scholarly journals Spectral clustering in regression-based biological networks

2019 ◽  
Author(s):  
Sheila M. Gaynor ◽  
Xihong Lin ◽  
John Quackenbush
Keyword(s):  
Community Detection ◽  
Biological Networks ◽  
Spectral Clustering ◽  
Complex Structure ◽  
Gene Clusters ◽  
Biological Data ◽  
Tuning Parameter ◽  
Affinity Matrix ◽  
The Matrix ◽  
The Stability

AbstractBiological networks often have complex structure consisting of meaningful clusters of nodes that are integral to understanding biological function. Community detection algorithms to identify the clustering, or community structure, of a network have been well established. These algorithms assume that data used in network construction is observed without error. However, oftentimes intermediary analyses such as regression are performed before constructing biological networks and the associated error is not propagated in community detection. In expression quantitative trait loci (eQTL) networks, one must first map eQTLs via linear regression in order to specify the matrix representation of the network. We study the effects of using estimates from regression models when applying the spectral clustering approach to community detection. We demonstrate the impacts on the affinity matrix and consider adjusted estimates of the affinity matrix for use in spectral clustering. We further provide a recommendation for selection of the tuning parameter in spectral clustering. We evaluate the proposed adjusted method for performing spectral clustering to detect gene clusters in eQTL data from the GTEx project and to assess the stability of communities in biological data.

scholarly journals Global spectral clustering in dynamic networks

2018 ◽  
Vol 115 (5) ◽  
pp. 927-932 ◽  
Author(s):  
Fuchen Liu ◽  
David Choi ◽  
Lu Xie ◽  
Kathryn Roeder
Keyword(s):  
Community Detection ◽  
Spectral Clustering ◽  
Signal To Noise Ratio ◽  
Dynamic Networks ◽  
Brain Regions ◽  
Tuning Parameter ◽  
Expression Data ◽  
Dynamic Community Detection ◽  
Dynamic Community ◽  
Better Than

Community detection is challenging when the network structure is estimated with uncertainty. Dynamic networks present additional challenges but also add information across time periods. We propose a global community detection method, persistent communities by eigenvector smoothing (PisCES), that combines information across a series of networks, longitudinally, to strengthen the inference for each period. Our method is derived from evolutionary spectral clustering and degree correction methods. Data-driven solutions to the problem of tuning parameter selection are provided. In simulations we find that PisCES performs better than competing methods designed for a low signal-to-noise ratio. Recently obtained gene expression data from rhesus monkey brains provide samples from finely partitioned brain regions over a broad time span including pre- and postnatal periods. Of interest is how gene communities develop over space and time; however, once the data are divided into homogeneous spatial and temporal periods, sample sizes are very small, making inference quite challenging. Applying PisCES to medial prefrontal cortex in monkey rhesus brains from near conception to adulthood reveals dense communities that persist, merge, and diverge over time and others that are loosely organized and short lived, illustrating how dynamic community detection can yield interesting insights into processes such as brain development.

scholarly journals A Multiple and Multi-Level Substructure Method for the Dynamics of Complex Structures

2021 ◽  
Vol 11 (12) ◽  
pp. 5570
Author(s):  
Binbin Wang ◽  
Jingze Liu ◽  
Zhifu Cao ◽  
Dahai Zhang ◽  
Dong Jiang
Keyword(s):  
Structural Characteristics ◽  
Complex Structure ◽  
Complex Structures ◽  
System Matrix ◽  
Substructure Method ◽  
Residual Structure ◽  
The Matrix ◽  
Multi Level ◽  
Fixed Interface ◽  
Selection Of

