Arbitrary Dimensional Data


  •   Frank Edughom Ekpar


It is a well-known fact that numerous issues in many fields of human endeavor including, but not limited to, science and engineering, medicine, law enforcement and security, economics and finance, governance, psychology, philosophy, religion, and many other fields require the management of arbitrary dimensional data. However, systems permitting direct and efficient management of arbitrary dimensional data currently do not exist. In fact, contemporary systems such as graphical user interfaces for the management of data typically lack even the very concept of arbitrary dimensionality – failing to provide any practical way or means of managing arbitrary dimensional data. Here, we establish the foundational principles for a system permitting practical, direct and efficient management of arbitrary dimensional data. Furthermore, we demonstrate the effectiveness of our system by applying it to an experiment involving eight-dimensional (8D) medical and scientific data sets. Our system has immediate, far-reaching implications for numerous fields of human endeavor – enabling hitherto impossible solutions and applications and leading to deeper insights and improved understanding of numerous issues.

Keywords: Arbitrary Dimensional Data, Multidimensional Data, Efficient Data Management, Intuitive Data Management, 3D Graphical User Interface, Big Data Representation, Dynamic View Prediction, Representative Matrix Formulation


Michio K. Sub-critical Closed String Field Theory in D Less Than 26. Phys. Rev. D 49, 5364-5376 (1994).

Klebanov, I. R. String Theory in Two Dimensions. Proceedings of the Trieste Spring School 1991, eds. J. Harvey et. al. (World Scientific, Singapore, 1992).

Ginsparg, P & Gregory, M. Lectures on 2D Gravity and 2D String Theory. YCTP. P23-92 (1992).

Jevicki, A. Developments in 2D String Theory. BROWN-HET-918 (1993).

Klebanov, I. R. & Polyakov, A. M. Interaction of Discrete States in Two-Dimensional String Theory. Mod. Phys. Lett. A6, 3273-3281 (1991).

Gross, D. J, Klebanov, I. R. & Newman, M. J. The Two-Point Correlation Functions of the One Dimensional Matrix Model. Nucl. Phys. B350, 621–634 (1991).

Ambjorn, A. & Jurkiewiz, J. Renormalization of 3d quantum gravity from matrix models. Phys. Letts. B581, 255-262 (2004).

D’Hoker, E. Lecture Notes on 2D Quantum Gravity and Liouville Theory. UCLA/91/TEP 35 (1991).

Gubser, S. S., Klebanov, I. R. & Polyakov, A. M. Gauge Theory Correlators from Non-Critical String Theory. Phys. Lett. B428, 105-114 (1998).

Arkani-Hamed, N., Cachazo, F., Cheung, C. & Kaplan, J. A Duality For The S Matrix. Journal of High Energy Physics (JHEP) 1003:020 (2010).

Arkani-Hamed, N., Dimopoulos, S. & Dvali, G. The Hierarchy Problem and New Dimensions at a Millimeter. Phys. Lett. B429, 263-272 (1998).

Kac, V. J. Simple Irreducible Graded Lie Algebras of Finite Growth. Math. USSR--Izvestija 2, 1271-1311 (1968).

Schrenk, K. J., Araújo, N. A. M., Andrade Jr, J. S. & Herrmann, H. J. Fracturing ranked surfaces. Nature Scientific Reports 2, 348 (2012).

Stark, C. P. An invasion percolation model of drainage network evolution. Nature 352, 423–425 (1991).

Maritan, A., Colaiori, F., Flammini, A., Cieplak, M. & Banavar, J. R. Universality classes of optimal channel networks. Science 272, 984–986 (1996).

Manna, S. S. & Subramanian, B. Quasirandom spanning tree model for the early river network. Phys. Rev. Lett. 76, 3460–3463 (1996).

Knecht, C. L., Trump, W., ben-Avraham, D. & Ziff, R. M. Retention capacity of random surfaces. Phys. Rev. Lett. 108, 045703 (2012).

Baek, S. K. & Kim, B. J. Critical condition of the water-retention model. arXiv:1111.0425.

Yan, J., Zhao, B., Wang, L., Zelenetz, A. & Schwartz, L. H. Marker-controlled watershed for lymphoma segmentation in sequential CT images. Med. Phys. 33, 2452–2460 (2006).

