STATES AND MICROSTATES IN A MEAN-FIELD APPROACH TO THE MINORITY GAME AND ITS GENERALIZATIONS

2006 ◽  
Vol 17 (03) ◽  
pp. 373-383
Author(s):  
INES CARIDI ◽  
HORACIO CEVA
Keyword(s):  
Mean Field ◽  
Main Idea ◽  
Virtual Agents ◽  
Minority Game ◽  
Strategy Space ◽  
Field Approach ◽  
Over Time

We developed a mean-field approach to the Minority Game, that allows us to reproduce the behavior of the model in the phase in which a so-called "dynamics of period two" is present. This dynamics describes the situation where the model is controlled by the presence of crowds of agents participating in the game. Our approach is based on the hypothesis that we can introduce states representative of the system, in such a form that averages over time can be replaced by averages over those states. The main idea is to work with virtual agents, rather than working with the actual set of agents of a particular game. Virtual agents are built from all the possible pairs of the strategies available in the model (the Full Strategy Space FSS). Moreover, we define an ensemble of microstates and, thereafter, states compatible with the specifications of the game. In this work we explain in detail how to introduce these elements, and how to actually calculate the ensemble of states and microstates. We have developed one generalization of the Minority Game as an attempt to make the model more realistic, by introducing interactions among the agents. We also discuss and explain the adequate ensemble of states and microstates for that generalization.

scholarly journals Inhomogeneous mean-field approach to collective excitations near the superfluid-Mott glass transition

2021 ◽  
pp. 168526
Author(s):  
Martin Puschmann ◽  
João C. Getelina ◽  
José A. Hoyos ◽  
Thomas Vojta
Keyword(s):  
Glass Transition ◽  
Mean Field ◽  
Collective Excitations ◽  
Field Approach

scholarly journals Effect of Bjerrum pairs on electrostatic properties in an electrolyte solution near charged surfaces: A mean-field approach

2021 ◽  
Author(s):  
Jun-Sik Sin
Keyword(s):  
Electrolyte Solution ◽  
Size Effects ◽  
Mean Field ◽  
Finite Size ◽  
Ion Association ◽  
Finite Size Effects ◽  
Field Approach ◽  
Electrostatic Properties ◽  
Charged Surfaces ◽  
Orientational Ordering

In this paper, we investigate the consequences of ion association, coupled with the considerations of finite size effects and orientational ordering of Bjerrum pairs as well as ions and water...

scholarly journals Electron liquid state in the symmetric Anderson lattice

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Igor N. Karnaukhov
Keyword(s):  
Low Temperatures ◽  
Arbitrary Dimension ◽  
Mean Field ◽  
Coulomb Repulsion ◽  
Anomalous Behavior ◽  
Effective Field ◽  
Kondo Lattice ◽  
Field Approach ◽  
Cubic Lattices ◽  
Half Filling

AbstractUsing mean field approach, we provide analytical and numerical solution of the symmetric Anderson lattice for arbitrary dimension at half filling. The symmetric Anderson lattice is equivalent to the Kondo lattice, which makes it possible to study the behavior of an electron liquid in the Kondo lattice. We have shown that, due to hybridization (through an effective field due to localized electrons) of electrons with different spins and momenta $$\mathbf{k} $$ k and $$\mathbf{k} +\overrightarrow{\pi }$$ k + π → , the gap in the electron spectrum opens at half filling. Such hybridization breaks the conservation of the total magnetic momentum of electrons, the spontaneous symmetry is broken. The state of electron liquid is characterized by a large Fermi surface. A gap in the spectrum is calculated depending on the magnitude of the on-site Coulomb repulsion and value of s–d hybridization for the chain, as well as for square and cubic lattices. Anomalous behavior of the heat capacity at low temperatures in the gapped state, which is realized in the symmetric Anderson lattice, was also found.

scholarly journals Quantal description of nucleon exchange in a stochastic mean-field approach

2015 ◽  
Vol 91 (5) ◽  
Author(s):  
S. Ayik ◽  
O. Yilmaz ◽  
B. Yilmaz ◽  
A. S. Umar ◽  
A. Gokalp ◽  
...  
Keyword(s):  
Mean Field ◽  
Field Approach

Characterization of Textured Aluminum Lines and Modelling of Stress Voiding

1994 ◽  
Vol 343 ◽  
Author(s):  
S.C. Wardle ◽  
B.L. Adams ◽  
C.S. Nichols ◽  
D.A. Smith
Keyword(s):  
Free Energy ◽  
Excess Free Energy ◽  
Mean Field ◽  
High Energy ◽  
Polycrystalline Structure ◽  
Field Approach ◽  
Bamboo Structure ◽  
Automated Technique ◽  
Theory And Modeling

ABSTRACTIt is well known from studies of individual interfaces that grain boundaries exhibit a spectrum of properties because their structure is misorientation dependent. Usually this variability is neglected and properties are modeled using a mean field approach. The limitations inherent in this approach can be overcome, in principle, using a combination of experimental techniques, theory and modeling. The bamboo structure of an interconnect is a particularly simple polycrystalline structure that can now be readily characterized experimentally and modeled in the computer. The grain misorientations in a [111] textured aluminum line have been measured using the new automated technique of orientational imaging microscopy. By relating boundary angle to diffusivity the expected stress voiding failure processes can be predicted through the link between misorientation angle, grain boundary excess free energy and diffusivity. Consequently it can be shown that the high energy boundaries are the favored failure sites thermodynamically and kinetically.

