89,309 research outputs found
Dynamic structural and topological phase transitions on the Warsaw Stock Exchange: A phenomenological approach
We study the crash dynamics of the Warsaw Stock Exchange (WSE) by using the
Minimal Spanning Tree (MST) networks. We find the transition of the complex
network during its evolution from a (hierarchical) power law MST network,
representing the stable state of WSE before the recent worldwide financial
crash, to a superstar-like (or superhub) MST network of the market decorated by
a hierarchy of trees (being, perhaps, an unstable, intermediate market state).
Subsequently, we observed a transition from this complex tree to the topology
of the (hierarchical) power law MST network decorated by several star-like
trees or hubs. This structure and topology represent, perhaps, the WSE after
the worldwide financial crash, and could be considered to be an aftershock. Our
results can serve as an empirical foundation for a future theory of dynamic
structural and topological phase transitions on financial markets
Modeling spatial uncertainties in geospatial data fusion and mining
Geospatial data analysis relies on Spatial Data Fusion and Mining (SDFM), which heavily depend on topology and geometry of spatial objects. Capturing and representing geometric characteristics such as orientation, shape, proximity, similarity, and their measurement are of the highest interest in SDFM. Representation of uncertain and dynamically changing topological structure of spatial objects including social and communication networks, roads and waterways under the influence of noise, obstacles, temporary loss of communication, and other factors. is another challenge. Spatial distribution of the dynamic network is a complex and dynamic mixture of its topology and geometry. Historically, separation of topology and geometry in mathematics was motivated by the need to separate the invariant part of the spatial distribution (topology) from the less invariant part (geometry). The geometric characteristics such as orientation, shape, and proximity are not invariant. This separation between geometry and topology was done under the assumption that the topological structure is certain and does not change over time. New challenges to deal with the dynamic and uncertain topological structure require a reexamination of this fundamental assumption. In the previous work we proposed a dynamic logic methodology for capturing, representing, and recording uncertain and dynamic topology and geometry jointly for spatial data fusion and mining. This work presents a further elaboration and formalization of this methodology as well as its application for modeling vector-to-vector and raster-to-vector conflation/registration problems and automated feature extraction from the imagery
On irreversible spread of influence in edge-weighted graphs
Various kinds of spread of influence occur in real world social and virtual
networks. These phenomena are formulated by activation processes and
irreversible dynamic monopolies in combinatorial graphs representing the
topology of the networks. In most cases the nature of influence is weighted and
the spread of influence depends on the weight of edges. The ordinary
formulation and results for dynamic monopolies do not work for such models. In
this paper we present a graph theoretical analysis for spread of weighted
influence and mention a real world example realizing the activation model with
weighted influence. Then we obtain some extremal bounds and algorithmic results
for activation process and dynamic monopolies in directed and undirected graphs
with weighted edges
On irreversible spread of influence in edge-weighted graphs
Various kinds of spread of influence occur in real world social and virtual networks. These phenomena are formulated by activation processes and irreversible dynamic monopolies in combinatorial graphs representing the topology of the networks. In most cases, the nature of influence is weighted and the spread of influence depends on the weight of edges. The ordinary formulation and results for dynamic monopolies do not work for such models. In this paper we present a graph theoretical analysis for spread of weighted influence and mention a real world example realizing the activation model with weighted influence. Then we obtain some extremal bounds and algorithmic results for activation process and dynamic monopolies in directed and undirected graphs with weighted edges
Dynamic Cell Structures: Radial Basis Function Networks with Perfect Topology Preservation
Dynamic Cell Structures (DCS) represent a family of artificial neural architectures suited both for unsupervised and supervised learning. They belong to the recently [Martinetz94] introduced class of Topology Representing Networks (TRN) which build perfectly topology preserving feature maps. DCS employ a modified Kohonen learning rule in conjunction with competitive Hebbian learning. The Kohonen type learning rule serves to adjust the synaptic weight vectors while Hebbian learning establishes a dynamic lateral connection structure between the units reflecting the topology of the feature manifold. In case of supervised learning, i.e. function approximation, each neural unit implements a Radial Basis Function, and an additional layer of linear output units adjusts according to a delta-rule. DCS is the first RBF-based approximation scheme attempting to concurrently learn and utilize a perfectly topology preserving map for improved performance. Simulations on a selection of CMU-Benchmarks indicate that the DCS idea applied to the Growing Cell Structure algorithm [Fritzke93b] leads to an efficient and elegant algorithm that can beat conventional models on similar tasks
Structural and topological phase transitions on the German Stock Exchange
We find numerical and empirical evidence for dynamical, structural and
topological phase transitions on the (German) Frankfurt Stock Exchange (FSE) in
the temporal vicinity of the worldwide financial crash. Using the Minimal
Spanning Tree (MST) technique, a particularly useful canonical tool of the
graph theory, two transitions of the topology of a complex network representing
FSE were found. First transition is from a hierarchical scale-free MST
representing the stock market before the recent worldwide financial crash, to a
superstar-like MST decorated by a scale-free hierarchy of trees representing
the market's state for the period containing the crash. Subsequently, a
transition is observed from this transient, (meta)stable state of the crash, to
a hierarchical scale-free MST decorated by several star-like trees after the
worldwide financial crash. The phase transitions observed are analogous to the
ones we obtained earlier for the Warsaw Stock Exchange and more pronounced than
those found by Onnela-Chakraborti-Kaski-Kert\'esz for S&P 500 index in the
vicinity of Black Monday (October 19, 1987) and also in the vicinity of January
1, 1998. Our results provide an empirical foundation for the future theory of
dynamical, structural and topological phase transitions on financial markets
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