Spontaneous symmetry breaking: exact results for a biased random walk model of an exclusion process

It has been recently suggested that a totally asymmetric exclusion process with two species on an open chain could exhibit spontaneous symmetry breaking in some range of the parameters defining its dynamics. The symmetry breaking is manifested by the existence of a phase in which the densities of the two species are not equal. In order to provide a more rigorous basis to these observations we consider the limit of the process when the rate at which particles leave the system goes to zero. In this limit the process reduces to a biased random walk in the positive quarter plane, with specific boundary conditions. The stationary probability measure of the position of the walker in the plane is shown to be concentrated around two symmetrically located points, one on each axis, corresponding to the fact that the system is typically in one of the two states of broken symmetry in the exclusion process. We compute the average time for the walker to traverse the quarter plane from one axis to the other, which corresponds to the average time separating two flips between states of broken symmetry in the exclusion process. This time is shown to diverge exponentially with the size of the chain.Comment: 42 page

'Your past makes you who you are': retrospective parenting and relational resilience amongst Black Caribbean British young people

In this article, we explore how Black Caribbean parents prepare their children for the challenges ahead–including anticipated discrimination–in order to boost their opportunities in education and work and eventually their social mobility. Drawing upon family case studies with Black Caribbean families in London, this article focuses on what we have defined as retrospective parenting to mean the use of narratives about the past as resources for parenting. Retrospective parenting draws on the struggles of a cumulative past and aims to transmit a sense of relational resilience, drawing simultaneously on individual, family, and community histories. We found that retrospective parenting had restorative purposes, with parents not only aiming to make up for their missed opportunities but also being preventive and progressive, conveying aims with forward-looking implications for the future of their children

Things change: Women’s and men’s marital disruption dynamics in Italy during a time of social transformations, 1970-2003

We study women’s and men’s marital disruption in Italy between 1970 and 2003. By applying an event-history analysis to the 2003 Italian variant of the Generations and Gender Survey we found that the spread of marital disruption started among middle-highly educated women. Then in recent years it appears that less educated women have also been able to dissolve their unhappy unions. Overall we can see the beginning of a reversed educational gradient from positive to negative. In contrast the trend in men’s marital disruption risk appears as a change over time common to all educational groups, although with persisting educational differentials.determinants, educational differences, event history analysis, gender difference, Italy, marital disruption

Packing and Hausdorff measures of stable trees

In this paper we discuss Hausdorff and packing measures of random continuous trees called stable trees. Stable trees form a specific class of L\'evy trees (introduced by Le Gall and Le Jan in 1998) that contains Aldous's continuum random tree (1991) which corresponds to the Brownian case. We provide results for the whole stable trees and for their level sets that are the sets of points situated at a given distance from the root. We first show that there is no exact packing measure for levels sets. We also prove that non-Brownian stable trees and their level sets have no exact Hausdorff measure with regularly varying gauge function, which continues previous results from a joint work with J-F Le Gall (2006).Comment: 40 page

The ansamycin antibiotic, rifamycin SV, inhibits BCL6 transcriptional repression and forms a complex with the BCL6-BTB/POZ domain

BCL6 is a transcriptional repressor that is over-expressed due to chromosomal translocations, or other abnormalities, in ~40% of diffuse large B-cell lymphoma. BCL6 interacts with co-repressor, SMRT, and this is essential for its role in lymphomas. Peptide or small molecule inhibitors, which prevent the association of SMRT with BCL6, inhibit transcriptional repression and cause apoptosis of lymphoma cells in vitro and in vivo. In order to discover compounds, which have the potential to be developed into BCL6 inhibitors, we screened a natural product library. The ansamycin antibiotic, rifamycin SV, inhibited BCL6 transcriptional repression and NMR spectroscopy confirmed a direct interaction between rifamycin SV and BCL6. To further determine the characteristics of compounds binding to BCL6-POZ we analyzed four other members of this family and showed that rifabutin, bound most strongly. An X-ray crystal structure of the rifabutin-BCL6 complex revealed that rifabutin occupies a partly non-polar pocket making interactions with tyrosine58, asparagine21 and arginine24 of the BCL6-POZ domain. Importantly these residues are also important for the interaction of BLC6 with SMRT. This work demonstrates a unique approach to developing a structure activity relationship for a compound that will form the basis of a therapeutically useful BCL6 inhibitor

