scholarly journals Exploring the locking stage of NFGAILS amyloid fibrillation via transition manifold analysis

2021 ◽  
Vol 94 (10) ◽  
Author(s):  
Andreas Bittracher ◽  
Johann Moschner ◽  
Beate Koksch ◽  
Roland Netz ◽  
Christof Schütte
Keyword(s):  
Stochastic Systems ◽  
Bond Distance ◽  
Massively Parallel ◽  
Islet Amyloid ◽  
Multi Scale ◽  
Machine Learning Methods ◽  
Hydrogen Bond Distance ◽  
Dynamical Simulations ◽  
Amyloid Fibrillation ◽  
The Mean

Abstract We demonstrate the application of the transition manifold framework to the late-stage fibrillation process of the NFGAILS peptide, a amyloidogenic fragment of the human islet amyloid polypeptide (hIAPP). This framework formulates machine learning methods for the analysis of multi-scale stochastic systems from short, massively parallel molecular dynamical simulations. We identify key intermediate states and dominant pathways of the process. Furthermore, we identify the optimally timescale-preserving reaction coordinate for the dock-lock process to a fixed pre-formed fibril and show that it exhibits strong correlation with the mean native hydrogen-bond distance. These results pave the way for a comprehensive model reduction and multi-scale analysis of amyloid fibrillation processes. Graphic Abstract

Stochastic homogenization and macroscopic modelling of composites and flow through porous media

2002 ◽  
pp. 337-378 ◽  
Author(s):  
Jozef Telega ◽  
Wlodzimierz Bielski
Keyword(s):  
Porous Medium ◽  
Random Distribution ◽  
Flow Through Porous Media ◽  
Macroscopic Models ◽  
Linear Elastic ◽  
Multi Scale ◽  
Convergence Method ◽  
Flow Through ◽  
The Mean ◽  
Random Porous Medium

The aim of this contribution is mainly twofold. First, the stochastic two-scale convergence in the mean developed by Bourgeat et al. [13] is used to derive the macroscopic models of: (i) diffusion in random porous medium, (ii) nonstationary flow of Stokesian fluid through random linear elastic porous medium. Second, the multi-scale convergence method developed by Allaire and Briane [7] for the case of several microperiodic scales is extended to random distribution of heterogeneities characterized by separated scales (stochastic reiterated homogenization). .

scholarly journals Multi-Scale Aggregation Graph Neural Networks Based on Feature Similarity for Semi-Supervised Learning

Entropy ◽  
2021 ◽  
Vol 23 (4) ◽  
pp. 403
Author(s):  
Xun Zhang ◽  
Lanyan Yang ◽  
Bin Zhang ◽  
Ying Liu ◽  
Dong Jiang ◽  
...  
Keyword(s):  
Neural Network ◽  
Supervised Learning ◽  
Structured Data ◽  
Similarity Matrix ◽  
Scale Feature ◽  
Multi Scale ◽  
Adjacent Node ◽  
Feature Similarity ◽  
The Mean ◽  
Graph Neural Networks

The problem of extracting meaningful data through graph analysis spans a range of different fields, such as social networks, knowledge graphs, citation networks, the World Wide Web, and so on. As increasingly structured data become available, the importance of being able to effectively mine and learn from such data continues to grow. In this paper, we propose the multi-scale aggregation graph neural network based on feature similarity (MAGN), a novel graph neural network defined in the vertex domain. Our model provides a simple and general semi-supervised learning method for graph-structured data, in which only a very small part of the data is labeled as the training set. We first construct a similarity matrix by calculating the similarity of original features between all adjacent node pairs, and then generate a set of feature extractors utilizing the similarity matrix to perform multi-scale feature propagation on graphs. The output of multi-scale feature propagation is finally aggregated by using the mean-pooling operation. Our method aims to improve the model representation ability via multi-scale neighborhood aggregation based on feature similarity. Extensive experimental evaluation on various open benchmarks shows the competitive performance of our method compared to a variety of popular architectures.

scholarly journals The Mean Stability Criteria in terms of Two Measures for Stochastic Differential Equations with Coefficient’s Uncertainty

2015 ◽  
Vol 2015 ◽  
pp. 1-7
Author(s):  
Rui Zhang ◽  
Yinjing Guo ◽  
Xiangrong Wang ◽  
Xueqing Zhang
Keyword(s):  
Optimal Control ◽  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Stochastic Stability ◽  
Stochastic Systems ◽  
Stability Criteria ◽  
Two Measures ◽  
The Mean ◽  
The Stability

This paper extends the stochastic stability criteria of two measures to the mean stability and proves the stability criteria for a kind of stochastic Itô’s systems. Moreover, by applying optimal control approaches, the mean stability criteria in terms of two measures are also obtained for the stochastic systems with coefficient’s uncertainty.

TRAFFIC FLOWS FORECASTING BASED ON MACHINE LEARNING

2022 ◽  
Vol 13 (1) ◽  
pp. 0-0
Keyword(s):  
Machine Learning ◽  
Traffic Flows ◽  
Random Forest Regression ◽  
Machine Learning Methods ◽  
Packet Arrival ◽  
Entire Flow ◽  
The Mean ◽  
Active Flow

The article aims to develop a model for forecasting the characteristics of traffic flows in real-time based on the classification of applications using machine learning methods to ensure the quality of service. It is shown that the model can forecast the mean rate and frequency of packet arrival for the entire flow of each class separately. The prediction is based on information about the previous flows of this class and the first 15 packets of the active flow. Thus, the Random Forest Regression method reduces the prediction error by approximately 1.5 times compared to the standard mean estimate for transmitted packets issued at the switch interface.

