scholarly journals The Phase Transition Analysis for the Random Regular Exact 2-(d,k)-SAT Problem

Symmetry ◽  
2021 ◽  
Vol 13 (7) ◽  
pp. 1231
Author(s):  
Guoxia Nie ◽  
Daoyun Xu ◽  
Xiaofeng Wang ◽  
Xi Wang
Keyword(s):  
Phase Transition ◽  
High Probability ◽  
Solution Space ◽  
Regular Structure ◽  
Generation Model ◽  
Transition Analysis ◽  
Sat Problem ◽  
Second Moments ◽  
Instance Generation ◽  
Theoretical Results

In a regular (d,k)-CNF formula, each clause has length k and each variable appears d times. A regular structure such as this is symmetric, and the satisfiability problem of this symmetric structure is called the (d,k)-SAT problem for short. The regular exact 2-(d,k)-SAT problem is that for a (d,k)-CNF formula F, if there is a truth assignment T, then exactly two literals of each clause in F are true. If the formula F contains only positive or negative literals, then there is a satisfiable assignment T with a size of 2n/k such that F is 2-exactly satisfiable. This paper introduces the (d,k)-SAT instance generation model, constructs the solution space, and employs the method of the first and second moments to present the phase transition point d* of the 2-(d,k)-SAT instance with only positive literals. When d<d*, the 2-(d,k)-SAT instance can be satisfied with high probability. When d>d*, the 2-(d,k)-SAT instance can not be satisfied with high probability. Finally, the verification results demonstrate that the theoretical results are consistent with the experimental results.

scholarly journals The Phase Transition Analysis for Random Regular Exact (s, c, k)—SAT Problem

IEEE Access ◽  
2021 ◽  
Vol 9 ◽  
pp. 26664-26673
Author(s):  
Xiaoling Mo ◽  
Daoyun Xu ◽  
Xi Wang
Keyword(s):  
Phase Transition ◽  
Transition Analysis ◽  
Sat Problem

scholarly journals A New Method for 3-Satisfiability Problem Solving Space Structure on Structural Entropy

Symmetry ◽  
2021 ◽  
Vol 13 (11) ◽  
pp. 2005
Author(s):  
Chen Liang ◽  
Xiaofeng Wang ◽  
Lei Lu ◽  
Pengfei Niu
Keyword(s):  
Phase Transition ◽  
Belief Propagation ◽  
Solution Space ◽  
Space Structure ◽  
Label Propagation ◽  
Frustration Theory ◽  
Problem Solution ◽  
Analysis Model ◽  
Sat Problem ◽  
Structure Information

Analyzing the solution space structure and evolution of 3satisfiability (3-SAT) problem is an important way to study the difficulty of the solving satisfiability (SAT) problem. However, there is no unified analysis model for the spatial structure and evolution of solutions under different constraint densities. The analysis of different phase transition points and solution regions is based on different metric analysis models. The solution space of 3-SAT problem is obtained by planting strategy and belief propagation. According to the distribution of the influence of frozen variables on the solution, a label propagation algorithm based on planting strategy is proposed, is used to find the solution cluster, and then the structure entropy is used to measure its structure information. The structure entropy analysis model of 3-SAT problem solution space is established, and the unified analysis framework of solution space evolution and satisfiability phase transition is given. The experimental results show that the model is effective and can accurately analyze the evolution process of solution space and satisfiability phase transition, and verify the accuracy of interference phase transition point threshold predicted by long-range frustration theory.

scholarly journals Phase transition analysis of the dynamic instability of microtubules

Nonlinearity ◽  
2014 ◽  
Vol 27 (9) ◽  
pp. 2165-2176 ◽  
Author(s):  
Shantia Yarahmadian ◽  
Masoud Yari
Keyword(s):  
Phase Transition ◽  
Dynamic Instability ◽  
Transition Analysis

Phase Transition Analysis of 5-Aminotetrazole from Room Temperature to the Melting Point

2010 ◽  
Vol 114 (39) ◽  
pp. 12572-12576 ◽  
Author(s):  
Shigeaki Obata ◽  
Satoshi Takeya ◽  
Hiroshi Fujihisa ◽  
Kazumasa Honda ◽  
Yoshito Gotoh
Keyword(s):  
Phase Transition ◽  
Melting Point ◽  
Room Temperature ◽  
Transition Analysis

Phase transition analysis in Z2 and U(1) lattice gauge theories

1981 ◽  
Vol 105 (1) ◽  
pp. 51-54 ◽  
Author(s):  
M. Falcioni ◽  
E. Marinari ◽  
M.L. Paciello ◽  
G. Parisi ◽  
B. Taglienti
Keyword(s):  
Phase Transition ◽  
Gauge Theories ◽  
Transition Analysis ◽  
Lattice Gauge ◽  
Lattice Gauge Theories

