9,478 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
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
Rashba spin-orbit coupling and spin precession in carbon nanotubes
The Rashba spin-orbit coupling in carbon nanotubes and its effect on
spin-dependent transport properties are analyzed theoretically. We focus on
clean non-interacting nanotubes with tunable number of subbands . The
peculiar band structure is shown to allow in principle for Datta-Das
oscillatory behavior in the tunneling magnetoresistance as a function of gate
voltage, despite the presence of multiple bands. We discuss the conditions for
observing Datta-Das oscillations in carbon nanotubes.Comment: 12 pages, published versio
Statistical mechanics for metabolic networks during steady-state growth
Which properties of metabolic networks can be derived solely from
stoichiometric information about the network's constituent reactions?
Predictive results have been obtained by Flux Balance Analysis (FBA), by
postulating that cells set metabolic fluxes within the allowed stoichiometry so
as to maximize their growth. Here, we generalize this framework to single cell
level using maximum entropy models from statistical physics. We define and
compute, for the core metabolism of Escherichia coli, a joint distribution over
all fluxes that yields the experimentally observed growth rate. This solution,
containing FBA as a limiting case, provides a better match to the measured
fluxes in the wild type and several mutants. We find that E. coli metabolism is
close to, but not at, the optimality assumed by FBA. Moreover, our model makes
a wide range of predictions: (i) on flux variability, its regulation, and flux
correlations across individual cells; (ii) on the relative importance of
stoichiometric constraints vs. growth rate optimization; (iii) on quantitative
scaling relations for singe-cell growth rate distributions. We validate these
scaling predictions using data from individual bacterial cells grown in a
microfluidic device at different sub-inhibitory antibiotic concentrations.
Under mild dynamical assumptions, fluctuation-response relations further
predict the autocorrelation timescale in growth data and growth rate adaptation
times following an environmental perturbation.Comment: 12 pages, 4 figure
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