9,161 research outputs found
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
Automated Driving and its Effect on the Safety Ecosystem: How do Compatibility Issues Affect the Transition Period?
AbstractDifferent components of automated vehicles are being made available commercially as we speak. Much research has been conducted into these components and many of these have been studied with respect to their effects on safety, but the transition period from non-automated driving to fully automated vehicles raises safety related issues dealing with mixed traffic situations. More in-depth knowledge should be gained in (the safety of) the behaviour of drivers of unequipped vehicles, enabling automated vehicles to predict and adequately respond to potentially unsafe behaviour, a concept we call backwards compatibility. Also, automated vehicle system design tends to be from an optimal system performance perspective which leads to driving patterns such as driving in the centre of a lane. Other (human) road users however likely exhibit driving behaviour in line with different rationales which allow for suboptimal driving patterns. As of yet, it remains unclear whether these patterns contain indications about the intentions of a driver and if or how other road users anticipate these. This could have two consequences with regard to mixed traffic situations. First of all, other road users might miss important cues from the behaviour of the automated vehicle (what we call forward incompatibility). Secondly, the occupant of an automated vehicle might expect human-like behaviour from the automated vehicle in safety-critical situations, lowering acceptance if this does not meet expectations. The current paper considers these issues and states that we need more insight in how road users use other road users’ behaviour to anticipate safety critical events, especially in the transition period towards fully automated vehicles
Multithermal Analysis of a CDS Coronal Loop
The observations from 1998 April 20 taken with the Coronal Diagnostics
Spectrometer CDS on SOHO of a coronal loop on the limb have shown that the
plasma was multi-thermal along each line of sight investigated, both before and
after background subtraction. The latter result relied on Emission Measure Loci
plots, but in this Letter, we used a forward folding technique to produce
Differential Emission Measure curves. We also calculate DEM-weighted
temperatures for the chosen pixels and find a gradient in temperature along the
loop as a function of height that is not compatible with the flat profiles
reported by numerous authors for loops observed with EIT on SOHO and TRACE. We
also find discrepancies in excess of the mathematical expectation between some
of the observed and predicted CDS line intensities. We demonstrate that these
differences result from well-known limitations in our knowledge of the atomic
data and are to be expected. We further show that the precision of the DEM is
limited by the intrinsic width of the ion emissivity functions that are used to
calculate the DEM. Hence we conclude that peaks and valleys in the DEM, while
in principle not impossible, cannot be confirmed from the data.Comment: 12 pages, 3 figures, Accepted by ApJ Letter
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
A Phase Transition for Circle Maps and Cherry Flows
We study weakly order preserving circle maps with a flat interval.
The main result of the paper is about a sharp transition from degenerate
geometry to bounded geometry depending on the degree of the singularities at
the boundary of the flat interval. We prove that the non-wandering set has zero
Hausdorff dimension in the case of degenerate geometry and it has Hausdorff
dimension strictly greater than zero in the case of bounded geometry. Our
results about circle maps allow to establish a sharp phase transition in the
dynamics of Cherry flows
No elliptic islands for the universal area-preserving map
A renormalization approach has been used in \cite{EKW1} and \cite{EKW2} to
prove the existence of a \textit{universal area-preserving map}, a map with
hyperbolic orbits of all binary periods. The existence of a horseshoe, with
positive Hausdorff dimension, in its domain was demonstrated in \cite{GJ1}. In
this paper the coexistence problem is studied, and a computer-aided proof is
given that no elliptic islands with period less than 20 exist in the domain. It
is also shown that less than 1.5% of the measure of the domain consists of
elliptic islands. This is proven by showing that the measure of initial
conditions that escape to infinity is at least 98.5% of the measure of the
domain, and we conjecture that the escaping set has full measure. This is
highly unexpected, since generically it is believed that for conservative
systems hyperbolicity and ellipticity coexist
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
Driven Brownian transport through arrays of symmetric obstacles
We numerically investigate the transport of a suspended overdamped Brownian
particle which is driven through a two-dimensional rectangular array of
circular obstacles with finite radius. Two limiting cases are considered in
detail, namely, when the constant drive is parallel to the principal or the
diagonal array axes. This corresponds to studying the Brownian transport in
periodic channels with reflecting walls of different topologies. The mobility
and diffusivity of the transported particles in such channels are determined as
functions of the drive and the array geometric parameters. Prominent transport
features, like negative differential mobilities, excess diffusion peaks, and
unconventional asymptotic behaviors, are explained in terms of two distinct
lengths, the size of single obstacles (trapping length) and the lattice
constant of the array (local correlation length). Local correlation effects are
further analyzed by continuously rotating the drive between the two limiting
orientations.Comment: 10 pages 13 figure
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