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

Quantification of Internal Stress-Strain Fields in Human Tendon: Unraveling the Mechanisms that Underlie Regional Tendon Adaptations and Mal-Adaptations to Mechanical Loading and the Effectiveness of Therapeutic Eccentric Exercise.

By virtue of their anatomical location between muscles and bones, tendons make it possible to transform contractile force to joint rotation and locomotion. However, tendons do not behave as rigid links, but exhibit viscoelastic tensile properties, thereby affecting the length and contractile force in the in-series muscle, but also storing and releasing elastic stain energy as some tendons are stretched and recoiled in a cyclic manner during locomotion. In the late 90s, advancements were made in the application of ultrasound scanning that allowed quantifying the tensile deformability and mechanical properties of human tendons in vivo. Since then, the main principles of the ultrasound-based method have been applied by numerous research groups throughout the world and showed that tendons increase their tensile stiffness in response to exercise training and chronic mechanical loading, in general, by increasing their size and improving their intrinsic material. It is often assumed that these changes occur homogenously, in the entire body of the tendon, but recent findings indicate that the adaptations may in fact take place in some but not all tendon regions. The present review focuses on these regional adaptability features and highlights two paradigms where they are particularly evident: (a) Chronic mechanical loading in healthy tendons, and (b) tendinopathy. In the former loading paradigm, local tendon adaptations indicate that certain regions may "see," and therefore adapt to, increased levels of stress. In the latter paradigm, local pathological features indicate that certain tendon regions may be "stress-shielded" and degenerate over time. Eccentric exercise protocols have successfully been used in the management of tendinopathy, without much sound understanding of the mechanisms underpinning their effectiveness. For insertional tendinopathy, in particular, it is possible that the effectiveness of a loading/rehabilitation protocol depends on the topography of the stress created by the exercise and is not only reliant upon the type of muscle contraction performed. To better understand the micromechanical behavior and regional adaptability/mal-adaptability of tendon tissue it is important to estimate its internal stress-strain fields. Recent relevant advancements in numerical techniques related to tendon loading are discussed

‘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

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

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

The Multi-Scale Infrastructure for Chemistry and Aerosols (MUSICA)

To explore the various couplings across space and time and between ecosystems in a consistent manner, atmospheric modeling is moving away from the fractured limited-scale modeling strategy of the past toward a unification of the range of scales inherent in the Earth system. This paper describes the forward-looking Multi-Scale Infrastructure for Chemistry and Aerosols (MUSICA), which is intended to become the next-generation community infrastructure for research involving atmospheric chemistry and aerosols. MUSICA will be developed collaboratively by the National Center for Atmospheric Research (NCAR) and university and government researchers, with the goal of serving the international research and applications communities. The capability of unifying various spatiotemporal scales, coupling to other Earth system components, and process-level modularization will allow advances in both fundamental and applied research in atmospheric composition, air quality, and climate and is also envisioned to become a platform that addresses the needs of policy makers and stakeholders

Barbarians at the British Museum: Anglo-Saxon Art, Race and Religion

A critical historiographical overview of art historical approaches to early medieval material culture, with a focus on the British Museum collections and their connections to religion