112 research outputs found
Survival Probability for Open Spherical Billiards
We study the survival probability for long times in an open spherical
billiard, extending previous work on the circular billiard. We provide details
of calculations regarding two billiard configurations, specifically a sphere
with a circular hole and a sphere with a square hole. The constant terms of the
long-term survival probability expansions have been derived analytically. Terms
that vanish in the long time limit are investigated analytically and
numerically, leading to connections with the Riemann hypothesis
Small-Worlds, Mazes and Random Walks
We establish a relationship between the Small-World behavior found in complex
networks and a family of Random Walks trajectories using, as a linking bridge,
a maze iconography. Simple methods to generate mazes using Random Walks are
discussed along with related issues and it is explained how to interpret mazes
as graphs and loops as shortcuts. Small-World behavior was found to be
non-logarithmic but power-law in this model, we discuss the reason for this
peculiar scalingComment: article, 7 figure
On Multifractal Structure in Non-Representational Art
Multifractal analysis techniques are applied to patterns in several abstract
expressionist artworks, paintined by various artists. The analysis is carried
out on two distinct types of structures: the physical patterns formed by a
specific color (``blobs''), as well as patterns formed by the luminance
gradient between adjacent colors (``edges''). It is found that the analysis
method applied to ``blobs'' cannot distinguish between artists of the same
movement, yielding a multifractal spectrum of dimensions between about 1.5-1.8.
The method can distinguish between different types of images, however, as
demonstrated by studying a radically different type of art. The data suggests
that the ``edge'' method can distinguish between artists in the same movement,
and is proposed to represent a toy model of visual discrimination. A ``fractal
reconstruction'' analysis technique is also applied to the images, in order to
determine whether or not a specific signature can be extracted which might
serve as a type of fingerprint for the movement. However, these results are
vague and no direct conclusions may be drawn.Comment: 53 pp LaTeX, 10 figures (ps/eps
Including metabolite concentrations into flux balance analysis: thermodynamic realizability as a constraint on flux distributions in metabolic networks
<p>Abstract</p> <p>Background</p> <p>In recent years, constrained optimization – usually referred to as flux balance analysis (FBA) – has become a widely applied method for the computation of stationary fluxes in large-scale metabolic networks. The striking advantage of FBA as compared to kinetic modeling is that it basically requires only knowledge of the stoichiometry of the network. On the other hand, results of FBA are to a large degree hypothetical because the method relies on plausible but hardly provable optimality principles that are thought to govern metabolic flux distributions.</p> <p>Results</p> <p>To augment the reliability of FBA-based flux calculations we propose an additional side constraint which assures thermodynamic realizability, i.e. that the flux directions are consistent with the corresponding changes of Gibb's free energies. The latter depend on metabolite levels for which plausible ranges can be inferred from experimental data. Computationally, our method results in the solution of a mixed integer linear optimization problem with quadratic scoring function. An optimal flux distribution together with a metabolite profile is determined which assures thermodynamic realizability with minimal deviations of metabolite levels from their expected values. We applied our novel approach to two exemplary metabolic networks of different complexity, the metabolic core network of erythrocytes (30 reactions) and the metabolic network iJR904 of <it>Escherichia coli </it>(931 reactions). Our calculations show that increasing network complexity entails increasing sensitivity of predicted flux distributions to variations of standard Gibb's free energy changes and metabolite concentration ranges. We demonstrate the usefulness of our method for assessing critical concentrations of external metabolites preventing attainment of a metabolic steady state.</p> <p>Conclusion</p> <p>Our method incorporates the thermodynamic link between flux directions and metabolite concentrations into a practical computational algorithm. The weakness of conventional FBA to rely on intuitive assumptions about the reversibility of biochemical reactions is overcome. This enables the computation of reliable flux distributions even under extreme conditions of the network (e.g. enzyme inhibition, depletion of substrates or accumulation of end products) where metabolite concentrations may be drastically altered.</p
Mind the Gap: Transitions Between Concepts of Information in Varied Domains
The concept of 'information' in five different realms – technological, physical, biological, social and philosophical – is briefly examined. The 'gaps' between these conceptions are dis‐ cussed, and unifying frameworks of diverse nature, including those of Shannon/Wiener, Landauer, Stonier, Bates and Floridi, are examined. The value of attempting to bridge the gaps, while avoiding shallow analogies, is explained. With information physics gaining general acceptance, and biology gaining the status of an information science, it seems rational to look for links, relationships, analogies and even helpful metaphors between them and the library/information sciences. Prospects for doing so, involving concepts of complexity and emergence, are suggested
Symmetry groups of fractals
This paper contains computer pictures of generalised
Mandelbrot and Mandelbar sets, and their associated
Julia sets, from which it is evident that their symmetry
groups possess an elegant and simple structure. We
show that (i) the Mandelbrot set M(p) generated by the
iteration zt+ ~ = ztp + c remains invariant under the
symmetry transforms of the dihedral group Dp_ 1 (i.e.,
these are isomet-ries of M(p)); (ii) the Mandelbar set
M(p) is invariant under the isometries inDp + 1; and (iii)
the Julia sets of points inside M(p) (or M(p)) are invariant
under the isometries in either Dp or just the cyclic
group Cp, depending on whether the seed point is on
or off a symmetry axis of the parent Mandelbrot (or
Mandelbar) set. The proofs are relatively easy, but
showing that there are no other isometries of these sets
is not so straightforward. As is often the case in the
theory of chaos, what is obvious geometrically is difficult
to prove analytically. For the generalised Mandelbrot
and Mandelbar sets with even p we have in fact
proved that the dihedral symmetry transforms are the
only isometries of these sets, but the method does not
appear to be applicable to odd p, or to the Julia sets
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