Folding Polyominoes into (Poly)Cubes

We study the problem of folding a polyomino $P$ into a polycube $Q$, allowing faces of $Q$ to be covered multiple times. First, we define a variety of folding models according to whether the folds (a) must be along grid lines of $P$ or can divide squares in half (diagonally and/or orthogonally), (b) must be mountain or can be both mountain and valley, (c) can remain flat (forming an angle of $180^\circ$), and (d) must lie on just the polycube surface or can have interior faces as well. Second, we give all the inclusion relations among all models that fold on the grid lines of $P$. Third, we characterize all polyominoes that can fold into a unit cube, in some models. Fourth, we give a linear-time dynamic programming algorithm to fold a tree-shaped polyomino into a constant-size polycube, in some models. Finally, we consider the triangular version of the problem, characterizing which polyiamonds fold into a regular tetrahedron.Comment: 30 pages, 19 figures, full version of extended abstract that appeared in CCCG 2015. (Change over previous version: Fixed a missing reference.

Cognitive finance: Behavioural strategies of spending, saving, and investing.

Research in economics is increasingly open to empirical results. The advances in behavioural approaches are expanded here by applying cognitive methods to financial questions. The field of "cognitive finance" is approached by the exploration of decision strategies in the financial settings of spending, saving, and investing. Individual strategies in these different domains are searched for and elaborated to derive explanations for observed irregularities in financial decision making. Strong context-dependency and adaptive learning form the basis for this cognition-based approach to finance. Experiments, ratings, and real world data analysis are carried out in specific financial settings, combining different research methods to improve the understanding of natural financial behaviour. People use various strategies in the domains of spending, saving, and investing. Specific spending profiles can be elaborated for a better understanding of individual spending differences. It was found that people differ along four dimensions of spending, which can be labelled: General Leisure, Regular Maintenance, Risk Orientation, and Future Orientation. Saving behaviour is strongly dependent on how people mentally structure their finance and on their self-control attitude towards decision space restrictions, environmental cues, and contingency structures. Investment strategies depend on how companies, in which investments are placed, are evaluated on factors such as Honesty, Prestige, Innovation, and Power. Further on, different information integration strategies can be learned in decision situations with direct feedback. The mapping of cognitive processes in financial decision making is discussed and adaptive learning mechanisms are proposed for the observed behavioural differences. The construal of a "financial personality" is proposed in accordance with other dimensions of personality measures, to better acknowledge and predict variations in financial behaviour. This perspective enriches economic theories and provides a useful ground for improving individual financial services

Iterated function systems and permutation representations of the Cuntz algebra

We study a class of representations of the Cuntz algebras O_N, N=2,3,..., acting on L^2(T) where T=R/2\pi Z. The representations arise in wavelet theory, but are of independent interest. We find and describe the decomposition into irreducibles, and show how the O_N-irreducibles decompose when restricted to the subalgebra UHF_N\subset O_N of gauge-invariant elements; and we show that the whole structure is accounted for by arithmetic and combinatorial properties of the integers Z. We have general results on a class of representations of O_N on Hilbert space H such that the generators S_i as operators permute the elements in some orthonormal basis for H. We then use this to extend our results from L^2(T) to L^2(T^d), d>1 ; even to L^2(\mathbf{T}) where \mathbf{T} is some fractal version of the torus which carries more of the algebraic information encoded in our representations.Comment: 84 pages, 11 figures, AMS-LaTeX v1.2b, full-resolution figures available at ftp://ftp.math.uiowa.edu/pub/jorgen/PermRepCuntzAlg in eps files with the same names as the low-resolution figures included her

An investigation of early attention in young children through the use of stroop task variants

