Mean-Field Spin Glass models from the Cavity--ROSt Perspective

The Sherrington-Kirkpatrick spin glass model has been studied as a source of insight into the statistical mechanics of systems with highly diversified collections of competing low energy states. The goal of this summary is to present some of the ideas which have emerged in the mathematical study of its free energy. In particular, we highlight the perspective of the cavity dynamics, and the related variational principle. These are expressed in terms of Random Overlap Structures (ROSt), which are used to describe the possible states of the reservoir in the cavity step. The Parisi solution is presented as reflecting the ansatz that it suffices to restrict the variation to hierarchal structures which are discussed here in some detail. While the Parisi solution was proven to be correct, through recent works of F. Guerra and M. Talagrand, the reasons for the effectiveness of the Parisi ansatz still remain to be elucidated. We question whether this could be related to the quasi-stationarity of the special subclass of ROSts given by Ruelle's hierarchal `random probability cascades' (also known as GREM).Comment: Based on talks given at `Young Res. Symp.', Lisbon 2003, and `Math. Phys. of Spin Glasses', Cortona 200

On the dynamics of interfaces in the ferromagnetic XXZ chain under weak perturbations

We study the time evolution of interfaces of the ferromagnetic XXZ chain in a magnetic field. A scaling limit is introduced where the strength of the magnetic field tends to zero and the microscopic time to infinity while keeping their product constant. The leading term and its first correction are determined and further analyzed in more detail for the case of a uniform magnetic field.Comment: 20 pages, 2 figures, uses conm-p-l.cls. 1 reference adde

Some Observations for Mean-Field Spin Glass Models

We obtain bounds to show that the pressure of a two-body, mean-field spin glass is a Lipschitz function of the underlying distribution of the random coupling constants, with respect to a particular semi-norm. This allows us to re-derive a result of Carmona and Hu, on the universality of the SK model, by a different proof, and to generalize this result to the Viana-Bray model. We also prove another bound, suitable when the coupling constants are not independent, which is what is necessary if one wants to consider ``canonical'' instead of ``grand canonical'' versions of the SK and Viana-Bray models. Finally, we review Viana-Bray type models, using the language of L\'evy processes, which is natural in this context.Comment: 15 pages, minor revision

An Extended Variational Principle for the SK Spin-Glass Model

The recent proof by F. Guerra that the Parisi ansatz provides a lower bound on the free energy of the SK spin-glass model could have been taken as offering some support to the validity of the purported solution. In this work we present a broader variational principle, in which the lower bound, as well as the actual value, are obtained through an optimization procedure for which ultrametic/hierarchal structures form only a subset of the variational class. The validity of Parisi's ansatz for the SK model is still in question. The new variational principle may be of help in critical review of the issue.Comment: 4 pages, Revtex

Coronavirus disease 2019 (COVID-19) in two pediatric patients with kidney disease on chronic immunosuppression: A case series

This article is made available for unrestricted research re-use and secondary analysis in any form or by any means with acknowledgement of the original source. These permissions are granted for the duration of the World Health Organization (WHO) declaration of COVID-19 as a global pandemic.Coronavirus disease 2019 (COVID‐19) is a highly infectious disease caused by the severe acute respiratory syndrome coronavirus 2 virus (SARS‐CoV‐2). While children appear to experience less severe disease than adults, those with underlying conditions such as kidney disease may be more susceptible to infection. Limited data are present for children with kidney disease, and there are limited prior reports of pediatric hemodialysis patients with COVID‐19. This report describes the mild clinical disease course of COVID‐19 in two pediatric patients with chronic kidney disease, one on hemodialysis and both on chronic immunosuppression. We review treatment in these patients, as well as our measures to reduce transmission among our hemodialysis patients and staff

Antiferromagnetic Potts model on the Erdos-Renyi random graph

We study the antiferromagnetic Potts model on the Poissonian Erd\"os-R\'enyi random graph. By identifying a suitable interpolation structure and an extended variational principle, together with a positive temperature second-moment analysis we prove the existence of a phase transition at a positive critical temperature. Upper and lower bounds on the temperature critical value are obtained from the stability analysis of the replica symmetric solution (recovered in the framework of Derrida-Ruelle probability cascades)and from a positive entropy argument.Comment: 36 pages, revisions to improve resul

Medical students' and facilitators' experiences of an Early Professional Contact course: Active and motivated students, strained facilitators

Background: Today, medical students are introduced to patient contact, communication skills, and clinical examination in the preclinical years of the curriculum with the purpose of gaining clinical experience. These courses are often evaluated from the student perspective. Reports with an additional emphasis on the facilitator perspective are scarce. According to constructive alignment, an influential concept from research in higher education, the learning climate between students and teachers is also of great importance. In this paper, we approach the learning climate by studying both students' and facilitators' course experiences.\ud \ud In 2001, a new "Early Professional Contact" longitudinal strand through term 1–4, was introduced at the Sahlgrenska Academy, University of Gothenburg, Sweden. General practitioners and hospital specialists were facilitators.\ud \ud The aim of this study was to assess and analyse students' and clinical facilitators' experiences of the Early Professional Contact course and to illuminate facilitators' working conditions.\ud \ud Methods: Inspired by a Swedish adaptation of the Course Experience Questionnaire, an Early Professional Contact Questionnaire was constructed. In 2003, on the completion of the first longitudinal strand, a student and facilitator version was distributed to 86 students and 21 facilitators. In the analysis, both Chi-square and the Mann-Whitney tests were used.\ud \ud Results: Sixty students (70%) and 15 facilitators (71%) completed the questionnaire. Both students and facilitators were satisfied with the course. Students reported gaining [inspiration] for their future work as doctors along with increased confidence in meeting patients. They also reported increased motivation for biomedical studies. Differences in attitudes between facilitators and students were found. Facilitators experienced a greater workload, less reasonable demands and less support, than students.\ud \ud Conclusion: In this project, a new Early Professional Contact course was analysed from both student and facilitator perspectives. The students experienced the course as providing them with a valuable introduction to the physician's professional role in clinical practice. In contrast, course facilitators often experienced a heavy workload and lack of support, despite thorough preparatory education. A possible conflict between the clinical facilitator's task as educator and member of the workplace is suggested. More research is needed on how doctors combine their professional tasks with work as facilitators

Proteome Sampling by the HLA Class I Antigen Processing Pathway

The peptide repertoire that is presented by the set of HLA class I molecules of an individual is formed by the different players of the antigen processing pathway and the stringent binding environment of the HLA class I molecules. Peptide elution studies have shown that only a subset of the human proteome is sampled by the antigen processing machinery and represented on the cell surface. In our study, we quantified the role of each factor relevant in shaping the HLA class I peptide repertoire by combining peptide elution data, in silico predictions of antigen processing and presentation, and data on gene expression and protein abundance. Our results indicate that gene expression level, protein abundance, and rate of potential binding peptides per protein have a clear impact on sampling probability. Furthermore, once a protein is available for the antigen processing machinery in sufficient amounts, C-terminal processing efficiency and binding affinity to the HLA class I molecule determine the identity of the presented peptides. Having studied the impact of each of these factors separately, we subsequently combined all factors in a logistic regression model in order to quantify their relative impact. This model demonstrated the superiority of protein abundance over gene expression level in predicting sampling probability. Being able to discriminate between sampled and non-sampled proteins to a significant degree, our approach can potentially be used to predict the sampling probability of self proteins and of pathogen-derived proteins, which is of importance for the identification of autoimmune antigens and vaccination targets