14,706 research outputs found
On the Complexity and Behaviour of Cryptocurrencies Compared to Other Markets
We show that the behaviour of Bitcoin has interesting similarities to stock
and precious metal markets, such as gold and silver. We report that whilst
Litecoin, the second largest cryptocurrency, closely follows Bitcoin's
behaviour, it does not show all the reported properties of Bitcoin. Agreements
between apparently disparate complexity measures have been found, and it is
shown that statistical, information-theoretic, algorithmic and fractal measures
have different but interesting capabilities of clustering families of markets
by type. The report is particularly interesting because of the range and novel
use of some measures of complexity to characterize price behaviour, because of
the IRS designation of Bitcoin as an investment property and not a currency,
and the announcement of the Canadian government's own electronic currency
MintChip.Comment: 16 pages, 11 figures, 4 table
The Fractal Dimension of SAT Formulas
Modern SAT solvers have experienced a remarkable progress on solving
industrial instances. Most of the techniques have been developed after an
intensive experimental testing process. Recently, there have been some attempts
to analyze the structure of these formulas in terms of complex networks, with
the long-term aim of explaining the success of these SAT solving techniques,
and possibly improving them.
We study the fractal dimension of SAT formulas, and show that most industrial
families of formulas are self-similar, with a small fractal dimension. We also
show that this dimension is not affected by the addition of learnt clauses. We
explore how the dimension of a formula, together with other graph properties
can be used to characterize SAT instances. Finally, we give empirical evidence
that these graph properties can be used in state-of-the-art portfolios.Comment: 20 pages, 11 Postscript figure
Temporal evolution of mesoscopic structure of some non-Euclidean systems using a Monte Carlo model
A Monte Carlo based computer model is presented to comprehend the contrasting
observations of Mazumder et al. [Phys. Rev. Lett. 93, 255704 (2004) and Phys.
Rev. B 72, 224208 (2005)], based on neutron-scattering measurements, on
temporal evolution of effective fractal dimension and characteristic length for
hydration of cement with light and heavy water. In this context, a theoretical
model is also proposed to elucidate the same.Comment: 31 Pages, 13 Figure
Stochastic Self-Similar and Fractal Universe
The structures formation of the Universe appears as if it were a classically
self-similar random process at all astrophysical scales. An agreement is
demonstrated for the present hypotheses of segregation with a size of
astrophysical structures by using a comparison between quantum quantities and
astrophysical ones. We present the observed segregated Universe as the result
of a fundamental self-similar law, which generalizes the Compton wavelength
relation. It appears that the Universe has a memory of its quantum origin as
suggested by R.Penrose with respect to quasi-crystal. A more accurate analysis
shows that the present theory can be extended from the astrophysical to the
nuclear scale by using generalized (stochastically) self-similar random
process. This transition is connected to the relevant presence of the
electromagnetic and nuclear interactions inside the matter. In this sense, the
presented rule is correct from a subatomic scale to an astrophysical one. We
discuss the near full agreement at organic cell scale and human scale too.
Consequently the Universe, with its structures at all scales (atomic nucleus,
organic cell, human, planet, solar system, galaxy, clusters of galaxy, super
clusters of galaxy), could have a fundamental quantum reason. In conclusion, we
analyze the spatial dimensions of the objects in the Universe as well as
spacetime dimensions. The result is that it seems we live in an El Naschie's E
infinity Cantorian spacetime; so we must seriously start considering fractal
geometry as the geometry of nature, a type of arena where the laws of physics
appear at each scale in a self--similar way as advocated long ago by the
Swedish school of astrophysics.Comment: 17 pages, 3 figures, accepted by Chaos, Solitons & Fractla
Strategic programming on graph rewriting systems
We describe a strategy language to control the application of graph rewriting
rules, and show how this language can be used to write high-level declarative
programs in several application areas. This language is part of a graph-based
programming tool built within the port-graph transformation and visualisation
environment PORGY.Comment: In Proceedings IWS 2010, arXiv:1012.533
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