13,570 research outputs found
On the strategy frequency problem in batch Minority Games
Ergodic stationary states of Minority Games with S strategies per agent can
be characterised in terms of the asymptotic probabilities with which
an agent uses of his strategies. We propose here a simple and general
method to calculate these quantities in batch canonical and grand-canonical
models. Known analytic theories are easily recovered as limiting cases and, as
a further application, the strategy frequency problem for the batch
grand-canonical Minority Game with S=2 is solved. The generalization of these
ideas to multi-asset models is also presented. Though similarly based on
response function techniques, our approach is alternative to the one recently
employed by Shayeghi and Coolen for canonical batch Minority Games with
arbitrary number of strategies.Comment: 17 page
On the transition to efficiency in Minority Games
The existence of a phase transition with diverging susceptibility in batch
Minority Games (MGs) is the mark of informationally efficient regimes and is
linked to the specifics of the agents' learning rules. Here we study how the
standard scenario is affected in a mixed population game in which agents with
the `optimal' learning rule (i.e. the one leading to efficiency) coexist with
ones whose adaptive dynamics is sub-optimal. Our generic finding is that any
non-vanishing intensive fraction of optimal agents guarantees the existence of
an efficient phase. Specifically, we calculate the dependence of the critical
point on the fraction of `optimal' agents focusing our analysis on three
cases: MGs with market impact correction, grand-canonical MGs and MGs with
heterogeneous comfort levels.Comment: 12 pages, 3 figures; contribution to the special issue "Viewing the
World through Spin Glasses" in honour of David Sherrington on the occasion of
his 65th birthda
Satellite Luminosities in Galaxy Groups
Halo model interpretations of the luminosity dependence of galaxy clustering
assume that there is a central galaxy in every sufficiently massive halo, and
that this central galaxy is very different from all the others in the halo. The
halo model decomposition makes the remarkable prediction that the mean
luminosity of the non-central galaxies in a halo should be almost independent
of halo mass: the predicted increase is about 20% while the halo mass increases
by a factor of more than 20. In contrast, the luminosity of the central object
is predicted to increase approximately linearly with halo mass at low to
intermediate masses, and logarithmically at high masses. We show that this
weak, almost non-existent mass-dependence of the satellites is in excellent
agreement with the satellite population in group catalogs constructed by two
different collaborations. This is remarkable, because the halo model prediction
was made without ever identifying groups and clusters. The halo model also
predicts that the number of satellites in a halo is drawn from a Poisson
distribution with mean which depends on halo mass. This, combined with the weak
dependence of satellite luminosity on halo mass, suggests that the Scott
effect, such that the luminosities of very bright galaxies are merely the
statistically extreme values of a general luminosity distribution, may better
apply to the most luminous satellite galaxy in a halo than to BCGs. If galaxies
are identified with halo substructure at the present time, then central
galaxies should be about 4 times more massive than satellite galaxies of the
same luminosity, whereas the differences between the stellar M/L ratios should
be smaller. Therefore, a comparison of the weak lensing signal from central and
satellite galaxies should provide useful constraints. [abridged]Comment: 8 pages, 3 figures. Matches version accepted by MNRA
Von Neumann's expanding model on random graphs
Within the framework of Von Neumann's expanding model, we study the maximum
growth rate r achievable by an autocatalytic reaction network in which
reactions involve a finite (fixed or fluctuating) number D of reagents. r is
calculated numerically using a variant of the Minover algorithm, and
analytically via the cavity method for disordered systems. As the ratio between
the number of reactions and that of reagents increases the system passes from a
contracting (r1). These results extend the
scenario derived in the fully connected model (D\to\infinity), with the
important difference that, generically, larger growth rates are achievable in
the expanding phase for finite D and in more diluted networks. Moreover, the
range of attainable values of r shrinks as the connectivity increases.Comment: 20 page
Constrained Allocation Flux Balance Analysis
New experimental results on bacterial growth inspire a novel top-down
approach to study cell metabolism, combining mass balance and proteomic
constraints to extend and complement Flux Balance Analysis. We introduce here
Constrained Allocation Flux Balance Analysis, CAFBA, in which the biosynthetic
costs associated to growth are accounted for in an effective way through a
single additional genome-wide constraint. Its roots lie in the experimentally
observed pattern of proteome allocation for metabolic functions, allowing to
bridge regulation and metabolism in a transparent way under the principle of
growth-rate maximization. We provide a simple method to solve CAFBA efficiently
and propose an "ensemble averaging" procedure to account for unknown protein
costs. Applying this approach to modeling E. coli metabolism, we find that, as
the growth rate increases, CAFBA solutions cross over from respiratory,
growth-yield maximizing states (preferred at slow growth) to fermentative
states with carbon overflow (preferred at fast growth). In addition, CAFBA
allows for quantitatively accurate predictions on the rate of acetate excretion
and growth yield based on only 3 parameters determined by empirical growth
laws.Comment: 21 pages, 6 figures (main) + 33 pages, various figures and tables
(supporting); for the supplementary MatLab code, see
http://tinyurl.com/h763es
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