Space Complexity of Stack Automata Models

This paper examines several measures of space complexity of variants of stack automata: non-erasing stack automata and checking stack automata. These measures capture the minimum stack size required to accept every word in the language of the automaton (weak measure), the maximum stack size used in any accepting computation on any accepted word (accept measure), and the maximum stack size used in any computation (strong measure). We give a detailed characterization of the accept and strong space complexity measures for checking stack automata. Exactly one of three cases can occur: the complexity is either bounded by a constant, behaves like a linear function, or it can not be bounded by any function of the length of the input word (and it is decidable which case occurs). However, this result does not hold for non-erasing stack automata; we provide an example where the space complexity grows proportionally to the square root of the length of the input. Furthermore, we study the complexity bounds of machines which accept a given language, and decidability of space complexity properties.

Benefits of Compiling and Analyzing Hydraulic-Design Data for Bridges

The hydraulic design of bridges is a discipline that requires a strong measure of engineering judgment. Developing good engineering judgment can take years of experience, and generally increases one project at a time. A supplemental tool that can promote the development of engineering knowledge and judgment is to compile, analyze, and graphically present hydraulic data associated with stream and bridge-design characteristics from previously analyzed bridges. If the data set is sufficiently large, graphs developed from such an effort can provide the engineer with an enhanced picture of stream and bridge-design characteristics, helping them further develop their engineering knowledge and judgment. Furthermore, such graphs can function as project scoping tools and hydraulic-design review tools. Using selected data from approximately 300 bridge-scour studies in South Carolina, previously conducted by the U.S. Geological Survey, and limited hydraulic bridge-design data for approximately 200 bridges in South Carolina, trends in stream and bridge-hydraulic characteristics were evaluated including channel width, floodplain width, flood flow depths, stream slopes, bridge backwater, bridge flow velocity, and bridge lengths. Selected relationships are presented in this paper and should serve as a valuable tool for better understanding stream and bridge-hydraulic characteristics in South Carolina.

The Covert and Overt Reassurance Seeking Inventory (CORSI): Development, validation and psychometric analyses

Background: Reassurance seeking (RS) is motivated by perceived general and social/relational threats across disorders, yet is often under-recognized because it occurs in covert (i.e. subtle) and overt forms. Covert safety-seeking behaviour may maintain disorders by preventing corrective learning and is therefore important to identify effectively. Aims: This study presents the validation and psychometric analyses of a novel measure of covert and overt, general and social/relational threat-related interpersonal RS. Method: An initial 30-item measure was administered to an undergraduate sample (N = 1626), as well as to samples of individuals diagnosed with obsessive compulsive disorder (OCD; n = 50), anxiety disorders (n = 60) and depression (n = 30). The data were subjected to exploratory and confirmatory factor analyses, and validation analyses. Results: An exploratory factor analysis using principal axis factoring with oblique rotation yielded five interpretable factors, after removing four complex items. The resulting 26-item measure, the Covert and Overt Reassurance Seeking Inventory (CORSI), evidenced good convergent and divergent validity and accounted for 54.99% of the total variance after extraction. Factor correlations ranged from r = .268 to .736, suggesting that they may be tapping into unique facets of RS behaviour. In comparison with undergraduate participants, all clinical groups had significantly higher total scores [t (51.80–840) = 3.92–5.84, p < .001]. The CFA confirmed the five-factor model with good fit following the addition of four covariance terms (goodness of fit index = .897, comparative fit index = .918, Tucker–Lewis index = .907, root mean square error approximation = .061). Conclusion: The CORSI is a brief, yet comprehensive and psychometrically strong measure of problematic RS. With further validation, the CORSI has potential for use within clinical and research contexts.

Measuring High School Curricular Intensity over Three Decades

This article presents a new measure of curricular intensity that is objective, parsimonious, clearly defined, replicable, and comparable over time for use by researchers interested in examining trends, causes, and outcomes of high school course taking. After proposing a reduced-form version of Adelman’s curricular intensity index comprised of number of courses completed in English and core science, highest math course completed, and whether students took at least one Advanced Placement course, I test the measure in four National Center for Education Statistics high school longitudinal studies using confirmatory factor analysis. I examine the methodological implications of the measure by conducting multigroup tests for invariance across cohorts to understand how curricular intensity changes over time and comparing the measure’s predictive validity to that of alternative measures of course taking. I then examine substantive implications of the measure through analysis of trends and inequalities in curricular intensity. The four course-taking variables combined create a strong measure of curricular intensity across cohorts that performs as well as or better than Adelman’s index in explaining variance in postsecondary outcomes and predicting postsecondary success. The measure accounts for shifts over time in the relative contribution of each course-taking variable to overall curricular intensity, facilitating more accurate comparisons across cohorts or data sets. I provide practical guidance for using the measure in other data sets, including state- and district-level data, to analyze overall trends and gaps in curricular intensity and its role in postsecondary success, and I discuss some potential uses of the measure for future research and policy.

A note on measure and expansiveness on uniform spaces

<p>We prove that the set of points doubly asymptotic to a point has measure zero with respect to any expansive outer regular measure for a bi-measurable map on a separable uniform space. Consequently, we give a class of measures which cannot be expansive for Denjoy home-omorphisms on S¹. We then investigate the existence of expansive measures for maps with various dynamical notions. We further show that measure expansive (strong measure expansive) homeomorphisms with shadowing have periodic (strong periodic) shadowing. We relate local weak specification and periodic shadowing for strong measure expansive systems.</p>

Psychometric Properties of the Spanish Version of the Self-Determination Inventory Student Self-Report: A Structural Equation Modeling Approach

Instruments to measure self-determination have only been available in the Spanish language to date, for adolescents with intellectual disability (ID). However, given the development of a new measure of self-determination for youth with and without disabilities, the Self-Determination Inventory, there is a need to adapt and validate this tool in the Spanish language so as to provide practitioners with a psychometrically strong measure of self-determination. This study provides evidence of reliability and validity of the Spanish version of the scale, empirically tested with a sample of 620 youth with and without disabilities in Spain. Specifically, validity was evidenced through structural equation modeling approaches, confirming the instrument adequacy to measure self-determination in Spanish speaking youth. Future lines of research are suggested.