Analysis of Random Point Images with the Use of Symbolic Computation Codes and Generalized Catalan Numbers

A. L. Reznik; A. V. Tuzikov; A. A. Solovev; A. V. Torgov

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Analysis of Random Point Images with the Use of Symbolic Computation Codes and Generalized Catalan Numbers

机译：使用符号计算代码和广义加泰罗尼亚数的随机点图像分析

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摘要

Original codes and combinatorial-geometrical computational schemes are presented, which are developed and applied for finding exact analytical formulas that describe the probability of errorless readout of random point images recorded by a scanning aperture with a limited number of threshold levels. Combinatorial problems encountered in the course of the study and associated with the new generalization of Catalan numbers are formulated and solved. An attempt is made to find the explicit analytical form of these numbers, which is, on the one hand, a necessary stage of solving the basic research problem and, on the other hand, an independent self-consistent problem.

机译：提出了原始代码和组合 - 几何计算方案，其被开发并应用用于查找描述由扫描孔径记录的无随机点图像的无误读数的概率，其中扫描光圈具有有限数量的阈值水平。制定和解决了研究过程中遇到的组合问题并与加泰罗尼亚数量的新泛化相关联。尝试找到这些数字的显式分析形式，即一方面是解决基本研究问题的必要阶段，另一方面是一个独立的自我一致的问题。

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《Optoelectronics, Instrumentation and Data Processing》 |2016年第6期|共8页
作者
A. L. Reznik; A. V. Tuzikov; A. A. Solovev; A. V. Torgov;
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作者单位

Institute of Automation and Electrometry Siberian Branch Russian Academy of Sciences;

United Institute of Informatics Problems National Academy of Sciences of Belarus;

Institute of Automation and Electrometry Siberian Branch Russian Academy of Sciences;

Institute of Automation and Electrometry Siberian Branch Russian Academy of Sciences;

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正文语种 eng
中图分类仪器、仪表;
关键词
Random image; Computer analytical calculations; Generalized Catalan numbers; Random compact groups;

机译：随机图像;计算机分析计算;广义加泰罗尼亚数;随机紧凑型组;

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1. Analysis of Random Point Images with the Use of Symbolic Computation Codes and Generalized Catalan Numbers [J] . A. L. Reznik, A. V. Tuzikov, A. A. Solovev, Optoelectronics, Instrumentation and Data Processing . 2016,第6期

机译：使用符号计算代码和广义加泰罗尼亚数的随机点图像分析
2. Analytic analysis on a generalized (2+1)-dimensional variable-coefficient kortewegde vries equation using symbolic computation [J] . Zhang C., Tian B., Li L.-L., International Journal of Modern Physics, B. Condensed Matter Physics, Statistical Physics, Applied Physics . 2010,第27期

机译：广义（2 + 1）维变系数kortewegde vries方程的符号分析
3. Speculative Image Computation for Distributed Symbolic Reachability Analysis [J] . MING-YING CHUNG, GIANFRANCO CIARDO Journal of logic and computation . 2011,第1期

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4. Advancing Scientific Computation by Improving Scientific Code Development: Symbolic Execution and Semantic Analysis [C] . Mark Stewart International Conference on Computational Science(ICCS 2005) pt.1; 20050522-25; Atlanta, GA(US) . 2005

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5. Design and Analysis of Random Linear Network Coding Schemes: Dense Codes, Chunked Codes and Overlapped Chunked Codes. [D] . Heidarzadeh, Anoosheh. 2013

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Analysis of Random Point Images with the Use of Symbolic Computation Codes and Generalized Catalan Numbers

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