1,593 research outputs found
Synchronizing to the Environment: Information Theoretic Constraints on Agent Learning
We show that the way in which the Shannon entropy of sequences produced by an
information source converges to the source's entropy rate can be used to
monitor how an intelligent agent builds and effectively uses a predictive model
of its environment. We introduce natural measures of the environment's apparent
memory and the amounts of information that must be (i) extracted from
observations for an agent to synchronize to the environment and (ii) stored by
an agent for optimal prediction. If structural properties are ignored, the
missed regularities are converted to apparent randomness. Conversely, using
representations that assume too much memory results in false predictability.Comment: 6 pages, 5 figures, Santa Fe Institute Working Paper 01-03-020,
http://www.santafe.edu/projects/CompMech/papers/stte.htm
Statistical Complexity of Simple 1D Spin Systems
We present exact results for two complementary measures of spatial structure
generated by 1D spin systems with finite-range interactions. The first, excess
entropy, measures the apparent spatial memory stored in configurations. The
second, statistical complexity, measures the amount of memory needed to
optimally predict the chain of spin values. These statistics capture distinct
properties and are different from existing thermodynamic quantities.Comment: 4 pages with 2 eps Figures. Uses RevTeX macros. Also available at
http://www.santafe.edu/projects/CompMech/papers/CompMechCommun.htm
Statistical Measures of Complexity: Why?
We review several statistical complexity measures proposed over the last
decade and a half as general indicators of structure or correlation. Recently,
Lopez-Ruiz, Mancini, and Calbet [Phys. Lett. A 209 (1995) 321] introduced
another measure of statistical complexity C_{LMC} that, like others, satisfies
the ``boundary conditions'' of vanishing in the extreme ordered and disordered
limits. We examine some properties of C_{LMC} and find that it is neither an
intensive nor an extensive thermodynamic variable and that it vanishes
exponentially in the thermodynamic limit for all one-dimensional finite-range
spin systems. We propose a simple alteration of C_{LMC} that renders it
extensive. However, this remedy results in a quantity that is a trivial
function of the entropy density and hence of no use as a measure of structure
or memory. We conclude by suggesting that a useful ``statistical complexity''
must not only obey the ordered-random boundary conditions of vanishing, it must
also be defined in a setting that gives a clear interpretation to what
structures are quantified.Comment: 7 pages with 2 eps Figures. Uses RevTeX macros. Also available at
http://www.santafe.edu/projects/CompMech/papers/CompMechCommun.html Submitted
to Phys. Lett.
The Temperature and Density Structure of the Solar Corona. I. Observations of the Quiet Sun with the EUV Imaging Spectrometer (EIS) on Hinode
Measurements of the temperature and density structure of the solar corona
provide critical constraints on theories of coronal heating. Unfortunately, the
complexity of the solar atmosphere, observational uncertainties, and the
limitations of current atomic calculations, particularly those for Fe, all
conspire to make this task very difficult. A critical assessment of plasma
diagnostics in the corona is essential to making progress on the coronal
heating problem. In this paper we present an analysis of temperature and
density measurements above the limb in the quiet corona using new observations
from the EUV Imaging Spectrometer (EIS) on \textit{Hinode}. By comparing the Si
and Fe emission observed with EIS we are able to identify emission lines that
yield consistent emission measure distributions. With these data we find that
the distribution of temperatures in the quiet corona above the limb is strongly
peaked near 1 MK, consistent with previous studies. We also find, however, that
there is a tail in the emission measure distribution that extends to higher
temperatures. EIS density measurements from several density sensitive line
ratios are found to be generally consistent with each other and with previous
measurements in the quiet corona. Our analysis, however, also indicates that a
significant fraction of the weaker emission lines observed in the EIS
wavelength ranges cannot be understood with current atomic data.Comment: Submitted to Ap
Testing the Unitarity of the CKM Matrix with a Space-Based Neutron Decay Experiment
If the Standard Model is correct, and fundamental fermions exist only in the
three generations, then the CKM matrix should be unitary. However, there
remains a question over a deviation from unitarity from the value of the
neutron lifetime. We discuss a simple space-based experiment that, at an orbit
height of 500 km above Earth, would measure the kinetic-energy, solid-angle,
flux spectrum of gravitationally bound neutrons (kinetic energy K<0.606 eV at
this altitude). The difference between the energy spectrum of neutrons that
come up from the Earth's atmosphere and that of the undecayed neutrons that
return back down to the Earth would yield a measurement of the neutron
lifetime. This measurement would be free of the systematics of laboratory
experiments. A package of mass kg could provide a 10^{-3} precision in
two years.Comment: 10 pages, 4 figures. Revised and updated for publicatio
Rhythmogenic neuronal networks, pacemakers, and k-cores
Neuronal networks are controlled by a combination of the dynamics of
individual neurons and the connectivity of the network that links them
together. We study a minimal model of the preBotzinger complex, a small
neuronal network that controls the breathing rhythm of mammals through periodic
firing bursts. We show that the properties of a such a randomly connected
network of identical excitatory neurons are fundamentally different from those
of uniformly connected neuronal networks as described by mean-field theory. We
show that (i) the connectivity properties of the networks determines the
location of emergent pacemakers that trigger the firing bursts and (ii) that
the collective desensitization that terminates the firing bursts is determined
again by the network connectivity, through k-core clusters of neurons.Comment: 4+ pages, 4 figures, submitted to Phys. Rev. Let
Optimal Weighting of Preclinical Alzheimer’s Cognitive Composite (PACC) Scales to Improve their Performance as Outcome Measures for Alzheimer’s Disease Clinical Trials
Introduction: Cognitive composite scales constructed by combining existing neuropsychometric tests are seeing wide application as endpoints for clinical trials and cohort studies of Alzheimer’s disease (AD) predementia conditions. Preclinical Alzheimer’s Cognitive Composite (PACC) scales are composite scores calculated as the sum of the component test scores weighted by the reciprocal of their standard deviations at the baseline visit. Reciprocal standard deviation is an arbitrary weighting in this context, and may be an inefficient utilization of the data contained in the component measures. Mathematically derived optimal composite weighting is a promising alternative.
Methods: Sample size projections using standard power calculation formulas were used to describe the relative performance of component measures and their composites when used as endpoints for clinical trials. Power calculations were informed by (n=1,333) amnestic mild cognitive impaired participants in the National Alzheimer’s Coordinating Center (NACC) Uniform Data Set.
Results: A composite constructed using PACC reciprocal standard deviation weighting was both less sensitive to change than one of its component measures and less sensitive to change than its optimally weighted counterpart. In standard sample size calculations informed by NACC data, a clinical trial using the PACC weighting would require 38% more subjects than a composite calculated using optimal weighting.
Discussion: These findings illustrate how reciprocal standard deviation weighting can result in inefficient cognitive composites, and underscore the importance of component weights to the performance of composite scales. In the future, optimal weighting parameters informed by accumulating clinical trial data may improve the efficiency of clinical trials in AD
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