There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

다중혈관 관상동맥 환자에서 y-문합을 이용하여 양쪽 내흉동맥만을 사용한 우회술의 조기 성적

Machine Learning is the study of methods for programming computers to learn. Computers are applied to a wide range of tasks, and for most of these it is relatively easy for programmers to design and implement the necessary software. However, there are many tasks for which this is difficult or impossible. These can be divided into four general categories. First, there are problems for which there exist no human experts. For example, in modern automated manufacturing facilities, there is a need to predict machine failures before they occur by analyzing sensor readings. Because the machines are new, there are no human experts who can be interviewed by a programmer to provide the knowledge necessary to build a computer system. A machine learning system can study recorded data and subsequent machine failures and learn prediction rules. Second, there are problems where human experts exist, but where they are unable to explain their expertise. This is the case in many perceptual tasks, such as speech recognition, hand-writing recognition, and natural language understanding. Virtually all humans exhibit expert-level abilities on these tasks, but none of them can describe the detailed steps that they follow as they perform them. Fortunately, humans can provide machines with examples of the inputs and correct outputs for these tasks, so machine learning algorithms can learn to map the inputs to the outputs. Third, there are problems where phenomena are changing rapidly. In finance, for example, people would like to predict the future behavior of the stock market, of consumer purchases, or of exchange rates. These behaviors change frequently, so that even if a programmer could construct a good predictive computer program, it would need to be rewritten frequently. A learning program can relieve the programmer of this burden by constantly modifying and tuning a set of learned prediction rules. Fourth, there are applications that need to be customized for each computer user separately. Consider, for example, a program to filter unwanted electronic mail messages. Different users will need different filters. It is unreasonable to expect each user to program his or her own rules, and it is infeasible to provide every user with a software engineer to keep the rules up-to-date. A machine learning system can learn which mail messages the user rejects and maintain the filtering rules automatically. Machine learning addresses many of the same research questions as the fields of statistics, data mining, and psychology, but with differences of emphasis. Statistics focuses on understanding the phenomena that have generated the data, often with the goal of testing different hypotheses about those phenomena. Data mining seeks to find patterns in the data that are understandable by people. Psychological studies of human learning aspire to understand the mechanisms underlying the various learning behaviors exhibited by people (concept learning, skill acquisition, strategy change, etc.).

Machine learning

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The concept of mind

We explore the effect of dimensionality on the nearest neighbor problem. We show that under a broad set of conditions (much broader than independent and identically distributed dimensions), as dimensionality increases, the distance to the nearest data point approaches the distance to the farthest data point. To provide a practical perspective, we present empirical results on both real and synthetic data sets that demonstrate that this effect can occur for as few as 10-15 dimensions. These results should not be interpreted to mean that high-dimensional indexing is never meaningful; we illustrate this point by identifying some high-dimensional workloads for which this effect does not occur. However, our results do emphasize that the methodology used almost universally in the database literature to evaluate high-dimensional indexing techniques is flawed, and should be modified. In particular, most such techniques proposed in the literature are not evaluated versus simple linear scan, and are evaluated over workloads for which nearest neighbor is not meaningful. Often, even the reported experiments, when analyzed carefully, show that linear scan would outperform the techniques being proposed on the workloads studied in high (10-15) dimensionality!.

When is nearest neighbor meaningful

In this book, we define several new neutrosophic algebraic structures and their related properties. The main focus of this book is to study the important class of neutrosophic rings such as neutrosophic LA-semigroup ring, neutrosophic loop ring, neutrosophic groupoid ring and so on. We also construct their generalization in each case to study these neutrosophic algebraic structures in a broader sense. The indeterminacy element “I“ gives rise to a bigger algebraic structure than the classical algebraic structures. It mainly classifies the algebraic structures in three categories such as: neutrosophic algebraic structures, strong neutrosophic algebraic structures, and classical algebraic structures respectively. This reveals the fact that a classic algebraic structure is a part of the neutrosophic algebraic structures. This opens a new way for the researcher to think in a broader way to visualize these vast neutrosophic algebraic structures.

/pdf/new-research-on-neutrosophic-algebraic-structures-15jjshm3f0.pdf

New research on neutrosophic algebraic structures

The concept of supermatrix for social scientists was first introduced by Paul Horst. The main purpose of his book was to introduce this concept to social scientists, students, teachers and research workers who lacked mathematical training. He wanted them to be equipped in a branch of mathematics that was increasingly valuable for the analysis of scientific data.

/pdf/super-fuzzy-matrices-and-super-fuzzy-models-for-social-2hsebgau9i.pdf

Super Fuzzy Matrices and Super Fuzzy Models for Social Scientists

Neutrosophic set theory is a mathematical tool for handling problems involving imprecise, indeterminacy and inconsistent data. In 2015, neutrosophic set theory is applied to BE-algebra, and the notion of neutrosophic filter is introduced. In this paper, some mistakes and deficiencies of original definition of neutrosophic filter are pointed out by some examples. Moreover, a new definition of neutrosophic filter is established, some basic properties are presented, and the relationships between fuzzy filters and neutrosophic filters are discussed. Finally, the concept of implicative neutrosophic filter in BE-algebra is introduced, and some necessary and sufficient conditions for a neutrosophic filter to be implicative are presented.

Redefined neutrosophic filters in BE-algebras

Based on the authors intensive investigation on the oriental dialectics, the paper presents a novel theoretical frame of matter element in the world leading science, extenics dealing with inconsistency or incompatibility, covering the widest range of application area from informatics, system engineering to management and finance. The dialectic matter-element is defined as the integral of all existing and prospecting ones based on all the infinite possible cognitive models. The novel model serves as the origin of constraint matter elements, the unity of both state description and cognitive action (cognition force with respect to neural science), a latent part of extenics, and possibly as essence of matter element. It explains, in a novel perspective, the origin of a name, and uncovers the source of contradiction and even the impetus of cognition.

/pdf/toward-dialectic-matter-element-of-extenics-model-4vnsijf00t.pdf

Toward Dialectic Matter Element of Extenics Model

The authors introduce the concept of neutrosophic super matrices and the new notion of quasi super matrices. This new notion of quasi super matrices contains the class of super matrices. The larger class contains more partitions of the usual simple matrices. Studies in this direction are interesting and find more applications in fuzzy models. The authors also suggest in this book some open problems.

/pdf/neutrosophic-super-matrices-and-quasi-super-matrices-2ye3u194k9.pdf

Florentin Smarandache

Papers

New research on neutrosophic algebraic structures

Super Fuzzy Matrices and Super Fuzzy Models for Social Scientists

Redefined neutrosophic filters in BE-algebras

Toward Dialectic Matter Element of Extenics Model

Neutrosophic Super Matrices and Quasi Super Matrices