14,883 research outputs found
R-local Delaunay inhibition model
Let us consider the local specification system of Gibbs point process with
inhib ition pairwise interaction acting on some Delaunay subgraph specifically
not con taining the edges of Delaunay triangles with circumscribed circle of
radius grea ter than some fixed positive real value . Even if we think that
there exists at least a stationary Gibbs state associated to such system, we do
not know yet how to prove it mainly due to some uncontrolled "negative"
contribution in the expression of the local energy needed to insert any number
of points in some large enough empty region of the space. This is solved by
introducing some subgraph, called the -local Delaunay graph, which is a
slight but tailored modification of the previous one. This kind of model does
not inherit the local stability property but satisfies s ome new extension
called -local stability. This weakened property combined with the local
property provides the existence o f Gibbs state.Comment: soumis \`{a} Journal of Statistical Physics 27 page
The dynamics of individual nucleosomes controls the chromatin condensation pathway: direct AFM visualization of variant chromatin
Chromatin organization and dynamics is studied in this work at scales ranging
from single nucleosome to nucleosomal array by using a unique combination of
biochemical assays, single molecule imaging technique and numerical modeling.
We demonstrate that a subtle modification in the nucleosome structure induced
by the histone variant H2A.Bbd drastically modifies the higher order
organization of the nucleosomal arrays. Importantly, as directly visualized by
AFM, conventional H2A nucleosomal arrays exhibit specific local organization,
in contrast to H2A.Bbd arrays, which show "beads on a string" structure. The
combination of systematic image analysis and theoretical modeling allows a
quantitative description relating the observed gross structural changes of the
arrays to their local organization. Our results strongly suggest that
higher-order organization of H1-free nucleosomal arrays is mainly determined by
the fluctuation properties of individual nucleosomes. Moreover, numerical
simulations suggest the existence of attractive interactions between
nucleosomes to provide the degree of compaction observed for conventional
chromatin fibers.Comment: Biophys J. in pres
Asymmetric simple exclusion process on a ring conditioned on enhanced flux
We show that in the asymmetric simple exclusion process (ASEP) on a ring,
conditioned on carrying a large flux, the particle experience an effective
long-range potential which in the limit of very large flux takes the simple
form , where are the particle positions, similar to the effective
potential between the eigenvalues of the circular unitary ensemble in random
matrices. Effective hopping rates and various quasistationary probabilities
under such a conditioning are found analytically using the Bethe ansatz and
determinantal free fermion techniques. Our asymptotic results extend to the
limit of large current and large activity for a family of reaction-diffusion
processes with on-site exclusion between particles. We point out an intriguing
generic relation between classical stationary probability distributions for
conditioned dynamics and quantum ground state wave functions, in particular, in
the case of exclusion processes, for free fermions.Comment: submitted to J. Stat. Mec
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