Ikedo, Y. et al. Development of a fully automatic scheme for detection of masses in whole breast ultrasound images. Med. Phys. 34, 4378–4388 (2007).

Kerr, B., Neuhauser, C., Bohannan, B. J. M. & Dean, A. M. Local migration promotes competitive restraint in a host-pathogen ’tragedy of the commons’. Nature 442, 75–78 (2006).

Mathiesen, J., Mitarai, N., Sneppen, K. & Trusina, A. Ecosystems with mutually exclusive interactions self-organize to a state of high diversity. Phys. Rev. Lett. 107, 188101 (2011).

Cieplak, M., Maritan, A. & Banavar, J. R. Optimal paths and domain walls in the strong disorder limit. Phys. Rev. Lett. 72, 2320–2323 (1994).

Cieplak, M., Maritan, A. & Banavar, J. R. Invasion percolation and Eden growth: geometry and universality. Phys. Rev. Lett. 76, 3754–3757 (1996).

Fehr, E. et al. New efficient methods for calculating watersheds. J. Stat. Mech. P09007 (2009).

Fehr, E., Kadau, D., Andrade Jr, J. S. & Herrmann, H. J. Impact of perturbations on watersheds. Phys. Rev. Lett. 106, 048501 (2011).

Andrade Jr, J. S., Oliveira, E. A., Moreira, A. A. & Herrmann, H. J. Fracturing the optimal paths. Phys. Rev. Lett. 103, 225503 (2009).

Oliveira, E. A., Schrenk, K. J., Araújo, N. A. M., Herrmann, H. J. & Andrade Jr, J. S. Optimal-path cracks in correlated and uncorrelated lattices. Phys. Rev. E 83, 046113 (2011).

Porto, M., Havlin, S., Schwarzer, S. & Bunde, A. Optimal path in strong disorder and shortest path in invasion percolation with trapping. Phys. Rev. Lett. 79, 4060–4062 (1997).

Porto, M., Schwartz, N., Havlin, S. & Bunde, A. Optimal paths in disordered media: scaling of the crossover from self-similar to self-affine behavior. Phys. Rev. E 60, R2448–R2451 (1999).

Barabási, A.-L. Invasion percolation and global optimization. Phys. Rev. Lett. 76, 3750–3753 (1996).

Dobrin, R. & Duxbury, P. M. Minimum spanning trees on random networks. Phys. Rev. Lett. 86, 5076–5079 (2001).

Jackson, T. S. & Read, N. Theory of minimum spanning trees. I. Mean-field theory and strongly disordered spin-glass model. Phys. Rev. E 81, 021130 (2010).

Çiftçi, K. Minimum spanning tree reflects the alterations of the default mode network during Alzheimer's disease. Ann. Biomed. Eng. 39, 1493–1504 (2011).

Goyal, S. & Puri, R. K. Formation of fragments in heavy-ion collisions using a modified clusterization method. Phys. Rev. C 83, 047601 (2011).

Hubbe, M., Harvati, K. & Neves, W. Paleoamerican morphology in the context of European and East Asian Late Pleistocene variation: implications for human dispersion into the New World. Am. J. Phys. Anthropol. 144, 442–453 (2011).

Dorsey, J., Xu, S., Smedresman, G., Rushmeier, H. E. & MacMillan, L. The Mental Canvas - A Tool for Conceptual Architectural Design and Analysis. Proc. IEEE Conf. on Comp. Graphics and Applications, 201-210 (2007).

Ekpar, F. E. Method and Apparatus for Creating Interactive Virtual Tours. United States Patent 7567274 (2009).

Walter, T., Shattuck, D. W., Baldock, R., Bastin, M. E., Carpenter, A. E., Duce, S., Jan, E. Fraser, A., Hamilton, N., Pieper, S., Ragan, M. A., Schneider, J. E., Tomancak, P. & Hériché, J. K. Visualization of image data from cells to organisms. Nature Methods 7, S26–S41 (2010).

Burt, P. J. & Adelson, E. H. The Laplacian Pyramid as a Compact Image Code. IEEE Trans. on Communications, 532-540 (1983).


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Ekpar, F.E. 2020. Arbitrary Dimensional Data. European Journal of Engineering and Technology Research. 5, 1 (Jan. 2020), 46–56. DOI: