On the localized phase of a copolymer in an emulsion: supercritical percolation regime

In this paper we study a two-dimensional directed self-avoiding walk model of a random copolymer in a random emulsion. The copolymer is a random concatenation of monomers of two types, $A$ and $B$, each occurring with density 1/2. The emulsion is a random mixture of liquids of two types, $A$ and $B$, organised in large square blocks occurring with density $p$ and $1-p$, respectively, where $p \in (0,1)$. The copolymer in the emulsion has an energy that is minus $\alpha$ times the number of $AA$-matches minus $\beta$ times the number of $BB$-matches, where without loss of generality the interaction parameters can be taken from the cone $\{(\alpha,\beta)\in\R^2\colon \alpha\geq |\beta|\}$. To make the model mathematically tractable, we assume that the copolymer is directed and can only enter and exit a pair of neighbouring blocks at diagonally opposite corners. In \cite{dHW06}, it was found that in the supercritical percolation regime $p \geq p_c$, with $p_c$ the critical probability for directed bond percolation on the square lattice, the free energy has a phase transition along a curve in the cone that is independent of $p$. At this critical curve, there is a transition from a phase where the copolymer is fully delocalized into the $A$-blocks to a phase where it is partially localized near the $AB$-interface. In the present paper we prove three theorems that complete the analysis of the phase diagram : (1) the critical curve is strictly increasing; (2) the phase transition is second order; (3) the free energy is infinitely differentiable throughout the partially localized phase.Comment: 43 pages and 10 figure

On the localized phase of a copolymer in an emulsion: supercritical percolation regime

Article / Letter to editorMathematisch Instituu

Interdisciplinary (retail) research: The business of geography and the geography of business

NoAt the 2005 British Academy of Management conference several well-known economic geographers, including Neil Wrigley, Gordon Clark, and Susan Christopherson, called for management researchers to engage with economic geographers on interrelated geographical and managerial issues in the study of (retail) firms. In this commentary we reflect upon the present geography -management interface.We begin by considering the term `interdisciplinary research' and its relationship to any management - geography interface. This is followed by a context-specific discussion of international retailing and the role of research on the retail transnational corporation (TNC) in developing an interdisciplinary agenda. This commentary represents an initial more business and management focused response to the call from geography academics for more/better interdisciplinary research at the geography - management interface

Missense mutations at homologous positions in the fourth and fifth laminin A G-like domains of eyes shut homolog cause autosomal recessive retinitis pigmentosa

Purpose: To describe two novel mutations in the eyes shut homolog (EYS) gene in two families with autosomal recessive retinitis pigmentosa (arRP) from Pakistan and Indonesia. Methods: Genome-wide linkage and homozygosity mapping were performed using single nucleotide polymorphism microarray analysis in affected members of the two arRP families. Sequence analysis was performed to identify genetic changes in protein coding exons of EYS. Results: In the Indonesian and Pakistani families, homozygous regions encompassing the EYS gene at 6q12 were identified, with maximum LOD scores of 1.8 and 3.6, respectively. Novel missense variants in the EYS gene (p.D2767Y and p.D3028Y) were found in the Pakistani and Indonesian families, respectively, that co-segregate with the disease phenotype. Interestingly, the missense variants are located at the same homologous position within the fourth and fifth laminin A G-like domains of EYS. Conclusions: To date, mostly protein-truncating mutations have been described in EYS, while only few patients have been described with pathogenic compound heterozygous missense mutations. The mutations p.D2767Y and p.D3028Y described in this study affect highly conserved residues at homologous positions in laminin A G-like domains and support the notion that missense mutations in EYS can cause arRP

Occurrence (1956) of Haemoproteus sacharovi and Plasmodium relictum in a Central Iowa Pigeon Colony

Naturally occurring infections of Plasmodium relictum and H aemoproteus sacharovi in pigeons of Central Iowa have recently been reported (Becker, Hollander and Pattillo, 1956). In that survey, involving pigeons of all ages, both microscopic examination of stained blood films and isodiagnosis were employed, but the examination of blood films stained in Giemsa was the sole procedure relied upon in the 1956 survey. The birds concerned were young, ranging in age from two to eight weeks. All belonged to the Central Iowa colony to which reference was made in the previous paper. A total of 114 blood films was examined, distributed by dates as follows: June 29, 32; July 21, 23; September 8, 33; September 18, 26. There were a few duplications among the birds examined on September 8 and September 18. The average ages (in weeks) of the squabs on the four dates were as follows: June 29, 4.7; July 21, 3.7; September 8, 3.6; September 18, 4.4. There were, in addition, two other young squabs which will be discussed later

Rimonabant improves cardiometabolic risk factors in overweight/obese patients with poorly controlled type 2 diabetes (HbA(1c)>= 8%) on monotherapy with metformin or sulfonylureas

peer reviewe

Properties of additive functionals of Brownian motion with resetting

We study the distribution of additive functionals of reset Brownian motion, a variation of normal Brownian motion in which the path is interrupted at a given rate and placed back to a given reset position. Our goal is two-fold: (1) For general functionals, we derive a large deviation principle in the presence of resetting and identify the large deviation rate function in terms of a variational formula involving large deviation rate functions without resetting. (2) For three examples of functionals (positive occupation time, area and absolute area), we investigate the effect of resetting by computing distributions and moments, using a formula that links the generating function with resetting to the generating function without resetting.Comment: 23 pages, 4 figure