Lyapunov 1-forms for flows

In this paper we find conditions which guarantee that a given flow $\Phi$ on a compact metric space $X$ admits a Lyapunov one-form $\omega$ lying in a prescribed \v{C}ech cohomology class $\xi\in \check H^1(X;\R)$. These conditions are formulated in terms of the restriction of $\xi$ to the chain recurrent set of $\Phi$. The result of the paper may be viewed as a generalization of a well-known theorem of C. Conley about the existence of Lyapunov functions.Comment: 27 pages, 3 figures. This revised version incorporates a few minor improvement

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

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

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

Retaining memory after hibernation: performance varies independently of activity levels in wild grey mouse (advance online)

Abstract Hibernation, a hypometabolic state associated with low body temperature and reduced metabolic and activity rates, represents one adaptation to harsh seasonal environmental conditions. As a consequence of hypometabolism, energetically costly neuronal processes also ought to be reduced. Since active neuronal pathways are prerequisites for learning and memory, and because previous studies revealed variable patterns, it remains unclear whether and how hibernating animals retain memories, however. Here, we investigated the effect of seasonally reduced activity on memory retention in 36 wild grey mouse lemurs (Microcebus murinus). Data from activity loggers confirmed that female grey mouse lemurs entered hibernation during the cool dry season, whereas males exhibited episodic bursts of activity throughout the austral winter. Thus, compared to males, we predicted females to show lower memory retention of visual and spatial stimulus?reward associations learned before hibernation. In contrast to our prediction, all individuals performed worse in the post-hibernation testing session in both types of tests, compared to the pre-hibernation learning session, and males (N =?11) performed even worse than females (N =?14) in the post-hibernation testing session. Although females (N =?9) equipped with activity loggers tended to be less active than males (N =?4), sex-specific activity levels were unrelated to interindividual differences in memory retention. Hence, the post-hibernation decrease in performance of grey mouse lemurs may reflect a more general disability to retain stimulus?reward associations than a lack of memory retention due to seasonal hypometabolism, as suggested for some species of bats or squirrels

Are Neutron-Rich Elements Produced in the Collapse of Strange Dwarfs ?

The structure of strange dwarfs and that of hybrid stars with same baryonic number is compared. There is a critical mass (M~0.24M_sun) in the strange dwarf branch, below which configurations with the same baryonic number in the hybrid star branch are more stable. If a transition occurs between both branches, the collapse releases an energy of about of 3x10^{50} erg, mostly under the form of neutrinos resulting from the conversion of hadronic matter onto strange quark matter. Only a fraction (~4%) is required to expel the outer neutron-rich layers. These events may contribute significantly to the chemical yield of nuclides with A>80 in the Galaxy, if their frequency is of about one per 1500 years.Comment: Accepted for publication in IJMP

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

Nekhoroshev theorem for the periodic Toda lattice

The periodic Toda lattice with $N$ sites is globally symplectomorphic to a two parameter family of $N-1$ coupled harmonic oscillators. The action variables fill out the whole positive quadrant of $\R^{N-1}$. We prove that in the interior of the positive quadrant as well as in a neighborhood of the origin, the Toda Hamiltonian is strictly convex and therefore Nekhoroshev's theorem applies on (almost) all parts of phase space.Comment: 28 page

128Xe and 130Xe: Testing He-shell burning in AGB stars

The s-process branching at 128I has been investigated on the basis of new, precise experimental (n,g) cross sections for the s-only isotopes 128Xe and 130Xe. This branching is unique, since it is essentially determined by the temperature- and density-sensitive stellar decay rates of 128I and only marginally affected by the specific stellar neutron flux. For this reason it represents an important test for He-shell burning in AGB stars. The description of the branching by means of the complex stellar scenario reveals a significant sensitivity to the time scales for convection during He shell flashes, thus providing constraints for this phenomenon. The s-process ratio 128Xe/130Xe deduced from stellar models allows for a (9+-3)% p-process contribution to solar 128Xe, in agreement with the Xe-S component found in meteoritic presolar SiC grains.Comment: 24 pages, 9 figures, accepted for publication in Astophysical Journa