2,851 research outputs found
A backward procedure for change-point detection with applications to copy number variation detection
Change-point detection regains much attention recently for analyzing array or
sequencing data for copy number variation (CNV) detection. In such
applications, the true signals are typically very short and buried in the long
data sequence, which makes it challenging to identify the variations
efficiently and accurately. In this article, we propose a new change-point
detection method, a backward procedure, which is not only fast and simple
enough to exploit high-dimensional data but also performs very well for
detecting short signals. Although motivated by CNV detection, the backward
procedure is generally applicable to assorted change-point problems that arise
in a variety of scientific applications. It is illustrated by both simulated
and real CNV data that the backward detection has clear advantages over other
competing methods especially when the true signal is short
The extremal genus embedding of graphs
Let Wn be a wheel graph with n spokes. How does the genus change if adding a
degree-3 vertex v, which is not in V (Wn), to the graph Wn? In this paper,
through the joint-tree model we obtain that the genus of Wn+v equals 0 if the
three neighbors of v are in the same face boundary of P(Wn); otherwise,
{\deg}(Wn + v) = 1, where P(Wn) is the unique planar embedding of Wn. In
addition, via the independent set, we provide a lower bound on the maximum
genus of graphs, which may be better than both the result of D. Li & Y. Liu and
the result of Z. Ouyang etc: in Europ. J. Combinatorics. Furthermore, we obtain
a relation between the independence number and the maximum genus of graphs, and
provide an algorithm to obtain the lower bound on the number of the distinct
maximum genus embedding of the complete graph Km, which, in some sense,
improves the result of Y. Caro and S. Stahl respectively
Bypassing the quadrature exactness assumption of hyperinterpolation on the sphere
This paper focuses on the approximation of continuous functions on the unit
sphere by spherical polynomials of degree via hyperinterpolation.
Hyperinterpolation of degree is a discrete approximation of the
-orthogonal projection of degree with its Fourier coefficients
evaluated by a positive-weight quadrature rule that exactly integrates all
spherical polynomials of degree at most . This paper aims to bypass this
quadrature exactness assumption by replacing it with the Marcinkiewicz--Zygmund
property proposed in a previous paper. Consequently, hyperinterpolation can be
constructed by a positive-weight quadrature rule (not necessarily with
quadrature exactness). This scheme is referred to as unfettered
hyperinterpolation. This paper provides a reasonable error estimate for
unfettered hyperinterpolation. The error estimate generally consists of two
terms: a term representing the error estimate of the original
hyperinterpolation of full quadrature exactness and another introduced as
compensation for the loss of exactness degrees. A guide to controlling the
newly introduced term in practice is provided. In particular, if the quadrature
points form a quasi-Monte Carlo (QMC) design, then there is a refined error
estimate. Numerical experiments verify the error estimates and the practical
guide.Comment: 22 pages, 7 figure
Learning Foresightful Dense Visual Affordance for Deformable Object Manipulation
Understanding and manipulating deformable objects (e.g., ropes and fabrics)
is an essential yet challenging task with broad applications. Difficulties come
from complex states and dynamics, diverse configurations and high-dimensional
action space of deformable objects. Besides, the manipulation tasks usually
require multiple steps to accomplish, and greedy policies may easily lead to
local optimal states. Existing studies usually tackle this problem using
reinforcement learning or imitating expert demonstrations, with limitations in
modeling complex states or requiring hand-crafted expert policies. In this
paper, we study deformable object manipulation using dense visual affordance,
with generalization towards diverse states, and propose a novel kind of
foresightful dense affordance, which avoids local optima by estimating states'
values for long-term manipulation. We propose a framework for learning this
representation, with novel designs such as multi-stage stable learning and
efficient self-supervised data collection without experts. Experiments
demonstrate the superiority of our proposed foresightful dense affordance.
Project page: https://hyperplane-lab.github.io/DeformableAffordanc
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