Data with Non-Euclidean Geometry and Its Characterization

Recently,dealing with the non-Euclidean data and its characterization is considered as one of the major issues by researchers.The first problem arises while defining the distinction among Euclidean and non-Euclidean geometry with its examples.The second problem arises while dealing with the non-Euclidean geometry in true,false,and uncertain regions.The third problem arises while investigating some patterns in non-Euclidean data sets.This paper focused on tackling these issues with some real-life examples in data processing,data visualization,knowledge representation,and quantum computing.

Advancements in Time Modeling: Relationalism, Divisional Structures, and Geometry

This article broadens terminology and approaches that continue to advance time modelling within a relationalist framework. Time is modeled as a single dimension, flowing continuously through independent privileged points. Introduced as absolute point-time, abstract continuous time is a backdrop for concrete relational-based time that is finite and discrete, bound to the limits of a real-world system. We discuss how discrete signals at a point are used to temporally anchor zero-temporal points [t = 0] in linear time. Object-oriented temporal line elements, flanked by temporal point elements, have a proportional geometric identity quantifiable by a standard unit system and can be mapped on a natural number line. Durations, line elements, are divisible into ordered unit ratio elements using ancient timekeeping formulas. The divisional structure provides temporal classes for rotational (Rt24t) and orbital (Rt18) sample periods, as well as a more general temporal class (Rt12) applicable to either sample or frame periods. We introduce notation for additive cyclic counts of sample periods, including divisional units, for calendar-like formatting. For system modeling, unit structures with dihedral symmetry, group order, and numerical order are shown to be applicable to Euclidean modelling. We introduce new functions for bijective and non-bijective mapping, modular arithmetic for cyclic-based time counts, and a novel formula relating to a subgroup of Pythagorean triples, preserving dihedral n-polygon symmetries. This article presents a new approach to model time in a relationalistic framework.

DESIGN OF QUASI-CYCLIC LDPC CODES BASED ON EUCLIDEAN GEOMETRIES

A new method for constructing Quasi-Cyclic (QC) Low-Density Parity-Check (LDPC) codes based on Euclidean Geometry (EG) is presented. The proposed method results in a class of QC-LDPC codes with girth of at least 6 and the designed codes perform very close to the Shannon limit with iterative decoding. Simulations show that the designed QC-LDPC codes have almost the same performance with the existing EG-LDPC codes.

A NOVEL CONSTRUCTION OF QUANTUM LDPC CODES BASED ON CYCLIC CLASSES OF LINES IN EUCLIDEAN GEOMETRIES

The dual-containing (or self-orthogonal) formalism of Calderbank-Shor-Steane (CSS) codes provides a universal connection between a classical linear code and a Quantum Error-Correcting Code (QECC). We propose a novel class of quantum Low Density Parity Check (LDPC) codes constructed from cyclic classes of lines in Euclidean Geometry (EG). The corresponding constructed parity check matrix has quasi-cyclic structure that can be encoded flexibility, and satisfies the requirement of dual-containing quantum code. Taking the advantage of quasi-cyclic structure, we use a structured approach to construct Generalized Parity Check Matrix (GPCM). This new class of quantum codes has higher code rate, more sparse check matrix, and exactly one four-cycle in each pair of two rows. Ex-perimental results show that the proposed quantum codes, such as EG(2,q)II-QECC, EG(3,q)II-QECC, have better performance than that of other methods based on EG, over the depolarizing channel and decoded with iterative decoding based on the sum-product decoding algorithm.

NEW CONSTRUCTIONS OF LDPC CODES BASED ON CIRCULANT PERMUTATION MATRICES FOR AWGN CHANNEL

Two new design approaches for constructing Low-Density Parity-Check(LDPC) codes are proposed.One is used to design regular Quasi-Cyclic LDPC(QC-LDPC) codes with girth at least 8.The other is used to design irregular LDPC codes.Both of their parity-check matrices are composed of Circulant Permutation Matrices(CPMs).When iteratively decoded with the Sum-Product Algorithm(SPA),these proposed codes exhibit good performances over the AWGN channel.

On the Apriority and Self-renewal of Cognitive Ability

Human cognition ability comes from sensory experience or gift concept.This is the difference between empiricism and rationalism in the two major factions of Western European philosophy in the 16th and 18th centuries.The weakness of empiricism is that it is impossible to obtain knowledge with universal necessity from complicated experience,and the inability to obtain new knowledge is the weakness of theory.How to reconcile the contradiction between the two has become a new theme.This paper will cut into the three aspects of philosophy,geometry,and modern business economy,and explore the innate nature of cognitive ability and the characteristics of human self-renewal that are manifested in the process of self-development of cognitive ability.Its significance is not only to explore the essence of human beings,but also to give hope to the multiple possibilities of human beings.

Implementation of the Contract

This is a fimdamental relationship ＂contract＂ in Hilbert geometric axiom system. But the axiom system does not define how contracts are implemented, requires only basic objects and relations contracts to meet the basic axioms I - V . But in Euclidean geometry is intuitive to put a ＂contract＂ understood as a ＂movement.＂ Now we are in the framework of Hilbert geometric axiom system, to ＂contract＂ and we have been accustomed to ＂movement＂ link, for simplicity, we have limited the discussion to the Euclidean plane geometry.

Relativistic Quantum Mechanical Condition for Expansion of the Universe

In this manuscript, we will discuss about the quantum mechanical system for the movement of non-intractable particle, non-intractable particle which attends every mass state in the universe, the form of a non-intractable particle is n = -m, this manuscript defines the stable cross system for the movement of n-i particles and elementary particles with a perfect black body at centre with proofs of picture of super massive black hole, the linear hamiltonian of the cross quantum mechanical system and with this, it’s co-related matrixes, then by the use of cross system of Non-Intractable Particles defining a new right angel theorem. Then the new black body relation free from plank constant depends on non interactive mechanics and m, which has already mentioned in non-interactive mechanics and it’s relation with galaxies. The unique property of cross system is that it is surrounded by the energy of 10e + e always, and at last the relation between zero point energy and dark energy.

Quasi-cyclic LDPC codes with high-rate and low error floor based on Euclidean geometries

An improved Euclidean geometry approach to design quasi-cyclic （QC） Low-density parity-check （LDPC） codes with high-rate and low error floor is presented. The constructed QC-LDPC codes with high-rate have lower error floor than the original codes. The distribution of the minimum weight codeword is analyzed, and a sufficient existence condition of the minimum weight codeword is found. Simulations show that a lot of QC-LDPC codes with lower error floor can be designed by reducing the number of the minimum weight codewords satisfying this sufficient condition.