The task of quantizing general relativity raises serious questions about the meaning of the present formulation and interpretation of quantum mechanics when applied to so fundamental a structure as the space-time geometry itself. This paper seeks to clarify the foundations of quantum mechanics. It presents a reformulation of quantum theory in a form believed suitable for application to general relativity. The aim is not to deny or contradict the conventional formulation of quantum theory, which has demonstrated its usefulness in an overwhelming variety of problems, but rather to supply a new, more general and complete formulation, from which the conventional interpretation can be deduced. The relationship of this new formulation to the older formulation is therefore that of a metatheory to a theory, that is, it is an underlying theory in which the nature and consistency, as well as the realm of applicability, of the older theory can be investigated and clarified.

"relative State" Formulation of Quantum Mechanics

Computational geometry

The Fabric of Reality

Blocks-based programming environments are becoming increasingly common in introductory programming courses, but to date, little comparative work has been done to understand if and how this approach affects students' emerging understanding of fundamental programming concepts. In an effort to understand how tools like Scratch and Blockly differ from more conventional text-based introductory programming languages with respect to conceptual understanding, we developed a set of "commutative" assessments. Each multiple-choice question on the assessment includes a short program that can be displayed in either a blocks- based or text-based form. The set of potential answers for each question includes the correct answer along with choices informed by prior research on novice programming misconceptions. In this paper we introduce the Commutative Assessment, discuss the theoretical and practical motivations for the assessment, and present findings from a study that used the assessment. The study had 90 high school students take the assessment at three points over the course of the first ten weeks of an introduction to programming course, alternating the modality (blocks vs. text) for each question over the course of the three administrations of the assessment. Our analysis reveals differences on performance between blocks-based and text-based questions as well as differences in the frequency of misconceptions based on the modality. Future work, potential implications, and limitations of these findings are also discussed.

Using Commutative Assessments to Compare Conceptual Understanding in Blocks-based and Text-based Programs

Several routing schemes in ad hoc networks first establish a virtual backbone and then route messages via back-bone nodes. One common way of constructing such a backbone is based on the construction of a minimum connected dominating set (CDS). In this paper we present a very simple distributed algorithm for computing a small CDS. Our algorithm has an approximation factor of at most 6.91, improving upon the previous best known approximation factor of 8 due to Wan et al. [INFOCOM'02], The improvement relies on a refined analysis of the relationship between the size of a maximal independent set and a minimum CDS in a unit disk graph. This subresult also implies improved approximation factors for many existing algorithm.

A Simple Improved Distributed Algorithm for Minimum CDS in Unit Disk Graphs

Research on the effectiveness of introductory programming environments often relies on post-test measures and attitudinal surveys to support its claims; but such instruments lack the ability to identify any explanatory mechanisms that can account for the results. This paper reports on a study designed to address this issue. Using Noss and Hoyles' constructs of webbing and situated abstractions, we analyze programming novices playing a program-to-play constructionist video game to identify how features of introductory programming languages, the environments in which they are situated, and the challenges learners work to accomplish, collectively affect novices' emerging understanding of programming concepts. Our analysis shows that novices de- velop the ability to use programming concepts by building on the suite of resources provided as they interact with the computational context of the learning environment. In taking this approach, we contribute to computer science education design literature by advancing our understanding of the relationship between rich, complex introductory programming environments and the learning experiences they promote.

/pdf/collaboration-collusion-and-plagiarism-in-computer-science-4agifxm9od.pdf

Collaboration, Collusion and Plagiarism in Computer Science Coursework.

Given a set P of n points and a set D of m unit disks on a 2-dimensional plane, the discrete unit disk cover (DUDC) problem is (i) to check whether each point in P is covered by at least one disk in D or not and (ii) if so, then find a minimum cardinality subset D* ⊆ D such that unit disks in D* cover all the points in P. The discrete unit disk cover problem is a geometric version of the general set cover problem which is NP-hard [14]. The general set cover problem is not approximable within c log |P|, for some constant c, but the DUDC problem was shown to admit a constant factor approximation. In this paper, we provide an algorithm with constant approximation factor 18. The running time of the proposed algorithm is O(n log n+m log m+mn). The previous best known tractable solution for the same problem was a 22-factor approximation algorithm with running time O(m2n4).

/pdf/on-the-discrete-unit-disk-cover-problem-2n2gqxd1vl.pdf

On the discrete unit disk cover problem

Given a set of n points and a set of m unit disks on a 2-dimensional plane, the discrete unit disk cover (DUDC) problem is (i) to check whether each point in is covered by at least one disk in or not and (ii) if so, then find a minimum cardinality subset such that the unit disks in cover all the points in . The discrete unit disk cover problem is a geometric version of the general set cover problem which is NP-hard. The general set cover problem is not approximable within , for some constant c, but the DUDC problem was shown to admit a constant factor approximation. In this paper, we provide an algorithm with constant approximation factor 18. The running time of the proposed algorithm is . The previous best known tractable solution for the same problem was a 22-factor approximation algorithm with running time .

Given a set ${\mathcal D}$ of m unit disks and a set ${\mathcal P}$ of n points in the plane, the discrete unit disk cover problem is to select a minimum cardinality subset ${\mathcal D}' \subseteq {\mathcal D}$ to cover ${\mathcal P}$. This problem is NP-hard [14] and the best previous practical solution is a 38-approximation algorithm by Carmi et al. [5]. We first consider the line-separable discrete unit disk cover problem (the set of disk centers can be separated from the set of points by a line) for which we present an O(n(log n + m))-time algorithm that finds an exact solution. Combining our line-separable algorithm with techniques from the algorithm of Carmi et al. [5] results in an O(m2n4) time 22-approximate solution to the discrete unit disk cover problem.

/pdf/an-improved-line-separable-algorithm-for-discrete-unit-disk-5b1zuxz3kb.pdf

An improved line-separable algorithm for discrete unit disk cover

We study optimization problems for the Euclidean Minimum Spanning Tree (MST) problem on imprecise data. To model imprecision, we accept a set of disjoint disks in the plane as input. From each member of the set, one point must be selected, and the MST is computed over the set of selected points. We consider both minimizing and maximizing the weight of the MST over the input. The minimum weight version of the problem is known as the Minimum Spanning Tree with Neighborhoods (MSTN) problem, and the maximum weight version (max-MSTN) has not been studied previously to our knowledge. We provide deterministic and parameterized approximation algorithms for the max-MSTN problem, and a parameterized algorithm for the MSTN problem. Additionally, we present hardness of approximation proofs for both settings.

https://web.cs.dal.ca/~mhe/publications/wowa12_spanningtree.pdf

Robert Fraser

Papers

Collaboration, Collusion and Plagiarism in Computer Science Coursework.

On the discrete unit disk cover problem

On the discrete unit disk cover problem

An improved line-separable algorithm for discrete unit disk cover

On Minimum- and Maximum-Weight Minimum Spanning Trees with Neighborhoods