| viXra.org > Combinatorics and Graph Theory > 2403 |
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| viXra.org > Combinatorics and Graph Theory > 2403 |
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[3] viXra:2403.0050 [pdf] submitted on 2024-03-12 07:14:48
Authors: Abdalrhman Alquaary
Comments: 9 Pages.
In an era where social media platforms play a crucial role in shaping public discourse, microblogging data emerges as a vital resource for understanding complex social interactions. This paper introduces MTNSA (Microblogging Text Network Sentiment Analysis), a groundbreaking approach that harnesses the richness of social media communication by analyzing three separate categories: the relationships between words, relationships between hashtags, and relationships between emojis. MTNSA utilizes innovative techniques leveraging network theory to unravel the thoughts and opinions in microblogging environments, enriching itself by integrating sentiment analysis into this framework. This innovative method provides a comprehensive view of the sentiments associated with each node, offering deeper insights into the emotional nuances of online discourse. MTNSA's unique design enables its application across multilingual discourses, as it focuses on uncovering relationships between nodes, making it a versatile tool for global analysis in diverse linguistic contexts. The ability of MTNSA to blend nodes and emotional contexts into a unified analytical model presents a significant advancement in our understanding of digital communication patterns. It equips researchers, marketers, and policymakers with a robust tool to decode the intricate language of social media, contributing profoundly to our comprehension of how emotions and ideas are expressed and disseminated in the digital realm, thereby opening new frontiers for analysis in the dynamic landscape of social media.
Category: Combinatorics and Graph Theory
[2] viXra:2403.0046 [pdf] submitted on 2024-03-10 23:17:59
Authors: Akira Saito
Comments: 5 Pages.
We present a method for determining the order parameters of the spin glass Ising model (a general Ising model) in its ground state. This solution is valid specifically for the ground state, revealing the final outcomes of interactions and providing a solution to combinatorial optimization problems. The solution is presented through differential equations related to the inverse temperature, which can be solved using Euler's method. If the tracing of states through inverse temperature allows for the determination of state variables in a practically finite time, it becomes relevant to the P=NP problem. Furthermore, the set of equations obtained is also shown to be equivalent to those used in Boltzmann machines.
Category: Combinatorics and Graph Theory
[1] viXra:2403.0044 [pdf] replaced on 2025-03-10 21:17:57
Authors: Majid Zohrehbandian
Comments: 14 Pages.
The vertex cover problem is a famous combinatorial problem, and its complexity has been heavily studied. While a 2-approximation for it can be trivially obtained, researchers have not been able to approximate it better than 2-o(1). In this paper, by introducing a new semidefinite programming formulation that satisfies new properties, we introduce an approximation algorithm for the vertex cover problem with a performance ratio of 1.999999 on arbitrary graphs, en route to answering an open question about the correctness of the unique games conjecture.
Category: Combinatorics and Graph Theory
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