268 research outputs found
The repulsive lattice gas, the independent-set polynomial, and the Lov\'asz local lemma
We elucidate the close connection between the repulsive lattice gas in
equilibrium statistical mechanics and the Lovasz local lemma in probabilistic
combinatorics. We show that the conclusion of the Lovasz local lemma holds for
dependency graph G and probabilities {p_x} if and only if the independent-set
polynomial for G is nonvanishing in the polydisc of radii {p_x}. Furthermore,
we show that the usual proof of the Lovasz local lemma -- which provides a
sufficient condition for this to occur -- corresponds to a simple inductive
argument for the nonvanishing of the independent-set polynomial in a polydisc,
which was discovered implicitly by Shearer and explicitly by Dobrushin. We also
present some refinements and extensions of both arguments, including a
generalization of the Lovasz local lemma that allows for "soft" dependencies.
In addition, we prove some general properties of the partition function of a
repulsive lattice gas, most of which are consequences of the alternating-sign
property for the Mayer coefficients. We conclude with a brief discussion of the
repulsive lattice gas on countably infinite graphs.Comment: LaTex2e, 97 pages. Version 2 makes slight changes to improve clarity.
To be published in J. Stat. Phy
Pleiotropic functions of the tumor- and metastasis-suppressing Matrix Metalloproteinase-8 in mammary cancer in MMTV-PyMT transgenic mice
Matrix metalloproteinase-8 (MMP-8; neutrophil collagenase) is an important regulator of innate immunity which has onco-suppressive actions in numerous tumor types
Spanning forests and the q-state Potts model in the limit q \to 0
We study the q-state Potts model with nearest-neighbor coupling v=e^{\beta
J}-1 in the limit q,v \to 0 with the ratio w = v/q held fixed. Combinatorially,
this limit gives rise to the generating polynomial of spanning forests;
physically, it provides information about the Potts-model phase diagram in the
neighborhood of (q,v) = (0,0). We have studied this model on the square and
triangular lattices, using a transfer-matrix approach at both real and complex
values of w. For both lattices, we have computed the symbolic transfer matrices
for cylindrical strips of widths 2 \le L \le 10, as well as the limiting curves
of partition-function zeros in the complex w-plane. For real w, we find two
distinct phases separated by a transition point w=w_0, where w_0 = -1/4 (resp.
w_0 = -0.1753 \pm 0.0002) for the square (resp. triangular) lattice. For w >
w_0 we find a non-critical disordered phase, while for w < w_0 our results are
compatible with a massless Berker-Kadanoff phase with conformal charge c = -2
and leading thermal scaling dimension x_{T,1} = 2 (marginal operator). At w =
w_0 we find a "first-order critical point": the first derivative of the free
energy is discontinuous at w_0, while the correlation length diverges as w
\downarrow w_0 (and is infinite at w = w_0). The critical behavior at w = w_0
seems to be the same for both lattices and it differs from that of the
Berker-Kadanoff phase: our results suggest that the conformal charge is c = -1,
the leading thermal scaling dimension is x_{T,1} = 0, and the critical
exponents are \nu = 1/d = 1/2 and \alpha = 1.Comment: 131 pages (LaTeX2e). Includes tex file, three sty files, and 65
Postscript figures. Also included are Mathematica files forests_sq_2-9P.m and
forests_tri_2-9P.m. Final journal versio
Colloquium: Mechanical formalisms for tissue dynamics
The understanding of morphogenesis in living organisms has been renewed by
tremendous progressin experimental techniques that provide access to
cell-scale, quantitative information both on theshapes of cells within tissues
and on the genes being expressed. This information suggests that
ourunderstanding of the respective contributions of gene expression and
mechanics, and of their crucialentanglement, will soon leap forward.
Biomechanics increasingly benefits from models, which assistthe design and
interpretation of experiments, point out the main ingredients and assumptions,
andultimately lead to predictions. The newly accessible local information thus
calls for a reflectionon how to select suitable classes of mechanical models.
