arXiv subjects

Wei Xiao

Publications and source records attributed to Wei Xiao.

139 records · Page 8Linked to original sources

arXiv2018

Decentralized Optimal Merging Control for Connected and Automated Vehicles

This paper addresses the optimal control of Connected and Automated Vehicles (CAVs) arriving from two roads at a merging point where the objective is to jointly minimize the travel time and energy consumption of each CAV. The solution guarantees that a speed-dependent safety constraint is always satisfied, both at the merging point and everywhere within a control zone which precedes it. We first analyze the case of no active constraints and prove that under certain conditions the safety constraint remains inactive, thus significantly simplifying the determination of an explicit decentralized solution. When these conditions do not apply, an explicit solution is still obtained that includes intervals over which the safety constraint is active. Our analysis allows us to study the tradeoff between the two objective function components (travel time and energy within the control zone). Simulation examples are included to compare the performance of the optimal controller to a baseline with human-driven vehicles with results showing improvements in both metrics.

eess.SY↗

arXiv2017

An Online Algorithm for Nonparametric Correlations

Nonparametric correlations such as Spearman's rank correlation and Kendall's tau correlation are widely applied in scientific and engineering fields. This paper investigates the problem of computing nonparametric correlations on the fly for streaming data. Standard batch algorithms are generally too slow to handle real-world big data applications. They also require too much memory because all the data need to be stored in the memory before processing. This paper proposes a novel online algorithm for computing nonparametric correlations. The algorithm has O(1) time complexity and O(1) memory cost and is quite suitable for edge devices, where only limited memory and processing power are available. You can seek a balance between speed and accuracy by changing the number of cutpoints specified in the algorithm. The online algorithm can compute the nonparametric correlations 10 to 1,000 times faster than the corresponding batch algorithm, and it can compute them based either on all past observations or on fixed-size sliding windows.

stat.AP↗

arXiv2017

Online Robust Principal Component Analysis with Change Point Detection

Robust PCA methods are typically batch algorithms which requires loading all observations into memory before processing. This makes them inefficient to process big data. In this paper, we develop an efficient online robust principal component methods, namely online moving window robust principal component analysis (OMWRPCA). Unlike existing algorithms, OMWRPCA can successfully track not only slowly changing subspace but also abruptly changed subspace. By embedding hypothesis testing into the algorithm, OMWRPCA can detect change points of the underlying subspaces. Extensive simulation studies demonstrate the superior performance of OMWRPCA compared with other state-of-art approaches. We also apply the algorithm for real-time background subtraction of surveillance video.

cs.LG↗

arXiv2017

Differential-operator representations of Weyl group and singular vectors

Given a suitable ordering of the positive root system associated with a semisimple Lie algebra, there exists a natural correspondence between Verma modules and related polynomial algebras. With this, the Lie algebra action on a Verma module can be interpreted as a differential operator action on polynomials, and thus on the corresponding truncated formal power series. We prove that the space of truncated formal power series is a differential-operator representation of the Weyl group $W$. We also introduce a system of partial differential equations to investigate singular vectors in the Verma module. It is shown that the solution space of the system in the space of truncated formal power series is the span of $\{w(1)\ |\ w\in W\}$. Those $w(1)$ that are polynomials correspond to singular vectors in the Verma module. This elementary approach by partial differential equations also gives a new proof of the well-known BGG-Verma Theorem.

math.RT↗

arXiv2017

Dirac cohomology and Euler-Poincaré pairing for weight modules

Let $\mathfrak{g}$ be a reductive Lie algebra over $\mathbb{C}$. For any simple weight module of $\mathfrak{g}$ with finite-dimensional weight spaces, we show that its Dirac cohomology is vanished unless it is a highest weight module. This completes the calculation of Dirac cohomology for simple weight modules since the Dirac cohomology of simple highest weight modules was carried out in our previous work. We also show that the Dirac index pairing of two weight modules which have infinitesimal characters agrees with their Euler-Poincaré pairing. The analogue of this result for Harish-Chandra modules is a consequence of the Kazhdan's orthogonality conjecture which was settled by the first named author and Binyong Sun.

math.RT↗

arXiv2016

Sampling Method for Fast Training of Support Vector Data Description

Support Vector Data Description (SVDD) is a popular outlier detection technique which constructs a flexible description of the input data. SVDD computation time is high for large training datasets which limits its use in big-data process-monitoring applications. We propose a new iterative sampling-based method for SVDD training. The method incrementally learns the training data description at each iteration by computing SVDD on an independent random sample selected with replacement from the training data set. The experimental results indicate that the proposed method is extremely fast and provides a good data description .

