arXiv subjects

Xia Liu

Publications and source records attributed to Xia Liu.

29 records · Page 2Linked to original sources

arXiv2020

Revisiting the distributions of Jupiter's irregular moons: II. orbital characteristics

This paper statistically describes the orbital distribution laws of Jupiter's irregular moons, most of which are members of the Ananke, Carme and Pasiphae groups. By comparing 19 known continuous distributions, it is verified that suitable distribution functions exist to describe the orbital distributions of these natural satellites. For each distribution type, interval estimation is used to estimate the corresponding parameter values. At a given significance level, a one-sample Kolmogorov-Smirnov non-parametric test is applied to verify the specified distribution, and we often select the one with the largest $p$-value. The results show that the semi-major axis, mean inclination and orbital period of the moons in the Ananke group and Carme group obey Stable distributions. In addition, according to Kepler's third law of planetary motion and by comparing the theoretically calculated best-fitting cumulative distribution function (CDF) with the observed CDF, we demonstrate that the theoretical distribution is in good agreement with the empirical distribution. Therefore, these characteristics of Jupiter's irregular moons are indeed very likely to follow some specific distribution laws, and it will be possible to use these laws to help study certain features of poorly investigated moons or even predict undiscovered ones.

astro-ph.EP↗

arXiv2020

Ice-Flower Systems And Star-graphic Lattices

Lattice theory has been believed to resist classical computers and quantum computers. Since there are connections between traditional lattices and graphic lattices, it is meaningful to research graphic lattices. We define the so-called ice-flower systems by our uncolored or colored leaf-splitting and leaf-coinciding operations. These ice-flower systems enable us to construct several star-graphic lattices. We use our star-graphic lattices to express some well-known results of graph theory and compute the number of elements of a particular star-graphic lattice. For more researching ice-flower systems and star-graphic lattices we propose Decomposition Number String Problem, finding strongly colored uniform ice-flower systems and connecting our star-graphic lattices with traditional lattices.

math.CO↗

arXiv2020

Approximation smooth and sparse functions by deep neural networks without saturation

Constructing neural networks for function approximation is a classical and longstanding topic in approximation theory. In this paper, we aim at constructing deep neural networks (deep nets for short) with three hidden layers to approximate smooth and sparse functions. In particular, we prove that the constructed deep nets can reach the optimal approximation rate in approximating both smooth and sparse functions with controllable magnitude of free parameters. Since the saturation that describes the bottleneck of approximate is an insurmountable problem of constructive neural networks, we also prove that deepening the neural network with only one more hidden layer can avoid the saturation. The obtained results underlie advantages of deep nets and provide theoretical explanations for deep learning.

cs.IT↗

arXiv2017

A Survey of Distributed Message Broker Queues

This paper surveys the message brokers that are in vogue today for distributed communication. Their primary goal is to facilitate the construction of decentralized topologies without single points of failure, enabling fault tolerance and high availability. These characteristics make them optimal for usage within distributed architectures. However, there are multiple protocols built to achieve this, and it would be beneficial to have a empirical comparison between their features and performance to determine their real-world applicability. This paper focuses on two popular protocols (Kafka and AMQP) and explores the divergence in their features as well as their performance under varied testing workloads.

cs.DC↗

arXiv2016

Greedy Criterion in Orthogonal Greedy Learning

Orthogonal greedy learning (OGL) is a stepwise learning scheme that starts with selecting a new atom from a specified dictionary via the steepest gradient descent (SGD) and then builds the estimator through orthogonal projection. In this paper, we find that SGD is not the unique greedy criterion and introduce a new greedy criterion, called "$δ$-greedy threshold" for learning. Based on the new greedy criterion, we derive an adaptive termination rule for OGL. Our theoretical study shows that the new learning scheme can achieve the existing (almost) optimal learning rate of OGL. Plenty of numerical experiments are provided to support that the new scheme can achieve almost optimal generalization performance, while requiring less computation than OGL.

cs.LG↗

arXiv2016

Maximum Leaf Spanning Trees of Growing Sierpinski Networks Models

The dynamical phenomena of complex networks are very difficult to predict from local information due to the rich microstructures and corresponding complex dynamics. On the other hands, it is a horrible job to compute some stochastic parameters of a large network having thousand and thousand nodes. We design several recursive algorithms for finding spanning trees having maximal leaves (MLS-trees) in investigation of topological structures of Sierpinski growing network models, and use MLS-trees to determine the kernels, dominating and balanced sets of the models. We propose a new stochastic method for the models, called the edge-cumulative distribution, and show that it obeys a power law distribution.

