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

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

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

Almost commuting unitary matrices related to time reversal

The behavior of fermionic systems depends on the geometry of the system and the symmetry class of the Hamiltonian and observables. Almost commuting matrices arise from band-projected position observables in such systems. One expects the mathematical behavior of almost commuting Hermitian matrices to depend on two factors. One factor will be the approximate polynomial relations satisfied by the matrices. The other factor is what algebra the matrices are in, either the matrices over A for A the real numbers, A the complex numbers or A the algebra of quaternions. There are potential obstructions keeping k-tuples of almost commuting operators from being close to a commuting k-tuple. We consider two-dimensional geometries and so this obstruction lives in KO_{-2}(A). This obstruction corresponds to either the Chern number or spin Chern number in physics. We show that if this obstruction is the trivial element in K-theory then the approximation by commuting matrices is possible.Comment: 33 pages, 2 figures. In version 2 some formulas have been corrected and some proofs have been rewritten to improve the expositio

Supportive Wind Conditions Influence Offshore Movements of Atlantic Coast Piping Plovers during Fall Migration

In advance of large-scale development of offshore wind energy facilities throughout the U.S. Atlantic Outer Continental Shelf (OCS), information on the migratory ecology and routes of federally threatened Atlantic Coast Piping Plovers (Charadrius melodus melodus) is needed to conduct risk assessments pursuant to the Endangered Species Act. We tagged adult Piping Plovers (n = 150) with digitally coded VHF transmitters at 2 breeding areas within the southern New England region of the U.S. Atlantic coast from 2015 to 2017. We tracked their migratory departure flights using a regional automated telemetry network (n = 30 stations) extending across a portion of the U.S. Atlantic Bight region, a section of the U.S. Atlantic coast, and adjacent waters of the Atlantic Ocean extending from Cape Cod, Massachusetts, to Cape Hatteras, North Carolina. Most adults departed within a 10-day window from July 19 to July 29, migrated nocturnally, and over 75% of individuals departed within 3 hr of local sunset on evenings with supportive winds. Piping Plovers migrated offshore directly across the mid-Atlantic Bight, from breeding areas in southern New England to stopover sites spanning from New York to North Carolina, USA, over 800 km away. During offshore migratory flights, Piping Plovers flew at estimated mean speeds of 42 km hr−1 and altitudes of 288 m (range of model uncertainty: 36–1,031 m). This study provides new information on the timing, weather conditions, routes, and altitudes of Piping Plovers during fall migration. This information can be used in estimations of collision risk that could potentially result from the construction of offshore wind turbines under consideration across large areas of the U.S. Atlantic OCS

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

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

Epifisiólisis femoral proxima: revisión de 44 casos

Se revisan 44 niños con 47 epifisiólisis femorales proximales. Veintitrés desplazamientos fueron leves, 18 moderados y 6 severos. Todas las epifisiólisis excepto 1 se trataron quirúrgicamente. En 10 casos se fijó profilácticamente la cadera contralateral. Existió penetración articular por el implante en 17 (30%) de las 56 caderas fijadas. El seguimiento medio ha sido de 56 meses (rango: 3 a 148 meses). Los resultados, según criterios clínicos y radiográficos, han sido excelentes o buenos en el 91% de los deslizamientos leves, el 77% de los moderados y el 33% de los severos. Las complicaciones fueron 2 casos de condrólisis, ambos asociados a penetración articular. En 2 (6%) de los pacientes donde no se realización profiláctica se produjo deslizamiento contralateral. En nuestro estudio los resultados se correlacionan con la cuantía del deslizamiento. No recomendamos la fijación profiláctica contraletal.We review 44 children with 47 slipped capital femoral epiphysis. There were 23 mild slips, 18 moderate, and 6 severe. Operative treatment was performed in all but one of the slips. In 10 cases prophylactic pinning of the contralateral hip was performed. Penetration of the joint by the implant was present in 17 (30%) of the 56 fixed hips. The average follow-up was 56 months (range: 3 to 178 months). The results, according to clinical and rocntgenographic parameters were excellent or good in 91% of mild slips, 77% of moderate and 33% of severe. As complications there were two cases of chondrolysis, both associated with joint penetration. In 2 (6%) patients where prophylactic pinning was not performed, contralateral hip slipping developed. In our study, results correlate with slip severity. We do not recommend prophylactic contralateral pinning