45,106 research outputs found

### Direct Visualisation of the Depth-Dependent Mechanical Properties of Full-Thickness Articular Cartilage.

The structural anisotropy of articular cartilage controls its deformation response. As proteoglycans and collagen vary with depth, simple uniaxial compression results in inhomogeneous deformation with distinct depth-dependent mechanical properties. Investigations into depth-dependent mechanical properties of articular cartilage have previously required tissue modification after specimen isolation. Such modifications include histological processes, freezing, subchondral bone removal, and fluorescent staining that may alter the tissue, limiting in vivo applicability

### Poisson process approximation: From Palm theory to Stein's method

This exposition explains the basic ideas of Stein's method for Poisson random
variable approximation and Poisson process approximation from the point of view
of the immigration-death process and Palm theory. The latter approach also
enables us to define local dependence of point processes [Chen and Xia (2004)]
and use it to study Poisson process approximation for locally dependent point
processes and for dependent superposition of point processes.Comment: Published at http://dx.doi.org/10.1214/074921706000001076 in the IMS
Lecture Notes Monograph Series
(http://www.imstat.org/publications/lecnotes.htm) by the Institute of
Mathematical Statistics (http://www.imstat.org

### Stein's method, Palm theory and Poisson process approximation

The framework of Stein's method for Poisson process approximation is
presented from the point of view of Palm theory, which is used to construct
Stein identities and define local dependence. A general result (Theorem
\refimportantproposition) in Poisson process approximation is proved by taking
the local approach.
It is obtained without reference to any particular metric, thereby allowing
wider applicability. A Wasserstein pseudometric is introduced for measuring the
accuracy of point process approximation. The pseudometric provides a
generalization of many metrics used so far, including the total variation
distance for random variables and the Wasserstein metric for processes as in
Barbour and Brown [Stochastic Process. Appl. 43 (1992) 9-31]. Also, through the
pseudometric, approximation for certain point processes on a given carrier
space is carried out by lifting it to one on a larger space, extending an idea
of Arratia, Goldstein and Gordon [Statist. Sci. 5 (1990)
403-434]. The error bound in the general result is similar in form to that
for Poisson approximation. As it yields the Stein factor 1/\lambda as in
Poisson approximation, it provides good approximation, particularly in cases
where \lambda is large. The general result is applied to a number of problems
including Poisson process modeling of rare words in a DNA sequence.Comment: Published by the Institute of Mathematical Statistics
(http://www.imstat.org) in the Annals of Probability
(http://www.imstat.org/aop/) at http://dx.doi.org/10.1214/00911790400000002

### Simulations of an energy dechirper based on dielectric lined waveguides

Terahertz frequency wakefields can be excited by ultra-short relativistic
electron bunches travelling through dielectric lined waveguide (DLW)
structures. These wakefields can either accelerate a witness bunch with high
gradient, or modulate the energy of the driving bunch. In this paper, we study
a passive dechirper based on the DLW to compensate the correlated energy spread
of the bunches accelerated by the laser plasma wakefield accelerator (LWFA). A
rectangular waveguide structure was employed taking advantage of its
continuously tunable gap during operation. The assumed 200 MeV driving bunch
had a Gaussian distribution with a bunch length of 3.0 {\mu}m, a relative
correlated energy spread of 1%, and a total charge of 10 pC. Both of the CST
Wakefield Solver and PIC Solver were used to simulate and optimize such a
dechirper. Effect of the time-dependent self-wake on the driving bunch was
analyzed in terms of the energy modulation and the transverse phase space

### S-Lemma with Equality and Its Applications

Let $f(x)=x^TAx+2a^Tx+c$ and $h(x)=x^TBx+2b^Tx+d$ be two quadratic functions
having symmetric matrices $A$ and $B$. The S-lemma with equality asks when the
unsolvability of the system $f(x)<0, h(x)=0$ implies the existence of a real
number $\mu$ such that $f(x) + \mu h(x)\ge0, ~\forall x\in \mathbb{R}^n$. The
problem is much harder than the inequality version which asserts that, under
Slater condition, $f(x)<0, h(x)\le0$ is unsolvable if and only if $f(x) + \mu
h(x)\ge0, ~\forall x\in \mathbb{R}^n$ for some $\mu\ge0$. In this paper, we
show that the S-lemma with equality does not hold only when the matrix $A$ has
exactly one negative eigenvalue and $h(x)$ is a non-constant linear function
($B=0, b\not=0$). As an application, we can globally solve $\inf\{f(x)\vert
h(x)=0\}$ as well as the two-sided generalized trust region subproblem
$\inf\{f(x)\vert l\le h(x)\le u\}$ without any condition. Moreover, the
convexity of the joint numerical range $\{(f(x), h_1(x),\ldots,
h_p(x)):~x\in\Bbb R^n\}$ where $f$ is a (possibly non-convex) quadratic
function and $h_1(x),\ldots,h_p(x)$ are affine functions can be characterized
using the newly developed S-lemma with equality.Comment: 34 page

### Enhancement of Coherent X ray Diffraction from Nanocrystals by Introduction of X ray Optics

Coherent X-ray Diffraction is applied to investigate the structure of individual nanocrystalline silver particles in the 100nm size range. In order to enhance the available signal, Kirkpatrick-Baez focusing optics have been introduced in the 34-ID-C beamline at APS. Concerns about the preservation of coherence under these circumstances are addressed through experiment and by calculations

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