Fresh look at randomly branched polymers

We develop a new, dynamical field theory of isotropic randomly branched polymers, and we use this model in conjunction with the renormalization group (RG) to study several prominent problems in the physics of these polymers. Our model provides an alternative vantage point to understand the swollen phase via dimensional reduction. We reveal a hidden Becchi-Rouet-Stora (BRS) symmetry of the model that describes the collapse ($\theta$-)transition to compact polymer-conformations, and calculate the critical exponents to 2-loop order. It turns out that the long-standing 1-loop results for these exponents are not entirely correct. A runaway of the RG flow indicates that the so-called $\theta^\prime$-transition could be a fluctuation induced first order transition.Comment: 4 page

Partially directed paths in a wedge

The enumeration of lattice paths in wedges poses unique mathematical challenges. These models are not translationally invariant, and the absence of this symmetry complicates both the derivation of a functional recurrence for the generating function, and solving for it. In this paper we consider a model of partially directed walks from the origin in the square lattice confined to both a symmetric wedge defined by $Y = \pm pX$, and an asymmetric wedge defined by the lines $Y= pX$ and Y=0, where $p > 0$ is an integer. We prove that the growth constant for all these models is equal to $1+\sqrt{2}$, independent of the angle of the wedge. We derive functional recursions for both models, and obtain explicit expressions for the generating functions when $p=1$. From these we find asymptotic formulas for the number of partially directed paths of length $n$ in a wedge when $p=1$. The functional recurrences are solved by a variation of the kernel method, which we call the ``iterated kernel method''. This method appears to be similar to the obstinate kernel method used by Bousquet-Melou. This method requires us to consider iterated compositions of the roots of the kernel. These compositions turn out to be surprisingly tractable, and we are able to find simple explicit expressions for them. However, in spite of this, the generating functions turn out to be similar in form to Jacobi $\theta$-functions, and have natural boundaries on the unit circle.Comment: 26 pages, 5 figures. Submitted to JCT

Culture (and religion) in constitutional adjudication

The faculty of law of the Potchefstroom University for Christian Higher Education in corroboration with the Konrad-Adenauer-Stifttung embarked on a study on Politics, Socio-Economic Issues and Culture in Constitutional Adjudication. The aim of the project is twofold. The first aim is to analyse the influence of political, socio-economic and cultural considerations on the constitutional court’s interpretation and application of the Bill of Rights. The second aim is to develop practical guidelines (based on the findings during the analysing process) for South African courts confronted with issues of a political, socio-economic and cultural nature. This article is concerned with initiating discussions of the decisions of the constitutional court with regard to cultural and religious rights. Before we can explore the role of political, socio-economic and cultural (and religious) rights in the decisions of the constitutional court it is important to discuss a few preliminary issues. In this article the meaning of culture and religion within the South African context receives some attention. Secondly, some preliminary comments regarding constitutional protection of culturally and religiously based rights will be made. We are well aware that this is a daunting task, not only in view of the seemingly abysmal gap between the applicable constitutional rights and values enshrined in the 1996 Constitution that, in some instances over centuries, brought about customs and practices within “traditional” communities which, seemingly, infringe on certain constitutional values and rights

Collapsing lattice animals and lattice trees in two dimensions

We present high statistics simulations of weighted lattice bond animals and lattice trees on the square lattice, with fugacities for each non-bonded contact and for each bond between two neighbouring monomers. The simulations are performed using a newly developed sequential sampling method with resampling, very similar to the pruned-enriched Rosenbluth method (PERM) used for linear chain polymers. We determine with high precision the line of second order transitions from an extended to a collapsed phase in the resulting 2-dimensional phase diagram. This line includes critical bond percolation as a multicritical point, and we verify that this point divides the line into two different universality classes. One of them corresponds to the collapse driven by contacts and includes the collapse of (weakly embeddable) trees, but the other is {\it not yet} bond driven and does not contain the Derrida-Herrmann model as special point. Instead it ends at a multicritical point $P^*$ where a transition line between two collapsed phases (one bond-driven and the other contact-driven) sparks off. The Derrida-Herrmann model is representative for the bond driven collapse, which then forms the fourth universality class on the transition line (collapsing trees, critical percolation, intermediate regime, and Derrida-Herrmann). We obtain very precise estimates for all critical exponents for collapsing trees. It is already harder to estimate the critical exponents for the intermediate regime. Finally, it is very difficult to obtain with our method good estimates of the critical parameters of the Derrida-Herrmann universality class. As regards the bond-driven to contact-driven transition in the collapsed phase, we have some evidence for its existence and rough location, but no precise estimates of critical exponents.Comment: 11 pages, 16 figures, 1 tabl

