Refining the characterization of projective graphs

Archdeacon showed that the class of graphs embeddable in the projective plane is characterized by a set of 35 excluded minors. Robertson, Seymour and Thomas in an unpublished result found the excluded minors for the class of k-connected graphs embeddable on the projective plane for k = 1,2,3. We give a short proof of that result and then determine the excluded minors for the class of internally 4-connected projective graphs. Hall showed that a 3-connected graph diff_x000B_erent from K5 is planar if and only if it has K3,3 as a minor. We provide two analogous results for projective graphs. For any minor-closed class of graphs C, we say that a set of k-connected graphs E disjoint from C is a k-connected excludable set for C if all but a _x000C_finite number of k-connected graphs not in C have a minor in E. Hall\u27s result is equivalent to saying that {K3,3} is a 3-connected excludable set for the class of planar graphs. We classify all minimal 3-connected excludable sets and fi_x000C_nd one minimal internally 4-connected excludable set for the class of projective graphs. In doing so, we also prove strong splitter theorems for 3-connected and internally 4-connected graphs that could have application to other problems of this type

Coherence in logical quantum channels

We study the effectiveness of quantum error correction against coherent noise. Coherent errors (for example, unitary noise) can interfere constructively, so that in some cases the average infidelity of a quantum circuit subjected to coherent errors may increase quadratically with the circuit size; in contrast, when errors are incoherent (for example, depolarizing noise), the average infidelity increases at worst linearly with circuit size. We consider the performance of quantum stabilizer codes against a noise model in which a unitary rotation is applied to each qubit, where the axes and angles of rotation are nearly the same for all qubits. In particular, we show that for the toric code subject to such independent coherent noise, and for minimal-weight decoding, the logical channel after error correction becomes increasingly incoherent as the length of the code increases, provided the noise strength decays inversely with the code distance. A similar conclusion holds for weakly correlated coherent noise. Our methods can also be used for analyzing the performance of other codes and fault-tolerant protocols against coherent noise. However, our result does not show that the coherence of the logical channel is suppressed in the more physically relevant case where the noise strength is held constant as the code block grows, and we recount the difficulties that prevented us from extending the result to that case. Nevertheless our work supports the idea that fault-tolerant quantum computing schemes will work effectively against coherent noise, providing encouraging news for quantum hardware builders who worry about the damaging effects of control errors and coherent interactions with the environment

Coherence in logical quantum channels

We study the effectiveness of quantum error correction against coherent noise. Coherent errors (for example, unitary noise) can interfere constructively, so that in some cases the average infidelity of a quantum circuit subjected to coherent errors may increase quadratically with the circuit size; in contrast, when errors are incoherent (for example, depolarizing noise), the average infidelity increases at worst linearly with circuit size. We consider the performance of quantum stabilizer codes against a noise model in which a unitary rotation is applied to each qubit, where the axes and angles of rotation are nearly the same for all qubits. In particular, we show that for the toric code subject to such independent coherent noise, and for minimal-weight decoding, the logical channel after error correction becomes increasingly incoherent as the length of the code increases, provided the noise strength decays inversely with the code distance. A similar conclusion holds for weakly correlated coherent noise. Our methods can also be used for analyzing the performance of other codes and fault-tolerant protocols against coherent noise. However, our result does not show that the coherence of the logical channel is suppressed in the more physically relevant case where the noise strength is held constant as the code block grows, and we recount the difficulties that prevented us from extending the result to that case. Nevertheless our work supports the idea that fault-tolerant quantum computing schemes will work effectively against coherent noise, providing encouraging news for quantum hardware builders who worry about the damaging effects of control errors and coherent interactions with the environment.Comment: 113 pages, 21 figures. Corrected typos, added references, and added subsections 1.2 and 1.3 (v2

Experimental determination of a double-valued drag relationship for glacier sliding

The contribution of glaciers to sea-level rise and their effects on landscape evolution depend on the poorly known relationship between sliding speed and drag at the ice/bed interface. Results from experiments with a new rotary laboratory device demonstrate empirically for the first time a double-valued drag relationship like that suggested by some sliding theories: steady drag on a rigid, sinusoidal bed increases, peaks and declines at progressively higher sliding speeds due to growth of cavities in the lee sides of bed undulations. Drag decreases with increased sliding speed if cavities extend beyond the inflection points of up-glacier facing surfaces, so that adverse bed slopes in contact with ice diminish with further cavity growth. These results indicate that shear tractions on glacier beds can potentially decrease due to increases in sliding speed driven by weather or climate variability, promoting even more rapid glacier motion by requiring greater strain rates to produce resistive stresses. Although a double-valued drag relationship has not yet been demonstrated for the complicated geometries of real glacier beds, both its potential major implications and the characteristically convex stoss surfaces of bumps on real glacier beds provide stimulus for exploring the effects of this relationship in ice-sheet models

Lattice-Boltzmann Method for Geophysical Plastic Flows

We explore possible applications of the Lattice-Boltzmann Method for the simulation of geophysical flows. This fluid solver, while successful in other fields, is still rarely used for geotechnical applications. We show how the standard method can be modified to represent free-surface realization of mudflows, debris flows, and in general any plastic flow, through the implementation of a Bingham constitutive model. The chapter is completed by an example of a full-scale simulation of a plastic fluid flowing down an inclined channel and depositing on a flat surface. An application is given, where the fluid interacts with a vertical obstacle in the channel.Comment: in W. Wu, R.I. Borja (Edts.) Recent advances in modelling landslides and debris flow, Springer Series in Geomechanics and Geoengineering (2014), ISBN 978-3-319-11052-3, pp. 131-14

The Stipulation of Extraprosodicity in Syllabic Phonology

Though the role of extraprosodicity has been thoroughly integrated into metrical theory, it has played a decidedly less pervasive part among the rules of syllabic phonology. Under Itô's(1986,1989) 'codafilter' account of syllable formation in certain types of languages, however, extraprosodicity of a word-final consonant is crucial both for maintaining the generalization that consonants in clusters must be homorganic and, when they are not, for determining the site of epenthesis. But in lieu of the coda filter and its extraprosodicity requirement, syllabification can be subject to a well-formedness condition which rules against consonant clusters in which each member is specified for Place, with epenthesis then applying precisely where it does because that is the only site which serves to remove violations. In further view of CV phonology's prediction of melodically empty skeletal representation and certain general principles of syllabic licensing, it is concluded that the role of stipulated segmental extraprosodicity is properly restricted to the metrical component of phonological theory

Report on Validation and Calibration of Fatty Acid Signatures in Blubber as Indicators of Prey in Hawaiian Monk Seal Diet

Pacific Islands Fisheries Science Center Administrative Reports are issued to promptly disseminate scientific and technical information to marine resource managers, scientists, and the general public. Their contents cover a range of topics, including biological and economic research, stock assessment, trends in fisheries, and other subjects. Administrative Reports typically have not been reviewed outside the Center. As such, they are considered informal publications. The material presented in Administrative Reports may later be published in the formal scientific literature after more rigorous verification, editing, and peer review. Other publications are free to cite Administrative Reports as they wish provided the informal nature of the contents is clearly indicated and proper credit is given to the author(s). Administrative Reports may be cited as follows: Iverson, S. J., B. S. Stewart, and P. K. Yochem. 2010. Report on validation and calibration of fatty acid signatures in blubber as indicators o