On equiangular lines in 17 dimensions and the characteristic polynomial of a Seidel matrix

For $e$ a positive integer, we find restrictions modulo $2^e$ on the coefficients of the characteristic polynomial $\chi_S(x)$ of a Seidel matrix $S$. We show that, for a Seidel matrix of order $n$ even (resp. odd), there are at most $2^{\binom{e-2}{2}}$ (resp. $2^{\binom{e-2}{2}+1}$) possibilities for the congruence class of $\chi_S(x)$ modulo $2^e\mathbb Z[x]$. As an application of these results, we obtain an improvement to the upper bound for the number of equiangular lines in $\mathbb R^{17}$, that is, we reduce the known upper bound from $50$ to $49$.Comment: 21 pages, fixed typo in Lemma 2.

Another construction of edge-regular graphs with regular cliques

We exhibit a new construction of edge-regular graphs with regular cliques that are not strongly regular. The infinite family of graphs resulting from this construction includes an edge-regular graph with parameters $(24,8,2)$. We also show that edge-regular graphs with $1$-regular cliques that are not strongly regular must have at least $24$ vertices.Comment: 7 page

Physiology of Skin

One of Montagna's greatest contributions to study of the biology of the skin has been his demolition of the artificial walls that traditionally separated the histologist from the physiologist. He has shown that only by relating function with structure can we shed light on the workings of the skin. He has stressed the fallacy of studying a single structural or functional unit in isolation from others. The skin represents an organization of many different functional units, and physiology of skin is the study of this organization. My purpose is to make a personal commentary on the achievements, failures, and prospects of understanding some aspects of the organization of the functional units. Twenty-five years ago, the importance of relating skin to internal organs and systems received much attention. We have long been aware that skin sometimes reacts to internal disease, but only recently has the impact of skin disorders on the circulatory, renal, and gastro-intestinal systems been recognized. As a result, our patients are now less likely to suffer from neglect of the whole which follows narrow over-specialized attention to the part. Increased interest in endocrine effects on the skin has revealed that several important physiologic activities of the skin are either partly or wholly regulated by hormones secreted by endocrine glands. Nevertheless, some physiologic activities in skin seem to be independent, their regulation being carried out by local mediating hormones. Other activities involve both central and local regulation. The nature and roles of these two control mechanisms and their interrelation constitute by far the most promising physiologic research in skin

The Geminga pulsar wind nebula in the mid-infrared and submillimetre

The nearby middle-aged Geminga pulsar has crossed the Galactic plane within the last ∼0.1 Myr. We present archival data from Wide-field Infrared Survey Explorer and from SCUBA and SCUBA-2 on the James Clerk Maxwell Telescope to assess whether any midinfrared and submillimetre emission arises from interaction of the pulsar wind nebula with the interstellar medium. A candidate shell and bow shock are reported. Given the low pulsar velocity and local density, dust grains appear able to penetrate into the nebula. A compact source seen towards the pulsar is fitted with a dust spectrum. If confirmed as a real association at higher resolution, this could be a circum-pulsar disc of at least a few Earth-masses, in which future planets could form

Effect of Nonsteroid Anti-Inflammatory and Antipyretic Drugs on Prostaglandin Biosynthesis by Human Skin

There is increasing evidence that prostaglandins are mediators of inflammation in skin and that prostaglandins are synthesised locally in response to the inflammatory stimulus. The effect of four nonsteroid anti-inflammatory or antipyretic drugs on prostaglandin biosynthesis by human skin has therefore been studied. Aspirin (0.56 mM) and indomethacin (0.28 mM) produced a small but significant inhibition of synthesis of prostaglandin E2. Indomethacin and chloroquine, but not aspirin, inhibited synthesis of prostaglandin F2a. Acetaminophen inhibited synthesis of prostaglandin F2, but did not inhibit prostaglandin E2 synthesis. None of the drugs studied are therapeutically effective anti-inflammatory agents in human skin and it may be significant that the inhibitory effects of aspirin and indomethacin on prostaglandin synthesis by skin are small compared with the effects of the same drugs on prostaglandin synthesis in other tissues

Real equiangular lines in dimension 18 and the Jacobi identity for complementary subgraphs

We show that the maximum cardinality of an equiangular line system in $\mathbb R^{18}$ is at most $59$. Our proof includes a novel application of the Jacobi identity for complementary subgraphs. In particular, we show that there does not exist a graph whose adjacency matrix has characteristic polynomial $(x-22)(x-2)^{42} (x+6)^{15} (x+8)^2$.Comment: 26 pages. Updated to match the published, journal versio

Forming the first planetary systems: debris around Galactic thick disc stars

The thick disc contains stars formed within the first Gyr of Galactic history, and little is known about their planetary systems. The Spitzer MIPS instrument was used to search 11 of the closest of these old low-metal stars for circumstellar debris, as a signpost that bodies at least as large as planetesimals were formed. A total of 22 thick disc stars has now been observed, after including archival data, but dust is not found in any of the systems. The data rule out a high incidence of debris among star systems from early in the Galaxy's formation. However, some stars of this very old population do host giant planets, at possibly more than the general incidence among low-metal Sun-like stars. As the Solar System contains gas giants but little cometary dust, the thick disc could host analogue systems that formed many Gyr before the Sun.Comment: accepted by MNRAS Letters; 5 pages, 4 figure