330 research outputs found
On multicurve models for the term structure
In the context of multi-curve modeling we consider a two-curve setup, with
one curve for discounting (OIS swap curve) and one for generating future cash
flows (LIBOR for a give tenor). Within this context we present an approach for
the clean-valuation pricing of FRAs and CAPs (linear and nonlinear derivatives)
with one of the main goals being also that of exhibiting an "adjustment factor"
when passing from the one-curve to the two-curve setting. The model itself
corresponds to short rate modeling where the short rate and a short rate spread
are driven by affine factors; this allows for correlation between short rate
and short rate spread as well as to exploit the convenient affine structure
methodology. We briefly comment also on the calibration of the model
parameters, including the correlation factor.Comment: 16 page
Analyticity of the Susceptibility Function for Unimodal Markovian Maps of the Interval
In a previous note [Ru] the susceptibility function was analyzed for some
examples of maps of the interval. The purpose of the present note is to give a
concise treatment of the general unimodal Markovian case (assuming real
analytic). We hope that it will similarly be possible to analyze maps
satisfying the Collet-Eckmann condition. Eventually, as explained in [Ru],
application of a theorem of Whitney [Wh] should prove differentiability of the
map restricted to a suitable set.Comment: 8 page
Characterisation of spatial network-like patterns from junctions' geometry
We propose a new method for quantitative characterization of spatial
network-like patterns with loops, such as surface fracture patterns, leaf vein
networks and patterns of urban streets. Such patterns are not well
characterized by purely topological estimators: also patterns that both look
different and result from different morphogenetic processes can have similar
topology. A local geometric cue -the angles formed by the different branches at
junctions- can complement topological information and allow to quantify the
large scale spatial coherence of the pattern. For patterns that grow over time,
such as fracture lines on the surface of ceramics, the rank assigned by our
method to each individual segment of the pattern approximates the order of
appearance of that segment. We apply the method to various network-like
patterns and we find a continuous but sharp dichotomy between two classes of
spatial networks: hierarchical and homogeneous. The first class results from a
sequential growth process and presents large scale organization, the latter
presents local, but not global organization.Comment: version 2, 14 page
Complex bounds for multimodal maps: bounded combinatorics
We proved the so called complex bounds for multimodal, infinitely
renormalizable analytic maps with bounded combinatorics: deep renormalizations
have polynomial-like extensions with definite modulus. The complex bounds is
the first step to extend the renormalization theory of unimodal maps to
multimodal maps.Comment: 20 pages, 3 figure
Delay of Disorder by Diluted Polymers
We study the effect of diluted flexible polymers on a disordered capillary
wave state. The waves are generated at an interface of a dyed water sugar
solution and a low viscous silicon oil. This allows for a quantitative
measurement of the spatio-temporal Fourier spectrum. The primary pattern after
the first bifurcation from the flat interface are squares. With increasing
driving strength we observe a melting of the square pattern. It is replaced by
a weak turbulent cascade. The addition of a small amount of polymers to the
water layer does not affect the critical acceleration but shifts the disorder
transition to higher driving strenghs and the short wave length - high
frequency fluctuations are suppressed
Hyperbolic outer billiards : a first example
We present the first example of a hyperbolic outer billiard. More precisely
we construct a one parameter family of examples which in some sense correspond
to the Bunimovich billiards.Comment: 11 pages, 8 figures, to appear in Nonlinearit
A Streamlined, Bi-Organelle, Multiplex PCR Approach to Species Identification: Application to Global Conservation and Trade Monitoring of the Great White Shark, Carcharodon carcharias
The great white shark, Carcharodon carcharias, is the most widely protected elasmobranch in the world, and is classified as Vulnerable by the IUCN and listed on Appendix III of CITES. Monitoring of trade in white shark products and enforcement of harvest and trade prohibitions is problematic, however, in large part due to difficulties in identifying marketed shark parts (e.g., dried fins, meat and processed carcasses) to species level. To address these conservation and management problems, we have developed a rapid, molecular diagnostic assay based on species-specific PCR primer design for accurate identification of white shark body parts, including dried fins. The assay is novel in several respects: It employs a multiplex PCR assay utilizing both nuclear (ribosomal internal transcribed spacer 2) and mitochondrial (cytochrome b) loci simultaneously to achieve a highly robust measure of diagnostic accuracy; it is very sensitive, detecting the presence of white shark DNA in a mixture of genomic DNAs from up to ten different commercially fished shark species pooled together in a single PCR tube; and it successfully identifies white shark DNA from globally distributed animals. In addition to its utility for white shark trade monitoring and conservation applications, this highly streamlined, bi-organelle, multiplex PCR assay may prove useful as a general model for the design of genetic assays aimed at detecting body parts from other protected and threatened species
Scarred Patterns in Surface Waves
Surface wave patterns are investigated experimentally in a system geometry
that has become a paradigm of quantum chaos: the stadium billiard. Linear waves
in bounded geometries for which classical ray trajectories are chaotic are
known to give rise to scarred patterns. Here, we utilize parametrically forced
surface waves (Faraday waves), which become progressively nonlinear beyond the
wave instability threshold, to investigate the subtle interplay between
boundaries and nonlinearity. Only a subset (three main types) of the computed
linear modes of the stadium are observed in a systematic scan. These correspond
to modes in which the wave amplitudes are strongly enhanced along paths
corresponding to certain periodic ray orbits. Many other modes are found to be
suppressed, in general agreement with a prediction by Agam and Altshuler based
on boundary dissipation and the Lyapunov exponent of the associated orbit.
Spatially asymmetric or disordered (but time-independent) patterns are also
found even near onset. As the driving acceleration is increased, the
time-independent scarred patterns persist, but in some cases transitions
between modes are noted. The onset of spatiotemporal chaos at higher forcing
amplitude often involves a nonperiodic oscillation between spatially ordered
and disordered states. We characterize this phenomenon using the concept of
pattern entropy. The rate of change of the patterns is found to be reduced as
the state passes temporarily near the ordered configurations of lower entropy.
We also report complex but highly symmetric (time-independent) patterns far
above onset in the regime that is normally chaotic.Comment: 9 pages, 10 figures (low resolution gif files). Updated and added
references and text. For high resolution images:
http://physics.clarku.edu/~akudrolli/stadium.htm
Pre-avalanche instabilities in a granular pile
We investigate numerically the transition between static equilibrium and
dynamic surface flow of a 2D cohesionless granular system driven by a
continuous gravity loading. This transition is characterized by intermittent
local dynamic rearrangements and can be described by an order parameter defined
as the density of critical contacts, e.g. contacts where the friction is fully
mobilized. Analysis of the spatial correlations of critical contacts shows the
occurence of ``fluidized'' clusters which exhibit a power-law divergence in
size at the approach of the stability limit. The results are compatible with
recent models that describe the granular system during the static/dynamic
transition as a multi-phase system.Comment: 9 pages, 6 figures, submitted to Phys. Rev. Let
Double exponential stability of quasi-periodic motion in Hamiltonian systems
We prove that generically, both in a topological and measure-theoretical
sense, an invariant Lagrangian Diophantine torus of a Hamiltonian system is
doubly exponentially stable in the sense that nearby solutions remain close to
the torus for an interval of time which is doubly exponentially large with
respect to the inverse of the distance to the torus. We also prove that for an
arbitrary small perturbation of a generic integrable Hamiltonian system, there
is a set of almost full positive Lebesgue measure of KAM tori which are doubly
exponentially stable. Our results hold true for real-analytic but more
generally for Gevrey smooth systems
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