arXiv subjects

Bo Jiang

Publications and source records attributed to Bo Jiang.

341 records · Page 19Linked to original sources

arXiv2016

Tensor and Its Tucker Core: the Invariance Relationships

In [13], Hillar and Lim famously demonstrated that "multilinear (tensor) analogues of many efficiently computable problems in numerical linear algebra are NP-hard". Despite many recent advancements, the state-of-the-art methods for computing such `tensor analogues' still suffer severely from the curse of dimensionality. In this paper we show that the Tucker core of a tensor however, retains many properties of the original tensor, including the CP rank, the border rank, the tensor Schatten quasi norms, and the Z-eigenvalues. When the core tensor is smaller than the original tensor, this property leads to considerable computational advantages as confirmed by our numerical experiments. In our analysis, we in fact work with a generalized Tucker-like decomposition that can accommodate any full column-rank factor matrices.

math.OC↗

arXiv2016

$L_p$-norm regularization algorithms for optimization over permutation matrices

Optimization problems over permutation matrices appear widely in facility layout, chip design, scheduling, pattern recognition, computer vision, graph matching, etc. Since this problem is NP-hard due to the combinatorial nature of permutation matrices, we relax the variable to be the more tractable doubly stochastic matrices and add an $L_p$-norm ($0 < p < 1$) regularization term to the objective function. The optimal solutions of the $L_p$-regularized problem are the same as the original problem if the regularization parameter is sufficiently large. A lower bound estimation of the nonzero entries of the stationary points and some connections between the local minimizers and the permutation matrices are further established. Then we propose an $L_p$ regularization algorithm with local refinements. The algorithm approximately solves a sequence of $L_p$ regularization subproblems by the projected gradient method using a nonmontone line search with the Barzilai-Borwein step sizes. Its performance can be further improved if it is combined with certain local search methods, the cutting plane techniques as well as a new negative proximal point scheme. Extensive numerical results on QAPLIB and the bandwidth minimization problem show that our proposed algorithms can often find reasonably high quality solutions within a competitive amount of time.

math.OC↗

arXiv2016

The Anion Effect on Li+ Ion Coordination Structure in Ethylene Carbonate Solutions

Rechargeable lithium ion batteries are an attractive alternative power source for a wide variety of applications. To optimize their performances, a complete description of the solvation properties of the ion in the electrolyte is crucial. A comprehensive understanding at the nanoscale of the solvation structure of lithium ions in nonaqueous carbonate electrolytes is, however, still unclear. We have measured by femtosecond vibrational spectroscopy the orientational correlation time of the CO stretching mode of Li+-bound and Li+-unbound ethylene carbonate molecules, in LiBF4, LiPF6, and LiClO4 ethylene carbonate solutions with different concentrations. Surprisingly, we have found that the coordination number of ethylene carbonate in the first solvation shell of Li+ is only two, in all solutions with concentrations higher than 0.5 M. Density functional theory calculations indicate that the presence of anions in the first coordination shell modifies the generally accepted tetrahedral structure of the complex, allowing only two EC molecules to coordinate to Li+ directly. Our results demonstrate for the first time, to the best of our knowledge, the anion influence on the overall structure of the first solvation shell of the Li+ ion. The formation of such a cation/solvent/anion complex provides a rational explanation for the ionic conductivity drop of lithium/carbonate electrolyte solutions at high concentrations.

physics.chem-ph↗

arXiv2016

Characterizing Real-Valued Multivariate Complex Polynomials and Their Symmetric Tensor Representations

In this paper we study multivariate polynomial functions in complex variables and the corresponding associated symmetric tensor representations. The focus is on finding conditions under which such complex polynomials/tensors always take real values. We introduce the notion of symmetric conjugate forms and general conjugate forms, and present characteristic conditions for such complex polynomials to be real-valued. As applications of our results, we discuss the relation between nonnegative polynomials and sums of squares in the context of complex polynomials. Moreover, new notions of eigenvalues/eigenvectors for complex tensors are introduced, extending properties from the Hermitian matrices. Finally, we discuss an important property for symmetric tensors, which states that the largest absolute value of eigenvalue of a symmetric real tensor is equal to its largest singular value; the result is known as Banach's theorem. We show that a similar result holds in the complex case as well.

math.OC↗

arXiv2015

To What Extent Is Stress Testing of Android TV Applications Automated in Industrial Environments?

