In the last decades, researchers have proposed a large number of theoretical models of timing. These models make different assumptions concerning how animals learn to time events and how such learning is represented in memory. However, few studies have examined these different assumptions either empirically or conceptually. For knowledge to accumulate, variation in theoretical models must be accompanied by selection of models and model ideas. To that end, we review two timing models, Scalar Expectancy Theory (SET), the dominant model in the field, and the Learning-to-Time (LeT) model, one of the few models dealing explicitly with learning. In the first part of this article, we describe how each model works in prototypical concurrent and retrospective timing tasks, identify their structural similarities, and classify their differences concerning temporal learning and memory. In the second part, we review a series of studies that examined these differences and conclude that both the memory structure postulated by SET and the state dynamics postulated by LeT are probably incorrect. In the third part, we propose a hybrid model that may improve on its parents. The hybrid model accounts for the typical findings in fixed-interval schedules, the peak procedure, mixed fixed interval schedules, simple and double temporal bisection, and temporal generalization tasks. In the fourth and last part, we identify seven challenges that any timing model must meet.

Abstract:Purpose: Project-Based Learning (PBL) is considered to be an active learning methodology which can be used to develop both technical and transversal competences in engineering programs. This methodology demands a great deal of work effort from the students and also from the teachers and it requires a meticulous plan and a well-managed project as well. These activities go far beyond the normal activities in traditional lectures, enabling to outpace the difficulties that spur along the way that may be both complex and demotivating. This The aim of this paper is to identify and discuss the main difficulties of the implementation of PBL, mainly from the teachers' perspectives. Additionally, some effective strategies will be recommended to overcome such difficulties. Findings: Integration of courses in the project; student assessment; growing number of students in each team and the need of physical spaces for them; and compartmentalized knowledge has emerged as the main difficulties. To overcome these difficulties some key strategies were recommended.Originality/value: A new perspective based on course teachers' views and experiences will deepen the understanding of the problems and provide inputs for the development of strategies that may improve the effectiveness of PBL and introduce changes for its successful implementation. These strategies are intended to be transferable to other contexts, as most of the problems and constraints are common to other active learning approaches.

Abstract. This paper considers model spaces in an H p setting. The existence of unbounded functions and the characterisation of maximal functions in a model space are studied, and decomposition results for Toeplitz kernels, in terms of model spaces, are established.Mathematics subject classification (2010): 47B35, 30H10.

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We consider kernels of unbounded Toeplitz operators in $$H^p({\mathbb {C}}^{+})$$ H p ( C + ) in terms of a factorization of their symbols. We study the existence of a minimal Toeplitz kernel containing a given function in $$H^p({\mathbb {C}}^{+})$$ H p ( C + ) , we describe the kernels of Toeplitz operators whose symbol possesses a certain factorization involving two different Hardy spaces and we establish relations between the kernels of two operators whose symbols differ by a factor which corresponds, in the unit circle, to a non-integer power of z. We apply the results to describe the kernels of Toeplitz operators with non-vanishing piecewise continuous symbols.