Stroop interference through the colour-word task has been a popular means of studying selective attention since its introduction in 1935. Little effort has been made to adapting a non-verbal task for use with pre-school children. Cramer (1976) devised a colour-picture task where pictures characteristically associated with a particular colour (such as a picture of a banana and the colour yellow) were presented in incongruous colours (e.g., a blue banana). A series of studies was conducted with children aged between 3 and 8 years of age which investigated facets of this colour-picture task. Two methods of responding were compared - a verbal response, and a manual response that allowed younger children to participate (a card-sorting technique). In addition to the basic colour-picture task where children named colours and forms, another task was introduced where children 'prescribed' the correct colour of incorrectly-coloured pictures (Santostefano, 1978; Sebovà & Árochovà, 1986). Results showed that children consistently displayed increased latencies when colour-naming and colour-sorting characteristically and uncharacteristically-coloured pictures. Interference was frequently found for inappropriately-coloured but not appropriately-coloured pictures in form-naming/sorting tasks. The prescribing task proved difficult for children to complete and produced increased latencies and error rates. Performance of the naming colour-picture task was compared to classic Stroop colour-word procedures in children aged between 5 and 8. There were correlations between colour naming in the colour-picture and colour-word tasks for children aged 5 - 7. Performance in the prescribing task did not correlate. It is concluded that the tasks are good measures of selective attention but not necessarily direct equivalents of the colour-word task. An evaluation of the verbal and non-verbal methods is also given

Neuromodulation of Spatial Associations: Evidence from Choice Reaction Tasks During Transcranial Direct Current Stimulation

Various portions of human behavior and cognition are influenced by covert implicit processes without being necessarily available to intentional planning. Implicit cognitive biases can be measured in behavioral tasks yielding SNARC effects for spatial associations of numerical and non-numerical sequences, or yielding the implicit association test effect for associations between insect-flower and negative-positive categories. By using concurrent neuromodulation with transcranial direct current stimulation (tDCS), subthreshold activity patterns in prefrontal cortical regions can be experimentally manipulated to reduce implicit processing. Thus, the application of tDCS can test neurocognitive hypotheses on a unique neurocognitive origin of implicit cognitive biases in different spatial-numerical and non-numerical domains. However, the effects of tDCS are not only determined by superimposed electric fields, but also by task characteristics. To outline the possibilities of task-specific targeting of tDCS, task characteristics and instructions can be varied systematically when combined with neuromodulation. In the present thesis, implicit cognitive processes are assessed in different paradigms concurrent to left-hemispheric prefrontal tDCS to investigate a verbal processing hypothesis for implicit associations in general. In psychological experiments, simple choice reaction tasks measure implicit SNARC and SNARC-like effects as relative left-hand vs. right-hand latency advantages for responding to smaller number or ordinal sequence targets. However, different combinations of polarity-dependent tDCS with stimuli and task procedures also reveal domain-specific involvements and dissociations. Discounting previous unified theories on the SNARC effect, polarity-specific neuromodulation effects dissociate numbers and weekday or month ordinal sequences. By considering also previous results and patient studies, I present a hybrid and augmented working memory account and elaborate the linguistic markedness correspondence principle as one critical verbal mechanism among competing covert coding mechanisms. Finally, a general stimulation rationale based on verbal working memory is tested in separate experiments extending also to non-spatial implicit association test effects. Regarding cognitive tDCS effects, the present studies show polarity asymmetry and task-induced activity dependence of state-dependent neuromodulation. At large, distinct combinations of the identical tDCS electrode configuration with different tasks influences behavioral outcomes tremendously, which will allow for improved task- and domain-specific targeting

How the Interaction of Domain and Situational Achievement Goals Influences Task Performance.

This thesis theoretically and empirically explores the application of achievement goal theory (AGT) for improving task performance. As one of most influential social-cognitive theories of achievement motivation, AGT has provided insight into the application of approach-based achievement goals by coaches and teachers to enhance performance. However, the question remains, which of the approach-based goals is the best? Using five empirical studies this thesis explores the consequences of the interaction between individuals’ domain goals and situationally imposed mastery and performance-approach goals on facilitating task performance. Study 1 (N = 15) piloted a methodology to examine the effects of the interaction between situational and domain goal congruency on sequence recall and goal valuation. Study 2 (N = 79) transitioned to the sport domain and considered the consequences of goal congruency for state anxiety, goal valuation, and reaction time performance. Study 3 (N = 129) embedded the methodological modifications noted in previous chapters and replicated an exploration of the facilitatory effects of congruent performance-approach goals identified in study 1. Study 4 (N = 81) then explored variations in the goal congruency relationship using a more complex physical task via the Speed, Time, Accuracy, Reaction, Response machine. The thesis contributes to a limited literature that uses within-subjects designs to investigate achievement goals and task performance. It provides initial evidence to affirm the importance of domain goals, the differentiation between imposed and adopted situational goals, and the need to consider the integrative effects on task performance. It also provides data that challenges previous notions of the debilitating effects of performance goals. Overall, the thesis advocates both the need for consistent conceptualisation and operationalisation of achievement goals and the consideration of the interacting relationships of AGT components

