Mathieu twining characters for K3

The analogue of the McKay-Thompson series for the proposed Mathieu group action on the elliptic genus of K3 is analysed. The corresponding NS-sector twining characters have good modular properties and satisfy remarkable replication identities. These observations provide strong support for the conjecture that the elliptic genus of K3 carries indeed an action of the Mathieu group M24.Comment: 19 page

Ambitwistor strings and the scattering equations at one loop

Ambitwistor strings are chiral, infinite tension analogues of conventional string theory whose target space is the space of complex null geodesics and whose spectrum consists exclusively of massless states. At genus zero, these strings underpin the Cachazo-He-Yuan formulae for tree level scattering of gravitons, gluons and scalars. In this paper we extend these formulae in a number of directions. Firstly, we consider Ramond sector vertex operators and construct simple amplitudes involving space-time fermions. These agree with tree amplitudes in ten dimensional supergravity and super Yang--Mills. We then show that, after the usual GSO projections, the ambitwistor string partition function is modular invariant. We consider the scattering equations at genus one, and calculate one loop scattering amplitudes for NS-NS external states in the Type II ambitwistor string. We conjecture that these give new representations of (the integrand of) one loop supergravity amplitudes and we show that they have the expected behaviour under factorization of the worldsheet in both non--separating and separating degenerations.Comment: 34 pages, no figures. v2: improvements to discussion, references update

Parallels between Pathogens and Gluten Peptides in Celiac Sprue

Pathogens are exogenous agents capable of causing disease in susceptible organisms. In celiac sprue, a disease triggered by partially hydrolyzed gluten peptides in the small intestine, the offending immunotoxins cannot replicate, but otherwise have many hallmarks of classical pathogens. First, dietary gluten and its peptide metabolites are ubiquitous components of the modern diet, yet only a small, genetically susceptible fraction of the human population contracts celiac sprue. Second, immunotoxic gluten peptides have certain unusual structural features that allow them to survive the harsh proteolytic conditions of the gastrointestinal tract and thereby interact extensively with the mucosal lining of the small intestine. Third, they invade across epithelial barriers intact to access the underlying gut-associated lymphoid tissue. Fourth, they possess recognition sequences for selective modification by an endogenous enzyme, transglutaminase 2, allowing for in situ activation to a more immunotoxic form via host subversion. Fifth, they precipitate a T cell–mediated immune reaction comprising both innate and adaptive responses that causes chronic inflammation of the small intestine. Sixth, complete elimination of immunotoxic gluten peptides from the celiac diet results in remission, whereas reintroduction of gluten in the diet causes relapse. Therefore, in analogy with antibiotics, orally administered proteases that reduce the host's exposure to the immunotoxin by accelerating gluten peptide destruction have considerable therapeutic potential. Last but not least, notwithstanding the power of in vitro methods to reconstitute the essence of the immune response to gluten in a celiac patient, animal models for the disease, while elusive, are likely to yield fundamentally new systems-level insights

Two-loop scattering amplitudes from ambitwistor strings: from genus two to the nodal Riemann sphere

We derive from ambitwistor strings new formulae for two-loop scattering amplitudes in supergravity and super-Yang-Mills theory, with any number of particles. We start by constructing a formula for the type II ambitwistor string amplitudes on a genus-two Riemann surface, and then study the localisation of the moduli space integration on a degenerate limit, where the genus-two surface turns into a Riemann sphere with two nodes. This leads to scattering amplitudes in supergravity, expressed in the formalism of the two-loop scattering equations. For super-Yang-Mills theory, we import `half' of the supergravity result, and determine the colour dependence by considering a current algebra on the nodal Riemann sphere, thereby completely specifying the two-loop analogue of the Parke-Taylor factor, including non-planar contributions. We also present in appendices explicit expressions for the Szego kernels and the partition functions for even spin structures, up to the relevant orders in the degeneration parameters, which may be useful for related investigations in conventional superstring theory.Comment: 66 pages plus appendices, 14 figures. v2: small changes, published version. v3: typos fixed in appendix

Metopic synostosis

Premature closure of the metopic suture results in a growth restriction of the frontal bones, which leads to a skull malformation known as trigonocephaly. Over the course of recent decades, its incidence has been rising, currently making it the second most common type of craniosynostosis. Treatment consists of a cranioplasty, usually preformed before the age of 1 year. Metopic synostosis is linked with an increased level of neurodevelopmental delays. Theories on the etiology of these delays range from a reduced volume of the anterior cranial fossa to intrinsic malformations of the brain. This paper aims to provide an overview of this entity by giving an update on the epidemiology, etiology, evolution of treatment, follow-up, and neurodevelopment of metopic synostosis