Rate of Convergence in Nonlinear Hartree Dynamics with Factorized Initial Data

The mean field dynamics of an $N$-particle weekly interacting Boson system can be described by the nonlinear Hartree equation. In this paper, we present estimates on the 1/N rate of convergence of many-body Schr\"{o}dinger dynamics to the one-body nonlinear Hartree dynamics with factorized initial data with two-body interaction potential $V$ in $L^3 (\mathbb{R}^3)+ L^{\infty} (\mathbb{R}^3)$.Comment: AMS LaTex, 21 page

One-shot Network Pruning at Initialization with Discriminative Image Patches

One-shot Network Pruning at Initialization (OPaI) is an effective method to decrease network pruning costs. Recently, there is a growing belief that data is unnecessary in OPaI. However, we obtain an opposite conclusion by ablation experiments in two representative OPaI methods, SNIP and GraSP. Specifically, we find that informative data is crucial to enhancing pruning performance. In this paper, we propose two novel methods, Discriminative One-shot Network Pruning (DOP) and Super Stitching, to prune the network by high-level visual discriminative image patches. Our contributions are as follows. (1) Extensive experiments reveal that OPaI is data-dependent. (2) Super Stitching performs significantly better than the original OPaI method on benchmark ImageNet, especially in a highly compressed model.Comment: BMVC 202

Physical States, Factorization and Nonlinear Structures in Two Dimensional Quantum Gravity

The nonlinear structures in 2D quantum gravity coupled to the $(q+1,q)$ minimal model are studied in the Liouville theory to clarify the factorization and the physical states. It is confirmed that the dressed primary states outside the minimal table are identified with the gravitational descendants. Using the discrete states of ghost number zero and one we construct the currents and investigate the Ward identities which are identified with the W and the Virasoro constraints. As nontrivial examples we derive the $L_0$, $L_1$ and $W_{-1}^{(3)}$ equations exactly. $L_n$ and $W^{(k)}_n$ equations are also discussed. We then explicitly show the decoupling of the edge states $O_j ~(j=0~ {\rm mod}~ q)$. We consider the interaction theory perturbed by the cosmological constant $O_1$ and the screening charge $S^+ =O_{2q+1}$. The formalism can be easily generalized to potential models other than the screening charge.Comment: 18 pages, LaTex, YITP/U-93-2

Rashba interferometers: Spin-dependent single and two-electron interference

Quantum transport in semiconductor nanostructures can be described theoretically in terms of the propagation and scattering of electron probability waves. Within this approach, elements of a phase-coherent electric circuit play a role similar to quantum-optical devices that can be characterised by scattering matrices. Electronic analogues of well-know optical interferometers have been fabricated and used to study special features of charge carriers in solids. We present results from our theoretical investigation into the interplay between spin precession and quantum interference in an electronic Mach-Zehnder interferometer with spin-orbit coupling of the Rashba type. Intriguing spin-dependent transport effects occur, which can be the basis for novel spintronic devices such as a magnet-less spin-controlled field-effect transistor and a variety of single-qubit gates. Their functionality arises entirely from spin-dependent interference of each single input electron with itself. We have also studied two-electron interference effects for the spin-dependent Mach-Zehnder interferometer, obtaining analytical expressions for its two-fermion-state scattering matrix. Using this result, we consider ways to generate two-electron output states for which the Rashba spin-subband quantum number and the output-arm index are entangled. Combining spin-dependent interference in our proposed Mach-Zehnder interferometer with a projective charge measurement at the output enables entanglement generation. As our particular scheme involves tuneable spin precession, electric-field control of entanglement production can be achieved.Comment: 7 pages, 5 figures, Elsevier style, submitted to special issue of Solid State Communications, v2: replacement to rectify formatting problems, v3: minor changes + 3 references adde

Local Inhomogeneity Effects on Nucleation Process in a High External Bias

Quantum nucleation processes in the presence of local moderate inhomogeneities are studied theoretically at high biases. The quantum nucleation rate Gamma is calculated for one-dimensional systems in a form Gamma = A e^(-B/hbar) by using the `bounce' method. The bias-dependence of the exponent B is shown to be changed by inhomogeneities. This change is explained by the reduction of the effective spatial dimension of the system. By studying the system-size dependence of the prefactor A, the condition for the appearance of inhomogeneity effects is evaluated. Nucleation rates in thermal activation regimes are also calculated, and compared with quantum tunneling regimes. For higher-dimensional systems, it is shown that the local approximation of inhomogeneity does not hold, and that spatial profiles of inhomogeneity become important.Comment: 10 pages, 6 figure

Rate of Convergence Towards Semi-Relativistic Hartree Dynamics

We consider the semi-relativistic system of $N$ gravitating Bosons with gravitation constant $G$. The time evolution of the system is described by the relativistic dispersion law, and we assume the mean-field scaling of the interaction where $N \to \infty$ and $G \to 0$ while $GN = \lambda$ fixed. In the super-critical regime of large $\lambda$, we introduce the regularized interaction where the cutoff vanishes as $N \to \infty$. We show that the difference between the many-body semi-relativistic Schr\"{o}dinger dynamics and the corresponding semi-relativistic Hartree dynamics is at most of order $N^{-1}$ for all $\lambda$, i.e., the result covers the sub-critical regime and the super-critical regime. The $N$ dependence of the bound is optimal.Comment: 29 page

