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 $A$ to be a regular quadratic algebra of global dimension three. We observe that there are examples of $A$ containing a dimension three regular cubic algebra $C$. If $B$ is another dimension three regular quadratic algebra, also containing $C$ as a subalgebra, then we can form the pushout algebra $D$ of the inclusions $i_1:C\hookrightarrow A$ and $i_2:C\hookrightarrow B$. We show that for a certain class of regular algebras $C\hookrightarrow A,B$, their pushouts $D$ 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 $D$

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 $\alpha\in(0,2)$. 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 $g\rightarrow q\bar{q}(gg)$ and $q\rightarrow qg$ ability. We obtain the almost fixed asymmetry value $0.12-0.16$ 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 $K$ mesons, octet baryons $\Sigma$,$\Xi$ and $\Delta$ 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