2,509 research outputs found
Adaptive Cluster Expansion for Inferring Boltzmann Machines with Noisy Data
We introduce a procedure to infer the interactions among a set of binary
variables, based on their sampled frequencies and pairwise correlations. The
algorithm builds the clusters of variables contributing most to the entropy of
the inferred Ising model, and rejects the small contributions due to the
sampling noise. Our procedure successfully recovers benchmark Ising models even
at criticality and in the low temperature phase, and is applied to
neurobiological data.Comment: Accepted for publication in Physical Review Letters (2011
Inferring DNA sequences from mechanical unzipping data: the large-bandwidth case
The complementary strands of DNA molecules can be separated when stretched
apart by a force; the unzipping signal is correlated to the base content of the
sequence but is affected by thermal and instrumental noise. We consider here
the ideal case where opening events are known to a very good time resolution
(very large bandwidth), and study how the sequence can be reconstructed from
the unzipping data. Our approach relies on the use of statistical Bayesian
inference and of Viterbi decoding algorithm. Performances are studied
numerically on Monte Carlo generated data, and analytically. We show how
multiple unzippings of the same molecule may be exploited to improve the
quality of the prediction, and calculate analytically the number of required
unzippings as a function of the bandwidth, the sequence content, the elasticity
parameters of the unzipped strands
Boosting search by rare events
Randomized search algorithms for hard combinatorial problems exhibit a large
variability of performances. We study the different types of rare events which
occur in such out-of-equilibrium stochastic processes and we show how they
cooperate in determining the final distribution of running times. As a
byproduct of our analysis we show how search algorithms are optimized by random
restarts.Comment: 4 pages, 3 eps figures. References update
Unzipping Dynamics of Long DNAs
The two strands of the DNA double helix can be `unzipped' by application of
15 pN force. We analyze the dynamics of unzipping and rezipping, for the case
where the molecule ends are separated and re-approached at constant velocity.
For unzipping of 50 kilobase DNAs at less than about 1000 bases per second,
thermal equilibrium-based theory applies. However, for higher unzipping
velocities, rotational viscous drag creates a buildup of elastic torque to
levels above kBT in the dsDNA region, causing the unzipping force to be well
above or well below the equilibrium unzipping force during respectively
unzipping and rezipping, in accord with recent experimental results of Thomen
et al. [Phys. Rev. Lett. 88, 248102 (2002)]. Our analysis includes the effect
of sequence on unzipping and rezipping, and the transient delay in buildup of
the unzipping force due to the approach to the steady state.Comment: 15 pages Revtex file including 9 figure
Solving satisfiability problems by fluctuations: The dynamics of stochastic local search algorithms
Stochastic local search algorithms are frequently used to numerically solve
hard combinatorial optimization or decision problems. We give numerical and
approximate analytical descriptions of the dynamics of such algorithms applied
to random satisfiability problems. We find two different dynamical regimes,
depending on the number of constraints per variable: For low constraintness,
the problems are solved efficiently, i.e. in linear time. For higher
constraintness, the solution times become exponential. We observe that the
dynamical behavior is characterized by a fast equilibration and fluctuations
around this equilibrium. If the algorithm runs long enough, an exponentially
rare fluctuation towards a solution appears.Comment: 21 pages, 18 figures, revised version, to app. in PRE (2003
The dynamics of proving uncolourability of large random graphs I. Symmetric Colouring Heuristic
We study the dynamics of a backtracking procedure capable of proving
uncolourability of graphs, and calculate its average running time T for sparse
random graphs, as a function of the average degree c and the number of vertices
N. The analysis is carried out by mapping the history of the search process
onto an out-of-equilibrium (multi-dimensional) surface growth problem. The
growth exponent of the average running time is quantitatively predicted, in
agreement with simulations.Comment: 5 figure
Beyond inverse Ising model: structure of the analytical solution for a class of inverse problems
I consider the problem of deriving couplings of a statistical model from
measured correlations, a task which generalizes the well-known inverse Ising
problem. After reminding that such problem can be mapped on the one of
expressing the entropy of a system as a function of its corresponding
observables, I show the conditions under which this can be done without
resorting to iterative algorithms. I find that inverse problems are local (the
inverse Fisher information is sparse) whenever the corresponding models have a
factorized form, and the entropy can be split in a sum of small cluster
contributions. I illustrate these ideas through two examples (the Ising model
on a tree and the one-dimensional periodic chain with arbitrary order
interaction) and support the results with numerical simulations. The extension
of these methods to more general scenarios is finally discussed.Comment: 15 pages, 6 figure
Low energy neutrino scattering measurements at future Spallation Source facilities
In the future several Spallation Source facilities will be available
worldwide. Spallation Sources produce large amount of neutrinos from
decay-at-rest muons and thus can be well adapted to accommodate
state-of-the-art neutrino experiments. In this paper low energy neutrino
scattering experiments that can be performed at such facilities are reviewed.
Estimation of expected event rates are given for several nuclei, electrons and
protons at a detector located close to the source. A neutrino program at
Spallation Sources comprises neutrino-nucleus cross section measurements
relevant for neutrino and core-collapse supernova physics, electroweak tests
and lepton-flavor violation searches.Comment: 12 pages, 4 figures, 5 table
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