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

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

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

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

Influence of gauge fluctuations on fermion pairing order parameter

Using a prototype model, we study the influence of gauge fluctuations on fermion pairing order parameter which has the gauge symmetry, and demonstrate that the gauge fluctuations can destroy the long range order of the fermion pairing order parameter, and make it only have short range correlation. If this parameter is a superconducting order parameter, we show that the Meissner effect of the system keeps intact, and the system is in the superconducting state even though the long range order of the superconducting order parameter is destroied by the gauge fluctuations. Our calculations support that the pseudo-gap region of the high Tc cuprate superconductivity is a spin pseudo-gap region rather than an electron pre-paired region.Comment: Latex, page12, no figure

Normal state property of the t-J model

Using the spin-hole coherent state representation and taking a long range antiferromagnetic N\`{e}el order as a background of the localized spin degree part, we have studied the normal state behavior of the t-J model, and shown that a strongly short-range antiferromagnetic correlation of the localized spin degree part is responsible for the anomalous non-Korringa-like relaxation behavior of the planar copper spin, the Korringa-like behavior of the planar oxygen spin may derive from the charge degree part describing a Zhang-Rice spin-singlet; The charge degree part feels a strongly staggered magnetic field induced by this short-range antiferromagnetic correlation as a doping hole hopping, this staggered magnetic field enforces the charge degrees to have different responses to external magnetic and electric fields and to show two relaxation rate behaviors corresponding to the planar resistivity and Hall angle, respectively. We have found that the temperature dependence of magnetoresistance is $T^{-n}$, $n\simeq 3$, near the optimal doping, $n\simeq 4$, in the underdoping region, violating Kohler's rule, the transport relaxation rate is of the order of $2k_{B}T$, all that are consistent with the normal state of the cuprate superconductors.Comment: 21 pages, no figures, Revte

Low Temperature Behavior of the Kondo Effect in Tomonaga-Luttinger Liquid

Using the bosonization method, we study the low temperature behavior of the Kondo effect in the Tomonaga-Luttinger liquid and clearly show that the power law temperature dependence of the impurity susceptibility is completely determined by the repulsive electron-electron interaction existing in the total spin channel and is independent of the electron-electron interaction existing in the charge channels.Comment: 15 pages, Late