An Android-based smart Television (TV) must reliably run its applications in an embedded program environment under diverse hardware resource conditions. Owing to the diverse hardware components used to build numerous TV models, TV simulators are usually not high enough in fidelity to simulate various TV models, and thus are only regarded as unreliable alternatives when stress testing such applications. Therefore, even though stress testing on real TV sets is tedious, it is the de facto approach to ensure the reliability of these applications in the industry. In this paper, we study to what extent stress testing of smart TV applications can be fully automated in the industrial environments. To the best of our knowledge, no previous work has addressed this important question. We summarize the find-ings collected from 10 industrial test engineers to have tested 20 such TV applications in a real production environment. Our study shows that the industry required test automation supports on high-level GUI object controls and status checking, setup of resource conditions and the interplay between the two. With such supports, 87% of the industrial test specifications of one TV model can be fully automated and 71.4% of them were found to be fully reusable to test a subsequent TV model with major up-grades of hardware, operating system and application. It repre-sents a significant improvement with margins of 28% and 38%, respectively, compared to stress testing without such supports.

cs.SE↗

arXiv2015

Reciprocity in Social Networks with Capacity Constraints

Directed links -- representing asymmetric social ties or interactions (e.g., "follower-followee") -- arise naturally in many social networks and other complex networks, giving rise to directed graphs (or digraphs) as basic topological models for these networks. Reciprocity, defined for a digraph as the percentage of edges with a reciprocal edge, is a key metric that has been used in the literature to compare different directed networks and provide "hints" about their structural properties: for example, are reciprocal edges generated randomly by chance or are there other processes driving their generation? In this paper we study the problem of maximizing achievable reciprocity for an ensemble of digraphs with the same prescribed in- and out-degree sequences. We show that the maximum reciprocity hinges crucially on the in- and out-degree sequences, which may be intuitively interpreted as constraints on some "social capacities" of nodes and impose fundamental limits on achievable reciprocity. We show that it is NP-complete to decide the achievability of a simple upper bound on maximum reciprocity, and provide conditions for achieving it. We demonstrate that many real networks exhibit reciprocities surprisingly close to the upper bound, which implies that users in these social networks are in a sense more "social" than suggested by the empirical reciprocity alone in that they are more willing to reciprocate, subject to their "social capacity" constraints. We find some surprising linear relationships between empirical reciprocity and the bound. We also show that a particular type of small network motifs that we call 3-paths are the major source of loss in reciprocity for real networks.

cs.SI↗

arXiv2015

Hadoop Scheduling Base On Data Locality

In hadoop, the job scheduling is an independent module, users can design their own job scheduler based on their actual application requirements, thereby meet their specific business needs. Currently, hadoop has three schedulers: FIFO, computing capacity scheduling and fair scheduling policy, all of them are take task allocation strategy that considerate data locality simply. They neither support data locality well nor fully apply to all cases of jobs scheduling. In this paper, we took the concept of resources-prefetch into consideration, and proposed a job scheduling algorithm based on data locality. By estimate the remaining time to complete a task, compared with the time to transfer a resources block, to preselect candidate nodes for task allocation. Then we preselect a non-local map tasks from the unfinished job queue as resources-prefetch tasks. Getting information of resources blocks of preselected map task, select a nearest resources blocks from the candidate node and transferred to local through network. Thus we would ensure data locality good enough. Eventually, we design a experiment and proved resources-prefetch method can guarantee good job data locality and reduce the time to complete the job to a certain extent.

cs.DC↗

arXiv2015

Bayesian nonparametric tests via sliced inverse modeling

We study the problem of independence and conditional independence tests between categorical covariates and a continuous response variable, which has an immediate application in genetics. Instead of estimating the conditional distribution of the response given values of covariates, we model the conditional distribution of covariates given the discretized response (aka "slices"). By assigning a prior probability to each possible discretization scheme, we can compute efficiently a Bayes factor (BF)-statistic for the independence (or conditional independence) test using a dynamic programming algorithm. Asymptotic and finite-sample properties such as power and null distribution of the BF statistic are studied, and a stepwise variable selection method based on the BF statistic is further developed. We compare the BF statistic with some existing classical methods and demonstrate its statistical power through extensive simulation studies. We apply the proposed method to a mouse genetics data set aiming to detect quantitative trait loci (QTLs) and obtain promising results.

stat.ME↗

arXiv2015

Towards a solid solution of real-time fire and flame detection

Although the object detection and recognition has received growing attention for decades, a robust fire and flame detection method is rarely explored. This paper presents an empirical study, towards a general and solid approach to fast detect fire and flame in videos, with the applications in video surveillance and event retrieval. Our system consists of three cascaded steps: (1) candidate regions proposing by a background model, (2) fire region classifying with color-texture features and a dictionary of visual words, and (3) temporal verifying. The experimental evaluation and analysis are done for each step. We believe that it is a useful service to both academic research and real-world application. In addition, we release the software of the proposed system with the source code, as well as a public benchmark and data set, including 64 video clips covered both indoor and outdoor scenes under different conditions. We achieve an 82% Recall with 93% Precision on the data set, and greatly improve the performance by state-of-the-arts methods.

