Using Column Generation to Solve Extensions to the Markowitz Model

We introduce a solution scheme for portfolio optimization problems with cardinality constraints. Typical portfolio optimization problems are extensions of the classical Markowitz mean-variance portfolio optimization model. We solve such type of problems using a method similar to column generation. In this scheme, the original problem is restricted to a subset of the assets resulting in a master convex quadratic problem. Then the dual information of the master problem is used in a sub-problem to propose more assets to consider. We also consider other extensions to the Markowitz model to diversify the portfolio selection within the given intervals for active weights.Comment: 16 pages, 3 figures, 2 tables, 1 pseudocod

Six- to eight-year-olds' performance in the Heart and Flower task: Emerging proactive cognitive control.

The Heart and Flower task is used worldwide to measure age-dependent and individual differences in executive functions and/or cognitive control. The task reliably maps age and individual differences and these have consistently been found to be predictive for different aspects of school readiness and academic achievement. The idea has been put forward that there is a developmental shift in how children approach such a task. While 6-year-olds' tend to adapt their task strategy ad hoc and reactively, older children increasingly engage in proactive cognitive control. Proactive cognitive control entails finding the right response speed without risking errors, always dependent on the cognitive conflict. The main goal of the present contribution was to examine children's adjustments of response speed as a function of age and cognitive conflict by addressing RTs surrounding errors (i.e., errors and post-error trials). Data from a large sample with three age groups was used (N = 106 6-year-olds' with a mean age of 6 years; 3 months; N = 108 7-year-olds' with a mean age of 7 years; 4 months; N = 78 8-year-olds' with a mean age of 8 years; 1 month). Response speed adjustments and the development thereof were targeted both across the Flower and Mixed block, respectively, and within these blocks focusing on errors and post-error slowing. Results revealed evidence for a developmental shift toward more efficient proactive cognitive control between 6 and 8 years of age, with the older but not the younger children strategically slowing down in the Mixed block and smoother post-error slowing. At the same time, we found that even the youngest age group has emerging proactive cognitive control skills at their disposal when addressing post-error slowing in the Flower block. The present study thus tracks the early roots of later efficient executive functions and cognitive control, contributes to a better understanding of how developmental progression in cognitive control is achieved, and highlights new avenues for research in this domain

Hearts, flowers, and fruits: All children need to reveal their post-error slowing.

Slowing down responses after errors (i.e., post-error slowing [PES]) is an established finding in adults. Yet PES in young children is still not well understood. In this study, we investigated (a) whether young children show PES in tasks with different types of cognitive conflict and differing demands on executive functions, (b) whether PES is adaptive and efficient in the sense that it is associated with better task performance, and (c) whether PES correlates between tasks. We tested 4- to 6-year-old children on the Funny Fruits task (FF; n = 143), a Stroop-like task that incorporates semantic conflict and taxes children's inhibition skills, and the Hearts and Flowers task (HF; n = 170), which incorporates spatial conflict and taxes children's inhibition skills in its incongruent block and taxes both inhibition and cognitive flexibility (rule-switching) skills in its mixed block. A subgroup of children were tested on both FF and HF (n = 74). Results revealed that, first, children showed PES in FF and both blocks of HF, indicating that PES occurs in both types of conflict and under varying executive demands. Second, PES was associated with task accuracy, but only for FF and the mixed HF. Third, a between-task association in PES emerged only between FF and the mixed HF. Together, these findings indicate that PES is still a developing strategy in young children; it is present but only adaptive for, and correlates between, semantic inhibition and spatial flexibility

Explicit and implicit confidence judgments and developmental differences in metamemory: an eye-tracking approach

In the present study, primary school children's ability to give accurate confidence judgments (CJ) was addressed, with a special focus on uncertainty monitoring. In order to investigate the effects of memory retrieval processes on monitoring judgments, item difficulty in a vocabulary learning task (Japanese symbols) was manipulated. Moreover, as a first exploratory step to uncover fast and retrieval bound (implicit) monitoring processes that take place before explicit CJ are openly reported, fixation time allocation during recognition and monitoring was recorded with an eye-tracking device. Results revealed developmental progression in uncertainty (but not in certainty) monitoring between the age of 7 and 9years. Differences in CJ across levels of item difficulty point to a substantial impact of retrieval processes on 9-yr-olds' but not on 7-yr-olds' monitoring. Eye-tracking data revealed an overall bias towards medium and high CJ, and confirmed evidence on developmental progression in monitoring skill

The impact of retrieval processes, age, general achievement level, and test scoring scheme for children's metacognitive monitoring and controlling

This multi-phase study examined the influence of retrieval processes on children's metacognitive processes in relation to and in interaction with achievement level and age. First, N = 150 9/10- and 11/12-year old high and low achievers watched an educational film and predicted their test performance. Children then solved a cloze test regarding the film content including answerable and unanswerable items and gave confidence judgments to every answer. Finally, children withdrew answers that they believed to be incorrect. All children showed adequate metacognitive processes before and during test taking with 11/12- year-olds outperforming 9/10-year-olds when considering characteristics of on-going retrieval processes. As to the influence of achievement level, high compared to low achievers proved to be more accurate in their metacognitive monitoring and controlling. Results suggest that both cognitive resources (operationalized through achievement level) and mnemonic experience (assessed through age) fuel metacognitive development. Nevertheless, when facing higher demands regarding retrieval processes, experience seems to play the more important rol

