231 research outputs found
Evolutionary branching in a stochastic population model with discrete mutational steps
Evolutionary branching is analysed in a stochastic, individual-based
population model under mutation and selection. In such models, the common
assumption is that individual reproduction and life career are characterised by
values of a trait, and also by population sizes, and that mutations lead to
small changes in trait value. Then, traditionally, the evolutionary dynamics is
studied in the limit of vanishing mutational step sizes. In the present
approach, small but non-negligible mutational steps are considered. By means of
theoretical analysis in the limit of infinitely large populations, as well as
computer simulations, we demonstrate how discrete mutational steps affect the
patterns of evolutionary branching. We also argue that the average time to the
first branching depends in a sensitive way on both mutational step size and
population size.Comment: 12 pages, 8 figures. Revised versio
Discrete Feynman-Kac formulas for branching random walks
Branching random walks are key to the description of several physical and
biological systems, such as neutron multiplication, genetics and population
dynamics. For a broad class of such processes, in this Letter we derive the
discrete Feynman-Kac equations for the probability and the moments of the
number of visits of the walker to a given region in the phase space.
Feynman-Kac formulas for the residence times of Markovian processes are
recovered in the diffusion limit.Comment: 4 pages, 3 figure
Daphnias: from the individual based model to the large population equation
The class of deterministic 'Daphnia' models treated by Diekmann et al. (J
Math Biol 61: 277-318, 2010) has a long history going back to Nisbet and Gurney
(Theor Pop Biol 23: 114-135, 1983) and Diekmann et al. (Nieuw Archief voor
Wiskunde 4: 82-109, 1984). In this note, we formulate the individual based
models (IBM) supposedly underlying those deterministic models. The models treat
the interaction between a general size-structured consumer population
('Daphnia') and an unstructured resource ('algae'). The discrete, size and
age-structured Daphnia population changes through births and deaths of its
individuals and throught their aging and growth. The birth and death rates
depend on the sizes of the individuals and on the concentration of the algae.
The latter is supposed to be a continuous variable with a deterministic
dynamics that depends on the Daphnia population. In this model setting we prove
that when the Daphnia population is large, the stochastic differential equation
describing the IBM can be approximated by the delay equation featured in
(Diekmann et al., l.c.)
A weighted configuration model and inhomogeneous epidemics
A random graph model with prescribed degree distribution and degree dependent
edge weights is introduced. Each vertex is independently equipped with a random
number of half-edges and each half-edge is assigned an integer valued weight
according to a distribution that is allowed to depend on the degree of its
vertex. Half-edges with the same weight are then paired randomly to create
edges. An expression for the threshold for the appearance of a giant component
in the resulting graph is derived using results on multi-type branching
processes. The same technique also gives an expression for the basic
reproduction number for an epidemic on the graph where the probability that a
certain edge is used for transmission is a function of the edge weight. It is
demonstrated that, if vertices with large degree tend to have large (small)
weights on their edges and if the transmission probability increases with the
edge weight, then it is easier (harder) for the epidemic to take off compared
to a randomized epidemic with the same degree and weight distribution. A recipe
for calculating the probability of a large outbreak in the epidemic and the
size of such an outbreak is also given. Finally, the model is fitted to three
empirical weighted networks of importance for the spread of contagious diseases
and it is shown that can be substantially over- or underestimated if the
correlation between degree and weight is not taken into account
Multifrequency VLA observations of the FR I radio galaxy 3C 31: morphology, spectrum and magnetic field
We present high-quality VLA images of the FR I radio galaxy 3C 31 in the
frequency range 1365 to 8440 MHz with angular resolutions from 0.25 to 40
arcsec. Our new images reveal complex, well resolved filamentary substructure
in the radio jets and tails. We also use these images to explore the spectral
structure of 3C 31 on large and small scales. We infer the apparent magnetic
