On Hamilton cycle decomposition of 6-regular circulant graphs

The circulant graph Sn, where S ⊆ Zn \ {0}, has vertex set Zn and edge set {{x, x + s}|x ∈ Zn, s ∈ S}. It is shown that there is a Hamilton cycle decomposition of every 6-regular circulant graph Sn in which S has an element of order n.

Enumeration of inequivalent cycle decompositions

A k-cycle decomposition of order n is a partition of the edges of the complete graph on n vertices into k-cycles. In this report a backtracking algorithm is developed to count the number of inequivalent k-cycle decompositions of order n.

Common multiples of complete graphs and a 4-cycle

A graph G is a common multiple of two graphs H-1 and H-2 if there exists a decomposition of G into edge-disjoint copies of H-1 and also a decomposition of G into edge-disjoint copies of H-2. In this paper, we consider the case where H-1 is the 4-cycle C-4 and H-2 is the complete graph with n vertices K-n. We determine, for all positive integers n, the set of integers q for which there exists a common multiple of C-4 and K-n having precisely q edges. (C) 2003 Elsevier B.V. All rights reserved.

Some equitably 3-colourable cycle decompositions

Let G be a graph in which each vertex has been coloured using one of k colours, say c(1), c(2),..., c(k). If an m-cycle C in G has n(i) vertices coloured c(i), i = 1, 2,..., k, and (i) - n(j) less than or equal to 1 for any i, j is an element of {1, 2,..., k}, then C is equitably k-coloured. An m-cycle decomposition C of a graph G is equitably k-colourable if the vertices of G can be coloured so that every m-cycle in C is equitably k-coloured. For m = 4,5 and 6, we completely settle the existence problem for equitably 3-colourable m-cycle decompositions of complete graphs and complete graphs with the edges of a 1-factor removed. (C) 2004 Elsevier B.V. All rights reserved.

Some equitably 3-colourable cycle decompositions of complete equipartite graphs

Let G be a graph in which each vertex has been coloured using one of k colours, say c(1), c(2),.. , c(k). If an m-cycle C in G has n(i) vertices coloured c(i), i = 1, 2,..., k, and vertical bar n(i) - n(j)vertical bar <= 1 for any i, j is an element of {1, 2,..., k}, then C is said to be equitably k-coloured. An m-cycle decomposition C of a graph G is equitably k-colourable if the vertices of G can be coloured so that every m-cycle in W is equitably k-coloured. For m = 3, 4 and 5 we completely settle the existence question for equitably 3-colourable m-cycle decompositions of complete equipartite graphs. (c) 2005 Elsevier B.V. All rights reserved.

Estimating sectoral cycles using cointegration and common features

This paper investigates the degree of short run and long run co-movement in U.S. sectoral output data by estimating sectoraI trends and cycles. A theoretical model based on Long and Plosser (1983) is used to derive a reduced form for sectoral output from first principles. Cointegration and common features (cycles) tests are performed; sectoral output data seem to share a relatively high number of common trends and a relatively low number of common cycles. A special trend-cycle decomposition of the data set is performed and the results indicate a very similar cyclical behavior across sectors and a very different behavior for trends. Indeed. sectors cyclical components appear as one. In a variance decomposition analysis, prominent sectors such as Manufacturing and Wholesale/Retail Trade exhibit relatively important transitory shocks.

Common cycles in macroeconomic aggregates

Reduced form estimation of multivariate data sets currently takes into account long-run co-movement restrictions by using Vector Error Correction Models (VECM' s). However, short-run co-movement restrictions are completely ignored. This paper proposes a way of taking into account short-and long-run co-movement restrictions in multivariate data sets, leading to efficient estimation of VECM' s. It enables a more precise trend-cycle decomposition of the data which imposes no untested restrictions to recover these two components. The proposed methodology is applied to a multivariate data set containing U.S. per-capita output, consumption and investment Based on the results of a post-sample forecasting comparison between restricted and unrestricted VECM' s, we show that a non-trivial loss of efficiency results whenever short-run co-movement restrictions are ignored. While permanent shocks to consumption still play a very important role in explaining consumption’s variation, it seems that the improved estimates of trends and cycles of output, consumption, and investment show evidence of a more important role for transitory shocks than previously suspected. Furthermore, contrary to previous evidence, it seems that permanent shocks to output play a much more important role in explaining unemployment fluctuations.

