A New Class of Non-Linear Stability Preserving Operators

We extend Br\"and\'en's recent proof of a conjecture of Stanley and describe a new class of non-linear operators that preserve weak Hurwitz stability and the Laguerre-P\'olya class.Comment: Fixed typos, spelling, and updated links in reference

Influencia del batido y de los parámetros de extracción en la calidad del aceite de oliva virgen

The mixing time, the temperature and the degree of dilution of olive paste are the main parameters liable to change during mixing and oil ext raction. They can greatly differ from a processing run to another, with variations being observed in Tuscan oil mills, between 26ºC and 36ºC, 40’ and 90’, and 10% and 50% respectively, for the temperature, the mixing time and the water added during the centrifugal extraction. This note reports on the results of some experimental trials run during the 1998 olive oil year in Tuscany. The mixing time and temperature as well as the olive paste dilution were changed one at a time and were assessed for their influence on extraction yield and oil quality. The best conditions to optimise the product yield and quality were identified.El tiempo de batido, la temperatura y el grado de dilución de la pasta de aceituna, son los principales parámetros que pueden sufrir cambios durante el batido y la extracción del aceite. Estos pueden diferir mucho de un proceso a otro, habiendo sido observadas variaciones en los aceites de molino de Toscana, entre 26ºC y 36ºC, 40’ y 90’, y 10% y 50% respectivamente, para la temperatura, el tiempo de batido y el agua añadida durante la extracción por centrifugación. Este artículo presenta los resultados de algunos ensayos experimentales realizados durante el año 1998 con aceite de oliva de Toscana. El tiempo de batido y la temperatura, así como la dilución de la pasta de aceitunas, se variaron uno a uno y se evaluaron por su influencia en el rendimiento de la extracción y la calidad del aceite. Las mejores condiciones para optimizar el rendimiento y la calidad del producto fueron identificadas

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 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

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

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

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

Nuclear poly(A)-binding protein aggregates misplace a pre-mRNA outside of SC35 speckle causing its abnormal splicing

A short abnormal polyalanine expansion in the polyadenylate-binding protein nuclear-1 (PABPN1) protein causes oculopharyngeal muscular dystrophy (OPMD). Mutated PABPN1 proteins accumulate as insoluble intranuclear aggregates in muscles of OPMD patients. While the roles of PABPN1 in nuclear polyadenylation and regulation of alternative poly(A) site choice have been established, the molecular mechanisms which trigger pathological defects in OPMD and the role of aggregates remain to be determined. Using exon array, for the first time we have identified several splicing defects in OPMD. In particular, we have demonstrated a defect in the splicing regulation of the muscle-specific Troponin T₃ (TNNT₃) mutually exclusive exons 16 and 17 in OPMD samples compared to controls. This splicing defect is directly linked to the SC₃₅ (SRSF2) splicing factor and to the presence of nuclear aggregates. As reported here, PABPN1 aggregates are able to trap TNNT₃ pre-mRNA, driving it outside nuclear speckles, leading to an altered SC₃₅ -mediated splicing. This results in a decreased calcium sensitivity of muscle fibers, which could in turn plays a role in muscle pathology. We thus report a novel mechanism of alternative splicing deregulation that may play a role in various other diseases with nuclear inclusions or foci containing an RNA binding protein