The Experts below are selected from a list of 22740 Experts worldwide ranked by ideXlab platform
Carole R Beal - One of the best experts on this subject based on the ideXlab platform.
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effects of linguistic complexity and math Difficulty on word problem solving by english learners
International Journal of Education, 2010Co-Authors: Otilia C Barbu, Carole R BealAbstract:Prior research suggests that linguistic complexity may impede mathematics word problem solving by English Learners, but results have been inconsistent. The present study employed an experimental design to investigate the effects of linguistic complexity and mathematics Difficulty on word problem solving by middle school English Learners. Results were consistent with predictions from Cognitive Load Theory: Performance was poorer for word problems written in more complex language compared to the same problems in easier text, and the weakest performance was observed for problems that were both linguistically and Mathematically challenging. A Confirmatory Factor Analysis suggested a model including a latent factor, hypothesized to be working memory, provided a good fit to the data. Additionally, linguistic complexity had a significant influence on students’ perceptions of the Mathematical Difficulty of the problems. The results are consistent with recent suggestions that English Learners’ lower performance in math reflects the additional cognitive demands associated with text comprehension.
Otilia C Barbu - One of the best experts on this subject based on the ideXlab platform.
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effects of linguistic complexity and math Difficulty on word problem solving by english learners
International Journal of Education, 2010Co-Authors: Otilia C Barbu, Carole R BealAbstract:Prior research suggests that linguistic complexity may impede mathematics word problem solving by English Learners, but results have been inconsistent. The present study employed an experimental design to investigate the effects of linguistic complexity and mathematics Difficulty on word problem solving by middle school English Learners. Results were consistent with predictions from Cognitive Load Theory: Performance was poorer for word problems written in more complex language compared to the same problems in easier text, and the weakest performance was observed for problems that were both linguistically and Mathematically challenging. A Confirmatory Factor Analysis suggested a model including a latent factor, hypothesized to be working memory, provided a good fit to the data. Additionally, linguistic complexity had a significant influence on students’ perceptions of the Mathematical Difficulty of the problems. The results are consistent with recent suggestions that English Learners’ lower performance in math reflects the additional cognitive demands associated with text comprehension.
Baier Christel - One of the best experts on this subject based on the ideXlab platform.
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On Skolem-hardness and saturation points in Markov decision processes
2020Co-Authors: Piribauer Jakob, Baier ChristelAbstract:The Skolem problem and the related Positivity problem for linear recurrence sequences are outstanding number-theoretic problems whose decidability has been open for many decades. In this paper, the inherent Mathematical Difficulty of a series of optimization problems on Markov decision processes (MDPs) is shown by a reduction from the Positivity problem to the associated decision problems which establishes that the problems are also at least as hard as the Skolem problem as an immediate consequence. The optimization problems under consideration are two non-classical variants of the stochastic shortest path problem (SSPP) in terms of expected partial or conditional accumulated weights, the optimization of the conditional value-at-risk for accumulated weights, and two problems addressing the long-run satisfaction of path properties, namely the optimization of long-run probabilities of regular co-safety properties and the model-checking problem of the logic frequency-LTL. To prove the Positivity- and hence Skolem-hardness for the latter two problems, a new auxiliary path measure, called weighted long-run frequency, is introduced and the Positivity-hardness of the corresponding decision problem is shown as an intermediate step. For the partial and conditional SSPP on MDPs with non-negative weights and for the optimization of long-run probabilities of constrained reachability properties (a U b), solutions are known that rely on the identification of a bound on the accumulated weight or the number of consecutive visits to certain sates, called a saturation point, from which on optimal schedulers behave memorylessly. In this paper, it is shown that also the optimization of the conditional value-at-risk for the classical SSPP and of weighted long-run frequencies on MDPs with non-negative weights can be solved in pseudo-polynomial time exploiting the existence of a saturation point.Comment: Conference version accepted for publication at ICALP'2
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On Skolem-Hardness and Saturation Points in Markov Decision Processes
