Your search

We introduce a variant of the Kronecker product, called the regional Kronecker product, that can be used to build new, larger multiple-pair latin squares from existing multiple-pair latin squares. We present applications to the existence and orthogonality of multiple-pair latin squares. © 2019 Elsevier B.V.

This paper is a sequel to [8] where we introduced an invariant, called canonical degree, of Cohen–Macaulay local rings that admit a canonical ideal. Here to each such ring R with a canonical ideal, we attach a different invariant, called bi-canonical degree, which in dimension 1 appears also in [12] as the residue of R. The minimal values of these functions characterize specific classes of Cohen–Macaulay rings. We give a uniform presentation of such degrees and discuss some computational opportunities offered by the bi-canonical degree. © 2019 Elsevier Inc.

Background: Few studies have explored changing patterns of alcohol consumption among young females and differences based on race/ethnicity. Objective: This study examined differences in alcohol consumption between black and white undergraduate females and compared trends in three different measures of alcohol consumption over a 10-year period from 2004 to 2014. Methods: The CORE Alcohol and Drug Survey was used to collect data from female undergraduates attending a public university in the northeastern USA. Classes were randomly selected into the sample; class acceptance was 68% and student participation was 96%. The chi-square test examined differences between groups and the Cochrane Armitage Test for Trend assessed changes over time. Results: In 2014, for every measure of alcohol consumption examined, a significantly larger percentage of white females engaged in the behavior compared to black females. Trend analysis from 2004 to 2014 demonstrated a narrowing of this gap. Controlling for age, any alcohol use in past 30 days and binge drinking in the past 2 weeks increased significantly for black females 21 years or older. Any alcohol use in the past 30 days decreased significantly for white females under 21 years. Conclusion: These findings introduce many questions which should be explored through additional research.

Low graduation rate is a significant and growing problem in U.S. higher education systems. Although previous studies have demonstrated the usefulness of building statistical models for predicting students' graduation outcomes, advanced machine learning models promise to improve the effectiveness of these models, and hone in on the “difference that makes a difference” not only on the group level, but also on the level of the individual student. In this paper we propose an ensemble support vector machines based model for predicting students' graduation. Up to about 100 features, including a set of psychological-educational factors, were employed to construct the predicting model. We evaluated the proposed model using data taken from a state university's longitudinal, cohort data sets from the incoming classes of students from 2011-2012 (n=350). The experimental results demonstrated the effectiveness of the model, with considerable accuracy, precision, and recall. This paper presents the results of analysis that were conducted in order to gauge the predictive capability of a machine learning algorithm to predict on-time graduation that took into consideration students' learning and development.

We study the relationship between the reduction number of a primary ideal of a local ring relative to one of its minimal reductions and the multiplicity of the corresponding Sally module. This paper is focused on three goals: (i) to develop a change of rings technique for the Sally module of an ideal to allow extension of results from Cohen–Macaulay rings to more general rings; (ii) to use the fiber of the Sally modules of almost complete intersection ideals to connect its structure to the Cohen–Macaulayness of the special fiber ring; (iii) to extend some of the results of (i) to two-dimensional Buchsbaum rings. Along the way, we provide an explicit realization of the S2S_{2} -fication of arbitrary Buchsbaum rings.

The purpose of this paper is to introduce new invariants of Cohen–Macaulay local rings. Our focus is the class of Cohen–Macaulay local rings that admit a canonical ideal. Attached to each such ring R with a canonical ideal C, there are integers–the type of R, the reduction number of C–that provide valuable metrics to express the deviation of R from being a Gorenstein ring. We enlarge this list with other integers–the roots of R and several canonical degrees. The latter are multiplicity based functions of the Rees algebra of C. © 2017 Elsevier Inc.

The original title for this work was “Mathematical Literacy, What Is It and Why You Need it”. The current title reflects that there can be no real learning in any subject, unless questions of who, what, when, where, why and how are raised in the minds of the learners. The book is not a mathematical text, and there are no assigned exercises or exams. It is written for reasonably intelligent and curious individuals, both those who value mathematics, aware of its many important applications and others who have been inappropriately exposed to mathematics, leading to indifference to the subject, fear and even loathing. These feelings are all consequences of meaningless presentations, drill, rote learning and being lost as the purpose of what is being studied. Mathematics education needs a radical reform. There is more than one way to accomplish this. Here the author presents his approach of wrapping mathematical ideas in a story. To learn one first must develop an interest in a problem and the curiosity to find how masters of mathematics have solved them. What is necessary to be mathematically literate? It’s not about solving algebraic equations or even making a geometric proof. These are valuable skills but not evidence of literacy. We often seek answers but learning to ask pertinent questions is the road to mathematical literacy. Here is the good news: new mathematical ideas have a way of finding applications. This is known as “the unreasonable effectiveness of mathematics.”

We introduce a novel application of feature ranking methods to the fault localization problem. We envision the problem of localizing causes of failures as instances of ranking program's elements where elements are conceptualized as features. In this paper, we define features as program's statements. However, in its fine-grained definition, the idea of program's features can refer to any traits of programs. This paper proposes feature ranking-based algorithms. The algorithms analyze execution traces of both passing and failing test cases, and extract the bug signatures from the failing test cases. The proposed procedure extracts possible combinations of program's elements when executed together from bug signatures. The feature ranking-based algorithms then order statements according to the suspiciousness of the combinations. When viewed as sequences, the combination of program's elements produced and traced in bug signatures can be utilized to reason about the common longest subsequence. The common longest subsequence of bug signatures represents the common statements executed by all failing test cases and thus provides a means for identifying statements that contain possible faults. Our evaluation indicates that the proposed feature-based fault localization outperforms existing fault localization ranking schemes. © 2017 World Scientific Publishing Company.

Vulnerabilities need to be detected and removed from software. Although previous studies demonstrated the usefulness of employing prediction techniques in deciding about vulnerabilities of software components, the improvement of effectiveness of these prediction techniques is still a grand challenging research question. This paper employed a technique based on a deep neural network with rectifier linear units trained with stochastic gradient descent method and batch normalization, for predicting vulnerable software components. The features are defined as continuous sequences of tokens in source code files. Besides, a statistical feature selection algorithm is then employed to reduce the feature and search space. We evaluated the proposed technique based on some Java Android applications, and the results demonstrated that the proposed technique could predict vulnerable classes, i.e., software components, with high precision, accuracy and recall.