1,354,785 research outputs found
Joining inner space to outer space
The purpose of this paper is to demonstrate that it is possible, in
principle, to obtain knowledge of the entire universe at the present time, even
if the radius of the universe is much larger than the radius of the observable
universe
Inner Space Preserving Generative Pose Machine
Image-based generative methods, such as generative adversarial networks
(GANs) have already been able to generate realistic images with much context
control, specially when they are conditioned. However, most successful
frameworks share a common procedure which performs an image-to-image
translation with pose of figures in the image untouched. When the objective is
reposing a figure in an image while preserving the rest of the image, the
state-of-the-art mainly assumes a single rigid body with simple background and
limited pose shift, which can hardly be extended to the images under normal
settings. In this paper, we introduce an image "inner space" preserving model
that assigns an interpretable low-dimensional pose descriptor (LDPD) to an
articulated figure in the image. Figure reposing is then generated by passing
the LDPD and the original image through multi-stage augmented hourglass
networks in a conditional GAN structure, called inner space preserving
generative pose machine (ISP-GPM). We evaluated ISP-GPM on reposing human
figures, which are highly articulated with versatile variations. Test of a
state-of-the-art pose estimator on our reposed dataset gave an accuracy over
80% on PCK0.5 metric. The results also elucidated that our ISP-GPM is able to
preserve the background with high accuracy while reasonably recovering the area
blocked by the figure to be reposed.Comment: http://www.northeastern.edu/ostadabbas/2018/07/23/inner-space-preserving-generative-pose-machine
Zero-Preserving Iso-spectral Flows Based on Parallel Sums
Driessel ["Computing canonical forms using flows", Linear Algebra and Its
Applications 2004] introduced the notion of quasi-projection onto the range of
a linear transformation from one inner product space into another inner product
space. Here we introduce the notion of quasi-projection onto the intersection
of the ranges of two linear transformations from two inner product spaces into
a third inner product space. As an application, we design a new family of
iso-spectral flows on the space of symmetric matrices that preserves zero
patterns. We discuss the equilibrium points of these flows. We conjecture that
these flows generically converge to diagonal matrices. We perform some
numerical experiments with these flows which support this conjecture. We also
compare our zero preserving flows with the Toda flow
Semi-indefinite-inner-product and generalized Minkowski spaces
In this paper we parallelly build up the theories of normed linear spaces and
of linear spaces with indefinite metric, called also Minkowski spaces for
finite dimensions in the literature.
In the first part of this paper we collect the common properties of the semi-
and indefinite-inner-products and define the semi-indefinite-inner-product and
the corresponding structure, the semi-indefinite-inner-product space. We give a
generalized concept of Minkowski space embedded in a
semi-indefinite-inner-product space using the concept of a new product, that
contains the classical cases as special ones.
In the second part of this paper we investigate the real, finite dimensional
generalized Minkowski space and its sphere of radius . We prove that it can
be regarded as a so-called Minkowski-Finsler space and if it is homogeneous one
with respect to linear isometries, then the Minkowski-Finsler distance its
points can be determined by the Minkowski-product
Cosmological entropy production and viscous processes in the (1+3+6)-dimensional space-times
The cosmological entropy production is studied in the (1+3+6)-dimensional
space-times consisting of the outer space (the 3-dimensional expanding section)
and the inner space (the 6-dimensional section). The inner space expands
initially and contracts later. First it is shown how the production of the
3-dimensional entropy S_3 within the horizon is strengthened by the dissipation
due to viscous processes between the two spaces, in which we consider the
viscosity caused by the gravitational-wave transport. Next it is shown under
what conditions we can have the critical epoch when S_3 reaches the value
10^{88} in the Guth level and at the same time the outer space is decoupled
from the inner space. Moreover, the total entropy S_9 in the 9-dimensional
space at the primeval expanding stage is also shown corresponding to S_3.Comment: 21 pages, 13 figure
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