83,792 research outputs found
Proliferation of the Phoenix Universe
Cyclic cosmology, in which the universe will experience alternating periods
of gravitational collapse and expansion, provides an interesting understanding
of the early universe and is described as "The Phoenix Universe". In usual
expectation, the cyclic universe should be homogeneous, however, with studying
the cosmological perturbations, we find that the amplification of curvature
perturbations on the large scale may rip the homogeneous universe into a
fissiparous multiverse after one or several cycles. Thus, we suggest that the
cyclic universe not only rebirths in the "fire" and will never ended, like the
Phoenix, but also proliferates eternally.Comment: 3 pages, 1 fig, invited essay for the Journal of Cosmolog
Time evolution of Two-qubit Entanglement
We show that the entanglement dynamics for a closed two-qubit system is part
of a 10-dimensional complex linear differential equation defined on a
supersphere, and the coefficients therein are completely determined by the
Hamiltonian. We apply the result to investigate two physical examples of
Josephson junction qubits and exchange Hamiltonians, deriving analytic
solutions for the time evolution of entanglement. The Hamiltonian coefficients
determines whether the entanglement is periodic. These results allow of
investigating how to generate and manipulate entanglements efficiently, which
are required by both quantum computation and quantum communication.Comment: 5 page
Inverse-Consistent Deep Networks for Unsupervised Deformable Image Registration
Deformable image registration is a fundamental task in medical image
analysis, aiming to establish a dense and non-linear correspondence between a
pair of images. Previous deep-learning studies usually employ supervised neural
networks to directly learn the spatial transformation from one image to
another, requiring task-specific ground-truth registration for model training.
Due to the difficulty in collecting precise ground-truth registration,
implementation of these supervised methods is practically challenging. Although
several unsupervised networks have been recently developed, these methods
usually ignore the inherent inverse-consistent property (essential for
diffeomorphic mapping) of transformations between a pair of images. Also,
existing approaches usually encourage the to-be-estimated transformation to be
locally smooth via a smoothness constraint only, which could not completely
avoid folding in the resulting transformation. To this end, we propose an
Inverse-Consistent deep Network (ICNet) for unsupervised deformable image
registration. Specifically, we develop an inverse-consistent constraint to
encourage that a pair of images are symmetrically deformed toward one another,
until both warped images are matched. Besides using the conventional smoothness
constraint, we also propose an anti-folding constraint to further avoid folding
in the transformation. The proposed method does not require any supervision
information, while encouraging the diffeomoprhic property of the transformation
via the proposed inverse-consistent and anti-folding constraints. We evaluate
our method on T1-weighted brain magnetic resonance imaging (MRI) scans for
tissue segmentation and anatomical landmark detection, with results
demonstrating the superior performance of our ICNet over several
state-of-the-art approaches for deformable image registration. Our code will be
made publicly available.Comment: 13 pages, 11 figure
Artin-Schelter Regular Algebras, Subalgebras, and Pushouts
Take to be a regular quadratic algebra of global dimension three. We
observe that there are examples of containing a dimension three regular
cubic algebra . If is another dimension three regular quadratic algebra,
also containing as a subalgebra, then we can form the pushout algebra
of the inclusions and . We
show that for a certain class of regular algebras , their
pushouts are regular quadratic algebras of global dimension four.
Furthermore, some of the point module structures of the dimension three
algebras get passed on to the pushout algebra
Symmetry analysis for time-fractional convection-diffusion equation
The time-fractional convection-diffusion equation is performed by Lie
symmetry analysis method which involves the Riemann-Liouville time-fractional
derivative of the order . In eight cases, the symmetries are
obtained and similarity reductions of the equation are deduced by means of
symmetry. It is shown that the fractional equation can be reduced into
fractional ordinary differential equations. Some group invariant solutions in
explicit form are obtained in some cases.Comment: 8 pages, 1 tabl
Conservation laws of some lattice equations
We derive infinitely many conservation laws for some multi-dimensionally
consistent lattice equations from their Lax pairs. These lattice equations are
the Nijhoff-Quispel-Capel equation, lattice Boussinesq equation, lattice
nonlinear Schr\"{o}dinger equation, modified lattice Boussinesq equation,
Hietarinta's Boussinesq-type equations, Schwarzian lattice Boussinesq equation
and Toda-modified lattice Boussinesq equation
Entropy Production and Thermal Conductivity of A Dilute Gas
It is known that the thermal conductivity of a dilute gas can be derived by
using kinetic theory. We present here a new derivation by starting with two
known entropy production principles: the steepest entropy ascent (SEA)
principle and the maximum entropy production (MEP) principle. A remarkable
feature of the new derivation is that it does not require the specification of
the existence of the temperature gradient. The known result is reproduced in a
similar form.Comment: 7 pages, 1 figur
Entropy and Ionic Conductivity
It is known that the ionic conductivity can be obtained by using the
diffusion constant and the Einstein relation. We derive it here by extracting
it from the steady electric current which we calculate in three ways, using
statistics analysis, an entropy method, and an entropy production approach
Sea Quark Flavor Asymmetry of Hadrons in Statistical Balance Model
We derive a Menta Carlo method to simulate kinetic equilibrium ensemble, and
get the same sea-quark flavor asymmetry as the linear equations method in
statistical model. In the recent paper, we introduce the spilt factors to
indicate the quarks' or gluons' spilt and
ability. We obtain the almost fixed asymmetry value
which consists with experimental measurements for proton, when the
spilt factors vary in a very wide range over four orders of magnitude. So, we
proof the sea quark asymmetry can be derived from statistic principle and not
sensitively dependents on the dynamics details of quarks and gluons in proton.
We also apply the Menta Carlo method of statistical model to predict the
sea-quark asymmetry values for mesons, octet baryons , and
baryons, even for exotic pentaquark states. All these asymmetry values
just only dependent on the valence quarks numbers in those hadrons.Comment: 15 pages, 1 figur
On decomposition of the ABS lattice equations and related B\"acklund transformations
The Adler-Bobenko-Suris (ABS) list contains all scalar quadrilateral
equations which are consistent around the cube. Each equation in the ABS list
admits a beautiful decomposition. In this paper, we first revisit these
decomposition formulas, by which we construct B\"acklund transformations (BTs)
and consistent triplets. Some BTs are used to construct new solutions, lattice
equations and weak Lax pairs.Comment: 20 page
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