Developmental progression in children’s and adolescents’ cognitive control

Background: Despite developmental progression in the ability to control behavior in service of goals during kindergarten period, little is known about cognitive control mechanisms in later childhood and adolescence. Method: The present study provides detailed insights into children’s and adolescents’ ability to flexibly and efficiently adapt their speed of responding in the context of a multiple-trial spatial conflict task. Based on the dual mechanisms of cognitive control, variability in response times, response consistency, trial-by trial adjustments surrounding errors, and developmental differences thereof were investigated. Results: Results showed that individuals become more reliable, more efficient, better adjusted, and thus of overall better in cognitive control with increasing age. Sequential adjustments of response times revealed that the participating 4th graders responded too fast when the task was running smoothly and slowed down too strongly after committing an error in comparison to 6th and 8th graders. Conclusion: The results suggest that the fine-tuning of speeded responses are key mechanisms for developmental progression in cognitive control. Furthermore, the current study attempts to increase researcher’s and practitioners’ awareness that detailed analysis of cognitive control processes in typically developing children and adolescents is needed for a better understanding when evaluating these processes in individuals with deviant cognitive development. Keywords: Cognitive Control; Error-Monitoring; Typical Developmen

Stop and think: Additional time supports monitoring processes in young children.

When children evaluate their certainty, monitoring is often inaccurate. Even though young children struggle to estimate their confidence, existing research shows that monitoring skills are developing earlier than expected. Using a paired associates learning task with integrated monitoring, we implemented a time window to-"Stop and Think"-before children generated their answers and evaluated their confidence in the chosen response. Results show that kindergarten and second grade children in the-"Stop and Think"-condition have higher monitoring accuracy than the control group. Implementing a time window thus seems to support children in their evaluation of different certainty levels. Relating individual differences in independently measured inhibitory control skills revealed a correlation between monitoring and inhibition for kindergarteners

Longitudinal associations between executive functions and metacognitive monitoring in 5- to 8-year-olds

Pronounced developmental progression during the transition to formal schooling can be found in executive functions (EF) and metacognition (MC). However, it is still unclear whether and how EF and MC influence each other during this transition. Previous research with young children suggests that inhibition may be a prerequisite for monitoring skills. Thus, the present longitudinal study investigated the association between the common subcomponents of EF (inhibition, working memory, and shifting) assessed in kindergarten (T1) and metacognitive monitoring assessed in 2nd grade (T2) in a sample of N = 84 children. In line with our hypothesis, the results revealed a significant link only between the EF subcomponent inhibition and later metacognitive monitoring. More precisely, children with better inhibition skills in kindergarten showed less overconfident monitoring in elementary school. Interestingly, the longitudinal relationship between inhibition and monitoring was not bidirectional. The findings indicate an essential role of early inhibition skills regarding emerging and developing elementary school children’s monitoring skills

Adversity in early childhood: Long-term effects on early academic skills

Background The dimensional adversity model (McLaughlin & Sheridan, 2016) proposes that deprivation and threat affect child development differently. However, empirical support for the dimensional adversity model stems predominately from adolescent samples. Objective We aimed to examine if deprivation and threat experiences in infancy have differential effects on pre-academic skills in early childhood. Furthermore, we addressed the effect of chronic vs. temporary adversity exposure in infancy. Participants and Setting The population-based sample consisted of 3481 infants (49% girls). New-borns and their families were followed longitudinally (6 months to 6 years of age). Methods Based on parental information, we computed four deprivation variables and three threat variables. Pre-academic cognitive and social-emotional skills were measured with a math and a vocabulary test and parental questionnaires on emotion regulation and behavioral problems. Results Results showed that infant deprivation (but not threat) is negatively associated with math scores (β = −0.06) and language skills (β = −0.04) in kindergarten. However, infant threat and deprivation were both associated with behavioral problems (β = 0.06; β = 0.04) and emotion-regulation difficulties (β = 0.04; β = 0.03) in kindergarten. Analyses comparing chronic vs. temporary adversity exposure showed that chronic exposure was strongly related to all cognitive and social-emotional outcomes. Conclusions We found partial support for the differential effects of deprivation and threat on pre-academic skills. Furthermore, the results suggest that particularly chronic adversity poses a potential risk for development - across domains of cognition and emotions

The Relationship between Executive Functions, Working Memory, and Intelligence in Kindergarten Children.

Executive functions (EF), working memory (WM), and intelligence are closely associated, but distinct constructs. What underlies the associations between these constructs, especially in childhood, is not well understood. In this pre-registered study, along with the traditional aggregate accuracy and RT-based measures of EF, we investigated post-error slowing (PES) in EF as a manifestation of metacognitive processes (i.e., monitoring and cognitive control) in relation to WM and intelligence. Thereby, we aimed to elucidate whether these metacognitive processes may be one underlying component to explain the associations between these constructs. We tested kindergarten children (Mage = 6.4 years, SDage = 0.3) in an EF, WM (verbal and visuospatial), and fluid (non-verbal) intelligence task. We found significant associations of mainly the inhibition component of EF with fluid intelligence and verbal WM, and between verbal WM and intelligence. No significant associations emerged between the PES in EF and intelligence or WM. These results suggest that in the kindergarten age, inhibition rather than monitoring and cognitive control might be the underlying component that explains the associations between EF, WM, and intelligence