Based on the fixed interface component mode synthesis, a multiple and multi-level substructure method for the modeling of complex structures is proposed in this paper. Firstly, the residual structure is selected according to the structural characteristics of the assembled complex structure. Secondly, according to the assembly relationship, the parts assembled with the residual structure are divided into a group of substructures, which are named the first-level substructure, the parts assembled with the first-level substructure are divided into a second-level substructure, and consequently the multi-level substructure model is established. Next, the substructures are dynamically condensed and assembled on the boundary of the residual structure. Finally, the substructure system matrix, which is replicated from the matrix of repeated physical geometry, is obtained by preserving the main modes and the constrained modes and the system matrix of the last level of the substructure is assembled to the upper level of the substructure, one level up, until it is assembled in the residual structure. In this paper, an assembly structure with three panels and a gear box is adopted to verify the method by simulation and a rotor is used to experimentally verify the method. The results show that the proposed multiple and multi-level substructure modeling method is not unique to the selection of residual structures, and different classification methods do not affect the calculation accuracy. The selection of 50% external nodes can further improve the analysis efficiency while ensuring the calculation accuracy.

scholarly journals Stability of Nonlinear Autonomous Quadratic Discrete Systems in the Critical Case

2010 ◽  
Vol 2010 ◽  
pp. 1-23 ◽  
Author(s):  
Josef Diblík ◽  
Denys Ya. Khusainov ◽  
Irina V. Grytsay ◽  
Zdenĕk Šmarda
Keyword(s):  
Lyapunov Functions ◽  
Critical Case ◽  
Autonomous Systems ◽  
Discrete Systems ◽  
Simple Eigenvalue ◽  
Discrete Equations ◽  
The Matrix ◽  
The Stability ◽  
Important Characterization

Many processes are mathematically simulated by systems of discrete equations with quadratic right-hand sides. Their stability is thought of as a very important characterization of the process. In this paper, the method of Lyapunov functions is used to derive classes of stable quadratic discrete autonomous systems in a critical case in the presence of a simple eigenvalueλ=1of the matrix of linear terms. In addition to the stability investigation, we also estimate stability domains.

scholarly journals BioNetLink - An Architecture for Working with Network Data

2014 ◽  
Vol 11 (2) ◽  
pp. 68-79
Author(s):  
Matthias Klapperstück ◽  
Falk Schreiber
Keyword(s):  
Experimental Data ◽  
Biological Networks ◽  
Regulatory Networks ◽  
Large Data ◽  
Biological Data ◽  
Network Data ◽  
Data Sets ◽  
Dynamic Views ◽  
Gene Regulatory ◽  
Multiple Network

Summary The visualization of biological data gained increasing importance in the last years. There is a large number of methods and software tools available that visualize biological data including the combination of measured experimental data and biological networks. With growing size of networks their handling and exploration becomes a challenging task for the user. In addition, scientists also have an interest in not just investigating a single kind of network, but on the combination of different types of networks, such as metabolic, gene regulatory and protein interaction networks. Therefore, fast access, abstract and dynamic views, and intuitive exploratory methods should be provided to search and extract information from the networks. This paper will introduce a conceptual framework for handling and combining multiple network sources that enables abstract viewing and exploration of large data sets including additional experimental data. It will introduce a three-tier structure that links network data to multiple network views, discuss a proof of concept implementation, and shows a specific visualization method for combining metabolic and gene regulatory networks in an example.

scholarly journals Coupled THM and Matrix Stability Modeling of Hydroshearing Stimulation in a Coupled Fracture-Matrix Hot Volcanic System

2018 ◽  
Vol 2018 ◽  
pp. 1-15 ◽  
Author(s):  
Yong Xiao ◽  
Jianchun Guo ◽  
Hehua Wang ◽  
Lize Lu ◽  
John McLennan ◽  
...  
Keyword(s):  
Heat Transfer ◽  
Thermal Conduction ◽  
Dominant Role ◽  
Injection Well ◽  
Time Step ◽  
Volcanic System ◽  
Induced Stress ◽  
The Matrix ◽  
Matrix Stability ◽  
The Stability

