Additionally we demonstrate that the IVIM model parameters cannot be accurately reconstructed using conventional numerical optimization methods due to the presence of infinite solutions in subspaces. The proposed method helps uncover multiple global minima by analyzing the local geometry of the model enabling the generation of reliable estimates of model parameters.


2021 ◽  
Author(s):  
Yadi Cheng ◽  
Xubiao Peng

The COVID-19 epidemic, caused by virus SARS-CoV-2, has been a pandemic and threatening everyone's health in the past two years. In SARS-CoV-2, the accessory protein ORF8 plays an important role in immune modulation. Here we present an in silico study on the effects of the disulfide bonds in ORF8, including the effects on the structures, the binding sites and free energy when ORF8 binds to the human leukocyte antigen (HLA-A). Using the explicit solvent Molecular Dynamics (MD) simulations, we collect the conformational ensembles on ORF8 with different disulfide bonds reduction schemes. With a new visualization technique on the local geometry, we analyze the effects of the disulfide bonds on the structure of ORF8. We find that the disulfide bonds have large influences on the loop regions of the surface. Moreover, by performing docking between HLA-A and the conformational ensembles of ORF8, we predict the preferred binding sites and find that most of them are little affected by the disulfide bonds. Further, we estimate the binding free energy between HLA-A and ORF8 with different disulfide bonds reductions. In the end, from the comparison with the available experimental results on the epitopes of ORF8, we validated our binding sites prediction. All the above observations may provide inspirations on inhibitor/drug design against ORF8 based on the binding pathway with HLA-A.


Physchem ◽  
2021 ◽  
Vol 1 (3) ◽  
pp. 250-258
Author(s):  
G. M. Pugliese ◽  
L. Tortora ◽  
E. Paris ◽  
T. Wakita ◽  
K. Terashima ◽  
...  

We have investigated the local structure of BiS2-based layered materials by Bi L3-edge extended X-ray absorption fine structure (EXAFS) measurements performed on single crystal samples with polarization of the X-ray beam parallel to the BiS2 plane. The results confirm highly instable nature of BiS2 layer, characterized by ferroelectric like distortions. The distortion amplitude, determined by the separation between the two in-plane (Bi-S1) bonds, is found to be highest in LaO0.77F0.23BiS2 with ΔR∼0.26 Å and lowest in NdO0.71F0.29BiS2 with ΔR∼0.13 Å. Among the systems with intrinsic doping, CeOBiS2 shows smaller distortion (ΔR∼0.15 Å) than PrOBiS2 (ΔR∼0.18 Å) while the highest distortion appears for EuFBiS2 revealing ΔR∼0.22 Å. It appears that the distortion amplitude is controlled by the nature of the RE(O,F) spacer layer in the RE(O,F)BiS2 structure. The X-ray absorption near edge structure (XANES) spectra, probing the local geometry, shows a spectral weight transfer that evolves systematically with the distortion amplitude in the BiS2-layer. The results provide a quantitative measurements of the local distortions in the instable BiS2-layer with direct implication on the physical properties of these materials.


2021 ◽  
Vol 12 (1) ◽  
Author(s):  
Antoine Aubret ◽  
Quentin Martinet ◽  
Jeremie Palacci

AbstractMachines enabled the Industrial Revolution and are central to modern technological progress: A machine’s parts transmit forces, motion, and energy to one another in a predetermined manner. Today’s engineering frontier, building artificial micromachines that emulate the biological machinery of living organisms, requires faithful assembly and energy consumption at the microscale. Here, we demonstrate the programmable assembly of active particles into autonomous metamachines using optical templates. Metamachines, or machines made of machines, are stable, mobile and autonomous architectures, whose dynamics stems from the geometry. We use the interplay between anisotropic force generation of the active colloids with the control of their orientation by local geometry. This allows autonomous reprogramming of active particles of the metamachines to achieve multiple functions. It permits the modular assembly of metamachines by fusion, reconfiguration of metamachines and, we anticipate, a shift in focus of self-assembly towards active matter and reprogrammable materials.


