12,658 research outputs found
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
Glassy states and microphase separation in cross-linked homopolymer blends
The physical properties of blends of distinct homopolymers, cross-linked
beyond the gelation point, are addressed via a Landau approach involving a pair
of coupled order-parameter fields: one describing vulcanisation, the other
describing local phase separation. Thermal concentration fluctuations, present
at the time of cross-linking, are frozen in by cross-linking, and the structure
of the resulting glassy fluctuations is analysed at the Gaussian level in
various regimes, determined by the relative values of certain physical
length-scales. The enhancement, due to gelation, of the stability of the blend
with respect to demixing is also analysed. Beyond the corresponding stability
limit, gelation prevents complete demixing, replacing it by microphase
separation, which occurs up to a length-scale set by the rigidity of the
network, as a simple variational scheme reveals.Comment: 7 pages, 6 figure
Random solids and random solidification: What can be learned by exploring systems obeying permanent random constraints?
In many interesting physical settings, such as the vulcanization of rubber,
the introduction of permanent random constraints between the constituents of a
homogeneous fluid can cause a phase transition to a random solid state. In this
random solid state, particles are permanently but randomly localized in space,
and a rigidity to shear deformations emerges. Owing to the permanence of the
random constraints, this phase transition is an equilibrium transition, which
confers on it a simplicity (at least relative to the conventional glass
transition) in the sense that it is amenable to established techniques of
equilibrium statistical mechanics. In this Paper I shall review recent
developments in the theory of random solidification for systems obeying
permanent random constraints, with the aim of bringing to the fore the
similarities and differences between such systems and those exhibiting the
conventional glass transition. I shall also report new results, obtained in
collaboration with Weiqun Peng, on equilibrium correlations and
susceptibilities that signal the approach of the random solidification
transition, discussing the physical interpretation and values of these
quantities both at the Gaussian level of approximation and, via a
renormalization-group approach, beyond.Comment: Paper presented at the "Unifying Concepts in Glass Physics" workshop,
International Centre for Theoretical Physics, Trieste, Italy (September
15-18, 1999
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
Search for direct production of charginos, neutralinos and sleptons in final states with two leptons and missing transverse momentum in pp collisions at √s = 8TeV with the ATLAS detector
Searches for the electroweak production of charginos, neutralinos and sleptons in final states characterized by the presence of two leptons (electrons and muons) and missing transverse momentum are performed using 20.3 fb−1 of proton-proton collision data at s√ = 8 TeV recorded with the ATLAS experiment at the Large Hadron Collider. No significant excess beyond Standard Model expectations is observed. Limits are set on the masses of the lightest chargino, next-to-lightest neutralino and sleptons for different lightest-neutralino mass hypotheses in simplified models. Results are also interpreted in various scenarios of the phenomenological Minimal Supersymmetric Standard Model
Elasticity near the vulcanization transition
Signatures of the vulcanization transition--amorphous solidification induced
by the random crosslinking of macromolecules--include the random localization
of a fraction of the particles and the emergence of a nonzero static shear
modulus. A semi-microscopic statistical-mechanical theory is presented of the
latter signature that accounts for both thermal fluctuations and quenched
disorder. It is found (i) that the shear modulus grows continuously from zero
at the transition, and does so with the classical exponent, i.e., with the
third power of the excess cross-link density and, quite surprisingly, (ii) that
near the transition the external stresses do not spoil the spherical symmetry
of the localization clouds of the particles.Comment: REVTEX, 5 pages. Minor change
- …