The spectrum and convergence rates of exclusion and interchange processes on the complete graph

We give a short and completely elementary method to find the full spectrum of the exclusion process and a nicely limited superset of the spectrum of the interchange process (a.k.a.\ random transpositions) on the complete graph. In the case of the exclusion process, this gives a simple closed form expression for all the eigenvalues and their multiplicities. This result is then used to give an exact expression for the distance in $L^2$ from stationarity at any time and upper and lower bounds on the convergence rate for the exclusion process. In the case of the interchange process, upper and lower bounds are similarly found. Our results strengthen or reprove all known results of the mixing time for the two processes in a very simple way.Comment: 16 page

Ectopic Cushing Syndrome Due to Colon Cancer With Dual Morphology

Efst á síðunni er hægt að nálgast greinina í heild sinni með því að smella á hlekkinnWe report a case of colon cancer, and the most interesting presentation was Cushing’s syndrome (CS). A 72-year-old woman was diagnosed with CS when admitted to hospital because of NSTEMI and heart failure. The patient succumbed to her illness only 4 weeks after presentation. The colon cancer was a combined adenocarcinoma and small cell carcinoma, solely the latter component responsible for producing adrenocorticotropin hormone (ACTH)

Strict inequalities of critical values in continuum percolation

We consider the supercritical finite-range random connection model where the points $x,y$ of a homogeneous planar Poisson process are connected with probability $f(|y-x|)$ for a given $f$. Performing percolation on the resulting graph, we show that the critical probabilities for site and bond percolation satisfy the strict inequality $p_c^{\rm site} > p_c^{\rm bond}$. We also show that reducing the connection function $f$ strictly increases the critical Poisson intensity. Finally, we deduce that performing a spreading transformation on $f$ (thereby allowing connections over greater distances but with lower probabilities, leaving average degrees unchanged) {\em strictly} reduces the critical Poisson intensity. This is of practical relevance, indicating that in many real networks it is in principle possible to exploit the presence of spread-out, long range connections, to achieve connectivity at a strictly lower density value.Comment: 38 pages, 8 figure

First observations of high-temperature submarine hydrothermal vents and massive anhydrite deposits off the north coast of Iceland

High-temperature (250°C) hydrothermal vents and massive anhydrite deposits have been found in a shallow water, sediment-filled graben near 66°36′N in the Tjornes Fracture Zone north of Iceland. The site is located about 30 km offshore, near the small island of Grimsey. The main vent field occurs at a depth of 400 m and consists of about 20 large-diameter (up to 10 m) mounds and 1–3 m chimneys and spires of anhydrite and talc. A north–south alignment of the mounds over a 1-km strike length of the valley floor suggests that their distribution is controlled by a buried fault. Widespread shimmering water and extensive white patches of anhydrite in the sediment between the mounds indicates that the entire 1-km2 area occupied by the vents is thermally active. A 2-man research submersible JAGO was used to map the area and to sample vent waters, gases, and chimneys. Actively boiling hydrothermal vents occur on most of the mounds, and extensive two-phase venting indicates that the field is underlain by a large boiling zone (200×300 m). The presence of boiling fluids in shallow aquifers beneath the deposits was confirmed by sediment coring. The highest-temperature pore fluids were encountered in talc- and anhydrite-rich sedimentary layers that occur up to 7 m below the mounds. Baked muds underlie the talc and anhydrite layers, and pyrite is common in stockwork-like fractures and veins in the hydrothermally altered sediments. However, massive sulfides (pyrite–marcasite crusts) were found in only one relict mound. Subseafloor boiling has likely affected the metal-carrying capacity of the hydrothermal fluids, and deposition of sulfides may be occurring at greater depth. Although the mounds and chimneys at Grimsey resemble other deposits at sedimented ridges (e.g. Middle Valley, Escanaba Trough, Guaymas Basin), the shallow water setting and extensive boiling of the hydrothermal fluids represent a distinctive new type of seafloor hydrothermal system