3,885 research outputs found
On Vague Computers
Vagueness is something everyone is familiar with. In fact, most people think
that vagueness is closely related to language and exists only there. However,
vagueness is a property of the physical world. Quantum computers harness
superposition and entanglement to perform their computational tasks. Both
superposition and entanglement are vague processes. Thus quantum computers,
which process exact data without "exploiting" vagueness, are actually vague
computers
Testing the Everett Interpretation of Quantum Mechanics with Cosmology
In this brief note, we argue that contrarily to what is still often stated,
the Everett many-worlds interpretation of quantum mechanics is not in principle
impossible to test. It is actually not more difficult (but not easier either)
to test than most other kinds of multiverse theories. We also remind why
multiverse scenarios can be falsified.Comment: 5 page
A comprehensive study of implicator-conjunctor based and noise-tolerant fuzzy rough sets: definitions, properties and robustness analysis
© 2014 Elsevier B.V. Both rough and fuzzy set theories offer interesting tools for dealing with imperfect data: while the former allows us to work with uncertain and incomplete information, the latter provides a formal setting for vague concepts. The two theories are highly compatible, and since the late 1980s many researchers have studied their hybridization. In this paper, we critically evaluate most relevant fuzzy rough set models proposed in the literature. To this end, we establish a formally correct and unified mathematical framework for them. Both implicator-conjunctor-based definitions and noise-tolerant models are studied. We evaluate these models on two different fronts: firstly, we discuss which properties of the original rough set model can be maintained and secondly, we examine how robust they are against both class and attribute noise. By highlighting the benefits and drawbacks of the different fuzzy rough set models, this study appears a necessary first step to propose and develop new models in future research.Lynn D’eer has been supported by the Ghent University Special Research Fund, Chris Cornelis was partially supported by the Spanish Ministry of Science and Technology under the project TIN2011-28488 and the Andalusian Research Plans P11-TIC-7765 and P10-TIC-6858, and by project PYR-2014-8 of the Genil Program of CEI BioTic GRANADA and Lluis Godo has been partially supported by the Spanish MINECO project EdeTRI TIN2012-39348-C02-01Peer Reviewe
Quantum Computation and Many Worlds
An Everett (`Many Worlds') interpretation of quantum mechanics due to
Saunders and Zurek is presented in detail. This is used to give a physical
description of the process of a quantum computation. Objections to such an
understanding are discussed.Comment: This paper has been superceded by arXiv:0802.2504v1 [quant-ph
Strings from Logic
What are strings made of? The possibility is discussed that strings are
purely mathematical objects, made of logical axioms. More precisely, proofs in
simple logical calculi are represented by graphs that can be interpreted as the
Feynman diagrams of certain large-N field theories. Each vertex represents an
axiom. Strings arise, because these large-N theories are dual to string
theories. These ``logical quantum field theories'' map theorems into the space
of functions of two parameters: N and the coupling constant. Undecidable
theorems might be related to nonperturbative field theory effects.Comment: Talk, 19 pp, 7 figure
Multiverse Predictions for Habitability: Fraction of Planets that Develop Life
In a multiverse context, determining the probability of being in our
particular universe depends on estimating its overall habitability compared to
other universes with different values of the fundamental constants. One of the
most important factors in determining this is the fraction of planets that
actually develop life, and how this depends on planetary conditions. Many
proposed possibilities for this are incompatible with the multiverse: if the
emergence of life depends on the lifetime of its host star, the size of the
habitable planet, or the amount of material processed, the chances of being in
our universe would be very low. If the emergence of life depends on the entropy
absorbed by the planet, however, our position in this universe is very natural.
Several proposed models for the subsequent development of life, including the
hard step model and several planetary oxygenation models, are also shown to be
incompatible with the multiverse. If any of these are observed to play a large
role in determining the distribution of life throughout our universe,
the~multiverse hypothesis will be ruled out to high significance.Comment: 29 pages, 6 figures, v2: matches published vresio
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