Role of next-nearest-neighbor hopping in thet-t’-Jmodel

In this paper, we investigate the so-called "Sznajd Model" (SM) in one dimension, which is a simple cellular automata approach to consensus formation among two opposite opinions (described by spin up or down). To elucidate the SM dynamics, we first provide results of computer simulations for the spatio-temporal evolution of the opinion distribution L(t), the evolution of magnetization m(t), the distribution of decision times P(τ) and relaxation times P(μ). In the main part of the paper, it is shown that the SM can be completely reformulated in terms of a linear voter model (VM), where the transition rates towards a given opinion are directly proportional to frequency of the respective opinion of the second-nearest neighbors (no matter what the nearest neighbors are). So, the SM dynamics can be reduced to one rule, "Just follow your second-nearest neighbor". The equivalence is demonstrated by extensive computer simulations that show the same behavior between SM and VM in terms of L(t), m(t), P(τ), P(μ), and the final attractor statistics. The reformulation of the SM in terms of a VM involves a new parameter σ, to bias between anti- and ferromagnetic decisions in the case of frustration. We show that σ plays a crucial role in explaining the phase transition observed in SM. We further explore the role of synchronous versus asynchronous update rules on the intermediate dynamics and the final attractors. As compared to the original SM, we find three additional attractors, two of them related to an asymmetric coexistence between the opposite opinions.

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Analysis and Identification of Aptamer-Compound Interactions with a Maximum Relevance Minimum Redundancy and Nearest Neighbor Algorithm

BioMed Research International ◽

10.1155/2016/8351204 ◽

2016 ◽

Vol 2016 ◽

pp. 1-9 ◽

Cited By ~ 6

Author(s):

ShaoPeng Wang ◽

Yu-Hang Zhang ◽

Jing Lu ◽

Weiren Cui ◽

Jerry Hu ◽

...

Keyword(s):

Feature Selection ◽

Quantum Chemical ◽

Nearest Neighbor ◽

Biological Processes ◽

Optimal Prediction ◽

Selection Methods ◽

Nearest Neighbor Algorithm ◽

Incremental Feature Selection ◽

Exponential Enrichment

The development of biochemistry and molecular biology has revealed an increasingly important role of compounds in several biological processes. Like the aptamer-protein interaction, aptamer-compound interaction attracts increasing attention. However, it is time-consuming to select proper aptamers against compounds using traditional methods, such as exponential enrichment. Thus, there is an urgent need to design effective computational methods for searching effective aptamers against compounds. This study attempted to extract important features for aptamer-compound interactions using feature selection methods, such as Maximum Relevance Minimum Redundancy, as well as incremental feature selection. Each aptamer-compound pair was represented by properties derived from the aptamer and compound, including frequencies of single nucleotides and dinucleotides for the aptamer, as well as the constitutional, electrostatic, quantum-chemical, and space conformational descriptors of the compounds. As a result, some important features were obtained. To confirm the importance of the obtained features, we further discussed the associations between them and aptamer-compound interactions. Simultaneously, an optimal prediction model based on the nearest neighbor algorithm was built to identify aptamer-compound interactions, which has the potential to be a useful tool for the identification of novel aptamer-compound interactions. The program is available upon the request.

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SUPERSOLID PHASE IN ONE-DIMENSIONAL BOSE–HUBBARD MODEL WITH EXTENDED RANGE INTERACTIONS: DMRG AND FIELD THEORETIC STUDY AT DIFFERENT DENSITIES

International Journal of Modern Physics B ◽

10.1142/s0217979211057700 ◽

2011 ◽

Vol 25 (01) ◽

pp. 159-169 ◽

Cited By ~ 1

Author(s):

MANORANJAN KUMAR ◽

SUJIT SARKAR ◽

S. RAMASESHA

Keyword(s):

Hubbard Model ◽

Nearest Neighbor ◽

Range Interaction ◽

Quantum Phases ◽

One Dimensional ◽

Density Matrix Renormalization ◽

Supersolid Phase ◽

Extended Range ◽

Half Filling

We use the Density Matrix Renormalization Group and the Abelian bosonization method to study the effect of density on quantum phases of one-dimensional extended Bose–Hubbard model. We predict the existence of supersolid phase and also other quantum phases for this system. We have analyzed the role of extended range interaction parameters on solitonic phase near half-filling. We discuss the effects of dimerization in nearest neighbor hopping and interaction as well as next nearest neighbor interaction on the plateau phase at half-filling.

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