30,184 research outputs found
A first step toward higher order chain rules in abelian functor calculus
One of the fundamental tools of undergraduate calculus is the chain rule. The
notion of higher order directional derivatives was developed by Huang,
Marcantognini, and Young, along with a corresponding higher order chain rule.
When Johnson and McCarthy established abelian functor calculus, they proved a
chain rule for functors that is analogous to the directional derivative chain
rule when . In joint work with Bauer, Johnson, and Riehl, we defined an
analogue of the iterated directional derivative and provided an inductive proof
of the analogue to the chain rule of Huang et al.
This paper consists of the initial investigation of the chain rule found in
Bauer et al., which involves a concrete computation of the case when . We
describe how to obtain the second higher order directional derivative chain
rule for abelian functors. This proof is fundamentally different in spirit from
the proof given in Bauer et al. as it relies only on properties of cross
effects and the linearization of functors
Compact strain-sensitive flexible photonic crystals for sensors
A promising fabrication route to produce absorbing flexible photonic crystals is presented, which exploits self-assembly during the shear processing of multi-shelled polymer spheres. When absorbing material is incorporated in the interstitial space surrounding high-refractive-index spheres, a dramatic enhancement in the transmission edge on the short-wavelength side of the band gap is observed. This effect originates from the shifting optical field spatial distribution as the incident wavelength is tuned around the band gap, and results in a contrast up to 100 times better than similar but nonabsorbing photonic crystals. An order-of-magnitude improvement in strain sensitivity is shown, suggesting the use of these thin films in photonic sensors
Crop identification technology assessment for remote sensing (CITARS). Volume 6: Data processing at the laboratory for applications of remote sensing
The results of classifications and experiments for the crop identification technology assessment for remote sensing are summarized. Using two analysis procedures, 15 data sets were classified. One procedure used class weights while the other assumed equal probabilities of occurrence for all classes. Additionally, 20 data sets were classified using training statistics from another segment or date. The classification and proportion estimation results of the local and nonlocal classifications are reported. Data also describe several other experiments to provide additional understanding of the results of the crop identification technology assessment for remote sensing. These experiments investigated alternative analysis procedures, training set selection and size, effects of multitemporal registration, spectral discriminability of corn, soybeans, and other, and analyses of aircraft multispectral data
Crop Identification Technology Assessment for Remote Sensing (CITARS)
The results of classifications and experiments performed for the Crop Identification Technology Assessment for Remote Sensing (CITARS) project are summarized. Fifteen data sets were classified using two analysis procedures. One procedure used class weights while the other assumed equal probabilities of occurrence for all classes. In addition, 20 data sets were classified using training statistics from another segment or date. The results of both the local and non-local classifications in terms of classification and proportion estimation are presented. Several additional experiments are described which were performed to provide additional understanding of the CITARS results. These experiments investigated alternative analysis procedures, training set selection and size, effects of multitemporal registration, the spectral discriminability of corn, soybeans, and other, and analysis of aircraft multispectral data
Annihilation Diagrams in Two-Body Nonleptonic Decays of Charmed Mesons
In the pole-dominance model for the two-body nonleptonic decays of charmed
mesons and , it is shown that the
contributions of the intermediate pseudoscalar and the axial-vector meson poles
cancel each other in the annihilation diagrams in the chiral limit. In the same
limit, the annihilation diagrams for the decays vanish
independently.Comment: 9 pages (+ 3 figures available upon request), UR-1316, ER-40685-766,
IC/93/21
Zipf's law in Nuclear Multifragmentation and Percolation Theory
We investigate the average sizes of the largest fragments in nuclear
multifragmentation events near the critical point of the nuclear matter phase
diagram. We perform analytic calculations employing Poisson statistics as well
as Monte Carlo simulations of the percolation type. We find that previous
claims of manifestations of Zipf's Law in the rank-ordered fragment size
distributions are not born out in our result, neither in finite nor infinite
systems. Instead, we find that Zipf-Mandelbrot distributions are needed to
describe the results, and we show how one can derive them in the infinite size
limit. However, we agree with previous authors that the investigation of
rank-ordered fragment size distributions is an alternative way to look for the
critical point in the nuclear matter diagram.Comment: 8 pages, 11 figures, submitted to PR
Diffeomorphic random sampling using optimal information transport
In this article we explore an algorithm for diffeomorphic random sampling of
nonuniform probability distributions on Riemannian manifolds. The algorithm is
based on optimal information transport (OIT)---an analogue of optimal mass
transport (OMT). Our framework uses the deep geometric connections between the
Fisher-Rao metric on the space of probability densities and the right-invariant
information metric on the group of diffeomorphisms. The resulting sampling
algorithm is a promising alternative to OMT, in particular as our formulation
is semi-explicit, free of the nonlinear Monge--Ampere equation. Compared to
Markov Chain Monte Carlo methods, we expect our algorithm to stand up well when
a large number of samples from a low dimensional nonuniform distribution is
needed.Comment: 8 pages, 3 figure
Remission of obesity among a nationally representative sample of US children
Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/147066/1/ijpo12457.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/147066/2/ijpo12457_am.pd
The X-ray Properties of the Nearby Star-Forming Galaxy IC 342: The XMM-Newton View
We present the X-ray properties of IC342 using XMM-Newton. Thirty-five
sources are detected coincident with the disk of IC342 (more than tripling the
number known), of which ~31 are likely to be intrinsic to IC342. This
population shows a range of spectral properties and has an X-ray luminosity
function slope and infrared luminosity comparable to that of starburst galaxies
such as M82 and the Antennae, while its relative lack of extended X-ray
emission is similar to the properties of quiescent spirals. We do detect
long-term variability between this observation and the 1991 ROSAT and 1993/2000
ASCA observations for five sources. Notably, the second most luminous source
IC342 X-2 is is found to be in its the lowest luminosity state observed for X-2
to date, although the slope of the spectrum is intermediate between the
previously observed low/hard and high/soft states. IC342 X-1, on the other
hand, is found to be in an identical state to that observed in 2000 with ASCA.
Assuming X-1 is in an anomalous very high (VH) state, then either (1) X-1 has
remained in this state between 2000 and 2002, and is therefore the longest
duration VH-state binary ever observed, or (2) it was simply caught in a VH
state by chance in both the 2000 ASCA and 2002 XMM-Newton observations. We have
also confirmed the ROSAT HRI result that the nucleus of IC342 is made up of
both point-like and extended emission. The relative fluxes of the two spectral
components suggest that the nucleus is complex, with a soft extended component
contributing approximately half of the total luminosity. (Abridged)Comment: AJ in press (December 2003), 9 pages, 7 figures, 2 tables,
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