Subjects: Mathematics >> Mathematical Physics submitted time 2020-11-23
Abstract： In this paper, we mainly discuss analytical expressions of positive definiteness for a special 4th order 3-dimensional symmetric tensor defined by the constructed model for a physical phenomenon. Firstly, an analytically necessary and sufficient conditions of 4th order 2-dimensional symmetric tensors are given to test its positive definiteness. Furthermore, by means of such a result, a necessary and sufficient condition of positive definiteness is obtained for a special 4th order 3-dimensional symmetric tensor. Such an analytical conditions can be used for verifying the vacuum stability of general scalar potentials of two real singlet scalar fields and the Higgs boson. The positive semi-definiteness conclusions are presented too.
Peer Review Status:
Awaiting Review
Subjects: Mathematics >> Computational Mathematics. submitted time 2020-10-19
Abstract： Before entering into a recommender system, an entity name must be embedded into a vector. Some popular models, such as word2vec, are based on the principle “words which are in the same syntactic position should embedded into similar vectors”. However, sequence of entity names has no syntactic structure, which led to the low quality of name vectors. Based on the principle “neighbouring names should embedded into similar vectors”, this paper proposes a novel algorithm named name2vec. Name2vec has new features: vector length equals 1, relative weight which has solved the low frequency problem, optimization objective function is mean square error rather than cross entropy. The quality of embedding is measured by the similarity of entity names. On there datasets from WEIBO.COM, name2vec has a better performance than word2veec.
Peer Review Status:Awaiting Review
Subjects: Mathematics >> Theoretical Computer Science submitted time 2020-10-10
Abstract： In this paper, we give a method to express the descending degree sum of squares of univariate positive semi-definite polynomials, and give an algorithm to get the descending degree sum of squares from known positive semi-definite polynomials. In the fourth section, we apply the idea and algorithm of the descending degree sum of squares to multivariate polynomials successfully.
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 >> 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 >> 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
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