APPLICATION OF CHAOS IN MEASUREMENT

Using the high sensitivity to initial values of chaotic systems, this paper describes an application of chaos in the field of measurement. A general method for signal coding based on symbolic sequences and the relationship between the variable (to be measured) and its symbolic sequence are presented. Some performances of the chaos based measurement system are also discussed. Theoretical analysis and experimental results show that chaotic systems are potentially attractive in the field of measurement.

Signed Directed Graph and Qualitative Trend Analysis Based Fault Diagnosis in Chemical Industry

In the past 30 years,signed directed graph(SDG) ,one of the qualitative simulation technologies,has been widely applied for chemical fault diagnosis.However,SDG based fault diagnosis,as any other qualitative method,has poor diagnostic resolution.In this paper,a new method that combines SDG with qualitative trend analysis(QTA) is presented to improve the resolution.In the method,a bidirectional inference algorithm based on assumption and verification is used to find all the possible fault causes and their corresponding consistent paths in the SDG model.Then an improved QTA algorithm is used to extract and analyze the trends of nodes on the consis-tent paths found in the previous step.New consistency rules based on qualitative trends are used to find the real causes from the candidate causes.The resolution can be improved.This method combines the completeness feature of SDG with the good diagnostic resolution feature of QTA.The implementation of SDG-QTA based fault diagno-sis is done using the integrated SDG modeling,inference and post-processing software platform.Its application is illustrated on an atmospheric distillation tower unit of a simulation platform.The result shows its good applicability and efficiency.

Linear Complexity of Some Binary Sequences Derived from Fermat Quotients

We determined the linear complexity of a family of p2-periodic binary threshold sequences and a family of p2-periodic binary sequences constructed using the Legendre symbol,both of which are derived from Fermat quotients modulo an odd prime p.If 2 is a primitive element modulo p2,the linear complexity equals to p2-p or p2-1,which is very close to the period and it is large enough for cryptographic purpose.

Prediction of metal futures price volatility and empirical analysis based on symbolic time series of high-frequency

The metal futures price fluctuation prediction model was constructed based on symbolic high-frequency time series using high-frequency data on the Shanghai Copper Futures Exchange from July 2014 to September 2018,and the sample was divided into 194 histogram time series employing symbolic time series.The next cycle was then predicted using the K-NN algorithm and exponential smoothing,respectively.The results show that the trend of the histogram of the copper futures earnings prediction is gentler than that of the actual histogram,the overall situation of the prediction results is better,and the overall fluctuation of the one-week earnings of the copper futures predicted and the actual volatility are largely the same.This shows that the results predicted by the K-NN algorithm are more accurate than those predicted by the exponential smoothing method.Based on the predicted one-week price fluctuations of copper futures,regulators and investors in China’s copper futures market can timely adjust their regulatory policies and investment strategies to control risks.

Karl Popper＇s Critical Rationalism＂ Corroboration versus Confirmation＊

This paper reviews and adds to previous arguments for the thesis that Karl Popper was mistaken to have rejected hypothetico-deductive confirmation. By turning from the positive idea of verification to the negative idea of criticism, Popper believed that he had turned his back on induction. He believed he had ＂solved＂ the ＂problem of induction＂ by providing a non-inductive account of corroboration. Popper used the term ＂corroboration＂ rather than confirmation which he believed was too closely allied to the notion of the inductive or probabilistic support that a theory can receive from evidence. Wesley Salmon＇s （1967） ＂concept of confirming evidence＂ and Clark Glymour＇s （1980） ＂bootstrap conception of evidence for theory＂ both defended respectively the thesis that passed tests can be confirmed by evidence or warranted by the degree of probability. Using a sequence of symbols in logical form or analysis, I shall further defend the concept to hypothetico-deductive confirmation in order to show that the known weaknesses of Popper＇s critical rationalism are remediable, once the notion of evidence for theories is brought back into consideration.

Traditional Architecture as the Medium of Public Ethical Value

Traditional Chinese architecture in the narrative of a system has existed more than 3,000 years. As the core values of the enlightenment function of social ethics, traditional architecture externalizes symbol of ＂state＂ sensual ethical echo. So metaphorical rules in architecture can combine with the normal life. Traditional architectural form as famous communication home Marshall McLuhan＇s ＂human extension＂, leads the order and the rules in the form of elevation. The spread of universal ethics, traditional architectural symmetry axis ceremony, and the adornment of the mythical thinking component, are traditional Chinese ethics of society to describe the core of creation through three points sequence structure constraint. The wisdom of metaphor in these ideas is the life gene of Chinese culture. In the construction of the contemporary social upheaval spreading vision, recognition of traditional architecture ethics through righteousness obviously has been recasting social ethics of ＂treatment＂.

漢代的出入關符與肩水金關

漢代出入肩水金關的關符可分爲序號符、家屬符。兩者皆中分,一半放在使用機構,一半放置在肩水金關,并不區别左右。序號符的一半平時存放在候官,使用者需前往候官申领,用晕蹄還,供其他人繼绩使用。家屬符的一半,可能交给使用者本人,出行時攜帶。通阔時,合符出入,通關者所持的原件并不留置金關,而是帶走,下次繼續使用。兩者時效均截止到當年年底。金關漢簡所見,序號符行用於昭帝時期,家屬符行用於宣帝至哀帝時期,很可能兩者存在存廢繼承關係。金關簡僅見肩水、橐他、廣地等三個候官塞的家屬符,未見肩水縣和北部居延都尉辖區的家屬符,這類符通用範圍有限。

On the Exponential Diophantine Equation x^2 + (3a^2 -1)~m = (4a^2 -1)~n

We apply a new, deep theorem of Bilu, Hanrot ＆ Voutier and some fine results on the representation of the solutions of quadratic Diophantine equations to solve completely the exponential Diophantine equation x^2＋（3a^2-1）^m = （4a^2-1）^n when 3a^2-1 is a prime or a prime power.

Symbolic representation based on trend features for knowledge discovery in long time series

The symbolic representation of time series has attracted much research interest recently. The high dimensionality typical of the data is challenging, especially as the time series becomes longer. The wide distribution of sensors collecting more and more data exacerbates the problem. Representing a time series effectively is an essential task for decision-making activities such as classification, prediction, and knowledge discovery. In this paper, we propose a new symbolic representation method for long time series based on trend features, called trend feature symbolic approximation （TFSA）. The method uses a two-step mechanism to segment long time series rapidly. Unlike some previous symbolic methods, it focuses on retaining most of the trend features and patterns of the original series. A time series is represented by trend symbols, which are also suitable for use in knowledge discovery, such as association rules mining. TFSA provides the lower bounding guarantee. Experimental results show that, compared with some previous methods, it not only has better segmentation efficiency and classification accuracy, but also is applicable for use in knowledge discovery from time series.

CATALAN NUMBERS, DYCK LANGUAGE AND TIME SERIES OF ELEMENTARY CELLULAR AUTOMATON OF RULE 56

A new approach to study the evolution complexity of cellular automata is proposed and explained thoroughly by an example of elementary cellular automaton of rule 56. Using the tools of distinct excluded blocks, computational search and symbolic dynamics, the mathematical structure underlying the time series generated from the elementary cellular automaton of rule 56 is analyzed and its complexity is determined, in which the Dyck language and Catalan numbers emerge naturally.