Pseudo-Harmonic Maps From Pseudo-Hermitian Manifolds to Riemannian Manifolds

In this paper, we discuss the heat flow of a pseudo-harmonic map from a closed pseudo-Hermitian manifold to a Riemannian manifold with non-positive sectional curvature, and prove the existence of the pseudo-harmonic map which is a generalization of Eells-Sampson's existence theorem. We also discuss the uniqueness of the pseudo-harmonic representative of its homotopy class which is a generalization of Hartman theorem, provided that the target manifold has negative sectional curvature

Synchronization reveals correlation between oscillators on networks

The understanding of synchronization ranging from natural to social systems has driven the interests of scientists from different disciplines. Here, we have investigated the synchronization dynamics of the Kuramoto dynamics departing from the fully synchronized regime. We have got the analytic expression of the dynamical correlation between pairs of oscillators that reveals the relation between the network dynamics and the underlying topology. Moreover, it also reveals the internal structure of networks that can be used as a new algorithm to detect community structures. Further, we have proposed a new measure about the synchronization in complex networks and scrutinize it in small-world and scale-free networks. Our results indicate that the more heterogeneous and "smaller" the network is, the more closely it would be synchronized by the collective dynamics.Comment: 4 pages, 3 figure

BFDA: A Matlab Toolbox for Bayesian Functional Data Analysis

We provide a MATLAB toolbox, BFDA, that implements a Bayesian hierarchical model to smooth multiple functional data with the assumptions of the same underlying Gaussian process distribution, a Gaussian process prior for the mean function, and an Inverse-Wishart process prior for the covariance function. This model-based approach can borrow strength from all functional data to increase the smoothing accuracy, as well as estimate the mean-covariance functions simultaneously. An option of approximating the Bayesian inference process using cubic B-spline basis functions is integrated in BFDA, which allows for efficiently dealing with high-dimensional functional data. Examples of using BFDA in various scenarios and conducting follow-up functional regression are provided. The advantages of BFDA include: (1) Simultaneously smooths multiple functional data and estimates the mean-covariance functions in a nonparametric way; (2) flexibly deals with sparse and high-dimensional functional data with stationary and nonstationary covariance functions, and without the requirement of common observation grids; (3) provides accurately smoothed functional data for follow-up analysis.Comment: A tool paper submitted to the Journal of Statistical Softwar

Growth theorems in slice analysis of several variables

In this paper, we define a class of slice mappings of several Clifford variables, and the corresponding slice regular mappings. Furthermore, we establish the growth theorem for slice regular starlike or convex mappings on the unit ball of several slice Clifford variables, as well as on the bounded slice domain which is slice starlike and slice circular

Topological Landau-Zener Bloch Oscillations in Photonic Floquet Lieb Lattices

The Lieb Lattice exhibits intriguing properties that are of general interest in both the fundamental physics and practical applications. Here, we investigate the topological Landau-Zener Bloch oscillation in a photonic Floquet Lieb lattice, where the dimerized helical waveguides is constructed to realize the synthetic spin-orbital interaction through the Floquet mechanism, rendering us to study the impacts of topological transition from trivial gaps to non-trivial ones. The compact localized states of flat bands supported by the local symmetry of Lieb lattice will be associated with other bands by topological invariants, Chern number, and involved into Landau-Zener transition during Bloch oscillation. Importantly, the non-trivial geometrical phases after topological transitions will be taken into account for constructive and destructive interferences of wave functions. The numerical calculations of continuum photonic medium demonstrate reasonable agreements with theoretical tight-binding model. Our results provide an ongoing effort to realize designed quantum materials with tailored properties.Comment: 5 pages, 4 figure

Image Reconstruction Image reconstruction by using local inverse for full field of view

