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

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

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

Production of seafood flavour formulations from enzymatic hydrolysates of fish by-products

© 2015 Published by Elsevier Ltd. Amino acid-rich extracts derived from fish by-products were utilised to generate flavour model systems with added glucose and/or fish oil. Combination of endo and exo peptidases resulted in the most marked increased in free amino acids, particularly for leucine, lysine and glutamic acid (48.3 ± 3.4 to 1423.4 ± 59.6, 43.3 ± 1.2 to 1485.4 ± 25.6 and 143.6 ± 21.7 to 980.9 ± 63.6 μg/g respectively).Main volatile products formed after heating the systems were 4-heptenal, 2,4-heptadienal, and some pyrazines. Increased concentrations of 1-octen-3-ol or 1-hepten-4-ol were also observed in the heated systems compared to the controls. All of these volatile compounds have been identified among the volatile profile of cooked seafood. Conversion of low value fish derived materials such as fish powder, into more valuable products such as flavour precursors and subsequently flavour compounds might be a commercially viable proposition for the fish industry

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