5,121 research outputs found
Depth, Highness and DNR degrees
We study Bennett deep sequences in the context of recursion theory; in
particular we investigate the notions of O(1)-deepK, O(1)-deepC , order-deep K
and order-deep C sequences. Our main results are that Martin-Loef random sets
are not order-deepC , that every many-one degree contains a set which is not
O(1)-deepC , that O(1)-deepC sets and order-deepK sets have high or DNR Turing
degree and that no K-trival set is O(1)-deepK.Comment: journal version, dmtc
Eye Tracker Accuracy: Quantitative Evaluation of the Invisible Eye Center Location
Purpose. We present a new method to evaluate the accuracy of an eye tracker
based eye localization system. Measuring the accuracy of an eye tracker's
primary intention, the estimated point of gaze, is usually done with volunteers
and a set of fixation points used as ground truth. However, verifying the
accuracy of the location estimate of a volunteer's eye center in 3D space is
not easily possible. This is because the eye center is an intangible point
hidden by the iris. Methods. We evaluate the eye location accuracy by using an
eye phantom instead of eyes of volunteers. For this, we developed a testing
stage with a realistic artificial eye and a corresponding kinematic model,
which we trained with {\mu}CT data. This enables us to precisely evaluate the
eye location estimate of an eye tracker. Results. We show that the proposed
testing stage with the corresponding kinematic model is suitable for such a
validation. Further, we evaluate a particular eye tracker based navigation
system and show that this system is able to successfully determine the eye
center with sub-millimeter accuracy. Conclusions. We show the suitability of
the evaluated eye tracker for eye interventions, using the proposed testing
stage and the corresponding kinematic model. The results further enable
specific enhancement of the navigation system to potentially get even better
results
A Force-Directed Approach for Offline GPS Trajectory Map Matching
We present a novel algorithm to match GPS trajectories onto maps offline (in
batch mode) using techniques borrowed from the field of force-directed graph
drawing. We consider a simulated physical system where each GPS trajectory is
attracted or repelled by the underlying road network via electrical-like
forces. We let the system evolve under the action of these physical forces such
that individual trajectories are attracted towards candidate roads to obtain a
map matching path. Our approach has several advantages compared to traditional,
routing-based, algorithms for map matching, including the ability to account
for noise and to avoid large detours due to outliers in the data whilst taking
into account the underlying topological restrictions (such as one-way roads).
Our empirical evaluation using real GPS traces shows that our method produces
better map matching results compared to alternative offline map matching
algorithms on average, especially for routes in dense, urban areas.Comment: 10 pages, 12 figures, accepted version of article submitted to ACM
SIGSPATIAL 2018, Seattle, US
Optimality in multiple comparison procedures
When many (m) null hypotheses are tested with a single dataset, the control
of the number of false rejections is often the principal consideration. Two
popular controlling rates are the probability of making at least one false
discovery (FWER) and the expected fraction of false discoveries among all
rejections (FDR). Scaled multiple comparison error rates form a new family that
bridges the gap between these two extremes. For example, the Scaled Expected
Value (SEV) limits the number of false positives relative to an arbitrary
increasing function of the number of rejections, that is, E(FP/s(R)). We
discuss the problem of how to choose in practice which procedure to use, with
elements of an optimality theory, by considering the number of false rejections
FP separately from the number of correct rejections TP. Using this framework we
will show how to choose an element in the new family mentioned above.Comment: arXiv admin note: text overlap with arXiv:1112.451
The sensitivity of rapidly rotating Rayleigh--B\'enard convection to Ekman pumping
The dependence of the heat transfer, as measured by the nondimensional
Nusselt number , on Ekman pumping for rapidly rotating Rayleigh-B\'enard
convection in an infinite plane layer is examined for fluids with Prandtl
number . A joint effort utilizing simulations from the Composite
Non-hydrostatic Quasi-Geostrophic model (CNH-QGM) and direct numerical
simulations (DNS) of the incompressible fluid equations has mapped a wide range
of the Rayleigh number - Ekman number parameter space within the
geostrophic regime of rotating convection. Corroboration of the -
relation at from both methods along with higher covered by
DNS and lower by the asymptotic model allows for this range of the heat
transfer results. For stress-free boundaries, the relation has the dissipation-free scaling of for all
. This is directly related to a geostrophic turbulent interior
that throttles the heat transport supplied to the thermal boundary layers. For
