50,154 research outputs found
Predictive Encoding of Contextual Relationships for Perceptual Inference, Interpolation and Prediction
We propose a new neurally-inspired model that can learn to encode the global
relationship context of visual events across time and space and to use the
contextual information to modulate the analysis by synthesis process in a
predictive coding framework. The model learns latent contextual representations
by maximizing the predictability of visual events based on local and global
contextual information through both top-down and bottom-up processes. In
contrast to standard predictive coding models, the prediction error in this
model is used to update the contextual representation but does not alter the
feedforward input for the next layer, and is thus more consistent with
neurophysiological observations. We establish the computational feasibility of
this model by demonstrating its ability in several aspects. We show that our
model can outperform state-of-art performances of gated Boltzmann machines
(GBM) in estimation of contextual information. Our model can also interpolate
missing events or predict future events in image sequences while simultaneously
estimating contextual information. We show it achieves state-of-art
performances in terms of prediction accuracy in a variety of tasks and
possesses the ability to interpolate missing frames, a function that is lacking
in GBM
The Yale-Potsdam Stellar Isochrones (YaPSI)
We introduce the Yale-Potsdam Stellar Isochrones (YaPSI), a new grid of
stellar evolution tracks and isochrones of solar-scaled composition. In an
effort to improve the Yonsei-Yale database, special emphasis is placed on the
construction of accurate low-mass models (Mstar < 0.6 Msun), and in particular
of their mass-luminosity and mass-radius relations, both crucial in
characterizing exoplanet-host stars and, in turn, their planetary systems. The
YaPSI models cover the mass range 0.15 to 5.0 Msun, densely enough to permit
detailed interpolation in mass, and the metallicity and helium abundance ranges
[Fe/H] = -1.5 to +0.3, and Y = 0.25 to 0.37, specified independently of each
other (i.e., no fixed Delta Y/Delta Z relation is assumed). The evolutionary
tracks are calculated from the pre-main sequence up to the tip of the red giant
branch. The isochrones, with ages between 1 Myr and 20 Gyr, provide UBVRI
colors in the Johnson-Cousins system, and JHK colors in the homogeneized
Bessell & Brett system, derived from two different semi-empirical Teff-color
calibrations from the literature. We also provide utility codes, such as an
isochrone interpolator in age, metallicity, and helium content, and an
interface of the tracks with an open-source Monte Carlo Markov-Chain tool for
the analysis of individual stars. Finally, we present comparisons of the YaPSI
models with the best empirical mass- luminosity and mass-radius relations
available to date, as well as isochrone fitting of well-studied steComment: 17 pages, 14 figures; accepted for publication in the Astrophysical
Journa
Binary morphological shape-based interpolation applied to 3-D tooth reconstruction
In this paper we propose an interpolation algorithm using a mathematical morphology morphing approach. The aim of this algorithm is to reconstruct the -dimensional object from a group of (n-1)-dimensional sets representing sections of that object. The morphing transformation modifies pairs of consecutive sets such that they approach in shape and size. The interpolated set is achieved when the two consecutive sets are made idempotent by the morphing transformation. We prove the convergence of the morphological morphing. The entire object is modeled by successively interpolating a certain number of intermediary sets between each two consecutive given sets. We apply the interpolation algorithm for 3-D tooth reconstruction
Mathematical Properties of a New Levin-Type Sequence Transformation Introduced by \v{C}\'{\i}\v{z}ek, Zamastil, and Sk\'{a}la. I. Algebraic Theory
\v{C}\'{\i}\v{z}ek, Zamastil, and Sk\'{a}la [J. Math. Phys. \textbf{44}, 962
- 968 (2003)] introduced in connection with the summation of the divergent
perturbation expansion of the hydrogen atom in an external magnetic field a new
sequence transformation which uses as input data not only the elements of a
sequence of partial sums, but also explicit estimates
for the truncation errors. The explicit
incorporation of the information contained in the truncation error estimates
makes this and related transformations potentially much more powerful than for
instance Pad\'{e} approximants. Special cases of the new transformation are
sequence transformations introduced by Levin [Int. J. Comput. Math. B
\textbf{3}, 371 - 388 (1973)] and Weniger [Comput. Phys. Rep. \textbf{10}, 189
- 371 (1989), Sections 7 -9; Numer. Algor. \textbf{3}, 477 - 486 (1992)] and
also a variant of Richardson extrapolation [Phil. Trans. Roy. Soc. London A
\textbf{226}, 299 - 349 (1927)]. The algebraic theory of these transformations
- explicit expressions, recurrence formulas, explicit expressions in the case
of special remainder estimates, and asymptotic order estimates satisfied by
rational approximants to power series - is formulated in terms of hitherto
unknown mathematical properties of the new transformation introduced by
\v{C}\'{\i}\v{z}ek, Zamastil, and Sk\'{a}la. This leads to a considerable
formal simplification and unification.Comment: 41 + ii pages, LaTeX2e, 0 figures. Submitted to Journal of
Mathematical Physic
Fault tolerance for holonomic quantum computation
We review an approach to fault-tolerant holonomic quantum computation on
stabilizer codes. We explain its workings as based on adiabatic dragging of the
subsystem containing the logical information around suitable loops along which
the information remains protected.Comment: 16 pages, this is a chapter in the book "Quantum Error Correction",
edited by Daniel A. Lidar and Todd A. Brun, (Cambridge University Press,
2013), at
http://www.cambridge.org/us/academic/subjects/physics/quantum-physics-quantum-information-and-quantum-computation/quantum-error-correctio
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