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.

On Hamilton cycles in locally connected graphs with vertex degree constraints

It is shown that every connected, locally connected graph with the maximum vertex degree Δ(G)=5 and the minimum vertex degree δ(G)3 is fully cycle extendable. For Δ(G)4, all connected, locally connected graphs, including infinite ones, are explicitly described. The Hamilton Cycle problem for locally connected graphs with Δ(G)7 is shown to be NP-complete

Decompositions of complete graphs into triangles and Hamilton cycles

For all odd integers n greater than or equal to 1, let G(n) denote the complete graph of order n, and for all even integers n greater than or equal to 2 let G,, denote the complete graph of order n with the edges of a 1-factor removed. It is shown that for all non-negative integers h and t and all positive integers n, G, can be decomposed into h Hamilton cycles and t triangles if and only if nh + 3t is the number of edges in G(n). (C) 2004 Wiley Periodicals, Inc.

Business cycle dynamics with duration dependence and leading indicators

Durland and McCurdy [Durland, J.M., McCurdy, T.H., 1994. Duration-dependent transitions in a Markov model of US GNP growth. Journal of Business and Economic Statistics 12, 279–288] investigated the issue of duration dependence in US business cycle phases using a Markov regime-switching approach, introduced by Hamilton [Hamilton, J., 1989. A new approach to the analysis of time series and the business cycle. Econometrica 57, 357–384] and extended to the case of variable transition parameters by Filardo [Filardo, A.J., 1994. Business cycle phases and their transitional dynamics. Journal of Business and Economic Statistics 12, 299–308]. In Durland and McCurdy’s model duration alone was used as an explanatory variable of the transition probabilities. They found that recessions were duration dependent whilst expansions were not. In this paper, we explicitly incorporate the widely-accepted US business cycle phase change dates as determined by the NBER, and use a state-dependent multinomial Logit modelling framework. The model incorporates both duration and movements in two leading indexes – one designed to have a short lead (SLI) and the other designed to have a longer lead (LLI) – as potential explanatory variables. We find that doing so suggests that current duration is not only a significant determinant of transition out of recessions, but that there is some evidence that it is also weakly significant in the case of expansions. Furthermore, we find that SLI has more informational content for the termination of recessions whilst LLI does so for expansions.

A mean-reverting stochastic model for the political business cycle

In this article, we look at the political business cycle problem through the lens of uncertainty. The feedback control used by us is the famous NKPC with stochasticity and wage rigidities. We extend the New Keynesian Phillips Curve model to the continuous time stochastic set up with an Ornstein-Uhlenbeck process. We minimize relevant expected quadratic cost by solving the corresponding Hamilton-Jacobi-Bellman equation. The basic intuition of the classical model is qualitatively carried forward in our set up but uncertainty also plays an important role in determining the optimal trajectory of the voter support function. The internal variability of the system acts as a base shifter for the support function in the risk neutral case. The role of uncertainty is even more prominent in the risk averse case where all the shape parameters are directly dependent on variability. Thus, in this case variability controls both the rates of change as well as the base shift parameters. To gain more insight we have also studied the model when the coefficients are time invariant and studied numerical solutions. The close relationship between the unemployment rate and the support function for the incumbent party is highlighted. The role of uncertainty in creating sampling fluctuation in this set up, possibly towards apparently anomalous results, is also explored.

Apoptosis and cell-cycle regulatory proteins in colorectal carcinoma: relationship to tumour stage and patient survival

The quantitative assessment of apoptotic index (AI) and mitotic index (MI) and the immunoreactivity of p53, bcl-2, p21, and mdm2 were examined in tumour and adjacent normal tissue samples from 30 patients with colonic and 22 with rectal adenocarcinoma. Individual features and combined profiles were correlated with clinicopathological parameters and patient survival data to assess their prognostic value. Increased AI was significantly associated with increased bcl-2 expression (p

Hyperacetylation in prostate cancer induces cell cycle aberrations, chromatin reorganization and altered gene expression profiles.

Histone acetylation is a fundamental mechanism in the regulation of local chromatin conformation and gene expression. Research has focused on the impact of altered epigenetic environments on the expression of specific genes and their pathways. However, changes in histone acetylation also have a global impact on the cell. In this study we used digital texture analysis to assess global chromatin patterns following treatment with trichostatin A (TSA) and have observed significant alterations in the condensation and distribution of higher-order chromatin, which were associated with altered gene expression profiles in both immortalised normal PNT1A prostate cell line and androgen-dependent prostate cancer cell line LNCaP. Furthermore, the extent of TSA-induced disruption was both cell cycle and cell line dependent. This was illustrated by the identification of sub-populations of prostate cancer cells expressing high levels of H3K9 acetylation in the G2/M phase of the cell cycle that were absent in normal cell populations. In addition, the analysis of enriched populations of G1 cells showed a global decondensation of chromatin exclusively in normal cells.

Hamilton-Waterloo problem with triangle and C9 factors

The Hamilton-Waterloo problem and its spouse-avoiding variant for uniform cycle sizes asks if Kv, where v is odd (or Kv - F, if v is even), can be decomposed into 2-factors in which each factor is made either entirely of m-cycles or entirely of n-cycles. This thesis examines the case in which r of the factors are made up of cycles of length 3 and s of the factors are made up of cycles of length 9, for any r and s. We also discuss a constructive solution to the general (m,n) case which fixes r and s.

Integrating health and sustainability in life cycle assessment

Until now health impact assessment and environmental impact assessment are two different issues, often not addressed together. Both issues have to be dealt with for sustainable building. The aim of this paper is to link healthy and sustainable housing in life cycle assessment. Two strategies are studied: clean air as a functional unity and health as a quality indicator. The strategies are illustrated with an example on the basis of Eco-Quantum, which is a Dutch whole-building assessment tool. It turns out that both strategies do not conflict with the LCA methodology. The LCA methodology has to be refined for this purpose.