22,352 research outputs found
Tail behavior of dependent V-statistics and its applications
We establish exponential inequalities and Cramer-type moderate deviation
theorems for a class of V-statistics under strong mixing conditions. Our theory
is developed via kernel expansion based on random Fourier features. This type
of expansion is new and useful for handling many notorious classes of kernels.
While the developed theory has a number of applications, we apply it to
lasso-type semiparametric regression estimation and high-dimensional multiple
hypothesis testing
One-Bit Quantization Design and Adaptive Methods for Compressed Sensing
There have been a number of studies on sparse signal recovery from one-bit
quantized measurements. Nevertheless, little attention has been paid to the
choice of the quantization thresholds and its impact on the signal recovery
performance. This paper examines the problem of one-bit quantizer design for
sparse signal recovery. Our analysis shows that the magnitude ambiguity that
ever plagues conventional one-bit compressed sensing methods can be resolved,
and an arbitrarily small reconstruction error can be achieved by setting the
quantization thresholds close enough to the original data samples without being
quantized. Note that unquantized data samples are unaccessible in practice. To
overcome this difficulty, we propose an adaptive quantization method that
adaptively adjusts the quantization thresholds in a way such that the
thresholds converges to the optimal thresholds. Numerical results are
illustrated to collaborate our theoretical results and the effectiveness of the
proposed algorithm
Electrically tunable quantum interfaces between photons and spin qubits in carbon nanotube quantum dots
We present a new scheme for quantum interfaces to accomplish the
interconversion of photonic qubits and spin qubits based on optomechanical
resonators and the spin-orbit-induced interactions in suspended carbon nanotube
quantum dots. This interface implements quantum spin transducers and further
enables electrical manipulation of local electron spin qubits, which lays the
foundation for all-electrical control of state transfer protocols between two
distant quantum nodes in a quantum network. We numerically evaluate the state
transfer processes and proceed to estimate the effect of each coupling strength
on the operation fidelities
Enhancing streamflow forecast and extracting insights using long-short term memory networks with data integration at continental scales
Recent observations with varied schedules and types (moving average,
snapshot, or regularly spaced) can help to improve streamflow forecasts, but it
is challenging to integrate them effectively. Based on a long short-term memory
(LSTM) streamflow model, we tested multiple versions of a flexible procedure we
call data integration (DI) to leverage recent discharge measurements to improve
forecasts. DI accepts lagged inputs either directly or through a convolutional
neural network (CNN) unit. DI ubiquitously elevated streamflow forecast
performance to unseen levels, reaching a record continental-scale median
Nash-Sutcliffe Efficiency coefficient value of 0.86. Integrating moving-average
discharge, discharge from the last few days, or even average discharge from the
previous calendar month could all improve daily forecasts. Directly using
lagged observations as inputs was comparable in performance to using the CNN
unit. Importantly, we obtained valuable insights regarding hydrologic processes
impacting LSTM and DI performance. Before applying DI, the base LSTM model
worked well in mountainous or snow-dominated regions, but less well in regions
with low discharge volumes (due to either low precipitation or high
precipitation-energy synchronicity) and large inter-annual storage variability.
DI was most beneficial in regions with high flow autocorrelation: it greatly
reduced baseflow bias in groundwater-dominated western basins and also improved
peak prediction for basins with dynamical surface water storage, such as the
Prairie Potholes or Great Lakes regions. However, even DI cannot elevate
high-aridity basins with one-day flash peaks. Despite this limitation, there is
much promise for a deep-learning-based forecast paradigm due to its
performance, automation, efficiency, and flexibility
Real-time Acceleration-continuous Path-constrained Trajectory Planning With Built-in Tradability Between Cruise and Time-optimal Motions
In this paper, a novel real-time acceleration-continuous path-constrained
trajectory planning algorithm is proposed with an appealing built-in
tradability mechanism between cruise motion and time-optimal motion. Different
from existing approaches, the proposed approach smoothens time-optimal
trajectories with bang-bang input structures to generate
acceleration-continuous trajectories while preserving the completeness
property. More importantly, a novel built-in tradability mechanism is proposed
and embedded into the trajectory planning framework, so that the proportion of
the cruise motion and time-optimal motion can be flexibly adjusted by changing
a user-specified functional parameter. Thus, the user can easily apply the
trajectory planning algorithm for various tasks with different requirements on
motion efficiency and cruise proportion. Moreover, it is shown that feasible
trajectories are computed more quickly than optimal trajectories. Rigorous
mathematical analysis and proofs are provided for these aforementioned results.