On the welfare costs of business cycles in the 20th century

Lucas (1987) has shown a surprising result in business-cycle research, that the welfare cost of business cycles are relatively small. Using standard assumptions on preferences and a reasonable reduced form for consumption, we computed these welfare costs for the pre- and post-WWII era, using three alternative trend-cycle decomposition methods. The post-WWII period is very era this basic result is dramatically altered. For the Beveridge and Nelson decomposition, and reasonable preference parameter and discount values, we get a compensation of about 5% of consumption, which is by all means a sizable welfare cost (about US$ 1,000.00 a year).

Changes in CO2 emissions over business cycle recessions and expansions in the United States: A decomposition analysis

This paper examines the asymmetry of changes in CO2 emissions over business cycle recessions and expansions using yearly data from 1949 and monthly data from 1973 for the United States (US). In addition, decomposition analysis is applied to investigate the relative roles of various proximate contributing factors to observed changes in total and per capita CO2 emissions and emissions intensity, over business cycle phases. The results suggest, inter alia, that aggregate emissions and emissions intensity reduce much faster in contractions than they increase in expansions. In addition, unlike the three previous expansions, in the most recent post-GFC US expansion, emissions per capita have continued to decline, and at a rate very similar to the rate of reduction in preceding contractions. This suggests the real possibility that the most recent contraction may have had an ongoing impact on the path of per capita emissions well beyond the immediate impact experienced during the contraction itself.

Sensitivity of organic matter decomposition to warming varies with its quality

The relationship between organic matter (OM) lability and temperature sensitivity is disputed, with recent observations suggesting that responses of relatively more resistant OM to increased temperature could be greater than, equivalent to, or less than responses of relatively more labile OM. This lack of clear understanding limits the ability to forecast carbon (C) cycle responses to temperature changes. Here, we derive a novel approach (denoted Q(10-q)) that accounts for changes in OM quality during decomposition and use it to analyze data from three independent sources. Results from new laboratory soil incubations (labile Q(10-q)=2.1 +/- 0.2; more resistant Q(10-q)=3.8 +/- 0.3) and reanalysis of data from other soil incubations reported in the literature (labile Q(10-q)=2.3; more resistant Q(10-q)=3.3) demonstrate that temperature sensitivity of soil OM decomposition increases with decreasing soil OM lability. Analysis of data from a cross-site, field litter bag decomposition study (labile Q(10-q)=3.3 +/- 0.2; resistant Q(10-q)=4.9 +/- 0.2) shows that litter OM follows the same pattern, with greater temperature sensitivity for more resistant litter OM. Furthermore, the initial response of cultivated soils, presumably containing less labile soil OM (Q(10-q)=2.4 +/- 0.3) was greater than that for undisturbed grassland soils (Q(10-q)=1.7 +/- 0.1). Soil C losses estimated using this approach will differ from previous estimates as a function of the magnitude of the temperature increase and the proportion of whole soil OM comprised of compounds sensitive to temperature over that temperature range. It is likely that increased temperature has already prompted release of significant amounts of C to the atmosphere as CO2. Our results indicate that future losses of litter and soil C may be even greater than previously supposed.

Aerobic carbon-cycle related microbial communities in boreal peatlands: responses to water-level drawdown

Boreal peatlands represent a considerable portion of the global carbon (C) pool. Water-level drawdown (WLD) causes peatland drying and induces a vegetation change, which affects the decomposition of soil organic matter and the release of greenhouse gases (CO2 and CH4). The objective of this thesis was to study the microbial communities related to the C cycle and their response to WLD in two boreal peatlands. Both sampling depth and site type had a strong impact on all microbial communities. In general, bacteria dominated the deeper layers of the nutrient-rich fen and the wettest surfaces of the nutrient-poor bog sites, whereas fungi seemed more abundant in the drier surfaces of the bog. WLD clearly affected the microbial communities but the effect was dependent on site type. The fungal and methane-oxidizing bacteria (MOB) community composition changed at all sites but the actinobacterial community response was apparent only in the fen after WLD. Microbial communities became more similar among sites after long-term WLD. Litter quality had a large impact on community composition, whereas the effects of site type and WLD were relatively minor. The decomposition rate of fresh organic matter was influenced slightly by actinobacteria, but not at all by fungi. Field respiration measurements in the northern fen indicated that WLD accelerates the decomposition of soil organic matter. In addition, a correlation between activity and certain fungal sequences indicated that community composition affects the decomposition of older organic matter in deeper peat layers. WLD had a negative impact on CH4 oxidation, especially in the oligotrophic fen. Fungal sequences were matched to taxa capable of utilizing a broad range of substrates. Most of the actinobacterial sequences could not be matched to characterized taxa in reference databases. This thesis represents the first investigation of microbial communities and their response to WLD among a variety of boreal peatland habitats. The results indicate that microbial community responses to WLD are complex but dependent on peatland type, litter quality, depth, and variable among microbes.