LIPIcs - Leibniz International Proceedings in Informatics. 47th International Colloquium on Automata Languages and Programming (ICALP 2020), 2020Co-Authors: Piribauer Jakob, Baier ChristelAbstract:The Skolem problem and the related Positivity problem for linear recurrence sequences are outstanding number-theoretic problems whose decidability has been open for many decades. In this paper, the inherent Mathematical Difficulty of a series of optimization problems on Markov decision processes (MDPs) is shown by a reduction from the Positivity problem to the associated decision problems which establishes that the problems are also at least as hard as the Skolem problem as an immediate consequence. The optimization problems under consideration are two non-classical variants of the stochastic shortest path problem (SSPP) in terms of expected partial or conditional accumulated weights, the optimization of the conditional value-at-risk for accumulated weights, and two problems addressing the long-run satisfaction of path properties, namely the optimization of long-run probabilities of regular co-safety properties and the model-checking problem of the logic frequency-LTL. To prove the Positivity- and hence Skolem-hardness for the latter two problems, a new auxiliary path measure, called weighted long-run frequency, is introduced and the Positivity-hardness of the corresponding decision problem is shown as an intermediate step. For the partial and conditional SSPP on MDPs with non-negative weights and for the optimization of long-run probabilities of constrained reachability properties (aU b), solutions are known that rely on the identification of a bound on the accumulated weight or the number of consecutive visits to certain sates, called a saturation point, from which on optimal schedulers behave memorylessly. In this paper, it is shown that also the optimization of the conditional value-at-risk for the classical SSPP and of weighted long-run frequencies on MDPs with non-negative weights can be solved in pseudo-polynomial time exploiting the existence of a saturation point. As a consequence, one obtains the decidability of the qualitative model-checking problem of a frequency-LTL formula that is not included in the fragments with known solutions
Xiangsheng Xu - One of the best experts on this subject based on the ideXlab platform.
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maximal monotone operator theory and its applications to thin film equation in epitaxial growth on vicinal surface
Calculus of Variations and Partial Differential Equations, 2018Co-Authors: Xin Yang Lu, Xiangsheng XuAbstract:In this work we consider $$\begin{aligned} w_t=\left[ \left( w_{hh}+c_0\right) ^{-3}\right] _{hh},\qquad w(0)=w^0, \end{aligned}$$ (1) which is derived from a thin film equation for epitaxial growth on vicinal surface. We formulate the problem as the gradient flow of a suitably-defined convex functional in a non-reflexive space. Then by restricting it to a Hilbert space and proving the uniqueness of its sub-differential, we can apply the classical maximal monotone operator theory. The Mathematical Difficulty is due to the fact that \(w_{hh}\) can appear as a positive Radon measure. We prove the existence of a global strong solution with hidden singularity. In particular, (1) holds almost everywhere when \(w_{hh}\) is replaced by its absolutely continuous part.
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maximal monotone operator theory and its applications to thin film equation in epitaxial growth on vicinal surface
arXiv: Analysis of PDEs, 2017Co-Authors: Xin Yang Lu, Xiangsheng XuAbstract:In this work we consider $$ w_t=[(w_{hh}+c_0)^{-3}]_{hh},\qquad w(0)=w^0, $$ which is derived from a thin film equation for epitaxial growth on vicinal surface. We formulate the problem as the gradient flow of a suitably-defined convex functional in a non-reflexive space. Then by restricting it to a Hilbert space and proving the uniqueness of its sub-differential, we can apply the classical maximal monotone operator theory. The Mathematical Difficulty is due to the fact that $w_{hh}$ can appear as a positive Radon measure. We prove the existence of a global strong solution. In particular, the equation holds almost everywhere when $w_{hh}$ is replaced by its absolutely continuous part.
Gerard Mulhern - One of the best experts on this subject based on the ideXlab platform.
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phonological awareness and Mathematical Difficulty a longitudinal perspective
British Journal of Development Psychology, 2010Co-Authors: Julieann Jordan, Judith Wylie, Gerard MulhernAbstract:The present longitudinal study sought to investigate the impact of poor phonology on children's Mathematical status. From a screening sample of 256 five-year-olds, 82 children were identified as either typically achieving (TA; N = 31), having comorbid poor phonology and Mathematical difficulties (PDMD; N = 31), or having only poor phonology (phonological Difficulty, PD; N = 20). Children were assessed on eight components of informal and formal mathematics achievement at ages 5-7 years. PD children were found to have significant impairments in some, mainly formal, components of mathematics by age 7 compared to TA children. Analysis also revealed that, by age 7, approximately half of the PD children met the criteria for PDMD, while the remainder exhibited less severe deficits in some components of formal mathematics. Children's Mathematical performance at age 5, however, did not predict which PD children were more likely to become PDMD at age 7, nor did they differ in terms of phonological awareness at age 5. However, those PD children who later became PDMD had lower scores on verbal and non-verbal tests of general ability.