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

Orbitofrontal epilepsy: Electroclinical analysis of surgical cases and literature review

Clinical and electrographic data were reviewed on 2 of our patients with orbitofrontal epilepsy who were seizure free at 5-year follow-up, and on 2 similar patients from the literature. One of our patients was lesional, and the other was nonlesional. Interictal EEG discharges were lateralized to the side of invasively recorded orbitofrontal seizures in the nonlesional case. In this case, no clinical manifestations occurred until the orbitofrontal discharge had spread to the opposite orbitofrontal and both mesial temporal areas. Unresponsiveness or arrest of activity were the initial manifestations of complex partial seizures in both cases. The 2 cases from the literature with long-term seizure-free follow-up had little impairment of awareness and displayed vigorous motor automatisms. Interictal epileptiform activity was bifrontally synchronous in 1 case. Ipsilateral frontotemporal discharges were seen in both. Invasive ictal epileptiform activity appeared maximal in the ipsilateral orbitofrontal region in both patients. No consistent electrographic or clinical pattern characterized these 4 cases. Seizures of orbitofrontal origin may be characterized by either unresponsiveness associated with oroalimentary automatisms or limited alteration of awareness and associated with vigorous motor automatisms. Invasive monitoring of the orbitofrontal cortex should be considered in nonlesional cases with complex partial seizures that show nonlocalizing ictal patterns and interictal frontal or frontotemporal epileptiform discharges. Copyright (C) 2004 S. Karger AG, Basel

Disordered Topological Insulators via C∗C^*-Algebras

The theory of almost commuting matrices can be used to quantify topological obstructions to the existence of localized Wannier functions with time-reversal symmetry in systems with time-reversal symmetry and strong spin-orbit coupling. We present a numerical procedure that calculates a Z_2 invariant using these techniques, and apply it to a model of HgTe. This numerical procedure allows us to access sizes significantly larger than procedures based on studying twisted boundary conditions. Our numerical results indicate the existence of a metallic phase in the presence of scattering between up and down spin components, while there is a sharp transition when the system decouples into two copies of the quantum Hall effect. In addition to the Z_2 invariant calculation in the case when up and down components are coupled, we also present a simple method of evaluating the integer invariant in the quantum Hall case where they are decoupled.Comment: Added detail regarding the mapping of almost commuting unitary matrices to almost commuting Hermitian matrices that form an approximate representation of the sphere. 6 pages, 6 figure

Gradual Change In Human Tooth Size In The Late Pleistocene And Post‐Pleistocene

Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/137561/1/evo05847.pd

Long-term yogurt consumption and risk of incident hypertension in adults

The Nurses' Health Study and Health Professionals Follow-up Study cohorts are supported by grants UM1 CA186107, UM1 CA176726, and UM1 CA167552 from the National Institutes of Health. The current analyses were supported by small grants from the National Dairy Council, the General Mills Bell Institute for Health and Nutrition, and the Boston Nutrition and Obesity Research Center. The Boston Nutrition Obesity Research Center is administratively based at Boston Medical Center and is funded by the National Institutes of Health (NIH/NIDDK) grant P30DK046200. (UM1 CA186107 - National Institutes of Health; UM1 CA176726 - National Institutes of Health; UM1 CA167552 - National Institutes of Health; small grants from the National Dairy Council; General Mills Bell Institute for Health and Nutrition; Boston Nutrition and Obesity Research Center; P30DK046200 - National Institutes of Health (NIH/NIDDK))Accepted manuscrip

Linked CSF reduction of phosphorylated tau and IL-8 in HIV associated neurocognitive disorder.

