72,487 research outputs found
Glass models on Bethe lattices
We consider ``lattice glass models'' in which each site can be occupied by at
most one particle, and any particle may have at most l occupied nearest
neighbors. Using the cavity method for locally tree-like lattices, we derive
the phase diagram, with a particular focus on the vitreous phase and the
highest packing limit. We also study the energy landscape via the
configurational entropy, and discuss different equilibrium glassy phases.
Finally, we show that a kinetic freezing, depending on the particular dynamical
rules chosen for the model, can prevent the equilibrium glass transitions.Comment: 24 pages, 11 figures; minor corrections + enlarged introduction and
conclusio
Edge usage, motifs and regulatory logic for cell cycling genetic networks
The cell cycle is a tightly controlled process, yet its underlying genetic
network shows marked differences across species. Which of the associated
structural features follow solely from the ability to impose the appropriate
gene expression patterns? We tackle this question in silico by examining the
ensemble of all regulatory networks which satisfy the constraint of producing a
given sequence of gene expressions. We focus on three cell cycle profiles
coming from baker's yeast, fission yeast and mammals. First, we show that the
networks in each of the ensembles use just a few interactions that are
repeatedly reused as building blocks. Second, we find an enrichment in network
motifs that is similar in the two yeast cell cycle systems investigated. These
motifs do not have autonomous functions, but nevertheless they reveal a
regulatory logic for cell cycling based on a feed-forward cascade of activating
interactions.Comment: 9 pages, 9 figures, to be published in Phys. Rev.
Symmetry-protected Topological Phases at Finite Temperature
We have applied the recently developed theory of topological Uhlmann numbers
to a representative model of a topological insulator in two dimensions, the
Qi-Wu-Zhang model. We have found a stable symmetry-protected topological (SPT)
phase under external thermal fluctuations in two-dimensions. A complete phase
diagram for this model is computed as a function of temperature and coupling
constants in the original Hamiltonian. It shows the appearance of large stable
phases of matter with topological properties compatible with thermal
fluctuations or external noise and the existence of critical lines separating
abruptly trivial phases from topological phases. These novel critical
temperatures represent thermal topological phase transitions. The initial part
of the paper comprises a self-contained explanation of the Uhlmann geometric
phase needed to understand the topological properties that it may acquire when
applied to topological insulators and superconductors.Comment: Contribution to the focus issue on "Artificial Graphene". Edited by
Maciej Lewenstein, Vittorio Pellegrini, Marco Polini and Mordechai (Moti)
Sege
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