Interpolation of nonlinear maps

Let $(X_0, X_1)$ and $(Y_0, Y_1)$ be complex Banach couples and assume that $X_1\subseteq X_0$ with norms satisfying $\|x\|_{X_0} \le c\|x\|_{X_1}$ for some $c > 0$. For any $0<\theta <1$, denote by $X_\theta = [X_0, X_1]_\theta$ and $Y_\theta = [Y_0, Y_1]_\theta$ the complex interpolation spaces and by $B(r, X_\theta)$, $0 \le \theta \le 1,$ the open ball of radius $r>0$ in $X_\theta$, centered at zero. Then for any analytic map $\Phi: B(r, X_0) \to Y_0+ Y_1$ such that $\Phi: B(r, X_0)\to Y_0$ and $\Phi: B(c^{-1}r, X_1)\to Y_1$ are continuous and bounded by constants $M_0$ and $M_1$, respectively, the restriction of $\Phi$ to $B(c^{-\theta}r, X_\theta)$, $0 < \theta < 1,$ is shown to be a map with values in $Y_\theta$ which is analytic and bounded by $M_0^{1-\theta} M_1^\theta$

Birkhoff normal form for the periodic Toda lattice

This volume contains the proceedings of a conference held at the Courant Institute in 2006 to celebrate the 60th birthday of Percy A. Deift. The program reflected the wide-ranging contributions of Professor Deift to analysis with emphasis on recent developments in Random Matrix Theory and integrable systems. The articles in this volume present a broad view on the state of the art in these fields. Topics on random matrices include the distributions and stochastic processes associated with local eigenvalue statistics, as well as their appearance in combinatorial models such as TASEP, last passage percolation and tilings. The contributions in integrable systems mostly deal with focusing NLS, the Camassa-Holm equation and the Toda lattice. A number of papers are devoted to techniques that are used in both fields. These techniques are related to orthogonal polynomials, operator determinants, special functions, Riemann-Hilbert problems, direct and inverse spectral theory. Of special interest is the article of Percy Deift in which he discusses some open problems of Random Matrix Theory and the theory of integrable systems

Global action-angle variables for the periodic Toda lattice

In this paper we construct global action-angle variables for the periodic Toda lattic

Global Birkhoff coordinates for the periodic Toda lattice

In this paper we prove that the periodic Toda lattice admits globally defined Birkhoff coordinates.Comment: 32 page

Qualitative features of periodic solutions of KdV

In this paper we prove new qualitative features of solutions of KdV on the circle. The first result says that the Fourier coefficients of a solution of KdV in Sobolev space $H^N,\, N\geq 0$, admit a WKB type expansion up to first order with strongly oscillating phase factors defined in terms of the KdV frequencies. The second result provides estimates for the approximation of such a solution by trigonometric polynomials of sufficiently large degree

Oral Immunization of Wildlife Against Rabies: Concept and First Field Experiments

The possibility of immunizing carnivores against rabies with live attenuated vaccine administered by the oral route was raised by North American scientists in the 1960s. Subsequently, several American and European teams tested different vaccine strains in the laboratory for efficacy and safety and studied vaccine stabilization, vaccine delivery systems, baIt acceptance by wl1d ammals, and bait distribution schemes. The first field trial of a cloned SAD (Street Alabama Dufferin) strain in baits designed to immunize foxes orally ~as conducted in an Alpine valley in Switzerland in 1978. A population containing ∼60% immune foxes at the valley entrance stopped the spread of the disease into untreated upper parts of the valley. T~e strategic use of oral vaccination of foxes in additional regions of SWItzerland resulted m freedom from the zoonosis in four-fifths of the countr

Oral Immunization of Wildlife Against Rabies: Concept and First Field Experiments

The possibility of immunizing carnivores against rabies with live attenuated vaccine administered by the oral route was raised by North American scientists in the 1960s. Subsequently, several American and European teams tested different vaccine strains in the laboratory for efficacy and safety and studied vaccine stabilization, vaccine delivery systems, baIt acceptance by wl1d ammals, and bait distribution schemes. The first field trial of a cloned SAD (Street Alabama Dufferin) strain in baits designed to immunize foxes orally ~as conducted in an Alpine valley in Switzerland in 1978. A population containing ∼60% immune foxes at the valley entrance stopped the spread of the disease into untreated upper parts of the valley. T~e strategic use of oral vaccination of foxes in additional regions of SWItzerland resulted m freedom from the zoonosis in four-fifths of the country

Addition theorems and the Drach superintegrable systems

We propose new construction of the polynomial integrals of motion related to the addition theorems. As an example we reconstruct Drach systems and get some new two-dimensional superintegrable Stackel systems with third, fifth and seventh order integrals of motion.Comment: 18 pages, the talk given on the conference "Superintegrable Systems in Classical and Quantum Mechanics", Prague 200

On geodesic exponential maps of the Virasoro group

We study the geodesic exponential maps corresponding to Sobolev type right-invariant (weak) Riemannian metricsμ(k) (k≥ 0) on the Virasoro group Vir and show that for k≥ 2, but not for k=0,1, each of them defines a smooth Fréchet chart of the unital element e ∈Vir. In particular, the geodesic exponential map corresponding to the Korteweg-de Vries (KdV) equation (k=0) is not a local diffeomorphism near the origi

End-to-End Learning of Video Super-Resolution with Motion Compensation

Learning approaches have shown great success in the task of super-resolving an image given a low resolution input. Video super-resolution aims for exploiting additionally the information from multiple images. Typically, the images are related via optical flow and consecutive image warping. In this paper, we provide an end-to-end video super-resolution network that, in contrast to previous works, includes the estimation of optical flow in the overall network architecture. We analyze the usage of optical flow for video super-resolution and find that common off-the-shelf image warping does not allow video super-resolution to benefit much from optical flow. We rather propose an operation for motion compensation that performs warping from low to high resolution directly. We show that with this network configuration, video super-resolution can benefit from optical flow and we obtain state-of-the-art results on the popular test sets. We also show that the processing of whole images rather than independent patches is responsible for a large increase in accuracy.Comment: Accepted to GCPR201