In this essay, I explore how cognitive science could illuminate the concept of beauty. Two results from the extensive literature on aesthetics guide my discussion. As the term "beauty" is overextended in general usage, I choose as my starting point the notion of "perfect form." Aesthetic theorists are in reasonable agreement about the criteria for…

Spreadsheets lend themselves naturally to recursive computations, since a formula can be defined as a function of one of more preceding cells. A hypothesized closed form for the "n"th term of a recursive sequence can be tested easily by using a spreadsheet to compute a large number of the terms. Similarly, a conjecture about the limit of a series…

We present a new SIR epidemiological model whose exact analytical solution can be calculated. In this model, unlike previous models, the infective population becomes zero at a finite time. Remarkably, these results can be derived from only an elementary knowledge of differential equations.

A procedure for estimating the reliability of test scores in the context of ecological momentary assessment (EMA) was proposed to take into account the characteristics of EMA measures. Two commonly used test scores in EMA were considered: the aggregated score (AGGS) and the within-person centered score (WPCS). Conceptually, AGGS and WPCS represent…

We propose a functional version of extended redundancy analysis that examines directional relationships among several sets of multivariate variables. As in extended redundancy analysis, the proposed method posits that a weighed composite of each set of exogenous variables influences a set of endogenous variables. It further considers endogenous…

The evaluation of the formative process in the University system has been assuming an ever increasing importance in the European countries. Within this context, the analysis of student performance and capabilities plays a fundamental role. In this work, the authors propose a multivariate latent growth model for studying the performances of a…

Aim: We aimed to explore the organization of the calendar knowledge base underlying date calculation by assessing the ability of savant calendar calculators to free recall a series of date lists. Method: Four experiments are reported that assessed recall of structural and non-structural features of the calendar in eight savant calendar calculators…

Effect size use has been increasing in the past decade in many research areas. Confidence intervals associated with effect sizes are encouraged to be reported. Prior work has investigated the performance of confidence interval estimation with Cohen's d. This study extends this line of work to the analysis of variance case with more than two…

All methods presented in textbooks for computing inverse "Z"-transforms of rational functions have some limitation: 1) the direct division method does not, in general, provide enough information to derive an analytical expression for the time-domain sequence "x"("k") whose "Z"-transform is "X"("z"); 2) computation using the inversion integral…

Adjusted Wald intervals for binomial proportions in one-sample and two-sample designs have been shown to perform about as well as the best available methods. The adjusted Wald intervals are easy to compute and have been incorporated into introductory statistics courses. An adjusted Wald interval for paired binomial proportions is proposed here and…

Acquisition of relational knowledge is a core process in cognitive development. Relational knowledge is dynamic and flexible, entails structure-consistent mappings between representations, has properties of compositionality and systematicity, and depends on binding in working memory. We review three types of computational models relevant to…

Does modeling matter? We address this question by providing a broad survey of the computational models of cognitive development that have been proposed and studied over the last three decades. We begin by noting the advantages and limitations of computational models. We then describe four key dimensions across which models of development can be…

In this article, the author shares his comments on statistical analysis for multisite trials, and focuses on the contribution of Stephen Raudenbush, Sean Reardon, and Takako Nomi to future research. Raudenbush, Reardon, and Nomi provide a major contribution to future research on variation in program impacts by showing how to use multisite trials…

In this work we discuss the trick of eliminating infinite potential of reference arguing that it corresponds to a constant of integration, in the problem of determining the electrostatic potential of an infinite line of charge with uniform density, and show how the problem must be tackled properly. The usual procedure is confusing for most…

A basketball player attempting a free throw has two parameters under his or her control: the angle of elevation and the force with which the ball is thrown. We compute upper and lower bounds for the initial velocity for suitable values of the angle of elevation, generating a subset of the configuration space of all successful free throws. A…