Image Retrieval using Histogram Factorization and Contextual Similarity Learning

Image retrieval has been a top topic in the field of both computer vision and machine learning for a long time. Content based image retrieval, which tries to retrieve images from a database visually similar to a query image, has attracted much attention. Two most important issues of image retrieval are the representation and ranking of the images. Recently, bag-of-words based method has shown its power as a representation method. Moreover, nonnegative matrix factorization is also a popular way to represent the data samples. In addition, contextual similarity learning has also been studied and proven to be an effective method for the ranking problem. However, these technologies have never been used together. In this paper, we developed an effective image retrieval system by representing each image using the bag-of-words method as histograms, and then apply the nonnegative matrix factorization to factorize the histograms, and finally learn the ranking score using the contextual similarity learning method. The proposed novel system is evaluated on a large scale image database and the effectiveness is shown.Comment: 4 page

Topological Superfluidity of Spin-Orbit Coupled Bilayer Fermi Gases

Topological superfluid, new quantum matter that possesses gapless exotic excitations known as Majorana fermions, has attracted extensive attention recently. These excitations, which can encode topological qubits, could be crucial ingredients for fault-tolerant quantum computation. However, creating and manipulating multiple Majorana fermions remain an ongoing challenge. Loading a topologically protected system in multi-layer structures would be a natural and simple way to achieve this goal. Here we investigate the system of bilayer Fermi gases with spin-orbit coupling and show that the topological condition is significantly influenced by the inter-layer tunneling, yielding two novel topological phases, which support more Majorana Fermions. We demonstrate the existence of such novel topological phases and associated multiple Majorana fermions using bilayer Fermi gases trapped inside a harmonic potential. This research pave a new way for generating multiple Majorana fermions and would be a significant step towards topological quantum computation.Comment: 34 pages, 5 figures, Comments welcom

Eigen-functional bosonization and Eikonal-type equations in one-dimensional strongly correlated electron system

With the eigen-functional bosonization method, we study one-dimensional strongly correlated electron systems with large momentum ($2k_{F}$ and/or $4k_{F}$) transfer term(s), and demonstrate that this kind of problems ends in to solve the Eikonal-type equations, and these equations are universal, and independent of whether or not the system is integrable. In contrast to usual perturbation theory, this method is valid not only for weak electron interaction, but also for strong electron interaction. Comparing with exact solution of some integrable models, it can give correct results in one-loop approximation. This method can also be used to study electron-phonon interaction systems, and two coupled spin chain or quantum wire systems.Comment: latex, pages 24, no figure

Exact expression of the ground state energy of quantum many-particle systems as a functional of the particle density

By introducing a phase field and solving the eigen-functional equation of particles, we obtain the exact expressions of the ground state energy as a functional of the particle density for interacting electron/boson systems, and a two-dimensional electron gas under an external magnetic field, respectively. With the eigen-functionals of the particles, we can construct the ground state wave-function of the systems. Moreover, with the expressions of the ground state energy, we can exactly determine the ground state energy and the ground state particle density of the systems by taking $\rho (x)=0$.Comment: 11 pages, latex fil

Unified theory of quantum many-particle systems

Using eigen-functional bosonization method, we study quantum many-particle systems, and show that the quantum many-particle problems end in to solve the differential equation of the phase fields which represent the particle correlation strength. Thus, the physical properties of these systems are completely determined by the differential equation of the phase fields. We mainly focus on the study of D-dimensional electron gas with/without transverse gauge fields, two-dimensional electron gas under an external magnetic field, D-dimensional boson systems, a D-dimensional Heisenberg model and a one-band Hubbard model on a square lattice, and give their exact (accurate for Heisenberg model) functional expressions of the ground state energy and action, and the eigen-functional wave functions of the fermions/bosons. With them, we can calculate a variety of correlation functions of the systems, such as single particle Green's functions and their ground state wave functions. In present theoretical framework, we can unifiably represent the Landau Fermi liquid, non-Fermi liquid ($D\geq 2$) and Tomonaga-Luttinger liquid.Comment: 38 pages, RevTex, no figur

Nuclear Bag Model and Nuclear Magnetic Moments

In 1991, we proposed a model in which nucleus is treated as a spherical symmetric MIT bag and nucleon satisfies the MIT bag model boundary condition. The model was employed to calculate nuclear magnetic moments. The results are in good agreement with experiment data. Now, we found this model is still interesting and illuminating.Comment: 5 pages, no figures, Late

An exact expression of the collective excitation energy gap of fractional quantum Hall effect

We have exactly solved the eigenequation of a two-dimensional Dirac fermion moving on the surface of a sphere under the influence of a radial magnetic field B, and obtained an exact expression of the collective excitation energy gap for the filling factors $\nu=p/(2mp\pm 1)$, m and p are non-zero integers, which is very well agreement with the computing results.Comment: Revtex, 11 pages, no figure

The hierarchical Green function approach to the two-dimensional Hubbard model

By introducing multipe-site correlation functions, we propose a hierarchical Green function approach, and apply it to study the characteristic properties of a 2D square lattice Hubbard model by solving the equation of motions of a one-particle Green function and related multipe-site correlation functions. Under a cut-off approximation and taking the Fourier representation of multipe-site correlation functions, we obtain an analytical expression of one-particle Green function with static correlation functions. Then we calculate the spectral density function of electrons, and obtain that besides two main peaks corresponding to the lower and upper Hubbard bands in the spectral density function, there emerge some novel states between these two main peaks, and the total spectral weight of these emerged states is proportional to the hole doping concentration . Meanwhile, there also emerge some collective modes related to possible charge/spin density wave and/or electronic pairing density wave ordering states. This calculation is completely consistent with the spectroscopy observations of the cuprate superconductors in normal states. On the other hand, the appearence of the static correlation functions in the one-particle Green function can be used to describe the intertwined orders observed in the normal state of the cuprate superconductors.Comment: 24p, no figuur

Electromagnetic fields, size, and copy of a single photon

Photons are almost involved in each field of science and daily life of everyone. However, there are still some fundamental and puzzling questions such as what a photon is.The expressions of electromagnetic fields of a photon are here proposed. On the basis of the present expressions, we calculate the energy, momentum, and spin angular momentum of a photon, derive the relations between the photon size and wavelength, and reveal the differences between a photon and its copy. The results show that the present expressions properly describe the particle characteristics of a photon; the length of a photon is half of the wavelength, and the radius is proportional to square root of the wavelength; a photon can ionize a hydrogen atom at the ground state only if its radius is less than the Bohr radius; a photon and its copy have the phase difference of {\pi} and constitute a phase-entangled photon pair; the phase-entangled n-photon train results from the sequential stimulated emissions and belongs to the Fock state. A laser beam is an ensemble of the n-photon trains and belongs to the coherent state. The threshold power of a laser is equal to the power of the n-photon train. These provide a bridge between the wave theory of light and quantum optics and will further advance research and application of the related fields.Comment: 4 pages, crrected typos, improved some descriptions and reference

Unified thoery of strongly correlated electron systems

In framework of eigen-functional bosonization method, we introduce an imaginary phase field to uniquely represent electron correlation, and demonstrate that the Landau Fermi liquid theory and the Tomonaga-Luttinger liquid theory can be unified. It is very clear in this framework that the Tomonaga-Luttinger liquid behavior of one-dimensional interacting electron gases originates from their Fermi structure, and the non-Landau-Fermi liquid behavior of 2D interacting electron gases is induced by the long-range electron interaction, while 3D interacting electron gases generally show the Landau Fermi liquid behavior.Comment: corrected some typos in eq. (13