6,781 research outputs found
On the Hyperbolicity of Lorenz Renormalization
We consider infinitely renormalizable Lorenz maps with real critical exponent
and combinatorial type which is monotone and satisfies a long return
condition. For these combinatorial types we prove the existence of periodic
points of the renormalization operator, and that each map in the limit set of
renormalization has an associated unstable manifold. An unstable manifold
defines a family of Lorenz maps and we prove that each infinitely
renormalizable combinatorial type (satisfying the above conditions) has a
unique representative within such a family. We also prove that each infinitely
renormalizable map has no wandering intervals and that the closure of the
forward orbits of its critical values is a Cantor attractor of measure zero.Comment: 63 pages; 10 figure
The multipliers of periodic points in one-dimensional dynamics
It will be shown that the smooth conjugacy class of an unimodal map which
does not have a periodic attractor neither a Cantor attractor is determined by
the multipliers of the periodic orbits. This generalizes a result by M.Shub and
D.Sullivan for smooth expanding maps of the circle
The genotype-phenotype relationship in multicellular pattern-generating models - the neglected role of pattern descriptors
Background: A deep understanding of what causes the phenotypic variation arising from biological patterning
processes, cannot be claimed before we are able to recreate this variation by mathematical models capable of
generating genotype-phenotype maps in a causally cohesive way. However, the concept of pattern in a
multicellular context implies that what matters is not the state of every single cell, but certain emergent qualities
of the total cell aggregate. Thus, in order to set up a genotype-phenotype map in such a spatiotemporal pattern
setting one is actually forced to establish new pattern descriptors and derive their relations to parameters of the
original model. A pattern descriptor is a variable that describes and quantifies a certain qualitative feature of the
pattern, for example the degree to which certain macroscopic structures are present. There is today no general
procedure for how to relate a set of patterns and their characteristic features to the functional relationships,
parameter values and initial values of an original pattern-generating model. Here we present a new, generic
approach for explorative analysis of complex patterning models which focuses on the essential pattern features
and their relations to the model parameters. The approach is illustrated on an existing model for Delta-Notch
lateral inhibition over a two-dimensional lattice.
Results: By combining computer simulations according to a succession of statistical experimental designs,
computer graphics, automatic image analysis, human sensory descriptive analysis and multivariate data modelling,
we derive a pattern descriptor model of those macroscopic, emergent aspects of the patterns that we consider
of interest. The pattern descriptor model relates the values of the new, dedicated pattern descriptors to the
parameter values of the original model, for example by predicting the parameter values leading to particular
patterns, and provides insights that would have been hard to obtain by traditional methods.
Conclusion: The results suggest that our approach may qualify as a general procedure for how to discover and
relate relevant features and characteristics of emergent patterns to the functional relationships, parameter values
and initial values of an underlying pattern-generating mathematical model
A Quick Mind with Letters Can Be a Slow Mind with Natural Scenes: Individual Differences in Attentional Selection
Background
Most people show a remarkable deficit in reporting the second of two targets (T2) when presented 200–500 ms after the first (T1), reflecting an ‘attentional blink’ (AB). However, there are large individual differences in the magnitude of the effect, with some people, referred to as ‘non-blinkers’, showing no such attentional restrictions.
Methodology/Principal Findings
Here we replicate these individual differences in a task requiring identification of two letters amongst digits, and show that the observed differences in T2 performance cannot be attributed to individual differences in T1 performance. In a second experiment, the generality of the non-blinkers' superior performance was tested using a task containing novel pictures rather than alphanumeric stimuli. A substantial AB was obtained in non-blinkers that was equivalent to that of ‘blinkers’.
Conclusion/Significance
The results suggest that non-blinkers employ an efficient target selection strategy that relies on well-learned alphabetic and numeric category sets.University of Groningen. Research School Behavioural and Cognitive Neuroscience
Development and operation of a pixel segmented liquid-filled linear array for radiotherapy quality assurance
A liquid isooctane (CH) filled ionization linear array for
radiotherapy quality assurance has been designed, built and tested. The
detector consists of 128 pixels, each of them with an area of 1.7 mm
1.7 mm and a gap of 0.5 mm. The small pixel size makes the detector ideal for
high gradient beam profiles like those present in Intensity Modulated Radiation
Therapy (IMRT) and radiosurgery. As read-out electronics we use the X-Ray Data
Acquisition System (XDAS) with the Xchip developed by the CCLRC.
