345 research outputs found
Approximating the monomer-dimer constants through matrix permanent
The monomer-dimer model is fundamental in statistical mechanics. However, it
is #P-complete in computation, even for two dimensional problems. A
formulation in matrix permanent for the partition function of the monomer-dimer
model is proposed in this paper, by transforming the number of all matchings of
a bipartite graph into the number of perfect matchings of an extended bipartite
graph, which can be given by a matrix permanent. Sequential importance sampling
algorithm is applied to compute the permanents. For two-dimensional lattice
with periodic condition, we obtain , where the exact value is
. For three-dimensional lattice with periodic condition,
our numerical result is , {which agrees with the best known
bound .}Comment: 6 pages, 2 figure
Matrix permanent and quantum entanglement of permutation invariant states
We point out that a geometric measure of quantum entanglement is related to
the matrix permanent when restricted to permutation invariant states. This
connection allows us to interpret the permanent as an angle between vectors. By
employing a recently introduced permanent inequality by Carlen, Loss and Lieb,
we can prove explicit formulas of the geometric measure for permutation
invariant basis states in a simple way.Comment: 10 page
Probabilities in the inflationary multiverse
Inflationary cosmology leads to the picture of a "multiverse," involving an
infinite number of (spatially infinite) post-inflationary thermalized regions,
called pocket universes. In the context of theories with many vacua, such as
the landscape of string theory, the effective constants of Nature are
randomized by quantum processes during inflation. We discuss an analytic
estimate for the volume distribution of the constants within each pocket
universe. This is based on the conjecture that the field distribution is
approximately ergodic in the diffusion regime, when the dynamics of the fields
is dominated by quantum fluctuations (rather than by the classical drift). We
then propose a method for determining the relative abundances of different
types of pocket universes. Both ingredients are combined into an expression for
the distribution of the constants in pocket universes of all types.Comment: 18 pages, RevTeX 4, 2 figures. Discussion of the full probability in
Sec.VI is sharpened; the conclusions are strengthened. Note added explaining
the relation to recent work by Easther, Lim and Martin. Some references adde
Zeros of the i.i.d. Gaussian power series: a conformally invariant determinantal process
Consider the zero set of the random power series f(z)=sum a_n z^n with i.i.d.
complex Gaussian coefficients a_n. We show that these zeros form a
determinantal process: more precisely, their joint intensity can be written as
a minor of the Bergman kernel. We show that the number of zeros of f in a disk
of radius r about the origin has the same distribution as the sum of
independent {0,1}-valued random variables X_k, where P(X_k=1)=r^{2k}. Moreover,
the set of absolute values of the zeros of f has the same distribution as the
set {U_k^{1/2k}} where the U_k are i.i.d. random variables uniform in [0,1].
The repulsion between zeros can be studied via a dynamic version where the
coefficients perform Brownian motion; we show that this dynamics is conformally
invariant.Comment: 37 pages, 2 figures, updated proof
Immobilization of aminophenylboronic acid on magnetic beads for the direct determination of glycoproteins by matrix assisted laser desorption ionization mass spectrometry
Post-processing with linear optics for improving the quality of single-photon sources
Published versio
All-loop calculation of the Reggeon field theory amplitudes via stochastic model
The evolution equations for Green functions of the Reggeon Field Theory (RFT)
are equivalent to those of the inclusive distributions for the
reaction-diffusion system of classical particles. We use this equivalence to
obtain numerically Green functions and amplitudes of the RFT with all loop
contributions included. The numerical realization of the approach is described
and some important applications including total and elastic proton--proton
cross sections are studied. It is shown that the loop diagram contribution is
essential but can be imitated in the eikonal cross section description by
changing the Pomeron intercept. A role of the quartic Pomeron coupling which is
an inherent part of the stochastic model is shown to be negligible for
available energies.Comment: In v2: discussion extended and one new figure added within section 4.
References added in sections 1 and
Somersault of Paramecium in extremely confined environments
We investigate various swimming modes of Paramecium in geometric confinements and a non-swimming self-bending behavior like a somersault, which is quite different from the previously reported behaviors. We observe that Paramecia execute directional sinusoidal trajectories in thick fluid films, whereas Paramecia meander around a localized region and execute frequent turns due to collisions with adjacent walls in thin fluid films. When Paramecia are further constrained in rectangular channels narrower than the length of the cell body, a fraction of meandering Paramecia buckle their body by pushing on the channel walls. The bucking (self-bending) of the cell body allows the Paramecium to reorient its anterior end and explore a completely new direction in extremely confined spaces. Using force deflection method, we quantify the Young’s modulus of the cell and estimate the swimming and bending powers exerted by Paramecium. The analysis shows that Paramecia can utilize a fraction of its swimming power to execute the self-bending maneuver within the confined channel and no extra power may be required for this new kind of self-bending behavior. This investigation sheds light on how micro-organisms can use the flexibility of the body to actively navigate within confined spaces
Role of the Epigenetic Regulator HP1γ in the Control of Embryonic Stem Cell Properties
The unique properties of embryonic stem cells (ESC) rely on long-lasting self-renewal and their ability to switch in all adult cell type programs. Recent advances have shown that regulations at the chromatin level sustain both ESC properties along with transcription factors. We have focused our interest on the epigenetic modulator HP1γ (Heterochromatin Protein 1, isoform γ) that binds histones H3 methylated at lysine 9 (meH3K9) and is highly plastic in its distribution and association with the transcriptional regulation of specific genes during cell fate transitions. These characteristics of HP1γ make it a good candidate to sustain the ESC flexibility required for rapid program changes during differentiation. Using RNA interference, we describe the functional role of HP1γ in mouse ESC. The analysis of HP1γ deprived cells in proliferative and in various differentiating conditions was performed combining functional assays with molecular approaches (RT-qPCR, microarray). We show that HP1γ deprivation slows down the cell cycle of ESC and decreases their resistance to differentiating conditions, rendering the cells poised to differentiate. In addition, HP1γ depletion hampers the differentiation to the endoderm as compared with the differentiation to the neurectoderm or the mesoderm. Altogether, our results reveal the role of HP1γ in ESC self-renewal and in the balance between the pluripotent and the differentiation programs
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