A variant of multitask n-vehicle exploration problem: maximizing every processor's average profit

We discuss a variant of multitask n-vehicle exploration problem. Instead of requiring an optimal permutation of vehicles in every group, the new problem asks all vehicles in a group to arrive at a same destination. It can also be viewed as to maximize every processor's average profit, given n tasks, and each task's consume-time and profit. Meanwhile, we propose a new kind of partition problem in fractional form, and analyze its computational complexity. Moreover, by regarding fractional partition as a special case, we prove that the maximizing average profit problem is NP-hard when the number of processors is fixed and it is strongly NP-hard in general. At last, a pseudo-polynomial time algorithm for the maximizing average profit problem and the fractional partition problem is presented, thanks to the idea of the pseudo-polynomial time algorithm for the classical partition problem.Comment: This work is part of what I did as a graduate student in the Academy of Mathematics and Systems Scienc

A Nonconvex Nonsmooth Regularization Method for Compressed Sensing and Low-Rank Matrix Completion

In this paper, nonconvex and nonsmooth models for compressed sensing (CS) and low rank matrix completion (MC) is studied. The problem is formulated as a nonconvex regularized leat square optimization problems, in which the l0-norm and the rank function are replaced by l1-norm and nuclear norm, and adding a nonconvex penalty function respectively. An alternating minimization scheme is developed, and the existence of a subsequence, which generate by the alternating algorithm that converges to a critical point, is proved. The NSP, RIP, and RIP condition for stable recovery guarantees also be analysed for the nonconvex regularized CS and MC problems respectively. Finally, the performance of the proposed method is demonstrated through experimental results.Comment: 19 pages,4 figure

A New Voltage Stability-Constrained Optimal Power Flow Model: Sufficient Condition, SOCP Representation, and Relaxation

A simple characterization of the solvability of power flow equations is of great importance in the monitoring, control, and protection of power systems. In this paper, we introduce a sufficient condition for power flow Jacobian nonsingularity. We show that this condition is second-order conic representable when load powers are fixed. Through the incorporation of the sufficient condition, we propose a voltage stability-constrained optimal power flow (VSC-OPF) formulation as a second-order cone program (SOCP). An approximate model is introduced to improve the scalability of the formulation to larger systems. Extensive computation results on Matpower and NESTA instances confirm the effectiveness and efficiency of the formulation.Comment: Accepted for publication in IEEE Transactions on Power System

Solvability of Power Flow Equations Through Existence and Uniqueness of Complex Fixed Point

Variations of loading level and changes in system topological property may cause the operating point of an electric power systems to move gradually towards the verge of its transmission capability, which can lead to catastrophic outcomes such as voltage collapse blackout. From a modeling perspective, voltage collapse is closely related to the solvability of power flow equations. Determining conditions for existence and uniqueness of solution to power flow equations is one of the fundamental problems in power systems that has great theoretical and practical significance. In this paper, we provide strong sufficient condition certifying the existence and uniqueness of power flow solutions in a subset of state (voltage) space. The novel analytical approach heavily exploits the contractive properties of the fixed-point form in complex domain, which leads to much sharper analytical conditions than previous ones based primarily on analysis in the real domain. Extensive computational experiments are performed which validate the correctness and demonstrate the effectiveness of the proposed condition

A Bayesian Stochastic Approximation Method

Motivated by the goal of improving the efficiency of small sample design, we propose a novel Bayesian stochastic approximation method to estimate the root of a regression function. The method features adaptive local modelling and nonrecursive iteration. Strong consistency of the Bayes estimator is obtained. Simulation studies show that our method is superior in finite-sample performance to Robbins--Monro type procedures. Extensions to searching for extrema and a version of generalized multivariate quantile are presented

Bounded link prediction for very large networks

Evaluation of link prediction methods is a hard task in very large complex networks because of the inhibitive computational cost. By setting a lower bound of the number of common neighbors (CN), we propose a new framework to efficiently and precisely evaluate the performances of CN-based similarity indices in link prediction for very large heterogeneous networks. Specifically, we propose a fast algorithm based on the parallel computing scheme to obtain all the node pairs with CN values larger than the lower bound. Furthermore, we propose a new measurement, called self-predictability, to quantify the performance of the CN-based similarity indices in link prediction, which on the other side can indicate the link predictability of a network.Comment: 9 figure

