Searcharxiv⌕ Search

arXiv subjects

Long Chen

Publications and source records attributed to Long Chen.

At least 595 records · Page 33Linked to original sources

MR-GNN: Multi-Resolution and Dual Graph Neural Network for Predicting Structured Entity Interactions

Predicting interactions between structured entities lies at the core of numerous tasks such as drug regimen and new material design. In recent years, graph neural networks have become attractive. They represent structured entities as graphs and then extract features from each individual graph using graph convolution operations. However, these methods have some limitations: i) their networks only extract features from a fix-sized subgraph structure (i.e., a fix-sized receptive field) of each node, and ignore features in substructures of different sizes, and ii) features are extracted by considering each entity independently, which may not effectively reflect the interaction between two entities. To resolve these problems, we present MR-GNN, an end-to-end graph neural network with the following features: i) it uses a multi-resolution based architecture to extract node features from different neighborhoods of each node, and, ii) it uses dual graph-state long short-term memory networks (L-STMs) to summarize local features of each graph and extracts the interaction features between pairwise graphs. Experiments conducted on real-world datasets show that MR-GNN improves the prediction of state-of-the-art methods.

cs.LG↗

Anisotropic Error Estimates of The Linear Nonconforming Virtual Element Methods

A refined a priori error analysis of the lowest order (linear) nonconforming Virtual Element Method (VEM) for approximating a model Poisson problem is developed in both 2D and 3D. A set of new geometric assumptions is proposed on shape regularity of polytopal meshes. A new error equation for the lowest order (linear) nonconforming VEM is derived for any choice of stabilization, and a new stabilization using a projection on an extended element patch is introduced for the error analysis on anisotropic elements.

math.NA↗

POEM: Pricing Longer for Edge Computing in the Device Cloud

Multiple access mobile edge computing has been proposed as a promising technology to bring computation services close to end users, by making good use of edge cloud servers. In mobile device clouds (MDC), idle end devices may act as edge servers to offer computation services for busy end devices. Most existing auction based incentive mechanisms in MDC focus on only one round auction without considering the time correlation. Moreover, although existing single round auctions can also be used for multiple times, users should trade with higher bids to get more resources in the cascading rounds of auctions, then their budgets will run out too early to participate in the next auction, leading to auction failures and the whole benefit may suffer. In this paper, we formulate the computation offloading problem as a social welfare optimization problem with given budgets of mobile devices, and consider pricing longer of mobile devices. This problem is a multiple-choice multi-dimensional 0-1 knapsack problem, which is a NP-hard problem. We propose an auction framework named MAFL for long-term benefits that runs a single round resource auction in each round. Extensive simulation results show that the proposed auction mechanism outperforms the single round by about 55.6% on the revenue on average and MAFL outperforms existing double auction by about 68.6% in terms of the revenue.

cs.NI↗

The effective dynamics of loop quantum $R^2$ cosmology

The effective dynamics of loop quantum $f (R)$ cosmology in Jordan frame is considered by using the dynamical system method and numerical method. To make the analyze in detail, we focus on $R^2$ model since it is simple and favored from observations. In classical theory, $(ϕ= 1, \dotϕ = 0)$ is the unique fixed point in both contracting and expanding states, and all solutions are either starting from the fixed point or evolving to the fixed point; while in loop theory, there exists a new fixed point (saddle point) at $(ϕ\simeq 2 / 3,\dotϕ = 0)$ in contracting state. We find the two critical solutions starting from the saddle point control the evolution of the solutions starting from the fixed point $(ϕ= 1, \dotϕ = 0)$ to bounce at small values of scalar field in $0 <ϕ< 1$. Other solutions, including the large field inflation solutions, all have the history with $ϕ< 0$ which we think of as a problem of the effective theory of loop quantum $f(R)$ theory. Another different thing from loop quantum cosmology with Einstein-Hilbert action is that there exist many solutions do not have bouncing behavior.

gr-qc↗

A Minimization Method for The Double-Well Energy Functional

In this paper an iterative minimization method is proposed to approximate the minimizer to the double-well energy functional arising in the phase-field theory. The method is based on a quadratic functional posed over a nonempty closed convex set and is shown to be unconditionally energy stable. By the minimization approach, we also derive an variant of the first-order scheme for the Allen-Cahn equation, which has been constructed in the context of Invariant Energy Quadratization, and prove its unconditional energy stability.