SARS-CoV-2 infection prevalence in healthcare workers and administrative and support staff: The first-wave experience at three academic hospitals in the Tshwane district of Gauteng Province, South Africa

Background. The availability of well and functional healthcare workers (HCWs) and support staff is pivotal to a country’s ability to manage the COVID-19 pandemic effectively. While HCWs have been identified as being at increased risk for acquisition of SARS-CoV-2 infection, there is a paucity of data pertaining to South African (SA) HCW-related infection rates. Global and provincial disparities in these numbers necessitate local data in order to mitigate risks.Objectives. To ascertain the overall SARS-CoV-2 infection rates and outcomes among all hospital staff at three hospitals in the Tshwane district of Gauteng Province, SA, and further determine associations with the development of severe COVID-19 disease.Methods. This retrospective audit was conducted across three academic hospitals in the Tshwane district for the period 1 June - 31 August 2020. Deidentified data from occupational health and safety departments at each hospital were used to calculate infection rates. A more detailed analysis at one of the three hospitals included evaluation of demographics, work description, possible source of SARS-CoV-2 exposure (community or hospital), comorbidities and outcomes.Results. The period prevalence of SARS-CoV-2 infections ranged from 6.1% to 15.4% between the three hospitals, with the average period prevalence being 11.1%. The highest incidence of SARS-CoV-2 infections was observed among administrative staff (2.8 cases per 1 000 staff days), followed by nursing staff (2.7 cases per 1 000 staff days). Medical doctors had the lowest incidence of 1.1 cases per 1 000 staff days. SARS-CoV-2 infections were categorised as either possibly community or possibly healthcare facility acquired for 26.6% and 73.4% of the infections, respectively. The administrative group had the highest proportion of possible community-acquired infections (41.8%), while doctors had the lowest (6.1%). The mean age of individuals with mild and severe disease was 41 years and 46.1 years, respectively (p=0.004). The presence of comorbidities was significantly associated with severity of disease (p=0.002).Conclusions. This study highlights that hospital staff, including administrative staff, are clearly at high risk for acquisition of SARS-CoV-2 infection during a surge.

HRT for women with premature ovarian insufficiency: a comprehensive review

BACKGROUND: Premature ovarian insufficiency (POI), often and misleadingly referred to as ‘premature menopause’, is defined as a loss of ovarian activity before the age of 40 years and is characterized by irregular or absent periods and reduced fertility. Symptoms include those associated with the natural menopause (night sweats and vaginal dryness), and with the long-term adverse effects of estrogen deficiency (osteoporosis and cardiovascular disease): the latter is believed to explain the shorter life expectancy associated with POI. OBJECTIVE AND RATIONALE: The objective of the current review was to collect all relevant studies supporting recommendations on the indications, treatment options, and risks of hormone replacement therapy (HRT) (estrogen, progestogens and androgens) for women with POI. SEARCH METHODS: The current review was written based on the best available evidence on the topic collected for the recently published ESHRE guideline on the management of women with POI. PUBMED/MEDLINE and the Cochrane library were searched in a stepwise approach. Relevant references were summarized in evidence tables, with assessment of the quality. OUTCOMES: HRT is strongly recommended for women with POI, mainly for vasomotor and genito-urinary symptom relief. In addition, HRT has been shown to have a role in bone protection and probably also in primary prevention of cardiovascular disease. There is little evidence on the optimal type, regimen and dose of HRT; patient preference for route and method of administration of each component of HRT must be considered when prescribing, as should contraceptive needs. In women with POI, physiological replacement of estrogen (and progesterone) is essential for their health, and the controversies that surround the use of HRT in postmenopausal women do not apply. WIDER IMPLICATIONS: New areas of study on HRT for women with POI should focus on life expectancy, quality of life and neurological function. Furthermore, randomized controlled trials comparing transdermal estradiol with oral estrogens with regard to efficacy, patient satisfaction and side effects are urgently needed. STUDY FUNDING/COMPETING INTERESTS: The authors received no funding for the review. The costs for the development of the ESHRE guideline were covered by ESHRE. The authors have no conflicts of interest to disclose

Another case of discrepancies when evaluating power theories using real data

Abstract: Most non-sinusoidal power theories have been developed from theoretical techniques, as well as relying on hypothetical and experimental networks to highlight the advantages of each. The drawback of the power theories is that no single one has been universally accepted as a benchmark for other developments. This paper will however show this weakness by means of evaluating two power theories in the time domain, using real recorded data