On the Toda Lattice Equation with Self-Consistent Sources

The Toda lattice hierarchy with self-consistent sources and their Lax representation are derived. We construct a forward Darboux transformation (FDT) with arbitrary functions of time and a generalized forward Darboux transformation (GFDT) for Toda lattice with self-consistent sources (TLSCS), which can serve as a non-auto-Backlund transformation between TLSCS with different degrees of sources. With the help of such DT, we can construct many type of solutions to TLSCS, such as rational solution, solitons, positons, negetons, and soliton-positons, soliton-negatons, positon-negatons etc., and study properties and interactions of these solutions.Comment: 20 page

Magnetic-field induced resistivity minimum with in-plane linear magnetoresistance of the Fermi liquid in SrTiO3-x single crystals

We report novel magnetotransport properties of the low temperature Fermi liquid in SrTiO3-x single crystals. The classical limit dominates the magnetotransport properties for a magnetic field perpendicular to the sample surface and consequently a magnetic-field induced resistivity minimum emerges. While for the field applied in plane and normal to the current, the linear magnetoresistance (MR) starting from small fields (< 0.5 T) appears. The large anisotropy in the transverse MRs reveals the strong surface interlayer scattering due to the large gradient of oxygen vacancy concentration from the surface to the interior of SrTiO3-x single crystals. Moreover, the linear MR in our case was likely due to the inhomogeneity of oxygen vacancies and oxygen vacancy clusters, which could provide experimental evidences for the unusual quantum linear MR proposed by Abrikosov [A. A. Abrikosov, Phys. Rev. B 58, 2788 (1998)].Comment: 5 pages, 4 figure

Naturalistic Affective Expression Classification by a Multi-Stage Approach Based on Hidden Markov Models

In naturalistic behaviour, the affective states of a person change at a rate much slower than the typical rate at which video or audio is recorded (e.g. 25fps for video). Hence, there is a high probability that consecutive recorded instants of expressions represent a same affective content. In this paper, a multi-stage automatic affective expression recognition system is proposed which uses Hidden Markov Models (HMMs) to take into account this temporal relationship and finalize the classification process. The hidden states of the HMMs are associated with the levels of affective dimensions to convert the classification problem into a best path finding problem in HMM. The system was tested on the audio data of the Audio/Visual Emotion Challenge (AVEC) datasets showing performance significantly above that of a one-stage classification system that does not take into account the temporal relationship, as well as above the baseline set provided by this Challenge. Due to the generality of the approach, this system could be applied to other types of affective modalities

Quasi-long range order in glass states of impure liquid crystals, magnets, and superconductors

In this review we consider glass states of several disordered systems: vortices in impure superconductors, amorphous magnets, and nematic liquid crystals in random porous media. All these systems can be described by the random-field or random-anisotropy O(N) model. Even arbitrarily weak disorder destroys long range order in the O(N) model. We demonstrate that at weak disorder and low temperatures quasi-long range order emerges. In quasi-long-range-ordered phases the correlation length is infinite and correlation functions obey power dependencies on the distance. In pure systems quasi-long range order is possible only in the lower critical dimension and only in the case of Abelian symmetry. In the presence of disorder this type of ordering turns out to be more common. It exists in a range of dimensions and is not prohibited by non-Abelian symmetries.Comment: 32 page

Enhancing synchronization in growing networks

Most real systems are growing. In order to model the evolution of real systems, many growing network models have been proposed to reproduce some specific topology properties. As the structure strongly influences the network function, designing the function-aimed growing strategy is also a significant task with many potential applications. In this letter, we focus on synchronization in the growing networks. In order to enhance the synchronizability during the network evolution, we propose the Spectral-Based Growing (SBG) strategy. Based on the linear stability analysis of synchronization, we show that our growing mechanism yields better synchronizability than the existing topology-aimed growing strategies in both artificial and real-world networks. We also observe that there is an optimal degree of new added nodes, which means adding nodes with neither too large nor too low degree could enhance the synchronizability. Furthermore, some topology measurements are considered in the resultant networks. The results show that the degree, node betweenness centrality from SBG strategy are more homogenous than those from other growing strategies. Our work highlights the importance of the function-aimed growth of the networks and deepens our understanding of it

