Global existence and blow-up of solutions for a general class of doubly dispersive nonlocal nonlinear wave equations

This study deals with the analysis of the Cauchy problem of a general class of nonlocal nonlinear equations modeling the bi-directional propagation of dispersive waves in various contexts. The nonlocal nature of the problem is reflected by two different elliptic pseudodifferential operators acting on linear and nonlinear functions of the dependent variable, respectively. The well-known doubly dispersive nonlinear wave equation that incorporates two types of dispersive effects originated from two different dispersion operators falls into the category studied here. The class of nonlocal nonlinear wave equations also covers a variety of well-known wave equations such as various forms of the Boussinesq equation. Local existence of solutions of the Cauchy problem with initial data in suitable Sobolev spaces is proven and the conditions for global existence and finite-time blow-up of solutions are established.Comment: 17 page

Characterizing lab instructors' self-reported learning goals to inform development of an experimental modeling skills assessment

The ability to develop, use, and refine models of experimental systems is a nationally recognized learning outcome for undergraduate physics lab courses. However, no assessments of students' model-based reasoning exist for upper-division labs. This study is the first step toward development of modeling assessments for optics and electronics labs. In order to identify test objectives that are likely relevant across many institutional contexts, we interviewed 35 lab instructors about the ways they incorporate modeling in their course learning goals and activities. The study design was informed by the Modeling Framework for Experimental Physics. This framework conceptualizes modeling as consisting of multiple subtasks: making measurements, constructing system models, comparing data to predictions, proposing causes for discrepancies, and enacting revisions to models or apparatus. We found that each modeling subtask was identified by multiple instructors as an important learning outcome for their course. Based on these results, we argue that test objectives should include probing students' competence with most modeling subtasks, and test items should be designed to elicit students' justifications for choosing particular modeling pathways. In addition to discussing these and other implications for assessment, we also identify future areas of research related to the role of modeling in optics and electronics labs.Comment: 24 pages, 2 figures, 5 tables; submitted to Phys. Rev. PE

Contextual Attention Recurrent Architecture for Context-aware Venue Recommendation

Venue recommendation systems aim to effectively rank a list of interesting venues users should visit based on their historical feedback (e.g. checkins). Such systems are increasingly deployed by Location-based Social Networks (LBSNs) such as Foursquare and Yelp to enhance their usefulness to users. Recently, various RNN architectures have been proposed to incorporate contextual information associated with the users' sequence of checkins (e.g. time of the day, location of venues) to effectively capture the users' dynamic preferences. However, these architectures assume that different types of contexts have an identical impact on the users' preferences, which may not hold in practice. For example, an ordinary context such as the time of the day reflects the user's current contextual preferences, whereas a transition context - such as a time interval from their last visited venue - indicates a transition effect from past behaviour to future behaviour. To address these challenges, we propose a novel Contextual Attention Recurrent Architecture (CARA) that leverages both sequences of feedback and contextual information associated with the sequences to capture the users' dynamic preferences. Our proposed recurrent architecture consists of two types of gating mechanisms, namely 1) a contextual attention gate that controls the influence of the ordinary context on the users' contextual preferences and 2) a time- and geo-based gate that controls the influence of the hidden state from the previous checkin based on the transition context. Thorough experiments on three large checkin and rating datasets from commercial LBSNs demonstrate the effectiveness of our proposed CARA architecture by significantly outperforming many state-of-the-art RNN architectures and factorisation approaches