66,671 research outputs found

### Chaotic temperature dependence in a model of spin glasses

We address the problem of chaotic temperature dependence in disordered glassy
systems at equilibrium by following states of a random-energy random-entropy
model in temperature; of particular interest are the crossings of the
free-energies of these states. We find that this model exhibits strong, weak or
no temperature chaos depending on the value of an exponent. This allows us to
write a general criterion for temperature chaos in disordered systems,
predicting the presence of temperature chaos in the Sherrington-Kirkpatrick and
Edwards-Anderson spin glass models, albeit when the number of spins is large
enough. The absence of chaos for smaller systems may justify why it is
difficult to observe chaos with current simulations. We also illustrate our
findings by studying temperature chaos in the naive mean field equations for
the Edwards-Anderson spin glass.Comment: 10 pages, 5 figures; To be published in European Physics Journal

### A geometrical picture for finite dimensional spin glasses

A controversial issue in spin glass theory is whether mean field correctly
describes 3-dimensional spin glasses. If it does, how can replica symmetry
breaking arise in terms of spin clusters in Euclidean space? Here we argue that
there exist system-size low energy excitations that are sponge-like, generating
multiple valleys separated by diverging energy barriers. The droplet model
should be valid for length scales smaller than the size of the system (theta >
0), but nevertheless there can be system-size excitations of constant energy
without destroying the spin glass phase. The picture we propose then combines
droplet-like behavior at finite length scales with a potentially mean field
behavior at the system-size scale.Comment: 7 pages; modified references, clarifications; to appear in EP

### Scaling universalities of kth-nearest neighbor distances on closed manifolds

Take N sites distributed randomly and uniformly on a smooth closed surface.
We express the expected distance from an arbitrary point on the
surface to its kth-nearest neighboring site, in terms of the function A(l)
giving the area of a disc of radius l about that point. We then find two
universalities. First, for a flat surface, where A(l)=\pi l^2, the k-dependence
and the N-dependence separate in . All kth-nearest neighbor distances
thus have the same scaling law in N. Second, for a curved surface, the average
\int d\mu over the surface is a topological invariant at leading and
subleading order in a large N expansion. The 1/N scaling series then depends,
up through O(1/N), only on the surface's topology and not on its precise shape.
We discuss the case of higher dimensions (d>2), and also interpret our results
using Regge calculus.Comment: 14 pages, 2 figures; submitted to Advances in Applied Mathematic

### 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

### Cut Size Statistics of Graph Bisection Heuristics

We investigate the statistical properties of cut sizes generated by heuristic
algorithms which solve approximately the graph bisection problem. On an
ensemble of sparse random graphs, we find empirically that the distribution of
the cut sizes found by ``local'' algorithms becomes peaked as the number of
vertices in the graphs becomes large. Evidence is given that this distribution
tends towards a Gaussian whose mean and variance scales linearly with the
number of vertices of the graphs. Given the distribution of cut sizes
associated with each heuristic, we provide a ranking procedure which takes into
account both the quality of the solutions and the speed of the algorithms. This
procedure is demonstrated for a selection of local graph bisection heuristics.Comment: 17 pages, 5 figures, submitted to SIAM Journal on Optimization also
available at http://ipnweb.in2p3.fr/~martin

### Large-scale low-energy excitations in 3-d spin glasses

We numerically extract large-scale excitations above the ground state in the
3-dimensional Edwards-Anderson spin glass with Gaussian couplings. We find that
associated energies are O(1), in agreement with the mean field picture. Of
further interest are the position-space properties of these excitations. First,
our study of their topological properties show that the majority of the
large-scale excitations are sponge-like. Second, when probing their geometrical
properties, we find that the excitations coarsen when the system size is
increased. We conclude that either finite size effects are very large even when
the spin overlap q is close to zero, or the mean field picture of homogeneous
excitations has to be modified.Comment: 11 pages, typos corrected, added reference

### 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.

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