Subjects: Mathematics >> Statistics and Probability Subjects: Statistics >> Mathematical Statistics Subjects: Information Science and Systems Science >> Basic Disciplines of Information Science and Systems Science submitted time 2024-04-11
Abstract: Statistical independence is a core concept in statistics and machine learning. Representing and measuring independence are of fundamental importance in related fields. Copula theory provides the tool for representing statistical independence, while Copula Entropy (CE) presents the tool for measuring statistical independence. This paper first introduces the theory of CE, including its definition, theorem, properties, and estimation method. The theoretical applications of CE to structure learning, association discovery, variable selection, causal discovery, system identification, time lag estimation, domain adaptation, multivariate normality test, two-sample test, and change point detection are reviewed. The relationships between the former four applications and their connection to correlation and causality are discussed. The frameworks based on CE, the kernel method, and distance correlation for measuring statistical independence and conditional independence are compared. The advantage of CE over other independence and conditional independence measures is evaluated. The applications of CE in theoretical physics, astrophysics, geophysics, theoretical chemistry, cheminformatics, materials science, hydrology, climatology, meteorology, environmental science, ecology, animal morphology, agronomy, cognitive neuroscience, motor neuroscience, computational neuroscience, psychology, system biology, bioinformatics, clinical diagnostics, geriatrics, psychiatry, public health, economics, management, sociology, pedagogy, computational linguistics, mass media, law, political science, military science, informatics, energy, food engineering, architecture, civil engineering, transportation, manufacturing, reliability, metallurgy, chemical engineering, aeronautics and astronautics, weapon, automobile, electronics, communication, high performance computing, cybersecurity, remote sensing, and finance are briefly introduced.
Peer Review Status:Awaiting Review
Subjects: Mathematics >> Applied Mathematics submitted time 2021-09-22
Abstract: In the early days of the epidemic of coronavirus disease 2019 (COVID-19), due to insufficient knowledge of the pandemic, inadequate nucleic acid tests, lack of timely data reporting, etc., the origin time of the onset of COVID-19 is difficult to determine. Therefore, source tracing is crucial for infectious disease prevention and control. The purpose of this paper is to infer the origin time of pandemic of COVID-19 based on a data and model hybrid driven method. We model the testing positive rate to fit its actual trend, and use the least squares estimation to obtain the optimal model parameters. Further, the kernel density estimation is applied to infer the origin time of pandemic given the specific confidence probability. By selecting 12 representative regions in the United States for analysis, the dates of the first infected case with 50% confidence probability are mostly between August and October 2019, which are earlier than the officially announced date of the first confirmed case in the United States on January 20, 2020. The experimental results indicate that the COVID-19 pandemic in the United States starts to spread around September 2019 with a high confidence probability. In addition, the existing confirmed cases are also used in Wuhan City and Zhejiang Province in China to infer the origin time of COVID-19 and provide the confidence probability. The results show that the spread of COVID-19 pandemic in China is likely to begin in late December 2019. " " "
Peer Review Status:Awaiting Review
Subjects: Physics >> Electromagnetism, Optics, Acoustics, Heat Transfer, Classical Mechanics, and Fluid Dynamics Subjects: Information Science and Systems Science >> Basic Disciplines of Information Science and Systems Science Subjects: Mathematics >> Mathematics (General) submitted time 2017-11-26
Abstract: The infrared imaging grayscale variation caused by the influence of atmosphere on infrared radiation transmission is a problem that infrared target tracking application needs to cope with. The object of this paper is to model the law of infrared imaging grayscale variation in Lie group, which is important to design an efficient and robust target tracking algorithm. This paper firstly analyzes the infrared radiation transmission model, and then derives the brightness model of infrared imaging by considering the mechanism of infrared imaging. Furthermore, it is theoretically proved that the infrared imaging grayscale variation caused by the atmosphere obeys to the Lie group structure, and a non-Euclidean mathematical representation of the infrared imaging grayscale variation is proposed. Finally, according to the infrared imaging grayscale variation model, the field experimental data collected under different environments are fitted, and the regression analysis results demonstrate the correctness of the model, which validates the rationality of the Lie group representation of the infrared imaging grayscale variation.