Studies concerning the collection efficiency dependence on the polarization
voltage and on the dose rate have been made in order to optimize the device
operation.
In the first tests we have studied dose rate and energy dependences, and
signal reproducibility. Dose rate dependence was found lower than 2.5 % up to 5
Gy min, and energy dependence lower than 2.1 % up to 20 cm depth in
solid water. Output factors and penumbras for several rectangular fields have
been measured with the linear array and were compared with the results obtained
with a 0.125 cm air ionization chamber and radiographic film,
respectively. Finally, we have acquired profiles for an IMRT field and for a
virtual wedge. These profiles have also been compared with radiographic film
measurements. All the comparisons show a good correspondence. Signal
reproducibility was within a 2% during the test period (around three months).
The device has proved its capability to verify on-line therapy beams with
good spatial resolution and signal to noise ratio.Comment: 16 pages, 12 figures Submitted to Phys. Med. Bio
Maximal Accuracy and Minimal Disturbance in the Arthurs-Kelly Simultaneous Measurement Process
The accuracy of the Arthurs-Kelly model of a simultaneous measurement of
position and momentum is analysed using concepts developed by Braginsky and
Khalili in the context of measurements of a single quantum observable. A
distinction is made between the errors of retrodiction and prediction. It is
shown that the distribution of measured values coincides with the initial state
Husimi function when the retrodictive accuracy is maximised, and that it is
related to the final state anti-Husimi function (the P representation of
quantum optics) when the predictive accuracy is maximised. The disturbance of
the system by the measurement is also discussed. A class of minimally
disturbing measurements is characterised. It is shown that the distribution of
measured values then coincides with one of the smoothed Wigner functions
described by Cartwright.Comment: 12 pages, 0 figures. AMS-Latex. Earlier version replaced with final
published versio
The Haroche-Ramsey experiment as a generalized measurement
A number of atomic beam experiments, related to the Ramsey experiment and a
recent experiment by Brune et al., are studied with respect to the question of
complementarity. Three different procedures for obtaining information on the
state of the incoming atom are compared. Positive operator-valued measures are
explicitly calculated. It is demonstrated that, in principle, it is possible to
choose the experimental arrangement so as to admit an interpretation as a joint
non-ideal measurement yielding interference and ``which-way'' information.
Comparison of the different measurements gives insight into the question of
which information is provided by a (generalized) quantum mechanical
measurement. For this purpose the subspaces of Hilbert-Schmidt space, spanned
by the operators of the POVM, are determined for different measurement
arrangements and different values of the parameters.Comment: REVTeX, 22 pages, 5 figure
Search for antiproton decay at the Fermilab Antiproton Accumulator
A search for antiproton decay has been made at the Fermilab Antiproton
Accumulator. Limits are placed on thirteen antiproton decay modes. The results
include the first explicit experimental limits on the muonic decay modes of the
antiproton, and the first limits on the decay modes e- gamma gamma, and e-
omega. The most stringent limit is for the decay mode pbar-> e- gamma. At 90%
C.L. we find that tau/B(pbar-> e- gamma) > 7 x 10^5 yr. The most stringent
limit for decay modes with a muon in the final state is for the decay pbar->
mu- gamma. At 90% C.L. we find that tau/B(pbar-> mu- gamma) > 5 x 10^4 yr.Comment: 20 pages, 8 figures. Submitted to Phys. Rev. D. Final results on 13
channels (was 15) are presente
Atomic Layer Deposition-Based Synthesis of Photoactive TiO2 Nanoparticle Chains by Using Carbon Nanotubes as Sacrificial Templates
Highly ordered and self supported anatase TiO2 nanoparticle chains were
fabricated by calcining conformally TiO2 coated multi-walled carbon nanotubes
(MWCNTs). During annealing, the thin tubular TiO2 coating that was deposited
onto the MWCNTs by atomic layer deposition (ALD) was transformed into chains of
TiO2 nanoparticles (~12 nm diameter) with an ultrahigh surface area (137 cm2
per cm2 of substrate), while at the same time the carbon from the MWCNTs was
removed. Photocatalytic tests on the degradation of acetaldehyde proved that
these forests of TiO2 nanoparticle chains are highly photo active under UV
light because of their well crystallized anatase phase
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