Ewens measures on compact groups and hypergeometric kernels

On unitary compact groups the decomposition of a generic element into product of reflections induces a decomposition of the characteristic polynomial into a product of factors. When the group is equipped with the Haar probability measure, these factors become independent random variables with explicit distributions. Beyond the known results on the orthogonal and unitary groups (O(n) and U(n)), we treat the symplectic case. In U(n), this induces a family of probability changes analogous to the biassing in the Ewens sampling formula known for the symmetric group. Then we study the spectral properties of these measures, connected to the pure Fisher-Hartvig symbol on the unit circle. The associated orthogonal polynomials give rise, as $n$ tends to infinity to a limit kernel at the singularity.Comment: New version of the previous paper "Hua-Pickrell measures on general compact groups". The article has been completely re-written (the presentation has changed and some proofs have been simplified). New references added

How I report breast magnetic resonance imaging studies for breast cancer staging and screening

Magnetic resonance imaging (MRI) of the breast is the most sensitive imaging technique for the diagnosis and local staging of primary breast cancer and yet, despite the fact that it has been in use for 20 years, there is little evidence that its widespread uncritical adoption has had a positive impact on patient-related outcomes. This has been attributed previously to the low specificity that might be expected with such a sensitive modality, but with modern techniques and protocols, the specificity and positive predictive value for malignancy can exceed that of breast ultrasound and mammography. A more likely explanation is that historically, clinicians have acted on MRI findings and altered surgical plans without prior histological confirmation. Furthermore, modern adjuvant therapy for breast cancer has improved so much that it has become a very tall order to show a an improvement in outcomes such as local recurrence rates. In order to obtain clinically useful information, it is necessary to understand the strengths and weaknesses of the technique and the physiological processes reflected in breast MRI. An appropriate indication for the scan, proper patient preparation and good scan technique, with rigorous quality assurance, are all essential prerequisites for a diagnostically relevant study. The use of recognised descriptors from a standardised lexicon is helpful, since assessment can then dictate subsequent recommendations for management, as in the American College of Radiology BI-RADS (Breast Imaging Reporting and Data System) lexicon (Morris et al., ACR BI-RADS® Atlas, Breast Imaging Reporting and Data System, 2013). It also enables audit of the service. However, perhaps the most critical factor in the generation of a meaningful report is for the reporting radiologist to have a thorough understanding of the clinical question and of the findings that will influence management. This has never been more important than at present, when we are in the throes of a remarkable paradigm shift in the treatment of both early stage and locally advanced breast cancer. ELECTRONIC SUPPLEMENTARY MATERIAL: The online version of this article (doi:10.1186/s40644-016-0078-0) contains supplementary material, which is available to authorized users

Microbial contributions to the persistence of coral reefs

On contemplating the adaptive capacity of reef organisms to a rapidly changing environment, the microbiome offers significant and greatly unrecognised potential. Microbial symbionts contribute to the physiology, development, immunity and behaviour of their hosts, and can respond very rapidly to changing environmental conditions, providing a powerful mechanism for acclimatisation and also possibly rapid evolution of coral reef holobionts. Environmentally acquired fluctuations in the microbiome can have significant functional consequences for the holobiont phenotype upon which selection can act. Environmentally induced changes in microbial abundance may be analogous to host gene duplication, symbiont switching / shuffling as a result of environmental change can either remove or introduce raw genetic material into the holobiont; and horizontal gene transfer can facilitate rapid evolution within microbial strains. Vertical transmission of symbionts is a key feature of many reef holobionts and this would enable environmentally acquired microbial traits to be faithfully passed to future generations, ultimately facilitating microbiome-mediated transgenerational acclimatisation (MMTA) and potentially even adaptation of reef species in a rapidly changing climate. In this commentary, we highlight the capacity and mechanisms for MMTA in reef species, propose a modified Price equation as a framework for assessing MMTA and recommend future areas of research to better understand how microorganisms contribute to the transgenerational acclimatisation of reef organisms, which is essential if we are to reliably predict the consequences of global change for reef ecosystems

Oxidative protein labeling in mass-spectrometry-based proteomics

Oxidation of proteins and peptides is a common phenomenon, and can be employed as a labeling technique for mass-spectrometry-based proteomics. Nonspecific oxidative labeling methods can modify almost any amino acid residue in a protein or only surface-exposed regions. Specific agents may label reactive functional groups in amino acids, primarily cysteine, methionine, tyrosine, and tryptophan. Nonspecific radical intermediates (reactive oxygen, nitrogen, or halogen species) can be produced by chemical, photochemical, electrochemical, or enzymatic methods. More targeted oxidation can be achieved by chemical reagents but also by direct electrochemical oxidation, which opens the way to instrumental labeling methods. Oxidative labeling of amino acids in the context of liquid chromatography(LC)–mass spectrometry (MS) based proteomics allows for differential LC separation, improved MS ionization, and label-specific fragmentation and detection. Oxidation of proteins can create new reactive groups which are useful for secondary, more conventional derivatization reactions with, e.g., fluorescent labels. This review summarizes reactions of oxidizing agents with peptides and proteins, the corresponding methodologies and instrumentation, and the major, innovative applications of oxidative protein labeling described in selected literature from the last decade