Invention of new statements for counterexamples

ArticleLiljedahl, P., Oesterle, S., Nicol, C., & Allan, D. (Eds.). (2014). Proceedings of the Joint Meeting of PME 38 and PME-NA 36 (Vol. 4):17-24 . Vancouver, Canada: PME.conference pape

Rethinking the discovery function of proof within the context of proofs and refutations

Proof and proving are important components of school mathematics and have multiple functions in mathematical practice. Among these functions of proof, this paper focuses on the discovery function that refers to invention of a new statement or conjecture by reflecting on or utilizing a constructed proof. Based on two cases in which eighth and ninth graders engaged in proofs and refutations, we demonstrate that facing a counterexample of a primitive statement can become a starting point of students’ activity for discovery, and that a proof of the primitive statement can function as a useful tool for inventing a new conjecture that holds for the counterexample. An implication for developing tasks by which students can experience this discovery function is mentioned.ArticleInternational Journal of Mathematical Education in Science and Technology. 45(7):1053-1067 (2014)journal articl

Interface reconstruction in superconducting CaCuO2/SrTiO3 superlattices: A hard x-ray photoelectron spectroscopy study

Here we report about the interface reconstruction in the recently discovered superconducting artificial superlattices based on insulating CaCuO2 and SrTiO3 blocks. Hard x-ray photoelectron spectroscopy shows that the valence bands alignment prevents any electronic reconstruction by direct charge transfer between the two blocks. We demonstrate that the electrostatic built-in potential is suppressed by oxygen redistribution in the alkaline earth interface planes. By using highly oxidizing growth conditions, the oxygen coordination in the reconstructed interfaces may be increased, resulting in the hole doping of the cuprate block and thus in the appearance of superconductivity.Comment: 9 pages, 6 figure

GDOM: Granulometry for the Detection of Obfuscated Malware

We describe the results of a master\u27s thesis in malware detection and discuss the connection to the learning goals of the project. As part of the thesis, we studied obfuscation of malware, conversion of files into images, image processing, and machine learning, a process of benefit to both the student and faculty. Malware detection becomes significantly more difficult when the malicious specimen is obfuscated or transformed in an attempt to avoid detection. However, computer files have been shown to exhibit evidence of structure when converted into images, so with image processing filters such as granulometry, it is possible to generate a set of features which will help characterize malicious and non-malicious files. If the structures of file-derived images are resistant to obfuscation, these images may be of valuable use in providing malware signatures. We explore image generated file features and their effectiveness to identify malware when used with various machine learning classifiers

Pulsed laser deposition of SrTiO3/LaGaO3 and SrTiO3/LaAlO3: plasma plume effects

Pulsed laser deposition of SrTiO3/LaGaO3 and SrTiO3/LaAlO3 interfaces has been analyzed with a focus on the kinetic energy of the ablated species. LaGaO3 and LaAlO3 plasma plumes were studied by fast photography and space-resolved optical emission spectroscopy. Reflection high energy electron diffraction was performed proving a layer-by-layer growth up to 10-1 mbar oxygen pressure. The role of the energetic plasma plume on the two-dimensional growth and the presence of interfacial defects at different oxygen growth pressure has been discussed in view of the conducting properties developing at such polar/non-polar interfaces

Proof problems with diagrams: An opportunity for experiencing proofs and refutations

It has become gradually accepted that proof and proving are essential at all grades of mathematical learning. Among the various aspects of proof and proving, this study addresses proofs and refutations described by Lakatos, in particular a part of increasing content by deductive guessing, to introduce an authentic process into mathematics classrooms. This paper analyzes proof problems with diagrams as an appropriate task for this mathematical action, and illustrates, with a sequence of three lessons in the eighth grade, that a certain type of such problems can provide students with an opportunity to engage in this action.ArticleFor the Learning of Mathematics. 34(1):36-42 (2014)journal articl

PEDF Promotes Retinal Neurosphere Formation and Expansion In Vitro

The retina is subject to degenerative conditions leading to blindness. Although retinal regeneration is possible in lower vertebrates, it does not occur in the adult mammalian retina. Retinal stem cell (RSC) research offers unique opportunities for developing clinical application for therapy. The ciliary body of adult mammals represents a source of quiescent RSC. These neural progenitors have a limited self-renewal potential in vitro but this can be improved by mitogens. Pigment Epithelium Derived Factor (PEDF), a member of the serpin gene family, is synthesized and secreted by retinal pigment epithelium (RPE) cells. We tested combinations of PEDF with fibroblast growth factor (FGF) during RSC growth to evaluate self-renewal and subsequent differentiation into retinal-like neuronal cell types. Medium supplemented with FGF + PEDF enhanced the RSC yield and more interestingly allowed expansion of the culture by increasing secondary retinal neurospheres after the 1st passage. This effect was accompanied by cell proliferation as revealed by BrdU incorporation. PEDF usage did not affect rod-like differentiation potential. This was demonstrated by immunofluorescence analysis of Rhodopsin and Pde6b that were found similarly expressed in cells derived from FGF or FGF + PEDF cultured RSC. Our studies suggest a possible application of PEDF in Retinal Stem Cell culture and transplantation