105,100 research outputs found
Testing Foundations of Biological Scaling Theory Using Automated Measurements of Vascular Networks
Scientists have long sought to understand how vascular networks supply blood
and oxygen to cells throughout the body. Recent work focuses on principles that
constrain how vessel size changes through branching generations from the aorta
to capillaries and uses scaling exponents to quantify these changes. Prominent
scaling theories predict that combinations of these exponents explain how
metabolic, growth, and other biological rates vary with body size.
Nevertheless, direct measurements of individual vessel segments have been
limited because existing techniques for measuring vasculature are invasive,
time consuming, and technically difficult. We developed software that extracts
the length, radius, and connectivity of in vivo vessels from contrast-enhanced
3D Magnetic Resonance Angiography. Using data from 20 human subjects, we
calculated scaling exponents by four methods--two derived from local properties
of branching junctions and two from whole-network properties. Although these
methods are often used interchangeably in the literature, we do not find
general agreement between these methods, particularly for vessel lengths.
Measurements for length of vessels also diverge from theoretical values, but
those for radius show stronger agreement. Our results demonstrate that vascular
network models cannot ignore certain complexities of real vascular systems and
indicate the need to discover new principles regarding vessel lengths
The human and mammalian cerebrum scale by computational power and information resistance
The cerebrum of mammals spans a vast range of sizes and yet has a very
regular structure. The amount of folding of the cortical surface and the
proportion of white matter gradually increase with size, but the underlying
mechanisms remain elusive. Here, two laws are derived to fully explain these
cerebral scaling relations. The first law holds that the long-range information
flow in the cerebrum is determined by the total cortical surface (i.e., the
number of neurons) and the increasing information resistance of long-range
connections. Despite having just one free parameter, the first law fits the
mammalian cerebrum better than any existing function, both across species and
within humans. According to the second law, the white matter volume scales,
with a few minor corrections, to the cortical surface area. It follows from the
first law that large cerebrums have much local processing and little global
information flow. Moreover, paradoxically, a further increase in long-range
connections would decrease the efficiency of information flow.Comment: 15 pages, 2 figures; 3 supplement
A Functional Wavelet-Kernel Approach for Continuous-time Prediction
We consider the prediction problem of a continuous-time stochastic process on
an entire time-interval in terms of its recent past. The approach we adopt is
based on functional kernel nonparametric regression estimation techniques where
observations are segments of the observed process considered as curves. These
curves are assumed to lie within a space of possibly inhomogeneous functions,
and the discretized times series dataset consists of a relatively small,
compared to the number of segments, number of measurements made at regular
times. We thus consider only the case where an asymptotically non-increasing
number of measurements is available for each portion of the times series. We
estimate conditional expectations using appropriate wavelet decompositions of
the segmented sample paths. A notion of similarity, based on wavelet
decompositions, is used in order to calibrate the prediction. Asymptotic
properties when the number of segments grows to infinity are investigated under
mild conditions, and a nonparametric resampling procedure is used to generate,
in a flexible way, valid asymptotic pointwise confidence intervals for the
predicted trajectories. We illustrate the usefulness of the proposed functional
wavelet-kernel methodology in finite sample situations by means of three
real-life datasets that were collected from different arenas
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