HIV-associated neurocognitive disorder (HAND) is a common condition in both developed and developing nations, but its cause is largely unknown. Previous research has inconsistently linked Alzheimer's disease (AD), viral burden, and inflammation to the onset of HAND in HIV-infected individuals. Here we simultaneously measured cerebrospinal fluid (CSF) levels of established amyloid and tau biomarkers for AD, viral copy numbers, and six key cytokines in 41 HIV-infected individuals off combination anti-retroviral therapy (14 with HAND) who underwent detailed clinical and neuropsychological characterization, and compared their CSF patterns with those from young healthy subjects, older healthy subjects with normal cognition, and older people with AD. HAND was associated with the lowest CSF levels of phosphorylated tau (p-Tau181) after accounting for age and race. We also found very high CSF levels of the pro-inflammatory interferon gamma-induced protein 10 (IP-10/CXCL10) in HIV regardless of cognition, but elevated CSF interleukin 8 (IL-8/CXCL8) only in HIV-NC but not HAND. Eleven HIV-infected subjects underwent repeat CSF collection six months later and showed strongly correlated longitudinal changes in p-Tau181 and IL-8 levels (R = 0.841). These data suggest reduced IL-8 relative to IP-10 and reduced p-Tau181 to characterize HAND

Random Walks on a Fluctuating Lattice: A Renormalization Group Approach Applied in One Dimension

We study the problem of a random walk on a lattice in which bonds connecting nearest neighbor sites open and close randomly in time, a situation often encountered in fluctuating media. We present a simple renormalization group technique to solve for the effective diffusive behavior at long times. For one-dimensional lattices we obtain better quantitative agreement with simulation data than earlier effective medium results. Our technique works in principle in any dimension, although the amount of computation required rises with dimensionality of the lattice.Comment: PostScript file including 2 figures, total 15 pages, 8 other figures obtainable by mail from D.L. Stei

Children’s learning from a Smokefree sports programme: implications for health education

Objective: This article reports on a qualitative evaluation of the Love Life, Smokefree Sports primary school pilot intervention. This 8-week programme used sports and physical activity sessions to convey Smokefree messages to 120 children aged 10 and 11 in two primary schools in Sheffield in 2018. The study aimed to understand children’s experiences of participating in the programme. Its objectives were to explore children’s recall of the health promotion messages associated with each of the learning sessions; explore children’s perceptions of the meaningfulness of those messages in the context of their everyday lives; and identify and understand any contextual factors that might impact upon children’s recall and/or the meaningfulness of the Smokefree messages. Method: Qualitative data were generated with 25 children through focus groups after the programme concluded. Data were analysed thematically using cross-sectional, categorical indexing. Results: Learning from the programme was particularly likely to be described as meaningful by children when they could interact with material and visual representations of complex ideas and when sessions involved strongly embodied experiences. However, children did not always find it easy to relate learning to their everyday lives and sometimes struggled to reconcile pre-existing, contextualised understandings with intervention messages. We mobilise the concept of critical health literacy as a theoretical lens through which to interpret these findings. Conclusion: Health education should be meaningful in the context of children’s everyday lives. Starting from the premise that children are active critical health literacy practitioners and working with them to design and evaluate health education initiatives can promote this

Spatial Heterogeneity Can Lead to Substantial Local Variations in COVID-19 Timing and Severity

Standard epidemiological models for COVID-19 employ variants of compartment (SIR) models at local scales, implicitly assuming spatially uniform local mixing. Here, we examine the effect of employing more geographically detailed diffusion models based on known spatial features of interpersonal networks, most particularly the presence of a long-tailed but monotone decline in the probability of interaction with distance, on disease diffusion. Based on simulations of unrestricted COVID-19 diffusion in 19 U.S cities, we conclude that heterogeneity in population distribution can have large impacts on local pandemic timing and severity, even when aggregate behavior at larger scales mirrors a classic SIR-like pattern. Impacts observed include severe local outbreaks with long lag time relative to the aggregate infection curve, and the presence of numerous areas whose disease trajectories correlate poorly with those of neighboring areas. A simple catchment model for hospital demand illustrates potential implications for health care utilization, with substantial disparities in the timing and extremity of impacts even without distancing interventions. Likewise, analysis of social exposure to others who are morbid or deceased shows considerable variation in how the epidemic can appear to individuals on the ground, potentially affecting risk assessment and compliance with mitigation measures. These results demonstrate the potential for spatial network structure to generate highly non-uniform diffusion behavior even at the scale of cities, and suggest the importance of incorporating such structure when designing models to inform healthcare planning, predict community outcomes, or identify potential disparities