Aggregated Feature Retrieval for MPEG-7 via Clustering

In this paper, we describe an approach to combining text and visual features from MPEG-7 descriptions of video. A video retrieval process is aligned to a text retrieval process based on the TF*IDF vector space model via clustering of low-level visual features. Our assumption is that shots within the same cluster are not only similar visually but also semantically, to a certain extent. Our experiments on the TRECVID2002 and TRECVID2003 collections show that adding extra meaning to a shot based on the shots from the same cluster is useful when each video in a collection contains a high proportion of similar shots, for example in documentaries

Measurement of binding energy of negatively charged excitons in GaAs/AlGaAs quantum wells

We report a photoluminescence study of electron-hole complexes in specially designed semiconductor heterostructures. Placing a remote dilute layer of donors at different distances \itshape d \normalfont from the quantum well leads to the transformation of luminescence spectra of neutral ($X$) and negatively charged ($X^{-}$) excitons. The onset of an additional spectral line and its energy dependence on \itshape d \normalfont allows us to unambiguously relate the so-called $X^{-}$ trion state with charged excitons bound on charged donors in a barrier. The results indicate the overestimation in free-trion binding energies from previous studies of GaAs/Al$_{0.3}$Ga$_{0.7}$As quantum wells, and give their corrected values for QWs of width 200 and 300 \AA \space in the limiting case of infinitely distant donors.Comment: 5 pages, 4 figure

Complex Dynamics of Correlated Electrons in Molecular Double Ionization by an Ultrashort Intense Laser Pulse

With a semiclassical quasi-static model we achieve an insight into the complex dynamics of two correlated electrons under the combined influence of a two-center Coulomb potential and an intense laser field. The model calculation is able to reproduce experimental data of nitrogen molecules for a wide range of laser intensities from tunnelling to over-the-barrier regime, and predicts a significant alignment effect on the ratio of double over single ion yield. The classical trajectory analysis allows to unveil sub-cycle molecular double ionization dynamics.Comment: 5 pages, 5 figures. to appear in Phys. Rev. Lett.(2007

Classical Trajectory Perspective on Double Ionization Dynamics of Diatomic Molecules Irradiated by Ultrashort Intense Laser Pulses

In the present paper, we develop a semiclassical quasi-static model accounting for molecular double ionization in an intense laser pulse. With this model, we achieve insight into the dynamics of two highly-correlated valence electrons under the combined influence of a two-center Coulomb potential and an intense laser field, and reveal the significant influence of molecular alignment on the ratio of double over single ion yield. Analysis on the classical trajectories unveils sub-cycle dynamics of the molecular double ionization. Many interesting features, such as the accumulation of emitted electrons in the first and third quadrants of parallel momentum plane, the regular pattern of correlated momentum with respect to the time delay between closest collision and ionization moment, are revealed and successfully explained by back analyzing the classical trajectories. Quantitative agreement with experimental data over a wide range of laser intensities from tunneling to over-the-barrier regime is presented.Comment: 8 pages, 9 figure

Existence theorems for a nonlinear second-order distributional differential equation

In this work, we are concerned with existence of solutions for a nonlinear second-order distributional differential equation, which contains measure differential equations and stochastic differential equations as special cases. The proof is based on the Leray--Schauder nonlinear alternative and Kurzweil--Henstock--Stieltjes integrals. Meanwhile, examples are worked out to demonstrate that the main results are sharp.Comment: This is a preprint of a paper whose final and definite form is with 'Journal of King Saud University - Science', ISSN 1018-3647. Submitted 05-March-2017; revised 24-April-2017; accepted for publication 26-April-201

Time Dependent Saddle Node Bifurcation: Breaking Time and the Point of No Return in a Non-Autonomous Model of Critical Transitions

There is a growing awareness that catastrophic phenomena in biology and medicine can be mathematically represented in terms of saddle-node bifurcations. In particular, the term `tipping', or critical transition has in recent years entered the discourse of the general public in relation to ecology, medicine, and public health. The saddle-node bifurcation and its associated theory of catastrophe as put forth by Thom and Zeeman has seen applications in a wide range of fields including molecular biophysics, mesoscopic physics, and climate science. In this paper, we investigate a simple model of a non-autonomous system with a time-dependent parameter $p(\tau)$ and its corresponding `dynamic' (time-dependent) saddle-node bifurcation by the modern theory of non-autonomous dynamical systems. We show that the actual point of no return for a system undergoing tipping can be significantly delayed in comparison to the {\em breaking time} $\hat{\tau}$ at which the corresponding autonomous system with a time-independent parameter $p_{a}= p(\hat{\tau})$ undergoes a bifurcation. A dimensionless parameter $\alpha=\lambda p_0^3V^{-2}$ is introduced, in which $\lambda$ is the curvature of the autonomous saddle-node bifurcation according to parameter $p(\tau)$, which has an initial value of $p_{0}$ and a constant rate of change $V$. We find that the breaking time $\hat{\tau}$ is always less than the actual point of no return $\tau^*$ after which the critical transition is irreversible; specifically, the relation $\tau^*-\hat{\tau}\simeq 2.338(\lambda V)^{-\frac{1}{3}}$ is analytically obtained. For a system with a small $\lambda V$, there exists a significant window of opportunity $(\hat{\tau},\tau^*)$ during which rapid reversal of the environment can save the system from catastrophe