cs.CV↗

arXiv2014

On the Complexity of Optimal Routing and Content Caching in Heterogeneous Networks

We investigate the problem of optimal request routing and content caching in a heterogeneous network supporting in-network content caching with the goal of minimizing average content access delay. Here, content can either be accessed directly from a back-end server (where content resides permanently) or be obtained from one of multiple in-network caches. To access a piece of content, a user must decide whether to route its request to a cache or to the back-end server. Additionally, caches must decide which content to cache. We investigate the problem complexity of two problem formulations, where the direct path to the back-end server is modeled as i) a congestion-sensitive or ii) a congestion-insensitive path, reflecting whether or not the delay of the uncached path to the back-end server depends on the user request load, respectively. We show that the problem is NP-complete in both cases. We prove that under the congestion-insensitive model the problem can be solved optimally in polynomial time if each piece of content is requested by only one user, or when there are at most two caches in the network. We also identify a structural property of the user-cache graph that potentially makes the problem NP-complete. For the congestion-sensitive model, we prove that the problem remains NP-complete even if there is only one cache in the network and each content is requested by only one user. We show that approximate solutions can be found for both models within a (1-1/e) factor of the optimal solution, and demonstrate a greedy algorithm that is found to be within 1% of optimal for small problem sizes. Through trace-driven simulations we evaluate the performance of our greedy algorithms, which show up to a 50% reduction in average delay over solutions based on LRU content caching.

cs.NI↗

arXiv2014

On the duration and intensity of cumulative advantage competitions

The role of skill (fitness) and luck (randomness) as driving forces on the dynamics of resource accumulation in a myriad of systems have long puzzled scientists. Fueled by undisputed inequalities that emerge from actual competitions, there is a pressing need for better understanding the effects of skill and luck in resource accumulation. When such competitions are driven by externalities such as cumulative advantage (CA), the rich-get-richer effect, little is known with respect to fundamental properties such as their duration and intensity. In this work we provide a mathematical understanding of how CA exacerbates the role of luck in detriment of skill in simple and well-studied competition models. We show, for instance, that if two agents are competing for resources that arrive sequentially at each time unit, an early stroke of luck can place the less skilled in the lead for an extremely long period of time, a phenomenon we call "struggle of the fittest". In the absence of CA, the more skilled quickly prevails despite any early stroke of luck that the less skilled may have. We prove that duration of a simple skill and luck competition model exhibit power law tails when CA is present, regardless of skill difference, which is in sharp contrast to exponential tails when CA is absent. Our findings have important implications to competitions not only in complex social systems but also in contexts that leverage such models.

physics.soc-ph↗

arXiv2014

Iteration Bounds for Finding the $ε$-Stationary Points for Structured Nonconvex Optimization

In this paper we study proximal conditional-gradient (CG) and proximal gradient-projection type algorithms for a block-structured constrained nonconvex optimization model, which arises naturally from tensor data analysis. First, we introduce a new notion of $ε$-stationarity, which is suitable for the structured problem under consideration. %, compared with other similar solution concepts. We then propose two types of first-order algorithms for the model based on the proximal conditional-gradient (CG) method and the proximal gradient-projection method respectively. If the nonconvex objective function is in the form of mathematical expectation, we then discuss how to incorporate randomized sampling to avoid computing the expectations exactly. For the general block optimization model, the proximal subroutines are performed for each block according to either the block-coordinate-descent (BCD) or the maximum-block-improvement (MBI) updating rule. If the gradient of the nonconvex part of the objective $f$ satisfies $\| \nabla f(x) - \nabla f(y)\|_q \le M \|x-y\|_p^δ$ where $δ=p/q$ with $1/p+1/q=1$, then we prove that the new algorithms have an overall iteration complexity bound of $O(1/ε^q)$ in finding an $ε$-stationary solution. If $f$ is concave then the iteration complexity reduces to $O(1/ε)$. Our numerical experiments for tensor approximation problems show promising performances of the new solution algorithms.

