On the Generalized Poisson Distribution

The Generalized Poisson Distribution (GPD) was introduced by Consul and Jain (1973). However, as remarked by Consul (1989), "It is very difficult to prove by direct summation that the sum of all the probabilities is unity". We give a shorter and more elegant proof based upon an application of Euler's classic difference lemma.Comment: 3 page

Minimum L1-distance projection onto the boundary of a convex set: Simple characterization

We show that the minimum distance projection in the L1-norm from an interior point onto the boundary of a convex set is achieved by a single, unidimensional projection. Application of this characterization when the convex set is a polyhedron leads to either an elementary minmax problem or a set of easily solved linear programs, depending upon whether the polyhedron is given as the intersection of a set of half spaces or as the convex hull of a set of extreme points. The outcome is an easier and more straightforward derivation of the special case results given in a recent paper by Briec.Comment: 5 page

Inquiry-based science teasching competence of pre-service primary teachers

In recent years, improving primary science education has received considerable attention. In particular, researchers and policymakers advocate the use of inquiry-based science teaching and learning, believing that pupils learn best through direct personal experience and by incorporating new information into their existing knowledge base. Therefore, corresponding educational paradigms have shifted from merely reproducing knowledge to asking scientifically oriented questions and searching for evidence when responding to those questions. This approach is considered to be the starting point for motivating pupils to apply research skills, construct meaning, and acquire scientific knowledge. Teachers’ competencies are essential for increasing pupils’ learning and for stimulating their interest in science. Research has indicated that primary school teachers find it difficult to become effective inquiry-based science teachers because they often lack key knowledge regarding how science inquiry works and—in particular—how to implement inquiry-based teaching in their classrooms (Lee, Hart, Cuevas & Enders, 2004; Van Zee et al., 2005; McDonald, 2009). In the absence of these key competencies, qualitatively poor or insufficient guidance and insufficient feedback could be received during the discovery process. High-quality teacher education that yields competent teachers is the foundation of any system of formal education. However, the Netherlands lacks a recent formal agreement between professionals regarding the competencies that teachers need in order to teach inquiry-based primary science. In light of this issue, this thesis has two key aims. The first aim is to clarify which competencies are needed in order to teach inquiry-based primary science. The second aim is to determine how various components of science-teaching competence are related. The first aim was achieved by performing a literature study and a Delphi study, and the second aim was achieved by performing empirical studies using a knowledge test, a list of attitude questions, and a case-based questionnaire designed to assess Pedagogical Content Knowledge (PCK)

Pattern Reduction in Paper Cutting

A large part of the paper industry involves supplying customers with reels of specified width in specifed quantities. These 'customer reels' must be cut from a set of wider 'jumbo reels', in as economical a way as possible. The first priority is to minimize the waste, i.e. to satisfy the customer demands using as few jumbo reels as possible. This is an example of the one-dimensional cutting stock problem, which has an extensive literature. Greycon have developed cutting stock algorithms which they include in their software packages. Greycon's initial presentation to the Study Group posed several questions, which are listed below, along with (partial) answers arising from the work described in this report. (1) Given a minimum-waste solution, what is the minimum number of patterns required? It is shown in Section 2 that even when all the patterns appearing in minimum-waste solutions are known, determining the minimum number of patterns may be hard. It seems unlikely that one can guarantee to find the minimum number of patterns for large classes of realistic problems with only a few seconds on a PC available. (2) Given an n → n-1 algorithm, will it find an optimal solution to the minimum- pattern problem? There are problems for which n → n - 1 reductions are not possible although a more dramatic reduction is. (3) Is there an efficient n → n-1 algorithm? In light of Question 2, Question 3 should perhaps be rephrased as 'Is there an efficient algorithm to reduce n patterns?' However, if an algorithm guaranteed to find some reduction whenever one existed then it could be applied iteratively to minimize the number of patterns, and we have seen this cannot be done easily. (4) Are there efficient 5 → 4 and 4 → 3 algorithms? (5) Is it worthwhile seeking alternatives to greedy heuristics? In response to Questions 4 and 5, we point to the algorithm described in the report, or variants of it. Such approaches seem capable of catching many higher reductions. (6) Is there a way to find solutions with the smallest possible number of single patterns? The Study Group did not investigate methods tailored specifically to this task, but the algorithm proposed here seems to do reasonably well. It will not increase the number of singleton patterns under any circumstances, and when the number of singletons is high there will be many possible moves that tend to eliminate them. (7) Can a solution be found which reduces the number of knife changes? The algorithm will help to reduce the number of necessary knife changes because it works by bringing patterns closer together, even if this does not proceed fully to a pattern reduction. If two patterns are equal across some of the customer widths, the knives for these reels need not be changed when moving from one to the other

A regional ocean circulation model for the mid-Cretaceous North Atlantic Basin: implications for black shale formation

High concentrations of organic matter accumulated in marine sediments during Oceanic Anoxic Events (OAEs) in the Cretaceous. Model studies examining these events invariably make use of global ocean circulation models. In this study, a regional model for the North Atlantic Basin during OAE2 at the Cenomanian-Turonian boundary has been developed. A first order check of the results has been performed by comparison with the results of a recent global Cenomanian CCSM3 run, from which boundary and initial conditions were obtained. The regional model is able to maintain tracer patterns and to produce velocity patterns similar to the global model. The sensitivity of the basin tracer and circulation patterns to changes in the geometry of the connections with the global ocean is examined with three experiments with different bathymetries near the sponges. Different geometries turn out to have little effect on tracer distribution, but do affect circulation and upwelling patterns. The regional model is also used to test the hypothesis that ocean circulation may have been behind the deposition of black shales during OAEs. Three scenarios are tested which are thought to represent pre-OAE, OAE and post-OAE situations. Model results confirm that Pacific intermediate inflow together with coastal upwelling could have enhanced primary production during OAE2. A low sea level in the pre-OAE scenario could have inhibited large scale black shale formation, as could have the opening of the Equatorial Atlantic Seaway in the post-OAE scenario