Pattern Functional Dependencies for Data Cleaning

Patterns (or regex-based expressions) are widely used to constrain the format of a domain (or a column), e.g., a Year column should contain only four digits, and thus a value like "1980-" might be a typo. Moreover, integrity constraints (ICs) defined over multiple columns, such as (conditional) functional dependencies and denial constraints, e.g., a ZIP code uniquely determines a city in the UK, have been widely used in data cleaning. However, a promising, but not yet explored, direction is to combine regex- and IC-based theories to capture data dependencies involving partial attribute values. For example, in an employee ID such as"F-9-107", "F" is sufficient to determine the finance department. Inspired by the above observation, we propose a novel class of ICs, called pattern functional dependencies (PFDs), to model fine-grained data dependencies gleaned from partial attribute values. These dependencies cannot be modeled using traditional ICs, such as (conditional) functional dependencies, which work on entire attribute values. We also present a set of axioms for the inference of PFDs, analogous to Armstrong's axioms for FDs, and study the complexity of consistency and implication analysis of PFDs. Moreover, we devise an effective algorithm to automatically discover PFDs even in the presence of errors in the data. Our extensive experiments on 15 real-world datasets show that our approach can effectively discover valid and useful PFDs over dirty data, which can then be used to detect data errors that are hard to capture by other types of ICs

When is working memory important for arithmetic?: the impact of strategy and age

Our ability to perform arithmetic relies heavily on working memory, the manipulation and maintenance of information in mind. Previous research has found that in adults, procedural strategies, particularly counting, rely on working memory to a greater extent than retrieval strategies. During childhood there are changes in the types of strategies employed, as well as an increase in the accuracy and efficiency of strategy execution. As such it seems likely that the role of working memory in arithmetic may also change, however children and adults have never been directly compared. This study used traditional dual-task methodology, with the addition of a control load condition, to investigate the extent to which working memory requirements for different arithmetic strategies change with age between 9-11 years, 12-14 years and young adulthood. We showed that both children and adults employ working memory when solving arithmetic problems, no matter what strategy they choose. This study highlights the importance of considering working memory in understanding the difficulties that some children and adults have with mathematics, as well as the need to include working memory in theoretical models of mathematical cognition

Sequential Neural Processes in Abacus Mental Addition: An EEG and fMRI Case Study

Abacus experts are able to mentally calculate multi-digit numbers rapidly. Some behavioral and neuroimaging studies have suggested a visuospatial and visuomotor strategy during abacus mental calculation. However, no study up to now has attempted to dissociate temporally the visuospatial neural process from the visuomotor neural process during abacus mental calculation. In the present study, an abacus expert performed the mental addition tasks (8-digit and 4-digit addends presented in visual or auditory modes) swiftly and accurately. The 100% correct rates in this expert’s task performance were significantly higher than those of ordinary subjects performing 1-digit and 2-digit addition tasks. ERPs, EEG source localizations, and fMRI results taken together suggested visuospatial and visuomotor processes were sequentially arranged during the abacus mental addition with visual addends and could be dissociated from each other temporally. The visuospatial transformation of the numbers, in which the superior parietal lobule was most likely involved, might occur first (around 380 ms) after the onset of the stimuli. The visuomotor processing, in which the superior/middle frontal gyri were most likely involved, might occur later (around 440 ms). Meanwhile, fMRI results suggested that neural networks involved in the abacus mental addition with auditory stimuli were similar to those in the visual abacus mental addition. The most prominently activated brain areas in both conditions included the bilateral superior parietal lobules (BA 7) and bilateral middle frontal gyri (BA 6). These results suggest a supra-modal brain network in abacus mental addition, which may develop from normal mental calculation networks