Rotational elasticity and couplings to linear elasticity

It is the aim of the paper to present a new point of view on rotational elasticity in a nonlinear setting using orthogonal matrices. The proposed model, in the linear approximation, can be compared to the well known equilibrium equations of static linear elasticity. An appropriate kinetic energy is identified and we present a dynamical model of rotational elasticity. The propagation of elastic waves in such a medium is studied and we find two classes of waves, transversal rotational waves and longitudinal rotational waves, both of which are solutions of the nonlinear partial differential equations. For certain parameter choices, the transversal wave velocity can be greater than the longitudinal wave velocity. Moreover, parameter ranges are identified where the model describes an auxetic material. However, in all cases the potential energy functional is positive definite. Finally, we couple the rotational waves to linear elastic waves to study the behaviour of the coupled system. We find wave like solutions to the coupled equations and can visualise our results with the help of suitable figures.Comment: 19 pages, 2 figures, heavily revised and largely extended versio

Noncommutative generalizations of theorems of Cohen and Kaplansky

This paper investigates situations where a property of a ring can be tested on a set of "prime right ideals." Generalizing theorems of Cohen and Kaplansky, we show that every right ideal of a ring is finitely generated (resp. principal) iff every "prime right ideal" is finitely generated (resp. principal), where the phrase "prime right ideal" can be interpreted in one of many different ways. We also use our methods to show that other properties can be tested on special sets of right ideals, such as the right artinian property and various homological properties. Applying these methods, we prove the following noncommutative generalization of a result of Kaplansky: a (left and right) noetherian ring is a principal right ideal ring iff all of its maximal right ideals are principal. A counterexample shows that the left noetherian hypothesis cannot be dropped. Finally, we compare our results to earlier generalizations of Cohen's and Kaplansky's theorems in the literature.Comment: 41 pages. To appear in Algebras and Representation Theory. Minor changes were made to the numbering system, in order to remain consistent with the published versio

Male breast cancer

Male breast cancer (MBC) is a rare disease representing less than 1% of all breast cancers (BC) and less than 1% of cancers in men. Age at presentation is mostly in the late 60s. MBC is recognized as an estrogen-driven disease, specifically related to hyperestrogenism. About 20% of MBC patients have family history for BC. Mutations in BRCA1 and, predominantly, BRCA2, account for approximately 10% of MBC cases. Because of its rarity, MBC is often compared with female BC (FBC). Based on age-frequency distribution, age-specific incidence rate patterns and prognostic factors profiles, MBC is considered similar to late-onset, postmenopausal estrogen/progesterone receptor positive (ER+/PR+) FBC. However, clinical and pathological characteristics of MBC do not exactly overlap FBC. Compared with FBC, MBC has been reported to occur later in life, present at a higher stage, and display lower histologic grade, with a higher proportion of ER+ and PR+ tumors. Although rare, MBC remains a substantial cause for morbidity and mortality in men, probably because of its occurrence in advanced age and delayed diagnosis. Diagnosis and treatment of MBC generally is similar to that of FBC. Men tend to be treated with mastectomy rather than breast-conserving surgery. The backbone of adjuvant therapy or palliative treatment for advanced disease is endocrine, mostly tamoxifen. Use of FBC-based therapy led to the observation that treatment outcomes for MBC are worse and that survival rates for MBC do not improve like FBC. These different outcomes may suggest a non-appropriate utilization of treatments and that different underlying pathogenetic mechanisms may exist between male and female BC