Peer Review Status:Awaiting Review
Subjects: Mathematics >> Mathematics (General) submitted time 2020-02-18
Abstract: " " "Novel Coronavirus Pneumonia (NCP, or alternatively 2019-nCoV), initially blown up in Wuhan in December of 2019, has been quickly spread all over China, and even other countries of the world, which has produced an important effect to the agricultural and industrial activities, and daily life. It is expected that a well-known recognition is essential to the effective prevention of the disease. Based on the daily announced numbers of the infective people from the National and Hubei provincial Health commissions, a logistic model is applied in this paper for data fitting, in order to provide some scientific information for the effective prevention and controlling of the disease. Using the parameters obtained from the data simulation, a susceptible-infected (SI) model is used to forecast the future trend of the NCP. Our work indicated that the epidemic will last at least two additional weeks in Hubei, but should come to an apex in one week in other areas of China. "
Peer Review Status:Awaiting Review
Subjects: Mathematics >> Mathematics (General) submitted time 2017-06-22
Abstract:考虑股票选取的多因子问题,在传统模型的基础上,利用MATLAB软件建立使用加权回归(权由日期和涨跌幅综合决定)的股票基本面指标、技术指标对相对收益率的多因子模型,并且引入支持向量机作为风控,最终获得了一个收益较好的量化投资模型。
Peer Review Status:Awaiting Review
Subjects: Physics >> The Physics of Elementary Particles and Fields Subjects: Mathematics >> Mathematical Physics submitted time 2018-10-08
Abstract: In the present paper, we have systematically explored the general rules for all kinds of combination of Hodge star and exterior differentiation operators. We have derived the unified forms of the non-vanishing and independent operators made up of arbitrary numbers of Hodge star and exterior differentiation operators. On basis of this, we have explicitly investigated the interaction of all the combined operators. What is more, all the operators have been classified according to the ranks of the newly generated differential forms. As an application, it has been demonstrated that the Maxwell’s equations for U(1) gauge field can be constructed from the linear combinations of two (n-1)-forms. "
Peer Review Status:Awaiting Review
Subjects: Mathematics >> Modeling and Simulation submitted time 2017-05-25
Abstract:Millions of people benefit form Traditional Chinese Medicine TCM every day. Unfortunately till now TCM has not been accepted as science by world especially western people. Bian Zheng Lun Zhi is distillation of TCM. Syndrome is key in system of Bian Zheng Lun Zhi. Study about the syndrome is core of study of basic theory of TCM. We creatively interpret TCM through a view of cognitive science and take syndromes of TCM as concepts of brain. This paper try to introduce syndrome to western people in order to let western people understand our viewpoints more easily the best method is to adopt a manner that is easily understood by them already exists and has been thought to be right. So we employ neural network presented by foreign people as brain model instead of network presented by us Using two classic case of TCM we successfully clarify the three main properties of syndrome in TCM.
Peer Review Status:Awaiting Review
Subjects: Mathematics >> Statistics and Probability submitted time 2019-07-21
Abstract: " Based on the point of view of neuroethology and cognition-psychology, general frame of theory for intelligent systems is presented by means of principle of relative entropy minimizing in this paper. Cream of the general frame of theory is to present and to prove basic principle of intelligent systems: entropy increases or decreases together with intelligence in the intelligent systems. The basic principle is of momentous theoretical significance and practical significance .From the basic principle can not only derive two kind of learning algorithms (statistical simulating annealing algorithms and annealing algorithms of mean-field theory approximation) for training large kinds of stochastic neural networks,but also can thoroughly dispel misgivings created by second law of thermodynamics on 'peoplespsychology ,hence make one be fully confident of facing life.Because of Human society, natural world, and even universe all are intelligent systems. "
Peer Review Status:Awaiting Review
Subjects: Mathematics >> Applied Mathematics Subjects: Management Science >> Management Engineering Subjects: Information Science and Systems Science >> Other Disciplines of Information Science and Systems Science submitted time 2020-03-31
Abstract: The goal of this paper is to establish the general framework of consensus equilibria for Mining-Pool Games in Blockchain Ecosystems, and in particular to explain the stable in the sense for the existence of consensus equilibria related to mining gap game’s behaviors by using one new concept called “consensus games (CG)” in Blockchain Ecosystems, here, the Blockchain ecosystem mainly means the economic activities by taking into the account of three types of different factors which are expenses, reward mechanism and mining power for the work on blockschain by applying the key consensus called “Proof of Work” due to Nakamoto in 2008. In order to do so, we first give an outline how the general existence of consensus equilibria for Mining-Pool Games is formulated, and then used to explain the stable for Gap Games for Bitcoin in the sense by the existence of consensus equilibria under the framework of Blockchain consensus, we then establish a general existence result for consensus equilibria of general mining gap games by using the profit functions for miners as the payoffs in game theory.As applications, the general existence results for consensus equilibria of Gap games are established, which not only help us to claim the existence for the general stability for Gap games under the general framework of Blockchain ecosystems, but also allow us to illustrate a number of different phenomenons on the study of mining-pool games with possible impacts due to miners’ gap behaviors with scenarios embedded in Bitcoin economics. Our study on the explanation for the stability of mining gap game for Blockchain ecosystems shows that the concept of consensus equilibria may play a important role for the development of fundamental theory for consensus economics.
