79,051 research outputs found
The Baruch College Solution: A Laboratory for Improving Communication Skills of Non-Native Speakers of American English
Functional Regression
Functional data analysis (FDA) involves the analysis of data whose ideal
units of observation are functions defined on some continuous domain, and the
observed data consist of a sample of functions taken from some population,
sampled on a discrete grid. Ramsay and Silverman's 1997 textbook sparked the
development of this field, which has accelerated in the past 10 years to become
one of the fastest growing areas of statistics, fueled by the growing number of
applications yielding this type of data. One unique characteristic of FDA is
the need to combine information both across and within functions, which Ramsay
and Silverman called replication and regularization, respectively. This article
will focus on functional regression, the area of FDA that has received the most
attention in applications and methodological development. First will be an
introduction to basis functions, key building blocks for regularization in
functional regression methods, followed by an overview of functional regression
methods, split into three types: [1] functional predictor regression
(scalar-on-function), [2] functional response regression (function-on-scalar)
and [3] function-on-function regression. For each, the role of replication and
regularization will be discussed and the methodological development described
in a roughly chronological manner, at times deviating from the historical
timeline to group together similar methods. The primary focus is on modeling
and methodology, highlighting the modeling structures that have been developed
and the various regularization approaches employed. At the end is a brief
discussion describing potential areas of future development in this field
Genomic and proteomic profiling for cancer diagnosis in dogs
Global gene expression, whereby tumours are classified according to similar gene expression patterns or ‘signatures’ regardless of cell morphology or tissue characteristics, is being increasingly used in both the human and veterinary fields to assist in cancer diagnosis and prognosis. Many studies on canine tumours have focussed on RNA expression using techniques such as microarrays or next generation sequencing. However, proteomic studies combining two-dimensional polyacrylamide gel electrophoresis or two-dimensional differential gel electrophoresis with mass spectrometry have also provided a wealth of data on gene expression in tumour tissues. In addition, proteomics has been instrumental in the search for tumour biomarkers in blood and other body fluids
An Open Mapping Theorem
It is proved that any surjective morphism onto a
locally compact group is open for every cardinal . This answers a
question posed by Karl Heinrich Hofmann and the second author
Scheme Independence to all Loops
The immense freedom in the construction of Exact Renormalization Groups means
that the many non-universal details of the formalism need never be exactly
specified, instead satisfying only general constraints. In the context of a
manifestly gauge invariant Exact Renormalization Group for SU(N) Yang-Mills, we
outline a proof that, to all orders in perturbation theory, all explicit
dependence of beta function coefficients on both the seed action and details of
the covariantization cancels out. Further, we speculate that, within the
infinite number of renormalization schemes implicit within our approach, the
perturbative beta function depends only on the universal details of the setup,
to all orders.Comment: 18 pages, 8 figures; Proceedings of Renormalization Group 2005,
Helsinki, Finland, 30th August - 3 September 2005. v2: Published in jphysa;
minor changes / refinements; refs. adde
String-Like Lagrangians from a Generalized Geometry
This note will use Hitchin's generalized geometry and a model of axionic
gravity developed by Warren Siegel in the mid-nineties to show that the
construction of Lagrangians based on the inner product arising from the pairing
of a vector and its dual can lead naturally to the low-energy Lagrangian of the
bosonic string.Comment: Conclusions basically unchanged, but presentation streamlined
significantly. Published versio
Existence and uniqueness theorems for massless fields on a class of spacetimes with closed timelike curves
We study the massless scalar field on asymptotically flat spacetimes with
closed timelike curves (CTC's), in which all future-directed CTC's traverse one
end of a handle (wormhole) and emerge from the other end at an earlier time.
For a class of static geometries of this type, and for smooth initial data with
all derivatives in on {\cI}^{-}, we prove existence of smooth solutions
which are regular at null and spatial infinity (have finite energy and finite
-norm) and have the given initial data on \cI^-. A restricted uniqueness
theorem is obtained, applying to solutions that fall off in time at any fixed
spatial position. For a complementary class of spacetimes in which CTC's are
confined to a compact region, we show that when solutions exist they are unique
in regions exterior to the CTC's. (We believe that more stringent uniqueness
theorems hold, and that the present limitations are our own.) An extension of
these results to Maxwell fields and massless spinor fields is sketched.
Finally, we discuss a conjecture that the Cauchy problem for free fields is
well defined in the presence of CTC's whenever the problem is well-posed in the
geometric-optics limit. We provide some evidence in support of this conjecture,
and we present counterexamples that show that neither existence nor uniqueness
is guaranteed under weaker conditions. In particular, both existence and
uniqueness can fail in smooth, asymptotically flat spacetimes with a compact
nonchronal region.Comment: 47 pages, Revtex, 7 figures (available upon request
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