Discrete-Time Control for Systems of Interacting Objects with Unknown Random Disturbance Distributions: A Mean Field Approach

2015 ◽  
Vol 74 (1) ◽  
pp. 197-227 ◽  
Author(s):  
Carmen G. Higuera-Chan ◽  
Héctor Jasso-Fuentes ◽  
J. Adolfo Minjárez-Sosa
Keyword(s):  
Discrete Time ◽  
Mean Field ◽  
Random Disturbance ◽  
Field Approach ◽  
Time Control

scholarly journals A mean field approach for optimization in discrete time

2010 ◽  
Vol 21 (1) ◽  
pp. 63-101 ◽  
Author(s):  
Nicolas Gast ◽  
Bruno Gaujal
Keyword(s):  
Discrete Time ◽  
Mean Field ◽  
Field Approach

scholarly journals Replica-mean-field limits of fragmentation-interaction-aggregation processes

2022 ◽  
pp. 1-22
Author(s):  
François Baccelli ◽  
Michel Davydov ◽  
Thibaud Taillefumier
Keyword(s):  
Point Process ◽  
Discrete Time ◽  
Infinite Number ◽  
Mean Field ◽  
Asymptotic Independence ◽  
State Variables ◽  
Field Approach ◽  
Aggregation Processes ◽  
Mean Field Limits ◽  
Time Point

Abstract Network dynamics with point-process-based interactions are of paramount modeling interest. Unfortunately, most relevant dynamics involve complex graphs of interactions for which an exact computational treatment is impossible. To circumvent this difficulty, the replica-mean-field approach focuses on randomly interacting replicas of the networks of interest. In the limit of an infinite number of replicas, these networks become analytically tractable under the so-called ‘Poisson hypothesis’. However, in most applications this hypothesis is only conjectured. In this paper we establish the Poisson hypothesis for a general class of discrete-time, point-process-based dynamics that we propose to call fragmentation-interaction-aggregation processes, and which are introduced here. These processes feature a network of nodes, each endowed with a state governing their random activation. Each activation triggers the fragmentation of the activated node state and the transmission of interaction signals to downstream nodes. In turn, the signals received by nodes are aggregated to their state. Our main contribution is a proof of the Poisson hypothesis for the replica-mean-field version of any network in this class. The proof is obtained by establishing the propagation of asymptotic independence for state variables in the limit of an infinite number of replicas. Discrete-time Galves–Löcherbach neural networks are used as a basic instance and illustration of our analysis.

scholarly journals ONE DIMENSIONAL ASYNCHRONOUS COOPERATIVE PARRONDO'S GAMES

2003 ◽  
Vol 03 (04) ◽  
pp. L389-L398 ◽  
Author(s):  
ZORAN MIHAILOVIĆ ◽  
MILAN RAJKOVIĆ
Keyword(s):  
Computer Simulation ◽  
Markov Chain ◽  
Discrete Time ◽  
Transition Probabilities ◽  
Mean Field ◽  
Discrete Time Markov Chain ◽  
One Dimensional ◽  
Field Approach ◽  
The Mean ◽  
The One

A discrete-time Markov chain solution with exact rules for general computation of transition probabilities of the one-dimensional cooperative Parrondo's games is presented. We show that winning and the occurrence of the paradox depends on the number of players. Analytical results are compared to the results of the computer simulation and to the results based on the mean-field approach.

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...

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