30,131 research outputs found
Ten virtues of structured graphs
This paper extends the invited talk by the first author about the virtues
of structured graphs. The motivation behind the talk and this paper relies on our
experience on the development of ADR, a formal approach for the design of styleconformant,
reconfigurable software systems. ADR is based on hierarchical graphs
with interfaces and it has been conceived in the attempt of reconciling software architectures
and process calculi by means of graphical methods. We have tried to
write an ADR agnostic paper where we raise some drawbacks of flat, unstructured
graphs for the design and analysis of software systems and we argue that hierarchical,
structured graphs can alleviate such drawbacks
The failure tolerance of mechatronic software systems to random and targeted attacks
This paper describes a complex networks approach to study the failure
tolerance of mechatronic software systems under various types of hardware
and/or software failures. We produce synthetic system architectures based on
evidence of modular and hierarchical modular product architectures and known
motifs for the interconnection of physical components to software. The system
architectures are then subject to various forms of attack. The attacks simulate
failure of critical hardware or software. Four types of attack are
investigated: degree centrality, betweenness centrality, closeness centrality
and random attack. Failure tolerance of the system is measured by a 'robustness
coefficient', a topological 'size' metric of the connectedness of the attacked
network. We find that the betweenness centrality attack results in the most
significant reduction in the robustness coefficient, confirming betweenness
centrality, rather than the number of connections (i.e. degree), as the most
conservative metric of component importance. A counter-intuitive finding is
that "designed" system architectures, including a bus, ring, and star
architecture, are not significantly more failure-tolerant than interconnections
with no prescribed architecture, that is, a random architecture. Our research
provides a data-driven approach to engineer the architecture of mechatronic
software systems for failure tolerance.Comment: Proceedings of the 2013 ASME International Design Engineering
Technical Conferences & Computers and Information in Engineering Conference
IDETC/CIE 2013 August 4-7, 2013, Portland, Oregon, USA (In Print
Hierarchical Models for Independence Structures of Networks
We introduce a new family of network models, called hierarchical network
models, that allow us to represent in an explicit manner the stochastic
dependence among the dyads (random ties) of the network. In particular, each
member of this family can be associated with a graphical model defining
conditional independence clauses among the dyads of the network, called the
dependency graph. Every network model with dyadic independence assumption can
be generalized to construct members of this new family. Using this new
framework, we generalize the Erd\"os-R\'enyi and beta-models to create
hierarchical Erd\"os-R\'enyi and beta-models. We describe various methods for
parameter estimation as well as simulation studies for models with sparse
dependency graphs.Comment: 19 pages, 7 figure
Measuring satisfaction in societies with opinion leaders and mediators
An opinion leader-follower model (OLF) is a two-action collective decision-making model for societies, in which three kinds of actors are considered:Preprin
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
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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