Data Mining - Concepts and Techniques.

This is a review of Collected Works of John Tate. Parts I, II, edited by Barry Mazur and Jean-Pierre Serre. American Mathematical Society, Providence, Rhode Island, 2016. For several decades it has been clear to the friends and colleagues of John Tate that a “Collected Works” was merited. The award of the Abel Prize to Tate in 2010 added impetus, and finally, in Tate’s ninety-second year we have these two magnificent volumes, edited by Barry Mazur and Jean-Pierre Serre. Beyond Tate’s published articles, they include five unpublished articles and a selection of his letters, most accompanied by Tate’s comments, and a collection of photographs of Tate. For an overview of Tate’s work, the editors refer the reader to [4]. Before discussing the volumes, I describe some of Tate’s work. 1. Hecke L-series and Tate’s thesis Like many budding number theorists, Tate’s favorite theorem when young was Gauss’s law of quadratic reciprocity. When he arrived at Princeton as a graduate student in 1946, he was fortunate to find there the person, Emil Artin, who had discovered the most general reciprocity law, so solving Hilbert’s ninth problem. By 1920, the German school of algebraic number theorists (Hilbert, Weber, . . .) together with its brilliant student Takagi had succeeded in classifying the abelian extensions of a number field K: to each group I of ideal classes in K, there is attached an extension L of K (the class field of I); the group I determines the arithmetic of the extension L/K, and the Galois group of L/K is isomorphic to I. Artin’s contribution was to prove (in 1927) that there is a natural isomorphism from I to the Galois group of L/K. When the base field contains an appropriate root of 1, Artin’s isomorphism gives a reciprocity law, and all possible reciprocity laws arise this way. In the 1930s, Chevalley reworked abelian class field theory. In particular, he replaced “ideals” with his “idèles” which greatly clarified the relation between the local and global aspects of the theory. For his thesis, Artin suggested that Tate do the same for Hecke L-series. When Hecke proved that the abelian L-functions of number fields (generalizations of Dirichlet’s L-functions) have an analytic continuation throughout the plane with a functional equation of the expected type, he saw that his methods applied even to a new kind of L-function, now named after him. Once Tate had developed his harmonic analysis of local fields and of the idèle group, he was able prove analytic continuation and functional equations for all the relevant L-series without Hecke’s complicated theta-formulas. Received by the editors September 5, 2016. 2010 Mathematics Subject Classification. Primary 01A75, 11-06, 14-06. c ©2017 American Mathematical Society

The collected works

The notion of fuzziness as defined in this paper relates to situations in which the source of imprecision is not a random variable or a stochastic process, but rather a class or classes which do not possess sharply defined boundaries, e.g., the “class of bald men,” or the “class of numbers which are much greater than 10,” or the “class of adaptive systems,” etc. A basic concept which makes it possible to treat fuzziness in a quantitative manner is that of a fuzzy set, that is, a class in which there may be grades of membership intermediate between full membership and non-membership. Thus, a fuzzy set is characterized by a membership function which assigns to each object its grade of membership (a number lying between 0 and 1) in the fuzzy set. After a review of some of the relevant properties of fuzzy sets, the notions of a fuzzy system and a fuzzy class of systems are introduced and briefly analyzed. The paper closes with a section dealing with optimization under fuzzy constraints in which an approach to...

Fuzzy sets and systems

Several outbreak prediction models for COVID-19 are being used by officials around the world to make informed decisions and enforce relevant control measures. Among the standard models for COVID-19 global pandemic prediction, simple epidemiological and statistical models have received more attention by authorities, and these models are popular in the media. Due to a high level of uncertainty and lack of essential data, standard models have shown low accuracy for long-term prediction. Although the literature includes several attempts to address this issue, the essential generalization and robustness abilities of existing models need to be improved. This paper presents a comparative analysis of machine learning and soft computing models to predict the COVID-19 outbreak as an alternative to susceptible–infected–recovered (SIR) and susceptible-exposed-infectious-removed (SEIR) models. Among a wide range of machine learning models investigated, two models showed promising results (i.e., multi-layered perceptron, MLP; and adaptive network-based fuzzy inference system, ANFIS). Based on the results reported here, and due to the highly complex nature of the COVID-19 outbreak and variation in its behavior across nations, this study suggests machine learning as an effective tool to model the outbreak. This paper provides an initial benchmarking to demonstrate the potential of machine learning for future research. This paper further suggests that a genuine novelty in outbreak prediction can be realized by integrating machine learning and SEIR models.