We review both mechanical ingredientssuggested by the current knowledge of
tissue behaviour, and modelling methods that can helpgenerate a rheological
diagram or a constitutive equation. We distinguish cell scale ("intra-cell")and
tissue scale ("inter-cell") contributions. We recall the mathematical framework
developpedfor continuum materials and explain how to transform a constitutive
equation into a set of partialdifferential equations amenable to numerical
resolution. We show that when plastic behaviour isrelevant, the dissipation
function formalism appears appropriate to generate constitutive equations;its
variational nature facilitates numerical implementation, and we discuss
adaptations needed in thecase of large deformations. The present article
gathers theoretical methods that can readily enhancethe significance of the
data to be extracted from recent or future high throughput
biomechanicalexperiments.Comment: 33 pages, 20 figures. This version (26 Sept. 2015) contains a few
corrections to the published version, all in Appendix D.2 devoted to large
deformation
The impact of Stieltjes' work on continued fractions and orthogonal polynomials
Stieltjes' work on continued fractions and the orthogonal polynomials related
to continued fraction expansions is summarized and an attempt is made to
describe the influence of Stieltjes' ideas and work in research done after his
death, with an emphasis on the theory of orthogonal polynomials
The geometry of the magnetic field in the central molecular zone measured by PILOT
We present the first far infrared (FIR) dust emission polarization map covering the full extent of Milky Way’s central molecular zone (CMZ). The data, obtained with the PILOT balloon-borne experiment, covers the Galactic center region − 2° < ℓ < 2°, − 4° < b < 3° at a wavelength of 240 μm and an angular resolution of 2.2′. From our measured dust polarization angles, we infer a magnetic field orientation projected onto the plane of the sky (POS) that is remarkably ordered over the full extent of the CMZ, with an average tilt angle of ≃22° clockwise with respect to the Galactic plane. Our results confirm previous claims that the field traced by dust polarized emission is oriented nearly orthogonally to the field traced by GHz radio synchrotron emission in the Galactic center region. The observed field structure is globally compatible with the latest Planck polarization data at 353 and 217 GHz. Upon subtraction of the extended emission in our data, the mean field orientation that we obtain shows good agreement with the mean field orientation measured at higher angular resolution by the JCMT within the 20 and 50 km s−1 molecular clouds. We find no evidence that the magnetic field orientation is related to the 100 pc twisted ring structure within the CMZ. The low polarization fraction in the Galactic center region measured with Planck at 353 GHz combined with a highly ordered projected field orientation is unusual. This feature actually extends to the whole inner Galactic plane. We propose that it could be caused by the increased number of turbulent cells for the long lines of sight towards the inner Galactic plane or to dust properties specific to the inner regions of the Galaxy. Assuming equipartition between magnetic pressure and ram pressure, we obtain magnetic field strength estimates of the order of 1 mG for several CMZ molecular clouds
Pilot optical alignment
PILOT (Polarized Instrument for Long wavelength Observations of the Tenuous interstellar medium) is a balloonborne astronomy experiment designed to study the polarization of dust emission in the diffuse interstellar medium in our Galaxy. The PILOT instrument allows observations at wavelengths 240 μm and 550 μm with an angular resolution of about two arcminutes. The observations performed during the two first flights performed from Timmins, Ontario Canada, and from Alice-springs, Australia, respectively in September 2015 and in April 2017 have demonstrated the good performances of the instrument. Pilot optics is composed of an off axis Gregorian type telescope combined with a refractive re-imager system. All optical elements, except the primary mirror, which is at ambient temperature, are inside a cryostat and cooled down to 3K. The whole optical system is aligned on ground at room temperature using dedicated means and procedures in order to keep the tight requirements on the focus position and ensure the instrument optical performances during the various phases of a flight. We’ll present the optical performances and the firsts results obtained during the two first flight campaigns. The talk describes the system analysis, the alignment methods, and finally the inflight performances
Ductile deformation within Upper Himalaya Crystalline Sequence and geological implications, in Nyalam area, Southern Tibet
Targeting pathogen metabolism without collateral damage to the host
The development of drugs that can inactivate disease-causing cells (e.g. cancer cells or parasites) without causing collateral damage to healthy or to host cells is complicated by the fact that many proteins are very similar between organisms. Nevertheless, due to subtle, quantitative differences between the biochemical reaction networks of target cell and host, a drug can limit the flux of the same essential process in one organism more than in another. We identified precise criteria for this â €network-based' drug selectivity, which can serve as an alternative or additive to structural differences. We combined computational and experimental approaches to compare energy metabolism in the causative agent of sleeping sickness, Trypanosoma brucei, with that of human erythrocytes, and identified glucose transport and glyceraldehyde-3-phosphate dehydrogenase as the most selective antiparasitic targets. Computational predictions were validated experimentally in a novel parasite-erythrocytes co-culture system. Glucose-transport inhibitors killed trypanosomes without killing erythrocytes, neurons or liver cells
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