We show that a wide variety of generalized increasing subsequence problems admit a one parameter family of extensions for which we can exactly compute the mean length of the longest increasing subsequence. By the nature of the extension, this gives upper bounds on the mean in the unextended model, which turn out to be asymptotically tight for all of the models that have so far been analyzed. A ...

This paper is concerned with certain connections between the ensemble of n × n unitary matrices—specifically the characteristic function of the random variable tr(U)—and combinatorics—specifically Ulam’s problem concerning the distribution of the length of the longest increasing subsequence in permutation groups—and the appearance of Painlevé functions in the answers to apparently unrelated que...

The interplay between two-dimensional percolation growth models and one-dimensional particle processes has been a fruitful source of interesting mathematical phenomena. In this paper we develop a connection between the construction of Busemann functions in the Hammersley last-passage percolation model with i.i.d. random weights, and the existence, ergodicity and uniqueness of equilibrium (or ti...

The link between antenatal care (ANC) and facility delivery is a specific example of the effect of early medical contacts on later use of essential services. The role of ANC in improving maternal health remains unclear. High levels of ANC are reported in a number of countries where skilled delivery remains uncommon. ANC may influence the use of services by increasing willingness to use services...

Skilled birth attendance (SBA) and healthcare facility (HCF) delivery are effective means of reducing maternal mortality. However, their uptake remains low in many low-income countries. The present study utilized semi-structured interviews with 85 pregnant women attending an antenatal clinic in Akwatia, Ghana (May-July 2010) to better understand the barriers to SBA and HCF delivery through the ...

IEEE 802.16, also known as WiMAX (Worldwide Inter-operability for Microwave Access), is a new wireless access technology for current increasing demand of wireless high-speed broadband service. Efficient and effective deployment of such a network to service an area of users with certain traffic demands is an important network planning problem. This network planning can be formulated in a similar...

Background: Boron Neutron Capture Therapy (BNCT) is a very promising treatment for patients suffering gliobastoma multiforme, an aggressive type of brain cancer, where conventional radiation therapies fail. Thermal neutrons are suitable for the direct treatment of cancers which are located at near-tissue-surface deep-seated tumors need harder, epithermal neutron energy spectra. Materials and Me...