First-Principle Study on the Structural Phase Transition, and Electronic Structures of Cobalt under Pressure

2015 ◽  
Vol 729 ◽  
pp. 15-20
Author(s):  
Hong Bo Zhu ◽  
Dun Qiang Tan ◽  
Zhi Huang Xiong
Keyword(s):  
Phase Transition ◽  
Electronic Structures ◽  
Density Functional ◽  
Structural Parameters ◽  
Structural Phase ◽  
First Principles Calculation ◽  
Functional Theory ◽  
Calculated Equilibrium ◽  
Theoretical Results ◽  
Good Agreement

The structural phase transitions and electronic structures of Co are investigated by using the first-principles calculation based on density-functional theory (DFT). Our calculated equilibrium structural parameters of Co are in good agreement with the available experimental data and other theoretical results. The calculated phase transition hcp-Co → fcc-Co at ca. 125.25 GPa. The magnetic moment of hcp-Co and fcc-Co drops to zero at 155 GPa and 77 GPa, respectively.

Phase Transition Analysis between LiFePO4and FePO4by In-Situ Time-Resolved X-ray Absorption and X-ray Diffraction

2013 ◽  
Vol 160 (5) ◽  
pp. A3061-A3065 ◽  
Author(s):  
Yuki Orikasa ◽  
Takehiro Maeda ◽  
Yukinori Koyama ◽  
Taketoshi Minato ◽  
Haruno Murayama ◽  
...  
Keyword(s):  
Phase Transition ◽  
X Ray Diffraction ◽  
Transition Analysis ◽  
Time Resolved ◽  
X Ray ◽  
X Ray Absorption

scholarly journals ARPGE: a computer program to automatically reconstruct the parent grains from electron backscatter diffraction data

2007 ◽  
Vol 40 (6) ◽  
pp. 1183-1188 ◽  
Author(s):  
Cyril Cayron
Keyword(s):  
Phase Transition ◽  
Computer Program ◽  
Diffraction Data ◽  
Electron Backscatter Diffraction ◽  
Parent Phase ◽  
Martensitic Transformations ◽  
Variant Selection ◽  
Electron Backscatter ◽  
Backscatter Diffraction ◽  
Theoretical Results

A computer program calledARPGEwritten in Python uses the theoretical results generated by the computer programGenOVato automatically reconstruct the parent grains from electron backscatter diffraction data obtained on phase transition materials with or without residual parent phase. The misorientations between daughter grains are identified with operators, the daughter grains are identified with indexed variants, the orientations of the parent grains are determined, and some statistics on the variants and operators are established. Some examples with martensitic transformations in iron and titanium alloys were treated. Variant selection phenomena were revealed.

scholarly journals Estimating Stochastic Linear Combination of Non-Linear Regressions

2020 ◽  
Vol 34 (04) ◽  
pp. 6137-6144
Author(s):  
Di Wang ◽  
Xiangyu Guo ◽  
Chaowen Guan ◽  
Shi Li ◽  
Jinhui Xu
Keyword(s):  
Machine Learning ◽  
Linear Combination ◽  
Statistical Models ◽  
High Probability ◽  
Estimation Errors ◽  
Zero Bias ◽  
Multi Index ◽  
Non Linear ◽  
Linear Regressions ◽  
Theoretical Results

In this paper we study the problem of estimating stochastic linear combination of non-linear regressions, which has a close connection with many machine learning and statistical models such as non-linear regressions, the Single Index, Multi-index, Varying Coefficient Index Models and Two-layer Neural Networks. Specifically, we first show that with some mild assumptions, if the variate vector x is multivariate Gaussian, then there is an algorithm whose output vectors have ℓ2-norm estimation errors of O(√p/n) with high probability, where p is the dimension of x and n is the number of samples. Then we extend our result to the case where x is sub-Gaussian using the zero-bias transformation, which could be seen as a generalization of the classic Stein's lemma. We also show that with some additional assumptions there is an algorithm whose output vectors have ℓ∞-norm estimation errors of O(1/√p + √p/n) with high probability. Finally, for both Gaussian and sub-Gaussian cases we propose a faster sub-sampling based algorithm and show that when the sub-sample sizes are large enough then the estimation errors will not be sacrificed by too much. Experiments for both cases support our theoretical results. To the best of our knowledge, this is the first work that studies and provides theoretical guarantees for the stochastic linear combination of non-linear regressions model.

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