On a counterexample to a conjecture by Blackadar

Blackadar conjectured that if we have a split short-exact sequence 0 -> I -> A -> A/I -> 0 where I is semiprojective and A/I is isomorphic to the complex numbers, then A must be semiprojective. Eilers and Katsura have found a counterexample to this conjecture. Presumably Blackadar asked that the extension be split to make it more likely that semiprojectivity of I would imply semiprojectivity of A. But oddly enough, in all the counterexamples of Eilers and Katsura the quotient map from A to A/I is split. We will show how to modify their examples to find a non-semiprojective C*-algebra B with a semiprojective ideal J such that B/J is the complex numbers and the quotient map does not split.Comment: 6 page

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

Music in Boston

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Climigration? Population and climate change in Arctic Alaska

Residents of towns and villages in Arctic Alaska live on “the front line of climate change.” Some communities face immediate threats from erosion and flooding associated with thawing permafrost, increasing river flows, and reduced sea ice protection of shorelines. The term climigration, referring to migration caused by climate change, originally was coined for these places. Although initial applications emphasized the need for government relocation policies, it has elsewhere been applied more broadly to encompass unplanned migration as well. Some historical movements have been attributed to climate change, but closer study tends to find multiple causes, making it difficult to quantify the climate contribution. Clearer attribution might come from comparisons of migration rates among places that are similar in most respects, apart from known climatic impacts. We apply this approach using annual 1990–2014 time series on 43 Arctic Alaska towns and villages. Within-community time plots show no indication of enhanced out-migration from the most at-risk communities. More formally, there is no significant difference between net migration rates of at-risk and other places, testing several alternative classifications. Although climigration is not detectable to date, growing risks make either planned or unplanned movements unavoidable in the near future

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

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

Piano Key Weir for Enlargement of the West Fork of Eno River Reservoir

The West Fork of Eno River Reservoir Dam is located near Hillsborough, North Carolina, USA. The earthen embankment dam provides an impoundment used by the town for water supply. The project was originally completed in 2000 with forethought by the owner for an expansion, which was anticipated in the original design. Currently, the design of that expansion to raise the reservoir level for increased water supply is underway. Following a detailed analysis of viable upgrades, a piano key (PK) weir (anticipated as the first to be constructed in the USA) was selected by the owner due to its effectiveness in meeting project requirements. Presented herein are the site-specific characteristics of the existing auxiliary chute spillway, the proposed PK weir, and additional modifications to the chute. This paper also presents site-specific information including the existing auxiliary chute spillway, the new PK weir, and additional modifications to the auxiliary chute. The results include the comparison of four PK weir hydraulic design methods for sizing the spillway. Details and results of a CFD model are also included. Finally, additional significant design considerations are presented, which include: anticipated hydraulic conditions in the downstream chute and identified existing structure deficiencies; estimated spillway design flood hydraulic force distributions taken from the CFD model; the PK key weir stability summary; and other important project aspects including embankment modifications and seepage control measures. It is anticipated that this project will be of interest to those concerned with dam safety and will further encourage the consideration of PK weirs in the USA