Grassmannian flows and applications to nonlinear partial differential equations

We show how solutions to a large class of partial differential equations with nonlocal Riccati-type nonlinearities can be generated from the corresponding linearized equations, from arbitrary initial data. It is well known that evolutionary matrix Riccati equations can be generated by projecting linear evolutionary flows on a Stiefel manifold onto a coordinate chart of the underlying Grassmann manifold. Our method relies on extending this idea to the infinite dimensional case. The key is an integral equation analogous to the Marchenko equation in integrable systems, that represents the coodinate chart map. We show explicitly how to generate such solutions to scalar partial differential equations of arbitrary order with nonlocal quadratic nonlinearities using our approach. We provide numerical simulations that demonstrate the generation of solutions to Fisher--Kolmogorov--Petrovskii--Piskunov equations with nonlocal nonlinearities. We also indicate how the method might extend to more general classes of nonlinear partial differential systems.Comment: 26 pages, 2 figure

CATALISE: A multinational and multidisciplinary Delphi consensus study. Identifying language impairments in children

Delayed or impaired language development is a common developmental concern, yet thereis little agreement about the criteria used to identify and classify language impairments inchildren. Children's language difficulties are at the interface between education, medicineand the allied professions, who may all adopt different approaches to conceptualising them.Our goal in this study was to use an online Delphi technique to see whether it was possibleto achieve consensus among professionals on appropriate criteria for identifying childrenwho might benefit from specialist services. We recruited a panel of 59 experts representingten disciplines (including education, psychology, speech-language therapy/pathology, paediatricsand child psychiatry) from English-speaking countries (Australia, Canada, Ireland,New Zealand, United Kingdom and USA). The starting point for round 1 was a set of 46statements based on articles and commentaries in a special issue of a journal focusing onthis topic. Panel members rated each statement for both relevance and validity on a sevenpointscale, and added free text comments. These responses were synthesised by the firsttwo authors, who then removed, combined or modified items with a view to improving consensus.The resulting set of statements was returned to the panel for a second evaluation(round 2). Consensus (percentage reporting 'agree' or 'strongly agree') was at least 80 percentfor 24 of 27 round 2 statements, though many respondents qualified their responsewith written comments. These were again synthesised by the first two authors. The resultingconsensus statement is reported here, with additional summary of relevant evidence, and aconcluding commentary on residual disagreements and gaps in the evidence base.</p

Phase 2 of CATALISE: a multinational and multidisciplinary Delphi consensus study of problems with language development: Terminology.

Background: Lack of agreement about criteria and terminology for children’s language problems affects access to services as well as hindering research and practice. We report the second phase of a study using an online Delphi method to address these issues. In the first phase, we focused on criteria for language disorder. Here we consider terminology.Methods: The Delphi method is an iterative process in which an initial set of statements is rated by a panel of experts, who then have the opportunity to view anonymised ratings from other panel members. On this basis they can either revise their views or make a case for their position. The statements are then revised based on panel feedback, and again rated by and commented on by the panel. In this study, feedback from a second round was used to prepare a final set of statements in narrative form. The panel included 57 individuals representing a range of professions and nationalities. Results: We achieved at least 78% agreement for 19 of 21 statements within two rounds of ratings. These were collapsed into 12 statements for the final consensus reported here. The term ‘Language Disorder’ is recommended to refer to a profile of difficulties that causes functional impairment in everyday life and is associated with poor prognosis. The term, ‘Developmental Language Disorder’ (DLD) was endorsed for use when the language disorder was not associated with a known biomedical aetiology. It was also agreed that (a) presence of risk factors (neurobiological or environmental) does not preclude a diagnosis of DLD, (b) DLD can co-occur with other neurodevelopmental disorders (e.g. ADHD) and (c) DLD does not require a mismatch between verbal and nonverbal ability. Conclusions: This Delphi exercise highlights reasons for disagreements about terminology for language disorders and proposes standard definitions and nomenclature. </p

Detectable clonal mosaicism and its relationship to aging and cancer

In an analysis of 31,717 cancer cases and 26,136 cancer-free controls from 13 genome-wide association studies, we observed large chromosomal abnormalities in a subset of clones in DNA obtained from blood or buccal samples. We observed mosaic abnormalities, either aneuploidy or copy-neutral loss of heterozygosity, of >2 Mb in size in autosomes of 517 individuals (0.89%), with abnormal cell proportions of between 7% and 95%. In cancer-free individuals, frequency increased with age, from 0.23% under 50 years to 1.91% between 75 and 79 years (P = 4.8 × 10(-8)). Mosaic abnormalities were more frequent in individuals with solid tumors (0.97% versus 0.74% in cancer-free individuals; odds ratio (OR) = 1.25; P = 0.016), with stronger association with cases who had DNA collected before diagnosis or treatment (OR = 1.45; P = 0.0005). Detectable mosaicism was also more common in individuals for whom DNA was collected at least 1 year before diagnosis with leukemia compared to cancer-free individuals (OR = 35.4; P = 3.8 × 10(-11)). These findings underscore the time-dependent nature of somatic events in the etiology of cancer and potentially other late-onset diseases