9,501 research outputs found
Comparison of Randomized Multifocal Mapping and Temporal Phase Mapping of Visual Cortex for Clinical Use
fMRI is becoming an important clinical tool for planning and guidance of surgery to treat brain tumors, arteriovenous malformations, and epileptic foci. For visual cortex mapping, the most popular paradigm by far is temporal phase mapping, although random multifocal stimulation paradigms have drawn increased attention due to their ability to identify complex response fields and their random properties. In this study we directly compared temporal phase and multifocal vision mapping paradigms with respect to clinically relevant factors including: time efficiency, mapping completeness, and the effects of noise. Randomized, multifocal mapping accurately decomposed the response of single voxels to multiple stimulus locations and made correct retinotopic assignments as noise levels increased despite decreasing sensitivity. Also, multifocal mapping became less efficient as the number of stimulus segments (locations) increased from 13 to 25 to 49 and when duty cycle was increased from 25% to 50%. Phase mapping, on the other hand, activated more extrastriate visual areas, was more time efficient in achieving statistically significant responses, and had better sensitivity as noise increased, though with an increase in systematic retinotopic mis-assignments. Overall, temporal phase mapping is likely to be a better choice for routine clinical applications though random multifocal mapping may offer some unique advantages for selected applications
Free-floating planets from core accretion theory: microlensing predictions
We calculate the microlensing event rate and typical time-scales for the
free-floating planet (FFP) population that is predicted by the core accretion
theory of planet formation. The event rate is found to be ~
of that for the stellar population. While the stellar microlensing event
time-scale peaks at around 20 days, the median time-scale for FFP events (~0.1
day) is much shorter. Our values for the event rate and the median time-scale
are significantly smaller than those required to explain the \cite{Sum+11}
result, by factors of ~13 and ~16, respectively. The inclusion of planets at
wide separations does not change the results significantly. This discrepancy
may be too significant for standard versions of both the core accretion theory
and the gravitational instability model to explain satisfactorily. Therefore,
either a modification to the planet formation theory is required, or other
explanations to the excess of short-time-scale microlensing events are needed.
Our predictions can be tested by ongoing microlensing experiment such as
KMTNet, and by future satellite missions such as WFIRST and Euclid.Comment: 6 pages, 5 figures, MNRAS in pres
Invertibility in groupoid C*-algebras
Given a second-countable, Hausdorff, \'etale, amenable groupoid G with
compact unit space, we show that an element a in C*(G) is invertible if and
only if \lambda_x(a) is invertible for every x in the unit space of G, where
\lambda_x refers to the "regular representation" of C*(G) on l_2(G_x). We also
prove that, for every a in C*(G), there exists some x in G^{(0)} such that
||a|| = ||\lambda_x(a)||.Comment: 8 page
Correlations and Pairing Between Zeros and Critical Points of Gaussian Random Polynomials
We study the asymptotics of correlations and nearest neighbor spacings
between zeros and holomorphic critical points of , a degree N Hermitian
Gaussian random polynomial in the sense of Shiffman and Zeldtich, as N goes to
infinity. By holomorphic critical point we mean a solution to the equation
Our principal result is an explicit asymptotic formula
for the local scaling limit of \E{Z_{p_N}\wedge C_{p_N}}, the expected joint
intensity of zeros and critical points, around any point on the Riemann sphere.
Here and are the currents of integration (i.e. counting
measures) over the zeros and critical points of , respectively. We prove
that correlations between zeros and critical points are short range, decaying
like e^{-N\abs{z-w}^2}. With \abs{z-w} on the order of however,
\E{Z_{p_N}\wedge C_{p_N}}(z,w) is sharply peaked near causing zeros
and critical points to appear in rigid pairs. We compute tight bounds on the
expected distance and angular dependence between a critical point and its
paired zero.Comment: 35 pages, 3 figures. Some typos corrected and Introduction revise
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