2,664 research outputs found
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 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 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 via the convolution of
the point measure with a nonnegative kernel. 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 first scaling
time and population size to pass to the nonlocal PDE, and then scaling the
kernel that determines local population density; and also (when the limit is a
reaction-diffusion equation) 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: offspring are thrown off in
a Gaussian distribution around the location of the parent, and reach (instant)
maturity with a probability that can depend on the 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 governed by a nonlinear diffusion. Using a lookdown
representation, we retain information about genealogies and, in the case of
deterministic limiting models, use this to deduce the backwards in time motion
of the ancestral lineage of a sampled individual. 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 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
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
Mott-Kondo Insulator Behavior in the Iron Oxychalcogenides
We perform a combined experimental-theoretical study of the
Fe-oxychalcogenides (FeO\emph{Ch}) series
LaOFeO\emph{M} (\emph{M}=S, Se), which is the latest
among the Fe-based materials with the potential \ to show unconventional
high-T 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
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