191 research outputs found

### On the Helix-Coil transition in grafted chains

The helix-coil transition is modified by grafting to a surface. This
modification is studied for short peptides capable of forming $\alpha$-helices.
Three factors are involved: (i) the grafting can induced change of the boundary
free energy of the helical domain (ii) the van der Waals attraction between the
helices and (iii) the crowding induced stretching of the coils. As a result the
helix-coil transition acquires ``all or nothing'' characteristics. In addition
the transition temperature is elevated and the transition itself sharpens as
the grafting density increases.Comment: 6 pages, 1 figures, europhys.sty and euromacro.sty Submitted to
Europhys. Let

### Reply to A. Louis Comment

Reply to A. Louis Comment: Fluid-solid phase-separation in hard-sphere
mixtures is unrelated to bond-percolationComment: Reply to a comment of PRL 82 p960 To be published in PR

### Rigorous Bounds to Retarded Learning

We show that the lower bound to the critical fraction of data needed to infer
(learn) the orientation of the anisotropy axis of a probability distribution,
determined by Herschkowitz and Opper [Phys.Rev.Lett. 86, 2174 (2001)], is not
always valid. If there is some structure in the data along the anisotropy axis,
their analysis is incorrect, and learning is possible with much less data
points.Comment: 1 page, 1 figure. Comment accepted for publication in Physical Review
Letter

### Finite size scaling of the bayesian perceptron

We study numerically the properties of the bayesian perceptron through a
gradient descent on the optimal cost function. The theoretical distribution of
stabilities is deduced. It predicts that the optimal generalizer lies close to
the boundary of the space of (error-free) solutions. The numerical simulations
are in good agreement with the theoretical distribution. The extrapolation of
the generalization error to infinite input space size agrees with the
theoretical results. Finite size corrections are negative and exhibit two
different scaling regimes, depending on the training set size. The variance of
the generalization error vanishes for $N \rightarrow \infty$ confirming the
property of self-averaging.Comment: RevTeX, 7 pages, 7 figures, submitted to Phys. Rev.

### Kovacs effect and fluctuation-dissipation relations in 1D kinetically constrained models

Strong and fragile glass relaxation behaviours are obtained simply changing
the constraints of the kinetically constrained Ising chain from symmetric to
purely asymmetric. We study the out-of-equilibrium dynamics of those two models
focusing on the Kovacs effect and the fluctuation--dissipation relations. The
Kovacs or memory effect, commonly observed in structural glasses, is present
for both constraints but enhanced with the asymmetric ones. Most surprisingly,
the related fluctuation-dissipation (FD) relations satisfy the FD theorem in
both cases. This result strongly differs from the simple quenching procedure
where the asymmetric model presents strong deviations from the FD theorem.Comment: 13 pages and 7 figures. To be published in J. Phys.

### Phase transitions in optimal unsupervised learning

We determine the optimal performance of learning the orientation of the
symmetry axis of a set of P = alpha N points that are uniformly distributed in
all the directions but one on the N-dimensional sphere. The components along
the symmetry breaking direction, of unitary vector B, are sampled from a
mixture of two gaussians of variable separation and width. The typical optimal
performance is measured through the overlap Ropt=B.J* where J* is the optimal
guess of the symmetry breaking direction. Within this general scenario, the
learning curves Ropt(alpha) may present first order transitions if the clusters
are narrow enough. Close to these transitions, high performance states can be
obtained through the minimization of the corresponding optimal potential,
although these solutions are metastable, and therefore not learnable, within
the usual bayesian scenario.Comment: 9 pages, 8 figures, submitted to PRE, This new version of the paper
contains one new section, Bayesian versus optimal solutions, where we explain
in detail the results supporting our claim that bayesian learning may not be
optimal. Figures 4 of the first submission was difficult to understand. We
replaced it by two new figures (Figs. 4 and 5 in this new version) containing
more detail

### Optical conductivity of URu$_2$Si$_2$ in the Kondo Liquid and Hidden-Order Phases

We measured the polarized optical conductivity of URu$_2$Si$_2$ from room
temperature down to 5 K, covering the Kondo state, the coherent Kondo liquid
regime, and the hidden-order phase. The normal state is characterized by an
anisotropic behavior between the ab plane and c axis responses. The ab plane
optical conductivity is strongly influenced by the formation of the coherent
Kondo liquid: a sharp Drude peak develops and a hybridization gap at 12 meV
leads to a spectral weight transfer to mid-infrared energies. The c axis
conductivity has a different behavior: the Drude peak already exists at 300 K
and no particular anomaly or gap signature appears in the coherent Kondo liquid
regime. When entering the hidden-order state, both polarizations see a dramatic
decrease in the Drude spectral weight and scattering rate, compatible with a
loss of about 50 % of the carriers at the Fermi level. At the same time a
density-wave like gap appears along both polarizations at about 6.5 meV at 5 K.
This gap closes respecting a mean field thermal evolution in the ab plane.
Along the c axis it remains roughly constant and it "fills up" rather than
closing.Comment: 10 pages, 7 figure

### The Effects of Stacking on the Configurations and Elasticity of Single Stranded Nucleic Acids

Stacking interactions in single stranded nucleic acids give rise to
configurations of an annealed rod-coil multiblock copolymer. Theoretical
analysis identifies the resulting signatures for long homopolynucleotides: A
non monotonous dependence of size on temperature, corresponding effects on
cyclization and a plateau in the extension force law. Explicit numerical
results for poly(dA) and poly(rU) are presented.Comment: 4 pages and 2 figures. Accepted in Phys. Rev. E Rapid Com

### Topological Quantum Glassiness

Quantum tunneling often allows pathways to relaxation past energy barriers
which are otherwise hard to overcome classically at low temperatures. However,
this is not always the case. In this paper we provide simple exactly solvable
examples where the barriers each system encounters on its approach to lower and
lower energy states become increasingly large and eventually scale with the
system size. If the environment couples locally to the physical degrees of
freedom in the system, tunnelling under large barriers requires processes whose
order in perturbation theory is proportional to the width of the barrier. This
results in quantum relaxation rates that are exponentially suppressed in system
size: For these quantum systems, no physical bath can provide a mechanism for
relaxation that is not dynamically arrested at low temperatures. The examples
discussed here are drawn from three dimensional generalizations of Kitaev's
toric code, originally devised in the context of topological quantum computing.
They are devoid of any local order parameters or symmetry breaking and are thus
examples of topological quantum glasses. We construct systems that have slow
dynamics similar to either strong or fragile glasses. The example with
fragile-like relaxation is interesting in that the topological defects are
neither open strings or regular open membranes, but fractal objects with
dimension $d^* = ln 3/ ln 2$.Comment: (18 pages, 4 figures, v2: typos and updated figure); Philosophical
Magazine (2011

### Fluctuation-dissipation relations in the activated regime of simple strong-glass models

We study the out-of-equilibrium fluctuation-dissipation (FD) relations in the
low temperature, finite time, physical aging regime of two simple models with
strong glass behaviour, the Fredrickson-Andersen model and the square-plaquette
interaction model. We explicitly show the existence of unique, waiting-time
independent dynamical FD relations. While in the Fredrickson-Andersen model the
FD theorem is obeyed at all times, the plaquette model displays piecewise
linear FD relations, similar to what is found in disordered mean-field models
and in simulations of supercooled liquids, and despite the fact that its static
properties are trivial. We discuss the wider implications of these results.Comment: 4 pages, 3 figure

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