Metrization of the T-Alphabet: Measuring the Distance between Multidimensional Real Discrete Sequences

Iterated Function System (IFS) models have been used to represent discrete sequences where the attractor of the IFS is piece-wise self-affine in R2 or R3 (R is the set of real numbers). In this paper, the piece-wise self-affine IFS model is extended from R3 to Rn (n is an integer greater than 3), which is called the multi-dimensional piece-wise self-affine fractal interpolation model. This model uses a "mapping partial derivative" and a constrained inverse algorithm to identify the model parameters. The model values depend continuously on all the model parameters, and represent most data which are not multi-dimensional self-affine in Rn. Therefore, the result is very general. Moreover, the multi-dimensional piece-wise self-affine fractal interpolation model in tensor form is more terse than in the usual matrix form.

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VISUAL AND AUDITORY CUES SIGNIFICANTLY REDUCE HUMAN'S INTRINSIC BIASES WHEN TASKED TO GENERATE A RANDOM NUMBER SEQUENCE

International Journal of Modern Physics C ◽

10.1142/s0129183110015324 ◽

2010 ◽

Vol 21 (05) ◽

pp. 567-581 ◽

Cited By ~ 3

Author(s):

IRENE CRISOLOGO ◽

RENE BATAC ◽

ANTHONY LONGJAS ◽

ERIKA FILLE LEGARA ◽

CHRISTOPHER MONTEROLA

Keyword(s):

Visual Cues ◽

Random Number ◽

Pattern Analysis ◽

Number Sequence ◽

Random Series ◽

Auditory Cues ◽

Statistical Framework ◽

Number Distribution ◽

Discrete Sequences

Humans are deemed ineffective in generating a seemingly random number sequence primarily because of inherent biases and fatigue. Here, we establish statistically that human-generated number sequence in the presence of visual cues considerably reduce one's tendency to be fixated to a certain group of numbers allowing the number distribution to be statistically uniform. We also show that a stitching procedure utilizing auditory cues significantly minimizes human's intrinsic biases towards doublet and sequential ordering of numbers. The article provides extensive experimentation and comprehensive pattern analysis of the sequences formed when humans are tasked to generate a random series using numbers "0" to "9." In the process, we develop a statistical framework for analyzing the apparent randomness of finite discrete sequences via numerical measurements.

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A new fractal algorithm to model discrete sequences

Chinese Physics B ◽

10.1088/1674-1056/19/9/090509 ◽

2010 ◽

Vol 19 (9) ◽

pp. 090509 ◽

Cited By ~ 2

Author(s):

Zhai Ming-Yue ◽

Heidi Kuzuma ◽

James W Rector

Keyword(s):

Discrete Sequences

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Traces of Hörmander Algebras on Discrete Sequences

Analysis and Mathematical Physics ◽

10.1007/978-3-7643-9906-1_19 ◽

2009 ◽

pp. 397-408 ◽

Cited By ~ 2

Author(s):

Xavier Massaneda ◽

Joaquim Ortega-Cerdà ◽

Myriam Ounal’es

Keyword(s):

Discrete Sequences

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A Visual Lexicon

Public Journal of Semiotics ◽

10.37693/pjos.2007.1.8814 ◽

2007 ◽

Vol 1 (1) ◽

pp. 35-56 ◽

Cited By ~ 24

Author(s):

Neil Cohn

Keyword(s):

Visual Language ◽

Image Content ◽

Verbal Language ◽

Visual Elements ◽

Discrete Sequences ◽

Lexical Items ◽

Primary Unit

One of the most recognizable graphic components of the visual language of “comics” is the “panel,” a demarcated frame of image content put into discrete sequences, thereby seeming to be the primary unit of expression. However, meaningful visual elements do exist that are both smaller and larger than this encapsulation of image and text. Spoken languages also have variation in sizes of lexical items above and below their primary sequential unit of the “word.” This paper will address these varying levels of representation in visual language in comparison to the structural make-up of verbal language, to aim toward at what it means to have “visual lexical items.”

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Local approximation of discrete processes by interpolation polynomials

Information Technology and Nanotechnology ◽

10.18287/1613-0073-2019-2416-104-110 ◽

2019 ◽

pp. 104-110

Author(s):

A A Kolpakov ◽

Yu A Kropotov

Keyword(s):

Data Processing ◽

Processing System ◽

Local Approximation ◽

Algebraic Polynomials ◽

Data Processing System ◽

Multichannel System ◽

Multichannel Data ◽

Discrete Sequences ◽

Interpolation Polynomials

This paper discusses the structure of the devices and their defining formulas used for local approximation using power-algebraic polynomials when the observed data are nown exactly. A multichannel system for processing discrete sequences is considered. On the basis of the considered system the research of acceleration of calculations in the system from specialized computational modules is carried out. The carried out researches have shown, that the developed model of multichannel data processing system allows to reduce essentially time for data processing.

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