scholarly journals Optimal Base Station Network Based on Topological Data Analysis

Author(s):  
Minhao Lyu

The decision of which base stations need to be removed due to the cost is always a difficult problem, because the influence on the cover rate of the network caused by the removal should be kept to a minimum. However, the common methods to solve this problem such as K-means Clustering show a low accuracy. Barcode, which belongs to TDA, has the possibility to show the result by identifying the Persistent Homology of base station network. This essay mainly illustrates the specific problem of optimal base station network, which applies the TDA(Topological Data Analysis) methods to find which base stations need removing due to the cost K-means Clustering and Topological Data Analysis methods were mainly used. With the simulated distribution of telecommunication users, K-means Clustering algorithm was used to locate 30 best base stations. By comparing the minimum distance between the results (K=25 and K=30), K-means Clustering was used again to decide base station points to be removed. Then TDA was used to select which 5 base stations should be removed through observing barcode. By repeating above steps five times, Finally the average and variance of cover area in original network, K-means Clustering and TDA were compared. The experiment showed that the average cover rate of original network was 81.20% while the result of TDA and K-means Clustering were 92.13% and 89.87%. It was proved by simulation that it is more efficient to use TDA methods to construct the optimal base station network.

2021 ◽  
Vol 83 (3) ◽  
Author(s):  
Maria-Veronica Ciocanel ◽  
Riley Juenemann ◽  
Adriana T. Dawes ◽  
Scott A. McKinley

AbstractIn developmental biology as well as in other biological systems, emerging structure and organization can be captured using time-series data of protein locations. In analyzing this time-dependent data, it is a common challenge not only to determine whether topological features emerge, but also to identify the timing of their formation. For instance, in most cells, actin filaments interact with myosin motor proteins and organize into polymer networks and higher-order structures. Ring channels are examples of such structures that maintain constant diameters over time and play key roles in processes such as cell division, development, and wound healing. Given the limitations in studying interactions of actin with myosin in vivo, we generate time-series data of protein polymer interactions in cells using complex agent-based models. Since the data has a filamentous structure, we propose sampling along the actin filaments and analyzing the topological structure of the resulting point cloud at each time. Building on existing tools from persistent homology, we develop a topological data analysis (TDA) method that assesses effective ring generation in this dynamic data. This method connects topological features through time in a path that corresponds to emergence of organization in the data. In this work, we also propose methods for assessing whether the topological features of interest are significant and thus whether they contribute to the formation of an emerging hole (ring channel) in the simulated protein interactions. In particular, we use the MEDYAN simulation platform to show that this technique can distinguish between the actin cytoskeleton organization resulting from distinct motor protein binding parameters.


2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Scott Broderick ◽  
Ruhil Dongol ◽  
Tianmu Zhang ◽  
Krishna Rajan

AbstractThis paper introduces the use of topological data analysis (TDA) as an unsupervised machine learning tool to uncover classification criteria in complex inorganic crystal chemistries. Using the apatite chemistry as a template, we track through the use of persistent homology the topological connectivity of input crystal chemistry descriptors on defining similarity between different stoichiometries of apatites. It is shown that TDA automatically identifies a hierarchical classification scheme within apatites based on the commonality of the number of discrete coordination polyhedra that constitute the structural building units common among the compounds. This information is presented in the form of a visualization scheme of a barcode of homology classifications, where the persistence of similarity between compounds is tracked. Unlike traditional perspectives of structure maps, this new “Materials Barcode” schema serves as an automated exploratory machine learning tool that can uncover structural associations from crystal chemistry databases, as well as to achieve a more nuanced insight into what defines similarity among homologous compounds.


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