On proximity and hierarchy : exploring and modelling space using multilevel modelling and spatial econometrics

Spatial econometrics and also multilevel modelling techniques are increasingly part of the regional scientists‟ toolbox. Both approaches are used to model spatial autocorrelation in a wide variety of applications. However, it is not always clear on which basis researchers make a choice between spatial econometrics and spatial multilevel modelling. Therefore it is useful to compare both techniques. Spatial econometrics incorporates neighbouring areas into the model design; and thus interprets spatial proximity as defined in Tobler‟s first law of geography. On the other hand, multilevel modelling using geographical units takes a more hierarchical approach. In this case the first law of geography can be rephrased as „everything is related to everything else, but things in the same region are more related than things in different regions‟. The hierarchy (multilevel) and the proximity (spatial econometrics) approach are illustrated using Belgian mobility data and productivity data of European regions. One of the advantages of a multilevel model is that it can incorporate more than two levels (spatial scales). Another advantage is that a multilevel structure can easily reflect an administrative structure with different government levels. Spatial econometrics on the other hand works with a unique set of neighbours which has the advantage that there still is a relation between neighbouring municipalities separated by a regional boundary. The concept of distance can also more easily be incorporated in a spatial econometrics setting. Both spatial econometrics and spatial multilevel modelling proved to be valuable techniques in spatial research but more attention should go to the rationale why one of the two approaches is chosen. We conclude with some comments on models which make a combination of both techniques

An Analytical Study of Large SPARQL Query Logs

With the adoption of RDF as the data model for Linked Data and the Semantic Web, query specification from end- users has become more and more common in SPARQL end- points. In this paper, we conduct an in-depth analytical study of the queries formulated by end-users and harvested from large and up-to-date query logs from a wide variety of RDF data sources. As opposed to previous studies, ours is the first assessment on a voluminous query corpus, span- ning over several years and covering many representative SPARQL endpoints. Apart from the syntactical structure of the queries, that exhibits already interesting results on this generalized corpus, we drill deeper in the structural char- acteristics related to the graph- and hypergraph represen- tation of queries. We outline the most common shapes of queries when visually displayed as pseudographs, and char- acterize their (hyper-)tree width. Moreover, we analyze the evolution of queries over time, by introducing the novel con- cept of a streak, i.e., a sequence of queries that appear as subsequent modifications of a seed query. Our study offers several fresh insights on the already rich query features of real SPARQL queries formulated by real users, and brings us to draw a number of conclusions and pinpoint future di- rections for SPARQL query evaluation, query optimization, tuning, and benchmarking

On the profile of sign changing solutions of an almost critical problem in the ball

We study the existence and the profile of sign-changing solutions to the slightly subcritical problem -\De u=|u|^{2^*-2-\eps}u \hbox{in} \cB, \quad u=0 \hbox{on}\partial \cB, where \cB is the unit ball in \rr^N, $N\geq 3$, $2^*=\frac{2N}{N-2}$ and \eps>0 is a small parameter. Using a Lyapunov-Schmidt reduction we discover two new non-radial solutions having 3 bubbles with different nodal structures. An interesting feature is that the solutions are obtained as a local minimum and a local saddle point of a reduced function, hence they do not have a global min-max description.Comment: 3 figure

Odd-petal states and persistent flows in spin-orbit-coupled Bose-Einstein condensates

We study the phase diagram of a Rashba spin-orbit-coupled Bose-Einstein condensate confined in a two-dimensional toroidal trap. In the immiscible regime we find an azimuthally periodic density distribution, with the periodicity highly tuneable as a function of the spin-orbit coupling strength and which favours an odd number of petals in each component. This allows for a wide range of states that can be created. We further show that in the miscible regime, both components possess states with persistent flows with a unit winding number difference between them and with the absolute values of these winding numbers depending on the spin-orbit coupling strength. All features of the odd-petal and the persistent flow states can be explained using a simple but effective model.Comment: 5 pages, 2 figure