scholarly journals The critical infection rate of the high-dimensional two-stage contact process

2018 ◽  
Vol 140 ◽  
pp. 115-125 ◽  
Author(s):  
Xiaofeng Xue
Keyword(s):  
Infection Rate ◽  
Contact Process ◽  
High Dimensional ◽  
Two Stage

scholarly journals New Results for the Two-Stage Contact Process

2015 ◽  
Vol 52 (01) ◽  
pp. 258-268 ◽  
Author(s):  
Eric Foxall
Keyword(s):  
Contact Process ◽  
Duality Relation ◽  
Two Stage ◽  
Open Questions

In this paper, we continue the work started by Steve Krone on the two-stage contact process. We give a simplified proof of the duality relation and answer most of the open questions posed in Krone (1999). We also fill in the details of an incomplete proof.

On the critical infection rate of the one-dimensional basic contact process: numerical results

1988 ◽  
Vol 25 (1) ◽  
pp. 1-8 ◽  
Author(s):  
Herbert Ziezold ◽  
Christian Grillenberger
Keyword(s):  
Markov Process ◽  
Infected Cell ◽  
Infection Rate ◽  
Lower Bounds ◽  
Contact Process ◽  
Critical Value ◽  
Critical Values ◽  
One Dimensional ◽  
The One ◽  
The Right

Instead of the basic contact process on with infection rate λ we consider for m ≧ 0 the Markov process starting with ξ0(k) = 1 for k ≧ 0 and ξ0(k)= 0 for k < 0 and with changing only those k which are at most m places to the right of the left-most infected cell. For m = 0, 1,· ··, 14 direct computations give critical values which are lower bounds for the critical value of the original basic contact process.

Visualizing and Evaluating High-Dimensional Mappings of Sets of High Performance Designs

2019 ◽  
Author(s):  
Clinton B. Morris ◽  
Michael R. Haberman ◽  
Carolyn C. Seepersad
Keyword(s):  
High Performance ◽  
Design Space Exploration ◽  
Design Space ◽  
Space Structure ◽  
Three Dimensions ◽  
High Dimensional ◽  
Underlying Structure ◽  
Visualization Technique ◽  
Two Stage ◽  
Input Design

Abstract Design space exploration can reveal the underlying structure of design problems. In a set-based approach, for example, exploration can map sets of designs or regions of the design space that meet specific performance requirements. For some problems, promising designs may cluster in multiple regions of the input design space, and the boundaries of those clusters may be irregularly shaped and difficult to predict. Visualizing the promising regions can clarify the design space structure, but design spaces are typically high-dimensional, making it difficult to visualize the space in three dimensions. To convey the structure of such high-dimensional design regions, a two-stage approach is proposed to (1) identify and (2) visualize each distinct cluster or region of interest in the input design space. This paper focuses on the visualization stage of the approach. Rather than select a singular technique to map high-dimensional design spaces to low-dimensional, visualizable spaces, a selection procedure is investigated. Metrics are available for comparing different visualizations, but the current metrics either overestimate the quality or favor selection of certain visualizations. Therefore, this work introduces and validates a more objective metric, termed preservation, to compare the quality of alternative visualization strategies. Furthermore, a new visualization technique previously unexplored in the design automation community, t-Distributed Neighbor Embedding, is introduced and compared to other visualization strategies. Finally, the new metric and visualization technique are integrated into a two-stage visualization strategy to identify and visualize clusters of high-performance designs for a high-dimensional negative stiffness metamaterials design problem.

Stable Variable Selection for High-dimensional Genomic Data with Strong Correlations

2021 ◽  
Author(s):  
Reetika Sarkar ◽  
Sithija Manage ◽  
Xiaoli Gao
Keyword(s):  
Variable Selection ◽  
Genomic Data ◽  
High Dimensional ◽  
Strong Correlations ◽  
Computationally Efficient ◽  
Two Stage ◽  
Selection Of Variables ◽  
Level Variable ◽  
Stable Variable ◽  
Selection Of

Abstract Background: High-dimensional genomic data studies are often found to exhibit strong correlations, which results in instability and inconsistency in the estimates obtained using commonly used regularization approaches including both the Lasso and MCP, and related methods. Result: In this paper, we perform a comparative study of regularization approaches for variable selection under different correlation structures, and propose a two-stage procedure named rPGBS to address the issue of stable variable selection in various strong correlation settings. This approach involves repeatedly running of a two-stage hierarchical approach consisting of a random pseudo-group clustering and bi-level variable selection. Conclusion: Both the simulation studies and high-dimensional genomic data analysis have demonstrated the advantage of the proposed rPGBS method over most commonly used regularization methods. In particular, the rPGBS results in more stable selection of variables across a variety of correlation settings, as compared to recent work addressing variable selection with strong correlations. Moreover, the rPGBS is computationally efficient across various settings.

Two-stage extreme learning machine for high-dimensional data

2014 ◽  
Vol 7 (5) ◽  
pp. 765-772 ◽  
Author(s):  
Peng Liu ◽  
Yihua Huang ◽  
Lei Meng ◽  
Siyuan Gong ◽  
Guopeng Zhang
Keyword(s):  
Extreme Learning Machine ◽  
High Dimensional Data ◽  
High Dimensional ◽  
Two Stage ◽  
Learning Machine
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