6,403 research outputs found

### Control of a lane-drop bottleneck through variable speed limits

In this study, we formulate the VSL control problem for the traffic system in
a zone upstream to a lane-drop bottleneck based on two traffic flow models: the
Lighthill-Whitham-Richards (LWR) model, which is an infinite-dimensional
partial differential equation, and the link queue model, which is a
finite-dimensional ordinary differential equation. In both models, the
discharging flow-rate is determined by a recently developed model of capacity
drop, and the upstream in-flux is regulated by the speed limit in the VSL zone.
Since the link queue model approximates the LWR model and is much simpler, we
first analyze the control problem and develop effective VSL strategies based on
the former. First for an open-loop control system with a constant speed limit,
we prove that a constant speed limit can introduce an uncongested equilibrium
state, in addition to a congested one with capacity drop, but the congested
equilibrium state is always exponentially stable. Then we apply a feedback
proportional-integral (PI) controller to form a closed-loop control system, in
which the congested equilibrium state and, therefore, capacity drop can be
removed by the I-controller. Both analytical and numerical results show that,
with appropriately chosen controller parameters, the closed-loop control system
is stable, effect, and robust. Finally, we show that the VSL strategies based
on I- and PI-controllers are also stable, effective, and robust for the LWR
model. Since the properties of the control system are transferable between the
two models, we establish a dual approach for studying the control problems of
nonlinear traffic flow systems. We also confirm that the VSL strategy is
effective only if capacity drop occurs. The obtained method and insights can be
useful for future studies on other traffic control methods and implementations
of VSL strategies.Comment: 31 pages, 14 figure

### Optimality of Graphlet Screening in High Dimensional Variable Selection

Consider a linear regression model where the design matrix X has n rows and p
columns. We assume (a) p is much large than n, (b) the coefficient vector beta
is sparse in the sense that only a small fraction of its coordinates is
nonzero, and (c) the Gram matrix G = X'X is sparse in the sense that each row
has relatively few large coordinates (diagonals of G are normalized to 1).
The sparsity in G naturally induces the sparsity of the so-called graph of
strong dependence (GOSD). We find an interesting interplay between the signal
sparsity and the graph sparsity, which ensures that in a broad context, the set
of true signals decompose into many different small-size components of GOSD,
where different components are disconnected.
We propose Graphlet Screening (GS) as a new approach to variable selection,
which is a two-stage Screen and Clean method. The key methodological innovation
of GS is to use GOSD to guide both the screening and cleaning. Compared to
m-variate brute-forth screening that has a computational cost of p^m, the GS
only has a computational cost of p (up to some multi-log(p) factors) in
screening.
We measure the performance of any variable selection procedure by the minimax
Hamming distance. We show that in a very broad class of situations, GS achieves
the optimal rate of convergence in terms of the Hamming distance. Somewhat
surprisingly, the well-known procedures subset selection and the lasso are rate
non-optimal, even in very simple settings and even when their tuning parameters
are ideally set

### Charged BTZ-like black hole solutions and the diffusivity-butterfly velocity relation

We show that there exists a class of charged BTZ-like black hole solutions in
Lifshitz spacetime with a hyperscaling violating factor. The charged BTZ is
characterized by a charge-dependent logarithmic term in the metric function. As
concrete examples, we give five such charged BTZ-like black hole solutions and
the standard charged BTZ metric can be regarded as a special instance of them.
In order to check the recent proposed universal relations between diffusivity
and the butterfly velocity, we first compute the diffusion constants of the
standard charged BTZ black holes and then extend our calculation to arbitrary
dimension $d$, exponents $z$ and $\theta$. Remarkably, the case $d=\theta$ and
$z=2$ is a very special in that the charge diffusion $D_c$ is a constant and
the energy diffusion $D_e$ might be ill-defined, but $v^2_B\tau$ diverges. We
also compute the diffusion constants for the case that the DC conductivity is
finite but in the absence of momentum relaxation.Comment: 30 pages, 2 figure

### Orbital angular momentum mode-demultiplexing scheme with partial angular receiving aperture

For long distance orbital angular momentum (OAM) based transmission, the conventional whole beam receiving scheme encounters the difficulty of large aperture due to the divergence of OAM beams. We propose a novel partial receiving scheme, using a restricted angular aperture to receive and demultiplex multi-OAM-mode beams. The scheme is theoretically analyzed to show that a regularly spaced OAM mode set remain orthogonal and therefore can be de-multiplexed. Experiments have been carried out to verify the feasibility. This partial receiving scheme can serve as an effective method with both space and cost savings for the OAM communications. It is applicable to both free space OAM optical communications and radio frequency (RF) OAM communications

### Toward optimal multistep forecasts in non-stationary autoregressions

This paper investigates multistep prediction errors for non-stationary
autoregressive processes with both model order and true parameters unknown. We
give asymptotic expressions for the multistep mean squared prediction errors
and accumulated prediction errors of two important methods, plug-in and direct
prediction. These expressions not only characterize how the prediction errors
are influenced by the model orders, prediction methods, values of parameters
and unit roots, but also inspire us to construct some new predictor selection
criteria that can ultimately choose the best combination of the model order and
prediction method with probability 1. Finally, simulation analysis confirms the
satisfactory finite sample performance of the newly proposed criteria.Comment: Published in at http://dx.doi.org/10.3150/08-BEJ165 the Bernoulli
(http://isi.cbs.nl/bernoulli/) by the International Statistical
Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm

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