Almost Commuting Orthogonal Matrices

We show that almost commuting real orthogonal matrices are uniformly close to exactly commuting real orthogonal matrices. We prove the same for symplectic unitary matrices. This is in contrast to the general complex case, where not all pairs of almost commuting unitaries are close to commuting pairs. Our techniques also yield results about almost normal matrices over the reals and the quaternions.Comment: 13 pages, 3 figure

Illiberalism: A Primer and Call to Action for Social Workers

Liberal democracies had been ascendant in the post-World War II era. President Trump is part of a wave of nationalist, anti-immigrant politicians with autocratic tendencies who are challenging liberal democracy. The term given to the governing philosophy of these leaders is illiberalism. This paper is meant to be a primer on illiberalism for social workers, describing this ideology and the threat illiberalism poses for democracy, our social welfare system, and the interests of social work clients. We conclude with a discussion on what social workers can do to defend democracy in light of the historic mission to advance social justice

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

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

Quiste óseo unicameral de astrágalo: Consideraciones terapéuticas a propósito de un caso

El quiste óseo unicameral se localiza excepcionalmente en el astrágalo, y só- lo once casos han sido publicados previamente en la literatura médica. Se presenta un nuevo caso en una niña de cinco años de edad, que por su tamaño y localización fue tratado quirúrgicamente con legrado y aposición de aloinjerto. Consideramos que en los quistes óseos de localización en astrágalo y que ocupan más del 30-40% de su volumen deben evitarse las perforaciones y punciones intraquísticas debido al riesgo de fractura y necrosis del mismo.Unicameral bone cysts are very rarely found in the talus and we have only been able to find 11 previously reported in the literature consulted. We report a further case occurring in a five-year-old girl because of its site and location treated surgically by means of curettage and allograft. We believe that in bone cysts occupying more than 30-40% of the talus, perforations and intracystic punctures should be avoided due to the risk of fracture and necrosis

Staying in place during times of change in Arctic Alaska: The implications of attachment,alternatives, and buffering

The relationship between stability and change in social-ecological systems has received considerable attention in recent years, including the expectation that significant environmental changes will drive observable consequences for individuals, communities, and populations. Migration, as one example of response to adverse economic or environmental changes, has been observed in many places, including parts of the Far North. In Arctic Alaska, a relative lack of demographic or migratory response to rapid environmental and other changes has been observed. To understand why Arctic Alaska appears different, we draw on the literature on environmentally driven migration, focusing on three mechanisms that could account for the lack of response: attachment, the desire to remain in place, or the inability to relocate successfully; alternatives, ways to achieve similar outcomes through different means; and buffering, the reliance on subsidies or use of reserves to delay impacts. Each explanation has different implications for research and policy, indicating a need to further explore the relative contribution that each makes to a given situation in order to develop more effective responses locally and regionally. Given that the Arctic is on the front lines of climate change, these explanations are likely relevant to the ways changes play out in other parts of the world. Our review also underscores the importance of further attention to the details of social dynamics in climate change impacts and responses

Angiomatosis quística esquelética : a propósito de 1 caso

La angiomatosis quística esquelética es una enfermedad rara caracterizada por una afectación multifocal del esqueleto consistente en una proliferación anómala de vasos sanguíneos, linfáticos o ambos y en la que frecuentemente existe afectación de otros tejidos. Se presenta el caso de un varón de 4 años que sufrió una fractura patológica de húmero derecho. Un mapa óseo y una biopsia abierta condujeron al diagnóstico. No se evidenció afectación extraesquelética. Se ha realizado un seguimiento de 19 años en los que sus lesiones han sufrido un curso progresivo. Se revisa la literatura al respecto.Cystic angiomatosis of bone is a rare multicentric skeletal lesión caused by proliferation of blood vessels, lymphatics, or both and often accompanied by angiomatous lesions in other tissues. We report a case of a 4-year-old boy who suffered a pathologic fracture of the right humerus. A bone scan and an open biopsy lead to diagnosis. Visceral involvement was not found. The patient has been followed for 19 years and his lesions have showed progression

Almost commuting self-adjoint matrices --- the real and self-dual cases

We show that a pair of almost commuting self-adjoint, symmetric matrices is close to a pair of commuting self-adjoint, symmetric matrices (in a uniform way). Moreover we prove that the same holds with self-dual in place of symmetric. The notion of self-dual Hermitian matrices is important in physics when studying fermionic systems that have time reversal symmetry. Since a symmetric, self-adjoint matrix is real, we get a real version of Huaxin Lin's famous theorem on almost commuting matrices. Similarly the self-dual case gives a version for matrices over the quaternions. We prove analogous results for element of real C^*-algebras of "low rank." In particular, these stronger results apply to paths of almost commuting Hermitian matrices that are real or self-dual. Along the way we develop a theory of semiprojectivity for real C^*-algebras.Comment: Expanded references. 33 page