field structure by correcting for Faraday rotation. Some of the intensity
substructure in the jets is clearly related to structure in their apparent
magnetic field: there are arcs of emission where the degree of linear
polarization increases, with the apparent magnetic field parallel to the ridges
of the arcs. The spectral indices are significantly steeper (0.62) within 7
arcsec of the nucleus than between 7 and 50 arcsec (0.52 - 0.57). The spectra
of the jet edges are also slightly flatter than the average for their
surroundings. At larger distances, the jets are clearly delimited from
surrounding larger-scale emission both by their flatter radio spectra and by
sharp brightness gradients. The spectral index of 0.62 in the first 7 arcsec of
3C 31's jets is very close to that found in other FR I galaxies where their
jets first brighten in the radio and where X-ray synchrotron emission is most
prominent. Farther from the nucleus, where the spectra flatten, X-ray emission
is fainter relative to the radio. The brightest X-ray emission from FR I jets
is therefore not associated with the flattest radio spectra, but with a
particle-acceleration process whose characteristic energy index is 2.24. The
spectral flattening with distance from the nucleus occurs where our
relativistic jet models require deceleration, and the flatter-spectra at the
jet edges may be associated with transverse velocity shear. (Slightly abridged)Comment: 17 pages, 13 figures, accepted for publication in MNRA
The 74MHz System on the Very Large Array
The Naval Research Laboratory and the National Radio Astronomy Observatory
completed implementation of a low frequency capability on the VLA at 73.8 MHz
in 1998. This frequency band offers unprecedented sensitivity (~25 mJy/beam)
and resolution (~25 arcsec) for low-frequency observations. We review the
hardware, the calibration and imaging strategies, comparing them to those at
higher frequencies, including aspects of interference excision and wide-field
imaging. Ionospheric phase fluctuations pose the major difficulty in
calibrating the array. Over restricted fields of view or at times of extremely
quiescent ionospheric ``weather'', an angle-invariant calibration strategy can
be used. In this approach a single phase correction is devised for each
antenna, typically via self-calibration. Over larger fields of view or at times
of more normal ionospheric ``weather'' when the ionospheric isoplanatic patch
size is smaller than the field of view, we adopt a field-based strategy in
which the phase correction depends upon location within the field of view. This
second calibration strategy was implemented by modeling the ionosphere above
the array using Zernike polynomials. Images of 3C sources of moderate strength
are provided as examples of routine, angle-invariant calibration and imaging.
Flux density measurements indicate that the 74 MHz flux scale at the VLA is
stable to a few percent, and tied to the Baars et al. value of Cygnus A at the
5 percent level. We also present an example of a wide-field image, devoid of
bright objects and containing hundreds of weaker sources, constructed from the
field-based calibration. We close with a summary of lessons the 74 MHz system
offers as a model for new and developing low-frequency telescopes. (Abridged)Comment: 73 pages, 46 jpeg figures, to appear in ApJ
Introducing a Pictographic Language for Envisioning a Rich Variety of Enactive Systems with Different Degrees of Complexity
Notwithstanding the considerable amount of progress that has been made in recent years, the parallel fields of cognitive science and cognitive systems lack a unifying methodology for describing, understanding, simulating and implementing advanced cognitive behaviours. Growing interest in ’enactivism’ - as pioneered by the Chilean biologists Humberto Maturana and Francisco Varela - may lead to new perspectives in these areas, but a common framework for expressing many of the key concepts is still missing. This paper attempts to lay a tentative foundation in that direction by extending Maturana and Varela’s pictographic depictions of autopoietic unities to create a rich visual language for envisioning a wide range of enactive systems - natural or artificial - with different degrees of complexity. It is shown how such a diagrammatic taxonomy can help in the comprehension of important relationships between a variety of complex concepts from a pan-theoretic perspective. In conclusion, it is claimed that visual language is not only valuable for teaching and learning, but also offers important insights into the design and implementation of future advanced robotic systems
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