The solution space of metabolic networks: producibility, robustness and fluctuations

Flux analysis is a class of constraint-based approaches to the study of biochemical reaction networks: they are based on determining the reaction flux configurations compatible with given stoichiometric and thermodynamic constraints. One of its main areas of application is the study of cellular metabolic networks. We briefly and selectively review the main approaches to this problem and then, building on recent work, we provide a characterization of the productive capabilities of the metabolic network of the bacterium E.coli in a specified growth medium in terms of the producible biochemical species. While a robust and physiologically meaningful production profile clearly emerges (including biomass components, biomass products, waste etc.), the underlying constraints still allow for significant fluctuations even in key metabolites like ATP and, as a consequence, apparently lay the ground for very different growth scenarios.Comment: 10 pages, prepared for the Proceedings of the International Workshop on Statistical-Mechanical Informatics, March 7-10, 2010, Kyoto, Japa

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 $q$ 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

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 $\phi_a$ with which an agent uses $a$ 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

Wavevector-dependent spin filtering and spin transport through magnetic barriers in graphene

We study the spin-resolved transport through magnetic nanostructures in monolayer and bilayer graphene. We take into account both the orbital effect of the inhomogeneous perpendicular magnetic field as well as the in-plane spin splitting due to the Zeeman interaction and to the exchange coupling possibly induced by the proximity of a ferromagnetic insulator. We find that a single barrier exhibits a wavevector-dependent spin filtering effect at energies close to the transmission threshold. This effect is significantly enhanced in a resonant double barrier configuration, where the spin polarization of the outgoing current can be increased up to 100% by increasing the distance between the barriers

Tricritical Ising Model with a Boundary

We study the integrable and supersymmetric massive $\hat\phi_{(1,3)}$ deformation of the tricritical Ising model in the presence of a boundary. We use constraints from supersymmetry in order to compute the exact boundary $S$-matrices, which turn out to depend explicitly on the topological charge of the supersymmetry algebra. We also solve the general boundary Yang-Baxter equation and show that in appropriate limits the general reflection matrices go over the supersymmetry preserving solutions. Finally, we briefly discuss the possible connection between our reflection matrices and boundary perturbations within the framework of perturbed boundary conformal field theory

Effective low-energy theory of superconductivity in carbon nanotube ropes

We derive and analyze the low-energy theory of superconductivity in carbon nanotube ropes. A rope is modelled as an array of metallic nanotubes, taking into account phonon-mediated as well as Coulomb interactions, and arbitrary Cooper pair hopping amplitudes (Josephson couplings) between different tubes. We use a systematic cumulant expansion to construct the Ginzburg-Landau action including quantum fluctuations. The regime of validity is carefully established, and the effect of phase slips is assessed. Quantum phase slips are shown to cause a depression of the critical temperature Tc below the mean-field value, and a temperature-dependent resistance below Tc. We compare our theoretical results to recent experimental data of Kasumov {\sl et al.} [Phys. Rev. B {\bf 68}, 214521 (2003)] for the sub-$T_c$ resistance, and find good agreement with only one free fit parameter. Ropes of nanotubes therefore represent superconductors in the one-dimensional few-channel limit

Abelian Hall Fluids and Edge States: a Conformal Field Theory Approach

We show that a Coulomb gas Vertex Operator representation of 2D Conformal Field Theory gives a complete description of abelian Hall fluids: as an euclidean theory in two space dimensions leads to the construction of the ground state wave function for planar and toroidal geometry and characterizes the spectrum of low energy excitations; as a $1+1$ Minkowski theory gives the corresponding dynamics of the edge states. The difference between a generic Hall fluid and states of the Jain's sequences is emphasized and the presence, in the latter case, of of an $\hat {U}(1)\otimes \hat {SU}(n)$ extended algebra and the consequent propagation on the edges of a single charged mode and $n-1$ neutral modes is discussed.Comment: Latex, 22 page

Quantum Integrability of Certain Boundary Conditions

We study the quantum integrability of the O(N) nonlinear $\sigma$ (nls) model and the O(N) Gross-Neveu (GN) model on the half-line. We show that the \nls model is integrable with Neumann, Dirichlet and a mixed boundary condition, and that the GN model is integrable if \psi_+^a\x=\pm\psi_-^a\x. We also comment on the boundary condition found by Corrigan and Sheng for the O(3) nls model.Comment: 11 pages, Latex file, minor changes, one reference adde