6,100 research outputs found
Dynamics of multi-frequency minority games
The dynamics of minority games with agents trading on different time scales
is studied via dynamical mean-field theory. We analyze the case where the
agents' decision-making process is deterministic and its stochastic
generalization with finite heterogeneous learning rates. In each case, we
characterize the macroscopic properties of the steady states resulting from
different frequency and learning rate distributions and calculate the
corresponding phase diagrams. Finally, the different roles played by regular
and occasional traders, as well as their impact on the system's global
efficiency, are discussed.Comment: 9 pages, 5 figure
Percolation and lack of self-averaging in a frustrated evolutionary model
We present a stochastic evolutionary model obtained through a perturbation of
Kauffman's maximally rugged model, which is recovered as a special case. Our
main results are: (i) existence of a percolation-like phase transition in the
finite phase space case; (ii) existence of non self-averaging effects in the
thermodynamic limit. Lack of self-averaging emerges from a fragmentation of the
space of all possible evolutions, analogous to that of a geometrically broken
object. Thus the model turns out to be exactly solvable in the thermodynamic
limit.Comment: 22 pages, 1 figur
Maximal irredundant families of minimal size in the alternating group
Let be a finite group. A family of maximal subgroups of
is called `irredundant' if its intersection is not equal to the intersection of
any proper subfamily. is called `maximal irredundant' if
is irredundant and it is not properly contained in any other
irredundant family. We denote by \mbox{Mindim}(G) the minimal size of a
maximal irredundant family of . In this paper we compute \mbox{Mindim}(G)
when is the alternating group on letters
Covers and Normal Covers of Finite Groups
For a finite non cyclic group , let be the smallest integer
such that contains proper subgroups with the
property that every element of is contained in for some and We prove that if is a noncyclic permutation
group of degree then We then investigate the
structure of the groups with (where is
the size of a minimal cover of ) and of those with $\gamma(G)=2.
Statistics of optimal information flow in ensembles of regulatory motifs
Genetic regulatory circuits universally cope with different sources of noise
that limit their ability to coordinate input and output signals. In many cases,
optimal regulatory performance can be thought to correspond to configurations
of variables and parameters that maximize the mutual information between inputs
and outputs. Such optima have been well characterized in several biologically
relevant cases over the past decade. Here we use methods of statistical field
theory to calculate the statistics of the maximal mutual information (the
`capacity') achievable by tuning the input variable only in an ensemble of
regulatory motifs, such that a single controller regulates N targets. Assuming
(i) sufficiently large N, (ii) quenched random kinetic parameters, and (iii)
small noise affecting the input-output channels, we can accurately reproduce
numerical simulations both for the mean capacity and for the whole
distribution. Our results provide insight into the inherent variability in
effectiveness occurring in regulatory systems with heterogeneous kinetic
parameters.Comment: 14 pages, 6 figure
Quantifying the entropic cost of cellular growth control
We quantify the amount of regulation required to control growth in living
cells by a Maximum Entropy approach to the space of underlying metabolic states
described by genome-scale models. Results obtained for E. coli and human cells
are consistent with experiments and point to different regulatory strategies by
which growth can be fostered or repressed. Moreover we explicitly connect the
`inverse temperature' that controls MaxEnt distributions to the growth
dynamics, showing that the initial size of a colony may be crucial in
determining how an exponentially growing population organizes the phenotypic
space.Comment: 3 page
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