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: 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 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 >> Mathematics (General) submitted time 2018-09-22
Abstract: "
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 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: Mathematics >> Statistics and Probability submitted time 2024-02-04
Abstract: The three frameworks for theories of consciousness taken most seriously by neuroscientists are that consciousness is a biological state of the brain,the global workspace perspective,and the perspective of higher state.Consciousness is discussed from viewpoint of theory of Entropy—partition of complex system in present article. Human brain’s system self-organizably and adaptively implements partition 、 aggregation and integration, and consciousness emerges.The Gibss representation of consciousness is proved and That consciousness originates from quantum mechanical processes of brain activity is explained by means of SW entropy
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 >> 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: 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 >> 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 >> Computational Mathematics. submitted time 2019-04-10
Abstract: This paper proposes a novel method named Polyhedron Regression(PR) for Click-Through-Rate prediction, aiming to take the place of Factorization Machines(FM). PR constructs a convex polyhedra with hyperplanes to separate positive samples from negative samples. PR has intuitionistic geometrical interpretations and a Lipschitz continuous surface, converges to global optimum point from arbitrary initial values. Compared with FM, PR has better classification accuracy, interpretability and surface smoothness on the three artificial datasets. With comparable parameters and computation, PR achieves better AUC than FM on Avazu and Criteo datasets.
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 >> Mathematical Physics submitted time 2019-11-23
Abstract: " The strict opositivity of 4th order symmetric tensor may apply to detect vacuum stability of general scalar potential. For finding analytical expressions of (strict) opositivity of 4th order symmetric tensor, we may reduce its order to 3rd order to better deal with it. So, it is provided that several analytically sufficient conditions for the copositivity of 3th order 2 dimensional (3 dimensional) symmetric tensors. Subsequently, applying these conclusions to 4th order tensors, the analytically sufficient conditions of copositivity are proved for 4th order 2 dimensional and 3 dimensional symmetric tensors. Finally, we apply these results to present analytical vacuum stability conditions for vacuum stability for $\mathbb{Z}_3$ scalar dark matter. "
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 >> Control and Optimization. submitted time 2019-08-30
Abstract: " In particle physics, scalar potentials have to be bounded from below in order for the physics to make sense. The precise expressions of checking lower bound of scalar potentials are essential, which is an analytical expression of checking copositivity and positive definiteness of tensors given by such scalar potentials. Because the tensors given by general scalar potential are 4th order and symmetric, our work mainly focuses on finding precise expressions to test copositivity and positive definiteness of 4th order tensors in this paper. First of all, an analytically sufficient and necessary condition of positive definiteness is provided for 4th order 2 dimensional symmetric tensors. For 4th order 3 dimensional symmetric tensors, we give two analytically sufficient conditions of (strictly) cpositivity by using proof technique of reducing orders or dimensions of such a tensor. Furthermore, an analytically sufficient and necessary condition of copositivity is showed for 4th order 2 dimensional symmetric tensors. We also give several distinctly analytically sufficient conditions of (strict) copositivity for 4th order 2 dimensional symmetric tensors. Finally, we apply these results to check lower bound of scalar potentials, and to present analytical vacuum stability conditions for potentials of two real scalar fields and the Higgs boson. "
Peer Review Status:Awaiting Review
Subjects: Mathematics >> Modeling and Simulation submitted time 2019-10-23
Abstract: Radiation symmetry evaluation is critical to the laser driven Inertial Confinement Fusion (ICF), which is usually done by solving a view-factor equation model. The model is nonlinear, and the number of equations can be very large when the size of discrete mesh element is very small to achieve a prescribed accuracy, which may lead to an intensive equation solving process. In this paper, an efficient radiation symmetry analysis approach based on sparse representation is presented, in which, 1) the Spherical harmonics, annular Zernike polynomials and Legendre-Fourier polynomials are employed to sparsely represent the radiation flux on the capsule and cylindrical cavity, and the nonlinear energy equilibrium equations are transformed into the equations with sparse coefficients, which means there are many redundant equations, 2) only a few equations are selected to recover such sparse coefficients with Latin hypercube sampling, 3) a Conjugate Gradient Subspace Thresholding Pursuit (CGSTP) algorithm is then given to rapidly obtain such sparse coefficients equation with as few iterations as possible. Finally, the proposed method is validated with two experiment targets for Shenguang II and Shenguang III laser facility in China. The results show that only one tenth of computation time is required to solve one tenth of equations to achieve the radiation flux with comparable accuracy. Further more, the solution is much more efficient as the size of discrete mesh element decreases, in which, only 1.2% computation time is required to obtain the accurate result.
Peer Review Status:Awaiting Review
Subjects: Mathematics >> Mathematics (General) submitted time 2022-06-30
Abstract:This paper discusses the properties the spaces of fuzzy sets in a metric space?equipped with the endograph metric and the sendograph metric, respectively.?We fist give some relations among the endograph metric, the sendograph?metric and the -convergence, and then investigate the level characterizations?of the endograph metric and the -convergence. By using the above results,?we give some relations among the endograph metric, the sendograph metric,?the supremum metric and the dp* metric. On the basis of the above results,?we present the characterizations of total boundedness, relative compactness?and compactness in the space of compact positive -cuts fuzzy sets equipped?with the endograph metric, and in the space of compact support fuzzy sets?equipped with the sendograph metric, respectively. Furthermore, we give?completions of these metric spaces, respectively.
Peer Review Status:Awaiting Review
Subjects: Mathematics >> Computational Mathematics. submitted time 2018-03-22
Abstract: In this paper, I found the two reasons of overfitting of logistic regression: boundary samples occupy a larger and larger share as the length of normal vector becomes longer and longer, boundary samples do not fit their probability density function well. With the help of insight in overfitting, I propose a acceleration method for logistic regression and got a training speedup of 38.25 on MNIST dataset, a training speedup of 5.61 on CIFAR10 dataset.
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