A simple proof of the Markoff conjecture for prime powers

We give a simple and independent proof of the result of Jack Button and Paul Schmutz that the Markoff conjecture on the uniqueness of the Markoff triples (a,b,c), where a, b, and c are in increasing order, holds whenever $c$ is a prime power.Comment: 5 pages, no figure

Prevalence, associated factors, and relationship to quality of life of lower urinary tract symptoms: a cross‐sectional, questionnaire survey of cancer patients

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/98277/1/ijcp12141.pd

Looking forwards and backwards: dynamics and genealogies of locally regulated populations

We introduce a broad class of mechanistic spatial models to describe how spatially heterogeneous populations live, die, and reproduce. Individuals are represented by points of a point measure, whose birth and death rates can depend both on spatial position and local population density, defined at a location to be the convolution of the point measure with a suitable non-negative integrable kernel centred on that location. We pass to three different scaling limits: an interacting superprocess, a nonlocal partial differential equation (PDE), and a classical PDE. The classical PDE is obtained both by a two-step convergence argument, in which we first scale time and population size and pass to the nonlocal PDE, and then scale the kernel that determines local population density; and in the important special case in which the limit is a reaction-diffusion equation, directly by simultaneously scaling the kernel width, timescale and population size in our individual based model. A novelty of our model is that we explicitly model a juvenile phase. The number of juveniles produced by an individual depends on local population density at the location of the parent; these juvenile offspring are thrown off in a (possibly heterogeneous, anisotropic) Gaussian distribution around the location of the parent; they then reach (instant) maturity with a probability that can depend on the local population density at the location at which they land. Although we only record mature individuals, a trace of this two-step description remains in our population models, resulting in novel limits in which the spatial dynamics are governed by a nonlinear diffusion. Using a lookdown representation, we are able to retain information about genealogies relating individuals in our population and, in the case of deterministic limiting models, we use this to deduce the backwards in time motion of the ancestral lineage of an individual sampled from the population. We observe that knowing the history of the population density is not enough to determine the motion of ancestral lineages in our model. We also investigate (and contrast) the behaviour of lineages for three different deterministic models of a population expanding its range as a travelling wave: the Fisher-KPP equation, the Allen-Cahn equation, and a porous medium equation with logistic growth

Intraosseous angiosarcoma with secondary aneurysmal bone cysts presenting as an elusive diagnostic challenge

Angiosarcoma of bone is an exceedingly rare primary bone malignancy that can present as an aggressive osteolytic lesion. Histological diagnosis can be extremely challenging, as the pathological features often resemble that of aneurysmal bone cysts. We report an interesting and peculiar case of an intraosseous angiosarcoma that presented as a diagnostic dilemma and discuss the relevant radiological and pathologic findings

Mott-Kondo Insulator Behavior in the Iron Oxychalcogenides

We perform a combined experimental-theoretical study of the Fe-oxychalcogenides (FeO\emph{Ch}) series La$_{2}$O$_{2}$Fe$_{2}$O\emph{M}$_{2}$ (\emph{M}=S, Se), which is the latest among the Fe-based materials with the potential \ to show unconventional high-T$_{c}$ superconductivity (HTSC). A combination of incoherent Hubbard features in X-ray absorption (XAS) and resonant inelastic X-ray scattering (RIXS) spectra, as well as resitivity data, reveal that the parent FeO\emph{Ch} are correlation-driven insulators. To uncover microscopics underlying these findings, we perform local density approximation-plus-dynamical mean field theory (LDA+DMFT) calculations that unravel a Mott-Kondo insulating state. Based upon good agreement between theory and a range of data, we propose that FeO\emph{Ch} may constitute a new, ideal testing ground to explore HTSC arising from a strange metal proximate to a novel selective-Mott quantum criticality

Extracting density-density correlations from in situ images of atomic quantum gases

We present a complete recipe to extract the density-density correlations and the static structure factor of a two-dimensional (2D) atomic quantum gas from in situ imaging. Using images of non-interacting thermal gases, we characterize and remove the systematic contributions of imaging aberrations to the measured density-density correlations of atomic samples. We determine the static structure factor and report results on weakly interacting 2D Bose gases, as well as strongly interacting gases in a 2D optical lattice. In the strongly interacting regime, we observe a strong suppression of the static structure factor at long wavelengths.Comment: 15 pages, 5 figure