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In this work, we study the opinion dynamics of the Sznajd model with anticonformity on a fully-connected network. We consider four agents with two different configurations; three against one (3–1) and two against two (2–2). We consider two different individual behaviors, conformity and anticonformity, and observe the effect on the critical behavior of the model. We analyze the differences between the phase transitions that occur for both agent configurations. We find that both agent configurations have a different critical point. The critical point of the 3–1 agent is smaller than that of the 2–2 agent configuration. From the simulation and analytical result, we find that the critical point for the 3–1 occurs at $p_c=0.2$, and for the 2–2, at $p_c=0.5$. From the social viewpoint, the consensus process in a population is faster with a larger influencer in the same number of small group of the population. In addition, we find the critical exponents for both configurations are the same, that are $\beta \approx 0.5,\gamma \approx 1$ and $\nu \approx 2$. Our results suggest that both models are identical and in the mean-field Ising universality class.

In this paper, we give a systematic review of the theory of Gibbs measures of Potts model on Cayley trees (developed since 2013) and discuss many applications of the Potts model to real world situations: mainly biology, physics, and some examples of alloy behavior, cell sorting, financial engineering, flocking birds, flowing foams, image segmentation, medicine, sociology, etc.

The purpose of this review paper is to present systematically all known results on Gibbs measures on Cayley trees (Bethe lattices). There are about 150 papers which contain mathematically rigorous results about Gibbs measures on Cayley trees. This review is mainly based on the recently published mathematical papers. The method used for the description of Gibbs measures on Cayley trees is the method of Markov random field theory and recurrent equations of this theory, but the modern theory of Gibbs measures on trees uses new tools such as group theory, information flows on trees, node-weighted random walks, contour methods on trees and nonlinear analysis. We discuss all the mentioned methods which were developed recently. Thus, the paper informs the reader about what is (mathematically) done in the theory of Gibbs measures on trees and about where the corresponding results were published. We only give proofs which were not published in literature. Moreover, we give several open problems.

In this paper, we consider a Hard-Core (HC) model with two spin values on Cayley trees. The conception of alternative Gibbs measure is introduced and translational invariance conditions for alternative Gibbs measures are found. Also, we show that the existence of alternative Gibbs measures which are not translation-invariant. In addition, we study free energy of the model.

Shell model calculations have been performed in $f_{5/2}p{g}_{9/2}$ model space using two different interactions viz. jj44bpn and jun45pn to explore nuclear structure in ${}^{63,65,67}$Ga. Calculated excitation energies are compared with previously reported experimental values and a good agreement has been observed. Transitions strengths are also calculated using two sets of effective charges for proton and neutron and are compared with nearby ${}^{62,64,66}$Zn isotopes. Occupation probabilities of protons and neutrons corresponding to individual orbitals (namely $f_{5/2}$, $p_{3/2}$, $p_{1/2}$ and $g_{9/2}$ orbital), and dominant particle configurations for individual spin states have been presented as well. Calculations suggest major role of intruder $1g_{9/2}$ orbital in constructing the wave functions of higher angular momentum states, whereas, the lower excited states are mainly dominated by contributions from $fp$ orbitals.

Workflow modeling languages allow for the specification of executable business processes. They, however, typically do not provide any guidance for the adaptation of workflow models, i.e. they do not offer any methods or tools explaining and highlighting which adaptations of the models are feasible and which are not. Therefore, an approach to identify so-called configurable elements of a workflow modeling language and to add configuration opportunities to workflow models is presented in this paper. Configurable elements are the elements of a workflow model that can be modified such that the behavior represented by the model is restricted. More precisely, a configurable element can be either set to enabled, to blocked, or to hidden. To ensure that such configurations lead only to desirable models, our approach allows for imposing so-called requirements on the model's configuration. They have to be fulfilled by any configuration, and limit therefore the freedom of configuration choices. The identification of configurable elements within the workflow modeling language of YAWL and the derivation of the new "configurable YAWL" language provide a concrete example for a rather generic approach. A transformation of configured models into lawful YAWL models demonstrates its applicability.

For the solid-on-solid (SOS) model with an external field and with spin values from the set of all integers on a Cayley tree, each (gradient) Gibbs measure corresponds to a boundary law (an infinite-dimensional vector function defined on vertices of the Cayley tree) satisfying a nonlinear functional equation. Recently some translation-invariant and height-periodic (non-normalizable) solutions to the equation are found. Here, our aim is to find non-height-periodic and non-normalizable boundary laws for the SOS model. By such a solution one can construct a non-probability Gibbs measure. We find explicitly several non-normalizable boundary laws. Moreover, we reduce the problem to solving of a nonlinear, second-order difference equation. We give analytic and numerical analyses of the difference equation.

This study examines the complex and evolutionary nature of supply network configuration. Taking a bottom-up approach, we examine how supply network configuration at the macro-level evolves as a result of individual retailers' dynamic choice of procurement strategies at the micro-level. Employing agent-based modeling, we focus on the effects of switch cost and distributors' ordering policy on the evolution of supply network configuration. Our results show that (1) supply networks tend to evolve into a set of separate supply chains when switch cost is high and into an integrated network when switch cost is low, (2) a responsive ordering policy adopted by distributors is more conducive to the integrated network configuration than a non-responsive policy, and (3) lack of coordination among retailers in their dynamic choice of procurement strategies hurts not only the overall system performance, but also retailers themselves. More importantly, our study demonstrates the capabilities of agent-based modeling as a methodology for researching complex supply network issues.