no-slip boundaries, the existence of ageostrophic viscous boundary layers and
their associated Ekman pumping yields a more complex 2D surface in
parameter space. For results suggest that the surface can be
expressed as indicating the
dissipation-free scaling law is enhanced by Ekman pumping by the multiplicative
prefactor where . It follows for
that the geostrophic turbulent interior remains the flux bottleneck
in rapidly rotating Rayleigh-B\'enard convection. For , where DNS
and asymptotic simulations agree quantitatively, it is found that the effects
of Ekman pumping are sufficiently strong to influence the heat transport with
diminished exponent and .Comment: 9 pages, 14 figure
The effects of Ekman pumping on quasi-geostrophic Rayleigh-Benard convection
Numerical simulations of 3D, rapidly rotating Rayleigh-Benard convection are
performed using an asymptotic quasi-geostrophic model that incorporates the
effects of no-slip boundaries through (i) parameterized Ekman pumping boundary
conditions, and (ii) a thermal wind boundary layer that regularizes the
enhanced thermal fluctuations induced by pumping. The fidelity of the model,
obtained by an asymptotic reduction of the Navier-Stokes equations that
implicitly enforces a pointwise geostrophic balance, is explored for the first
time by comparisons of simulations against the findings of direct numerical
simulations and laboratory experiments. Results from these methods have
established Ekman pumping as the mechanism responsible for significantly
enhancing the vertical heat transport. This asymptotic model demonstrates
excellent agreement over a range of thermal forcing for Pr ~1 when compared
with results from experiments and DNS at maximal values of their attainable
rotation rates, as measured by the Ekman number (E ~ 10^{-7}); good qualitative
agreement is achieved for Pr > 1. Similar to studies with stress-free
boundaries, four spatially distinct flow morphologies exists. Despite the
presence of frictional drag at the upper and/or lower boundaries, a strong
non-local inverse cascade of barotropic (i.e., depth-independent) kinetic
energy persists in the final regime of geostrophic turbulence and is dominant
at large scales. For mixed no-slip/stress-free and no-slip/no-slip boundaries,
Ekman friction is found to attenuate the efficiency of the upscale energy
transport and, unlike the case of stress-free boundaries, rapidly saturates the
barotropic kinetic energy. For no-slip/no-slip boundaries, Ekman friction is
strong enough to prevent the development of a coherent dipole vortex
condensate. Instead vortex pairs are found to be intermittent, varying in both
time and strength.Comment: 20 pages, 10 figure
Depth, Highness and DNR Degrees
A sequence is Bennett deep [5] if every recursive approximation of the
Kolmogorov complexity of its initial segments from above satisfies that the difference
between the approximation and the actual value of the Kolmogorov complexity of
the initial segments dominates every constant function. We study for different lower
bounds r of this difference between approximation and actual value of the initial segment
complexity, which properties the corresponding r(n)-deep sets have. We prove
that for r(n) = εn, depth coincides with highness on the Turing degrees. For smaller
choices of r, i.e., r is any recursive order function, we show that depth implies either
highness or diagonally-non-recursiveness (DNR). In particular, for left-r.e. sets, order
depth already implies highness. As a corollary, we obtain that weakly-useful sets are
either high or DNR. We prove that not all deep sets are high by constructing a low
order-deep set.
Bennett's depth is defined using prefix-free Kolmogorov complexity. We show that
if one replaces prefix-free by plain Kolmogorov complexity in Bennett's depth definition,
one obtains a notion which no longer satisfies the slow growth law (which
stipulates that no shallow set truth-table computes a deep set); however, under this
notion, random sets are not deep (at the unbounded recursive order magnitude). We
improve Bennett's result that recursive sets are shallow by proving all K-trivial sets
are shallow; our result is close to optimal.
For Bennett's depth, the magnitude of compression improvement has to be achieved
almost everywhere on the set. Bennett observed that relaxing to infinitely often is
meaningless because every recursive set is infinitely often deep. We propose an alternative
infinitely often depth notion that doesn't suffer this limitation (called i.o.
depth).We show that every hyperimmune degree contains a i.o. deep set of magnitude
εn, and construct a π01- class where every member is an i.o. deep set of magnitude
εn. We prove that every non-recursive, non-DNR hyperimmune-free set is i.o. deep
of constant magnitude, and that every nonrecursive many-one degree contains such
a set
A characterization of semisimple plane polynomial automorphisms
It is well-known that an element of the linear group GLn(C) is semisimple if and only
if its conjugacy class is Zariski closed. The aim of this paper is to show that the same
result holds for the group of complex plane polynomial automorphisms
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