math.NA↗

Energy-Efficient Offloading in Mobile Edge Computing with Edge-Cloud Collaboration

Multiple access mobile edge computing is an emerging technique to bring computation resources close to end mobile users. By deploying edge servers at WiFi access points or cellular base stations, the computation capabilities of mobile users can be extended. Existing works mostly assume the remote cloud server can be viewed as a special edge server or the edge servers are willing to cooperate, which is not practical. In this work, we propose an edge-cloud cooperative architecture where edge servers can rent for the remote cloud servers to expedite the computation of tasks from mobile users. With this architecture, the computation offloading problem is modeled as a mixed integer programming with delay constraints, which is NP-hard. The objective is to minimize the total energy consumption of mobile devices. We propose a greedy algorithm as well as a simulated annealing algorithm to effectively solve the problem. Extensive simulation results demonstrate that, the proposed greedy algorithm and simulated annealing algorithm can achieve the near optimal performance. On average, the proposed greedy algorithm can achieve the same application completing time budget performance of the Brute Force optional algorithm with only 31\% extra energy cost. The simulated annealing algorithm can achieve similar performance with the greedy algorithm.

cs.DC↗

Coalitional Game Based Carpooling Algorithms for Quality of Experience

Carpooling service is an effective solution to balance the limited number of taxicabs and the soaring demands from users, Thus, how to motivate more passengers to participate in carpooling is essential, especially in extreme weather or in rush hours. Most of existing works focus on improving the availability, convenience and security of carpooling service, while ignoring to guarantee the quality of experience of passengers. In this work, we focus on how to fulfill the expected sojourn time of passengers in carpooling service using coalition game. We formulate the QoE guarantee problem as a benefit allocation problem. To solve the problem, we quantify the impatience of passengers due to detouring time delay, depending on their own expected sojourn time and expected compensation per unit time of delay. The algorithm named PCA is proposed to minimize the impatience of all passengers, under which we calculate the compensation for passengers based on Shapley value. We prove that PCA can guarantee the fairness of passengers. Extensive simulation results demonstrate that PCA can minimize the impatience of passengers. Moreover, compared with the existing algorithm DST, PCA can reduce the payment of each passenger by 14.4 percent averagely with only 13.3 percent loss of driver's revenue. However, the least expected revenue of the driver can still be fulfilled, which produces a win-win solution for both passengers and drivers in carpooling.

cs.NI↗

COUSTIC: Combinatorial Double auction for Task Assignment in Device-to-Device Clouds

With the emerging technologies of Internet of Things (IOTs), the capabilities of mobile devices have increased tremendously. However, in the big data era, to complete tasks on one device is still challenging. As an emerging technology, crowdsourcing utilizing crowds of devices to facilitate large scale sensing tasks has gaining more and more research attention. Most of existing works either assume devices are willing to cooperate utilizing centralized mechanisms or design incentive algorithms using double auctions. Which is not practical to deal with the case when there is a lack of centralized controller for the former, and not suitable to the case when the seller device is also resource constrained for the later. In this paper, we propose a truthful incentive mechanism with combinatorial double auction for crowd sensing task assignment in device-to-device (D2D) clouds, where a single mobile device with intensive sensing task can hire a group of idle neighboring devices. With this new mechanism, time critical sensing tasks can be handled in time with a distributed nature. We prove that the proposed mechanism is truthful, individual rational, budget balance and computational efficient. Our simulation results demonstrate that combinatorial double auction mechanism gets a 26.3% and 15.8% gains in comparison to existing double auction scheme and the centralized maximum matching based algorithm respectively.

cs.NI↗

Cross-Resolution Person Re-identification with Deep Antithetical Learning

Images with different resolutions are ubiquitous in public person re-identification (ReID) datasets and real-world scenes, it is thus crucial for a person ReID model to handle the image resolution variations for improving its generalization ability. However, most existing person ReID methods pay little attention to this resolution discrepancy problem. One paradigm to deal with this problem is to use some complicated methods for mapping all images into an artificial image space, which however will disrupt the natural image distribution and requires heavy image preprocessing. In this paper, we analyze the deficiencies of several widely-used objective functions handling image resolution discrepancies and propose a new framework called deep antithetical learning that directly learns from the natural image space rather than creating an arbitrary one. We first quantify and categorize original training images according to their resolutions. Then we create an antithetical training set and make sure that original training images have counterparts with antithetical resolutions in this new set. At last, a novel Contrastive Center Loss(CCL) is proposed to learn from images with different resolutions without being interfered by their resolution discrepancies. Extensive experimental analyses and evaluations indicate that the proposed framework, even using a vanilla deep ReID network, exhibits remarkable performance improvements. Without bells and whistles, our approach outperforms previous state-of-the-art methods by a large margin.

