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

Purine and pyrimidine antagonism in a pyrimidine-deficient mutant of Neurospora

The present study is concerned with the inhibition of growth of the pyrimidine-deficient Neurospora mutant, No. 1298, by the naturally occurring purine ribonucleotides and ribonucleosides. This experimentally produced strain, unlike the wild type, is unable to synthesize the pyrimidine ribonucleosides on a medium containing inorganic salts, carbohydrate, and biotin. Normal growth takes place, however, when the medium is supplemented with either cytidine or uridine or the corresponding nucleotides. It has been found that adenosine and adenosine-3-phosphate (yeast adenylic acid) inhibit the utilization of the pyrimidine compounds to a varying degree. An amount of adenine nucleoside which is sufficient to inhibit growth completely on the quantity of cytidine used has no inhibitory effect on an equivalent amount of uridine. The addition of an equimolar amount of uridine to a mixture of cytidine and adenosine in which no growth takes place results in the elimination of the antagonism. In contrast to the effect of adenosine and adenylic acid on this mutant strain of Neurospora, adenine shows no inhibitory properties at comparable concentrations. A similar inhibitory effect on the utilization of the pyrimidine nucleosides was found for guanosine and guanylic acid, but larger amounts of these compounds were required to produce inhibition under the same conditions. Guanine like adenine failed to cause inhibition at moderate concentrations

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

A mass formula for baryon resonances

Light-baryon resonances with u,d, and s quarks only can be classified using the non-relativistic quark model. When we assign to baryon resonances with total angular momenta J intrinsic orbital angular momenta L and spin S we make the following observations: plotting the squared masses of the light-baryon resonances against these intrinsic orbital angular momenta L, Delta's with even and odd parity can be described by the same Regge trajectory. For a given L, nucleon resonances with spin S=3/2 are approximately degenerate in mass with Delta resonances of same total orbital momentum L. To which total angular momentum L and S couple has no significant impact on the baryon mass. Nucleons with spin 1/2 are shifted in mass; the shift is - in units of squared masses - proportional to the component in the wave function which is antisymmetric in spin and flavor. Sequential resonances in the same partial wave are separated in mass square by the same spacing as observed in orbital angular momentum excitations. Based on these observations, a new baryon mass formula is proposed which reproduces nearly all known baryon masses.Comment: 4 pages, 1 figur

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