cs.DS↗

arXiv2015

Growing Network Models Having Part Edges Removed/added Randomly

Since network motifs are an important property of networks and some networks have the behaviors of rewiring or reducing or adding edges between old vertices before new vertices entering the networks, we construct our non-randomized model N(t) and randomized model N'(t) that have the predicated fixed subgraphs like motifs and satisfy both properties of growth and preferential attachment by means of the recursive algorithm from the lower levels of the so-called bound growing network models. To show the scale-free property of the randomized model N'(t), we design a new method, called edge-cumulative distribution, and democrat two edge-cumulative distributions of N(t) and N'(t) are equivalent to each other.

cs.SI↗

arXiv2014

Is Extreme Learning Machine Feasible? A Theoretical Assessment (Part II)

An extreme learning machine (ELM) can be regarded as a two stage feed-forward neural network (FNN) learning system which randomly assigns the connections with and within hidden neurons in the first stage and tunes the connections with output neurons in the second stage. Therefore, ELM training is essentially a linear learning problem, which significantly reduces the computational burden. Numerous applications show that such a computation burden reduction does not degrade the generalization capability. It has, however, been open that whether this is true in theory. The aim of our work is to study the theoretical feasibility of ELM by analyzing the pros and cons of ELM. In the previous part on this topic, we pointed out that via appropriate selection of the activation function, ELM does not degrade the generalization capability in the expectation sense. In this paper, we launch the study in a different direction and show that the randomness of ELM also leads to certain negative consequences. On one hand, we find that the randomness causes an additional uncertainty problem of ELM, both in approximation and learning. On the other hand, we theoretically justify that there also exists an activation function such that the corresponding ELM degrades the generalization capability. In particular, we prove that the generalization capability of ELM with Gaussian kernel is essentially worse than that of FNN with Gaussian kernel. To facilitate the use of ELM, we also provide a remedy to such a degradation. We find that the well-developed coefficient regularization technique can essentially improve the generalization capability. The obtained results reveal the essential characteristic of ELM and give theoretical guidance concerning how to use ELM.

cs.LG↗

arXiv2013

Priority-aware Gray-box Placement of Virtual Machines in Cloud Platforms

Virtual machine (VM) placement is very important for cloud platforms. While techniques, such as live virtual machine migration, are very useful to balance the load in the data centers, they are expensive operations. In this position paper, we propose to minimize the chance of the load hot spots in the data center by applying the workload patterns of the VMs in the virtual machine placement algorithms - place VMs that require a lot of same type of resource across different physical servers. In this way, the resource competition of VMs on the same physical server is significantly mitigated. Meanwhile, we also consider the priorities of applications and VMs in our virtual machine placement algorithms.

cs.NI↗

arXiv2013

The Economic Trend of Video Game Industry

In recent years the game industry has had a huge growth. We've seen new game consoles, great looking games and an increase in the number of people playing them. We are presently in the seventh generation of video games which focuses on consoles released since 2004. For home consoles,the seventh generation began on November 22, 2005 with the release of Xbox 360 and continued with the release of PlayStation 3 on November 11, 2006, and Wii on November 19, 2006. The current generation is having a console battle between Nintendo's Wii, Microsoft's Xbox 360, and Sony's PlayStation 3.The appearance of the three new consoles not only offers various purchase choices, but also greatly affects economy and culture.

cs.CY↗

arXiv2013

The wireless router based on the linux system

With the expansion of computer networks,the mobile terminal with wireless access capability experience a sharp increase in the number of wireless routers, especially low cost wireless routers are becoming very important network equipment. This paper designs a wireless router based on the ARM platform, the Linux system. First, there is a research and analysis on the working principle and implementation of Network Address Translation (NAT) technology. Then I study the IPTABLES components under the Linux system and use it when processing data packets which go into the chain and the table and finally using laptop with Ethernet card and the WIFI card to build the Linux operating system. Related routing forwarding rules are defined between the two cards and use IPTABLES to achieve a laptop as a wireless WIFI hotspot providing routing and network connections to other computer services. It proves this paper's design, and production feasibility. The paper also discusses the design and production method of the wireless router with ARM board feasibility.

cs.NI↗