The iterative refinement method (IRM) has been very successfully applied in many different fields for examples the modern quantum chemical calculation and CT image reconstruction. It is proved that the refinement method can create an exact inverse from an approximate inverse with a few iterations. The IRM has been used in CT image reconstruction to lower the radiation dose. The IRM utilize the errors between the original measured data and the recalculated data to correct the reconstructed images. However if it is not smooth inside the object, there often is an over-correction along the boundary of the organs in the reconstructed images. The over-correction increase the noises especially on the edges inside the image. One solution to reduce the above mentioned noises is using some kind of filters. Filtering the noise before/after/between the image reconstruction processing. However filtering the noises also means reduce the resolution of the reconstructed images. The filtered image is often applied to the image automation for examples image segmentation or image registration but diagnosis. For diagnosis, doctor would prefer the original images without filtering process. In the time these authors of this manuscript did the work of interior image reconstruction with local inverse method, they noticed that the local inverse method does not only reduced the truncation artifacts but also reduced the artifacts and noise introduced from filtered back-projection method without truncation. This discovery lead them to develop the sub-regional iterative refinement (SIRM) image reconstruction method. The SIRM did good job to reduce the artifacts and noises in the reconstructed images. The SIRM divide the image to many small sub-regions. To each small sub-region the principle of local inverse method is applied.Comment: 39 pages, 9 figure

Berry phases of quantum trajectories in semiconductors under strong terahertz fields

Quantum evolution of particles under strong fields can be essentially captured by a small number of quantum trajectories that satisfy the stationary phase condition in the Dirac-Feynmann path integrals. The quantum trajectories are the key concept to understand extreme nonlinear optical phenomena, such as high-order harmonic generation (HHG), above-threshold ionization (ATI), and high-order terahertz sideband generation (HSG). While HHG and ATI have been mostly studied in atoms and molecules, the HSG in semiconductors can have interesting effects due to possible nontrivial "vacuum" states of band materials. We find that in a semiconductor with non-vanishing Berry curvature in its energy bands, the cyclic quantum trajectories of an electron-hole pair under a strong terahertz field can accumulate Berry phases. Taking monolayer MoS$_2$ as a model system, we show that the Berry phases appear as the Faraday rotation angles of the pulse emission from the material under short-pulse excitation. This finding reveals an interesting transport effect in the extreme nonlinear optics regime.Comment: 5 page

The modified Poynting theorem and the concept of mutual energy

The goal of this article is to derive the reciprocity theorem, mutual energy theorem from Poynting theorem instead of from Maxwell equation. The Poynting theorem is generalized to the modified Poynting theorem. In the modified Poynting theorem the electromagnetic field is superimposition of different electromagnetic fields including the retarded potential and advanced potential, time-offset field. The media epsilon (permittivity) and mu (permeability) can also be different in the different fields. The concept of mutual energy is introduced which is the difference between the total energy and self-energy. Mixed mutual energy theorem is derived. We derive the mutual energy from Fourier domain. We obtain the time-reversed mutual energy theorem and the mutual energy theorem. Then we derive the mutual energy theorem in time-domain. The instantaneous modified mutual energy theorem is derived. Applying time-offset transform and time integral to the instantaneous modified mutual energy theorem, the time-correlation modified mutual energy theorem is obtained. Assume there are two electromagnetic fields one is retarded potential and one is advanced potential, the convolution reciprocity theorem can be derived. Corresponding to the modified time-correlation mutual energy theorem and the time-convolution reciprocity theorem in Fourier domain, there is the modified mutual energy theorem and the Lorentz reciprocity theorem. Hence all mutual energy theorem and the reciprocity theorems are put in one frame of the concept of the mutual energy. 3 new Complementary theorems are derived. The inner product is introduced for two different electromagnetic fields in both time domain and Fourier domain for the application of the wave expansion.Comment: Derivation of the mutual energy theorem from Fourier domain is added. Time-reversed transform, time-reversed mutual energy theorem, time reversed reciprocity theorem, mixed mutual energy theorem are added, Complementary theorems are adde

Path Independence of Additive Functionals for SDEs under G-framework

The path independence of additive functionals for SDEs driven by the G-Brownian motion is characterized by nonlinear PDEs. The main result generalizes the existing ones for SDEs driven by the standard Brownian motion

Nonlinear optical response induced by non-Abelian Berry curvature in time-reversal-invariant insulators

We propose a general framework of nonlinear optics induced by non-Abelian Berry curvature in time-reversal-invariant (TRI) insulators. We find that the third-order response of a TRI insulator under optical and terahertz light fields is directly related to the integration of the non-Abelian Berry curvature over the Brillouin zone. We apply the result to insulators with rotational symmetry near the band edge. Under resonant excitations, the optical susceptibility is proportional to the flux of the Berry curvature through the iso-energy surface, which is equal to the Chern number of the surface times $2\pi$. For the III-V compound semiconductors, microscopic calculations based on the six-band model give a third-order susceptibility with the Chern number of the iso-energy surface equal to three