A Transparent and Decentralized Model of Perception and Action for Intelligent Virtual Agents

2014 ◽  
Vol 23 (04) ◽  
pp. 1460020 ◽  
Author(s):  
George Anastassakis ◽  
Themis Panayiotopoulos
Keyword(s):  
Knowledge Representation ◽  
Virtual Environment ◽  
Virtual World ◽  
Perception And Action ◽  
Virtual Agents ◽  
Virtual Agent ◽  
Complex Interactions ◽  
Intelligent Virtual Agents ◽  
Decentralized Model ◽  
Over Time

Intelligent virtual agent behaviour is a crucial element of any virtual environment application as it essentially brings the environment to life, introduces believability and realism and enables complex interactions and evolution over time. However, the development of mechanisms for virtual agent perception and action is neither a trivial nor a straight-forward task. In this paper we present a model of perception and action for intelligent virtual agents that meets specific requirements and can as such be systematically implemented, can seamlessly and transparently integrate with knowledge representation and intelligent reasoning mechanisms, is highly independent of virtual world implementation specifics, and enables virtual agent portability and reuse.

scholarly journals Friendship paradox in growth networks: analytical and empirical analysis

2021 ◽  
Vol 6 (1) ◽  
Author(s):  
Sergei P. Sidorov ◽  
Sergei V. Mironov ◽  
Alexey A. Grigoriev
Keyword(s):  
Real World ◽  
Preferential Attachment ◽  
Empirical Studies ◽  
Mean Field ◽  
Network Models ◽  
Average Degree ◽  
Closure Model ◽  
Triadic Closure ◽  
Attachment Mechanism ◽  
Over Time

AbstractMany empirical studies have shown that in social, citation, collaboration, and other types of networks in real world, the degree of almost every node is less than the average degree of its neighbors. This imbalance is well known in sociology as the friendship paradox and states that your friends are more popular than you on average. If we introduce a value equal to the ratio of the average degree of the neighbors for a certain node to the degree of this node (which is called the ‘friendship index’, FI), then the FI value of more than 1 for most nodes indicates the presence of the friendship paradox in the network. In this paper, we study the behavior of the FI over time for networks generated by growth network models. We will focus our analysis on two models based on the use of the preferential attachment mechanism: the Barabási–Albert model and the triadic closure model. Using the mean-field approach, we obtain differential equations describing the dynamics of changes in the FI over time, and accordingly, after obtaining their solutions, we find the expected values of this index over iterations. The results show that the values of FI are decreasing over time for all nodes in both models. However, for networks constructed in accordance with the triadic closure model, this decrease occurs at a much slower rate than for the Barabási–Albert graphs. In addition, we analyze several real-world networks and show that their FI distributions follow a power law. We show that both the Barabási–Albert and the triadic closure networks exhibit the same behavior. However, for networks based on the triadic closure model, the distributions of FI are more heavy-tailed and, in this sense, are closer to the distributions for real networks.

THE INNER CRUST OF NEUTRON STARS IN RELATIVISTIC MEAN FIELD APPROACH

2008 ◽  
Vol 17 (09) ◽  
pp. 1765-1773 ◽  
Author(s):  
JIGUANG CAO ◽  
ZHONGYU MA ◽  
NGUYEN VAN GIAI
Keyword(s):  
Boundary Conditions ◽  
Neutron Stars ◽  
Mean Field ◽  
Bcs Theory ◽  
Neutron Density ◽  
Field Approach ◽  
Hartree Fock ◽  
Relativistic Mean Field ◽  
Density Distributions ◽  
Rmf Model

The microscopic properties and superfluidity of the inner crust in neutron stars are investigated in the framework of the relativistic mean field(RMF) model and BCS theory. The Wigner-Seitz(W-S) cell of inner crust is composed of neutron-rich nuclei immersed in a sea of dilute, homogeneous neutron gas. The pairing properties of nucleons in the W-S cells are treated in BCS theory with Gogny interaction. In this work, we emphasize on the choice of the boundary conditions in the RMF approach and superfluidity of the inner crust. Three kinds of boundary conditions are suggested. The properties of the W-S cells with the three kinds of boundary conditions are investigated. The neutron density distributions in the RMF and Hartree-Fock-Bogoliubov(HFB) models are compared.

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