9,762 research outputs found
Deformations of Gabor Frames
The quantum mechanical harmonic oscillator Hamiltonian generates a
one-parameter unitary group W(\theta) in L^2(R) which rotates the
time-frequency plane. In particular, W(\pi/2) is the Fourier transform. When
W(\theta) is applied to any frame of Gabor wavelets, the result is another such
frame with identical frame bounds. Thus each Gabor frame gives rise to a
one-parameter family of frames, which we call a deformation of the original.
For example, beginning with the usual tight frame F of Gabor wavelets generated
by a compactly supported window g(t) and parameterized by a regular lattice in
the time-frequency plane, one obtains a family of frames F_\theta generated by
the non-compactly supported windows g_\theta=W(theta)g, parameterized by
rotated versions of the original lattice. This gives a method for constructing
tight frames of Gabor wavelets for which neither the window nor its Fourier
transform have compact support. When \theta=\pi/2, we obtain the well-known
Gabor frame generated by a window with compactly supported Fourier transform.
The family F_\theta therefore interpolates these two familiar examples.Comment: 8 pages in Plain Te
Robust Optimal Risk Sharing and Risk Premia in Expanding Pools
We consider the problem of optimal risk sharing in a pool of cooperative
agents. We analyze the asymptotic behavior of the certainty equivalents and
risk premia associated with the Pareto optimal risk sharing contract as the
pool expands. We first study this problem under expected utility preferences
with an objectively or subjectively given probabilistic model. Next, we develop
a robust approach by explicitly taking uncertainty about the probabilistic
model (ambiguity) into account. The resulting robust certainty equivalents and
risk premia compound risk and ambiguity aversion. We provide explicit results
on their limits and rates of convergence, induced by Pareto optimal risk
sharing in expanding pools
Bounding Bloat in Genetic Programming
While many optimization problems work with a fixed number of decision
variables and thus a fixed-length representation of possible solutions, genetic
programming (GP) works on variable-length representations. A naturally
occurring problem is that of bloat (unnecessary growth of solutions) slowing
down optimization. Theoretical analyses could so far not bound bloat and
required explicit assumptions on the magnitude of bloat. In this paper we
analyze bloat in mutation-based genetic programming for the two test functions
ORDER and MAJORITY. We overcome previous assumptions on the magnitude of bloat
and give matching or close-to-matching upper and lower bounds for the expected
optimization time. In particular, we show that the (1+1) GP takes (i)
iterations with bloat control on ORDER as well as
MAJORITY; and (ii) and
(and for )
iterations without bloat control on MAJORITY.Comment: An extended abstract has been published at GECCO 201
Rapid changes in ice core gas records Part 2: Understanding the rapid rise in atmospheric CO2 at the onset of the Bølling/Allerød
During the last glacial/interglacial transition the Earth's climate underwent rapid changes around 14.6 kyr ago. Temperature proxies from ice cores revealed the onset of the Bølling/Allerød (B/A) warm period in the north and the start of the Antarctic Cold Reversal in the south. Furthermore, the B/A is accompanied by a rapid sea level rise of about 20 m during meltwater pulse (MWP) 1A, whose exact timing is matter of current debate. In situ measured CO<sub>2</sub> in the EPICA Dome C (EDC) ice core also revealed a remarkable jump of 10±1 ppmv in 230 yr at the same time. Allowing for the age distribution of CO<sub>2</sub> in firn we here show, that atmospheric CO<sub>2</sub> rose by 20–35 ppmv in less than 200 yr, which is a factor of 2–3.5 larger than the CO<sub>2</sub> signal recorded in situ in EDC. Based on the estimated airborne fraction of 0.17 of CO<sub>2</sub> we infer that 125 Pg of carbon need to be released to the atmosphere to produce such a peak. Most of the carbon might have been activated as consequence of continental shelf flooding during MWP-1A. This impact of rapid sea level rise on atmospheric CO<sub>2</sub> distinguishes the B/A from other Dansgaard/Oeschger events of the last 60 kyr, potentially defining the point of no return during the last deglaciation
An Entropy Stable Nodal Discontinuous Galerkin Method for the Two Dimensional Shallow Water Equations on Unstructured Curvilinear Meshes with Discontinuous Bathymetry
We design an arbitrary high-order accurate nodal discontinuous Galerkin
spectral element approximation for the nonlinear two dimensional shallow water
equations with non-constant, possibly discontinuous, bathymetry on
unstructured, possibly curved, quadrilateral meshes. The scheme is derived from
an equivalent flux differencing formulation of the split form of the equations.