Peer Review Status:Awaiting Review
Subjects: Mathematics >> Theoretical Computer Science submitted time 2017-11-17
Abstract: This paper proposes a new linear classification method named Focusing Classification, with the goal of taking the place of Logistic Regression. Focusing Classification has some advantages: length of its normal vector is limited, intuitional geometrical explanation, parameters' initial values are close to the best values. numerical experiments on the MNIST dataset demonstrate that Focusing Classification has better performance than Logistic Regression on length of its normal vector, accuracy and rate of convergence. With initial parameter values, Focusing Classification gains an accuracy of 97.31%.
Peer Review Status:Awaiting Review
Subjects: Mathematics >> Mathematics (General) submitted time 2018-09-22
Abstract: "
Peer Review Status:Awaiting Review
Subjects: Mathematics >> Applied Mathematics submitted time 2016-07-07
Abstract:自博弈论中有趣的海盗分金问题(Pirate Game(PG))提出以来,其在理论分析上,仅摘要:自博弈论中有趣的海盗分金问题(Pirate Game(PG))提出以来,其在理论分析上,仅限于逆向递推法和数列递推法。本文首先借鉴这两种方法建立一阶差分模型;而后,考虑到每个海盗不是绝对理性的,等级高的海盗需要依赖等级低一级的海盗的决策而做出最优决策,建立二阶时滞差分模型,在数学原理上对 PG 做深入分析:当τ= 0 时,与实际情况偏差较大;当时滞量 τ=1 时,模型的解和一阶差分模型的解一致,即在现实生活中也存在着做决策时直接咨询自己的第一副手的社会群体。从而,在现代分析方法的层次上,本文给出一个 PG 的新的合理的数学解释。
Peer Review Status:Awaiting Review
Subjects: Mathematics >> Statistics and Probability submitted time 2018-11-07
Abstract: Abstract. In studying of a class of random neural network, some of relative researchers have proposed Markov model of neural network. Wherein Markov property of the neural network is based on “assuming”. To reveal mechanism of generating of Markov property in neural network, it is studied how infinite-dimensional random neural network (IDRNN) forms inner Markov representation of environment information in this paper.Because of equivalence between markov property and Gibbsian our conclusion is that knowledge is eventually expressed by extreme Gibbs probability measure—ergodic Gibbs probability measure in IDRNN. This conclusion is also applicable to quantum mechanical level of IDRNN. Hence one can see “ concept “- “ consciousness” is generated at particle(ion) level in the brain and is experienced at the level of the neurons; We have discussed also ergodicity of IDRNN with random neural potential. " "
Peer Review Status:Awaiting Review
Subjects: Mathematics >> Computational Mathematics. Subjects: Information Science and Systems Science >> Basic Disciplines of Information Science and Systems Science submitted time 2020-03-16
Abstract: "
Peer Review Status:Awaiting Review
Subjects: Mathematics >> Control and Optimization. submitted time 2020-06-16
Abstract: Quantization is a popular technique to reduce communication in distributed optimization. Motivated by the classical work on inexact gradient descent (GD) \cite{bertsekas2000gradient}, we provide a general convergence analysis framework for inexact GD that is tailored for quantization schemes. We also propose a quantization scheme Double Encoding and Error Diminishing (DEED). DEED can achieve small communication complexity in three settings: frequent-communication large-memory, frequent-communication small-memory, and infrequent-communication (e.g. federated learning). More specifically, in the frequent-communication large-memory setting, DEED can be easily combined with Nesterov's method, so that the total number of bits required is $ \tilde{O}( \sqrt{\kappa} \log 1/\epsilon )$, where $\tilde{O}$ hides numerical constant and $\log \kappa $ factors. In the frequent-communication small-memory setting, DEED combined with SGD only requires $\tilde{O}( \kappa \log 1/\epsilon)$ number of bits in the interpolation regime. In the infrequent communication setting, DEED combined with Federated averaging requires a smaller total number of bits than Federated Averaging. All these algorithms converge at the same rate as their non-quantized versions, while using a smaller number of bits.
