81,679 research outputs found
Length of a curve is quasi-convex along a Teichmuller geodesic
We show that for every simple closed curve \alpha, the extremal length and
the hyperbolic length of \alpha are quasi-convex functions along any
Teichmuller geodesic. As a corollary, we conclude that, in Teichmuller space
equipped with the Teichmuller metric, balls are quasi- convex.Comment: 25 pages, 2 figure
Modeling Pitch Trajectories in Fastpitch Softball
The fourth-order Runge–Kutta method is used to numerically integrate the equations of motion for a fastpitch softball pitch and to create a model from which the trajectories of drop balls, rise balls and curve balls can be computed and displayed. By requiring these pitches to pass through the strike zone, and by assuming specific values for the initial speed, launch angle and height of each pitch, an upper limit on the lift coefficient can be predicted which agrees with experimental data. This approach also predicts the launch angles necessary to put rise balls, drop balls and curve balls in the strike zone, as well as a value of the drag coefficient that agrees with experimental data. Finally, Adair’s analysis of a batter’s swing is used to compare pitches that look similar to a batter starting her swing, yet which diverge before reaching the home plate, to predict when she is likely to miss or foul the ball
On the {\L}ojasiewicz exponent, special direction and maximal polar quotient
For a local singular plane curve germ we characterize all
nonsingular \lambda\in\bbC\{X,Y\} such that the {\L}ojasiewicz exponent of
\grad\,f is not attained on the polar curve \bJ(\lambda,f)=0. When is
not Morse we prove that for the same 's the maximal polar quotient
is strictly less than its generic value . Our main
tool is the Eggers tree of singularity constructed as a decorated graph of
relations between balls in the space of branches defined by using a logarithmic
distance.Comment: 39 pages, 16 figure
Some local--global phenomena in locally finite graphs
In this paper we present some results for a connected infinite graph with
finite degrees where the properties of balls of small radii guarantee the
existence of some Hamiltonian and connectivity properties of . (For a vertex
of a graph the ball of radius centered at is the subgraph of
induced by the set of vertices whose distance from does not
exceed ). In particular, we prove that if every ball of radius 2 in is
2-connected and satisfies the condition for
each path in , where and are non-adjacent vertices, then
has a Hamiltonian curve, introduced by K\"undgen, Li and Thomassen (2017).
Furthermore, we prove that if every ball of radius 1 in satisfies Ore's
condition (1960) then all balls of any radius in are Hamiltonian.Comment: 18 pages, 6 figures; journal accepted versio
Uniform shrinking and expansion under isotropic Brownian flows
We study some finite time transport properties of isotropic Brownian flows.
Under a certain nondegeneracy condition on the potential spectral measure, we
prove that uniform shrinking or expansion of balls under the flow over some
bounded time interval can happen with positive probability. We also provide a
control theorem for isotropic Brownian flows with drift. Finally, we apply the
above results to show that under the nondegeneracy condition the length of a
rectifiable curve evolving in an isotropic Brownian flow with strictly negative
top Lyapunov exponent converges to zero as with positive
probability
Minimax hypothesis testing for curve registration
This paper is concerned with the problem of goodness-of-fit for curve
registration, and more precisely for the shifted curve model, whose application
field reaches from computer vision and road traffic prediction to medicine. We
give bounds for the asymptotic minimax separation rate, when the functions in
the alternative lie in Sobolev balls and the separation from the null
hypothesis is measured by the l2-norm. We use the generalized likelihood ratio
to build a nonadaptive procedure depending on a tuning parameter, which we
choose in an optimal way according to the smoothness of the ambient space.
Then, a Bonferroni procedure is applied to give an adaptive test over a range
of Sobolev balls. Both achieve the asymptotic minimax separation rates, up to
possible logarithmic factors
Functional estimation and hypothesis testing in nonparametric boundary models
Consider a Poisson point process with unknown support boundary curve ,
which forms a prototype of an irregular statistical model. We address the
problem of estimating non-linear functionals of the form .
Following a nonparametric maximum-likelihood approach, we construct an
estimator which is UMVU over H\"older balls and achieves the (local) minimax
rate of convergence. These results hold under weak assumptions on which
are satisfied for , . As an application, we consider the
problem of estimating the -norm and derive the minimax separation rates in
the corresponding nonparametric hypothesis testing problem. Structural
differences to results for regular nonparametric models are discussed.Comment: 21 pages, 1 figur
Monotonicity Analysis over Chains and Curves
Chains are vector-valued signals sampling a curve. They are important to
motion signal processing and to many scientific applications including location
sensors. We propose a novel measure of smoothness for chains curves by
generalizing the scalar-valued concept of monotonicity. Monotonicity can be
defined by the connectedness of the inverse image of balls. This definition is
coordinate-invariant and can be computed efficiently over chains. Monotone
curves can be discontinuous, but continuous monotone curves are differentiable
a.e. Over chains, a simple sphere-preserving filter shown to never decrease the
degree of monotonicity. It outperforms moving average filters over a synthetic
data set. Applications include Time Series Segmentation, chain reconstruction
from unordered data points, Optical Character Recognition, and Pattern
Matching.Comment: to appear in Proceedings of Curves and Surfaces 200
A deconvolution approach to estimation of a common shape in a shifted curves model
This paper considers the problem of adaptive estimation of a mean pattern in a randomly shifted curve model. We show that this problem can be transformed into a linear inverse problem, where the density of the random shifts plays the role of a convolution operator. An adaptive estimator of the mean pattern, based on wavelet thresholding is proposed. We study its consistency for the quadratic risk as the number of observed curves tends to infinity, and this estimator is shown to achieve a near-minimax rate of convergence over a large class of Besov balls. This rate depends both on the smoothness of the common shape of the curves and on the decay of the Fourier coefficients of the density of the random shifts. Hence, this paper makes a connection between mean pattern estimation and the statistical analysis of linear inverse problems, which is a new point of view on curve registration and image warping problems. We also provide a new method to estimate the unknown random shifts between curves. Some numerical experiments are given to illustrate the performances of our approach and to compare them with another algorithm existing in the literature
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