60,394 research outputs found

### Mean first-passage time for maximal-entropy random walks in complex networks

We perform an in-depth study for mean first-passage time (MFPT)---a primary
quantity for random walks with numerous applications---of maximal-entropy
random walks (MERW) performed in complex networks. For MERW in a general
network, we derive an explicit expression of MFPT in terms of the eigenvalues
and eigenvectors of the adjacency matrix associated with the network. For MERW
in uncorrelated networks, we also provide a theoretical formula of MFPT at the
mean-field level, based on which we further evaluate the dominant scalings of
MFPT to different targets for MERW in uncorrelated scale-free networks, and
compare the results with those corresponding to traditional unbiased random
walks (TURW). We show that the MFPT to a hub node is much lower for MERW than
for TURW. However, when the destination is a node with the least degree or a
uniformly chosen node, the MFPT is higher for MERW than for TURW. Since MFPT to
a uniformly chosen node measures real efficiency of search in networks, our
work provides insight into general searching process in complex networks.Comment: Definitive version accepted for publication in Scientific Report

### Random walks in weighted networks with a perfect trap: An application of Laplacian spectra

In this paper, we propose a general framework for the trapping problem on a
weighted network with a perfect trap fixed at an arbitrary node. By utilizing
the spectral graph theory, we provide an exact formula for mean first-passage
time (MFPT) from one node to another, based on which we deduce an explicit
expression for average trapping time (ATT) in terms of the eigenvalues and
eigenvectors of the Laplacian matrix associated with the weighted graph, where
ATT is the average of MFPTs to the trap over all source nodes. We then further
derive a sharp lower bound for the ATT in terms of only the local information
of the trap node, which can be obtained in some graphs. Moreover, we deduce the
ATT when the trap is distributed uniformly in the whole network. Our results
show that network weights play a significant role in the trapping process. To
apply our framework, we use the obtained formulas to study random walks on two
specific networks: trapping in weighted uncorrelated networks with a deep trap,
the weights of which are characterized by a parameter, and L\'evy random walks
in a connected binary network with a trap distributed uniformly, which can be
looked on as random walks on a weighted network. For weighted uncorrelated
networks we show that the ATT to any target node depends on the weight
parameter, that is, the ATT to any node can change drastically by modifying the
parameter, a phenomenon that is in contrast to that for trapping in binary
networks. For L\'evy random walks in any connected network, by using their
equivalence to random walks on a weighted complete network, we obtain the
optimal exponent characterizing L\'evy random walks, which have the minimal
average of ATTs taken over all target nodes.Comment: Definitive version accepted for publication in Physical Review

### Time-to-Event Model-Assisted Designs to Accelerate Phase I Clinical Trials

Two useful strategies to speed up drug development are to increase the
patient accrual rate and use novel adaptive designs. Unfortunately, these two
strategies often conflict when the evaluation of the outcome cannot keep pace
with the patient accrual rate and thus the interim data cannot be observed in
time to make adaptive decisions. A similar logistic difficulty arises when the
outcome is of late onset. Based on a novel formulation and approximation of the
likelihood of the observed data, we propose a general methodology for
model-assisted designs to handle toxicity data that are pending due to fast
accrual or late-onset toxicity, and facilitate seamless decision making in
phase I dose-finding trials. The dose escalation/de-escalation rules of the
proposed time-to-event model-assisted designs can be tabulated before the trial
begins, which greatly simplifies trial conduct in practice compared to that
under existing methods. We show that the proposed designs have desirable finite
and large-sample properties and yield performance that is superior to that of
more complicated model-based designs. We provide user-friendly software for
implementing the designs.Comment: 31 page

### Integrating Inter-vehicular Communication, Vehicle Localization, and a Digital Map for Cooperative Adaptive Cruise Control with Target Detection Loss

Adaptive Cruise Control (ACC) is an Advanced Driver Assistance System (ADAS)
that enables vehicle following with desired inter-vehicular distances.
Cooperative Adaptive Cruise Control (CACC) is upgraded ACC that utilizes
additional inter-vehicular wireless communication to share vehicle states such
as acceleration to enable shorter gap following. Both ACC and CACC rely on
range sensors such as radar to obtain the actual inter-vehicular distance for
gap-keeping control. The range sensor may lose detection of the target, the
preceding vehicle, on curvy roads or steep hills due to limited angle of view.
Unfavourable weather conditions, target selection failure, or hardware issue
may also result in target detection loss. During target detection loss, the
vehicle following system usually falls back to Cruise Control (CC) wherein the
follower vehicle maintains a constant speed. In this work, we propose an
alternative way to obtain the inter-vehicular distance during target detection
loss to continue vehicle following. The proposed algorithm integrates
inter-vehicular communication, accurate vehicle localization, and a digital map
with lane center information to approximate the inter-vehicular distance.
In-lab robot following experiments demonstrated that the proposed algorithm
provided desirable inter-vehicular distance approximation. Although the
algorithm is intended for vehicle following application, it can also be used
for other scenarios that demand vehicles' relative distance approximation. The
work also showcases our in-lab development effort of robotic emulation of
traffic for connected and automated vehicles

