Suatu Kajian Tentang B-Aljabar

Abstrak. Penelitian ini merupakan penelitian kajian kepustakaan yang bertujuan untuk mengkaji konsep dan sifat-sifat terkait B-Aljabar. Konsep B-Aljabar dalam penelitian ini berdasarkan penelitian yang telah dilakukan oleh Neggers dan Kim serta Allen. Seluruh pembahasan dalam penelitian ini menggunakan himpunan tegas, baik himpunan berhingga maupun himpunan tidak berhingga. Hasilnya, dapat diberikan bukti yang lebih lengkap dari sifat-sifat B-Aljabar serta hubungannya dengan grup. Suatu grup dengan definisi operasi khusus dan elemen identitas merupakan B-Aljabar. Lebih lanjut dapat diturunkan beberapa teorema grup kedalam B-Aljabar seperti pemetaan natural dan Teorema Isomorfisma 1 yang dalam pembuktiannya memiliki kemiripan dengan pembuktian pada grup dengan tetap menggunakan sifat-sifat B-Aljabar itu sendiri.Kata Kunci: B-Aljabar, B-Subaljabar, B-Homomorfisma, B-IsomorfismaAbstract. This research is a literature studies that aims at reviewing the concepts and properties of B-Algebras. The concept of B-Algebras in this article is based on research that has been done by Neggers and Kim and Allen. All discussions in this article use the firm sets, both finite sets and infinite sets. As a result, more complete evidence of the properties of B-Algebras can be given and its relationship with the group. A group with a specific operation and has as an identity element is a B-Algebras. Moreover, a number of group theorems can be derived into B-Algebra such as natural mapping and the First Isomorphism Theorems which in their proof have similarities to the proofs of groups while still using the properties of B-Algebra itself.Keywords: B-Algebras, B-Subalgebras, B-Homomorphism, B-Isomorphism

Natural mapping between voice commands and APIs

After a voice control system transforms audio input into a natural language sentence, its main purpose is to map this sentence to a specific action in the API (application programming interface) that should be performed. This mapping is usually specified after the API is already designed. In this paper, we show how an API can be designed with voice control in mind, which makes this mapping natural. The classes, methods, and parameters in the source code are named and typed according to the terms expected in the natural language commands. When this is insufficient, annotations (attribute-oriented programming) are used to define synonyms, string-to-object maps, or other properties. We also describe the mapping process and present a preliminary implementation called VCMapper. In its evaluation on a third-party dataset, it was successfully used to map all the sentences, while a large portion of the mapping was performed using only naming and typing conventions.

Learning Optimal Decision Trees with SAT

Explanations of machine learning (ML) predictions are of fundamental importance in different settings. Moreover, explanations should be succinct, to enable easy understanding by humans. Decision trees represent an often used approach for developing explainable ML models, motivated by the natural mapping between decision tree paths and rules. Clearly, smaller trees correlate well with smaller rules, and so one challenge is to devise solutions for computing smallest size decision trees given training data. Although simple to formulate, the computation of smallest size decision trees turns out to be an extremely challenging computational problem, for which no practical solutions are known. This paper develops a SAT-based model for computing smallest-size decision trees given training data. In sharp contrast with past work, the proposed SAT model is shown to scale for publicly available datasets of practical interest.

Mapping the surgery exact sequence for topological manifolds to analysis

In this paper we prove the existence of a natural mapping from the surgery exact sequence for topological manifolds to the analytic surgery exact sequence of Higson and Roe. This generalizes the fundamental result of Higson and Roe, but in the treatment given by Piazza and Schick, from smooth manifolds to topological manifolds. Crucial to our treatment is the Lipschitz signature operator of Teleman. We also give a generalization to the equivariant setting of the product defined by Siegel in his Ph.D. thesis. Geometric applications are given to stability results for rho classes. We also obtain a proof of the APS delocalized index theorem on odd dimensional manifolds, both for the spin Dirac operator and the signature operator, thus extending to odd dimensions the results of Piazza and Schick. Consequently, we are able to discuss the mapping of the surgery sequence in all dimensions.

Mapping i2 on the free paratopological groups

Let FP(X) be the free paratopological group over a topological space X. For each nonnegative integer n ? N, denote by FPn(X) the subset of FP(X) consisting of all words of reduced length at most n, and in by the natural mapping from (X ? X?1 ? {e})n to FPn(X). We prove that the natural mapping i2:(X ? X?1 d ?{e})2 ? FP2(X) is a closed mapping if and only if every neighborhood U of the diagonal ?1 in Xd x X is a member of the finest quasi-uniformity on X, where X is a T1-space and Xd denotes X when equipped with the discrete topology in place of its given topology.