/pdf/covid-19-outbreak-prediction-with-machine-learning-4dszh5r2ie.pdf

COVID-19 outbreak prediction with machine learning

Interpolative reasoning does not only help reduce the complexity of fuzzy models but also makes inference in sparse rule-based systems possible. This paper presents an interpolative reasoning method by means of scale and move transformations. It can be used to interpolate fuzzy rules involving complex polygon, Gaussian or other bell-shaped fuzzy membership functions. The method works by first constructing a new inference rule via manipulating two given adjacent rules, and then by using scale and move transformations to convert the intermediate inference results into the final derived conclusions. This method has three advantages thanks to the proposed transformations: 1) it can handle interpolation of multiple antecedent variables with simple computation; 2) it guarantees the uniqueness as well as normality and convexity of the resulting interpolated fuzzy sets; and 3) it suggests a variety of definitions for representative values, providing a degree of freedom to meet different requirements. Comparative experimental studies are provided to demonstrate the potential of this method

/pdf/fuzzy-interpolative-reasoning-via-scale-and-move-e4f0uma7dh.pdf

Fuzzy interpolative reasoning via scale and move transformations

In this paper we analyze in detail the central role of number ‘137’, the so-called Fine Structure Constant in the collaboration of Pauli and Jung. First, we present the fascination or the obsession of Pauli for the interpretation of number ‘137’. Second, we treat the spontaneous messages originating from unconscious concerning number ‘137’ in the wellknown dreams of Pauli. We restrict our investigations to the dreams containing the especially important formulae of Fine Structure Constant (4π + π + π), and also that containing the so-called background models of mathematical control systems. Third, we shortly mention four of the numerous synchronicities arising during the Pauli–Jung collaboration.

Number archetypes and "background" control theory concerning the fine structure constant

The first published result in fuzzy rule interpolation was the /spl alpha/-cut based fuzzy rule interpolation, termed as KH-interpolation, originally devoted for complexity reduction. Some deficiencies of this method were presented, such as abnormal conclusion for a certain configuration of the involved fuzzy sets. This inspired several authors to propose various conceptually different fuzzy interpolation approaches, however, none of those algorithms has such a low computational complexity as the KH-method. In the frequent practical cases of using piecewise linear sets only with three of four characteristic points the new methods maintain their relatively high complexity. The goal of this paper is to modify properly the original /spl alpha/-cut based interpolation approach to eliminate the abnormality problem and to ensure normal conclusion in the practical case when the fuzzy sets are of a finite number of characteristic points, while at the same time maintaining the advantageous properties of the original method. A concise analysis of the proposed method is also presented.

http://ieeexplore.ieee.org/iel5/6417/17219/00793270.pdf

A new method for avoiding abnormal conclusion for /spl alpha/-cut based rule interpolation

Climate change impacts and adaptations are the subjects to ongoing issues that attract the attention of many researchers. Insight into the wind power potential in an area and its probable variation due to climate change impacts can provide useful information for energy policymakers and strategists for sustainable development and management of the energy. In this study, spatial variation of wind power density at the turbine hub-height and its variability under future climatic scenarios are taken under consideration. An ANFIS based post-processing technique was employed to match the power outputs of the regional climate model with those obtained from the reference data. The near-surface wind data obtained from a regional climate model are employed to investigate climate change impacts on the wind power resources in the Caspian Sea. Subsequent to converting near-surface wind speed to turbine hub-height speed and computation of wind power density, the results have been investigated to reveal mean annual power, seasonal, and monthly variability for a 20-year period in the present (1981-2000) and in the future (2081-2100). The findings of this study indicated that the middle and northern parts of the Caspian Sea are placed with the highest values of wind power. However, the results of the post-processing technique using adaptive neuro-fuzzy inference system (ANFIS) model showed that the real potential of the wind power in the area is lower than those of projected from the regional climate model.

Modeling Climate Change Impact on Wind Power Resources Using Adaptive Neuro-Fuzzy Inference System

/pdf/coronary-artery-disease-diagnosis-ranking-the-significant-15rr514juw.pdf

Coronary Artery Disease Diagnosis: Ranking the Significant Features Using Random Trees Model

Background control and number archetype in perspective of the Pauli-Jung correspondence

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