304,248 research outputs found
A hierarchical network formation model
We present a network formation model based on a particularly interesting class of networks in social settings, where individuals' positions are determined according to a topic-based or hierarchical taxonomy. In this game-theoretic model, players are located in the leaves of a complete b-ary tree as the seed network with the objective of minimizing their collective distances to others in the network. In the grid-based model of Even-Dar and Kearns [3], they demonstrate the existence of small diameter networks with the threshold of a = 2 where the cost of a new link depends on the distance between the two endpoints to the power of a. We show the appearance of small diameter equilibrium networks with the threshold of a = 1/4 in the hierarchical or tree-based networks. Moreover, the general set of equilibrium networks in our model are guaranteed to exist and they are pairwise Nash stable with transfers [2]
A hierarchical network formation model
We present a network formation model based on a particularly interesting class of networks in social settings, where individuals' positions are determined according to a topic-based or hierarchical taxonomy. In this game-theoretic model, players are located in the leaves of a complete b-ary tree as the seed network with the objective of minimizing their collective distances to others in the network. In the grid-based model of Even-Dar and Kearns [3], they demonstrate the existence of small diameter networks with the threshold of a = 2 where the cost of a new link depends on the distance between the two endpoints to the power of a. We show the appearance of small diameter equilibrium networks with the threshold of a = 1/4 in the hierarchical or tree-based networks. Moreover, the general set of equilibrium networks in our model are guaranteed to exist and they are pairwise Nash stable with transfers [2]
Coevolution of dynamical states and interactions in dynamic networks
We explore the coupled dynamics of the internal states of a set of
interacting elements and the network of interactions among them. Interactions
are modeled by a spatial game and the network of interaction links evolves
adapting to the outcome of the game. As an example we consider a model of
cooperation, where the adaptation is shown to facilitate the formation of a
hierarchical interaction network that sustains a highly cooperative stationary
state. The resulting network has the characteristics of a small world network
when a mechanism of local neighbor selection is introduced in the adaptive
network dynamics. The highly connected nodes in the hierarchical structure of
the network play a leading role in the stability of the network. Perturbations
acting on the state of these special nodes trigger global avalanches leading to
complete network reorganization.Comment: 4 pages, 5 figures, for related material visit
http:www.imedea.uib.es/physdept
A hierarchical anti-Hebbian network model for the formation of spatial cells in three-dimensional space.
Three-dimensional (3D) spatial cells in the mammalian hippocampal formation are believed to support the existence of 3D cognitive maps. Modeling studies are crucial to comprehend the neural principles governing the formation of these maps, yet to date very few have addressed this topic in 3D space. Here we present a hierarchical network model for the formation of 3D spatial cells using anti-Hebbian network. Built on empirical data, the model accounts for the natural emergence of 3D place, border, and grid cells, as well as a new type of previously undescribed spatial cell type which we call plane cells. It further explains the plausible reason behind the place and grid-cell anisotropic coding that has been observed in rodents and the potential discrepancy with the predicted periodic coding during 3D volumetric navigation. Lastly, it provides evidence for the importance of unsupervised learning rules in guiding the formation of higher-dimensional cognitive maps
Scale free networks from a Hamiltonian dynamics
Contrary to many recent models of growing networks, we present a model with
fixed number of nodes and links, where it is introduced a dynamics favoring the
formation of links between nodes with degree of connectivity as different as
possible. By applying a local rewiring move, the network reaches equilibrium
states assuming broad degree distributions, which have a power law form in an
intermediate range of the parameters used. Interestingly, in the same range we
find non-trivial hierarchical clustering.Comment: 4 pages, revtex4, 5 figures. v2: corrected statements about
equilibriu
From innovation to diversification: a simple competitive model
Few attempts have been proposed in order to describe the statistical features
and historical evolution of the export bipartite matrix countries/products. An
important standpoint is the introduction of a products network, namely a
hierarchical forest of products that models the formation and the evolution of
commodities. In the present article, we propose a simple dynamical model where
countries compete with each other to acquire the ability to produce and export
new products. Countries will have two possibilities to expand their export:
innovating, i.e. introducing new goods, namely new nodes in the product
networks, or copying the productive process of others, i.e. occupying a node
already present in the same network. In this way, the topology of the products
network and the country-product matrix evolve simultaneously, driven by the
countries push toward innovation.Comment: 8 figures, 8 table
Growth and Containment of a Hierarchical Criminal Network
We model the hierarchical evolution of an organized criminal network via
antagonistic recruitment and pursuit processes. Within the recruitment phase, a
criminal kingpin enlists new members into the network, who in turn seek out
other affiliates. New recruits are linked to established criminals according to
a probability distribution that depends on the current network structure. At
the same time, law enforcement agents attempt to dismantle the growing
organization using pursuit strategies that initiate on the lower level nodes
and that unfold as self-avoiding random walks. The global details of the
organization are unknown to law enforcement, who must explore the hierarchy
node by node. We halt the pursuit when certain local criteria of the network
are uncovered, encoding if and when an arrest is made; the criminal network is
assumed to be eradicated if the kingpin is arrested. We first analyze
recruitment and study the large scale properties of the growing network; later
we add pursuit and use numerical simulations to study the eradication
probability in the case of three pursuit strategies, the time to first
eradication and related costs. Within the context of this model, we find that
eradication becomes increasingly costly as the network increases in size and
that the optimal way of arresting the kingpin is to intervene at the early
stages of network formation. We discuss our results in the context of dark
network disruption and their implications on possible law enforcement
strategies.Comment: 16 pages, 11 Figures; New title; Updated figures with color scheme
better suited for colorblind readers and for gray scale printin
Directed Communication Networks
In this paper we model the formation of directed communication networks.A directed communication network is represented by a directed graph.Firstly, we study an allocation rule satisfying two appealing properties, component efficiency and directed fairness.We show that such an allocation rule exists if and only if we restrict ourselves to a class of directed graphs that naturally comes to the fore in the setting of hierarchical structures.Subsequently, we discuss several possibilities to model the formation of directed communication networks and provide some preliminary results
- …