8,914 research outputs found
Estimation of Scribble Placement for Painting Colorization
Image colorization has been a topic of interest since
the mid 70’s and several algorithms have been proposed that
given a grayscale image and color scribbles (hints) produce a colorized image. Recently, this approach has been introduced in the field of art conservation and cultural heritage, where B&W photographs of paintings at previous stages have been colorized. However, the questions of what is the minimum number of scribbles necessary and where they should be placed in an image remain unexplored. Here we address this limitation using an iterative algorithm that provides insights as to the relationship between locally vs. globally important scribbles. Given a color image we randomly select scribbles and we attempt to color the
grayscale version of the original.We define a scribble contribution measure based on the reconstruction error. We demonstrate our approach using a widely used colorization algorithm and images from a Picasso painting and the peppers test image. We show that areas isolated by thick brushstrokes or areas with high textural variation are locally important but contribute very little to the
overall representation accuracy. We also find that for the case of Picasso on average 10% of scribble coverage is enough and that flat areas can be presented by few scribbles. The proposed method can be used verbatim to test any colorization algorithm
The classification ofseparable simple C*-algebras which are inductive limits of continuous-trace C*-algebraswith spectrum homeomorphic to the closed interval [0,1]
A classification is given of certain separable nuclear C*-algebras not
necessarily of real rank zero, namely, the class of separable simple
C*-algebras which are inductive limits of continuous-trace C*-algebras whose
building blocks have spectrum homeomorphic to the closed interval [0,1], or to
a disjoint union of copies of this space. Also, the range of the invariant is
calculated.Comment: 41 pages, 6figure
Natural Halting Probabilities, Partial Randomness, and Zeta Functions
We introduce the zeta number, natural halting probability and natural
complexity of a Turing machine and we relate them to Chaitin's Omega number,
halting probability, and program-size complexity. A classification of Turing
machines according to their zeta numbers is proposed: divergent, convergent and
tuatara. We prove the existence of universal convergent and tuatara machines.
Various results on (algorithmic) randomness and partial randomness are proved.
For example, we show that the zeta number of a universal tuatara machine is
c.e. and random. A new type of partial randomness, asymptotic randomness, is
introduced. Finally we show that in contrast to classical (algorithmic)
randomness--which cannot be naturally characterised in terms of plain
complexity--asymptotic randomness admits such a characterisation.Comment: Accepted for publication in Information and Computin
Most Programs Stop Quickly or Never Halt
Since many real-world problems arising in the fields of compiler
optimisation, automated software engineering, formal proof systems, and so
forth are equivalent to the Halting Problem--the most notorious undecidable
problem--there is a growing interest, not only academically, in understanding
the problem better and in providing alternative solutions. Halting computations
can be recognised by simply running them; the main difficulty is to detect
non-halting programs. Our approach is to have the probability space extend over
both space and time and to consider the probability that a random -bit
program has halted by a random time. We postulate an a priori computable
probability distribution on all possible runtimes and we prove that given an
integer k>0, we can effectively compute a time bound T such that the
probability that an N-bit program will eventually halt given that it has not
halted by T is smaller than 2^{-k}. We also show that the set of halting
programs (which is computably enumerable, but not computable) can be written as
a disjoint union of a computable set and a set of effectively vanishing
probability. Finally, we show that ``long'' runtimes are effectively rare. More
formally, the set of times at which an N-bit program can stop after the time
2^{N+constant} has effectively zero density.Comment: Shortened abstract and changed format of references to match Adv.
Appl. Math guideline
Secular models and Kozai resonance for planets in coorbital non-coplanar motion
In this work, we construct and test an analytical and a semianalytical
secular models for two planets locked in a coorbital non-coplanar motion,
comparing some results with the case of restricted three body problem.
The analytical average model replicates the numerical N-body integrations,
even for moderate eccentricities ( 0.3) and inclinations
(), except for the regions corresponding to quasi-satellite
and Lidov-Kozai configurations. Furthermore, this model is also useful in the
restricted three body problem, assuming very low mass ratio between the
planets. We also describe a four-degree-of-freedom semianalytical model valid
for any type of coorbital configuration in a wide range of eccentricities and
inclinations.
{Using a N-body integrator, we have found that the phase space of the General
Three Body Problem is different to the restricted case for inclined systems,
and establish the location of the Lidov-Kozai equilibrium configurations
depending on mass ratio. We study the stability of periodic orbits in the
inclined systems, and find that apart from the robust configurations ,
, and is possible to harbour two Earth-like planets in orbits
previously identified as unstable and also in Euler configurations,
with bounded chaos.Comment: 15 pages. 20 figure
Tidal evolution of close-in exoplanets in co-orbital configurations
In this paper, we study the behavior of a pair of co-orbital planets, both
orbiting a central star on the same plane and undergoing tidal interactions.
Our goal is to investigate final orbital configurations of the planets,
initially involved in the 1/1 mean-motion resonance (MMR), after long-lasting
tidal evolution. The study is done in the form of purely numerical simulations
of the exact equations of motions accounting for gravitational and tidal
forces. The results obtained show that, at least for equal mass planets, the
combined effects of the resonant and tidal interactions provoke the orbital
instability of the system, often resulting in collision between the planets. We
first discuss the case of two hot-super-Earth planets, whose orbital dynamics
can be easily understood in the frame of our semi-analytical model of the 1/1
MMR. Systems consisting of two hot-Saturn planets are also briefly discussed.Comment: 18 pages, 8 figures. Accepted for publication in Celestial Mechanics
and Dynamical Astronom
Von Neumann Normalisation of a Quantum Random Number Generator
In this paper we study von Neumann un-biasing normalisation for ideal and
real quantum random number generators, operating on finite strings or infinite
bit sequences. In the ideal cases one can obtain the desired un-biasing. This
relies critically on the independence of the source, a notion we rigorously
define for our model. In real cases, affected by imperfections in measurement
and hardware, one cannot achieve a true un-biasing, but, if the bias "drifts
sufficiently slowly", the result can be arbitrarily close to un-biasing. For
infinite sequences, normalisation can both increase or decrease the
(algorithmic) randomness of the generated sequences. A successful application
of von Neumann normalisation---in fact, any un-biasing transformation---does
exactly what it promises, un-biasing, one (among infinitely many) symptoms of
randomness; it will not produce "true" randomness.Comment: 27 pages, 2 figures. Updated to published versio
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