Almost Commuting Matrices, Localized Wannier Functions, and the Quantum Hall Effect

For models of non-interacting fermions moving within sites arranged on a surface in three dimensional space, there can be obstructions to finding localized Wannier functions. We show that such obstructions are $K$-theoretic obstructions to approximating almost commuting, complex-valued matrices by commuting matrices, and we demonstrate numerically the presence of this obstruction for a lattice model of the quantum Hall effect in a spherical geometry. The numerical calculation of the obstruction is straightforward, and does not require translational invariance or introducing a flux torus. We further show that there is a $Z_2$ index obstruction to approximating almost commuting self-dual matrices by exactly commuting self-dual matrices, and present additional conjectures regarding the approximation of almost commuting real and self-dual matrices by exactly commuting real and self-dual matrices. The motivation for considering this problem is the case of physical systems with additional antiunitary symmetries such as time reversal or particle-hole conjugation. Finally, in the case of the sphere--mathematically speaking three almost commuting Hermitians whose sum of square is near the identity--we give the first quantitative result showing this index is the only obstruction to finding commuting approximations. We review the known non-quantitative results for the torus.Comment: 35 pages, 2 figure

Epilogue for the IJSME Special Issue: Metacognition for science and mathematics learning in technology-infused learning environments

Epilogue for the IJSME Special Issue: Metacognition for science and mathematics learning in technology-infused learning environment

The Differential Effect of Anxiety and ADHD Symptoms on Inhibitory Control and Sustained Attention for Threat Stimuli: A Go/No-Go Eye-Movement Study

Objective: This study examined the synergistic effects of ADHD and anxiety symptoms on attention and inhibitory control depending on the emotional content of the stimuli. Method: Fifty-four typically developing individuals (27 children/adolescents and 27 adults) completed an eye-movement based emotional Go/No-Go task, using centrally presented (happy, angry) faces and neutral/symbolic stimuli. Sustained attention was measured through saccade latencies and saccadic omission errors (Go trials), and inhibitory control through saccadic commission errors (No-Go trials). ADHD and anxiety were assessed dimensionally. Results: Elevated ADHD symptoms were associated with more commission errors and slower saccade latencies for angry (vs. happy) faces. In contrast, angry faces were linked to faster saccade onsets when anxiety symptoms were high, and this effect prevailed when both anxiety and ADHD symptoms were high. Conclusion: Social threat impacted performance in individuals with sub-clinical anxiety and ADHD differently. The effects of anxiety on threat processing prevailed when both symptoms were high

Leibniz Seminorms and Best Approximation from C*-subalgebras

We show that if B is a C*-subalgebra of a C*-algebra A such that B contains a bounded approximate identity for A, and if L is the pull-back to A of the quotient norm on A/B, then L is strongly Leibniz. In connection with this situation we study certain aspects of best approximation of elements of a unital C*-algebra by elements of a unital C*-subalgebra.Comment: 24 pages. Intended for the proceedings of the conference "Operator Algebras and Related Topics". v2: added a corollary to the main theorem, plus several minor improvements v3: much simplified proof of a key lemma, corollary to main theorem added v4: Many minor improvements. Section numbers increased by

Interpretation of ambiguous situations: evidence for a dissociation between social and physical threat in Williams syndrome

There is increasing evidence that Williams syndrome (WS) is associated with elevated anxiety that is non-social in nature, including generalised anxiety and fears. To date very little research has examined the cognitive processes associated with this anxiety. In the present research, attentional bias for non-social threatening images in WS was examined using a dot-probe paradigm. Participants were 16 individuals with WS aged between 13 and 34 years and two groups of typically developing controls matched to the WS group on chronological age and attentional control ability respectively. The WS group exhibited a significant attention bias towards threatening images. In contrast, no bias was found for group matched on attentional control and a slight bias away from threat was found in the chronological age matched group. The results are contrasted with recent findings suggesting that individuals with WS do not show an attention bias for threatening faces and discussed in relation to neuroimaging research showing elevated amygdala activation in response to threatening non-social scenes in WS

Role of DNA methylation and epigenetic silencing of HAND2 in endometrial cancer development

