Algorithms

496 KiB

Open AccessArticle

Requirements for Semantic Educational Recommender Systems in Formal E-Learning Scenarios

by Olga C. Santos and Jesus G. Boticario

Algorithms 2011, 4(2), 131-154; https://doi.org/10.3390/a4030131 - 20 Jul 2011

Cited by 50 | Viewed by 11285

This paper analyzes how recommender systems can be applied to current e-learning systems to guide learners in personalized inclusive e-learning scenarios. Recommendations can be used to overcome current limitations of learning management systems in providing personalization and accessibility features. Recommenders can take advantage of standards-based solutions to provide inclusive support. To this end we have identified the need for developing semantic educational recommender systems, which are able to extend existing learning management systems with adaptive navigation support. In this paper we present three requirements to be considered in developing these semantic educational recommender systems, which are in line with the service-oriented approach of the third generation of learning management systems, namely: (i) a recommendation model; (ii) an open standards-based service-oriented architecture; and (iii) a usable and accessible graphical user interface to deliver the recommendations. Full article

(This article belongs to the Special Issue Recommender Systems in E-Learning Settings)

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309 KiB

Open AccessArticle

Alternatives to the Least Squares Solution to Peelle’s Pertinent Puzzle

by Tom Burr, Todd Graves, Nicolas Hengartner, Toshihiko Kawano, Feng Pan and Patrick Talou

Algorithms 2011, 4(2), 115-130; https://doi.org/10.3390/a4020115 - 23 Jun 2011

Cited by 6 | Viewed by 7176

Abstract

Peelle’s Pertinent Puzzle (PPP) was described in 1987 in the context of estimating fundamental parameters that arise in nuclear interaction experiments. In PPP, generalized least squares (GLS) parameter estimates fell outside the range of the data, which has raised concerns that GLS is somehow flawed and has led to suggested alternatives to GLS estimators. However, there have been no corresponding performance comparisons among methods, and one suggested approach involving simulated data realizations is statistically incomplete. Here we provide performance comparisons among estimators, introduce approximate Bayesian computation (ABC) using density estimation applied to simulated data realizations to produce an alternative to the incomplete approach, complete the incompletely specified approach, and show that estimation error in the assumed covariance matrix cannot always be ignored. Full article

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347 KiB

Open AccessArticle

Goodness-of-Fit Tests For Elliptical and Independent Copulas through Projection Pursuit

by Jacques Touboul

Algorithms 2011, 4(2), 87-114; https://doi.org/10.3390/a4020087 - 26 Apr 2011

Cited by 3 | Viewed by 7735

Abstract

Two goodness-of-fit tests for copulas are being investigated. The first one deals with the case of elliptical copulas and the second one deals with independent copulas. These tests result from the expansion of the projection pursuit methodology that we will introduce in the present article. This method enables us to determine on which axis system these copulas lie as well as the exact value of these very copulas in the basis formed by the axes previously determined irrespective of their value in their canonical basis. Simulations are also presented as well as an application to real datasets. Full article

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179 KiB

Open AccessArticle

Approximating the Minimum Tour Cover of a Digraph

by Viet Hung Nguyen

Algorithms 2011, 4(2), 75-86; https://doi.org/10.3390/a4020075 - 20 Apr 2011

Cited by 2 | Viewed by 6952

Abstract

Given a directed graph G with non-negative cost on the arcs, a directed tour cover T of G is a cycle (not necessarily simple) in G such that either head or tail (or both of them) of every arc in G is touched by T. The minimum directed tour cover problem (DToCP), which is to find a directed tour cover of minimum cost, is NP-hard. It is thus interesting to design approximation algorithms with performance guarantee to solve this problem. Although its undirected counterpart (ToCP) has been studied in recent years, in our knowledge, the DToCP remains widely open. In this paper, we give a 2 log2(n)-approximation algorithm for the DToCP. Full article

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Algorithms, Volume 4, Issue 2 (June 2011) – 4 articles , Pages 75-154

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