Sheaf Theory Approach to Distributed Applications: Analysing Heterogeneous Data in Air Traffic Monitoring

Seyed Mansourbeigi

doi:doi:10.11648/j.ijdsa.20170305.11

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Sheaf Theory Approach to Distributed Applications: Analysing Heterogeneous Data in Air Traffic Monitoring

Seyed Mansourbeigi

Published in International Journal of Data Science and Analysis (Volume 3, Issue 5)

Received: 6 September 2017 Accepted: 23 September 2017 Published: 23 October 2017

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Abstract

The goal of the present article is to demonstrate a mathematical modeling for distributed applications. The present paper applies tools from topology and sheaf theory as an appropriate mathematical modeling to reflect interactions among elements of distributed applications resources. Sensors are characterized from their topological representations in distributed network system. This modeling is applied for the study of the air traffic monitoring system and discuss the model in detail.

Published in	International Journal of Data Science and Analysis (Volume 3, Issue 5)
DOI	10.11648/j.ijdsa.20170305.11
Page(s)	34-39
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2024. Published by Science Publishing Group

Keywords

Cellular Sheaf, Stalks, Cosheaf Homology, Sheaf Cohomology

References

[1]	M. Robinson, C. Joslyn, E. Hogan, and C. Capraro, “Conglomeration of Heterogeneous Content using Local Topology,” American University, Mar. 2015.
[2]	M. Robinson, “Sheaves are the canonical data structure for sensor integration,” Inf. Fusion, vol. 36, pp. 208–224, Jul. 2017.
[3]	L. Monteiro and F. Pereira, “A sheaf-theoretic model of concurrency,” in Proceeding of Logic in Computer Science, 1986, pp. 66–76.
[4]	Ehrich H. D., Goguen J. A., Sernadas A., “A categorial theory of objects as observed processes \| SpringerLink.” [Online]. Available: https://link.springer.com/chapter/10.1007/BFb0019445. [Accessed: 03-Sep-2017].
[5]	J. A. Goguen, “Sheaf Semantics for Concurrent Interacting Objects,” in Mathematical Structures in Computer Science, 1992, pp. 159–191.
[6]	G. L. Cattani and G. Winskel, “Presheaf models for concurrency,” in Computer Science Logic, 1996, pp. 58–75.
[7]	Cırstea, C, “A distributed semantics for FOOPS,” University of Oxford, Technical Report PRG-TR-20-95, 1995.
[8]	G. Malcolm, “Component-Based Specification of Distributed Systems,” Electron. Notes Theor. Comput. Sci., vol. 160, pp. 211–224, Aug. 2006.
[9]	G. Malcolm, “Sheaves, Objects, and Distributed Systems,” Electron. Notes Theor. Comput. Sci., vol. 225, pp. 3–19, Jan. 2009.
[10]	Nicholas A. Scoville and Karthik Yegnesh, “Cosheaf Theoretical Constructions in Networks and Persistent Homology,” International Mathematics Research Notices, 2009.
[11]	J. M. Curry, “Dualities between cellular sheaves and cosheaves,” J. Pure Appl. Algebra, Jun. 2017.

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APA Style

Seyed Mansourbeigi. (2017). Sheaf Theory Approach to Distributed Applications: Analysing Heterogeneous Data in Air Traffic Monitoring. International Journal of Data Science and Analysis, 3(5), 34-39. https://doi.org/10.11648/j.ijdsa.20170305.11

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ACS Style

Seyed Mansourbeigi. Sheaf Theory Approach to Distributed Applications: Analysing Heterogeneous Data in Air Traffic Monitoring. Int. J. Data Sci. Anal. 2017, 3(5), 34-39. doi: 10.11648/j.ijdsa.20170305.11

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AMA Style

Seyed Mansourbeigi. Sheaf Theory Approach to Distributed Applications: Analysing Heterogeneous Data in Air Traffic Monitoring. Int J Data Sci Anal. 2017;3(5):34-39. doi: 10.11648/j.ijdsa.20170305.11

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@article{10.11648/j.ijdsa.20170305.11,
  author = {Seyed Mansourbeigi},
  title = {Sheaf Theory Approach to Distributed Applications: Analysing Heterogeneous Data in Air Traffic Monitoring},
  journal = {International Journal of Data Science and Analysis},
  volume = {3},
  number = {5},
  pages = {34-39},
  doi = {10.11648/j.ijdsa.20170305.11},
  url = {https://doi.org/10.11648/j.ijdsa.20170305.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijdsa.20170305.11},
  abstract = {The goal of the present article is to demonstrate a mathematical modeling for distributed applications. The present paper applies tools from topology and sheaf theory as an appropriate mathematical modeling to reflect interactions among elements of distributed applications resources. Sensors are characterized from their topological representations in distributed network system. This modeling is applied for the study of the air traffic monitoring system and discuss the model in detail.},
 year = {2017}
}

