The role of phonological and executive working memory resources in simple arithmetic strategies

The current study investigated the role of the central executive and the phonological loop in arithmetic strategies to solve simple addition problems (Experiment 1) and simple subtraction problems (Experiment 2). The choice/no-choice method was used to investigate strategy execution and strategy selection independently. The central executive was involved in both retrieval and procedural strategies, but played a larger role in the latter than in the former. Active phonological processes played a role in procedural strategies only. Passive phonological resources, finally, were only needed when counting was used to solve subtraction problems. No effects of working memory load on strategy selection were observed

Integrating a Global Induction Mechanism into a Sequent Calculus

Most interesting proofs in mathematics contain an inductive argument which requires an extension of the LK-calculus to formalize. The most commonly used calculi for induction contain a separate rule or axiom which reduces the valid proof theoretic properties of the calculus. To the best of our knowledge, there are no such calculi which allow cut-elimination to a normal form with the subformula property, i.e. every formula occurring in the proof is a subformula of the end sequent. Proof schemata are a variant of LK-proofs able to simulate induction by linking proofs together. There exists a schematic normal form which has comparable proof theoretic behaviour to normal forms with the subformula property. However, a calculus for the construction of proof schemata does not exist. In this paper, we introduce a calculus for proof schemata and prove soundness and completeness with respect to a fragment of the inductive arguments formalizable in Peano arithmetic.Comment: 16 page

Working memory in children with reading and/or mathematical disabilities

Elementary school children with reading disabilities (RD; n = 17), mathematical disabilities (MD; n = 22), or combined reading and mathematical disabilities (RD+MD; n = 28) were compared to average achieving (AA; n = 45) peers on working memory measures. On all working memory components, 2 (RD vs. no RD) x 2 (MD vs. no MD) factorial ANCOVAs revealed clear differences between children with and without RD. Children with MD had lower span scores than the AA children on measures of the phonological loop and the central executive. A significant interaction effect between RD and MD was found only for listening recall and had a small, partial effect size. In addition, analyses showed that the best logistic regression model consisted of a visuospatial and a central executive task. The model significantly distinguished between the AA and clinical groups and between the MD and RD+MD groups. Evidence was found for domain-general working memory problems in children with learning disabilities. Management of working memory loads in structured learning activities in the classroom, at home, or during therapy may help these children to cope with their problems in a more profound manner

On the complexity of finding and counting solution-free sets of integers

Given a linear equation $\mathcal{L}$, a set $A$ of integers is $\mathcal{L}$-free if $A$ does not contain any `non-trivial' solutions to $\mathcal{L}$. This notion incorporates many central topics in combinatorial number theory such as sum-free and progression-free sets. In this paper we initiate the study of (parameterised) complexity questions involving $\mathcal{L}$-free sets of integers. The main questions we consider involve deciding whether a finite set of integers $A$ has an $\mathcal{L}$-free subset of a given size, and counting all such $\mathcal{L}$-free subsets. We also raise a number of open problems.Comment: 27 page

Do multiplication and division strategies rely on executive and phonological working memory resources?

The role of executive and phonological working-memory resources in simple arithmetic was investigated in two experiments. Participants had to solve simple multiplication problems (e.g., 4 x 8; Experiment 1) or simple division problems (e.g., 42 : 7; Experiment 2) under no-load, phonological-load, and executive-load conditions. The choice/no-choice method was used to investigate strategy execution and strategy selection independently. Results on strategy execution showed that executive working memory resources were involved in direct memory retrieval of both multiplication and division facts. Executive working-memory resources were also needed to execute nonretrieval strategies. Phonological working-memory resources, on the other hand, tended to be involved in non-retrieval strategies only. Results on strategy selection showed no effects of working-memory load. Finally, correlation analyses showed that both strategy execution and strategy selection correlated with individual-difference variables such as gender, math anxiety, associative strength, calculator use, arithmetic skill, and math experience

Specification-Driven Predictive Business Process Monitoring

Predictive analysis in business process monitoring aims at forecasting the future information of a running business process. The prediction is typically made based on the model extracted from historical process execution logs (event logs). In practice, different business domains might require different kinds of predictions. Hence, it is important to have a means for properly specifying the desired prediction tasks, and a mechanism to deal with these various prediction tasks. Although there have been many studies in this area, they mostly focus on a specific prediction task. This work introduces a language for specifying the desired prediction tasks, and this language allows us to express various kinds of prediction tasks. This work also presents a mechanism for automatically creating the corresponding prediction model based on the given specification. Differently from previous studies, instead of focusing on a particular prediction task, we present an approach to deal with various prediction tasks based on the given specification of the desired prediction tasks. We also provide an implementation of the approach which is used to conduct experiments using real-life event logs.Comment: This article significantly extends the previous work in https://doi.org/10.1007/978-3-319-91704-7_7 which has a technical report in arXiv:1804.00617. This article and the previous work have a coauthor in commo

Customer-oriented risk assessment in Network Utilities

For companies that distribute services such as telecommunications, water, energy, gas, etc., quality perceived by the customers has a strong impact on the fulfillment of financial goals, positively increasing the demand and negatively increasing the risk of customer churn (loss of customers). Failures by these companies may cause customer affection in a massive way, augmenting the intention to leave the company. Therefore, maintenance performance and specifically service reliability has a strong influence on financial goals. This paper proposes a methodology to evaluate the contribution of the maintenance department in economic terms, based on service unreliability by network failures. The developed methodology aims to provide an analysis of failures to facilitate decision making about maintenance (preventive/predictive and corrective) costs versus negative impacts in end-customer invoicing based on the probability of losing customers. Survival analysis of recurrent failures with the General Renewal Process distribution is used for this novel purpose with the intention to be applied as a standard procedure to calculate the expected maintenance financial impact, for a given period of time. Also, geographical areas of coverage are distinguished, enabling the comparison of different technical or management alternatives. Two case studies in a telecommunications services company are presented in order to illustrate the applicability of the methodology

Preschool predictors of mathematics in first grade children with autism spectrum disorder

AbstractUp till now, research evidence on the mathematical abilities of children with autism spectrum disorder (ASD) has been scarce and provided mixed results. The current study examined the predictive value of five early numerical competencies for four domains of mathematics in first grade. Thirty-three high-functioning children with ASD were followed up from preschool to first grade and compared with 54 typically developing children, as well as with normed samples in first grade. Five early numerical competencies were tested in preschool (5–6 years): verbal subitizing, counting, magnitude comparison, estimation, and arithmetic operations. Four domains of mathematics were used as outcome variables in first grade (6–7 years): procedural calculation, number fact retrieval, word/language problems, and time-related competences. Children with ASD showed similar early numerical competencies at preschool age as typically developing children. Moreover, they scored average on number fact retrieval and time-related competences and higher on procedural calculation and word/language problems compared to the normed population in first grade. When predicting first grade mathematics performance in children with ASD, both verbal subitizing and counting seemed to be important to evaluate at preschool age. Verbal subitizing had a higher predictive value in children with ASD than in typically developing children. Whereas verbal subitizing was predictive for procedural calculation, number fact retrieval, and word/language problems, counting was predictive for procedural calculation and, to a lesser extent, number fact retrieval. Implications and directions for future research are discussed