Using Machine Learning to Forecast Future Earnings

In this essay, we have comprehensively evaluated the feasibility and suitability of adopting the Machine Learning Models on the forecast of corporation fundamentals (i.e. the earnings), where the prediction results of our method have been thoroughly compared with both analysts' consensus estimation and traditional statistical models. As a result, our model has already been proved to be capable of serving as a favorable auxiliary tool for analysts to conduct better predictions on company fundamentals. Compared with previous traditional statistical models being widely adopted in the industry like Logistic Regression, our method has already achieved satisfactory advancement on both the prediction accuracy and speed. Meanwhile, we are also confident enough that there are still vast potentialities for this model to evolve, where we do hope that in the near future, the machine learning model could generate even better performances compared with professional analysts

Covariance Matrix Estimation from Linearly-Correlated Gaussian Samples

Covariance matrix estimation concerns the problem of estimating the covariance matrix from a collection of samples, which is of extreme importance in many applications. Classical results have shown that $O(n)$ samples are sufficient to accurately estimate the covariance matrix from $n$-dimensional independent Gaussian samples. However, in many practical applications, the received signal samples might be correlated, which makes the classical analysis inapplicable. In this paper, we develop a non-asymptotic analysis for the covariance matrix estimation from correlated Gaussian samples. Our theoretical results show that the error bounds are determined by the signal dimension $n$, the sample size $m$, and the shape parameter of the distribution of the correlated sample covariance matrix. Particularly, when the shape parameter is a class of Toeplitz matrices (which is of great practical interest), $O(n)$ samples are also sufficient to faithfully estimate the covariance matrix from correlated samples. Simulations are provided to verify the correctness of the theoretical results.Comment: 8 pages, 3 figure,a typo in Figure 3 is fixe

X-ray and Optical Plateau Following the Main Bursts in Gamma-Ray Bursts and SNe II-P: A hint to the similar late injection behavior?

We analyze the emission plateaus in the X-ray afterglow lightcurves of gamma-ray bursts (GRBs) and in the optical lightcurves of Type II superpernovae (SNe IIP) in order to study whether they have similar late energy injection behaviors. We show that correlations of bolometric energies (or luminosities) between the prompt explosions and the plateaus for the two phenomena are similar. The Type II SNe are in the low energy end of the GRBs. The bolometric energies (or luminosities) in prompt phase E_{\rm expl} (or L_{\rm expl}) and in plateau phase E_{\rm plateau} (or L_{\rm plateau}) share relations of E_{\rm expl} \propto E_{\rm plateau}^{0.73\pm 0.14} and L_{\rm expl} \propto L_{\rm plateau}^{\sim 0.70}. These results may indicate a similar late energy injection behavior to reproduce the observed plateaus of the plateaus in the two phenomena.Comment: 10 pages, 3 tables, 1 figure, RAA accepte

Second Order Necessary Conditions for Optimal Control Problems on Riemannian Manifolds

This work is concerned with an optimal control problem on a Riemannian manifold, for which two typical cases are considered. The first case is when the endpoint is free. For this case, the control set is assumed to be a separable metric space. By introducing suitable dual equations, which depend on the curvature tensor of the manifold, we establish the second order necessary and sufficient optimality conditions of integral form. In particular, when the control set is a Polish space, the second order necessary condition is reduced to a pointwise form. As a key preliminary result and also an interesting byproduct, we derive a geometric lemma, which may have some independent interest. The second case is when the endpoint is fixed. For this more difficult case, the control set is assumed to be open in an Euclidian space. We obtain the second order necessary and sufficient optimality conditions, in which the curvature tensor also appears explicitly. Our optimality conditions can be used to recover the following famous geometry result: Any geodesic connecting two fixed points on a Riemannian manifold satisfies the second variation of energy; while the existing optimality conditions in control literatures fail to give the same result.Comment: 53 page