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TY  - JOUR
T1  - Sheaf Theory Approach to Distributed Applications: Analysing Heterogeneous Data in Air Traffic Monitoring
AU  - Seyed Mansourbeigi
Y1  - 2017/10/23
PY  - 2017
N1  - https://doi.org/10.11648/j.ijdsa.20170305.11
DO  - 10.11648/j.ijdsa.20170305.11
T2  - International Journal of Data Science and Analysis
JF  - International Journal of Data Science and Analysis
JO  - International Journal of Data Science and Analysis
SP  - 34
EP  - 39
PB  - Science Publishing Group
SN  - 2575-1891
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AB  - The goal of the present article is to demonstrate a mathematical modeling for distributed applications. The present paper applies tools from topology and sheaf theory as an appropriate mathematical modeling to reflect interactions among elements of distributed applications resources. Sensors are characterized from their topological representations in distributed network system. This modeling is applied for the study of the air traffic monitoring system and discuss the model in detail.
VL  - 3
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ER  -

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Author Information

Seyed Mansourbeigi

Department of Computer Science, College of Engineering, Utah State University, Logan, USA

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Plain Text BibTeX RIS

APA Style

Seyed Mansourbeigi. (2017). Sheaf Theory Approach to Distributed Applications: Analysing Heterogeneous Data in Air Traffic Monitoring. International Journal of Data Science and Analysis, 3(5), 34-39. https://doi.org/10.11648/j.ijdsa.20170305.11

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ACS Style

Seyed Mansourbeigi. Sheaf Theory Approach to Distributed Applications: Analysing Heterogeneous Data in Air Traffic Monitoring. Int. J. Data Sci. Anal. 2017, 3(5), 34-39. doi: 10.11648/j.ijdsa.20170305.11

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AMA Style

Seyed Mansourbeigi. Sheaf Theory Approach to Distributed Applications: Analysing Heterogeneous Data in Air Traffic Monitoring. Int J Data Sci Anal. 2017;3(5):34-39. doi: 10.11648/j.ijdsa.20170305.11

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@article{10.11648/j.ijdsa.20170305.11,
  author = {Seyed Mansourbeigi},
  title = {Sheaf Theory Approach to Distributed Applications: Analysing Heterogeneous Data in Air Traffic Monitoring},
  journal = {International Journal of Data Science and Analysis},
  volume = {3},
  number = {5},
  pages = {34-39},
  doi = {10.11648/j.ijdsa.20170305.11},
  url = {https://doi.org/10.11648/j.ijdsa.20170305.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijdsa.20170305.11},
  abstract = {The goal of the present article is to demonstrate a mathematical modeling for distributed applications. The present paper applies tools from topology and sheaf theory as an appropriate mathematical modeling to reflect interactions among elements of distributed applications resources. Sensors are characterized from their topological representations in distributed network system. This modeling is applied for the study of the air traffic monitoring system and discuss the model in detail.},
 year = {2017}
}

Copy | Download

TY  - JOUR
T1  - Sheaf Theory Approach to Distributed Applications: Analysing Heterogeneous Data in Air Traffic Monitoring
AU  - Seyed Mansourbeigi
Y1  - 2017/10/23
PY  - 2017
N1  - https://doi.org/10.11648/j.ijdsa.20170305.11
DO  - 10.11648/j.ijdsa.20170305.11
T2  - International Journal of Data Science and Analysis
JF  - International Journal of Data Science and Analysis
JO  - International Journal of Data Science and Analysis
SP  - 34
EP  - 39
PB  - Science Publishing Group
SN  - 2575-1891
UR  - https://doi.org/10.11648/j.ijdsa.20170305.11
AB  - The goal of the present article is to demonstrate a mathematical modeling for distributed applications. The present paper applies tools from topology and sheaf theory as an appropriate mathematical modeling to reflect interactions among elements of distributed applications resources. Sensors are characterized from their topological representations in distributed network system. This modeling is applied for the study of the air traffic monitoring system and discuss the model in detail.
VL  - 3
IS  - 5
ER  -

Copy | Download