29,522 research outputs found
Contracting Graphs to Split Graphs and Threshold Graphs
We study the parameterized complexity of Split Contraction and Threshold
Contraction. In these problems we are given a graph G and an integer k and
asked whether G can be modified into a split graph or a threshold graph,
respectively, by contracting at most k edges. We present an FPT algorithm for
Split Contraction, and prove that Threshold Contraction on split graphs, i.e.,
contracting an input split graph to a threshold graph, is FPT when
parameterized by the number of contractions. To give a complete picture, we
show that these two problems admit no polynomial kernels unless NP\subseteq
coNP/poly.Comment: 14 pages, 4 figure
Confidence Intervals for High-Dimensional Linear Regression: Minimax Rates and Adaptivity
Confidence sets play a fundamental role in statistical inference. In this
paper, we consider confidence intervals for high dimensional linear regression
with random design. We first establish the convergence rates of the minimax
expected length for confidence intervals in the oracle setting where the
sparsity parameter is given. The focus is then on the problem of adaptation to
sparsity for the construction of confidence intervals. Ideally, an adaptive
confidence interval should have its length automatically adjusted to the
sparsity of the unknown regression vector, while maintaining a prespecified
coverage probability. It is shown that such a goal is in general not
attainable, except when the sparsity parameter is restricted to a small region
over which the confidence intervals have the optimal length of the usual
parametric rate. It is further demonstrated that the lack of adaptivity is not
due to the conservativeness of the minimax framework, but is fundamentally
caused by the difficulty of learning the bias accurately.Comment: 31 pages, 1 figur
Classification of Cosmological Trajectories
In the context of effective Friedmann equation we classify the cosmologies in
multi-scalar models with an arbitrary scalar potential according to their
geometric properties. It is shown that all flat cosmologies are geodesics with
respect to a conformally rescaled metric on the `augmented' target space.
Non-flat cosmologies with V=0 are also investigated. It is shown that geodesics
in a `doubly-augmented' target space yield cosmological trajectories for any
curvature when projected onto a given hypersurface.Comment: 10 page
Self-supervised CNN for Unconstrained 3D Facial Performance Capture from an RGB-D Camera
We present a novel method for real-time 3D facial performance capture with
consumer-level RGB-D sensors. Our capturing system is targeted at robust and
stable 3D face capturing in the wild, in which the RGB-D facial data contain
noise, imperfection and occlusion, and often exhibit high variability in
motion, pose, expression and lighting conditions, thus posing great challenges.
The technical contribution is a self-supervised deep learning framework, which
is trained directly from raw RGB-D data. The key novelties include: (1)
learning both the core tensor and the parameters for refining our parametric
face model; (2) using vertex displacement and UV map for learning surface
detail; (3) designing the loss function by incorporating temporal coherence and
same identity constraints based on pairs of RGB-D images and utilizing sparse
norms, in addition to the conventional terms for photo-consistency, feature
similarity, regularization as well as geometry consistency; and (4) augmenting
the training data set in new ways. The method is demonstrated in a live setup
that runs in real-time on a smartphone and an RGB-D sensor. Extensive
experiments show that our method is robust to severe occlusion, fast motion,
large rotation, exaggerated facial expressions and diverse lighting
A high order semi-Lagrangian discontinuous Galerkin method for Vlasov-Poisson simulations without operator splitting
In this paper, we develop a high order semi-Lagrangian (SL) discontinuous
Galerkin (DG) method for nonlinear Vlasov-Poisson (VP) simulations without
operator splitting. In particular, we combine two recently developed novel
techniques: one is the high order non-splitting SLDG transport method [Cai, et
al., J Sci Comput, 2017], and the other is the high order characteristics
tracing technique proposed in [Qiu and Russo, J Sci Comput, 2017]. The proposed
method with up to third order accuracy in both space and time is locally mass
conservative, free of splitting error, positivity-preserving, stable and robust