Background: Endometrial cancer incidence is continuing to rise in the wake of the current ageing and obesity epidemics. Much of the risk for endometrial cancer development is influenced by the environment and lifestyle. Accumulating evidence suggests that the epigenome serves as the interface between the genome and the environment and that hypermethylation of stem cell polycomb group target genes is an epigenetic hallmark of cancer. The objective of this study was to determine the functional role of epigenetic factors in endometrial cancer development. Methods and Findings: Epigenome-wide methylation analysis of >27,000 CpG sites in endometrial cancer tissue samples (n = 64) and control samples (n = 23) revealed that HAND2 (a gene encoding a transcription factor expressed in the endometrial stroma) is one of the most commonly hypermethylated and silenced genes in endometrial cancer. A novel integrative epigenome-transcriptome-interactome analysis further revealed that HAND2 is the hub of the most highly ranked differential methylation hotspot in endometrial cancer. These findings were validated using candidate gene methylation analysis in multiple clinical sample sets of tissue samples from a total of 272 additional women. Increased HAND2 methylation was a feature of premalignant endometrial lesions and was seen to parallel a decrease in RNA and protein levels. Furthermore, women with high endometrial HAND2 methylation in their premalignant lesions were less likely to respond to progesterone treatment. HAND2 methylation analysis of endometrial secretions collected using high vaginal swabs taken from women with postmenopausal bleeding specifically identified those patients with early stage endometrial cancer with both high sensitivity and high specificity (receiver operating characteristics area under the curve = 0.91 for stage 1A and 0.97 for higher than stage 1A). Finally, mice harbouring a Hand2 knock-out specifically in their endometrium were shown to develop precancerous endometrial lesions with increasing age, and these lesions also demonstrated a lack of PTEN expression. Conclusions: HAND2 methylation is a common and crucial molecular alteration in endometrial cancer that could potentially be employed as a biomarker for early detection of endometrial cancer and as a predictor of treatment response. The true clinical utility of HAND2 DNA methylation, however, requires further validation in prospective studies.publishedVersio

Intrasexual competition as a predictor of women's judgments of revenge pornography offending

Recent legislative developments have led to a marked increase in the empirical investigation of motivations and judgments of so-called acts of "revenge pornography" offending. In two independently sampled studies, we used moderation analyses to investigate whether higher levels of intrasexual competition predicted more lenient judgments of revenge pornography offenses as a function of sex (Study 1, N = 241), and whether such relationships would be further moderated by physical attractiveness (Study 2, N = 402). Potential covariates of callous-unemotional traits, empathy, and victimization history were controlled for. Opposing our hypotheses, we consistently observed a trend for higher levels of intrasexual competition being associated with more lenient judgments of revenge pornography offenses involving male victims by female participants. The results are discussed in terms of intrasexual competition potentially sharing variance with unobserved constructs in the wider sexological literature, and of the key relevance of these findings for future empirical investigation into judgments of nonconsensual image–based offending

Measuring Reciprocity in High Functioning Children and Adolescents with Autism Spectrum Disorders

Few instruments have been developed that measure impairments in reciprocity, a defining feature of autism. We introduce a new test assessing the quality of reciprocal behaviour: the interactive drawing test (IDT). Children and adolescents (n = 49) with and without high functioning autism spectrum disorders (HFASD) were invited to collaborate with an experimenter in making a joint drawing. Within both groups the performance on collaborative reciprocity improved with age. However, compared to the control group, HFASD participants showed less collaborative and more basic reciprocal behaviour and preferred to draw their own objects. They were less tolerant of the experimenter’s input as well. Performance on the IDT was independent of estimated verbal IQ. Reciprocal behaviour in self-initiated objects corresponded with more parental reported autistic traits, while reciprocal behaviour in other-initiated objects corresponded with less autistic traits. The findings of this study suggest that IDT is a promising instrument to assess reciprocity

Indicated prevention interventions for anxiety in children and adolescents: a review and meta-analysis of school-based programs

Anxiety disorders are among the most common youth mental health disorders. Early intervention can reduce elevated anxiety symptoms. School-based interventions exist but it is unclear how effective targeted approaches are for reducing symptoms of anxiety. This review and meta-analysis aimed to determine the effectiveness of school-based indicated interventions for symptomatic children and adolescents. The study was registered with PROSPERO [CRD42018087628]. We searched MEDLINE, EMBASE, PsycINFO, and the Cochrane Library for randomised-controlled trials comparing indicated programs for child and adolescent (5–18 years) anxiety to active or inactive control groups. Data were extracted from papers up to December 2019. The primary outcome was efficacy (mean change in anxiety symptom scores). Sub-group and sensitivity analyses explored intervention intensity and control type. We identified 20 studies with 2076 participants. Eighteen studies were suitable for meta-analysis. A small positive effect was found for indicated programs compared to controls on self-reported anxiety symptoms at post-test (g = − 0.28, CI = − 0.50, − 0.05, k = 18). This benefit was maintained at 6 (g = − 0.35, CI = − 0.58, − 0.13, k = 9) and 12 months (g = − 0.24, CI = − 0.48, 0.00, k = 4). Based on two studies, > 12 month effects were very small (g = − 0.01, CI = − 0.38, 0.36). No differences were found based on intervention intensity or control type. Risk of bias and variability between studies was high (I2 = 78%). Findings show that school-based indicated programs for child and adolescent anxiety can produce small beneficial effects, enduring for up to 12 months. Future studies should include long-term diagnostic assessments