A coupled thermal-hydraulic-mechanical (THM) model is developed to simulate the combined effect of fracture fluid flow, heat transfer from the matrix to injected fluid, and shearing dilation behaviors in a coupled fracture-matrix hot volcanic reservoir system. Fluid flows in the fracture are calculated based on the cubic law. Heat transfer within the fracture involved is thermal conduction, thermal advection, and thermal dispersion; within the reservoir matrix, thermal conduction is the only mode of heat transfer. In view of the expansion of the fracture network, deformation and thermal-induced stress model are added to the matrix node’s in situ stress environment in each time step to analyze the stability of the matrix. A series of results from the coupled THM model, induced stress, and matrix stability indicate that thermal-induced aperture plays a dominant role near the injection well to enhance the conductivity of the fracture. Away from the injection well, the conductivity of the fracture is contributed by shear dilation. The induced stress has the maximum value at the injection point; the deformation-induced stress has large value with smaller affected range; on the contrary, thermal-induced stress has small value with larger affected range. Matrix stability simulation results indicate that the stability of the matrix nodes may be destroyed; this mechanism is helpful to create complex fracture networks.

Spectral clustering based on histogram of oriented gradient (HOG) of coal using laser-induced breakdown spectroscopy

2021 ◽  
Author(s):  
Ji Chen ◽  
Kaiping Zhan ◽  
Qingzhou Li ◽  
Zhiyang Tang ◽  
Chenwei Zhu ◽  
...  
Keyword(s):  
Spectral Clustering ◽  
Matrix Effects ◽  
Unsupervised Clustering ◽  
Laser Induced Breakdown Spectroscopy ◽  
Histogram Of Oriented Gradient ◽  
Breakdown Spectroscopy ◽  
Laser Induced Breakdown ◽  
The Matrix ◽  
Quantification Accuracy

The quantification accuracy of laser-induced breakdown spectroscopy was limited due to matrix effects. In this work, a method named unsupervised-clustering-based quantification (UCQ) was proposed to reduce the matrix effects by...

Allocation of fracturing intervals and justification of fracture parameters in the pre-Jurassic deposits

2021 ◽  
pp. 9-19
Author(s):  
P. A. Boronin ◽  
N. V. Gilmanova ◽  
N. Yu. Moskalenko
Keyword(s):  
Permeability Coefficient ◽  
Complex Structure ◽  
High Flow ◽  
Well Testing ◽  
Rock Matrix ◽  
Unconventional Reservoir ◽  
Flow Rates ◽  
Matrix Permeability ◽  
The Matrix ◽  
Standard Set

The object of research in this article is the productive deposits of the pre-Jurassic complex. The pre-Jurassic complex is of great interest, this is an unconventional reservoir with a complex structure and developed fractured zones. High flow rates cannot be determined by the rock matrix, since the matrix permeability coefficient is on average 2−3 md. In this regard, there is the problem of separation of fractured intervals according to a standard set of well testing.

A Statistical Test for the Stability of Covariance Structure

2013 ◽  
Vol 63 (2) ◽  
Author(s):  
Nur Syahidah Yusoff ◽  
Maman Abdurachman Djauhari
Keyword(s):  
Covariance Matrix ◽  
Complex Structure ◽  
Covariance Structure ◽  
Statistical Test ◽  
Dispersion Measure ◽  
Data Sets ◽  
Scalar Representation ◽  
Multivariate Dispersion ◽  
Sample Covariance ◽  
The Stability

The stability of covariance matrix is a major issue in multivariate analysis. As can be seen in the literature, the most popular and widely used tests are Box M-test and Jennrich J-test introduced by Box in 1949 and Jennrich in 1970, respectively. These tests involve determinant of sample covariance matrix as multivariate dispersion measure. Since it is only a scalar representation of a complex structure, it cannot represent the whole structure. On the other hand, they are quite cumbersome to compute when the data sets are of high dimension since they do not only involve the computation of determinant of covariance matrix but also the inversion of a matrix. This motivates us to propose a new statistical test which is computationally more efficient and, if it is used simultaneously with M-test or J-test, we will have a better understanding about the stability of covariance structure. An example will be presented to illustrate its advantage

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