math.OC↗

arXiv2014

Variable selection for general index models via sliced inverse regression

Variable selection, also known as feature selection in machine learning, plays an important role in modeling high dimensional data and is key to data-driven scientific discoveries. We consider here the problem of detecting influential variables under the general index model, in which the response is dependent of predictors through an unknown function of one or more linear combinations of them. Instead of building a predictive model of the response given combinations of predictors, we model the conditional distribution of predictors given the response. This inverse modeling perspective motivates us to propose a stepwise procedure based on likelihood-ratio tests, which is effective and computationally efficient in identifying important variables without specifying a parametric relationship between predictors and the response. For example, the proposed procedure is able to detect variables with pairwise, three-way or even higher-order interactions among $p$ predictors with a computational time of $O(p)$ instead of $O(p^k)$ (with $k$ being the highest order of interactions). Its excellent empirical performance in comparison with existing methods is demonstrated through simulation studies as well as real data examples. Consistency of the variable selection procedure when both the number of predictors and the sample size go to infinity is established.

stat.ME↗

arXiv2014

A Framework of Constraint Preserving Update Schemes for Optimization on Stiefel Manifold

This paper considers optimization problems on the Stiefel manifold $X^{\mathsf{T}}X=I_p$, where $X\in \mathbb{R}^{n \times p}$ is the variable and $I_p$ is the $p$-by-$p$ identity matrix. A framework of constraint preserving update schemes is proposed by decomposing each feasible point into the range space of $X$ and the null space of $X^{\mathsf{T}}$. While this general framework can unify many existing schemes, a new update scheme with low complexity cost is also discovered. Then we study a feasible Barzilai-Borwein-like method under the new update scheme. The global convergence of the method is established with an adaptive nonmonotone line search. The numerical tests on the nearest low-rank correlation matrix problem, the Kohn-Sham total energy minimization and a specific problem from statistics demonstrate the efficiency of the new method. In particular, the new method performs remarkably well for the nearest low-rank correlation matrix problem in terms of speed and solution quality and is considerably competitive with the widely used SCF iteration for the Kohn-Sham total energy minimization.

math.OC↗

arXiv2013

Tensor Principal Component Analysis via Convex Optimization

This paper is concerned with the computation of the principal components for a general tensor, known as the tensor principal component analysis (PCA) problem. We show that the general tensor PCA problem is reducible to its special case where the tensor in question is super-symmetric with an even degree. In that case, the tensor can be embedded into a symmetric matrix. We prove that if the tensor is rank-one, then the embedded matrix must be rank-one too, and vice versa. The tensor PCA problem can thus be solved by means of matrix optimization under a rank-one constraint, for which we propose two solution methods: (1) imposing a nuclear norm penalty in the objective to enforce a low-rank solution; (2) relaxing the rank-one constraint by Semidefinite Programming. Interestingly, our experiments show that both methods yield a rank-one solution with high probability, thereby solving the original tensor PCA problem to optimality with high probability. To further cope with the size of the resulting convex optimization models, we propose to use the alternating direction method of multipliers, which reduces significantly the computational efforts. Various extensions of the model are considered as well.

math.OC↗

arXiv2013

On Modeling Economic Default Time: A Reduced-Form Model Approach

In the aftermath of the global financial crisis, much attention has been paid to investigating the appropriateness of the current practice of default risk modeling in banking, finance and insurance industries. A recent empirical study by Guo et al.(2008) shows that the time difference between the economic and recorded default dates has a significant impact on recovery rate estimates. Guo et al.(2011) develop a theoretical structural firm asset value model for a firm default process that embeds the distinction of these two default times. To be more consistent with the practice, in this paper, we assume the market participants cannot observe the firm asset value directly and developed a reduced-form model to characterize the economic and recorded default times. We derive the probability distribution of these two default times. The numerical study on the difference between these two shows that our proposed model can both capture the features and fit the empirical data.

q-fin.CP↗

arXiv2007

Self-Retracting Motion of Graphite Microflakes

We report the observation of a novel phenomenon, the self-retracting motion of graphite, in which tiny flakes of graphite, after being displaced to various suspended positions from islands of highly orientated pyrolytic graphite, retract back onto the islands under no external influences. Our repeated probing and observing such flakes of various sizes indicate the existence of a critical size of flakes, approximately 35 micrometer, above which the self-retracting motion does not occur under the operation. This helps to explain the fact that the self-retracting motion of graphite has not been reported, because samples of natural graphite are typical larger than this critical size. In fact, reports of this phenomenon have not been found in the literature for single crystals of any kinds. A model that includes the static and dynamic shear strengths, the van der Waals interaction force, and the edge dangling bond interaction effect, was used to explain the observed phenomenon. These findings may conduce to create nano-electromechanical systems with a wide range of mechanical operating frequency from mega to giga hertzs.

cond-mat.mtrl-sci↗