2021 ◽  
Vol 2021 ◽  
pp. 1-19
Author(s):  
Shicheng Li ◽  
Shumin Lai ◽  
Yan Jiang ◽  
Wenle Wang ◽  
Yugen Yi

Anomaly detection (AD) aims to distinguish the data points that are inconsistent with the overall pattern of the data. Recently, unsupervised anomaly detection methods have aroused huge attention. Among these methods, feature representation (FR) plays an important role, which can directly affect the performance of anomaly detection. Sparse representation (SR) can be regarded as one of matrix factorization (MF) methods, which is a powerful tool for FR. However, there are some limitations in the original SR. On the one hand, it just learns the shallow feature representations, which leads to the poor performance for anomaly detection. On the other hand, the local geometry structure information of data is ignored. To address these shortcomings, a graph regularized deep sparse representation (GRDSR) approach is proposed for unsupervised anomaly detection in this work. In GRDSR, a deep representation framework is first designed by extending the single layer MF to a multilayer MF for extracting hierarchical structure from the original data. Next, a graph regularization term is introduced to capture the intrinsic local geometric structure information of the original data during the process of FR, making the deep features preserve the neighborhood relationship well. Then, a L1-norm-based sparsity constraint is added to enhance the discriminant ability of the deep features. Finally, a reconstruction error is applied to distinguish anomalies. In order to demonstrate the effectiveness of the proposed approach, we conduct extensive experiments on ten datasets. Compared with the state-of-the-art methods, the proposed approach can achieve the best performance.


2021 ◽  
Author(s):  
Radu Alexandru Rosu ◽  
Peer Schütt ◽  
Jan Quenzel ◽  
Sven Behnke

AbstractDeep convolutional neural networks have shown outstanding performance in the task of semantically segmenting images. Applying the same methods on 3D data still poses challenges due to the heavy memory requirements and the lack of structured data. Here, we propose LatticeNet, a novel approach for 3D semantic segmentation, which takes raw point clouds as input. A PointNet describes the local geometry which we embed into a sparse permutohedral lattice. The lattice allows for fast convolutions while keeping a low memory footprint. Further, we introduce DeformSlice, a novel learned data-dependent interpolation for projecting lattice features back onto the point cloud. We present results of 3D segmentation on multiple datasets where our method achieves state-of-the-art performance. We also extend and evaluate our network for instance and dynamic object segmentation.


2021 ◽  
Vol 2021 ◽  
pp. 1-10
Author(s):  
Xia Miao ◽  
Ziyao Yu ◽  
Ming Liu

The partial differential equation learning model is applied to another high-level visual-processing problem: face recognition. A novel feature selection method based on partial differential equation learning model is proposed. The extracted features are invariant to rotation and translation and more robust to illumination changes. In the evaluation of students’ concentration in class, this paper firstly uses the face detection algorithm in face recognition technology to detect the face and intercept the expression data, and calculates the rise rate. Then, the improved model of concentration analysis and evaluation of a college Chinese class is used to recognize facial expression, and the corresponding weight is given to calculate the expression score. Finally, the head-up rate calculated at the same time is multiplied by the expression score as the final concentration score. Through the experiment and analysis of the experimental results in the actual classroom, the corresponding conclusions are drawn and teaching suggestions are provided for teachers. For each face, a large neighborhood set is firstly selected by the k -nearest neighbor method, and then, the sparse representation of sample points in the neighborhood is obtained, which effectively combines the locality of k -nearest neighbor and the robustness of sparse representation. In the sparse preserving nonnegative block alignment algorithm, a discriminant partial optimization model is constructed by using sparse reconstruction coefficients to describe local geometry and weighted distance to describe class separability. The two algorithms obtain good clustering and recognition results in various cases of real and simulated occlusion, which shows the effectiveness and robustness of the algorithm. In order to verify the reliability of the model, this paper verified the model through in-class practice tests, teachers’ questions, and interviews with students and teachers. The results show that the proposed joint evaluation method based on expression and head-up rate has high accuracy and reliability.


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