cs.CV↗

Anisotropic Error Estimates of The Linear Virtual Element Method on Polygonal Meshes

A refined a priori error analysis of the lowest order (linear) Virtual Element Method (VEM) is developed for approximating a model two dimensional Poisson problem. A set of new geometric assumptions is proposed on shape regularity of polygonal meshes. A new universal error equation for the lowest order (linear) VEM is derived for any choice of stabilization, and a new stabilization using broken half-seminorm is introduced to incorporate short edges naturally into the a priori error analysis on isotropic elements. The error analysis is then extended to a special class of anisotropic elements with high aspect ratio originating from a body-fitted mesh generator, which uses straight lines to cut a shape regular background mesh. Lastly, some commonly used tools for triangular elements are revisited for polygonal elements to give an in-depth view of these estimates' dependence on shapes.

math.NA↗

ENGINE:Cost Effective Offloading in Mobile Edge Computing with Fog-Cloud Cooperation

Mobile Edge Computing (MEC) as an emerging paradigm utilizing cloudlet or fog nodes to extend remote cloud computing to the edge of the network, is foreseen as a key technology towards next generation wireless networks. By offloading computation intensive tasks from resource constrained mobile devices to fog nodes or the remote cloud, the energy of mobile devices can be saved and the computation capability can be enhanced. For fog nodes, they can rent the resource rich remote cloud to help them process incoming tasks from mobile devices. In this architecture, the benefit of short computation and computation delay of mobile devices can be fully exploited. However, existing studies mostly assume fog nodes possess unlimited computing capacity, which is not practical, especially when fog nodes are also energy constrained mobile devices. To provide incentive of fog nodes and reduce the computation cost of mobile devices, we provide a cost effective offloading scheme in mobile edge computing with the cooperation between fog nodes and the remote cloud with task dependency constraint. The mobile devices have limited budget and have to determine which task should be computed locally or sent to the fog. To address this issue, we first formulate the offloading problem as a task finish time inimization problem with given budgets of mobile devices, which is NP-hard. We then devise two more algorithms to study the network performance. Simulation results show that the proposed greedy algorithm can achieve the near optimal performance. On average, the Brute Force method and the greedy algorithm outperform the simulated annealing algorithm by about 28.13% on the application finish time.

cs.NI↗

A note on the error estimate of the virtual element methods

This short note reports a new derivation of the optimal order of the a priori error estimates for conforming virtual element methods (VEM) on 3D polyhedral meshes based on an error equation. The geometric assumptions, which are necessary for the optimal order of the conforming VEM error estimate in the $H^1$-seminorm, are relaxed for that in a bilinear form-induced energy norm.

math.NA↗

Real-time Multiple People Tracking with Deeply Learned Candidate Selection and Person Re-Identification

Online multi-object tracking is a fundamental problem in time-critical video analysis applications. A major challenge in the popular tracking-by-detection framework is how to associate unreliable detection results with existing tracks. In this paper, we propose to handle unreliable detection by collecting candidates from outputs of both detection and tracking. The intuition behind generating redundant candidates is that detection and tracks can complement each other in different scenarios. Detection results of high confidence prevent tracking drifts in the long term, and predictions of tracks can handle noisy detection caused by occlusion. In order to apply optimal selection from a considerable amount of candidates in real-time, we present a novel scoring function based on a fully convolutional neural network, that shares most computations on the entire image. Moreover, we adopt a deeply learned appearance representation, which is trained on large-scale person re-identification datasets, to improve the identification ability of our tracker. Extensive experiments show that our tracker achieves real-time and state-of-the-art performance on a widely used people tracking benchmark.

cs.CV↗

Differential decay rates of CP-even and CP-odd Higgs bosons to top and bottom quarks at NNLO QCD