Peer Review Status:Awaiting Review
Subjects: Mathematics >> Control and Optimization. submitted time 2017-07-25
Abstract:In this paper, one of our main purposes is to prove the boundedness of solution set of tensor complementarity problem with B tensor such that the specific bounds only depend on the structural properties of tensor. To achieve this purpose, firstly, we present that each B tensor is strictly semi-positive and each B$_0$ tensor is semi-positive. Subsequencely, the strictly lower and upper bounds of different operator norms are given for two positively homogeneous operators defined by B tensor. Finally, with the help of the upper bounds of different operator norms, we show the strcitly lower bound of solution set of tensor complementarity problem with B tensor. Furthermore, the upper bounds of spectral radius and $E$-spectral radius of B (B$_0$) tensor are obtained, respectively, which achieves our another objective. In particular, such the upper bounds only depend on the principal diagonal entries of tensors.
Peer Review Status:Awaiting Review
Subjects: Mathematics >> Algebra and Number Theory submitted time 2016-05-19
Abstract:For CM elliptic curve over rational field with analytic rank one, for any potential good ordinary prime p, not dividing the number of roots of unity in the complex multiplication field, we show the p-part of its Shafarevich-Tate group has order predicted by the Birch and Swinnerton-Dyer conjecture.
Peer Review Status:Awaiting Review
Subjects: Mathematics >> Computational Mathematics. Subjects: Mathematics >> Applied Mathematics submitted time 2017-08-22
Abstract:Many numerical methods have been proposed in the last 30 years for inverse problems. While very successful in many cases, progress has lagged in other areas of applications which are forced to rely on {\em limited-aperture} measurements. In this paper, we introduce some techniques to retrieve the other data that can not be measured directly. We consider the inverse acoustic scattering of time harmonic plane waves and take the scattering amplitude to be the measurements. Assume that the scattering amplitude can only be measured with observation directions restricted in $S^{n-1}_0$, which is compactly supported in the unit sphere. Based on the reciprocity relation of the scattering amplitude, we prove a special symmetric structure of the corresponding multi-static response matrix. This will also be verified by numerical examples. Combining this, with the help of the Green's formula for the scattered field, we introduce an iterative scheme to retrieve approximate {\em full-aperture} scattering amplitude. As an application, using a recently proposed direct sampling method [28], we consider the fast and robust sampling methods with {\em limited-aperture} measurements. Some numerical simulations are conducted with noisy data, and the results will further verify the effectiveness and robustness of the proposed data retrieval method and of the sampling method for inverse acoustic scattering problems.
Peer Review Status:Awaiting Review
Subjects: Mathematics >> Applied Mathematics submitted time 2017-04-07
Abstract:研究了动态围堵嫌犯问题, 假设网络边长相等, 交巡警与嫌犯的速度相等. 建立了嫌犯移动信息更新下的交巡警调度问题的0-1线性整数规划模型, 模型利用点截集条件使调度后的警力形成围堵圈, 并对嫌犯的逃跑行为建模, 由此得到了动态围堵嫌犯问题的动态模拟模型. 算例考虑分割非等边长网络的边, 然后将分割后的网络视为等边长网络.
Peer Review Status:Awaiting Review
Subjects: Mathematics >> Logic submitted time 2018-09-28
Abstract: In order to fundamentally eliminate all kinds of paradoxes existing in mathematic foundation and make mathematics architecture on a highly reliable basis, it was found that formal logic can only be used in the discussion domain (called the feasible domain) in which all of the three laws, i,e, the law of identity, the law of non-contradictory and the law of excluded middle are hold true. Otherwise, various errors including public opinion will occur. It was concluded that in feasible domain, as long as the premise is reliable and the derivation is strict, no paradox exists. Some historically famous paradoxes such as liar paradox and barber paradox were therefore analyzed. At the same time, the logical mistakes in the application of Piano axiom, in the proofs of Cantor's theorem, the interval method and diagonal argument were pointed out. Suggestion for a uniform definition of natural numbers, rational numbers and irrational numbers to avoid any errors was therefore proposed. " "
Peer Review Status:Awaiting Review