Mining clusters from data is an important endeavor in many applications. The $k$-means method a popular, efficient, and distribution-free approach for clustering numerical-valued data, but does not apply categorical-valued observations. $k$-modes addresses this lacuna by replacing the Euclidean with Hamming distance means modes objective function. We provide novel, computationally efficient imp...

With distributed computing beginning to play a major role in modern Computer Science, the theory of grammar systems and distributed automata has been developed in order to model distributed computing. In this paper, we introduce the notion of distributed automata in the sequential sense. Distributed Automata are a group of automata working in unison to accept one language. We build the theory o...

The COVID-19 pandemic has caused significant economic contractions and employment vulnerabilities for the economies, including Turkey. exacerbated structural challenges related to high unemployment, low labor force participation, widespread informality. This study aims analyze differences in market between 2019 2020 years For this purpose, we used clustering method. While applying method, educa...

We study the bosonic and fermionic zero modes in noncommutative instanton backgrounds based on the ADHM construction. In k instanton background in U(N) gauge theory, we show how to explicitly construct 4Nk (2Nk) bosonic (fermionic) zero modes in the adjoint representation and 2k (k) bosonic (fermionic) zero modes in the fundamental representation from the ADHM construction. The number of fermio...

We study the bosonic and fermionic zero-modes in noncommutative instanton backgrounds based on the ADHM construction. In k instanton background in U(N) gauge theory, we show how to explicitly construct 4Nk (2Nk) bosonic (fermionic) zero-modes in the adjoint representation and 2k (k) bosonic (fermionic) zero-modes in the fundamental representation from the ADHM construction. The number of fermio...

The purpose of Multi-modal Multi-criteria Personalized Route Planning (MMPRP) is to provide an optimal route between an origin-destination pair by considering weights of effective criteria in a way this route can be a combination of public and private modes of transportation. In this paper, the fuzzy analytical hierarchy process (fuzzy AHP) and the quantifier-guided ordered weighted averaging (...

1 Problem In view of recent interest in orbital angular momentum modes in optical fibers, 1 discuss angular momentum in the modes of a circular waveguide of radius a, with perfectly conducting walls and filled with a medium of index of refraction n. 2 Solution Circular-waveguide modes were first discussed in 1893 by J.J. Thomson in sec. 300 of [2] and then by Rayleigh in 1897 [3]. 2 Although th...

The effects of a radiation field (RF) on the unstable modes developed in a relativistic electron beam-plasma interaction are investigated assuming that ω(0) > ω(p), where ω(0) is the frequency of the RF and ω(p) is the plasma frequency. These unstable modes are parametrically coupled to each other due to the RF and are a mix between two-stream and parametric instabilities. The dispersion equati...

Clustering is one of the most important data mining techniques that partitions data according to some similarity criterion. The problems of clustering categorical data have attracted much attention from the data mining research community recently. As the extension of the k-Means algorithm, the k-Modes algorithm has been widely applied to categorical data clustering by replacing means with modes...