We consider the decay of a neutral Higgs boson of arbitrary CP nature to a massive quark antiquark pair at next-to-next-to-leading order in perturbative QCD. Our analysis is made at the differential level using the antenna subtraction framework. We apply our general set-up to the decays of a CP-even and CP-odd heavy Higgs boson to a top-quark top-antiquark pair and to the decay of the 125 GeV Higgs boson to a massive bottom-quark bottom-antiquark pair. In the latter case we calculate, in particular, the two-jet, three-jet, and four-jet decay rates and, for two-jet events, the energy distribution of the leading jet.

hep-ph↗

Decoupling of Mixed Methods Based on Generalized Helmholtz Decompositions

A framework to systematically decouple high order elliptic equations into combination of Poisson-type and Stokes-type equations is developed. The key is to systematically construct the underling commutative diagrams involving the complexes and Helmholtz decompositions in a general way. Discretizing the decoupled formulation leads to a natural superconvergence between the Galerkin projection and the decoupled approximation. Examples include but not limit to: the primal formulations and mixed formulations of biharmonic equation, fourth order curl equation, and triharmonic equation etc. As a by-product, Helmholtz decompositions for many dual spaces are obtained.

math.NA↗

Improving Negative Sampling for Word Representation using Self-embedded Features

Although the word-popularity based negative sampler has shown superb performance in the skip-gram model, the theoretical motivation behind oversampling popular (non-observed) words as negative samples is still not well understood. In this paper, we start from an investigation of the gradient vanishing issue in the skipgram model without a proper negative sampler. By performing an insightful analysis from the stochastic gradient descent (SGD) learning perspective, we demonstrate that, both theoretically and intuitively, negative samples with larger inner product scores are more informative than those with lower scores for the SGD learner in terms of both convergence rate and accuracy. Understanding this, we propose an alternative sampling algorithm that dynamically selects informative negative samples during each SGD update. More importantly, the proposed sampler accounts for multi-dimensional self-embedded features during the sampling process, which essentially makes it more effective than the original popularity-based (one-dimensional) sampler. Empirical experiments further verify our observations, and show that our fine-grained samplers gain significant improvement over the existing ones without increasing computational complexity.

cs.LG↗

A Preconditioner based on Non-uniform Row Sampling for Linear Least Squares Problems

Least squares method is one of the simplest and most popular techniques applied in data fitting, imaging processing and high dimension data analysis. The classic methods like QR and SVD decomposition for solving least squares problems has a large computational cost. Iterative methods such as CG and Kaczmarz can reduce the complexity if the matrix is well conditioned but failed for the ill conditioned cases. Preconditioner based on randomized row sampling algorithms have been developed but destroy the sparsity. In this paper, a new preconditioner is constructed by non-uniform row sampling with a probability proportional to the squared norm of rows. Then Gauss Seidel iterations are applied to the normal equation of the sampled matrix which aims to grab the high frequency component of solution. After all, PCG is used to solve the normal equation with this preconditioner. Our preconditioner can keep the sparsity and improve the poor conditioning for highly overdetermined matrix. Experimental studies are presented on several different simulations including dense Gaussian matrix, `semi Gaussian' matrix, sparse random matrix, `UDV' matrix, and random graph Laplacian matrix to show the effectiveness of the proposed least square solver.

math.NA↗

Maximum Principle Based Algorithms for Deep Learning

The continuous dynamical system approach to deep learning is explored in order to devise alternative frameworks for training algorithms. Training is recast as a control problem and this allows us to formulate necessary optimality conditions in continuous time using the Pontryagin's maximum principle (PMP). A modification of the method of successive approximations is then used to solve the PMP, giving rise to an alternative training algorithm for deep learning. This approach has the advantage that rigorous error estimates and convergence results can be established. We also show that it may avoid some pitfalls of gradient-based methods, such as slow convergence on flat landscapes near saddle points. Furthermore, we demonstrate that it obtains favorable initial convergence rate per-iteration, provided Hamiltonian maximization can be efficiently carried out - a step which is still in need of improvement. Overall, the approach opens up new avenues to attack problems associated with deep learning, such as trapping in slow manifolds and inapplicability of gradient-based methods for discrete trainable variables.

cs.LG↗