Putting some order in person memory: memory for (serial) order in impression formation

American Psychological Association (PsycINFO Classification Categories and Codes) 2340 Cognitive Processes; 2343 Learning & Memory; 3000 Social Psychology; 3040 Social Perception and CognitionThe present work examines the representation and retrieval of order information in person memory. The study of memory for serial order has been absent from the research on the underling memory processes of impression formation, which has been focusing exclusively on item information. In this work we argue that our understanding of person memory is incomplete without an account for order and item information representation and retrieval. According to a chaining hypothesis, we predicted that the organizational processes involved in impression formation would hinder the ability to represent order by means of associations between items in successive positions. The first three experiments indicated, contradicting our hypothesis, that when people form impressions they are able to represent, retrieve and use order information for order judgements and (serial) recall. The two following studies, experiment 4 and 5, directly manipulated the associations that were built in memory when people formed impressions, to understand whether order information representation was based on associations between items that appeared in successive serial positions. Results showed that the ability to use order information was unaffected by changes in the structure of non-serial inter-item associations, which suggests that order representation is not derived from mere serial associations. Experiment 6, the last from the set of experiments reported here, suggested that the representation of order information is less dependent on episodic memory, in contrast to item information. The findings from this set of 6 experiments suggested, firstly, that when people form impressions they are able to reconstruct serial order (even when such order has no meaning), and secondly, that order representation in person memory seem not to be derived from the inter-item associations formed at encoding. Finally, an ordinal proposal for the representation and use of order in person memory is discussed.O objectivo central do presente trabalho é o estudo da representação e recuperação da informação de ordem em memória de pessoas. A memória de ordem serial tem permanecido fora da investigação sobre os processos mnésicos subjacentes à formação de impressões, investigação esta que se tem centrado exclusivamente na informação de item. Argumentamos que o conhecimento sobre memória de pessoas não pode ser completo sem que haja uma compreensão dos processos envolvidos na representação e recuperação da informação de ordem. De acordo com a hipótese de chaining, os processos que caracterizam a formação de impressões prejudicam o estabelecimento de associações entre itens em posições sucessivas, interferindo com a representação da informação de ordem. As três primeiras experiências sugerem, contrariamente ao esperado, que quando as pessoas formam impressões estão a representar informação de ordem, que pode ser utilizada em tarefas de julgamento e recordação. Nas experiências 4 e 5 manipulámos directamente as associações que se formam durante a codificação, quando as pessoas formam impressões, tentando perceber se a representação de ordem se basearia em associações entre itens em posições seriais sucessivas. Os resultados indicam que, independentemente da mudança na densidade associativa da rede, a capacidade de os participantes acederem e utilizarem informação de ordem não é afectada. Estes dados sugerem que a representação da informação não acontece pela mera associação de itens em posições sucessivas. A experiência 6 sugere que a representação da informação de ordem, em contraste com a informação de item, depende menos da memória episódica. Este conjunto de resultados sugere (i) que quando as pessoas formam impressões são capazes de reconstruir a ordem e (ii) que a representação da informação de ordem em memória de pessoas não é dependente das associações que se estabelecem entre os itens, durante a codificação. Finalmente, uma proposta ordinal para a representação e recuperação da ordem em memória de pessoas é discutida.The present work was sponsored by a Doctoral Grant (Ref. SFRH/BD/23748/2005) of the Science and Technology Foundation (FCT), Portugal, and the Program POCI2010, which is funded by the Portuguese Ministry of Science, Technology and Higher Education, and the European Social Fund (Community Support Framework III)