9,446 research outputs found
Simple unity among the fundamental equations of science
The Price equation describes the change in populations. Change concerns some
value, such as biological fitness, information or physical work. The Price
equation reveals universal aspects for the nature of change, independently of
the meaning ascribed to values. By understanding those universal aspects, we
can see more clearly why fundamental mathematical results in different
disciplines often share a common form. We can also interpret more clearly the
meaning of key results within each discipline. For example, the mathematics of
natural selection in biology has a form closely related to information theory
and physical entropy. Does that mean that natural selection is about
information or entropy? Or do natural selection, information and entropy arise
as interpretations of a common underlying abstraction? The Price equation
suggests the latter. The Price equation achieves its abstract generality by
partitioning change into two terms. The first term naturally associates with
the direct forces that cause change. The second term naturally associates with
the changing frame of reference. In the Price equation's canonical form, total
change remains zero because the conservation of total probability requires that
all probabilities invariantly sum to one. Much of the shared common form for
the mathematics of different disciplines may arise from that seemingly trivial
invariance of total probability, which leads to the partitioning of total
change into equal and opposite components of the direct forces and the changing
frame of reference.Comment: arXiv admin note: text overlap with arXiv:1810.0926
Real-Time 6DOF Pose Relocalization for Event Cameras with Stacked Spatial LSTM Networks
We present a new method to relocalize the 6DOF pose of an event camera solely
based on the event stream. Our method first creates the event image from a list
of events that occurs in a very short time interval, then a Stacked Spatial
LSTM Network (SP-LSTM) is used to learn the camera pose. Our SP-LSTM is
composed of a CNN to learn deep features from the event images and a stack of
LSTM to learn spatial dependencies in the image feature space. We show that the
spatial dependency plays an important role in the relocalization task and the
SP-LSTM can effectively learn this information. The experimental results on a
publicly available dataset show that our approach generalizes well and
outperforms recent methods by a substantial margin. Overall, our proposed
method reduces by approx. 6 times the position error and 3 times the
orientation error compared to the current state of the art. The source code and
trained models will be released.Comment: 7 pages, 5 figure
Bayesian Methods for Analysis and Adaptive Scheduling of Exoplanet Observations
We describe work in progress by a collaboration of astronomers and
statisticians developing a suite of Bayesian data analysis tools for extrasolar
planet (exoplanet) detection, planetary orbit estimation, and adaptive
scheduling of observations. Our work addresses analysis of stellar reflex
motion data, where a planet is detected by observing the "wobble" of its host
star as it responds to the gravitational tug of the orbiting planet. Newtonian
mechanics specifies an analytical model for the resulting time series, but it
is strongly nonlinear, yielding complex, multimodal likelihood functions; it is
even more complex when multiple planets are present. The parameter spaces range
in size from few-dimensional to dozens of dimensions, depending on the number
of planets in the system, and the type of motion measured (line-of-sight
velocity, or position on the sky). Since orbits are periodic, Bayesian
generalizations of periodogram methods facilitate the analysis. This relies on
the model being linearly separable, enabling partial analytical
marginalization, reducing the dimension of the parameter space. Subsequent
analysis uses adaptive Markov chain Monte Carlo methods and adaptive importance
sampling to perform the integrals required for both inference (planet detection
and orbit measurement), and information-maximizing sequential design (for
adaptive scheduling of observations). We present an overview of our current
techniques and highlight directions being explored by ongoing research.Comment: 29 pages, 11 figures. An abridged version is accepted for publication
in Statistical Methodology for a special issue on astrostatistics, with
selected (refereed) papers presented at the Astronomical Data Analysis
Conference (ADA VI) held in Monastir, Tunisia, in May 2010. Update corrects
equation (3
Cooperative localization by dual foot-mounted inertial sensors and inter-agent ranging
The implementation challenges of cooperative localization by dual
foot-mounted inertial sensors and inter-agent ranging are discussed and work on
the subject is reviewed. System architecture and sensor fusion are identified
as key challenges. A partially decentralized system architecture based on
step-wise inertial navigation and step-wise dead reckoning is presented. This
architecture is argued to reduce the computational cost and required
communication bandwidth by around two orders of magnitude while only giving
negligible information loss in comparison with a naive centralized
implementation. This makes a joint global state estimation feasible for up to a
platoon-sized group of agents. Furthermore, robust and low-cost sensor fusion
for the considered setup, based on state space transformation and
marginalization, is presented. The transformation and marginalization are used
to give the necessary flexibility for presented sampling based updates for the
inter-agent ranging and ranging free fusion of the two feet of an individual
agent. Finally, characteristics of the suggested implementation are
demonstrated with simulations and a real-time system implementation.Comment: 14 page
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