2,497 research outputs found
Inverse Scattering and Acousto-Optic Imaging
We propose a tomographic method to reconstruct the optical properties of a
highly-scattering medium from incoherent acousto-optic measurements. The method
is based on the solution to an inverse problem for the diffusion equation and
makes use of the principle of interior control of boundary measurements by an
external wave field.Comment: 10 page
Phase Space Models for Stochastic Nonlinear Parabolic Waves: Wave Spread and Singularity
We derive several kinetic equations to model the large scale, low Fresnel
number behavior of the nonlinear Schrodinger (NLS) equation with a rapidly
fluctuating random potential. There are three types of kinetic equations the
longitudinal, the transverse and the longitudinal with friction. For these
nonlinear kinetic equations we address two problems: the rate of dispersion and
the singularity formation.
For the problem of dispersion, we show that the kinetic equations of the
longitudinal type produce the cubic-in-time law, that the transverse type
produce the quadratic-in-time law and that the one with friction produces the
linear-in-time law for the variance prior to any singularity.
For the problem of singularity, we show that the singularity and blow-up
conditions in the transverse case remain the same as those for the homogeneous
NLS equation with critical or supercritical self-focusing nonlinearity, but
they have changed in the longitudinal case and in the frictional case due to
the evolution of the Hamiltonian
The Cop Number of the One-Cop-Moves Game on Planar Graphs
Cops and robbers is a vertex-pursuit game played on graphs. In the classical
cops-and-robbers game, a set of cops and a robber occupy the vertices of the
graph and move alternately along the graph's edges with perfect information
about each other's positions. If a cop eventually occupies the same vertex as
the robber, then the cops win; the robber wins if she can indefinitely evade
capture. Aigner and Frommer established that in every connected planar graph,
three cops are sufficient to capture a single robber. In this paper, we
consider a recently studied variant of the cops-and-robbers game, alternately
called the one-active-cop game, one-cop-moves game or the lazy-cops-and-robbers
game, where at most one cop can move during any round. We show that Aigner and
Frommer's result does not generalise to this game variant by constructing a
connected planar graph on which a robber can indefinitely evade three cops in
the one-cop-moves game. This answers a question recently raised by Sullivan,
Townsend and Werzanski.Comment: 32 page
Core and penumbra estimation using deep learning-based AIF in association with clinical measures in computed tomography perfusion
Objectives:Â To investigate whether utilizing a convolutional neural network (CNN)-based arterial input function (AIF) improves the volumetric estimation of core and penumbra in association with clinical measures in stroke patients.
Methods: The study included 160 acute ischemic stroke patients (male = 87, female = 73, median age = 73 years) with approval from the institutional review board. The patients had undergone CTP imaging, NIHSS and ASPECTS grading. convolutional neural network (CNN) model was trained to fit a raw AIF curve to a gamma variate function. CNN AIF was utilized to estimate the core and penumbra volumes which were further validated with clinical scores.
Results: Penumbra estimated by CNN AIF correlated positively with the NIHSS score (r = 0.69; p  20) and lower ASPECT score ( 10 s, Tmax > 10 s volumes were statistically significantly higher (p < .05).
Conclusions:Â With inclusion of the CNN AIF in perfusion imaging pipeline, penumbra and core estimations are more reliable as they correlate with scores representing neurological deficits in stroke.
Critical relevance statement:Â With CNN AIF perfusion imaging pipeline, penumbra and core estimations are more reliable as they correlate with scores representing neurological deficits in stroke
Kinetic Limit for Wave Propagation in a Random Medium
We study crystal dynamics in the harmonic approximation. The atomic masses
are weakly disordered, in the sense that their deviation from uniformity is of
order epsilon^(1/2). The dispersion relation is assumed to be a Morse function
and to suppress crossed recollisions. We then prove that in the limit epsilon
to 0 the disorder averaged Wigner function on the kinetic scale, time and space
of order epsilon^(-1), is governed by a linear Boltzmann equation.Comment: 71 pages, 3 figure
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