Comparative simulation and experimental results on omnidirectional wheeled
mobile robots demonstrate the capability of the proposed algorithm in terms of
flexible tunning between cruise and time-optimal motions, as well as higher
computational efficiency.Comment: 12 pages, 19 figure
Diffusive KPP Equations with Free Boundaries in Time Almost Periodic Environments: I. Spreading and Vanishing Dichotomy
In this series of papers, we investigate the spreading and vanishing dynamics
of time almost periodic diffusive KPP equations with free boundaries. Such
equations are used to characterize the spreading of a new species in time
almost periodic environments with free boundaries representing the spreading
fronts. In this first part, we show that a spreading-vanishing dichotomy occurs
for such free boundary problems, that is, the species either successfully
spreads to all the new environment and stabilizes at a time almost periodic
positive solution, or it fails to establish and dies out eventually. The
results of this part extend the existing results on spreading-vanishing
dichotomy for time and space independent, or time periodic and space
independent, or time independent and space periodic diffusive KPP equations
with free boundaries. The extension is nontrivial and is ever done for the
first time.Comment: 31 page
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Pattern Coupled Sparse Bayesian Learning for Recovery of Time Varying Sparse Signals
We consider the problem of recovering block-sparse signals whose structures
are unknown \emph{a priori}. Block-sparse signals with nonzero coefficients
occurring in clusters arise naturally in many practical scenarios. However, the
knowledge of the block structure is usually unavailable in practice. In this
paper, we develop a new sparse Bayesian learning method for recovery of
block-sparse signals with unknown cluster patterns. Specifically, a
pattern-coupled hierarchical Gaussian prior model is introduced to characterize
the statistical dependencies among coefficients, in which a set of
hyperparameters are employed to control the sparsity of signal coefficients.
Unlike the conventional sparse Bayesian learning framework in which each
individual hyperparameter is associated independently with each coefficient, in
this paper, the prior for each coefficient not only involves its own
hyperparameter, but also the hyperparameters of its immediate neighbors. In
doing this way, the sparsity patterns of neighboring coefficients are related
to each other and the hierarchical model has the potential to encourage
structured-sparse solutions. The hyperparameters, along with the sparse signal,
are learned by maximizing their posterior probability via an
expectation-maximization (EM) algorithm. Numerical results show that the
proposed algorithm presents uniform superiority over other existing methods in
a series of experiments
Quasi-Cyclic Codes Over Finite Chain Rings
In this paper, we mainly consider quasi-cyclic (QC) codes over finite chain
rings. We study module structures and trace representations of QC codes, which
lead to some lower bounds on the minimum Hamming distance of QC codes.
Moreover, we investigate the structural properties of 1-generator QC codes.
Under some conditions, we discuss the enumeration of 1-generator QC codes and
describe how to obtain the one and only one generator for each 1-generator QC
code.Comment: 2
Skew Generalized Quasi-Cyclic Codes over Finite Fields
In this work, we study a class of generalized quasi-cyclic (GQC) codes called
skew GQC codes. By the factorization theory of ideals, we give the Chinese
Remainder Theorem over the skew polynomial ring, which leads to a canonical
decomposition of skew GQC codes. We also focus on some characteristics of skew
GQC codes in details. For a 1-generator skew GQC code, we define the
parity-check polynomial, determine the dimension and give a lower bound on the
minimum Hamming distance. The skew quasi-cyclic (QC) codes are also discussed
briefly.Comment: 1
Optimal Task Assignment and Power Allocation for NOMA Mobile-Edge Computing Networks
Mobile edge computing (MEC) can enhance the computing capability of mobile
devices, and non-orthogonal multiple access (NOMA) can provide high data rates.
Combining these two technologies can effectively benefit the network with
spectrum and energy efficiency. In this paper, we investigate the task
completion time minimization in NOMA multiuser MEC networks, where multiple
users can offload their tasks simultaneously via the same frequency band. We
adopt the \emph{partial} offloading, in which each user can partition its
computation task into offloading computing and locally computing parts. We aim
to minimize the maximum task latency among users by optimizing their tasks
partition ratios and offloading transmit power. By considering the energy
consumption and transmitted power limitation of each user, the formulated
problem is quasi-convex. Thus, a bisection search (BSS) iterative algorithm is
proposed to obtain the minimum task completion time. To reduce the complexity
of the BSS algorithm and evaluate its optimality, we further derive the
closed-form expressions of the optimal task partition ratio and offloading
power for two-user NOMA MEC networks based on the analysed results. Simulation
results demonstrate the convergence and optimality of the proposed a BSS
algorithm and the effectiveness of the proposed optimal derivation
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