PARALLEL ACCELERATION ALGORITHM FOR SPIN MODELS

1992 ◽  
Vol 03 (04) ◽  
pp. 605-610 ◽  
Author(s):  
G.V. BHANOT ◽  
S.L. ADLER
Keyword(s):  
Massively Parallel ◽  
Xy Model ◽  
Spin Models ◽  
Cluster Algorithms ◽  
Multi Scale ◽  
Connection Machine ◽  
Parallel Supercomputer ◽  
Parallel Acceleration

We describe and implement a multi-scale acceleration algorithm for spin models on a massively parallel supercomputer, the Connection Machine CM-200. Unlike usual cluster algorithms, our algorithm is completely parallelizable. The time to update all variables in a system of volume Ld scales as Ld log 2L. We prove this by computing the time for one lattice sweep for the 2-d XY model for our algorithm on lattices of size up to 2048×2048.

scholarly journals Designing accurate emulators for scientific processes using calibration-driven deep models

2020 ◽  
Vol 11 (1) ◽  
Author(s):  
Jayaraman J. Thiagarajan ◽  
Bindya Venkatesh ◽  
Rushil Anirudh ◽  
Peer-Timo Bremer ◽  
Jim Gaffney ◽  
...  
Keyword(s):  
Mean Squared Error ◽  
Mean Absolute Error ◽  
Absolute Error ◽  
Heterogeneous Data ◽  
Small Data ◽  
Machine Learning Methods ◽  
Squared Error ◽  
Noise Structure ◽  
The Mean ◽  
Modern Machine

Abstract Predictive models that accurately emulate complex scientific processes can achieve speed-ups over numerical simulators or experiments and at the same time provide surrogates for improving the subsequent analysis. Consequently, there is a recent surge in utilizing modern machine learning methods to build data-driven emulators. In this work, we study an often overlooked, yet important, problem of choosing loss functions while designing such emulators. Popular choices such as the mean squared error or the mean absolute error are based on a symmetric noise assumption and can be unsuitable for heterogeneous data or asymmetric noise distributions. We propose Learn-by-Calibrating, a novel deep learning approach based on interval calibration for designing emulators that can effectively recover the inherent noise structure without any explicit priors. Using a large suite of use-cases, we demonstrate the efficacy of our approach in providing high-quality emulators, when compared to widely-adopted loss function choices, even in small-data regimes.

The crystal and molecular structure of thioformaldehyde trimer

1967 ◽  
Vol 45 (4) ◽  
pp. 353-357 ◽  
Author(s):  
J. E. Fleming ◽  
H. Lynton
Keyword(s):  
Crystal And Molecular Structure ◽  
Three Dimensional ◽  
Bond Distance ◽  
Orthorhombic Space Group ◽  
Significant Difference ◽  
The Mean ◽  
Temperature Factors ◽  
No Absorption ◽  
Good Agreement ◽  
Atomic Parameters

Crystals of thioformaldehyde trimer, (CH2S)3 are orthorhombic, space group Pmn21 with a = 7.697 Å [Formula: see text], b = 7.067 Å [Formula: see text], c = 5.323 Å [Formula: see text]. There are two molecules in the unit cell with sulfur and carbon atoms in positions (4b) and (2a). The atomic parameters for sulfur and carbon have been determined from a three-dimensional analysis using observed and calculated differential syntheses with isotropic temperature factors. No absorption corrections were applied to the intensity data and no attempt has been made to establish the hydrogen positions. The final discrepancy index is R = 0.093. The molecule has the chair configuration and shows no significant difference between the lengths of any S—C bonds. The mean S—C bond distance is 1.818 Å and the standard deviation of the mean is 0.003 Å. This value is in good agreement with the commonly accepted value of 1.817 ± 0.005 Å for the S—C paraffinic bond.

Mean momentum balance in moderately favourable pressure gradient turbulent boundary layers

2008 ◽  
Vol 617 ◽  
pp. 107-140 ◽  
Author(s):  
M. METZGER ◽  
A. LYONS ◽  
P. FIFE
Keyword(s):  
Pressure Gradient ◽  
Boundary Layers ◽  
Outer Region ◽  
Present Theory ◽  
Momentum Equation ◽  
Turbulent Boundary Layers ◽  
Momentum Balance ◽  
Physical Layers ◽  
Multi Scale ◽  
The Mean

Moderately favourable pressure gradient turbulent boundary layers are investigated within a theoretical framework based on the unintegrated two-dimensional mean momentum equation. The present theory stems from an observed exchange of balance between terms in the mean momentum equation across different regions of the boundary layer. This exchange of balance leads to the identification of distinct physical layers, unambiguously defined by the predominant mean dynamics active in each layer. Scaling domains congruent with the physical layers are obtained from a multi-scale analysis of the mean momentum equation. Scaling behaviours predicted by the present theory are evaluated using direct measurements of all of the terms in the mean momentum balance for the case of a sink-flow pressure gradient generated in a wind tunnel with a long development length. Measurements also captured the evolution of the turbulent boundary layers from a non-equilibrium state near the wind tunnel entrance towards an equilibrium state further downstream. Salient features of the present multi-scale theory were reproduced in all the experimental data. Under equilibrium conditions, a universal function was found to describe the decay of the Reynolds stress profile in the outer region of the boundary layer. Non-equilibrium effects appeared to be manifest primarily in the outer region, whereas differences in the inner region were attributed solely to Reynolds number effects.

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