Novel Metaknowledge-based Processing Technique for Multimedia Big Data clustering challenges

Past research has challenged us with the task of showing relational patterns between text-based data and then clustering for predictive analysis using Golay Code technique. We focus on a novel approach to extract metaknowledge in multimedia datasets. Our collaboration has been an on-going task of studying the relational patterns between datapoints based on metafeatures extracted from metaknowledge in multimedia datasets. Those selected are significant to suit the mining technique we applied, Golay Code algorithm. In this research paper we summarize findings in optimization of metaknowledge representation for 23-bit representation of structured and unstructured multimedia data in order toComment: IEEE Multimedia Big Data (BigMM 2015

23-bit Metaknowledge Template Towards Big Data Knowledge Discovery and Management

The global influence of Big Data is not only growing but seemingly endless. The trend is leaning towards knowledge that is attained easily and quickly from massive pools of Big Data. Today we are living in the technological world that Dr. Usama Fayyad and his distinguished research fellows discussed in the introductory explanations of Knowledge Discovery in Databases (KDD) predicted nearly two decades ago. Indeed, they were precise in their outlook on Big Data analytics. In fact, the continued improvement of the interoperability of machine learning, statistics, database building and querying fused to create this increasingly popular science- Data Mining and Knowledge Discovery. The next generation computational theories are geared towards helping to extract insightful knowledge from even larger volumes of data at higher rates of speed. As the trend increases in popularity, the need for a highly adaptive solution for knowledge discovery will be necessary. In this research paper, we are introducing the investigation and development of 23 bit-questions for a Metaknowledge template for Big Data Processing and clustering purposes. This research aims to demonstrate the construction of this methodology and proves the validity and the beneficial utilization that brings Knowledge Discovery from Big Data.Comment: IEEE Data Science and Advanced Analytics (DSAA'2014

Local height probabilities in a composite Andrews-Baxter-Forrester model

We study the local height probabilities in a composite height model, derived from the restricted solid-on-solid model introduced by Andrews, Baxter and Forrester, and their connection with conformal field theory characters. The obtained conformal field theories also describe the critical behavior of the model at two different critical points. In addition, at criticality, the model is equivalent to a one-dimensional chain of anyons, subject to competing two- and three-body interactions. The anyonic-chain interpretation provided the original motivation to introduce the composite height model, and by obtaining the critical behaviour of the composite height model, the critical behaviour of the anyonic chains is established as well. Depending on the overall sign of the hamiltonian, this critical behaviour is described by a diagonal coset-model, generalizing the minimal models for one sign, and by Fateev-Zamolodchikov parafermions for the other.Comment: 34 pages, 5 figures; v2: expanded introduction, references added and other minor change

K-matrices for non-abelian quantum Hall states

Two fundamental aspects of so-called non-abelian quantum Hall states (the q-pfaffian states and more general) are a (generalized) pairing of the participating electrons and the non-abelian statistics of the quasi-hole excitations. In this paper, we show that these two aspects are linked by a duality relation, which can be made manifest by considering the K-matrices that describe the exclusion statistics of the fundamental excitations in these systems.Comment: LaTeX, 12 page

Big Line Bundles over Arithmetic Varieties

We prove a Hilbert-Samuel type result of arithmetic big line bundles in Arakelov geometry, which is an analogue of a classical theorem of Siu. An application of this result gives equidistribution of small points over algebraic dynamical systems, following the work of Szpiro-Ullmo-Zhang. We also generalize Chambert-Loir's non-archimedean equidistribution

Macroscopic properties of A-statistics

A-statistics is defined in the context of the Lie algebra sl(n+1). Some thermal properties of A-statistics are investigated under the assumption that the particles interact only via statistical interaction imposed by the Pauli principle of A-statistics. Apart from the general case, three particular examples are studied in more detail: (a) the particles have one and the same energy and chemical potential; (b) equidistant energy spectrum; (c) two species of particles with one and the same energy and chemical potential within each class. The grand partition functions and the average number of particles are among the thermodynamical quantities written down explicitly.Comment: 27 pages, 4 figures; to be published in J. Phys.

Prime power indices in factorised groups

[EN] Let the group G = AB be the product of the subgroups A and B. We determine some structural properties of G when the p-elements in A. B have prime power indices in G, for some prime p. More generally, we also consider the case that all prime power order elements in A. B have prime power indices in G. In particular, when G = A = B, we obtain as a consequence some known results.The first author is supported by Proyecto Prometeo II/2015/011, Generalitat Valenciana (Spain), and the second author is supported by Proyecto MTM2014-54707-C3-1-P, Ministerio de Economia, Industria y Competitividad (Spain). The results in this paper are part of the third author's Ph.D. thesis, and he acknowledges the predoctoral grant ACIF/2016/170, Generalitat Valenciana (Spain).Felipe Román, MJ.; Martínez-Pastor, A.; Ortiz-Sotomayor, VM. (2017). Prime power indices in factorised groups. Mediterranean Journal of Mathematics. 14(6):1-15. https://doi.org/10.1007/s00009-017-1023-6S115146Amberg, B., Franciosi, S., de Giovanni, F.: Products of Groups. Oxford University Press Inc., New York (1992)Baer, R.: Group elements of prime power index. Trans. Am. Math. Soc. 75, 20–47 (1953)Ballester-Bolinches, A., Cossey, J., Li, Y.: Mutually permutable products and conjugacy classes. Monatsh. Math. 170, 305–310 (2013)Ballester-Bolinches, A., Esteban-Romero, R., Asaad, M.: Products of finite groups, vol. 53 of de Gruyter Expositions in Mathematics, Berlin (2010)Berkovich, Y., Kazarin, L.S.: Indices of elements and normal structure of finite groups. J. Algebra 283, 564–583 (2005)Camina, A.R., Camina, R.D.: Implications of conjugacy class size. J. Group Theory 1(3), 257–269 (1998)Camina, A.R., Shumyatsky, P., Sica, C.: On elements of prime-power index in finite groups. J. Algebra 323, 522–525 (2010)Chillag, D., Herzog, M.: On the length of the conjugacy classes of finite groups. J. Algebra 131, 110–125 (1990)Doerk, K., Hawkes, T.: Finite Soluble Groups, vol. 4 of de Gruyter Expositions in Mathematics, Berlin (1992)Felipe, M.J., Martínez-Pastor, A., Ortiz-Sotomayor, V.M.: On finite groups with square-free conjugacy class sizes. Int. J. Group Theory (to appear)Kurzweil, H., Stellmacher, B.: The theory of finite groups: an introduction. Springer, New York (2004)Liu, X., Wang, Y., Wei, H.: Notes on the length of conjugacy classes of finite groups. J. Pure Appl. Algebra 196, 111–117 (2005

Analytic curves in algebraic varieties over number fields

We establish algebraicity criteria for formal germs of curves in algebraic varieties over number fields and apply them to derive a rationality criterion for formal germs of functions, which extends the classical rationality theorems of Borel-Dwork and P\'olya-Bertrandias valid over the projective line to arbitrary algebraic curves over a number field. The formulation and the proof of these criteria involve some basic notions in Arakelov geometry, combined with complex and rigid analytic geometry (notably, potential theory over complex and $p$-adic curves). We also discuss geometric analogues, pertaining to the algebraic geometry of projective surfaces, of these arithmetic criteria.Comment: 55 pages. To appear in "Algebra, Arithmetic, and Geometry: In Honor of Y.i. Manin", Y. Tschinkel & Yu. Manin editors, Birkh\"auser, 200