The strong interaction limit of continuous-time weakly self-avoiding walk

The strong interaction limit of the discrete-time weakly self-avoiding walk (or Domb--Joyce model) is trivially seen to be the usual strictly self-avoiding walk. For the continuous-time weakly self-avoiding walk, the situation is more delicate, and is clarified in this paper. The strong interaction limit in the continuous-time setting depends on how the fugacity is scaled, and in one extreme leads to the strictly self-avoiding walk, in another to simple random walk. These two extremes are interpolated by a new model of a self-repelling walk that we call the "quick step" model. We study the limit both for walks taking a fixed number of steps, and for the two-point function

Yang-Mills Measure and the Master Field on the Sphere

AbstractWe study the Yang–Mills measure on the sphere with unitary structure group. In the limit where the structure group has high dimension, we show that the traces of loop holonomies converge in probability to a deterministic limit, which is known as the master field on the sphere. The values of the master field on simple loops are expressed in terms of the solution of a variational problem. We show that, given its values on simple loops, the master field is characterized on all loops of finite length by a system of differential equations, known as the Makeenko–Migdal equations. We obtain a number of further properties of the master field. On specializing to families of simple loops, our results identify the high-dimensional limit, in non-commutative distribution, of the Brownian bridge in the group of unitary matrices starting and ending at the identity.</jats:p

Characterisation of mutants influencing epigenetic gene silencing in the mouse

The field of epigenetics emerged primarily from studies in Drosophila, and is now being studied intensively by mammalian biologists. In order to increase our knowledge of epigenetic gene control in the mouse, I have studied modifiers of epigenetic gene silencing. My main method of investigation involved the characterisation of mutants from a sensitised ENU mutagenesis screen performed previously in our laboratory. The screen was carried out in an FVB/NJ strain carrying a variegating GFP transgene expressed in erythrocytes. To date we have recovered 12 dominant (D) and seven recessive (R) mutant mouse lines from this screen that display altered transgene expression. We have named these Mommes (Modifiers of murine metastable epialleles). I investigated the phenotype and attempted to identify the underlying causative mutation of two of these Momme mutants. MommeD6 is a semi-dominant, homozygous lethal mutation that acts as a suppressor of variegation with respect to the GFP transgene. This mutation has a large effect on the level of expression of the transgene in expressing cells, but little effect on the percentage of cells expressing the transgene. MommeD6 is linked to a 2.5 Mbp interval on chromosome 14. MommeD9 is a semi-dominant, homozygous lethal mutation that acts as an enhancer of variegation with respect to the GFP transgene. Mutants have a tendency to become obese as they age, show abnormal haematology profiles, and females develop infertility. MommeD9 is linked to a 17.4 Mbp region on chromosome 7. I produced and studied a strain carrying the same GFP transgene but in a new strain background, C57BL/6J. This strain provided an opportunity to look for strain-specific modifiers of expression of the GFP transgene. Several regions were mapped to chromosomal locations. Further work will be needed to identify the genes involved. This mouse will be useful in future mutagenesis screens of this type

Dualité de Schur-Weyl, mouvement brownien sur les groupes de Lie compacts classiques et étude asymptotique de la mesure de Yang-Mills

In the following text, we are interested in the study of Lie-groups valued random variables. We give a deformation of the Weingarten calculus introduced by Benoît Collins and Piotr Sniady. We study the asymptotic behavior of Brownian motion on compact Lie groups in high dimensions and obtain new fluctuations results. Two new objects called the planar gaussian master field and the planar oriented master field are introduced here to describe the asymptotic behavior of the Yang-Mills measure as the dimension of the structure group is large.On s'intéresse dans cette thèse à l'étude de variables aléatoires sur les groupes de Lie compacts classiques. On donne une déformation du calcul de Weingarten tel qu'il a été introduit par B. Collins et P. Sniady. On fait une étude asymptotique du mouvement brownien sur les groupes de Lie compacts de grande dimension en obtenant des nouveaux résultats de fluctuations. Deux nouveaux objets, que l'on appelle champ maître gaussien planaire et champ maître orienté planaire, sont introduits pour décrire le comportement asymptotique des mesures de Yang-Mills pour des groupes de structure de grande dimension

The parabolic Anderson model on Riemann surfaces

We show well-posedness for the parabolic Anderson model on 2-dimensional closed Riemannian manifolds. To this end we extend the notion of regularity structures to curved space, and explicitly construct the minimal structure required for this equation. A central ingredient is the appropriate re-interpretation of the polynomial model, which we build up to any order

Integer moments of complex Wishart matrices and Hurwitz numbers

We give formulae for the cumulants of complex Wishart (LUE) and inverse Wishart matrices (inverse LUE). Their large-N expansions are generating functions of double (strictly and weakly) monotone Hurwitz numbers which count constrained factorisations in the symmetric group. The two expansions can be compared and combined with a duality relation proved in [F. D. Cunden, F. Mezzadri, N. O'Connell and N. J. Simm, arXiv:1805.08760] to obtain: i) a combinatorial proof of the reflection formula between moments of LUE and inverse LUE at genus zero and, ii) a new functional relation between the generating functions of monotone and strictly monotone Hurwitz numbers. The main result resolves the integrality conjecture formulated in [F. D. Cunden, F. Mezzadri, N. J. Simm and P. Vivo, J. Phys. A 49 (2016)] on the time-delay cumulants in quantum chaotic transport. The precise combinatorial description of the cumulants given here may cast new light on the concordance between random matrix and semiclassical theories

Clinical course of suspected familial and sporadic idiopathic pulmonary fibrosis: Data from the PROOF-Next registry.

peer reviewed[en] BACKGROUND AND OBJECTIVE: Real-life data on suspected familial fibrosis, defined as the occurrence of the disease in a patient younger than 50 and/or having at least one relative affected by pulmonary fibrosis remain scarce. METHODS: The Belgian and Luxembourg IPF registry (PROOF-Next) is a multicentric prospective longitudinal and observational study set in Belgium and Luxembourg. We compared characteristics and clinical course of patients with suspected familial pulmonary fibrosis (FPF) and sporadic IPF. RESULTS: We included 618 patients in the analysis, of whom 76 (12%) fulfilled criteria for FPF. They were significantly younger than sIPF (median age (range) 65 (43-87), vs. 72 (51-98), p = 0.0001). Male gender proportion and smoking status did not differ between groups, but the number of pack-year among current and former smokers was lower in FPF (20 vs. 25, p = 0.02). Besides, 87% of FPF and 76% of sIPF were treated with antifibrotic (p = 0.047). Baseline pulmonary function tests were similar in both groups, as well as median time before progression and transplant-free survival. Finally, genetic testing, performed in a minority, led to the identification of 10 telomerase-related gene variants. CONCLUSION: Although younger and exposed to less tobacco, patients with FPF show an equally aggressive progression as observed in sporadic IPF patients. These results warrant early referral of FPF patients to expert centres for optimal management

Correlation of Broncho-Alveolar Lavage Cell Count and Pulmonary Function Tests in the Era of Antifibrotics: Data from the Belgium-Luxembourg IPF registry

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