cs.LG↗

arXiv2016

Robust regression for optimal individualized treatment rules

Because different patients may response quite differently to the same drug or treatment, there is increasing interest in discovering individualized treatment rule. In particular, people are eager to find the optimal individualized treatment rules, which if followed by the whole patient population would lead to the "best" outcome. In this paper, we propose new estimators based on robust regression with general loss functions to estimate the optimal individualized treatment rules. The new estimators possess the following nice properties: first, they are robust against skewed, heterogeneous, heavy-tailed errors or outliers; second, they are robust against misspecification of the baseline function; third, under certain situations, the new estimator coupled with pinball loss approximately maximizes the outcome's conditional quantile instead of conditional mean, which leads to a different optimal individualized treatment rule comparing with traditional Q- and A-learning. Consistency and asymptotic normality of the proposed estimators are established. Their empirical performance is demonstrated via extensive simulation studies and an analysis of an AIDS data.

stat.ME↗

arXiv2016

A Probabilistic Machine Learning Approach to Detect Industrial Plant Faults

Fault detection in industrial plants is a hot research area as more and more sensor data are being collected throughout the industrial process. Automatic data-driven approaches are widely needed and seen as a promising area of investment. This paper proposes an effective machine learning algorithm to predict industrial plant faults based on classification methods such as penalized logistic regression, random forest and gradient boosted tree. A fault's start time and end time are predicted sequentially in two steps by formulating the original prediction problems as classification problems. The algorithms described in this paper won first place in the Prognostics and Health Management Society 2015 Data Challenge.

stat.ML↗

arXiv2015

Differential equations and singular vectors in Verma modules

Xu introduced a system of partial differential equations to investigate singular vectors in the Verma modules of highest weight $λ$ over $\mathfrak{sl}(n,\mathbb{C})$. He proved that the solution space of this system in the space of truncated power series is spanned by $\{σ(1)\ |\ σ\in S_n\}$. We present an explicit formula of the solution $s_α(1)$ for every positive root $α$ and showed directly that $s_α(1)$ is a polynomial if and only if $\langleλ+ρ,α\rangle$ is a nonnegative integer. From this, we can recover a formula of singular vectors given by Malikov et al.

math.RT↗

arXiv2015

Dirac operators and cohomology for Lie superalgebras

Vogan raised the idea of Dirac cohomology to study representations of semisimple Lie groups and Lie algebras. He conjectured that the infinitesimal character of Harish-Chandra modules are determined by their Dirac cohomology. Huang and Pandžić proved this conjecture and initiated the research on Dirac cohomology for Lie superalgebras based on Kostant's results. The aim of the present paper is to study Dirac cohomology of unitary representations for the general linear superalgebra and its relation to nilpotent Lie superalgebra cohomology.

math.RT↗

arXiv2011

Second order hydrodynamic coefficients from 3-point stress tensor correlators via AdS/CFT

We study second order relativistic viscous hydrodynamics in 4-dimensional conformal field theories. We derive Kubo-type relations for second order hydrodynamic coefficients in terms of 3-point stress tensor retarded correlators. For N=4 super Yang-Mills theory at strong coupling and at finite temperature we compute these stress tensor 3-point correlators, using AdS/CFT, by evaluating real-time cubic Witten diagrams in the AdS-Schwarzschild background. The small momentum expansion of the 3-point correlators in terms of first and second order hydrodynamic coefficients is matched with the AdS result. We arrive at the same expressions for the hydrodynamic coefficients which multiply terms quadratic in the shear and vorticity tensors in the hydrodynamic expansion of the stress tensor as did Bhattacharyya, Hubeny, Minwalla and Rangamani \cite{Bhattacharyya:2008jc}. Our method extends the results of Baier et al \cite{Baier:2007ix}, and allows for a unified treatment of hydrodynamic coefficients, which are extracted from 2-, and now, 3-point retarded stress tensor correlators in the AdS-Schwarzschild background.

hep-th↗

arXiv2009

Stopping distance for high energy jets in weakly-coupled quark-gluon plasmas

We derive a simple formula for the stopping distance for a high-energy quark traveling through a weakly-coupled quark gluon plasma. The result is given to next-to-leading-order in an expansion in inverse logarithms ln(E/T), where T is the temperature of the plasma. We also define a stopping distance for gluons and give a leading-log result. Discussion of stopping distance has a theoretical advantage over discussion of energy loss rates in that stopping distances can be generalized to the case of strong coupling, where one may not speak of individual partons.

hep-ph↗

arXiv2008

High-energy jet quenching in weakly-coupled quark-gluon plasmas

$\hat q$ is the average squared transverse momentum transfer per unit length to a high-energy particle traversing a QCD medium such as a quark-gluon plasma. We find the (UV-regulated) value of $\hat q$ to leading order in the weak coupling limit, $\alphas(T) \ll 1$. We then use this value to generalize previous analytic results on the gluon bremsstrahlung and pair production rates for massless high-energy particles in a weakly-coupled quark-gluon plasma, at next-to-leading logarithmic order.

hep-ph↗