Spinodal Decomposition in Tellurite-Based Glasses Induced by Excimer Laser Irradiation

Tellurite-based glasses in the TeO2-K3Li2Nb5O15, TeO2-Ba5Li2Ti2Nb8O30, and V2Te2O9 were fabricated by the conventional melt-quenching technique. Amorphous and glassy characteristics of the as-quenched samples were established via the X-ray powder diffraction technique and differential thermal analysis, respectively. The as-quenched samples were irradiated by an excimer laser (248 nm). The effect of laser power, duration of irradiation, and the frequency of the laser pulses on the surface features of the above glasses were studied. The optical microscopic studies carried out on the above systems revealed the presence of quasi-periodic and periodic structures on their surfaces. The local compositional variations of these structures were confirmed by back-scattered electron imaging using scanning electron microscope accompanied by energy-dispersive X-ray analysis. These results were convincing enough to state that the glasses in the present investigations had undergone spinodal decomposition on laser irradiation. The incidence of the interconnected texture of two different phases was observed owing to the quenching effect produced by the heating and cooling cycle of the successive laser pulses. Ring- and line-shaped patterns were also observed, respectively, when the pulse frequency of the laser and the duration of irradiation were increased.

Carbon dynamics in peatlands under changing hydrology : Effects of water level drawdown on litter quality, microbial enzyme activities and litter decomposition rates

Pristine peatlands are carbon (C) accumulating wetland ecosystems sustained by a high water level (WL) and consequent anoxia that slows down decomposition. Persistent WL drawdown as a response to climate and/or land-use change directly affects decomposition: increased oxygenation stimulates decomposition of the old C (peat) sequestered under prior anoxic conditions. Responses of the new C (plant litter) in terms of quality, production and decomposability, and the consequences for the whole C cycle of peatlands are not fully understood. WL drawdown induces changes in plant community resulting in shift in dominance from Sphagnum and graminoids to shrubs and trees. There is increasing evidence that the indirect effects of WL drawdown via the changes in plant communities will have more impact on the ecosystem C cycling than any direct effects. The aim of this study is to disentangle the direct and indirect effects of WL drawdown on the new C by measuring the relative importance of 1) environmental parameters (WL depth, temperature, soil chemistry) and 2) plant community composition on litter production, microbial activity, litter decomposition rates and, consequently, on the C accumulation. This information is crucial for modelling C cycle under changing climate and/or land-use. The effects of WL drawdown were tested in a large-scale experiment with manipulated WL at two time scales and three nutrient regimes. Furthermore, the effect of climate on litter decomposability was tested along a north-south gradient. Additionally, a novel method for estimating litter chemical quality and decomposability was explored by combining Near infrared spectroscopy with multivariate modelling. WL drawdown had direct effects on litter quality, microbial community composition and activity and litter decomposition rates. However, the direct effects of WL drawdown were overruled by the indirect effects via changes in litter type composition and production. Short-term (years) responses to WL drawdown were small. In long-term (decades), dramatically increased litter inputs resulted in large accumulation of organic matter in spite of increased decomposition rates. Further, the quality of the accumulated matter greatly changed from that accumulated in pristine conditions. The response of a peatland ecosystem to persistent WL drawdown was more pronounced at sites with more nutrients. The study demonstrates that the shift in vegetation composition as a response to climate and/or land-use change is the main factor affecting peatland ecosystem C cycle and thus dynamic vegetation is a necessity in any models applied for estimating responses of C fluxes to changes in the environment. The time scale for vegetation changes caused by hydrological changes needs to extend to decades. This study provides grouping of litter types (plant species and part) into functional types based on their chemical quality and/or decomposability that the models could utilize. Further, the results clearly show a drop in soil temperature as a response to WL drawdown when an initially open peatland converts into a forest ecosystem, which has not yet been considered in the existing models.

Decomposition in lake sediments: bacterial action and interaction

This review discusses the processes involved in the decomposition of organic carbon derived initially from structural components of algae and other primary producers. It describes how groups of bacteria interact in time and space in a eutrophic lake. The relative importance of anaerobic and aerobic processes are discussed. The bulk of decomposition occurs within the sediment. The role of bacteria in the nitrogen cycle and the iron cycle, and in sulphate reduction and methanogenesis as the terminal metabolism of organic carbon are described.