Improved sorting networks with O(log n) depth

The sorting network described by Ajtai, KomlOs and Szemeredi was the first to achieve a depth of O(Iog n). The networks introduced here are simplifications and improvements based strongly on their work. While the constants obtained for the depth bound still prevent the construction being of practical value, the structure of the presentation offers a convenient basis for further development

On the complexity of string folding

A fold of a finite string S over a given alphabet is an embedding of S in some fixed infinite grid, such as the square or cubic mesh. The score of a fold is the number of pairs of matching string symbols which are embedded at adjacent grid vertices. Folds of strings and sets of strings in two- and three-dimensional meshes are considered, and the corresponding problems of optimizing the score or achieving a given target score are shown to be NP-hard

Gravity-driven draining of a thin rivulet with constant width down a slowly varying substrate

The locally unidirectional gravity-driven draining of a thin rivulet with constant width but slowly varying contact angle down a slowly varying substrate is considered. Specifically, the flow of a rivulet in the azimuthal direction from the top to the bottom of a large horizontal cylinder is investigated. In particular, it is shown that, despite behaving the same locally, this flow has qualitatively different global behaviour from that of a rivulet with constant contact angle but slowly varying width. For example, whereas in the case of constant contact angle there is always a rivulet that runs all the way from the top to the bottom of the cylinder, in the case of constant width this is possible only for sufficiently narrow rivulets. Wider rivulets with constant width are possible only between the top of the cylinder and a critical azimuthal angle on the lower half of the cylinder. Assuming that the contact lines de-pin at this critical angle (where the contact angle is zero) the rivulet runs from the critical angle to the bottom of the cylinder with zero contact angle, monotonically decreasing width and monotonically increasing maximum thickness. The total mass of fluid on the cylinder is found to be a monotonically increasing function of the value of the constant width

The depth of all Boolean functions

It is shown that every Boolean function of n arguments has a circuit of depth n+1 over the basis {f|f:{0,1}^2 -> {0,1}}

Cooperatives and family businesses

Cooperatives provide a significant contribution to the economy, a large proportion of the UK’s economy is also supported by family businesses. Indeed, it is estimated that family businesses account for almost 25% of the UK’s gross domestic product (GDP). As such these two areas are of increasing importance when considering the accountability and governance responsibilities of organisations. With new questions arising every day to challenge the contributions that cooperatives and family business make to our communities, it is essential that we have the tools to clearly demonstrate their worth. Likewise, given the importance of the role boards play in the success or failure of cooperative organisations and family businesses, and the importance of these organisations in the wider economy, it is prudent to develop some knowledge and understanding of the complexities of the way in which these boards are structured and the role that they play in achieving accountability and governance within their organisation. The chapter considers the following: who governs; board roles and board relationships with management; board size and director selection processes; the importance of board members participation; and the input of managers in relation to accountability and governance in these two sectors. The chapter begins with a short overview of the evolution of cooperatives and what constitutes a family business. This is followed by a discussion of the organisational model and governance structures and their effectiveness

Finding the median

An algorithm is described which determines the median of n elements using in the worst case a number of comparison asymptotic to 3n

Chlorination and oxidation of heparin and hyaluronan by hypochlorous acid and hypochlorite anions: effect of sulfate groups on reaction pathways and kinetics.

Hypochlorous acid (HOCl), produced in inflammatory conditions by the enzyme myeloperoxidase, and its anion hypochlorite (OCl(-)) exist in vivo at almost equal concentrations. Their reactions with hyaluronan and heparin (as a model for sulfated glycosaminoglycans in the extracellular matrix) have been studied as a function of pH. The major product in these reactions is the chloramide derivative of the glycosaminoglycans. Spectral, chloramide yield, and kinetic measurements show sharply contrasting behavior of heparin and hyaluronan and the data allow the calculation of second-order rate constants for the reactions of both HOCl and OCl(-) for all reaction pathways leading to the formation of chloramides and also oxidation products. By comparison with hyaluronan, it can be demonstrated that both N-sulfate and O-sulfate groups in heparin influence the proportions of these pathways in this glycosaminoglycan. Evidence is also given for further oxidation pathways involving a reaction of HOCl with the chloramide product of hyaluronan but not with heparin. The significance of these results for the mechanisms of inflammation, particularly for fragmentation of extracellular matrix glycosaminoglycans, is discussed

Turbofan forced mixer lobe flow modeling. 1: Experimental and analytical assessment

A joint analytical and experimental investigation of three-dimensional flowfield development within the lobe region of turbofan forced mixer nozzles is described. The objective was to develop a method for predicting the lobe exit flowfield. In the analytical approach, a linearized inviscid aerodynamical theory was used for representing the axial and secondary flows within the three-dimensional convoluted mixer lobes and three-dimensional boundary layer analysis was applied thereafter to account for viscous effects. The experimental phase of the program employed three planar mixer lobe models having different waveform shapes and lobe heights for which detailed measurements were made of the three-dimensional velocity field and total pressure field at the lobe exit plane. Velocity data was obtained using Laser Doppler Velocimetry (LDV) and total pressure probing and hot wire anemometry were employed to define exit plane total pressure and boundary layer development. Comparison of data and analysis was performed to assess analytical model prediction accuracy. As a result of this study a planar mixed geometry analysis was developed. A principal conclusion is that the global mixer lobe flowfield is inviscid and can be predicted from an inviscid analysis and Kutta condition

Workshop on the Polar Regions of Mars: Geology, Glaciology, and Climate History, part 1

Papers and abstract of papers presented at the workshop are presented. Some representative titles are as follows: Glaciation in Elysium; Orbital, rotational, and climatic interactions; Water on Mars; Rheology of water-silicate mixtures at low temperatures; Evolution of the Martian atmosphere (the role of polar caps); Is CO2 ice permanent; Dust transport into Martian polar latitudes; Mars observer radio science (MORS) observations in polar regions; and Wind transport near the poles of Mars (timescales of changes in deposition and erosion)