139,451 research outputs found
Entropy Generation in Computation and the Second Law of Thermodynamics
Landauer discussed the minimum energy necessary for computation and stated
that erasure of information is accompanied by heat generation to the amount of
kT ln2/bit. Modifying the above statement, we claim that erasure of information
is accompanied by entropy generation k ln2/bit. Some new concepts will be
introduced in the field of thermodynamics that are implicitly included in our
statement. The new concepts that we will introduce are ``partitioned state'',
which corresponds to frozen state such as in ice, ``partitioning process'' and
``unifying process''. Developing our statement, i.e., our thermodynamics of
computation, we will point out that the so-called ``residual entropy'' does not
exist in the partitioned state. We then argue that a partioning process is an
entropy decreasing process. Finally we reconsider the second law of
thermodynamics especially when computational processes are involved.Comment: 5 pages, 2 figure
Faster computation of the Tate pairing
This paper proposes new explicit formulas for the doubling and addition step
in Miller's algorithm to compute the Tate pairing. For Edwards curves the
formulas come from a new way of seeing the arithmetic. We state the first
geometric interpretation of the group law on Edwards curves by presenting the
functions which arise in the addition and doubling. Computing the coefficients
of the functions and the sum or double of the points is faster than with all
previously proposed formulas for pairings on Edwards curves. They are even
competitive with all published formulas for pairing computation on Weierstrass
curves. We also speed up pairing computation on Weierstrass curves in Jacobian
coordinates. Finally, we present several examples of pairing-friendly Edwards
curves.Comment: 15 pages, 2 figures. Final version accepted for publication in
Journal of Number Theor
Two-point functions of quenched lattice QCD in Numerical Stochastic Perturbation Theory. (I) The ghost propagator in Landau gauge
This is the first of a series of two papers on the perturbative computation
of the ghost and gluon propagators in SU(3) Lattice Gauge Theory. Our final aim
is to eventually compare with results from lattice simulations in order to
enlight the genuinely non-perturbative content of the latter. By means of
Numerical Stochastic Perturbation Theory we compute the ghost propagator in
Landau gauge up to three loops. We present results in the infinite volume and
limits, based on a general strategy that we discuss in detail.Comment: 27 pages, 11 figure
Orientation, sphericity and roundness evaluation of particles using alternative 3D representations
Sphericity and roundness indices have been used mainly in geology to analyze the shape of particles. In this paper, geometric methods are proposed as an alternative to evaluate the orientation, sphericity and roundness indices of 3D objects. In contrast to previous works based on digital images, which use the voxel model, we represent the particles with the Extreme Vertices Model, a very concise representation for binary volumes. We define the orientation with three mutually orthogonal unit vectors. Then, some sphericity indices based on length measurement of the three representative axes of the particle can be computed. In addition, we propose a ray-casting-like approach to evaluate a 3D roundness index. This method provides roundness measurements that are highly correlated with those provided by the Krumbein's chart and other previous approach. Finally, as an example we apply the presented methods to analyze the sphericity and roundness of a real silica nano dataset.Postprint (published version
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