2,115 research outputs found
AANR spaces and absolute retracts for tree-like continua
summary:Continua that are approximative absolute neighborhood retracts (AANR’s) are characterized as absolute terminal retracts, i.e., retracts of continua in which they are embedded as terminal subcontinua. This implies that any AANR continuum has a dense arc component, and that any ANR continuum is an absolute terminal retract. It is proved that each absolute retract for any of the classes of: tree-like continua, -dendroids, dendroids, arc-like continua and arc-like -dendroids is an approximative absolute retract (so it is an AANR). Consequently, all these continua have the fixed point property, which is a new result for absolute retracts for tree-like continua. Related questions are asked
On completeness of spaces of open mappings on continua
AbstractAmong other things it is proved that the set of all open mappings between compacta X and Y is topologically complete if X is locally connected and Y is a graph, and this set is not topologically complete if it is nonempty and Y is a manifold of dimension >1, or Y is the Menger universal curve, or Y is a pseudo-arc
Supremacy distribution in evolving networks
We study a supremacy distribution in evolving Barabasi-Albert networks. The
supremacy of a node is defined as a total number of all nodes that
are younger than and can be connected to it by a directed path. For a
network with a characteristic parameter the supremacy of an
individual node increases with the network age as in an
appropriate scaling region. It follows that there is a relation between a node degree and its supremacy and the supremacy
distribution scales as . Analytic calculations basing on
a continuum theory of supremacy evolution and on a corresponding rate equation
have been confirmed by numerical simulations.Comment: 4 pages, 4 figure
Log-periodic oscillations due to discrete effects in complex networks
We show that discretization of internode distribution in complex networks
affects internode distances l_ij calculated as a function of degrees (k_i k_j)
and an average path length as function of network size N. For dense
networks there are log-periodic oscillations of above quantities. We present
real-world examples of such a behavior as well as we derive analytical
expressions and compare them to numerical simulations. We consider a simple
case of network optimization problem, arguing that discrete effects can lead to
a nontrivial solution.Comment: 5 pages, 5 figures, REVTE
Ferromagnetic fluid as a model of social impact
The paper proposes a new model of spin dynamics which can be treated as a
model of sociological coupling between individuals. Our approach takes into
account two different human features: gregariousness and individuality. We will
show how they affect a psychological distance between individuals and how the
distance changes the opinion formation in a social group. Apart from its
sociological aplications the model displays the variety of other interesting
phenomena like self-organizing ferromagnetic state or a second order phase
transition and can be studied from different points of view, e.g. as a model of
ferromagnetic fluid, complex evolving network or multiplicative random process.Comment: 8 pages, 5 figure
- …