Direct electronic measurement of the spin Hall effect

The generation, manipulation and detection of spin-polarized electrons in nanostructures define the main challenges of spin-based electronics[1]. Amongst the different approaches for spin generation and manipulation, spin-orbit coupling, which couples the spin of an electron to its momentum, is attracting considerable interest. In a spin-orbit-coupled system, a nonzero spin-current is predicted in a direction perpendicular to the applied electric field, giving rise to a "spin Hall effect"[2-4]. Consistent with this effect, electrically-induced spin polarization was recently detected by optical techniques at the edges of a semiconductor channel[5] and in two-dimensional electron gases in semiconductor heterostructures[6,7]. Here we report electrical measurements of the spin-Hall effect in a diffusive metallic conductor, using a ferromagnetic electrode in combination with a tunnel barrier to inject a spin-polarized current. In our devices, we observe an induced voltage that results exclusively from the conversion of the injected spin current into charge imbalance through the spin Hall effect. Such a voltage is proportional to the component of the injected spins that is perpendicular to the plane defined by the spin current direction and the voltage probes. These experiments reveal opportunities for efficient spin detection without the need for magnetic materials, which could lead to useful spintronics devices that integrate information processing and data storage.Comment: 5 pages, 4 figures. Accepted for publication in Nature (pending format approval

Linear dynamics of weakly viscous accretion disks: A disk analog of Tollmien-Schlichting waves

This paper discusses new perspectives and approaches to the problem of disk dynamics where, in this study, we focus on the effects of viscous instabilities influenced by boundary effects. The Boussinesq approximation of the viscous large shearing box equations is analyzed in which the azimuthal length scale of the disturbance is much larger than the radial and vertical scales. We examine the stability of a non-axisymmetric potential vorticity mode, i.e. a PV-anomaly. in a configuration in which buoyant convection and the strato-rotational instability do not to operate. We consider a series of boundary conditions which show the PV-anomaly to be unstable both on a finite and semi-infinite radial domains. We find these conditions leading to an instability which is the disk analog of Tollmien-Schlichting waves. When the viscosity is weak, evidence of the instability is most pronounced by the emergence of a vortex sheet at the critical layer located away from the boundary where the instability is generated. For some boundary conditions a necessary criterion for the onset of instability for vertical wavelengths that are a sizable fraction of the layer's thickness and when the viscosity is small is that the appropriate Froude number of the flow be greater than one. This instability persists if more realistic boundary conditions are applied, although the criterion on the Froude number is more complicated. The unstable waves studied here share qualitative features to the instability seen in rotating Blasius boundary layers. The implications of these results are discussed. An overall new strategy for exploring and interpreting disk instability mechanisms is also suggested.Comment: Accepted for publication in Astronomy and Astrophysics. 18 pages. This version 3 with corrected style fil

Clinical implications of increased lymph vessel density in the lymphatic metastasis of early-stage invasive cervical carcinoma: a clinical immunohistochemical method study

<p>Abstract</p> <p>Background</p> <p>Cervical cancer is the most common malignant gynecological cancer, and lymphatic metastasis can occur in the early stage of tumor growth. Lymphatic vessel endothelial hyaluronan receptor-1 (LYVE-1), a marker for lymphatic endothelium, provides powerful tools for studying tumor lymphangiogenesis. The purpose of this study is to investigate the clinical implications of lymphangiogenesis in the metastasis of early-stage invasive cervical carcinoma.</p> <p>Methods</p> <p>We used immunohistochemical (IHC) staining with the antibody against LYVE-1 to measure lymph vessel density in 41 cases of early-stage invasive cervical carcinoma and 12 cases of normal cervical samples. We then analyzed the correlation between lymph vessel density and clinicopathological features of the tumors.</p> <p>Results</p> <p>(1) The majority of peritumoral lymphatics were enlarged, dilated, and irregular. In contrast, intratumoral lymph vessels were small and collapsed. The peritumoral lymphatic vessel density (PLVD) was significantly higher than the intratumoral lymphatic vessel density (ILVD) (<it>P </it>< 0.01). (2) Both ILVD and PLVD were significantly higher than the LVD of the control cervixes (<it>P </it>< 0.01). (3) Both ILVD and PLVD were significantly associated with lymph node metastasis (ILVD, <it>P </it>< 0.05; PLVD, <it>P </it>< 0.01) and lymphatic vessel invasion (ILVD, <it>P </it>< 0.05; PLVD, <it>P </it>< 0.01). Both the ILVD and PLVD in patients with histological grade HG2 and HG3 were significantly higher than those with HG1 (<it>P </it>< 0.05).</p> <p>Conclusion</p> <p>Tumor lymphangiogenesis in early-stage invasive cervical carcinoma may play an important role in the process of lymphatic metastasis.</p