Discrete Tomography Data Footprint Reduction by Information Conservation

• Autorzy: Fiorini R. A. , Laguteta G.
• Języki publikacji: EN

Abstrakty

EN

The first impact of Discrete Tomography (DT) applied to nanoscale technology has been to generate enormous quantity of data. Data Footprint Reduction (DFR) is the process of employing one or more techniques to store a given set of data in less storage space. The very best modern lossless compressors use classical probabilistic models only, and are unable to match high end application requirements, like “Arbitrary Bit Depth” (ABD) resolution and “Dynamic Upscale Regeneration” (DUR), with full information conservation. This paper explores, at core level, the basic properties and relationships of Q Arithmetic to achieve full numeric information conservation and regeneration, algorithmically. That knowledge shows strong connections to modular group theory and combinatorial optimization. Traditional Q Arithmetic can be even regarded as a highly sophisticated open logic, powerful and flexible LTR and RTL formal numeric language of languages, with self-defining consistent word and rule, starting from elementary generator and relation. This new awareness can guide the development of successful more convenient algorithm and application.

Słowa kluczowe

EN

arithmetic geometry; biomedical cybernetics; biomedical engineering; data footprint reduction; discrete tomography; healthcare; lossless compression; public health

• Wydawca: IOS Press
• Czasopismo: Fundamenta Informaticae
• Rocznik: 2013
• Tom: Vol. 125, nr 3/4
• Strony: 261--272
• Opis fizyczny: Bibliogr. 23 poz.

Twórcy

autor

Fiorini R. A.

• Dipartimento di Bioingegneria, Politecnico di Milano, P.za Leonardo da Vinci 32, 20133 Milano, Italy

autor

Laguteta G.

• Dipartimento di Bioingegneria, Politecnico di Milano, P.za Leonardo da Vinci 32, 20133 Milano, Italy

Bibliografia

• [1] Fermat’s little theorem, From Wikipedia, the free encyclopedia: http://en.wikipedia.org/wiki/ Fermats_little_theorem.
• [2] Batenburg, K. J., Bals, S., Sijbers, J., Kubel, C., Midgley, P. A., Hernandez, J. C., Kaiser, U., Encina, E. R., Coronado, E. A., Tendeloo, G. V.: 3D imaging of nanomaterials by discrete tomography, Ultramicroscopy, 109, 2009, 730-740.
• [3] Chomsky, A. N.: Syntactic structures, 1957, TheHague/Paris: Mouton.
• [4] Chomsky, N., Schutzenberger, M. P.: The algebraic theory of context-free languages in “Computer Programming and Formal Systems”, 1963, 118-161, P. Braffort and D. Hirschbert (Eds.), North Holland: Amsterdam.
• [5] Durrett, R.: Probability: Theory and Examples, Fourth Edition, Cambridge: Cambridge University Press, 2010.
• [6] Erdos, P. P., Schmutz, C., Eric: Carmichael’s lambda function, Acta Arithmetica, 58, 1991, 363-385.
• [7] Euler, L.: Tractatus de numeroroum doctrina capita sedecim quae supersunt, Comment. Arithmet, 2, 1849, 182-283, (This was actually written 1748-1750, but was only published posthumously);Opera Omnia, Series prima, Vols IV, Leipzig and Berlin: Teubner.
• [8] Fiorini, R. A.: A Note on the Structure of Rational Numbers, SUDAAR Report to Prof. J. David Powell, 7, 1987, 1-10, Stanford University, Stanford, CA, USA.
• [9] Fiorini, R. A., Dacquino, G.: On the logic structure of exact rational representation in fixed-radix number systems, Proc. Math. Methods for Learning: Advances in Knowledge Discovery and Data Mining, Vercellis, C.(ed.), 2004, 87-96, June 21-24, Como, Italy.
• [10] Fiorini, R. A., Dacquino, G.: Improved object optimal synthetic description, modeling, learning and discrimination by GEOGINE computational kernel, SPIE Proceedings, Intelligent Computing: Theory and Applications III, Priddy, K. L.(ed.), 5803, 2005, 12-23, Ed., March 28-29, Orlando, Florida, USA.
• [11] Fiorini, R. A., Laguteta, G., Condorelli, A.: Discrete Tomography Data Footprint Reduction by Natural Compression, submitted to ’’Principia Informaticae” Journal, 2012.
• [12] Fiorini, R. A., Santacroce, G.: Systems Science and Biomedical Cybernetics for Healthcare Safety Management, Proc. International Symposium, The Economic Crisis: Time For A Paradigm Shift - Towards a Systems Approach, Universitat de Valencia, January 24-25, 2013.
• [13] Franklin, G. F., Powell, J. D., Emami-Naeini, A.: Feedback Control of Dynamic Systems, Pearson Higher Education, Inc., Upper Saddle River, NJ, USA, 2010.
• [14] Franklin, G. F., Powell, J. D., Workman, M.: Digital Control of Dynamic Systems, Third edition, Ellis-Kagle Press, Half Moon Bay, CA, USA, 1998.
• [15] Jinschek, J. R., Batenburg, K. J., Calderon, H. A., Kilaas, R., Radmilovic, V., Kisielowski, C.: 3-D reconstruction of the atomic positions in a simulated gold nanocrystal based on discrete tomography, Ultramicroscopy, 108, 2008, 589-604.
• [16] Lashley, K. S.: “The problem of serial order in behaviour”, Cerebral mechanisms in behaviour, 1951, L. A. Jeffress ed.
• [17] Licata, I.: La logica aperta della mente, Torino: Codice edizioni, 2008.
• [18] Segal, D.: Polycyclic groups, Cambridge University Press, Cambridge, 1983.
• [19] Shannon, C. E.: A Mathematical Theory of Communication, Bell Syst Tech. Journal, 27(3), 1948, 379-423.
• [20] Sloane, N. J. A.: Sequences A04561 in “The On-Line Encyclopedia of Integer Sequences”, 2012, http: //oeis.org/A04561.
• [21] Weisstein, E. W.: Full Reptend Prime, (1999-2012), Website:http://mathworld.wolfram.com/ FullReptendPrime.html.
• [22] Wells, D.: The Penguin Dictionary of Curious and Interesting Numbers, Middlesex, England: Penguin Books, 1986.
• [23] Young, D. M., Gregory, R. T.: A Survey of Numerical Mathematics, vol.I and II, 1973, Reading, Mass.: Addison Wesley.