Nuclear pairing reduction due to rotation and blocking

Nuclear pairing gaps of normally deformed and superdeformed nuclei are investigated using the particle-number conserving (PNC) formalism for the cranked shell model, in which the blocking effects are treated exactly. Both rotational frequency $\omega$-dependence and seniority (number of unpaired particles) $\nu$-dependence of the pairing gap $\tilde{\Delta}$ are investigated. For the ground-state bands of even-even nuclei, PNC calculations show that in general $\tilde{\Delta}$ decreases with increasing $\omega$, but the $\omega$-dependence is much weaker than that calculated by the number-projected Hartree-Fock-Bogolyubov approach. For the multiquasiparticle bands (seniority $\nu> 2$), the pairing gaps keep almost $\omega$-independent. As a function of the seniority $\nu$, the bandhead pairing gaps $\tilde{\Delta}(\nu,\omega=0)$ decrease slowly with increasing $\nu$. Even for the highest seniority $\nu$ bands identified so far, $\tilde{\Delta}(\nu,\omega=0)$ remains greater than 70% of $\tilde{\Delta}(\nu=0,\omega=0)$.Comment: 15 pages, 5 figure

Classical Poisson structures and r-matrices from constrained flows

We construct the classical Poisson structure and $r$-matrix for some finite dimensional integrable Hamiltonian systems obtained by constraining the flows of soliton equations in a certain way. This approach allows one to produce new kinds of classical, dynamical Yang-Baxter structures. To illustrate the method we present the $r$-matrices associated with the constrained flows of the Kaup-Newell, KdV, AKNS, WKI and TG hierarchies, all generated by a 2-dimensional eigenvalue problem. Some of the obtained $r$-matrices depend only on the spectral parameters, but others depend also on the dynamical variables. For consistency they have to obey a classical Yang-Baxter-type equation, possibly with dynamical extra terms.Comment: 16 pages in LaTe

Metallic state in La-doped YBa2_2Cu3_3Oy_y thin films with nn-type charge carriers

We report hole and electron doping in La-doped YBa$_2$Cu$_3$O$_y$(YBCO) thin films synthesized by pulsed laser deposition technique and subsequent \emph{in-situ} postannealing in oxygen ambient and vaccum. The $n$-type samples show a metallic behavior below the Mott limit and a high carrier density of $\sim2.8$ $\times$ 10$^{21}$ cm$^{-3}$ at room temperature (\emph{T}) at the optimally reduced condition. The in-plane resistivity ($\rho$$_{ab}$) of the $n$-type samples exhibits a quadratic \emph{T} dependence in the moderate-\emph{T} range and shows an anomaly at a relatively higher \emph{T} probably related to pseudogap formation analogous to underdoped Nd$_{2-x}$Ce$_x$CuO$_4$ (NCCO). Furthermore, $\rho$$_{ab}$(T), \emph{T}$_c$ and \emph{T} with minimum resistivity (\emph{T}$_{min}$) were investigated in both $p$- and $n$-side. The present results reveal the $n$-$p$ asymmetry (symmetry) within the metallic-state region in an underdoped cuprate and suggest the potential toward ambipolar superconductivity in a single YBCO system.Comment: 4 pages, 5 figure

Carrier freeze-out induced metal-insulator transition in oxygen deficient SrTiO3 films

We report the optical, electrical transport, and magnetotransport properties of high quality oxygen deficient SrTiO3 (STO) single crystal film fabricated by pulsed laser deposition and reduced in the vacuum chamber. The oxygen vacancy distribution in the thin film is expected to be uniform. By comparing the electrical properties with oxygen deficient bulk STO, it was found that the oxygen vacancies in bulk STO is far from uniform over the whole material. The metal-insulator transition (MIT) observed in the oxygen deficient STO film was found to be induced by the carrier freeze-out effect. The low temperature frozen state can be re-excited by an electric field, Joule heating, and surprisingly also a large magnetic field.Comment: 5 pages, 5 figure

Inviscid dynamical structures near Couette flow

Consider inviscid fluids in a channel {-1<y<1}. For the Couette flow v_0=(y,0), the vertical velocity of solutions to the linearized Euler equation at v_0 decays in time. At the nonlinear level, such inviscid damping has not been proved. First, we show that in any (vorticity) H^{s}(s<(3/2)) neighborhood of Couette flow, there exist non-parallel steady flows with arbitrary minimal horizontal period. This implies that nonlinear inviscid damping is not true in any (vorticity) H^{s}(s<(3/2)) neighborhood of Couette flow and for any horizontal period. Indeed, the long time behavior in such neighborhoods are very rich, including nontrivial steady flows, stable and unstable manifolds of nearby unstable shears. Second, in the (vorticity) H^{s}(s>(3/2)) neighborhood of Couette, we show that there exist no non-parallel steadily travelling flows v(x-ct,y), and no unstable shears. This suggests that the long time dynamics in H^{s}(s>(3/2)) neighborhoods of Couette might be much simpler. Such contrasting dynamics in H^{s} spaces with the critical power s=(3/2) is a truly nonlinear phenomena, since the linear inviscid damping near Couette is true for any initial vorticity in L^2