for large time stepping size. The SLDG VP solver is applied to classic
benchmark test problems such as Landau damping and two-stream instabilities for
VP simulations. Efficiency and effectiveness of the proposed scheme is
extensively tested. Tremendous CPU savings are shown by comparisons between the
proposed SL DG scheme and the classical Runge-Kutta DG method
A self-organized particle moving model on scale free network with behavior
In this paper we propose a self-organized particle moving model on scale free
network with the algorithm of the shortest path and preferential walk. The
over-capacity property of the vertices in this particle moving system on
complex network is studied from the holistic point of view. Simulation results
show that the number of over-capacity vertices forms punctuated equilibrium
processes as time elapsing, that the average number of over-capacity vertices
under each local punctuated equilibrium process has power law relationship with
the local punctuated equilibrium value. What's more, the number of
over-capacity vertices has the bell-shaped temporal correlation and
behavior. Finally, the average lifetime of particles accumulated before
time is analyzed to find the different roles of the shortest path algorithm
and the preferential walk algorithm in our model.Comment: 8 pages, 5 figure
Non-parametric threshold estimation for classical risk process perturbed by diffusion
In this paper,we consider a macro approximation of the flow of a risk
reserve, The process is observed at discrete time points. Because we cannot
directly observe each jump time and size then we will make use of a technique
for identifying the times when jumps larger than a suitably defined threshold
occurred. We estimate the jump size and survival probability of our risk
process from discrete observations
Hidden Messenger from Quantum Geometry: Towards Information Conservation in Quantum Gravity
The back reactions of Hawking radiation allow nontrivial correlations between
consecutive Hawking quanta, which gives a possible way of resolving the paradox
of black hole information loss known as the hidden messenger method. In a
recent work of Ma {\it et al} [arXiv:1711.10704], this method is enhanced by a
general derivation using small deviations of the states of Hawking quanta off
canonical typicality. In this paper, we use this typicality argument to study
the effects of generic back reactions on the quantum geometries described by
spin network states, and discuss the viability of entropy conservation in loop
quantum gravity. We find that such back reactions lead to small area
deformations of quantum geometries including those of quantum black holes. This
shows that the hidden-messenger method is still viable in loop quantum gravity,
which is a first step towards resolving the paradox of black hole information
loss in quantum gravity.Comment: 13 page
A high order semi-Lagrangian discontinuous Galerkin method for the two-dimensional incompressible Euler equations and the guiding center Vlasov model without operator splitting
In this paper, we generalize a high order semi-Lagrangian (SL) discontinuous
Galerkin (DG) method for multi-dimensional linear transport equations without
operator splitting developed in Cai et al. (J. Sci. Comput. 73: 514-542, 2017)
to the 2D time dependent incompressible Euler equations in the vorticity-stream
function formulation and the guiding center Vlasov model. We adopt a local DG
method for Poisson's equation of these models. For tracing the characteristics,
we adopt a high order characteristics tracing mechanism based on a
prediction-correction technique. The SLDG with large time-stepping size might
be subject to extreme distortion of upstream cells. To avoid this problem, we
propose a novel adaptive time-stepping strategy by controlling the relative
deviation of areas of upstream cells.Comment: arXiv admin note: text overlap with arXiv:1709.0253
Proof of a congruence on sums of powers of -binomial coefficients
We prove that, if and are nonnegative
integers, then \begin{align*}
\frac{[a_1+\cdots+a_m+1]!}{[a_1]!\ldots[a_m]!}\sum^{n-1}_{h=0}q^h\prod_{i=1}^m{h\brack
a_i} \equiv 0\pmod{[n]}, \end{align*} where ,
, and . The case confirms
a recent conjecture of Z.-W. Sun. We also show that, if is a
prime, then \begin{align*} \frac{[a+b+1]!}{[a]![b]!}\sum_{h=0}^{p-1}q^h{h\brack
a}{h\brack b} \equiv (-1)^{a-b} q^{ab-{a\choose 2}-{b\choose
2}}[p]\pmod{[p]^2}. \end{align*}Comment: 5 page
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