A method for determining consensus of hierarchical incomplete ordered partitions and coverings of sets is presented in this chapter. Incomplete ordered partitions and coverings are often used in expert information analysis. These structures should be useful when an expert has to classify elements of a set into given classes, but referring to several elements he does not know to which classes th...

Within a semiparametric framework we propose a test of shape invariance of Engel curves, which is a necessary condition for base independence. Using Canadian family expenditure data for 1996 we reject shape invariance for the fuel and clothing share equations. ∗The first author would like to acknowledge SSHRC of Canada for financial support.

We consider the practical problem of constructing binary space partitions (BSPs) for a set S of n orthogonal, nonintersecting, two-dimensional rectangles in IR3 such that the aspect ratio of each rectangle in S is at most , for some constant 1. We present an n2O(plogn )-time algorithm to build a binary space partition of size n2O(plogn ) for S. We also show that if m of the n rectangles in S ha...

The load partitioning between the two phases in a cold rolled duplex stainless steel sheet have been experimentally studied in situ during loading, via X-ray diffraction, for different loading directions. The microstresses in the two phases were found to decrease when loading in the transverse direction, while they increase during loading in the rolling and 45°-direction. Due to strong crystall...

A special case of an elegant result due to Anderson proves that the number of (s, s + 1)-core partitions is finite and is given by the Catalan number Cs. Amdeberhan recently conjectured that the number of (s, s + 1)-core partitions into distinct parts equals the Fibonacci number Fs+1. We prove this conjecture by enumerating, more generally, (s, ds− 1)-core partitions into distinct parts. We do ...

We study basis partitions, introduced by Hansraj Gupta in 1978. For this family of partitions, we give a recurrence, a generating function, identities relating basis partitions to more familiar families of partitions, and a new characterization of basis partitions.

In this paper, we develop a simple technique for constructing a Binary Space Partition (BSP) for a set of orthogonal rectangles in R 3. Our algorithm has the novel feature that it tunes its performance to the geometric properties of the rectangles, e.g., their aspect ratios. We have implemented our algorithm and tested its performance on real data sets. We have also systematically compared the ...

In this paper, we give combinatorial proofs and new generalizations of q-series identities of Dilcher and Uchimura related to divisor function. Some interesting combinatorial results related to partition and arm length are also presented.

We present a general method for evaluating and visualizing evolutionary dynamics of self-replicators using a graph-based representation for genealogy. Through a transformation from the space of species and mutations to the space of nodes and links, evolutionary dynamics are understood as a flow in graph space. Mapping functions are introduced to translate graph nodes to points in an n-dimension...

 Mobile sensor networks rely heavily on inter-sensor connectivity for collection of data. Nodes in these networks monitor different regions of an area of interest and collectively present a global overview of some monitored activities or phenomena. A failure of a sensor leads to loss of connectivity and may cause partitioning of the network into disjoint segments. A number of approaches have be...