Windows into Elementary Mathematics:Alternate public images of mathematics and mathematicians

Research on students’ (and teachers’) images of mathematics and mathematicians reveals a number of stereotypical images, most of which are negative. In this paper we present an overview of some these images and stereotypes and consider the questions: (1) how might the image of mathematics and mathematicians be a problem in mathematics education, and (2) what can be done to remedy the situation? Also, we consider an outreach project called Windows into Elementary Mathematics. In this project mathematicians are interviewed about their perspectives on elementary mathematics topics and their interviews are videotaped and are posted online, along with supporting images and interactive content. In this context we consider the questions: (3) what is the Windows project about, and (4) how might it offer an alternate (and perhaps better) image of mathematics and mathematicians? Lastly, we share an example where activities from the project were used in a math-for-teachers course.

Os álbuns fotojornalísticos online e a construção do acontecimento: atribuições de sentido a partir da composição imagética dos protestos de junho

Given that the choices involved in the selection of compositional techniques in photography are mediated by values, this article aims to analyze the compositional techniques of photographs published by photojournalistic online albums during the protests of June 2013 in Brazil. These albums feature professional and amateur photographs considered "the best" of this event and, interestingly, the chosen photographs have several composition techniques in common. We will examine these images from the perspective of significant effects that these techniques engender with the objective of examining the meanings that were attributed to that event in those albums.

Automatic lumen segmentation in IVOCT images using binary morphological reconstruction

Abstract Background Atherosclerosis causes millions of deaths, annually yielding billions in expenses round the world. Intravascular Optical Coherence Tomography (IVOCT) is a medical imaging modality, which displays high resolution images of coronary cross-section. Nonetheless, quantitative information can only be obtained with segmentation; consequently, more adequate diagnostics, therapies and interventions can be provided. Since it is a relatively new modality, many different segmentation methods, available in the literature for other modalities, could be successfully applied to IVOCT images, improving accuracies and uses. Method An automatic lumen segmentation approach, based on Wavelet Transform and Mathematical Morphology, is presented. The methodology is divided into three main parts. First, the preprocessing stage attenuates and enhances undesirable and important information, respectively. Second, in the feature extraction block, wavelet is associated with an adapted version of Otsu threshold; hence, tissue information is discriminated and binarized. Finally, binary morphological reconstruction improves the binary information and constructs the binary lumen object. Results The evaluation was carried out by segmenting 290 challenging images from human and pig coronaries, and rabbit iliac arteries; the outcomes were compared with the gold standards made by experts. The resultant accuracy was obtained: True Positive (%) = 99.29 ± 2.96, False Positive (%) = 3.69 ± 2.88, False Negative (%) = 0.71 ± 2.96, Max False Positive Distance (mm) = 0.1 ± 0.07, Max False Negative Distance (mm) = 0.06 ± 0.1. Conclusions In conclusion, by segmenting a number of IVOCT images with various features, the proposed technique showed to be robust and more accurate than published studies; in addition, the method is completely automatic, providing a new tool for IVOCT segmentation.

Use of an Online Photo Management and Sharing Application to Create a Searchable Digital Dental Radiograph Repository

Problem: Dental radiographs generally display one or more findings/diagnoses, and are linked to a unique set of patient demographics, medical history and other findings not represented by the image. However, this information is not associated with radiographs in any type of meta format, and images are not searchable based on any clinical criteria (1,2). The purpose of this pilot study is to create an online, searchable data repository of dental radiographs to be used for patient care, teaching and research. [See PDF for complete abstract]

Improving 4D plan quality for PBS-based liver tumour treatments by combining online image guided beam gating with rescanning.

Pencil beam scanned (PBS) proton therapy has many advantages over conventional radiotherapy, but its effectiveness for treating mobile tumours remains questionable. Gating dose delivery to the breathing pattern is a well-developed method in conventional radiotherapy for mitigating tumour-motion, but its clinical efficiency for PBS proton therapy is not yet well documented. In this study, the dosimetric benefits and the treatment efficiency of beam gating for PBS proton therapy has been comprehensively evaluated. A series of dedicated 4D dose calculations (4DDC) have been performed on 9 different 4DCT(MRI) liver data sets, which give realistic 4DCT extracting motion information from 4DMRI. The value of 4DCT(MRI) is its capability of providing not only patient geometries and deformable breathing characteristics, but also includes variations in the breathing patterns between breathing cycles. In order to monitor target motion and derive a gating signal, we simulate time-resolved beams' eye view (BEV) x-ray images as an online motion surrogate. 4DDCs have been performed using three amplitude-based gating window sizes (10/5/3 mm) with motion surrogates derived from either pre-implanted fiducial markers or the diaphragm. In addition, gating has also been simulated in combination with up to 19 times rescanning using either volumetric or layered approaches. The quality of the resulting 4DDC plans has been quantified in terms of the plan homogeneity index (HI), total treatment time and duty cycle. Results show that neither beam gating nor rescanning alone can fully retrieve the plan homogeneity of the static reference plan. Especially for variable breathing patterns, reductions of the effective duty cycle to as low as 10% have been observed with the smallest gating rescanning window (3 mm), implying that gating on its own for such cases would result in much longer treatment times. In addition, when rescanning is applied on its own, large differences between volumetric and layered rescanning have been observed as a function of increasing number of re-scans. However, once gating and rescanning is combined, HI to within 2% of the static plan could be achieved in the clinical target volume, with only moderately prolonged treatment times, irrespective of the rescanning strategy used. Moreover, these results are independent of the motion surrogate used. In conclusion, our results suggest image guided beam gating, combined with rescanning, is a feasible, effective and efficient motion mitigation approach for PBS-based liver tumour treatments.