Exact solutions to the time-dependent supersymmetric muliphoton Jaynes-Cummings model and the Chiao-Wu model

By using both the Lewis-Riesenfeld invariant theory and the invariant-related unitary transformation formulation, the present paper obtains the exact solutions to the time-dependent supersymmetric two-level multiphoton Jaynes-Cummings model and the Chiao-Wu model that describes the propagation of a photon inside the optical fiber. On the basis of the fact that the two-level multiphoton Jaynes-Cummings model possesses the supersymmetric structure, an invariant is constructed in terms of the supersymmetric generators by working in the sub-Hilbert-space corresponding to a particular eigenvalue of the conserved supersymmetric generators (i.e., the time-independent invariant). By constructing the effective Hamiltonian that describes the interaction of the photon with the medium of the optical fiber, it is further verified that the particular solution to the Schr\"{o}dinger equation is the eigenfunction of the second-quantized momentum operator of photons field. This, therefore, means that the explicit expression (rather than the hidden form that involves the chronological product) for the time-evolution operator of wave function is obtained by means of the invariant theories.Comment: 14 pages, Latex. This is a revised version of the published paper: Shen J Q, Zhu H Y 2003 Ann. Phys.(Leipzig) Vol.12 p.131-14

Joint & Progressive Learning from High-Dimensional Data for Multi-Label Classification

Despite the fact that nonlinear subspace learning techniques (e.g. manifold learning) have successfully applied to data representation, there is still room for improvement in explainability (explicit mapping), generalization (out-of-samples), and cost-effectiveness (linearization). To this end, a novel linearized subspace learning technique is developed in a joint and progressive way, called \textbf{j}oint and \textbf{p}rogressive \textbf{l}earning str\textbf{a}teg\textbf{y} (J-Play), with its application to multi-label classification. The J-Play learns high-level and semantically meaningful feature representation from high-dimensional data by 1) jointly performing multiple subspace learning and classification to find a latent subspace where samples are expected to be better classified; 2) progressively learning multi-coupled projections to linearly approach the optimal mapping bridging the original space with the most discriminative subspace; 3) locally embedding manifold structure in each learnable latent subspace. Extensive experiments are performed to demonstrate the superiority and effectiveness of the proposed method in comparison with previous state-of-the-art methods.Comment: accepted in ECCV 201

A unified approach to exact solutions of time-dependent Lie-algebraic quantum systems

By using the Lewis-Riesenfeld theory and the invariant-related unitary transformation formulation, the exact solutions of the {\it time-dependent} Schr\"{o}dinger equations which govern the various Lie-algebraic quantum systems in atomic physics, quantum optics, nuclear physics and laser physics are obtained. It is shown that the {\it explicit} solutions may also be obtained by working in a sub-Hilbert-space corresponding to a particular eigenvalue of the conserved generator ({\it i. e.}, the {\it time-independent} invariant) for some quantum systems without quasi-algebraic structures. The global and topological properties of geometric phases and their adiabatic limit in time-dependent quantum systems/models are briefly discussed.Comment: 11 pages, Latex. accepted by Euro. Phys. J.

Gravitomagnetic Field and Time-Dependent Spin-Rotation Coupling

The Kerr metric of spherically symmetric gravitational field is analyzed through the coordinate transformation from the rotating frame to fixing frame, and consequently that the inertial force field (with the exception of the centrifugal force field) in the rotating system is one part of its gravitomagnetic field is verified. We investigate the spin-rotation coupling and, by making use of Lewis-Riesenfeld invariant theory, we obtain exact solutions of the Schr\"{o}dinger equation of a spinning particle in a time-dependent rotating reference frame. A potential application of these exact solutions to the investigation of Earth$^{,}$s rotating frequency fluctuation by means of neutron-gravity interferometry experiment is briefly discussed in the present paper.Comment: 6 pages, 0 figures, Late

Tumor-associated EGFR over-expression specifically activates Stat3 and Smad7 resulting in desensitization of TGF-β signaling

Transforming Growth Factor-[beta] (TGF-[beta]) and Epidermal Growth Factor (EGF) signaling pathways are both independently implicated as key regulators in tumor formation and progression. Here, we demonstrate that activation of the tumor-associated and over-expressed EGFR desensitizes TGF-[beta] signaling and its cytostatic regulation through specific Stat3 activation and Smad7 induction. In normal and tumor human cell lines, reduction of TGF-[beta]-mediated Smad2 phosphorylation, nuclear translocation and Smad3 target gene activation were observed where EGFR is over-expressed, but not in cells which expressed EGFR at normal levels. The EGFR downstream signaling molecules phosphatidyinositol-3 Kinase (PI3K) or mitogen-activated protein kinase/ERK kinase (MEK) are not responsible for the down-regulation of TGF-[beta] signaling since blockade of them by specific pharmacological inhibitors LY294002 and U0126 had little effects on the sensitivity of TGF-[beta] signaling. We identified Stat3 as a signaling molecule activated specifically and persistently by over-expressed EGFR, but not by normal levels. Importantly, Stat3 is responsible for the reduced TGF-[beta] sensitivity, since its knockdown by siRNA restored TGF-[beta] signaling sensitivity. Furthermore, over-expressed EGFR, through Stat3 activates Smad7 promoter activity, increasing its protein levels, which is a negative regulator of TGF-[beta] signaling. Consequently, cells were re-sensitized to TGF-[beta] when Smad7 expression was reduced using siRNA. Therefore we establish a novel EGFR-Stat3-Smad7-TGF-[beta] signaling molecular axis where tumor-associated over-expression of EGFR in epithelial cells results in hyperactivation of Stat3, which activates Smad7 expression, compromising the TGF-[beta]'s cytostatic regulation of epithelium and consequent tumor formation