We prove that this discretisation exactly preserves the local mass and
momentum. Furthermore, combined with a special numerical interface flux
function, the method exactly preserves the mathematical entropy, which is the
total energy for the shallow water equations. By adding a specific form of
interface dissipation to the baseline entropy conserving scheme we create a
provably entropy stable scheme. That is, the numerical scheme discretely
satisfies the second law of thermodynamics. Finally, with a particular
discretisation of the bathymetry source term we prove that the numerical
approximation is well-balanced. We provide numerical examples that verify the
theoretical findings and furthermore provide an application of the scheme for a
partial break of a curved dam test problem
A Provably Stable Discontinuous Galerkin Spectral Element Approximation for Moving Hexahedral Meshes
We design a novel provably stable discontinuous Galerkin spectral element
(DGSEM) approximation to solve systems of conservation laws on moving domains.
To incorporate the motion of the domain, we use an arbitrary
Lagrangian-Eulerian formulation to map the governing equations to a fixed
reference domain. The approximation is made stable by a discretization of a
skew-symmetric formulation of the problem. We prove that the discrete
approximation is stable, conservative and, for constant coefficient problems,
maintains the free-stream preservation property. We also provide details on how
to add the new skew-symmetric ALE approximation to an existing discontinuous
Galerkin spectral element code. Lastly, we provide numerical support of the
theoretical results
Continuous phase stabilization and active interferometer control using two modes
We present a computer-based active interferometer stabilization method that
can be set to an arbitrary phase difference and does not rely on modulation of
the interfering beams. The scheme utilizes two orthogonal modes propagating
through the interferometer with a constant phase difference between them to
extract a common phase and generate a linear feedback signal. Switching times
of 50ms over a range of 0 to 6 pi radians at 632.8nm are experimentally
demonstrated. The phase can be stabilized up to several days to within 3
degrees.Comment: 3 pages, 2 figure
Bomb radiocarbon and tag-recapture dating of sandbar shark (Carcharhinus plumbeus)
The sandbar shark (Carcharhinus plumbeus) was the cornerstone species of western North Atlantic and Gulf of Mexico large coastal shark fisheries until 2008 when they
were allocated to a research-only fishery. Despite decades of fishing on this species, important life history
parameters, such as age and growth, have not been well known. Some validated age and growth information exists for sandbar shark, but more comprehensive life history information is needed. The complementary application of bomb radiocarbon and tag-recapture dating was used in this
study to determine valid age-estimation criteria and longevity estimates for this species. These two methods
indicated that current age interpretations based on counts of growth bands in vertebrae are accurate to 10 or 12 years. Beyond these years, we could not determine with certainty when such an underestimation of age begins; however, bomb radiocarbon and tag-recapture data indicated that large adult sharks were considerably older than the estimates derived from counts of growth bands. Three adult sandbar sharks were 20 to 26 years old based on bomb radiocarbon results and were a 5- to 11-year increase over the previous age estimates for these sharks. In support of
these findings, the tag-recapture data provided results that were consistent with bomb radiocarbon dating and
further supported a longevity that exceeds 30 years for this species
Counting Homomorphisms to Trees Modulo a Prime
Many important graph theoretic notions can be encoded as counting graph homomorphism problems, such as partition functions in statistical physics, in particular independent sets and colourings. In this article we study the complexity of #_pHomsToH, the problem of counting graph homomorphisms from an input graph to a graph H modulo a prime number p. Dyer and Greenhill proved a dichotomy stating that the tractability of non-modular counting graph homomorphisms depends on the structure of the target graph. Many intractable cases in non-modular counting become tractable in modular counting due to the common phenomenon of cancellation. In subsequent studies on counting modulo 2, however, the influence of the structure of H on the tractability was shown to persist, which yields similar dichotomies.
Our main result states that for every tree H and every prime p the problem #_pHomsToH is either polynomial time computable or #_pP-complete. This relates to the conjecture of Faben and Jerrum stating that this dichotomy holds for every graph H when counting modulo 2. In contrast to previous results on modular counting, the tractable cases of #_pHomsToH are essentially the same for all values of the modulo when H is a tree. To prove this result, we study the structural properties of a homomorphism. As an important interim result, our study yields a dichotomy for the problem of counting weighted independent sets in a bipartite graph modulo some prime p. These results are the first suggesting that such dichotomies hold not only for the one-bit functions of the modulo 2 case but also for the modular counting functions of all primes p
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