Identically Self-Dual Matroids

<p>In this thesis we focus on identically self-dual matroids and their minors. We show that every sparse paving matroid is a minor of an identically self-dual sparse paving matroid. The same result is true if the property sparse paving is replaced with the property of representability and more specifically, F-representable where F is a field of characteristic 2, an algebraically closed field, or equal to GF(p) for a prime p = 3 (mod 4). We extend a result of Lindstrom [11] saying that no identically self-dual matroid is regular and simple. We assert that this also applies to all matroids which can be obtained by contracting an identically self-dual matroid. Finally, we present a characterisation of identically self-dual frame matroids and prove that the class of self-dual matroids is not axiomatisable.</p>

Identically Self-Dual Matroids

<p>In this thesis we focus on identically self-dual matroids and their minors. We show that every sparse paving matroid is a minor of an identically self-dual sparse paving matroid. The same result is true if the property sparse paving is replaced with the property of representability and more specifically, F-representable where F is a field of characteristic 2, an algebraically closed field, or equal to GF(p) for a prime p = 3 (mod 4). We extend a result of Lindstrom [11] saying that no identically self-dual matroid is regular and simple. We assert that this also applies to all matroids which can be obtained by contracting an identically self-dual matroid. Finally, we present a characterisation of identically self-dual frame matroids and prove that the class of self-dual matroids is not axiomatisable.</p>

Partial Gabor frames and dual frames

The theory of Gabor frames has been extensively investigated. This paper addresses partial Gabor systems. We introduce the concepts of partial Gabor system, frame and dual frame. We present some conditions for a partial Gabor system to be a partial Gabor frame, and using these conditions, we characterize partial dual frames. We also give some examples. It is noteworthy that the density theorem does not hold for general partial Gabor systems.

Measuring agency in children: the development and validation of the War Child Agency Assessment Scale - Palestinian version (WCAAS-Pal).

In the present article, we aimed at construing a new quantitative measure of children's agency in Palestine. Within a socio-ecological and culturally and contextually informed perspective, the study introduces the development of a new instrument to investigate and evaluate children's agentic practices within their living contexts and their daily lives. First, we evaluated the model of measurement of WCAAS-Pal using a sequential exploratory factor analysis (EFA) and confirmatory factor analysis (CFA). Following the principles of testing a quantitative measure in the context of the dual-frame sampling method, the process of validating the quantitative measure was conducted on a group of 1,166 Palestinian children aged 9 to 14 years (m = 11.58, sd = 1.54). Second, a sample of 251 Palestinian children aged between 9 and 14 years (m = 11.82, sd = 1.53) was used to compute the reliability of the instrument along with both convergent and divergent validity using the Children Hope Scale and the Children Revised Impact of Event Scale-Arabic Version measures, respectively. The results of the EFA suggested a baseline seven-factor structure to be further assessed via CFA. A complex web of agency domains that might contribute to the child psychological functioning when forced to leave in conditions of ongoing threat and military violence emerged from the analysis.

A Novel Platform for Integrating 360° Videos Within a Virtual Study Abroad Experience

The rising popularity of high-immersion media has found its way to educational use cases, but such media have not yet been extensively evaluated in their ability to provide fully featured study abroad experiences. As recent events have catapulted virtual study abroad programs to the forefront, and as universities seek to build attractive and effective programs, the necessity of systems that provide immersion and student engagement has become apparent. Using the new concept of Dual-Frame System Design, this paper seeks to find if design thinking methodologies can meet these needs while maintaining system reliability, flexibility, and ease of use. Using off-the-shelf components, including a 360° video camera, smartphones, and personal computers, a system was created and tested through a mixed-methods approach based on a user study of 25 US college students. The results of this research may be useful in the creation of high-immersion virtual study abroad experiences, as well as advancing the interdisciplinary frameworks necessary to make these systems broadly available.

Factors Associated With Mental Health Symptoms During the COVID-19 Pandemic in Hong Kong

Background: The COVID-19 pandemic has led to an increasing mental health burden. We examined the factors associated with mental health symptoms in Chinese general adults in Hong Kong.Methods: We conducted a dual-frame (landline and mobile) survey on Chinese adults aged 18 years or older in April 2020. Shortage of preventive materials, perceptions of the outbreak (each item range 1–5), and reduction in income were assessed. Mental health symptoms measured included stress (Perceived Stress Scale-4, range 0–16), anxiety (General Anxiety Disorders-2, range 0–6, cutoff &gt;2), and depressive symptoms (Patient Health Questionnaire-2, range 0–6, cutoff &gt;2). Results were weighted by the general population distribution. Associations were analyzed by multivariable linear (for stress) and logistic (for anxiety and depressive symptoms) regression adjusting for sociodemographic and health-related covariates, including confirmed or in close contacts of confirmed cases, chronic disease, self-rated health, and smoking and alcohol drinking behavior.Results: Of the 1,501 participants (52.5% female, 55.0 aged 30–59 years), the average stress score was 7.20 (SD 2.12). 218 (15.8%) and 206 (14.8%) participants had anxiety and depressive symptoms, respectively. Shortage in facemasks (20.8%), alcohol-based hand sanitizers (13.9%), and cleaning products (7.3%) was reported. Participants generally disagree with the perception of at risk of getting infected in the coming 6 months (mean 2.2, SD 1.1), but tended to agree with the perception of worry that the people around pose a threat to them (mean 3.6, SD 0.9) and the outbreak has greatly affected their daily life (mean 3.7, SD 0.9). 59.3% employed participants had income reduction and 6.2% had become unemployed since the outbreak. Stress, anxiety, and depressive symptoms were more prevalent in those with shortages of preventive materials and negative perceptions of the outbreak (all P &lt; 0.05). Reduction in income and unemployment were associated with more mental health symptoms (all P &lt; 0.05).Conclusions: Shortage of preventive materials, negative perceptions, financial loss, and unemployment were prevalent during the outbreak and found in association with higher stress and more anxiety and depressive symptoms. Further research and urgent actions are warranted to relieve stress and promote mental health, targeting the many risk factors identified by our study.