Are there more almost separable partitions than separable partitions?

A partition of a set of n points in d-dimensional space into p parts is called an (almost) separable partition if the convex hulls formed by the parts are (almost) pairwise disjoint. These two partition classes are the most encountered ones in clustering and other partition problems for high-dimensional points and their usefulness depends critically on the issue whether their numbers are small. The problem of bounding separable partitions has been well studied in the literature (Alon and Onn in Discrete Appl. Math. 91:39–51, 1999; Barnes et al. in Math. Program. 54:69–86, 1992; Harding in Proc. Edinb. Math. Soc. 15:285–289, 1967; Hwang et al. in SIAM J. Optim. 10:70–81, 1999; Hwang and Rothblum in J. Comb. Optim. 21:423–433, 2011a). In this paper, we prove that for d≤2 or p≤2, the maximum number of almost separable partitions is equal to the maximum number of separable partitions.     

Generalized perfect domination in graphs

Let k be a positive integer and G=(V,E) be a graph. A vertex subset D of a graph G is called a perfect k-dominating set of G, if every vertex v of G, not in D, is adjacent to exactly k vertices of D. The minimum cardinality of a perfect k-dominating set of G is the perfect k-domination number γ _kp (G). In this paper, we give characterizations of graphs for which γ _kp (G)=γ(G)+k?2 and prove that the perfect k-domination problem is NP-complete even when restricted to bipartite graphs and chordal graphs. Also, by using dynamic programming techniques, we obtain an algorithm to determine the perfect k-domination number of trees.     

Current Constraints and Future Directions for Risk Adapted Land-Use Planning Practices in the High-Density Asian Setting of Ho Chi Minh City

The need to integrate adaptation efforts into land-use planning policies has been only recently recognized in Ho Chi Minh City. The city's latest planning guidance addresses both flooding resilience and mitigation of urban heat. This paper outlines the development contexts and the current barriers for adapted land-use planning within the city. The key challenge for land-use planning is communicating the important functions and services of open and natural urban spaces and effectively guiding the mainly individual developer-driven development. As the realization of non-structural adaptation measures is in strong contrast to the current market-driven private and short-term developer interests, the main development trajectories are questioned and synergies identified.     

Distribution of the cross-correlations of squared residuals in ARIMA models

ABSTRACT The distribution of the cross-correlations of squared residuals from Box-Jenkins models is considered in very general conditions, and the asymptotic distribution is derived. A test for a lagged relationship in volatility for economic time series under instantaneous causality is proposed, and its empirical behaviour is studied. An example involving the international stock market's volatility is studied, and an interesting result is observed.     

A metadata approach to statistical query processing

Concerning the task of integrating census and survey data from different sources as it is carried out by supranational statistical agencies, a formal metadata approach is investigated which supports data integration and table processing simultaneously. To this end, a metadata model is devised such that statistical query processing is accomplished by means of symbolic reasoning on machine-readable, operative metadata. As in databases, statistical queries are stated as formal expressions specifying declaratively what the intended output is; the operations necessary to retrieve appropriate available source data and to aggregate source data into the requested macrodata are derived mechanically. Using simple mathematics, this paper focuses particularly on the metadata model devised to harmonize semantically related data sources as well as the table model providing the principal data structure of the proposed system. Only an outline of the general design of a statistical information system based on the proposed metadata model is given and the state of development is summarized briefly.     

NEIGHBOUR ANALYSIS WITH ADJUSTMENT FOR INTERPLOT COMPETITION

In field experiments involving a large number of experimental plots, a neighbour analysis can be used to control environmental variation by estimating the trend within blocks. The effect of interplot competition is another important source of variation which has an influence on the estimation of treatment contrasts. To reduce the effect of the variation from these sources and to improve the precision of comparison between treatments, a spatial model is proposed for incorporating both trend effect and interplot competition. It is a modification to the residual maximum likelihood neighbour analysis of Gleeson & Cullis (1987) using the two neighbouring treatment effects to estimate interplot competition. A real example is used to illustrate this methodology. The results indicate that the extended model gives no appreciable difference in standard error of mean differences compared with the model taking into account the trend effect only. However, the rankings of estimated treatment means do differ. More research using both real and simulated data is required before such models that incorporate trend and competition effects can be confidently recommended.