On positivity of Ehrhart polynomials

Ehrhart discovered that the function that counts the number of lattice points in dilations of an integral polytope is a polynomial. We call the coefficients of this polynomial Ehrhart coefficients, and say a polytope is Ehrhart positive if all Ehrhart coefficients are positive (which is not true for all integral polytopes). The main purpose of this article is to survey interesting families of polytopes that are known to be Ehrhart positive and discuss the reasons from which their Ehrhart positivity follows. We also include examples of polytopes that have negative Ehrhart coefficients and polytopes that are conjectured to be Ehrhart positive, as well as pose a few relevant questions.Comment: 40 pages, 7 figures. To appear in in Recent Trends in Algebraic Combinatorics, a volume of the Association for Women in Mathematics Series, Springer International Publishin

‘Messy Democracy’: Democratic pedagogy and its discontents

This paper reflects on a recent participatory installation by the artists’ collective @.ac, entitled Messy Democracy, as a case study to raise questions concerning the ‘distribution of the sensible’ within the neoliberal art school. The project set up a quasi-autonomous artists’ space within Hanover Project gallery 9 April–3 May, 2018 at University of Central Lancashire, Preston. This exhibition functioned as a space of collective pedagogy, co-labour and ‘dissensus’ situated in relation to the wider operation of the department of Fine Art. It also sought to operate as a critical alternative to contemporary models of the art school, rooted in notions of usefulness and romantic self-realisation, but re-structured in the service of ‘commodification’ and ‘financialisation’ in wake of the Browne Report (2010). Most importantly, Messy Democracy represented a ‘theatocractic’ ‘undercommons’ for alternate and counter-hegemonic subjectivities to emerge. However, hierarchical logics, resulting from the hegemonic ‘distribution of the sensible’ stubbornly persisted even within this nascent pedagogic democracy

Genomic Relationships, Novel Loci, and Pleiotropic Mechanisms across Eight Psychiatric Disorders

Genetic influences on psychiatric disorders transcend diagnostic boundaries, suggesting substantial pleiotropy of contributing loci. However, the nature and mechanisms of these pleiotropic effects remain unclear. We performed analyses of 232,964 cases and 494,162 controls from genome-wide studies of anorexia nervosa, attention-deficit/hyper-activity disorder, autism spectrum disorder, bipolar disorder, major depression, obsessive-compulsive disorder, schizophrenia, and Tourette syndrome. Genetic correlation analyses revealed a meaningful structure within the eight disorders, identifying three groups of inter-related disorders. Meta-analysis across these eight disorders detected 109 loci associated with at least two psychiatric disorders, including 23 loci with pleiotropic effects on four or more disorders and 11 loci with antagonistic effects on multiple disorders. The pleiotropic loci are located within genes that show heightened expression in the brain throughout the lifespan, beginning prenatally in the second trimester, and play prominent roles in neurodevelopmental processes. These findings have important implications for psychiatric nosology, drug development, and risk prediction.Peer reviewe

Therapeutic Management of Primary Immunodeficiency in Older Patients

Primary immunodeficiency disease (PID) has traditionally been viewed as a group of illnesses seen in the paediatric age group. New advances in diagnosis and treatment have led to an increase in the number of elderly PID patients. However, there is lack of research evidence on which to base clinical management in this group of patients. Management decisions often have to be based therefore on extrapolations from other patient cohorts or from younger patients. Data from the European Society for Immunodeficiencies demonstrates that the vast majority of elderly patients suffer from predominantly antibody deficiency syndromes. We review the management of PID disease in the elderly, with a focus on antibody deficiency disease

Role of biomechanics in the understanding of normal, injured, and healing ligaments and tendons

Ligaments and tendons are soft connective tissues which serve essential roles for biomechanical function of the musculoskeletal system by stabilizing and guiding the motion of diarthrodial joints. Nevertheless, these tissues are frequently injured due to repetition and overuse as well as quick cutting motions that involve acceleration and deceleration. These injuries often upset this balance between mobility and stability of the joint which causes damage to other soft tissues manifested as pain and other morbidity, such as osteoarthritis