Metric sparsification and operator norm localization

We study an operator norm localization property and its applications to the coarse Novikov conjecture in operator K-theory. A metric space X is said to have operator norm localization property if there exists a positive number c such that for every r>0, there is R>0 for which, if m is a positive locally finite Borel measure on X, H is a separable infinite dimensional Hilbert space and T is a bounded linear operator acting on L^2(X,m) with propagation r, then there exists an unit vector v satisfying with support of diameter at most R and such that |Tv| is larger or equal than c|T|. If X has finite asymptotic dimension, then X has operator norm localization property. In this paper, we introduce a sufficient geometric condition for the operator norm localization property. This is used to give many examples of finitely generated groups with infinite asymptotic dimension and the operator norm localization property. We also show that any sequence of expanding graphs does not possess the operator norm localization property

Redox Stable Anodes for Solid Oxide Fuel Cells

Solid oxide fuel cells (SOFCs) can convert chemical energy from the fuel directly to electrical energy with high efficiency and fuel flexibility. Ni-based cermets have been the most widely adopted anode for SOFCs. However, the conventional Ni-based anode has low tolerance to sulfur-contamination, is vulnerable to deactivation by carbon build-up (coking) from direct oxidation of hydrocarbon fuels, and suffers volume instability upon redox cycling. Among these limitations, the redox instability of the anode is particularly important and has been intensively studied since the SOFC anode may experience redox cycling during fuel cell operations even with the ideal pure hydrogen as the fuel. This review aims to highlight recent progresses on improving redox stability of the conventional Ni-based anode through microstructure optimization and exploration of alternative ceramic-based anode materials

A Large Population Size Can Be Unhelpful in Evolutionary Algorithms

The utilization of populations is one of the most important features of evolutionary algorithms (EAs). There have been many studies analyzing the impact of different population sizes on the performance of EAs. However, most of such studies are based computational experiments, except for a few cases. The common wisdom so far appears to be that a large population would increase the population diversity and thus help an EA. Indeed, increasing the population size has been a commonly used strategy in tuning an EA when it did not perform as well as expected for a given problem. He and Yao (2002) showed theoretically that for some problem instance classes, a population can help to reduce the runtime of an EA from exponential to polynomial time. This paper analyzes the role of population further in EAs and shows rigorously that large populations may not always be useful. Conditions, under which large populations can be harmful, are discussed in this paper. Although the theoretical analysis was carried out on one multi-modal problem using a specific type of EAs, it has much wider implications. The analysis has revealed certain problem characteristics, which can be either the problem considered here or other problems, that lead to the disadvantages of large population sizes. The analytical approach developed in this paper can also be applied to analyzing EAs on other problems.Comment: 25 pages, 1 figur