6,245 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 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
Streaming Tree Transducers
Theory of tree transducers provides a foundation for understanding
expressiveness and complexity of analysis problems for specification languages
for transforming hierarchically structured data such as XML documents. We
introduce streaming tree transducers as an analyzable, executable, and
expressive model for transforming unranked ordered trees in a single pass.
Given a linear encoding of the input tree, the transducer makes a single
left-to-right pass through the input, and computes the output in linear time
using a finite-state control, a visibly pushdown stack, and a finite number of
variables that store output chunks that can be combined using the operations of
string-concatenation and tree-insertion. We prove that the expressiveness of
the model coincides with transductions definable using monadic second-order
logic (MSO). Existing models of tree transducers either cannot implement all
MSO-definable transformations, or require regular look ahead that prohibits
single-pass implementation. We show a variety of analysis problems such as
type-checking and checking functional equivalence are solvable for our model.Comment: 40 page
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
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
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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