A Cooperative Development System for an Interactive Introductory Programming Course

We present a system for a cooperative development of computer programs that was created for the lab sessions of an introductory programming course at the University of Ljubljana, Slovenia. The system relieved the students from the tedious task of retyping programs developed by the teaching assistant and enabled them to cooperate with the teaching assistant in solving programming problems. We thus made the lab sessions more efficient and interactive and brought them closer to the spirit of active learning approaches

On a Linear Program for Minimum-Weight Triangulation

Minimum-weight triangulation (MWT) is NP-hard. It has a polynomial-time constant-factor approximation algorithm, and a variety of effective polynomial- time heuristics that, for many instances, can find the exact MWT. Linear programs (LPs) for MWT are well-studied, but previously no connection was known between any LP and any approximation algorithm or heuristic for MWT. Here we show the first such connections: for an LP formulation due to Dantzig et al. (1985): (i) the integrality gap is bounded by a constant; (ii) given any instance, if the aforementioned heuristics find the MWT, then so does the LP.Comment: To appear in SICOMP. Extended abstract appeared in SODA 201

On a linear program for minimum-weight triangulation

Minimum-weight triangulation (MWT) is NP-hard. It has a polynomial-time constant-factor approximation algorithm, and a variety of effective polynomial-time heuristics that, for many instances, can find the exact MWT. Linear programs (LPs) for MWT are well-studied, but previously no connection was known between any LP and any approximation algorithm or heuristic for MWT. Here we show the first such connections: For an LP formulation due to Dantzig, Hoffman, and Hu [Math. Programming, 31 (1985), pp. 1-14], (i) the integrality gap is constant, and (ii) given any instance, if the aforementioned heuristics find the MWT, then so does the LP. © 2014 Society for Industrial and Applied Mathematics

Dense Motion Estimation for Smoke

Motion estimation for highly dynamic phenomena such as smoke is an open challenge for Computer Vision. Traditional dense motion estimation algorithms have difficulties with non-rigid and large motions, both of which are frequently observed in smoke motion. We propose an algorithm for dense motion estimation of smoke. Our algorithm is robust, fast, and has better performance over different types of smoke compared to other dense motion estimation algorithms, including state of the art and neural network approaches. The key to our contribution is to use skeletal flow, without explicit point matching, to provide a sparse flow. This sparse flow is upgraded to a dense flow. In this paper we describe our algorithm in greater detail, and provide experimental evidence to support our claims.Comment: ACCV201

Minimum-weight triangulation is NP-hard

A triangulation of a planar point set S is a maximal plane straight-line graph with vertex set S. In the minimum-weight triangulation (MWT) problem, we are looking for a triangulation of a given point set that minimizes the sum of the edge lengths. We prove that the decision version of this problem is NP-hard. We use a reduction from PLANAR-1-IN-3-SAT. The correct working of the gadgets is established with computer assistance, using dynamic programming on polygonal faces, as well as the beta-skeleton heuristic to certify that certain edges belong to the minimum-weight triangulation.Comment: 45 pages (including a technical appendix of 13 pages), 28 figures. This revision contains a few improvements in the expositio

Pragmatic Isomorphism Proofs Between Coq Representations: Application to Lambda-Term Families

There are several ways to formally represent families of data, such as lambda terms, in a type theory such as the dependent type theory of Coq. Mathematical representations are very compact ones and usually rely on the use of dependent types, but they tend to be difficult to handle in practice. On the contrary, implementations based on a larger (and simpler) data structure combined with a restriction property are much easier to deal with. In this work, we study several families related to lambda terms, among which Motzkin trees, seen as lambda term skeletons, closable Motzkin trees, corresponding to closed lambda terms, and a parameterized family of open lambda terms. For each of these families, we define two different representations, show that they are isomorphic and provide tools to switch from one representation to another. All these datatypes and their associated transformations are implemented in the Coq proof assistant. Furthermore we implement random generators for each representation, using the QuickChick plugin

On the closed Ramsey numbers Rcl(ω+n,3)R^{cl}(\omega+n,3)

In this paper, we contribute to the study of topological partition relations for pairs of countable ordinals and prove that, for all integers $n \geq 3$, \begin{align*} R^{cl}(\omega+n,3) &\geq \omega^2 \cdot n + \omega \cdot (R(n,3)-n)+n\\ R^{cl}(\omega+n,3) &\leq \omega^2 \cdot n + \omega \cdot (R(2n-3,3)+1)+1 \end{align*} where $R^{cl}(\cdot,\cdot)$ and $R(\cdot,\cdot)$ denote the closed Ramsey numbers and the classical Ramsey numbers respectively. We also establish the following asymptotically weaker upper bound $$R^{cl}(\omega+n,3) \leq \omega^2 \cdot n + \omega \cdot (n^2-4)+1$$ eliminating the use of Ramsey numbers. These results improve the previously known upper and lower bounds

Height at the withers estimation in the horses based on the internal dimension of cranial cavity

The investigations were carried out on 17 modern half-breed horse skulls and their metacarpal and metatarsal bones. The basal length (BL), total length (TL), internal cranial cavity dimension and maximal length of metacarpus and metatarsus and maximal lateral length of metacarpus and metatarsus were measured according to Kiesewalter and von den Driesch. During height at the withers estimation, the Kiesewaler and Vitt methods were used. The Wyrost and Kucharczyk mathematical formula was modified for height at the withers calculation (Hestmd = 1.016 × D) in horses. All height at the withers estimation methods were statistically analysed and compared. The analysis of variance ANOVA proved the lack of significant difference between the investigated values. The results achieved using Wyrost and Kucharczyk modified method are strongly comparable to Kiesewalter methods results computed using the metacarpal and metatarsal bones measurements. The height at the withers calculated on the basis of TL slightly differs from 2 above-mentioned methods. The BL Vitt’s method was the least exact

A Cooperative Development System for an Interactive Introductory Programming Course

We present a system for a cooperative development of computer programs that was created for the lab sessions of an introductory programming course at the University of Ljubljana, Slovenia. The system relieved the students from the tedious task of retyping programs developed by the teaching assistant and enabled them to cooperate with the teaching assistant in solving programming problems. We thus made the lab sessions more efficient and interactive and brought them closer to the spirit of active learning approaches