Counting interesting elections

We provide an elementary proof of a formula for the number of northeast lattice paths that lie in a certain region of the plane. Equivalently, this formula counts the lattice points inside the Pitman--Stanley polytope of an n-tuple.Comment: 7 pages, 1 figure; published versio

Pattern avoidance in binary trees

This paper considers the enumeration of trees avoiding a contiguous pattern. We provide an algorithm for computing the generating function that counts n-leaf binary trees avoiding a given binary tree pattern t. Equipped with this counting mechanism, we study the analogue of Wilf equivalence in which two tree patterns are equivalent if the respective n-leaf trees that avoid them are equinumerous. We investigate the equivalence classes combinatorially. Toward establishing bijective proofs of tree pattern equivalence, we develop a general method of restructuring trees that conjecturally succeeds to produce an explicit bijection for each pair of equivalent tree patterns.Comment: 19 pages, many images; published versio

Influence of biomass burning during recent fluctuations in the slow growth of global tropospheric methane

During the past 15 years the annual growth rate of tropospheric methane (CH4) has shown striking changes over 2-3 year periods, varying from + 1% yr-1 to slightly negative values (-0.2% yr-1). These fluctuations are superimposed on an overall slowdown of the CH4 growth rate since the 1980s. Here we use our complementary measurement of other compounds (ethane, tetrachloroethene) to confirm the influence of biomass burning on large global CH4 pulses in 1998 and 2002-2003. Methane growth rate fluctuations also track ENSO indices, most likely via the influence of ENSO activity on large-scale biomass burning. We also report the seventh year of near-zero growth of global CH4 levels (Dec. 1998-Dec. 2005). The global CH4 mixing ratio was 1772 ± 1 ppbv in 2005, and CH4 increases of 118-376 ppbv between 2000-2020 (ten scenarios in the 2001 IPCC report, to levels around 1900+ ppbv by 2020, now appear quite unlikely. Copyright 2006 by the American Geophysical Union

Spatiotemporal variation of methane and other trace hydrocarbon concentrations in the valley of Mexico

Mexico City is the world's largest and most polluted urban center. We examine the distribution of methane and other hydrocarbons within the Valley of Mexico, using it as a model for the role developing megacities will play in the next century of geochemical cycling. Seventy-five whole air samples were analyzed with multivariate statistical techniques, including factor analysis using principal components. Methane concentrations are highly variable in space and time, due to air circulations and source distribution. Landfills and open sewage canals are major inputs. Emissions into and out from the valley are modeled to be ∼515 t per day. Per capita emission is 0.01 t per annum per person, consistent with the global average for human related anaerobic generation. Natural gas leaks are small, and likely to be higher in other developing megacities; Mexican natural gas use has been discouraged out of earthquake safety concerns. In contrast, liquefied petroleum gas loss constitutes the major emission of propane and butane estimated at a leak rate of 5-10%. Kyoto and other environmental conventions have ignored methane as a greenhouse gas. Our analysis underscores the need to consider methane and other hydrocarbons, and the urbanization process, in future emission protocols. © 2002 Elsevier Science Ltd. All rights reserved

The role of circumstance monitoring on the diagnostic interpretation of condition monitoring data

Circumstance monitoring, a recently coined termed defines the collection of data reflecting the real network working environment of in-service equipment. This ideally complete data set should reflect the elements of the electrical, mechanical, thermal, chemical and environmental stress factors present on the network. This must be distinguished from condition monitoring, which is the collection of data reflecting the status of in-service equipment. This contribution investigates the significance of considering circumstance monitoring on diagnostic interpretation of condition monitoring data. Electrical treeing partial discharge activity from various harmonic polluted waveforms have been recorded and subjected to a series of machine learning techniques. The outcome provides a platform for improved interpretation of the harmonic influenced partial discharge patterns. The main conclusion of this exercise suggests that any diagnostic interpretation is dependent on the immunity of condition monitoring measurements to the stress factors influencing the operational conditions. This enables the asset manager to have an improved holistic view of an asset's health

Dimethyl disulfide (DMDS) and dimethyl sulfide (DMS) emissions from biomass burning in Australia

We identify dimethyl disulfide (DMDS) as the major reduced sulfur-containing gas emitted from bushfires in Australia's Northern Territory. Like dimethyl sulfide (DMS), DMDS is oxidized in the atmosphere to sulfur dioxide (SO2) and methane sulfonic acid (MSA), which are intermediates in the formation of sulfuric acid (H2SO4). The mixing ratios of DMDS and DMS were the highest we have ever detected, with maximum values of 113 and 35 ppbv, respectively, whereas background values were below the detection limit (10 pptv). Molar emission ratios relative to carbon monoxide (CO) were [1.6 ± 0.1] × 10-5 and [6.2 ± 0.3] × 10-6, for DMDS and DMS respectively, while molar emission ratios relative to carbon dioxide (CO2) were [4.7 ± 0.4] × 10 6 and [1.4 ± 0.4] × 10 7, respectively. Assuming these observations are representative of biomass burning, we estimate that biomass burning could yield up to 175 Gg/yr of DMDS (119 Gg S/yr) and 13 Gg/yr of DMS