Output-sensitive autocompletion search

We consider the following autocompletion search scenario: imagine a user of a search engine typing a query; then with every keystroke display those completions of the last query word that would lead to the best hits, and also display the best such hits. The following problem is at the core of this feature: for a fixed document collection, given a set D of documents, and an alphabetical range W of words, compute the set of all word-in-document pairs (w, d) from the collection such that w ∈ W and d ∈ D. We present a new data structure with the help of which such autocompletion queries can be processed, on the average, in time linear in the input plus output size, independent of the size of the underlying document collection. At the same time, our data structure uses no more space than an inverted index. Actual query processing times on a large test collection correlate almost perfectly with our theoretical bound.

Student difficulty in constructing proofs: The need for strategic knowledge

The ability to construct proofs is an important skill for all mathematicians. Despite its importance, students have great difficulty with this task. In this paper, I first demonstrate that undergraduates often are aware of and able to apply the facts required to prove a statement but still fail to prove it. They thus fail to construct a proof because they could not use the syntactic knowledge that they had. By comparing doctoral students and undergraduates constructing proofs in abstract algebra, I have hypothesized four types of `strategic knowledge' – knowledge of how to choose which facts and theorems to apply – which the doctoral students appeared to possess and undergraduates did not. The doctoral students appeared to know the powerful proof techniques in abstract algebra, which theorems are most important, when particular facts and theorems are likely to be useful, and when one should or should not try and prove theorems using symbol manipulation. This revised version was published online in July 2006 with corrections to the Cover Date.     

Privacy: an institutional fact

Let us show how property is grasped as an institutional fact. If Jones steals a computer, he does not own it in the sense of property, but only exercises control towards it. If he buys the computer, he controls it too, and moreover owns it in the sense of property. In other words, simply exercising control towards something is a brute fact. This control counts as property only in a certain context: the computer counts as Jones’s property only if he got it through a licit transfer. This is why property is not a brute fact, and is therefore an institutional fact. The same kind of reasoning applies to privacy. When a personal information P about Jones is openly diffused, it seems that P becomes public. From this point of view, a violation of privacy equates to a publication. The problem about this account is the following: who would call “publication of a book” the hacking of it on its author’s computer? No one, because the word “publication” is an institutional word that only refers to a licit diffusion. Considering this answer, we may conclude as follows: if the diffusion of P is illicit, P still counts as private, even if everyone knows about it. If that conclusion is true, privacy is an institutional fact.     

Factors mathematicians profess to consider when presenting pedagogical proofs

This paper concerns proof presentation at the university level. We report on a study in which we observed ten mathematicians constructing or revising proofs for pedagogical purposes. We highlight the factors that they claimed to consider when completing these tasks. We found that intended audience and medium (lecture or textbook) influenced proof presentation. We also found that, although mathematicians generally valued pedagogical proofs featuring diagrams and emphasizing main ideas, these mathematicians did not always incorporate these aspects in the proofs they constructed or revised.     

Why and how mathematicians read proofs: further evidence from a survey study

In a recent paper (Weber & Mejia-Ramos, Educational Studies in Mathematics, 76, 329–344, 2011), we reported findings from two small-scale interview studies on the reasons why and the ways in which mathematicians read proofs. Based on these findings, we designed an Internet-based survey that we distributed to practicing mathematicians working in top mathematics departments in the USA. Surveyed mathematicians (N?=?118) agreed to a great extent with the interviewed mathematicians in the exploratory studies. First, the mathematicians reported that they commonly read published proofs to gain different types of insight, not to check the correctness of the proofs. Second, they stated that when reading these proofs, they commonly: (a) appeal to the reputation of the author and the journal, (b) study how certain steps in the proof apply to specific examples, and (c) focus on the overarching ideas and methods in the proofs. In this paper, we also report findings from another section of the survey that focused on how participants reviewed proofs submitted for publication. The comparison of participant responses to questions in these two sections of the survey suggests that reading a published proof of a colleague and refereeing a proof for publication are substantially different activities for mathematicians.     

Physical performance in female handball players according to playing position

Demands for female handball players are not yet sufficiently specified, especially not with respect to position-specific performance. For optimal match preparation, individual training based on specific demands of each position is necessary. Consequently, the aim of the study was to gain insight into position-specific differences in female handball players in order to establish position-specific training recommendations. Data from 652 female players from German leagues of all levels were analyzed using a test-battery assessing handball-relevant physical performance factors. Players were tested during their usual training in their regular training locations for running, throwing speed, jumping height, reaction-speed, basic running endurance, arm and abdominal muscle strength and hamstrings and lower back flexibility. Significant differences between positions were found for several parameters, while the differences were pronounced variably at the different performance levels. For example, goalkeepers performed worst in the Half-Cooper test (p?<?0.001) at elite level with wings displaying the best values. Halfbacks had the highest throwing speed (p?<?0.001) and jumping heights (p?<?0.002) at elite level. Goalkeepers were slowest for best and mean value out of five attempts (p?<?0.001; p?<?0.010) in 20?m sprint but, together with wings outperformed half and centre backs at elite level in 30?m sprint (best out of two attempts, p?<?0.001). Goalkeepers also did fewer chin ups than wing and back players at elite level (p?<?0.003). The present study demonstrated positional differences regarding physical performance parameters, thus suggesting the need to intensify position-specific training, especially for goalkeepers during preparation and in-season. Also, position-specific testing during selection-processes might be indicated.