Skew Calabi-Yau Algebras and Homological Identities

A skew Calabi-Yau algebra is a generalization of a Calabi-Yau algebra which allows for a non-trivial Nakayama automorphism. We prove three homological identities about the Nakayama automorphism and give several applications. The identities we prove show (i) how the Nakayama automorphism of a smash product algebra A # H is related to the Nakayama automorphisms of a graded skew Calabi-Yau algebra A and a finite-dimensional Hopf algebra H that acts on it; (ii) how the Nakayama automorphism of a graded twist of A is related to the Nakayama automorphism of A; and (iii) that Nakayama automorphism of a skew Calabi-Yau algebra A has trivial homological determinant in case A is noetherian, connected graded, and Koszul.Comment: 39 pages; minor changes, mostly in the Introductio

Skew Calabi-Yau triangulated categories and Frobenius Ext-algebras

We investigate the conditions that are sufficient to make the Ext-algebra of an object in a (triangulated) category into a Frobenius algebra and compute the corresponding Nakayama automorphism. As an application, we prove the conjecture that hdet($\mu_A$) = 1 for any noetherian Artin-Schelter regular (hence skew Calabi-Yau) algebra A.Comment: 31 page

Reading, Writing, and Breathing

This report looks at the distribution of air toxics, respiratory hazard, and school children in the state of California. The report finds evidence of disproportionate exposure and a potential link between such exposure and school-level academic performance, and calls for policy changes that can better situate environmental health concerns within initiatives for school improvement

Still Toxic After All These Years: Air Quality and Environmental Justice in the San Francisco Bay Area

From West Oakland's diesel-choked neighborhoods to San Francisco's traffic-snarled Mission District to the fenceline communitis abutting Richmond's refineries, poor and minority residents of the San Francisco Bay Area get more than their share of exposure to air pollution and environmental hazards. That's the conclusion of a new report issued by the Center for Justice, Tolerance & Community (CJTC) at the University of California, Santa Cruz. The first published analysis of the overall state of environmental disparity in the nine-county region, the report is entitled, "Still Toxic After All These Years... Air Quality and Environmental Justice in the Bay Area.

Approximate Bayesian Computation by Subset Simulation

A new Approximate Bayesian Computation (ABC) algorithm for Bayesian updating of model parameters is proposed in this paper, which combines the ABC principles with the technique of Subset Simulation for efficient rare-event simulation, first developed in S.K. Au and J.L. Beck [1]. It has been named ABC- SubSim. The idea is to choose the nested decreasing sequence of regions in Subset Simulation as the regions that correspond to increasingly closer approximations of the actual data vector in observation space. The efficiency of the algorithm is demonstrated in two examples that illustrate some of the challenges faced in real-world applications of ABC. We show that the proposed algorithm outperforms other recent sequential ABC algorithms in terms of computational efficiency while achieving the same, or better, measure of ac- curacy in the posterior distribution. We also show that ABC-SubSim readily provides an estimate of the evidence (marginal likelihood) for posterior model class assessment, as a by-product

Minding The Climate Gap: What's at Stake if California's Climate Law isn't Done Right and Right Away

Minding the Climate Gap: What's at Stake if California's Climate Law isn't Done Right and Right Away details how incentivizing the reduction of greenhouse gases -- which cause climate change -- from facilities operating in the most polluted neighborhoods could generate major public health benefits. The study also details how revenues generated from charging polluters could be used to improve air quality and create jobs in the neighborhoods that suffer from the dirtiest air. In California, children in poverty, together with all people in poverty, live disproportionately near large facilities emitting toxic air pollution and greenhouse gases.People of color in the state experience over seventy percent more of the dangerous pollution coming from major greenhouse gas polluters as whites, and the disparity is particularly sharp for African Americans. The racial differential in proximity to pollution is not just a function of income: people of color are more likely to live near these polluting facilities than whites with similar incomes. Continuing to move forward with California's climate law presents the opportunity to save lives and bolster California's economy by focusing pollution reductions in neighborhoods suffering the worst public health impacts