### Learning from Synthetic Data for Crowd Counting in the Wild

Recently, counting the number of people for crowd scenes is a hot topic
because of its widespread applications (e.g. video surveillance, public
security). It is a difficult task in the wild: changeable environment,
large-range number of people cause the current methods can not work well. In
addition, due to the scarce data, many methods suffer from over-fitting to a
different extent. To remedy the above two problems, firstly, we develop a data
collector and labeler, which can generate the synthetic crowd scenes and
simultaneously annotate them without any manpower. Based on it, we build a
large-scale, diverse synthetic dataset. Secondly, we propose two schemes that
exploit the synthetic data to boost the performance of crowd counting in the
wild: 1) pretrain a crowd counter on the synthetic data, then finetune it using
the real data, which significantly prompts the model's performance on real
data; 2) propose a crowd counting method via domain adaptation, which can free
humans from heavy data annotations. Extensive experiments show that the first
method achieves the state-of-the-art performance on four real datasets, and the
second outperforms our baselines. The dataset and source code are available at
https://gjy3035.github.io/GCC-CL/.Comment: Accepted by CVPR201

### How to reach the orbital configuration of the inner three planets in HD 40307 Planet System ?

The formation of the present configuration of three hot super-Earths in the
planet system HD 40307 is a challenge to dynamical astronomers. With the two
successive period ratios both near and slightly larger than 2, the system may
have evolved from pairwise 2:1 mean motion resonances (MMRs). In this paper, we
investigate the evolutions of the period ratios of the three planets after the
primordial gas disk was depleted. Three routines are found to probably result
in the current configuration under tidal dissipation with the center star, they
are: (i) through apsidal alignment only; (ii) out of pairwise 2:1 MMRs, then
through apsidal alignment; (iii) out of the 4:2:1 Laplace Resonance (LR) , then
through apsidal alignment. All the three scenarios require the initial
eccentricities of planets $\sim0.15$, which implies a planetary scattering
history during and after the gas disk was depleted. All the three routines will
go through the apsidal alignment phase, and enter a state with near-zero
eccentricities finally. We also find some special characteristics for each
routine. If the system went through pairwise 2:1 MMRs at the beginning, the MMR
of the outer two planets would be broken first to reach the current state. As
for routine (iii), the planets would be out of the Laplace Resonance at the
place where some high-order resonances are located. At the high-order
resonances 17:8 or 32:15 of the planets c and d, the system will possibly enter
the current state as the final equilibrium.Comment: 16 pages, 8 figures, Accepted by SCIENCE CHINA Physics, Mechanics &
Astronom

### Numerical Renormalization Group Calculations For Similarity Solutions and Travelling Waves

We present a numerical implementation of the renormalization group (RG) for
partial differential equations, constructing similarity solutions and
travelling waves. We show that for a large class of well-localized initial
conditions, successive iterations of an appropriately defined discrete RG
transformation in space and time will drive the system towards a fixed point.
This corresponds to a scale-invariant solution, such as a similarity or
travelling-wave solution, which governs the long-time asymptotic behavior. We
demonstrate that the numerical RG method is computationally very efficient.Comment: 14 pages, Postscript file of paper and 3 figures distributed as
self-unpacking uuencoded compressed tar file.Also available by anonymous ftp
to gijoe.mrl.uiuc.edu (128.174.119.153), file /pub/numrg.u

### A symmetric 2-tensor canonically associated to Q-curvature and its applications

In this article, we define a symmetric 2-tensor canonically associated to
Q-curvature called J-tensor on any Riemannian manifold with dimension at least
three. The relation between J-tensor and Q-curvature is precisely like Ricci
tensor and scalar curvature. Thus it can be interpreted as a higher-order
analogue of Ricci tensor. This tensor can also be used to understand
Chang-Gursky-Yang's theorem on 4-dimensional Q-singular metrics. Moreover, we
show an Almost-Schur Lemma holds for Q-curvature, which gives an estimate of
Q-curvature on closed manifolds.Comment: 14 pages, new remarks, references and acknowledgement added in the
introductio

### Learning the mapping $\mathbf{x}\mapsto \sum_{i=1}^d x_i^2$: the cost of finding the needle in a haystack

The task of using machine learning to approximate the mapping
$\mathbf{x}\mapsto\sum_{i=1}^d x_i^2$ with $x_i\in[-1,1]$ seems to be a trivial
one. Given the knowledge of the separable structure of the function, one can
design a sparse network to represent the function very accurately, or even
exactly. When such structural information is not available, and we may only use
a dense neural network, the optimization procedure to find the sparse network
embedded in the dense network is similar to finding the needle in a haystack,
using a given number of samples of the function. We demonstrate that the cost
(measured by sample complexity) of finding the needle is directly related to
the Barron norm of the function. While only a small number of samples is needed
to train a sparse network, the dense network trained with the same number of
samples exhibits large test loss and a large generalization gap. In order to
control the size of the generalization gap, we find that the use of explicit
regularization becomes increasingly more important as $d$ increases. The
numerically observed sample complexity with explicit regularization scales as
$\mathcal{O}(d^{2.5})$, which is in fact better than the theoretically
predicted sample complexity that scales as $\mathcal{O}(d^{4})$. Without
explicit regularization (also called implicit regularization), the numerically
observed sample complexity is significantly higher and is close to
$\mathcal{O}(d^{4.5})$

### Estimating Densities with Non-Parametric Exponential Families

We propose a novel approach for density estimation with exponential families
for the case when the true density may not fall within the chosen family. Our
approach augments the sufficient statistics with features designed to
accumulate probability mass in the neighborhood of the observed points,
resulting in a non-parametric model similar to kernel density estimators. We
show that under mild conditions, the resulting model uses only the sufficient
statistics if the density is within the chosen exponential family, and
asymptotically, it approximates densities outside of the chosen exponential
family. Using the proposed approach, we modify the exponential random graph
model, commonly used for modeling small-size graph distributions, to address
the well-known issue of model degeneracy.Comment: 22 pages, 5 figure

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