1,231 research outputs found
Lyapunov 1-forms for flows
In this paper we find conditions which guarantee that a given flow on
a compact metric space admits a Lyapunov one-form lying in a
prescribed \v{C}ech cohomology class . These
conditions are formulated in terms of the restriction of to the chain
recurrent set of . 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 , 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 (NÂ =?11) performed even worse than females (NÂ =?14) in the post-hibernation testing session. Although females (NÂ =?9) equipped with activity loggers tended to be less active than males (NÂ =?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 sites is globally symplectomorphic to a
two parameter family of coupled harmonic oscillators. The action
variables fill out the whole positive quadrant of . 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
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