Manually determining concepts present in a group of questions is a challenging and time-consuming process. However, the process is an essential step while modeling a virtual learning environment since a mapping between concepts and questions using mastery level assessment and recommendation engines is required. In this article, we investigated…

Virtual resources team up to create a computational grid, which is used in computation-intensive problem solving. A majority of these problems require high performance resources to compute and generate results, making grid computation another type of high performance computing. The optimization in computational grids relates to resource…

We present an algorithm for a matrix-based Enigma-type encoder based on a variation of the Hill Cipher as an application of 2 × 2 matrices. In particular, students will use vector addition and 2 × 2 matrix multiplication by column vectors to simulate a matrix version of the German Enigma Encoding Machine as a basic example of cryptography. The…

This paper provides a tutorial on epistemic network analysis (ENA), a novel method for identifying and quantifying connections among elements in coded data and representing them in dynamic network models. Such models illustrate the structure of connections and measure the strength of association among elements in a network, and they quantify…

The formalism of quantum mechanics includes a rich collection of representations for describing quantum systems, including functions, graphs, matrices, histograms of probabilities, and Dirac notation. The varied features of these representations affect how computations are performed. For example, identifying probabilities of measurement outcomes…

This study was intended to provide a description of teaching and learning patterns seen in the lessons taught by experts and novices in Adapted Physical Education. Two experts who had won previous state teaching awards and served in leadership positions in state associations were filmed and their lessons were analyzed first to develop a systematic…

The Hill cipher is the simplest example of a "block cipher," which takes a block of plaintext as input, and returns a block of ciphertext as output. Although it is insecure by modern standards, its simplicity means that it is well suited for the teaching of such concepts as encryption modes, and properties of cryptographic hash functions. Although…

In this article, the authors have 2 aims. First, hierarchical, nonhierarchical, and nonstandard log-linear models are defined. Second, application scenarios are presented for nonhierarchical and nonstandard models, with illustrations of where these scenarios can occur. Parameters can be interpreted in regard to their formal meaning and in regard…

Hill ciphers are linear codes that use as input a "plaintext" vector [p-right arrow above] of size n, which is encrypted with an invertible n x n matrix E to produce a "ciphertext" vector [c-right arrow above] = E [middle dot] [p-right arrow above]. Informally, a near-field is a triple [left angle bracket]N; +, *[right angle bracket] that…

Presents new methods for compressing bit matrices in large information retrieval systems which exploit possible correlations between rows of words and columns of documents. Three encoding methods are tested and compared--Shannon-Fano, arithmetic, and Huffman--and an appendix discusses binomial coefficients. (20 references) (LRW)

This article describes Cryptography, defined as the science of encrypting and deciphering messages written in secret codes, it has played a vital role in securing information since ancient times. There are several cryptographic techniques and many make extensive use of mathematics to secure information. The author discusses an activity built…

Cryptography is the science that renders data unintelligible to prevent its unauthorized disclosure or modification. Presents an application of matrices used in linear transformations to illustrate a cryptographic system. An example is provided. (17 references) (MDH)